Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
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We wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
IntechOpen is proud to announce that 179 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
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Throughout the years, the list has named a total of 252 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\n
We wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
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\n\t\t\t
1. Introduction
\n\t\t\t
Silicon has been the miracle material for the electronics industry, and for the past twenty years, technology based on Si microelectronics has been the engine driving the digital revolution. For years, the rapid “Moore’s Law” miniaturization of device sizes has yielded an ever-increasing density of fast components integrated on Si chips: but during the time that the feature size was pushed down towards its ultimate physical limits, there has also been a tremendous effort to broaden the reach of Si technology by expanding its functionalities well beyond electronics. Si is now being increasingly investigated as a platform for building photonic devices. The field of Si photonics has seen impressive growth since early visions in the 1980s and 1990s [1,2]. The huge infrastructure of the global Si electronics industry is expected to benefit the fabrication of highly sophisticated Si photonic devices at costs that are lower than those currently required for compound semiconductors. Furthermore, the Si-based photonic devices make possible the monolithic integration of photonic devices with high speed Si electronics, thereby enabling an oncoming Si-based “optoelectronic revolution”.
\n\t\t\t
Among the many photonic devices that make up a complete set of necessary components in Si photonics including light emitters, amplifiers, photodetectors, waveguides, modulators, couplers and switches, the most difficult challenge is the lack of an efficient light source. The reason for this striking absence is that bulk Si has an indirect band gap where the minimum of the conduction band and the maximum of the valence band do not occur at the same value of crystal momentum in wave vector space (Fig. 1). Since photons have negligible momentum compared with that of electrons, the recombination of an electron-hole pair will not be able to emit a photon without the simultaneous emission or absorption of a phonon in order to conserve the momentum. Such a radiative recombination is a second-order effect occurring with a small probability, which competes with nonradiative processes that take place at much faster rates. As a result, as marvelous as it has been for electronics, bulk Si has not been the material of choice for making light emitting devices including lasers.
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Nevertheless, driven by its enormous payoff in technology advancement and commercialization, many research groups around the world have been seeking novel approaches to overcome the intrinsic problem of Si to develop efficient light sources based on Si. One interesting method is to use small Si nanocrystals dispersed in a dielectric matrix, often times SiO2. Such nano-scaled Si clusters are naturally formed by the thermal annealing of a Si-rich oxide thin film. Silicon nanocrystals situated in a much wider band gap SiO2 can effectively localize electrons with quantum confinement, which improves the radiative recombination probability, shifts the emission spectrum toward shorter wavelengths, and
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Figure 1.
Illustration of a photon emission process in (a) the direct and (b) the indirect band gap semiconductors.
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decreases the free carrier absorption. Optical gain and stimulated emission have been observed from these Si nanocrystals by both optical pumping [3,4] and electrical injection [5], but the origin of the observed optical gain has not been fully understood as the experiments were not always reproducible – results were sensitive to the methods by which the samples were prepared. In addition, before Si-nanocrystal based lasers can be demonstrated, the active medium has to be immersed in a tightly confined optical waveguide or cavity.
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Another approach is motivated by the light amplification in Er-doped optical fibers that utilize the radiative transitions in Er ions (Er3+) [6]. By incorporating Er3+ in Si, these ions can be excited by energy transfer from electrically injected electron-hole pairs in Si and will subsequently relax by emitting photons at the telecommunication wavelength of 1.55 µm. However, the concentration of Er3+ ions that can be doped in Si is relatively low and there is a significant energy back-transfer from the Er3+ ions to the Si host due to the resonance with a defect level in Si. As a result, both efficiency and maximum power output have been extremely low [7,8]. To reduce the back transfer of energy, SiO2 with an enlarged band gap has been proposed as host to remove the resonance between the defect and the Er3+ energy levels [9]. Once again, Si-rich oxide is employed to form Si nanocrystals in close proximity to Er3+ ions. The idea is to excite Er3+ ions with the energy transfer from the nearby Si nanocrystals. Light emitting diodes (LEDs) with efficiencies of about 10% have been demonstrated [10] on par with commercial devices made of GaAs, but with power output only in tens of µW. While there have been proposals to develop lasers using doped Er in Si-based dielectric, the goal remains elusive.
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The only approach so far that has led to the demonstration of lasing in Si exploited the effect of stimulated Raman scattering [11-13], analogous to that produced in fiber Raman amplifiers. With both the optical pumping and the Raman scattering below the band gap of Si, the indirectness of the Si band gap becomes irrelevant. Depending on whether it is a Stokes or anti-Stokes process, the Raman scattering either emits or absorbs an optical phonon. Such a nonlinear process requires optical pumping at very high intensities (~100MW/cm2) and the device lengths (~cm) are too large to be integrated with other photonic and electronic devices in any type of Si VLSI-type circuit [14].
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Meanwhile, the search for laser devices that can be integrated on Si chips has gone well beyond the monolithic approach to seek solutions using hybrid integration of III-V compounds with Si. A laser with an AlGaInAs quantum well (QW) active region bonded to a silicon waveguide cavity was demonstrated [15]. This fabrication technique allows for the optical waveguide to be defined by the CMOS compatible Si process while the optical gain is provided by III-V materials. Rare-earth doped visible-wavelength GaN lasers fabricated on Si substrates are also potentially compatible with the Si CMOS process [16]. Another effort produced InGaAs quantum dot lasers deposited directly on Si substrates with a thin GaAs buffer layer [17]. Although these hybrid approaches offer important alternatives, they do not represent the ultimate achievement of Si-based lasers monolithically integrated with Si electronics.
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While progress is being made along these lines and debates continue about which method offers the best promise, yet another approach emerged that has received a great deal of attention in the past decade—an approach in which the lasing mechanism is based on intersubband transitions (ISTs) in semiconductor QWs. Such transitions take place between quantum confined states (subbands) of conduction or valence bands and do not cross the semiconductor band gap. Since carriers remain in the same energy band (either conduction or valence), optical transitions are always direct in momentum space rendering the indirectness of the Si band gap irrelevant. Developing lasers using ISTs therefore provides a promising alternative that completely circumvents the issue of indirectness in the Si band gap. In addition, this type of laser can be conveniently designed to employ electrical pumping – the so-called quantum cascade laser (QCL). The pursuit of Si-based QCLs might turn out to be a viable path to achieving electrically pumped Si-based coherent emitters that are suitable for monolithic integration with Si photonic and electronic devices.
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In this chapter, lasing processes based on ISTs in QWs are explained by drawing a comparison to conventional band-to-band lasers. Approaches and results towards SiGe QCLs using ISTs in the valence band are overviewed, and the challenges and limitations of the SiGe valence-band QCLs are discussed with respect to materials and structures. In addition, ideas are proposed to develop conduction-band QCLs, among them a novel QCL structure that expands the material combination to SiGeSn. This is described in detail as a way to potentially overcome the difficulties that are encountered in the development of SiGe QCLs.
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2. Lasers based on intersubband transitions
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Research on quantum confined structures including semiconductor QWs and superlattices (SLs) was pioneered by Esaki and Tsu in 1970 [18]. Since then confined structures have been developed as the building blocks for a majority of modern-day semiconductor optoelectronic devices. QWs are formed by depositing a narrower band gap semiconductor with a layer thickness thinner than the deBroglie wavelength of the electron (~10nm) between two wider band gap semiconductors (Fig. 2(a)). The one-dimensional quantum confinement leads to quantized states (subbands) in the direction of growth \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\twithin both conduction and valence bands. The energy position of each subband depends on the band offset (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t) and the effective mass of the carrier. In directions perpendicular to \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t(in-plane), the carriers are unconfined and can thus propagate with an in-plane wave vector \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\twhich gives an energy dispersion for each subband. (Fig. 2(b))\n\t\t\t
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Figure 2.
Illustration of (a) conduction and valence subband formations in a semiconductor QW and (b) in-plane subband dispersions with optical transitions between conduction and valence subbands.
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Obviously, if the band offset is large enough, there could be multiple subbands present within either conduction or valence band as shown in Fig. 3 where two subbands are confined within the conduction band. The electron wavefunctions (Fig. 3(a)) and energy dispersions (Fig. 3(b)) are illustrated for the two subbands. The concept of ISTs refers to the physical process of a carrier transition between these subbands within either the conduction or valence band as illustrated in Fig. 3. Carriers originally occupying a higher energy subband can make a radiative transition to a lower subband by emitting a photon. Coherent sources utilizing this type of transition as the origin of light emission are called intersubband lasers.
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The original idea of creating light sources based on ISTs was proposed by Kazarinov and Suris [19] in 1971, but the first QCL was not demonstrated until 1994 by a group led by Capasso at Bell Laboratories [20]. In comparison with the conventional band-to-band lasers, lasers based on ISTs require much more complex design of the active region which consists of carefully arranged multiple QWs (MQWs). The reason for added complexity can be appreciated by comparing the very different band dispersions that are involved in these two types of lasers. In a conventional band-to-band laser, it appears that the laser states consist of two broad bands. But a closer look at the conduction and valence band dispersions (Fig. 2(b)) reveals a familiar four-level scheme where in addition to the upper laser states\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, located near the bottom of the conduction band and the lower laser states\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, near the top of the valence band, there are two other participating states - intermediate states\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, and ground states\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tg\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. The pumping process (either injection or optical) places electrons into the intermediate states, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, from which they quickly relax toward the upper laser states \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t by inelastic scattering intraband processes. This process is very fast, occurring on a sub-pico-second scale. But once they reach states\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, they tend to stay there for a much longer time determined by the band-to-band recombination rate which is on the order of nanoseconds. Electrons that went through lasing transitions to the lower laser states \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t will quickly scatter into the lower energy states of the valence band – ground states \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tg\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t --by the same fast inelastic intraband processes. (A more conventional way to look at this is the relaxation of holes toward the top of the valence band.) The population inversion between \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t and \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is therefore established mostly by the fundamental difference between the processes determining the lifetimes of upper and lower laser states. As a result, the lasing threshold can be reached when the whole population of the upper conduction band is only a tiny fraction of that of the lower valence band.
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Figure 3.
a) Two subbands formed within the conduction band confined in a QW and their election envelope functions, (b) in-plane energy dispersions of the two subbands. Radiative intersubband transition between the two subbands is highlighted.
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Let us now turn our attention to the intersubband transition shown in Fig. 3(b). The in-plane dispersions of the upper \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t and lower \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t conduction subbands are almost identical when the band nonparabolicity can be neglected. For all practical purposes they can be considered as two discrete levels. Then, in order to achieve population inversion it is necessary to have the whole population of the upper subband exceed that of the lower subband. For this reason, a three- or four-subband scheme becomes necessary to reach the lasing threshold. Even then, since the relaxation rates between different subbands are determined by the same intraband processes, a complex multiple QW structure needs to be designed to engineer the lifetimes of involved subbands.
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Still, intersubband lasers offer advantages in areas where the conventional band-to-band lasers simply cannot compete. In band-to-band lasers, lasing wavelengths are mostly determined by the intrinsic band gap of the semiconductors. There is very little room for tuning, accomplished by varying the structural parameters such as strain, alloy composition, and layer thickness. Especially for those applications in the mid-IR to far-IR range, there are no suitable semiconductors with the appropriate band gaps from which such lasers can be made. With the intersubband transitions, we are no longer limited by the availability of semiconductor materials to produce lasers in this long wavelength region. In addition, for ISTs between conduction subbands with parallel band dispersions, the intersubband lasers should therefore have a much narrower gain spectrum in comparison to the band-to-band lasers in which conduction and valence bands have opposite band curvatures.
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A practical design that featured a four-level intersubband laser pumped optically was proposed by Sun and Khurgin [21,22] in the early 1990s. This work laid out a comprehensive analysis of various intersubband processes that affect the lasing operation including scattering mechanisms that determine subband lifetimes, conditions for population inversion between two subbands, band engineering to achieve it, and optical gain sufficient to compensate for losses under realistic pumping intensity. The QCLs developed soon thereafter significantly expanded the design in order to accommodate electrical pumping by implementing a rather elaborate scheme of current injection with the use of a chirped SL as the injector region placed in between the active regions (Fig. 4). The QCL has a periodic structure with each period consisting of an active and an injector region. Both active and injector regions are composed of MQWs. By choosing combinations of layer thicknesses and material compositions, three subband levels with proper energy separations and wave function overlaps are obtained in the active region. The injector region, on the other hand, is designed with a sequence of QWs having decreasing well widths (chirped SL) such that they form a miniband under an electric bias that facilitates electron transport. The basic operating principle of a QCL is illustrated in Fig. 4. Electrons are first injected through a barrier into subband 3 (upper laser state) of the active region, they then undergo lasing transitions to subband 2 (lower laser state) by emitting photons, followed by fast depopulation into subband 1 via nonradiative processes. These electrons are subsequently transported through the injector region into the next active region where they repeat the process in a cascading manner, typically 20 to 100 times.
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Figure 4.
Schematic band diagram of two periods of a QCL structure with each period consisting of an active and an injector region. Lasing transitions are between the states 3 and 2 in the active regions with rapid depopulation of lower state 2 into state 1 which couples strongly with the minibands formed in injector regions that transport carriers to state 3 in the next period. The magnitude-squared wavefunctions for the three subbands in active regions are illustrated.
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Advances of QCLs since the first demonstration have resulted in dramatic performance improvement in spectral range, power and temperature. They have become the dominant mid-IR semiconductor laser sources covering the spectral range of \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tλ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t25\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t µm [23-25], many of them operating in the continuous-wave mode at room temperature with peak power reaching a few watts [26,27]. Meanwhile, QCLs have also penetrated deep into the THz regime loosely defined as the spectral region \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t100\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tGHz \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t THz or \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t30\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tλ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t3000\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t µm, bridging the gap between the far-IR and GHz microwaves. At present, spectral coverage from 0.84-5.0 THz has been demonstrated with operation in either the pulsed or continuous-wave mode at temperatures well above 100K [28].
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3. Intersubband theory
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In order to better explain the design considerations of intersubband lasers, it is necessary to introduce some basic physics that underlies the formation of subbands in QWs and their associated intersubband processes. The calculation procedures described here follows the envelope function approach based on the effective-mass approximation [29]. The \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t⋅\n\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tmethod [30] was outlined to obtain in-plane subband dispersions in the valence band. Optical gain for transitions between subbands in conduction and valence bands is derived. Various scattering mechanisms that determine the subband lifetimes are discussed with an emphasis on the carrier-phonon scattering processes.
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3.1. Subbands and dispersions
\n\t\t\t\t
Let us treat the conduction subbands first. It is well known in bulk material that near the band edge, the band dispersion with an isotropic effective mass follows a parabolic relationship. In a QW structure, along the in-plane direction (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) where electrons are unconfined, such curvature is preserved for a given subband\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, assuming the nonparabolicity that describes the energy-dependent effective mass \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tcan be neglected,
where\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the Planck constant and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the minimum energy of subband \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tin a QW structure. This minimum energy can be calculated as one of the eigen values of the Schrödinger equation along the growth direction\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t,
where the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-dependence of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t allows for different effective masses in different layers and\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t represents the conduction band edge along the growth direction\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t,. The envelope function of subband\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tφ\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, together with the electron Bloch function \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tR\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and the plane wave\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t⋅\n\t\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, gives the electron wavefunction in the QW structure as
where the position vector is decomposed into in-plane and growth directions\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tR\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. Since we are treating electron subbands, the Bloch function is approximately the same for all subbands and all \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-vectors. The electron envelope function can be given as a combination of the forward and backward propagations in a given region \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tof the QW structure (either a QW or a barrier region), \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tB\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are constants that need to be fixed with the continuity conditions at each of the interfaces\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t,
in conjunction with the relationship between the subband minimum energy \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and the quantized wave vector \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-direction
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t assumes either real or imaginary value depending on\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. The continuity conditions in Eq.(5) ensure continuous electron distribution and conservation of electron current across the interface.
\n\t\t\t\t
In the presence of an electric field \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tapplied in the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-direction, the potential term \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in the Schrödinger equation Eq.(2) becomes tilted along\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tthe\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t -direction according to\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. If the Coulomb effect due to the distribution of electrons in the subband needs to be taken into consideration, then the potential in region \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tof the QW structure with the conduction band edge \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t should be modified as
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\tϕ\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\ttakes into account the potential due to electron distributions in all subbands and can be obtained by solving the Poisson equation
consistently with Eq.(2), where\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the charge of a free electron, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the permittivity of free space, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-dependent dielectric constant of the QW structure, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the electron density of subband\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the n-type doping profile in the structure.
\n\t\t\t\t
In comparison with the conduction band, the situation in the valence band is far more complex mostly because of the interactions between subbands of different effective masses that produce strong nonparabolicity. The in-plane dispersion of valence subbands and their associated envelope functions can be obtained in the framework of the effective mass approximation by applying the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t⋅\n\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\ttheory [30] to QWs [31] where, in the most general treatment, an 8×8 Hamiltonian matrix is employed to describe the interactions between the conduction, heavy-hole (HH), light-hole (LH), and spin-orbit split off (SO) bands. Often times, for semiconductors in which the conduction band is separated far in energy from the valence band, the coupling of the conduction band can be ignored. For the group-IV semiconductors Si and Ge with indirect band gaps, this approximation is particularly adequate. In those structures where there is little strain such as GaAs/AlGaAs, the SO band coupling can also be ignored. The 8×8 Hamiltonian matrix can then be reduced to a 4×4 matrix. But for systems with appreciable lattice mismatch, strain induces strong coupling between LH and SO bands. For the SiGe system with a large lattice mismatch, the SO band should be included and a 6×6 matrix Hamiltonian equation needs to be solved to come up with the dispersion relations and envelope functions. Such a 6×6 matrix Hamiltonian equation can be solved exactly in multiple QW structures under the bias of an electric field. A procedure based on the Luttinger-Kohn Hamiltonian [32,33] is outlined as follows.
\n\t\t\t\t
The 6×6 Luttinger-Kohn Hamiltonian matrix including the uniaxial stress along (001) is given in the HH (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t), LH (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t), and SO (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) Bloch function space as
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the valence band edge profile (degenerate for HH and LH bands) of the QW structure,
in which\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the mass of a free electron, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tare the Luttinger parameters and\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tb\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tare the deformation potentials [34] with different values in QWs and barriers, and the lattice mismatch strain
with \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tbeing the lattice constants of the substrate (or buffer) and the layer material, and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t11\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t12\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t the stiffness constants.
\n\t\t\t\t
The Hamiltonian in Eq.(9) operates on wavefunctions that are combinations of six mutually orthogonal HH (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t), LH (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t), and SO (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) Bloch functions
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t⋯\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t6\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t forms a six-component envelope-function vector\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. Each component in a given region \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tof the QW structure (either QW or barrier), \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, is a superposition of the forward and backward propagations identical to Eq.(4) with constants \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tB\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t⋯\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t6\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tthat can be fixed by the continuity equations that require at each interface\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t,
to maintain undisruptive carrier distribution and current across the interface.
\n\t\t\t\t
It is important to point out that when the above described algorithms are used for the situation where an electric field is applied along the growth direction\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, it is necessary to digitize the potential term \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, i.e. the regions that are used in Eq.(4) are no longer defined by the QW and barrier boundaries; instead, there could be many regions within each QW or barrier depending on the number of digitization steps used to satisfy the accuracy requirement.
\n\t\t\t\t
This procedure applied at each wave vector point (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) produces the in-plane dispersion for each subband. An example is illustrated in Fig. 5 for a 70Å/50Å GaAs/Al0.3Ga 0.7As SL [35]. In-plane dispersions of three subbands (two for HH and one for LH) are shown where strong nonparabolicity is demonstrated. It can be seen from Fig. 5 that the band nonparabolicity could be so severe that the LH subband maximum is no longer at the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-point which leads to useful valence QCL design applications in Section IV.
\n\t\t\t
\n\t\t\t
Figure 5.
In-plane dispersions of subbands HH1, LH1, and HH2 for a 70 Å/50 Å GaAs/AlGaAs SL [35].
\n\t\t\t
\n\t\t\t\t
3.2. Optical gain
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For lasing to occur between two subbands, it is necessary to induce stimulated emission between them. To sustain such emission of photons, there must be sufficient optical gain to compensate various losses in the laser structure. The intersubband optical gain can be obtained by analyzing transition rates between two subbands.
\n\t\t\t\t
According to the Fermi Golden rule, the transition rate between two discrete states 1 and 2 that are coupled by a perturbation electro-magnetic (EM) field with a frequency of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the transition matrix element under the influence of a perturbation Hamiltonian \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t between the two states with an exact transition energy \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in the absence of any broadening. In reality, the transition line \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is not infinitely sharp and is always broadened. As a result, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis not known exactly, instead a probability for it to appear in the energy interval \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t→\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is described. In the case of homogeneous broadening, this probability should be given as \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\twith the Lorentzian lineshape centered at some peak transition energy \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the full width at half maximum (FWHM) that characterizes the broadening due to various homogeneous processes that include collisions and transitions. The transition rate in Eq.(15) should thus be modified by an integral that takes into account of this broadening as
essentially replacing the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-function in Eq.(15) with the Lorentzian lineshape Eq.(16).
\n\t\t\t\t
In the presence of an EM field with an optical potential vector \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tin a medium with isotropic effective mass, the perturbation Hamiltonian \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t that describe the interaction between the field and electron in isotropic subbands is
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the momentum operator.
\n\t\t\t\t
From Eq.(18), it is not difficult to see that the selection rules for intersubband transitions in the conduction band are such that only those EM fields that are polarized in the growth direction (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) can induce optical transitions. The transition matrix element can then be given as
It is not difficult to see from Eq.(17) that the transition rate induced by an EM field between two eigen states is the same for upward and downward transitions. Now let us apply Eq.(17) to intersubband transitions between the upper subband 2 and lower subband 1 in the conduction band (Fig. 3). Since momentums associated with photons are negligible, all photon-induced transitions are vertical in \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-space. It is therefore possible to obtain a net downward transition rate (in the units of number of transitions per unit time per unit sample area) between the two subbands by evaluating the following integral
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are the electron occupation probabilities of those states at the same \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tin subbands 1 and 2, respectively, and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tρ\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the reduced density of states (DOS) between \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, which is equal to DOS of subbands 1 (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tρ\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) and 2 (\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tρ\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) when they are parallel,\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tρ\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tρ\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tρ\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\tπ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tℏ\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. Since the Lorentzian lineshape in Eq.(23) should be much broader than the spread of the energy transitions between the two parallel subbands which can be approximated as sharply centered at the subband separation at their energy minima\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t12\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. Thus,
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are the total electron densities in subband 1 and 2 per unit area, respectively.
\n\t\t\t\t
The optical gain coefficient \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tthat describes the increase of the EM field intensity, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, as\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t can be defined as power increase per unit volume divided by the intensity, which in turn can be expressed in terms of the net downward transition rate Eq.(24) using the momentum and dipole matrix element relation
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the length of the QW structure that is equal to the length of one period in case of QCLs. In order to relate the EM field intensity \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tthat propagates in in-plane with the optical potential \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tpolarized along\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, a real expression for the potential \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\thas to be used
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the in-plane propagation wave vector of the EM field. It is easy to see that only one of the two terms on the right side of Eq.(26) couples with subbands 1 and 2,\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. Thus, the optical potential that participates in the transition matrix Eq.(19) is only half of its real amplitude,\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. Since the EM field intensity \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis related to the optical potential amplitude \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t as\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, Eq.(25) can be written as
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the speed of light in free space and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the effective index of refraction of the QCL dielectric medium. The population inversion \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is clearly necessary in order to achieve positive gain which peaks at the frequency \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t12\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\tℏ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\twith a value of
For transitions between valence subbands with nonparallel dispersions and strong mixing between HH, LH, and SO bands, we have to re-examine the intersubband transition rate. Consider the intersubband transition in Fig. 5 from the upper state \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in subband LH1 to the lower state \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in subband HH1, if the spread of intersubband transitions is wide enough compared to the homogeneous broadening, the Lorentzian lineshape in the net downward transition rate Eq.(23) can be approximated as a \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-function yielding
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tρ\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the reduced DOS for the transition between subbands LH1 and HH1, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are hole occupation probabilities at states with energy \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in subband LH1 and HH1, respectively, at the same in-plane wave vector \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tseparated by a photon energy\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tℏ\n\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, and the optical transition matrix between LH1 and HH1 taking into account of the mixing
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are respectively the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-th component of the envelope function vectors for subband LH1 and HH1 as defined in Eq.(12), and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are the corresponding hole effective mass in \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-direction with \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t4\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t for HH, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tfor LH, and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t5\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t6\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t for SO. The optical gain can then be expressed
in terms of momentum matrix \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t∂\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t∂\n\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t as well as dipole matrix elements \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t between the same \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-th component of the envelope function vectors of the two valence subbands.
\n\t\t\t\t
In comparison with the optical gain Eq.(28) for the conduction subbands, we can see that it is not necessary to have total population inversion, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, in order to have positive gain between the valence subbands. Instead, all we need is local population inversion \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t[\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t]\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\tℏ\n\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in the region where the intersubband transition takes place (those states near \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in Fig. 5).
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
3.3. Intersubband lifetimes
\n\t\t\t\t
It has been established in Eqs.(27) and (28) that the population inversion between the upper (2) and lower (1) subbands, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, is necessary in order to obtain optical gain. But what determines the population inversion? This question is answered with the analysis of lifetimes of these subbands as a result of various intersubband relaxation mechanisms including carrier-phonon, carrier-carrier, impurity, and interface roughness scattering processes. Among them, phonon scattering is the dominant process, especially when the energy separation between the two subbands exceeds that of an optical phonon, in which case the transitions from upper to lower subband are highly efficient with the emission of optical phonons. Different from the optical transitions, these scattering processes do not necessarily occur as vertical transitions in \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-space. In the case of phonon scattering, the conservation of in-plane momentum can be satisfied by a wide range of momentum of involved phonons as shown in Fig. 6(a) where intersubband as well as intrasubband transitions due to phonon scattering are illustrated.
\n\t\t\t\t
Figure 6.
a) Intersubband and intrasubband transitions due to electron-phonon scattering (b) the 22→11 transition induced by the electron-electron scattering.
\n\t\t\t\t
Up to now, practically all approaches in developing Si-based QCLs are based on materials from group-IV, mostly Si, Ge, SiGe alloy, and more recently, SiGeSn alloy. Different from the polar III-V and II-VI semiconductors, group-IV materials are nonpolar. The carrier scatterings by nonpolar optical phonons are much slower than those due to polar optical phonons [38]. Starting from Fermi Gold rule Eq.(15), the scattering rate for a carrier in subband 2 with the in-plane wave vector\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t to subband 1 with \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\'\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tby a phonon with an energy \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\tQ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand wave vector, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tQ\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, can be expressed as an integral over all the participating phonon states
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the electron-phonon interaction matrix element, the carrier energies \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\'\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are given by Eq.(1) for conduction subbands, but for valence subbands, they need to be obtained by the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t⋅\n\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tmethod described above. We will proceed with the following approximations: 1) all phonons are treated to be bulk-like by neglecting the phonon confinement effect in QW structures, 2) energies of acoustic phonons are negligible\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\tQ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t≈\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, and 3) optical phonon energies are taken as a constant\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\tQ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t≈\n\t\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. The matrix element of carrier-phonon interaction for different type of phonons can be written as [39,40]
where the upper sign is for absorption and lower for emission of one phonon,\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tK\n\t\t\t\t\t\t\t\t\t\tB\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the Boltzmann constant, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΩ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the volume of the lattice mode cavity, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the elastic constant for acoustic mode, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΞ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tare the acoustic and optical deformation potential, respectively, and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the number of optical phonons at temperature\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t
The Kronecker symbol \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\'\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in the matrix element Eq.(33) represents the in-plane momentum conservation \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\'\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t.\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t
\n\t\t\t\t
Since phonon modes have density of states\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΩ\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\tπ\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, the participating phonon states in the integral Eq.(32) can be expressed as
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the angle between \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. For conduction subbands with a parabolic dispersion Eq.(1), the phonon scattering rate Eq.(32) can be evaluated analytically
But for valence subbands where there is a strong nonparabolicity, Eq.(32) can no longer be integrated analytically. However, if we take the wave vector of the initial state in subband 2 to be at the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t-point\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, then the phonon wave vector\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\'\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, Eq.(38) can still be used to evaluate the phonon scattering rate between valence subbands by substituting the effective mass with some average effective mass in the final subband 1.
\n\t\t\t\t
The phonon scattering rate in Eq.(38) has been used to compare the lifetimes of two similar three-level systems, SiGe/Si and GaAs/AlGaAs, as shown in Fig. 7(a) [38]. The lifetime difference between the upper (3) and lower (2) subband is calculated as the function of the transition energy \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t which is varied by changing the barrier width between the two QWs that host the two subbands. The main result in Fig. 7(b) is that the lifetimes in the SiGe system can be an order of magnitude longer than in the GaAs/AlGaAs system because of SiGe’s lack of polar optical phonons. This property can potentially lead to significantly reduced lasing threshold for the SiGe system. The sudden drops in the lifetimes have to do with the shifting of subband energy separations \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, to either below or above the optical phonon energy.
\n\t\t\t\t
Figure 7.
a) HH valence band diagram of one period of a SiGe/Si SL with hole energy increase in the upward direction, and (b) comparison of Lifetime difference (\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t) between the SiGe/Si and GaAs/AlGaAs SL (in a similar three scheme) as a function of the transition energy (\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t) [38].
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Among the different phonon scattering processes – emission and absorption of acoustic and optical phonons, the emission of an optical phonon is by far the fastest process. But in far-IR QCLs when the subband energy separation is less than the optical phonon energy and the emission of an optical phonon is forbidden, phonon scattering may no longer be the dominant relaxation mechanism. Other scattering mechanisms need to be taken into consideration, such as the carrier-carrier [41], impurity [42], and interface roughness scatterings [43], all of which are elastic processes. The carrier-carrier scattering is a two-carrier process that is particularly important when carrier concentration is high which increases the possibility of two carriers interacting with each other. There are many possible outcomes as a result of this interaction in inducing intersubband as well as intrasubband transitions. Among them, the 22→11 process where both carriers originally in subband 2 end up in subband 1 is the most efficient one in terms of inducing intersubband transitions (Fig. 6(b)). It has been reported in experiment that the intersubband transition times on the order of tens of ps have been observed for carrier densities of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t9\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t~\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t11\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t/cm2 in GaAs/AlGaAs QWs [44]. In QCLs, since doping is mostly introduced away from the active region where optical transitions take place, impurity scattering does not seem to play a major role in determining the lifetimes of laser subbands, however, its influence on carrier transport in the injection region can be rather important. Interface roughness depends strongly on the process of structural growth, its impact on scattering should be more significant on narrow QWs, particularly for those transitions between two wavefunctions that are localized in MQWs that span across several interfaces.
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4. Valence band SiGe QCLs
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Up to now, all of the demonstrated QCLs are based on epitaxially grown III-V semiconductor heterostructures such as GaInAs/AlInAs, GaAs/AlGaAs, and InAs/AlSb, using electron subbands in conduction band. With the promise of circumventing the indirectness of Si band gap, a SiGe/Si laser based on intersubband transitions was first proposed by Sun et al in 1995 [38] where a comparative study was performed between the SiGe/Si and GaAs/AlGaAs systems. Since then there has been a series of theoretical and experimental investigations aimed at producing Si-based QCLs. A natural choice of the material system is SiGe because Si and Ge are both group-IV elements, SiGe alloys have been routinely deposited on Si to produce heterojunction bipolar transistors or as a strain-inducing layer for CMOS transistors [45].
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While QCLs based on SiGe alloys can be monolithically integrated on Si if successfully developed, there are significant challenges associated with this material system. First, there is a 4% lattice mismatch between Si and Ge. Layers of Si1-xGex alloys deposited on Si substrates induce strain which can be rather significant in QCLs because a working structure typically consists of at least hundreds of layers with a total thickness that easily exceeds the critical thickness above which the built-in strain simply relaxes to develop defects in the structure. In dealing with the issue of strain in SiGe/Si QC structures, one popular approach is to use strain balanced growth where the compressively strained Si1-xGex and tensile strained Si are alternately stacked on a relaxed Si1-yGey buffer deposited on a Si substrate where the buffer composition (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t) is chosen to produce strains in Si1-xGex and Si that compensate each other, so that the entire structure maintains a neutral strain profile [46,47]. Strain balanced structures have effectively eliminated the limitations of critical thickness and produced high quality SiGe/Si structures consisting of nearly 5000 layers (15 μm) by chemical vapor deposition [48].
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Second, the band offsets between compressively strained SiGe and tensile strained Si or between SiGe of different alloy compositions is such that the conduction band QWs are shallow, and nearly all band offsets are in valence band. Practically all of the investigations of SiGe QCLs are focused on intersubband transitions in the valence band. But the valence subband structure is much more complex in comparison with the conduction subbands because of the mixing between the HH, LH and SO bands. Their associated subbands are closely intertwined in energy making the design of valence QCLs extremely challenging. Third, any valence QCL design in general has to inevitably involve HH subbands since they occupy lower energies relative to LH subbands because of their large effective mass. In SiGe, the HH effective mass is high (~0.2\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t), which leads to small IST oscillator strength between the laser states and poor carrier transport behavior associated with their low mobilities.
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The challenge presented by the valence-band mixing also creates an opportunity to engineer desirable subband dispersions such that total population inversion between the subbands becomes unnecessary in a way analogous to the situation in conventional band-to-band lasers discussed in section II. It was reported in QCLs that the population inversion was only established locally in \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-space in the large\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t -vector region of the conduction subbands because the interactions between the subbands produced nonparallel in-plane dispersions [49]. In comparison with the conduction-band nonparabolicity, this effect is known to be much stronger in the valence band [31]. As a matter of fact, in the valence band of most diamond and zinc-blende semiconductors, LH and HH subbands usually anti-cross, and near the point of anti-crossing, the LH subband in-plane dispersion becomes electron-like. Thus, an earlier design was accomplished to effectively tailor the dispersions of two valence subbands in a GaAs/AlGaAs QW (Fig. 5) similar to those of the conduction and valence bands, in which one of the subbands is electron-like and the other hole-like, i.e., one of the subbands shall have its effective mass inverted [35]. If we now designate states near the Γ-point of subband LH1 as the intermediate states, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, states near the valley (inverted-effective-mass region) of subband LH1 as the upper laser states\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, states in subband HH1 vertically below the valley of subband LH1 as the lower laser states\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, and states near the Γ-point of subband HH1 as the ground states \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\tg\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t (counting the hole energy downward in Fig. 5), we can see that the situation closely resembles the one in the conventional band-to-band semiconductor laser. The upper and lower laser states can now be populated and depopulated through fast intrasubband processes, while the lifetime of the upper laser states is determined by a much slower intersubband process between subbands LH1 and HH1. Such a large lifetime difference between the upper and lower laser states is certainly favorable for achieving population inversion between them.
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The inverted mass approach was later on applied to the SiGe system [50,51]. Two slightly different schemes were developed, one utilized the inverted LH effective mass [50], and the other inverted HH mass [51]. In both cases, the effective mass inversion is the result of strong interaction between the valence subbands. The inverted-effective-mass feature requires the coupled subbands to be closely spaced in energy, typically less than all the optical phonon energies in the SiGe material system (37meV for the Ge-Ge mode, 64meV for the Si-Si mode, and 51meV for the Si-Ge mode [52]), which suppresses the nonradiative intersubband transitions due to the optical phonon scattering, but also limits the optical transitions in the THz regime. The structures under investigation were strain balanced with compressively strained Si1-xGex QW layers and the tensile strained Si barrier layers deposited on a relaxed Si1-yGey buffer layer (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t) on Si. The in-plane dispersions of the inverted LH scheme are shown in Fig. 8 for a 90Å/50Å Si0.7Ge0.3/Si super lattice (SL). Three lowest subbands are shown. The numbers 1, 2, 3, and 4 indicate how this inverted mass
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Figure 8.
Dispersions of subbands HH1, LH1 and HH2 in a 90Å/50Å Si0.7Ge0.3/Si SL strained balanced on a Si0.81Ge0.19 buffer, obtained with a \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t6\n\t\t\t\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\t\t\t6\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t valence band matrix taking into account HH, LH and SO interactions and strain effect [50].
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intersubband laser mimics the operation of a conventional band-to-band laser. The lifetime of the upper laser state 3 is long because the intersubband transition energy at 6THz (~50μm) is below that of optical phonons, allowing only much weaker acoustic phonon scattering between the two subbands. Calculation results have shown that optical gain in excess of 150/cm can be achieved without total population inversion being established between the LH and HH subbands.
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The inverted LH effective mass approach utilizes optical transitions between the LH and HH subband. It can be argued from the component overlap of the envelope functions in Eq.(30) that the optical transition matrix between subbands of different types is always smaller than that between subbands of the same type. We therefore tried to engineer the same inverted effective mass feature between two HH subbands. The challenge is to lift the LH subband above the HH2 subband. Once again, a strain balanced SL structure is considered but with different SiGe alloy compositions and layer thicknesses [51]. The band structure for a 90Å/35Å Si0.8Ge0.2/Si SL under an electric bias of 30kV/cm is shown in Fig. 9(a) where each QW has two active doublets formed by bringing HH1 and HH2 subbands in the neighboring QWs into resonance under the bias. There is a 3meV energy split within the doublet. The resulting in-plane dispersions for the two doublets are shown in Fig. 9(b). Simulation results showed that optical gain of 450/cm at 7.3THz can be achieved at a pumping current density of 1.5KA/cm2 at 77K.
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Figure 9.
a) Band diagram of the Si0.8Ge0.2/Si SL under an electric bias of 30 kV/cm. The labels (\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t…\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\trepresent the QWs in which the wave functions are localized [51], (b) Dispersions of the four levels (two doublets) in a QW.
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Electroluminescence (EL) from a SiGe/Si quantum cascade emitter was first demonstrated in a SiGe/Si quantum cascade emitter using HH to HH transitions in the mid-IR range in 2000 [53]. Since then several groups have observed EL from the same material system with different structures. EL emissions have been attributed to various optical transitions including HH-to-HH [54], LH-to-HH [55], and HH-to-LH [56], with emission spectra ranging from mid IR to THz (8 ~ 250μm). But lasing has not been observed. Improvement on the QCL design has been to be made. One of the most successful III-V QCL designs has been the approach of bound-to-continuum where the lower laser state sitting at the top of a miniband is delocalized over several QWs while the upper laser state is a bound state in the minigap as illustrated in Fig. 10 [57,58]. Electrons that are injected into the bound upper state 2 are prevented from escaping the bound state by the minigap, and then undergo lasing transitions to a lower state 1. The depopulation of the lower state 1 is accelerated through the efficient miniband carrier transport. Such a design has led to improved performance in terms of operating temperature as well as output power for III-V QCLs. A similar bound-to-continuum design has been implemented in SiGe with both bound and continuum formed by HH states, once again showing just EL with no lasing [59]. It is believed that in this structure LH states are mixed within the HH states. Although the impact of this intermixing has not been fully understood, these LH states can in principle present additional channels for carriers to relax from the upper laser state reducing its lifetime. An improved version has been sought after by lifting the LH states out of all involved HH states for bound and continuum with the use of strain, as a result, a clear intersubband TM polarized EL is shown suggesting that LH states have been pushed away from the HH radiative transitions [60].
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Figure 10.
Illustration of two periods of a bound-to-continuum QCL. Lasing transition occurs between an isolated bound upper state 2 (formed in the minigap) and a delocalized lower state 1 (sitting on top of a miniband).
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Nearly a decade has passed since the first experimental demonstration of EL from a SiGe/Si quantum cascade emitter [53]. During this period III-V QCLs have been improved dramatically to allow for commercialization and system integration for various applications, however there are still no SiGe QCLs. The seemingly inherent difficulties with the valence QCL approach have propelled some researchers back into the conduction band to look for solutions.
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5. Conduction band Si-based QCLs
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Before QCLs can be designed using conduction subbands, there must be sufficient conduction band offset. Contrary to the situation in compressively strained Si1-xGex, tensile strained Si1-xGex can have larger conduction band offset, but the conduction band minima occur at the two \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys whose effective mass (longitudinal) along the growth direction is very heavy (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t~\n\t\t\t\t\t\t\t\t0.9\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t) resulting in small oscillator strength and poor transport behavior possibly even worse than the HHs. Any approach of developing Si-based QCLs based on transitions between conduction subbands needs to necessarily go beyond the conventional methods in selecting the material system and growth technique.
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Prospects of developing such Si-based QCLs have been investigated theoretically. One approach stayed with the Si-rich SiGe/Si material system but instead of the conventional growth direction in (100), the structural orientation has been rotated to the [111] crystal plane [61]. Conduction band offset was calculated to be 160meV at the conduction band minima consisting of six-degenerate Δ-valleys, sufficient for designing far IR QCLs. The effective mass along (111) direction can be obtained as the geometric average of the longitudinal and transverse effective masses of the Δ -valley, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t~\n\t\t\t\t\t\t\t\t0.26\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, lower than that of longitudinal \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t~\n\t\t\t\t\t\t\t\t0.9\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t in the (100) structure. Another design relying on the Ge-rich Ge/SiGe material system has been proposed to construct conduction band QCLs using compressively strained Ge QWs and tensile strained Si0.22Ge0.78 alloy barriers grown on a relaxed [100] Si1-yGey buffer [62]. The intersubband transitions in this design are within the \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys which are the conduction band minima in Ge QWs whose effective mass along (100) direction has been determined to be\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t~\n\t\t\t\t\t\t\t\t0.12\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. Since Si1-xGex alloys with \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t0.85\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tare similar to Si in that the conduction band minima appear in the Δ -valleys, the conduction band lineup in the Ge/Si0.22Ge0.78 structure is rather complex with conduction band minima in Ge at \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys but in Si0.22Ge0.78 at \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys along the (100) growth direction. Although the band offset at the \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys is estimated to be as high as 138 meV, the overall band offset between the absolute conduction band minima in Ge and Si0.22Ge0.78 is only 41meV. Although the quantum confinement effect helps to lift those electron subbands at \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys, the two \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys are inevitably entangled with the \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys in the conduction band, leading to design complexity and potentially creating additional nonradiative decay channels for the upper laser state.
\n\t\t\t
Recently, a new group-IV material system that expands beyond the Si1-xGex alloys has been successfully demonstrated with the incorporation of Sn. These new ternary Ge1-x-ySixSny alloys have been studied for the possibility of forming direct band gap semiconductors[63-66]. Since the first successful growth of this alloy [67], device- quality epilayers with a wide range of alloy contents have been achieved [68,69]. Incorporation of Sn provides the opportunity to engineer separately the strain and band structure since we can vary the Si (x) and Sn (y) compositions independently. Certain alloy compositions of this material system offer three advantages: (1) the possibility of a “cleaner” conduction band lineup in which the L-valleys in both well and barrier sit below other valleys (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t), (2) an electron effective mass along the (001) growth direction that is much lower than the HH mass, and (3) a strain free structure that is lattice matched to Ge. In addition, recent advances in the direct growth of Ge layer on Si provide a relaxed matching buffer layer on a Si substrate upon which the strain-free Ge/Ge1-x-ySixSny is grown [70]. Based on this material system, a strain free QCL operating in the conduction L-valleys was proposed [71].
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Since band offsets between ternary Sn-containing alloys and Si or Ge are not known experimentally, we have calculated the conduction band minima for a lattice- matched heterostructure consisting of Ge and a ternary Ge1-x-ySixSny based on Jaros\' band offset theory [72] which is in good agreement with experiment for many heterojunction systems. For example, this theory predicts an average valence band offset, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0.48\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\teV for a Ge/Si heterostructure (higher energy on the Ge side), close to the accepted value of \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0.5\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t eV. The basic ingredients of our calculation are the average (between HH, LH, and SO bands) valence band offset between the two materials and the compositional dependence of the band structure of the ternary alloy. For the Ge/-Sn interface, Jaros’ theory predicts \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0.69\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t eV (higher energy on the Sn side). For the Ge1-x-ySixSny/Ge interface we have used the customary approach for alloy semiconductors, interpolating the average valence band offsets for the elementary heterojunctions Ge/Si and Ge/-Sn. Thus we used (in eV)
Once the average valence band offset is determined, the energies of individual conduction band edges in the Ge1-x-ySixSny alloy can be calculated relative to those in Ge from the compositional dependence of the spin-orbit splitting of the top valence band states and the compositional dependence of the energy separations between those conduction band edges and the top of the valence band in the alloy [73]. We have assumed that all required alloy energies can be interpolated between the known values for Si, Ge, and α-Sn as
The bowing parameters\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tb\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tGeSi\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tb\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tGeSn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, and \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tb\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tSiSn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t have been discussed in Refs. [74] and [75]. Finally, for the indirect conduction band minimum near the X-point, Weber and Alonso find
(in eV) for Ge1-xSix alloys [76]. On the other hand, the empirical pseudo-potential calculations of Chelikovsky and Cohen place this minimum at 0.90 eV in -Sn, virtually the same as its value in pure Ge [77]. We thus assume that the position of this minimum in ternary Ge1-x-ySixSny alloys is independent of the Sn concentration\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. The conduction band minima results are shown in Fig. 11 for Sn concentrations\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t0.1\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. The Si concentration \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\twas calculated using Vegard\'s law in such a way that the ternary Ge1-x-ySixSny is exactly lattice-matched with Ge.
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It can be seen from Fig. 11 that a conduction-band offset of 150 meV at L-valleys can be obtained between lattice-matched Ge and Ge0.76Si0.19Sn0.05 alloy while all other conduction-band valleys (Γ, X, etc) are above the L-valley band edge of the Ge0.76Si0.19Sn0.05 barrier. This band alignment presents a desirable alloy composition from which a QCL operating at L-valleys can be designed using Ge as QWs and Ge0.76Si0.19Sn0.05 as barriers without the complexity arising from other energy valleys.
\n\t\t\t
\n\t\t\t\tFigure 12 shows the QCL structure based upon Ge/ Ge0.76Si0.19Sn0.05 QWs. Only L-valley conduction-band lineups are shown in the potential diagram under an applied electric field of 10 kV/cm. In order to solve the Schrödinger equation to yield subbands and their associated envelope functions, it is necessary to determine the effective mass \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t along the (001) growth direction (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t) within the constant-energy ellipsoids at the L-valleys along the (111) direction which is tilted with respect to (100). Using the \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valley principal transverse effective mass\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0.08\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, and the longitudinal effective mass \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t1.60\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t for Ge, we obtain\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0.12\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. The squared magnitudes of all envelope functions are plotted at energy positions of their associated subbands. As shown in Fig. 12, each period of the QCL has an active region for lasing emission and an injector region for carrier transport. These two regions are separated by a 30 Å barrier. The active region is constructed with 3 coupled Ge QWs that give rise to three subbands marked 1, 2, and 3. The lasing transition at the wavelength of 49 µm is between the upper laser state 3 and the lower laser state 2. The injector region consists of 4 Ge QWs of decreasing well widths all
\n\t\t\t
Figure 11.
Conduction band minima at \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\tX\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\tpoints of Ge1-x-ySixSny that is lattice matched to Ge [71].
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Figure 12.
Formula: Eqn281.wmf>-valley conduction band profile and squared envelope functions under an electric field of 10kV/cm. Layer thicknesses in angstrom are marked with bold numbers for Ge QWs and regular for GeSiSn barriers. Array marks the injection barrier [71].
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separated by 20Å Ge0.76Si0.19Sn0.05 barriers. The depopulation of lower state 2 is through scattering to state 1 and to the miniband downstream formed in the injector region. These scattering processes are rather fast because of the strong overlap between the involved states. Another miniband in the injector region formed of quasi-bound states is situated 45 meV above the upper laser state 3, effectively preventing escape of electrons from upper laser state 3 into the injector region.
\n\t\t\t
The nonradiative transition rates between different subbands in such a low-doped nonpolar material system with low injection current should be dominated by deformation-potential scattering of nonpolar optical and acoustic phonons. For this Ge-rich structure, we have used bulk-Ge phonons for calculation of the scattering rate to yield lifetimes for the upper laser state \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t and the lower laser state\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, as well as the 3→2 scattering time \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t [78]. The results obtained from Eq.(38) are shown in Fig. 13 as a function of operating temperature. These lifetimes are at least one-order of magnitude longer than those of III-V QCLs owing to the nonpolar nature of GeSiSn alloys. The necessary condition for population inversion \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t32\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is satisfied throughout the temperature range. Using these predetermined lifetimes in the population rate equation under current injection:
where \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t∂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t∂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tη\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tJ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t∂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t∂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t32\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is the area carrier density per period in subband \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tunder injected current density \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\twith an injection efficiency\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJ\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, and \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tη\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is the area carrier density per period due to thermal population. Solving the above rate equation at steady state yields population inversion
which can then be used to evaluate the optical gain of the TM polarized mode following Eq.(28) at the lasing transition energy \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t32\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tη\n\t\t\t\t\t\t\t\t\t\tJ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t.\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tmeV as
For the QCL structure in Fig. 12, the following parameters are used: index of refraction\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t23\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t[\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t32\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tη\n\t\t\t\t\t\t\t\t\t\t\t\tJ\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t]\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t.\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, lasing transition FWHM \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t3.97\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tmeV, length of one period of the QCL \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t Å, area doping density per period of 1010 cm2, and unit injection efficiency\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t532\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t.
\n\t\t\t
Since the relatively small conduction band offset limits the lasing wavelength to the far-IR or THz regime (roughly 30 µm and beyond), the waveguide design can no longer rely on that of conventional dielectric waveguides such as those used in laser diodes and mid IR QCLs. This is mainly because the thickness required for the dielectric waveguide would have exceeded what can be realized with the epitaxial techniques employed to grow the laser structures. One solution is to place the QCL active structure between two metal layers to form the so-called plasmon waveguide [79,80]. While the deposition of top metal is trivial, placing bottom metal requires many processing steps such as substrate removal, metal deposition, and subsequent wafer bonding. The QCL waveguides are typically patterned into ridges as shown in Fig. 14.
\n\t\t\t
Figure 13.
Upper state lifetime\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tη\n\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t, lower state lifetime\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t, and scattering time \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t between them as a function of temperature.
\n\t\t\t
Figure 14.
Schematic of a ridge plasmon waveguide with the Ge/GeSiSn QCL sandwiched between two metal layers.
\n\t\t\t
This plasmon waveguide supports only TM polarized EM mode that is highly confined within the QCL region,\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t32\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. We can assume Drude model to describe the metal dielectric function
where \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\tM\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is the metal plasmon frequency, and \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is the metal loss (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\teV, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t8.11\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tmeV for Au [81]), and \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tħ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t65.8\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t for the Ge rich Ge/Ge0.76Si0.19Sn0.05 QCL active region. Consider the EM wave propagate along the \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t≈\n\t\t\t\t\t\t\t\t16\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-direction as shown in Fig. 14, its electric field can then be obtained as
where\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tcosh\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tcosh\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t[\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tcosh\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tcosh\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tsinh\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tsinh\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tcosh\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tcosh\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t̂\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, and \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\tM\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is a constant. The complex propagation constant \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tfollows these relations, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\'\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t"\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\twith\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tq\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. It is easy to see that the continuity of the normal component of the electric displacement is satisfied at the boundaries\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tω\n\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, the requirement of continuity of tangential electric field leads to
which determines the TM modes that can propagate in this plasmon waveguide. The waveguide loss \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t[\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\ttanh\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\ttanh\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t]\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is dominated by the metal loss, which can be determined from the imaginary part of the propagation constant, as\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. As a superposition of two surface plasmon modes bound to the two metal-dielectric interfaces at\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t"\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, this TM mode decays exponentially into the metal, providing an excellent optical confinement factor defined as\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. We have simulated the TM-polarized mode in a QCL structure of 40 periods (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t∫\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t∫\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t∞\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t∞\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\t\tE\n\t\t\t\t\t\t\t\t\t\t\t|\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tµm) that is confined by double-Au-plasmon waveguide and obtained near unity optical confinement \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t2.13\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t and waveguide loss \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t≈\n\t\t\t\t\t\t\t\t1.0\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t /cm. Assuming a mirror loss \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t110\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t /cm for a typical cavity length of 1 mm, the threshold current density \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t can be calculated from the balancing relationship, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tJ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, where \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΓ\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is the optical gain Eq.(44) obtained at the threshold\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. The result is shown in Fig. 15 for \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tJ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t that ranges from 22 A/cm2 at 5 K to 550 A/cm2 at 300 K. These threshold values are lower than those of III-V QCLs as a result of the longer scattering times due to nonpolar optical phonons.
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While GeSiSn epilayers with alloy compositions suitable for this QCL design have been grown with MOCVD [68,69], implementation of Ge/GeSiSn QCLs is currently challenged by the structural growth of the large number of hetero-layers in the QCL structure with very fine control of layer thicknesses and alloy compositions. Nevertheless, progress is being made towards experimental demonstration.
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Figure 15.
Simulated threshold current density of the Ge/GeSiSn QCL as a function of temperature.
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6. Summary
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Silicon-based lasers have been long sought after for the possibility of monolithic integration of photonics with high-speed Si electronics. Many parallel approaches are currently taken to reach this goal. Among them Si nanocrystals and Er-doped Si have been investigated rather extensively. While EL has been demonstrated, lasing has not been observed. The only reported lasing in Si so far has been achieved using stimulated Raman scattering which requires optical pumping at very high intensity on a device of large scale – impractical for integration with Si electronics. The QCLs that have been successfully developed in III-V semiconductors offer an important alternative for the development of Si-based lasers. The salient feature of QCLs is that lasing transitions take place between subbands that are within the conduction band without crossing the band gap. Such a scheme makes the indirect nature of the Si band gap irrelevant. In order to appreciate the QCL designs, some theoretical background underlying the basic operating principles has been introduced here. In particular, subband formation and energy dispersion in semiconductor QWs are described in the framework of envelope functions with the effective-mass approximation for both conduction and valence band taking into account mixing between HH, LH, and SO bands. Optical gain based on ISTs is derived and intersubband lifetimes are discussed with a more detailed treatment of carrier-phonon scattering.
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The development of Si-based QCLs has been primarily focused on ISTs between valence subbands in the Si-rich SiGe/Si material system. Such a material system has been routinely used in CMOS-compatible processes. There are two reasons for using holes instead of electrons. One is that the compressively strained Si1-xGex with tensile strained Si grown on a relaxed Si1-yGey has very small conduction band offset QWs are too shallow to allow for elaborate QCLs. Tensile strained Si1-xGex, on the other hand, can have larger conduction band offset, but the conduction band minima occur at the two \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tJ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\th\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys whose effective mass (longitudinal) along the growth direction is heavy (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t) resulting in small oscillator strength and poor transport behavior such as reduced tunneling probabilities. It is generally believed that SiGe QCLs have to be pursued within the valence band as a p-type device. But the situation in valence band also presents challenges in several perspectives. First, the strong mixing of HH, LH, and SO bands makes the QCL design exceedingly cumbersome albeit the opportunities presented by the strong nonparabolicity in valence subbands to take advantage of schemes such as the inverted effective mass where the total population inversion between subbands may not be necessary. Second, there is a great deal of uncertainty in various material parameters for the SiGe alloy – often times approximation has to be made to linearly extrapolate parameters from those of Si and Ge, thus, the accuracy of the designs has a great degree of ambiguity. Third, any valence QCLs have no choice but to deal with HH subbands; their large effective mass hinders carrier injection efficiency and leads to small IST oscillator strength between laser states. Fourth, for any significant band offset needed to implement QCLs, lattice-mismatch-induced strain in SiGe QWs and Si barriers even in strain balanced structures is significant, which presents a challenge in structural growth and device processing. While EL was demonstrated from a valence-band SiGe/Si quantum cascade emitter nearly a decade ago, lasing remains elusive.
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Recently, several ideas of developing Si-based conduction-band QCLs have emerged to circumvent the hurdles in the SiGe/Si valence-band approach. The proposals offer ways to increase the conduction band offset and to reduce the effective mass along the growth direction. One scheme proposes to orient the structural growth along the (111) direction, and another relies on ISTs in the \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t~\n\t\t\t\t\t\t\t\t0.9\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys of the conduction band in Ge-rich Ge/SiGe material system. The former has accomplished more in increasing the conduction-band offset, and the latter in reducing the effective mass. A third approach that expands the material system beyond SiGe to GeSiSn has been discussed in detail. A Ge/Ge0.76Si0.19Sn0.05 QCL that operates at \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys of the conduction band was designed. According to our estimation of the band lineup, this particular alloy composition gives a “clean” conduction band offset of 150meV at \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t-valleys with all other energy valleys conveniently out of the way. All QCL layers are lattice matched to a Ge buffer layer on a Si substrate and the entire structure is therefore strain free. The electron effective mass along the growth direction is much lighter than that of heavy holes bringing a significant improvement in tunneling rates and oscillator strengths. The lasing wavelength of this device is 49 µm. With different GeSiSn alloy compositions that are lattice matched to Ge, QCLs can be tuned to lase at other desired wavelengths. Lifetimes determined from the deformation potential scattering of nonpolar optical and acoustic phonons are at least an order of magnitude longer than those in III-V QCLs with polar optical phonons, leading to a reduction in threshold current density and the possibility of room temperature operation. While there are considerable challenges in material growth of this QCL design, advances in fine control of structural parameters including layer thicknesses and alloy compositions are moving towards implementation of conduction-band QCLs in the GeSiSn system.
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When are we going to realize Si-based lasers that can be integrated with Si electronics? Clearly, breakthroughs in material science and device innovation are necessary before that happens, but with the variety of approaches that are being pursued--driven by the potential pay-off in commercialization--the prospect is promising.
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\n\t\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/9889.pdf",chapterXML:"https://mts.intechopen.com/source/xml/9889.xml",downloadPdfUrl:"/chapter/pdf-download/9889",previewPdfUrl:"/chapter/pdf-preview/9889",totalDownloads:2815,totalViews:239,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:null,dateReviewed:null,datePrePublished:null,datePublished:"April 1st 2010",dateFinished:null,readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/9889",risUrl:"/chapter/ris/9889",book:{slug:"advances-in-lasers-and-electro-optics"},signatures:"Greg Sun",authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Lasers based on intersubband transitions",level:"1"},{id:"sec_3",title:"3. Intersubband theory",level:"1"},{id:"sec_3_2",title:"3.1. Subbands and dispersions",level:"2"},{id:"sec_4_2",title:"3.2. Optical gain",level:"2"},{id:"sec_5_2",title:"3.3. Intersubband lifetimes",level:"2"},{id:"sec_7",title:"4. Valence band SiGe QCLs",level:"1"},{id:"sec_8",title:"5. Conduction band Si-based QCLs",level:"1"},{id:"sec_9",title:"6. Summary",level:"1"}],chapterReferences:[{id:"B1",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLorenzo\n\t\t\t\t\t\t\tJ. P.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1986 “All-silicon active and passive guided-wave components for 𝜆=1.3 and 1.6µm,” IEEE Journal of Quantum Electronics QE-22\n\t\t\t\t\t873\n\t\t\t\t\t879 .\n\t\t\t'},{id:"B2",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1993 “Silicon-based optoelectronics,” Proceedings of the IEEE\n\t\t\t\t\t81\n\t\t\t\t\t1687\n\t\t\t\t\t1706 .\n\t\t\t'},{id:"B3",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPavesi\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDal Negro\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMazzoleni\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFranzo\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPriolo\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2000 “Optical gain in silicon nanocrystals,” Nature, 408\n\t\t\t\t\t440\n\t\t\t\t\t444 .\n\t\t\t'},{id:"B4",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRuan\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFauchet\n\t\t\t\t\t\t\tP. M.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDal Negro\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMazzoleni\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPavesi\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2003 “Stimulated emission in nanocrystalline silicon superlattice,” Applied Physics Letters\n\t\t\t\t\t83\n\t\t\t\t\t5479\n\t\t\t\t\t5481 .\n\t\t\t'},{id:"B5",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tChen\n\t\t\t\t\t\t\tM. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYen\n\t\t\t\t\t\t\tJ. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLi\n\t\t\t\t\t\t\tJ. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tChang\n\t\t\t\t\t\t\tJ. F.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTsai\n\t\t\t\t\t\t\tS. C.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTsai\n\t\t\t\t\t\t\tC. S.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004 “Stimulated emission in a nanostructured silicon pn-junction diode using current injection,” Applied Physics Letters\n\t\t\t\t\t84\n\t\t\t\t\t2163\n\t\t\t\t\t2165 .\n\t\t\t'},{id:"B6",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDesurvire\n\t\t\t\t\t\t\tE.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1994 Erbium-doped Fiber Amplifiers: Principles and Applications, Wiley, New York,\n\t\t\t'},{id:"B7",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFranzò\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCoffa\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1997 “Mechanism and performance of forward and reverse bias electroluminescence at 1.54 µm from Er-doped Si diodes,” Journal of Applied Physics\n\t\t\t\t\t81\n\t\t\t\t\t2784\n\t\t\t\t\t2793 .\n\t\t\t'},{id:"B8",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPriolo\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFranzò\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCoffa\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCarnera\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1998 “Excitation and nonradiative deexcitation processes of Er3+ in crystalline Si,” Physical Review B\n\t\t\t\t\t57\n\t\t\t\t\t4443\n\t\t\t\t\t4455 .\n\t\t\t'},{id:"B9",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKenyon\n\t\t\t\t\t\t\tA. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTrwoga\n\t\t\t\t\t\t\tP. F.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFederighi\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPitt\n\t\t\t\t\t\t\tC. W.\n\t\t\t\t\t\t\n\t\t\t\t\t (1994).“Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions,” Journal of Physics: Condensed Matter 6, L319\n\t\t\t\t\t324 .\n\t\t\t'},{id:"B10",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCastagna\n\t\t\t\t\t\t\tM. E.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCoffa\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tcarestia\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMessian\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBuongiorno\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2002 “Quantum dot materials and devices for light emission in silicon,” Proceedings of 32nd European Solid-State Device Research Conference (ESSDERC 2002), Fireze, Italy, D21.3\n\t\t\t'},{id:"B11",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCalps\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDimitropoulos\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRaghunathan\n\t\t\t\t\t\t\tV.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHan\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJalali\n\t\t\t\t\t\t\tB.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2003 “Observation of stimulated Raman scattering in silicon waveguides,” Optics Express\n\t\t\t\t\t11\n\t\t\t\t\t1731 -\n\t\t\t'},{id:"B12",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLiu\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRong\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPaniccia\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCohen\n\t\t\t\t\t\t\tO.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHak\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004 “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Optics Express 12, (2004) 4261-4268.\n\t\t\t'},{id:"B13",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBoyraz\n\t\t\t\t\t\t\tO.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJalali\n\t\t\t\t\t\t\tB.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004 “Demonstration of a silicon Raman laser,” Optics Express\n\t\t\t\t\t12\n\t\t\t\t\t5269\n\t\t\t\t\t5273 .\n\t\t\t'},{id:"B14",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJalali\n\t\t\t\t\t\t\tB.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2006 “Silicon photonics,” Journal of Lightwave Technology\n\t\t\t\t\t24\n\t\t\t\t\t4600\n\t\t\t\t\t4615 .\n\t\t\t'},{id:"B15",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPark\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFang\n\t\t\t\t\t\t\tA. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKodama\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBowers\n\t\t\t\t\t\t\tJ. E.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2005 “Hybrid silicon evanescent laser fabricated with a silicon waveguide and III-V offset quantum wells,” Optics Express\n\t\t\t\t\t13\n\t\t\t\t\t9460\n\t\t\t\t\t9464 .\n\t\t\t'},{id:"B16",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPark\n\t\t\t\t\t\t\tJ. H.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSteckl\n\t\t\t\t\t\t\tA. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2005 “Demonstration of a visible laser on silicon using Eu-doped GaN thin films,” Journal of Applied Physics 98, 056108\n\t\t\t'},{id:"B17",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMi\n\t\t\t\t\t\t\tZ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBhattacharya\n\t\t\t\t\t\t\tP.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYang\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPipe\n\t\t\t\t\t\t\tK. P.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2005 “Room-temperature self-organized In0.5Ga0.5As quantum dot laser on silicon,” Electronics Letters\n\t\t\t\t\t41\n\t\t\t\t\t742\n\t\t\t\t\t744 .\n\t\t\t'},{id:"B18",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tEsaki\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTsu\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1970 "Superlattice and negative differential conductivity in semiconductors", IBM Journal of Research and Development\n\t\t\t\t\t14\n\t\t\t\t\t61\n\t\t\t\t\t65 .\n\t\t\t'},{id:"B19",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKazarinov\n\t\t\t\t\t\t\tR. F.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSuris\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1971 “Electric and electromagnetic properties of semiconductors with a superlattice,” Soviet Physics- Semiconductors 5, 797.\n\t\t\t'},{id:"B20",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFaist\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCapasso\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSivco\n\t\t\t\t\t\t\tD. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHutchinson\n\t\t\t\t\t\t\tA. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSirtori\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCho\n\t\t\t\t\t\t\tA. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1994 “Quantum cascade laser,” Science\n\t\t\t\t\t264\n\t\t\t\t\t553\n\t\t\t\t\t556\n\t\t\t\t\n\t\t\t'},{id:"B21",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKhurgin\n\t\t\t\t\t\t\tJ. B.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1992 “Feasibility of optically pumped four-level infrared lasers,” in Intersubband Transitions in Quantum Wells, (Edited by E. Rosencher, B. Vinter, and B. Levine, Plenum Press, New York,), 219\n\t\t\t\t\t226\n\t\t\t\t\n\t\t\t'},{id:"B22",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKhurgin\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1993 “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE Jounral of Quantum Electronics QE-29\n\t\t\t\t\t1104\n\t\t\t\t\t1111 .\n\t\t\t'},{id:"B23",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRevin\n\t\t\t\t\t\t\tD. G.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCockburn\n\t\t\t\t\t\t\tJ. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSteer\n\t\t\t\t\t\t\tM. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAirey\n\t\t\t\t\t\t\tR. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHopkinson\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKrysa\n\t\t\t\t\t\t\tA. B.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWilson\n\t\t\t\t\t\t\tL. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMenzel\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2007 “InGaAs/AlAsSb/InP quantum cascade lasers operating at wavelengths close to 3 µm,” Applied Physics Letters 90, 021108.\n\t\t\t'},{id:"B24",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSemtsiv\n\t\t\t\t\t\t\tM. P.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWienold\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDressler\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMasselink\n\t\t\t\t\t\t\tW. T.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2007 “Short-wavelength (λ≈3.05 µm) InP-based strain-compensated quantum-cascade laser,” Applied Physics Letters 90, 051111.\n\t\t\t'},{id:"B25",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tColombelli\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCapasso\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGmachl\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHutchinson\n\t\t\t\t\t\t\tA. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSivco\n\t\t\t\t\t\t\tD. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTredicucci\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWanke\n\t\t\t\t\t\t\tM. C.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSergent\n\t\t\t\t\t\t\tA. M.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCho\n\t\t\t\t\t\t\tA. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2001 “Far-infrared surface-plasmon quantum-cascade lasers at 21.5 µm and 24 µm wavelengths,” Applied Physics Letters\n\t\t\t\t\t78\n\t\t\t\t\t2620\n\t\t\t\t\t2622 .\n\t\t\t'},{id:"B26",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBai\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSlivken\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDarvish\n\t\t\t\t\t\t\tS. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRazeghi\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008 “Room temperature continuous wave operation of quantum cascade lasers with 12.5% wall plug efficiency,” Applied Physics Letters 93, 021103.\n\t\t\t'},{id:"B27",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLyakh\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPflügl\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDiehl\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWang\n\t\t\t\t\t\t\tQ. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCapasso\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWang\n\t\t\t\t\t\t\tX. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFan\n\t\t\t\t\t\t\tJ. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTanbun-Ek\n\t\t\t\t\t\t\tT.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMaulini\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTsekoun\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGo\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKumar\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPatel\n\t\t\t\t\t\t\tN.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008 “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 µm,” Applied Physics Letters 92, 111110.\n\t\t\t'},{id:"B28",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWilliams\n\t\t\t\t\t\t\tB. S.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2007 “Tereahertz quantum-cascade lasers,” Nature Phtonics\n\t\t\t\t\t1\n\t\t\t\t\t517\n\t\t\t\t\t525 .\n\t\t\t'},{id:"B29",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWhite\n\t\t\t\t\t\t\tS. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSham\n\t\t\t\t\t\t\tL. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1981 “Electronic properties of flat-band semiconductor heterostructures,” Physical Review Letters\n\t\t\t\t\t47\n\t\t\t\t\t879\n\t\t\t\t\t882 .\n\t\t\t'},{id:"B30",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKane\n\t\t\t\t\t\t\tE. O.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1957 “Band structure of indium antimonide,” Journal Physics and Chemistry of Solids\n\t\t\t\t\t1\n\t\t\t\t\t249\n\t\t\t\t\t261 .\n\t\t\t'},{id:"B31",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBastard\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1998\n\t\t\t\t\tWave Mechanics Applied to Semiconductor Heterostructures (Les Editions de Physique, les Ulis),, Chapter 3.\n\t\t\t'},{id:"B32",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLuttinger\n\t\t\t\t\t\t\tJ. M.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKohn\n\t\t\t\t\t\t\tW.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1955 “Motion of Electrons and Holes in Perturbed Periodic Fields,” Physical Review 97\n\t\t\t\t\t869\n\t\t\t\t\t883 .\n\t\t\t'},{id:"B33",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLuttinger\n\t\t\t\t\t\t\tJ. M.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1956 “Quantum Theory of Cyclotron Resonance in Semiconductors: General Theory,” Physical Review 102\n\t\t\t\t\t1030\n\t\t\t\t\t1041 .\n\t\t\t'},{id:"B34",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBir\n\t\t\t\t\t\t\tG. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPikus\n\t\t\t\t\t\t\tG. E.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1974\n\t\t\t\t\tSymmetry and Strain-Induced Effects in Semiconductors (Wiley, New York,)\n\t\t\t'},{id:"B35",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLu\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKhurgin\n\t\t\t\t\t\t\tJ. B.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1998 “Valence intersubband lasers with inverted light-hole effective mass,” Applied Physics Letters\n\t\t\t\t\t72\n\t\t\t\t\t1481\n\t\t\t\t\t1483 .\n\t\t\t'},{id:"B36",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tVoon\n\t\t\t\t\t\t\tL. C. L. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRam-Mohan\n\t\t\t\t\t\t\tL. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1993 “Tight-binding representation of the optical matrix elements: theory and applications,” Physical Review B\n\t\t\t\t\t47\n\t\t\t\t\t15500\n\t\t\t\t\t15508 .\n\t\t\t'},{id:"B37",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWest\n\t\t\t\t\t\t\tL. C.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tEglash\n\t\t\t\t\t\t\tS. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1985 “First observation of an extremely large-dipole infrared transition within the conduction band of a GaAs quantum well,” Applied Physics Letters\n\t\t\t\t\t46\n\t\t\t\t\t1156\n\t\t\t\t\t1158 .\n\t\t\t'},{id:"B38",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFriedman\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1995 “Intersubband lasing lifetimes of SiGe/Si and GaAs/AlGaAs multiple quantum well structures,” Applied Physics Letters\n\t\t\t\t\t66\n\t\t\t\t\t3425\n\t\t\t\t\t3427 .\n\t\t\t'},{id:"B39",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRidley\n\t\t\t\t\t\t\tB. K.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1982 “The electron-phonon interaction in quasi-two-dimensional semiconductor quantum-well structures,” Journal of Physics C: Solid state Physics\n\t\t\t\t\t15\n\t\t\t\t\t5899\n\t\t\t\t\t5917 .\n\t\t\t'},{id:"B40",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPrice\n\t\t\t\t\t\t\tP. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1981 “Two-dimensional electron transport in semiconductor layers. I. Phonon scattering,” Annals of Physics\n\t\t\t\t\t133\n\t\t\t\t\t217\n\t\t\t\t\t239 .\n\t\t\t'},{id:"B41",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHarrison\n\t\t\t\t\t\t\tP.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2000\n\t\t\t\t\tQuantum Wells, Wires, and Dots, (John Wiley & Sons,) 272\n\t\t\t\t\n\t\t\t'},{id:"B42",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCallebaut\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKumar\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWilliams\n\t\t\t\t\t\t\tB. S.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHu\n\t\t\t\t\t\t\tQ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tReno\n\t\t\t\t\t\t\tJ. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004 “Importance of electron impurity scattering for electron transport in terahertz quantum-cascade lasers,” Applied Physics Letters\n\t\t\t\t\t84\n\t\t\t\t\t645\n\t\t\t\t\t647 .\n\t\t\t'},{id:"B43",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFerreira\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBastard\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1989 “Evaluation of some scattering times for electrons in unbiased and biased single-and multiple-quantum-well structures,” Physical Review B\n\t\t\t\t\t40\n\t\t\t\t\t1074\n\t\t\t\t\t1086 .\n\t\t\t'},{id:"B44",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHartig\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGanière\n\t\t\t\t\t\t\tJ. D.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSelbmann\n\t\t\t\t\t\t\tP. E.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDeveaud\n\t\t\t\t\t\t\tB.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRota\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1999 “Density dependence of carrier-carrier induced intersubband scattering in GaAs/AlGaAs quantum wells,” Physical Review B 60\n\t\t\t\t\t1500\n\t\t\t\t\t1503 .\n\t\t\t'},{id:"B45",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCressler\n\t\t\t\t\t\t\tJ. D.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008\n\t\t\t\t\tSiGe and Si Strained-Layer Epitaxy for Silicon Heterostructure Devices, CRC Press,\n\t\t\t'},{id:"B46",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFriedman\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLu\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1998 “Theory of the strain-symmetrized silicon-based Ge-Si superlattice laser,” IEEE Journal of Selected Topics in Quantum Electronics\n\t\t\t\t\t4\n\t\t\t\t\t1029\n\t\t\t\t\t1034 .\n\t\t\t'},{id:"B47",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFriedman\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLu\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1998 “Asymmetric strain-symmetrized Ge-Si interminiband laser,” IEEE Photonics Technology Letters\n\t\t\t\t\t10\n\t\t\t\t\t1715\n\t\t\t\t\t1717 .\n\t\t\t'},{id:"B48",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPaul\n\t\t\t\t\t\t\tD. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMatman\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLever\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIkonić\n\t\t\t\t\t\t\tZ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKelsall\n\t\t\t\t\t\t\tR. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tChrastina\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIsella\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tvon Känel\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMüller\n\t\t\t\t\t\t\tE.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tNeels\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008 “Si/SiGe bound-to-continuum terahertz quantum cascade emitters,” ECS Transactions. 16\n\t\t\t\t\t865\n\t\t\t\t\t874 .\n\t\t\t'},{id:"B49",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFaist\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCapasso\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSirtori\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSivco\n\t\t\t\t\t\t\tD. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHutchinson\n\t\t\t\t\t\t\tA. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHybertson\n\t\t\t\t\t\t\tM. S.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCho\n\t\t\t\t\t\t\tA. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1996 “Quantum cascade lasers without intersubband population inversion,” Physical Review Letters\n\t\t\t\t\t76\n\t\t\t\t\t411\n\t\t\t\t\t414 .\n\t\t\t'},{id:"B50",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFriedman\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2001 “SiGe/Si THz laser based on transitions between inverted mass light-hole and heavy-hole subbands,” Applied Physics Letters\n\t\t\t\t\t78\n\t\t\t\t\t401\n\t\t\t\t\t403 .\n\t\t\t'},{id:"B51",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2001 “Terahertz gain in SiGe/Si quantum staircase utilizing the heavy-hole inverted effective mass,” Applied Physics Letters\n\t\t\t\t\t79\n\t\t\t\t\t3639\n\t\t\t\t\t3641 .\n\t\t\t'},{id:"B52",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFasolino\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMolinari\n\t\t\t\t\t\t\tE.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMaan\n\t\t\t\t\t\t\tJ. C.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1989 “Resonant quasiconfined optical phonons in semiconductor superlattices,” Physical Review B 39\n\t\t\t\t\t3923\n\t\t\t\t\t3926 .\n\t\t\t'},{id:"B53",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDehlinger\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDiehl\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGennser\n\t\t\t\t\t\t\tU.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSigg\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFaist\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tEnsslin\n\t\t\t\t\t\t\tK.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGrützmacher\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMüller\n\t\t\t\t\t\t\tE.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2000 “Intersubband electroluminescence from silicon-based quantum cascade structures,” Science 290, 2277.\n\t\t\t'},{id:"B54",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBormann\n\t\t\t\t\t\t\tI.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBrunner\n\t\t\t\t\t\t\tK.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHackenbuchner\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZindler\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAbstreiter\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSchmult\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWegscheider\n\t\t\t\t\t\t\tW.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2002 “Midinfrared intersubband electroluminescence of Si/SiGe quantum cascade structures,” Applied Physics Letters\n\t\t\t\t\t80\n\t\t\t\t\t2260\n\t\t\t\t\t2262 .\n\t\t\t'},{id:"B55",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLynch\n\t\t\t\t\t\t\tS. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBates\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPaul\n\t\t\t\t\t\t\tD. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tNorris\n\t\t\t\t\t\t\tD. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCullis\n\t\t\t\t\t\t\tA. G.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIkonić\n\t\t\t\t\t\t\tZ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKelsall\n\t\t\t\t\t\t\tR. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHarrison\n\t\t\t\t\t\t\tP.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tArnone\n\t\t\t\t\t\t\tD. D.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPidgeon\n\t\t\t\t\t\t\tC. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2002 “Intersubband electroluminescence from Si/SiGe cascade emitters at terahertz frequencies,” Applied Physics Letters\n\t\t\t\t\t81\n\t\t\t\t\t1543\n\t\t\t\t\t1545 .\n\t\t\t'},{id:"B56",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBates\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLynch\n\t\t\t\t\t\t\tS. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPaul\n\t\t\t\t\t\t\tD. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIkonic\n\t\t\t\t\t\t\tZ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKelsall\n\t\t\t\t\t\t\tR. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHarrison\n\t\t\t\t\t\t\tP.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLiew\n\t\t\t\t\t\t\tS. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tNorris\n\t\t\t\t\t\t\tD. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCullis\n\t\t\t\t\t\t\tA. G.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTribe\n\t\t\t\t\t\t\tW. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tArnone\n\t\t\t\t\t\t\tD. D.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2003 “Interwell intersubband electroluminescence from Si/SiGe quantum cascade emitters,” Applied Physics Letters\n\t\t\t\t\t83\n\t\t\t\t\t4092\n\t\t\t\t\t4094 .\n\t\t\t'},{id:"B57",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFaist\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBeck\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAellen\n\t\t\t\t\t\t\tT.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGini\n\t\t\t\t\t\t\tE.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2001 “Quantum-cascade lasers based on a bound-to-continuum transition,” Applied Physics Letters\n\t\t\t\t\t78\n\t\t\t\t\t147\n\t\t\t\t\t149 .\n\t\t\t'},{id:"B58",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tScalar\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\tet al.\n\t\t\t\t\t\n\t\t\t\t\t2003 “Far infrared (λ≅87μm) bound-to-continuum quantum-cascade lasers operating up to 90K,” Applied Physics Letters\n\t\t\t\t\t82\n\t\t\t\t\t3165\n\t\t\t\t\t3167 .\n\t\t\t'},{id:"B59",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDiehl\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMentese\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMüller\n\t\t\t\t\t\t\tE.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGrützmacher\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSigg\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGennser\n\t\t\t\t\t\t\tU.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSagnes\n\t\t\t\t\t\t\tI.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCampiedelli\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKermarrec\n\t\t\t\t\t\t\tO.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBensahel\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFaist\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2002 “Electroluminescence from strain-compensated Si0.2Ge0.8/Si quantum cascade structures based on a bound-to-continuum transitions,” Applied Physics Letters\n\t\t\t\t\t81\n\t\t\t\t\t4700\n\t\t\t\t\t4702 .\n\t\t\t'},{id:"B60",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPaul\n\t\t\t\t\t\t\tD. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMatmon\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLever\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIkonić\n\t\t\t\t\t\t\tZ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKelsall\n\t\t\t\t\t\t\tR. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tChrastina\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIsella\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tvon\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKänel\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008 “Si/SiGe bound-to-continuum quantum cascade terahertz emitters,” Proceedings of SPIE 6996, 69961C.\n\t\t\t'},{id:"B61",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLever\n\t\t\t\t\t\t\tL.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tValavanis\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIkonić\n\t\t\t\t\t\t\tZ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKelsall\n\t\t\t\t\t\t\tR. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008 “Simulated [111] Si-SiGe THz quantum cascade laser,” Applied Physics Letters 92, 021124.\n\t\t\t'},{id:"B62",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDriscoll\n\t\t\t\t\t\t\tK.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPaiella\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2006 “Silicon-based injection lasers using electrical intersubband transitions in the L-valleys,” Applied Physics Letters 89, 191110.\n\t\t\t'},{id:"B63",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPerry\n\t\t\t\t\t\t\tC. H.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1991 “Predicted band gap of the new semiconductor SiGeSn,” Journal of Applied Physics\n\t\t\t\t\t69\n\t\t\t\t\t539\n\t\t\t\t\t541 .\n\t\t\t'},{id:"B64",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJenkins\n\t\t\t\t\t\t\tD. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDow\n\t\t\t\t\t\t\tJ. D.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1987 “Electronic properties of metastable GexSn1-x alloys,” Physical Review B 36\n\t\t\t\t\t7994\n\t\t\t\t\t8000 .\n\t\t\t'},{id:"B65",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHe\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAtwater\n\t\t\t\t\t\t\tH. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1997 “Interband Transitions in SnxGe\n\t\t\t\t\t1-x Alloys,” Physical Review Letters 79\n\t\t\t\t\t1937\n\t\t\t\t\t1940 .\n\t\t\t'},{id:"B66",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMenéndez\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKouvetakis\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004 “Type-I Ge/Ge1-x-ySixSny strained-layer heterostructures with a direct Ge bandgap,” Applied Physics Letters\n\t\t\t\t\t85\n\t\t\t\t\t1175\n\t\t\t\t\t1177 .\n\t\t\t'},{id:"B67",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBauer\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRitter\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCrozier\n\t\t\t\t\t\t\tP. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRen\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMenéndez\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWolf\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKouvetakis\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2003 “Synthesis of ternary SiGeSn semiconductors on Si(100) via SnxGe1-x buffer layers,” Applied Physics Letters\n\t\t\t\t\t83\n\t\t\t\t\t2163\n\t\t\t\t\t2165 .\n\t\t\t'},{id:"B68",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRoucka\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTolle\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCook\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tChizmeshya\n\t\t\t\t\t\t\tA. V. G.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKouvetakis\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tD’Costa\n\t\t\t\t\t\t\tV.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMenendez\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZhihao\n\t\t\t\t\t\t\tD. Chen\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZollner\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2005 “Versatile buffer layer architectures based on Ge1\n\t\t\t\t\t -xSnx alloys,” Applied Physics Letters 86, 191912.\n\t\t\t'},{id:"B69",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAella\n\t\t\t\t\t\t\tP.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCook\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTolle\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZollner\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tChizmeshya\n\t\t\t\t\t\t\tA. V. G.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKouvetakis\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004 “Optical and structural properties of SixSnyGe1-x-y alloys,” Applied Physics Letters\n\t\t\t\t\t84\n\t\t\t\t\t888\n\t\t\t\t\t890 .\n\t\t\t'},{id:"B70",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWistey\n\t\t\t\t\t\t\tM. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFang\n\t\t\t\t\t\t\tY. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTolle\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tChizmeshya\n\t\t\t\t\t\t\tA. V. G.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKouvetakis\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2007 “Chemical routes to Ge/Si(100) structures for low temperature Si-based semiconductor applications,” Applied Physics Letters 90, 082108.\n\t\t\t'},{id:"B71",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCheng\n\t\t\t\t\t\t\tH. H.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMenéndez\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKhurgin\n\t\t\t\t\t\t\tJ. B.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSoref\n\t\t\t\t\t\t\tR. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2007 “Strain-free Ge/GeSiSn quantum cascade lasers based on L-valley intersubband transitions,” Applied Physics Letters 90, 251105.\n\t\t\t'},{id:"B72",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJaros\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1988 “Simple analytic model for heterojunction band offsets,” Physical Review B\n\t\t\t\t\t37\n\t\t\t\t\t7112\n\t\t\t\t\t7114 .\n\t\t\t'},{id:"B73",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tVan de Walle\n\t\t\t\t\t\t\tC. G.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1989 “Band lineups and deformation potentials in the model-solid theory,” Physical Review B 39\n\t\t\t\t\t1871\n\t\t\t\t\t1883 .\n\t\t\t'},{id:"B74",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tD’Costa\n\t\t\t\t\t\t\tV. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCook\n\t\t\t\t\t\t\tC. S.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBirdwell\n\t\t\t\t\t\t\tA. G.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLittler\n\t\t\t\t\t\t\tC. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCanonico\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZollner\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKouvetakis\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMenéndez\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2006 “Optical critical points of thin-film Ge1\n\t\t\t\t\t -ySny alloys: A comparative Ge1-ySny/Ge1-xSix study,” Physical Review B 73, 125207.\n\t\t\t'},{id:"B75",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tD’Costa\n\t\t\t\t\t\t\tV. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCook\n\t\t\t\t\t\t\tC. S.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMenéndez\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTolle\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKouvetakis\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZollner\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2006 “Transferability of optical bowing parameters between binary and ternary group-IV alloys,” Solid State Communications\n\t\t\t\t\t138\n\t\t\t\t\t309\n\t\t\t\t\t313 .\n\t\t\t'},{id:"B76",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWeber\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAlonso\n\t\t\t\t\t\t\tM. I.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1989 “Near-band-gap photoluminescence of Si-Ge alloys,” Physical Review B 40\n\t\t\t\t\t5683\n\t\t\t\t\t5693 .\n\t\t\t'},{id:"B77",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCohen\n\t\t\t\t\t\t\tM. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBergstresser\n\t\t\t\t\t\t\tT. K.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1966 “Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures,” Physical Review 141\n\t\t\t\t\t789\n\t\t\t\t\t796 .\n\t\t\t'},{id:"B78",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRidley\n\t\t\t\t\t\t\tB. K.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1997\n\t\t\t\t\tElectrons and Phonons in semiconductor Multiplayers (Cambridge University Press, Cambridge, 1997), Chapter 1.\n\t\t\t'},{id:"B79",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWilliams\n\t\t\t\t\t\t\tB. S.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKumar\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCallebaut\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHu\n\t\t\t\t\t\t\tQ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tReno\n\t\t\t\t\t\t\tJ. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2003 ” Terahertz quantum cascade laser at 𝜆~100µm using metal waveguide for mode confinement,” Applied Physics Letters\n\t\t\t\t\t83\n\t\t\t\t\t2124\n\t\t\t\t\t2126 .\n\t\t\t'},{id:"B80",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tUnterrainer\n\t\t\t\t\t\t\tK.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tColombelli\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGmachl\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCapasso\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHwang\n\t\t\t\t\t\t\tH. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSergent\n\t\t\t\t\t\t\tA. M.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSivco\n\t\t\t\t\t\t\tD. L.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCho\n\t\t\t\t\t\t\tA. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2002 “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Applied Physics Letters\n\t\t\t\t\t80\n\t\t\t\t\t3060\n\t\t\t\t\t3062 .\n\t\t\t'},{id:"B81",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJohnson\n\t\t\t\t\t\t\tP. B.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tChristy\n\t\t\t\t\t\t\tR. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1972 “Optical Constants of the Noble Metals,” Physical Review B 6\n\t\t\t\t\t4370\n\t\t\t\t\t4379 .\n\t\t\t'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Greg Sun",address:"",affiliation:'
University of Massachusetts Boston, Massachusetts, U.S.A.
'}],corrections:null},book:{id:"3648",title:"Advances in Lasers and Electro Optics",subtitle:null,fullTitle:"Advances in Lasers and Electro Optics",slug:"advances-in-lasers-and-electro-optics",publishedDate:"April 1st 2010",bookSignature:"Nelson Costa and Adolfo Cartaxo",coverURL:"https://cdn.intechopen.com/books/images_new/3648.jpg",licenceType:"CC BY-NC-SA 3.0",editedByType:"Edited by",editors:[{id:"4669",title:"Mr.",name:"Nelson",middleName:null,surname:"Costa",slug:"nelson-costa",fullName:"Nelson Costa"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},chapters:[{id:"9878",title:"Optical, Photoluminescent, and Photoconductive Properties of Novel High-Performance Organic Semiconductors",slug:"optical-photoluminescent-and-photoconductive-properties-of-novel-high-performance-organic-semiconduc",totalDownloads:3490,totalCrossrefCites:0,signatures:"Oksana Ostroverkhova, Andrew D. Platt and Whitney E. B. Shepherd",authors:[null]},{id:"9858",title:"Nonlinear Optical Absorption of Organic Molecules for Applications in Optical Devices",slug:"nonlinear-optical-absorption-of-organic-molecules-for-applications-in-optical-devices",totalDownloads:3990,totalCrossrefCites:0,signatures:"Leonardo De Boni, Daniel S. Correa and Cleber R. Mendonca",authors:[null]},{id:"9870",title:"Optical and Spectroscopic Properties of Polymer Layers Doped with Rare Earth Ions",slug:"optical-and-spectroscopic-properties-of-polymer-layers-doped-with-rare-earth-ions",totalDownloads:2575,totalCrossrefCites:3,signatures:"Vaclav Prajzler, Oleksiy Lyutakov, Ivan Huttel, Jiri Oswald and Vitezslav Jerabek",authors:[null]},{id:"9865",title:"Pure χ(3) Third-Harmonic Generation in Noncentrosymmetric Media",slug:"pure-3-third-harmonic-generation-in-noncentrosymmetric-media",totalDownloads:2736,totalCrossrefCites:0,signatures:"Kentaro Miyata",authors:[null]},{id:"9862",title:"Semiconductor Ridge Microcavities Generating Counterpropagating Entangled Photons",slug:"semiconductor-ridge-microcavities-generating-counterpropagating-entangled-photons",totalDownloads:1533,totalCrossrefCites:0,signatures:"Xavier Caillet, Adeline Orieux, Ivan Favero, Giuseppe Leo and Sara Ducci",authors:[null]},{id:"9882",title:"Two-Wave Mixing in Broad-Area Semiconductor Amplifier",slug:"two-wave-mixing-in-broad-area-semiconductor-amplifier",totalDownloads:1882,totalCrossrefCites:0,signatures:"Mingjun Chi, Jean-Pierre Huignard and Paul Michael Petersen",authors:[null]},{id:"9879",title:"Frequency Conversion Based on Three-Wave Parametric Solitons",slug:"frequency-conversion-based-on-three-wave-parametric-solitons",totalDownloads:1609,totalCrossrefCites:0,signatures:"Fabio Baronio, Matteo Conforti, Costantino De Angelis, Antonio Degasperis, Sara Lombardo and Stefan Wabnitz",authors:[null]},{id:"9887",title:"Analogue of the Event Horizon in Fibers",slug:"analogue-of-the-event-horizon-in-fibers",totalDownloads:2315,totalCrossrefCites:0,signatures:"Friedrich Konig, Thomas G. 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1. Introduction
Water is an important resource that supports life on earth. Its availability plays key roles for attaining socio-economic developments globally [1]. It is also a priority toward meeting the United Nations Sustainable Development Goal (SDG) 6 that seeks to ensure access to water and sanitation for all [2]. This requires an adequate enabling environment and strong systems at country level. The United Nations General Assembly has called for country-led, coordinated efforts to provide financial resources and build capacity and technology transfer to help countries yield stronger and sustainable services [3]. Water is thus an essential resource for balancing the well-being of humans and healthy ecosystems.
The survival of humans and continuing social-economic developments depend on the supply of appropriate water quality and quantity. The relationship between humans and ecosystems is core as people strive to improve their well-being. Ecosystem services are beneficial to all living creatures including humans in a number of ways [4]. Water, for instance, contributes to ecological functions through the provisioning of habitat for aquatic life, including fish that is food for humans.
Water also provides ecosystem services that include freshwater supply, regulatory functions such as dilution and water purification, and fulfilling cultural necessities (e.g., water for traditional, esthetic, or medicinal and spiritual purposes). The benefits derived from ecosystem services are available to humans, regardless of where they live or where the services are generated. For example, urban dwellers enjoy river ecosystem service benefits including fishing for food or growing trees along the river banks, which can be used as timber to build houses or as firewood for cooking.
Ensuring sustainable management of aquatic ecosystems for improved food security is therefore important [5]. This is especially true in urban areas where human activities may pollute distant ecosystems through effluent discharges caused by industrial and domestic or mining activities [6]. Human activities can pollute water bodies and impact socio-economic developments negatively. Any changes in water quality can affect short- or long-term food security goals if aquatic resources are not properly managed.
This chapter discusses the effects of water quality and scarcity with respect to food security on the African continent. A comprehensive synthetic evaluation of various published and technical reports was conducted in order to draw the relationship between the potential of water and food security in the African region. The use, distribution, and requirement for food systems that promote water conservation to create sustainable food production are explored. Lastly, issues concerning water pollution and food safety are discussed to identify knowledge gaps that impede food security in Africa toward the attainment of the United Nations Sustainable Development Goals.
2. Water and human survival
This section seeks to highlight the basic human need for water and track the global water distribution and its importance in food security. Water is a basic unit of life and an essential nutrient that is required in amounts that exceed the body’s ability to produce it [7]. Like all nutrients, water performs different functions in the body [8]. Water is an essential component of cells, tissues, and organs required for digestion, absorption, and dissolution and as a carrier for nutrients, eliminating waste products; temperature regulation; and as a lubricant and shock absorber [9, 10, 11].
To achieve all these functions, total body water must be approximately 60% of body weight in males and 50% of body weight in females [12]. The water distribution is up to 60% intracellular (this amount is lower in females due to larger amounts of subcutaneous tissue and smaller muscle mass) and 20% in extracellular space [13]. The extracellular fluid compartment comprises fluid in blood, interstitial fluid, bone, connective tissue, and transcellular fluid. Variation in water intake depends on human health, weight, and human physical performance.
Human survival can be achieved with minimum water requirement where water lost through normal activities gets replenished [14]. The average adult body naturally loses almost 2–3 L of water daily which must be replenished to function on a day-to-day basis. This loss occurs mainly via urine, perspiration, feces, and exhaled air.
The amount of body water that gets lost depends on individual and environmental factors. These factors are affected by the climate a person lives in, his or her age, physical activity level, and kidney function [8]. To regulate the body’s water levels, the water input must balance water output through metabolic processes (0.3 L/day), fluid intake triggered by thirst (1.5 L/day), and solid foods triggered by appetite (approximates 0.7 L/day). Too little or too much water in the body can lead to less-than-optimal body function.
Early stages of decreased water intake in the form of dehydration can lead to difficulty in concentrating, headache, and sleepiness. Decreased water intake has also been associated with bladder and lower urinary tract cancer and increased risk of colorectal cancer as well as kidney stone formation [15]. Taking too much water can also put an unnecessary burden on the cardiovascular system and the kidneys and can cause a drop in the concentration of electrolytes in cells causing harm in the long run.
While water may be a renewable resource, it is unfortunate that there is only a finite amount and there are no substitutes. Without clean and safe water, human survival cannot be achieved. This has a great impact on the global burden of disease, health, education, and economic productivity of populations.
2.1 Water challenges affecting human survival
Water is an important component in a number of human functions, hygiene, and the overall maintenance of health. At the most basic level, water service must meet consumption and hygiene needs and sustain good health at household level [16]. Millions of the world’s poorest people, however, die each year from preventable diseases due to poor hygiene, lack of clean drinking water, and lack of proper sanitation facilities [17].
The reality is that water and sanitation are weakly integrated into countries’ poverty reduction strategies. Many national governments are failing to put in place the policies and finances needed to accelerate progress toward achieving clean water and adequate sanitation.
In many rural communities, lakes, dams, and stream that are the main sources of water run dry for long periods, forcing people to use unsafe water sources [18]. For the 2.1 billion people who lack access to clean water, they can only afford to get a measly 5 L a day and fail to meet the recommended basic minimum of 20 L a day required for human health, economic, and social development [19]. This is a far cry from the 200 L a day per person that people from rich countries consume on average in a day.
A report on global distribution of the global drinking water services in 2015 found that 71% of the global population (5.2 billion people) had access to a safely managed drinking water service [19]. The report further found that sub-Saharan Africa was the region with the lowest number of people with access to safe drinking water located on their premises. Only Australia and New Zealand had 100% access, where all of the population had basic services (including basic drinking water, sanitation, and hygiene) in their households.
The same report estimated that two-third of the total global population was living in water-stressed areas that experience water scarcity for at least 1 month in a year in 2015 [2]. Of the two-third, 844 million people lacked basic drinking water service and 263 million people were reported to be spending over 30 minutes per round trip to collect water from an improved water source [19].
Still, 159 million people were reported to collect drinking water directly from surface water sources and over half of these people were living in sub-Saharan Africa. These people share their domestic water sources with animals. A large fraction of the people that live in extremely vulnerable situations of water scarcity all year-round are found in Libya, Somalia, Pakistan, Morocco, Niger, and Jordan where 50–90% of the country’s population lives under those circumstances [20].
3. Global distribution of water
An estimated three fifth of the earth’s surface is covered by water, which makes up a total volume of almost 35 million km3 [2]. Of the available amount, only 200,000 km3 (1%) of this is fresh water that is usable by humans. This is the water that is expected to fulfill the demands of the increasing global population, meet the food production needs using the limited amount of arable land, and sustain industrialization.
Historically, people looked for location to set up their livelihoods near water supplies such as river bases that could provide drinking water and carry off waste. Over time, areas close to water sources became populated by industries and agricultural holdings which use water for irrigation and also to power industries [21].
Distribution of piped water is realized as a sign of progress toward achieving the SDGs. Industrialized countries (20%) have managed to achieve piped water coverage in 85% of their entire household. The poor countries, however, have only managed limited piped water coverage with only 25% of all their households having access [19]. Industrialized countries have been better able to achieve water security compared to poor countries and this is evident from the average water usage data of 200 L per person per day in rich countries compared to the 5 L per person per day in poor countries [18].
Factors that contribute to high water scarcity levels include areas with a high population density, areas with irrigated agriculture, and areas with very low natural water availability [20]. Geographically, water scarcity can be found in in the world’s arid areas with low water availability like the Sahara, Taklamakan, Gobi, and central Australian deserts.
Water scarcity has also been found to be intense in areas with high population density and irrigation intensity. Globally, these areas are found near river basins and include the Ganges basin in India, the Limpopo basin in Southern Africa, and the Murray-Darling basin in Australia [20].
Distribution by sectors shows that water use is spread between domestic, agriculture, and industry sectors. Agriculture accounts for over 70% of freshwater use [16, 22] and industry water use accounts for 20% globally. In spite of this, it is believed that there is enough water in the world for domestic, agriculture, and industry purposes; the only problem is how this water is distributed especially to the poor who are systematically excluded from the distribution.
Water use varies significantly by sector across the world. How do these three sectors use fresh water?
3.1 Agriculture
As discussed above, water use varies considerably across the world especially between the poor and rich. Agriculture is the biggest user of fresh water with Africa and Asia, accounting for the largest users under this sector with an estimated 85–90% of all freshwater [23]. Future demands for water for agriculture are threatened by climate change, technological development, and urbanization. The challenge is to produce more food to meet the growing population demands using less water and other resource inputs in an environmentally friendly manner [24]. Low-income countries’ average agriculture usage is estimated at 90%; 79% for middle income and only 41% in high incomes countries [22].
3.2 Industry
Industrial water use includes all the water used for manufacturing, energy generation, and other industrial activities such as dilution, steam generation, washing, and cooling of manufacturing equipment [25]. Globally, an estimated 20% of total available fresh water is used for industrial purposes. Within the industrial sector, hydropower and nuclear power generation uses 57–69% and the thermal power generation uses 0.5–3% [23]. Industries also pose a threat to fresh water because of the amount of wastewater it produces, its mobility, and loading of industrial pollutants and their potential impacts on water resources, human health, and the environment. High-income countries tend to use the largest portion of water on industries (17%), with low-income countries using the least with an average 2% [26].
3.3 Domestic
Domestic water is the most visible form of water and it shows the problem that exists in the distribution of fresh water between the rich and the poor. People in developed countries consume almost up to 10 times more water daily than those in developing countries. In developed countries, where large cities have centralized water supply and an efficient canal system, domestic consumption averages 200 L per person per day [23].
In developing countries within Asia, Africa, and Latin America regions, consumption in cities and towns is between 50 and 100 L per person per day, and in the water scarce areas within these regions, the amounts can be as low as 5 L per person per day [23]. Countries with the largest population, China followed by India, have the highest water use globally [26].
The change in water distribution will have a serious implication on people’s health and well-being, especially for people living in high population density areas, areas with irrigated agriculture, and areas with very low natural water availability. These are the estimated 1.8–2.9 billion people who experience severe water scarcity for at least 4–6 months per year and the 500 million people face severe water scarcity all year round [20].
The distribution of water between sectors is expected to change over the coming years as a result of population growth, increased water scarcity, and drought due to climate change. Water use for irrigation and other water using sectors of the economy are expected to experience extreme competition which will place more burden on food security.
4. Water in food security
Water forms an essential part in national food security. To attain food security, there must be an acceptable quantity and quality of water for health, livelihoods, ecosystems, and production [27, 28]. Any sustainable attainment of food safety and security for a fast-growing population requires thoughtful decisions to develop and manage water resources.
Food security and safety are key development agenda items in most developing regions (Global Panel on Agriculture and Food Systems for Nutrition, 2016). Global research and funding have been prioritized and channeled toward fighting against food insecurity. Although substantial progress globally is evident [29], the same cannot be said for some of the African regions. Sub-Saharan Africa continues to have less access to sufficient quantity and quality food for proper health and growth. The report also classified the sub-Saharan countries as food insecure, with limited access to safe food within their population.
Despite the global food security achievements realized in recent years, food security and limited access to food safety still remain as challenges in Africa. Water scarcity and irregular rainfall distribution are proving to be an impediment to Africa’s efforts to ensure food security. Agriculture production systems, which are the backbone of food security, are also adjusting to tightening water availability by reducing freshwater use especially in the African region. This has resulted in the emergence of new diets that are sensitive to the significant influences of water and land use [30].
As the water challenge for agricultural production in Africa increases, it is expected that the share of irrigated agriculture in global water use could rise by over 30% by 2030 [30]. Total global water demand could double by 2050. The increased competition for scarce water and land resources increases concerns about where the additional food will come from. The challenges are further exacerbated by climatic changes that cause irregularities in water availability across the African landscape [31].
Water requirements in agriculture vary significantly not only in terms of quantity, but also in terms of quality and timing depending on food type. This is very significant especially when it comes to staple foods such as maize, rice, and wheat that are critical in food security of many countries in Africa. Some of these countries have increased awareness toward conserving their national water supply by opting for virtual water trade—importing food from outside the country in the effort to conserve water resources and maintain food security [32]. Other countries have shifted food production within the agriculture sector focusing more on planting water-efficient crops.
Apart from water being important in production, it also plays a huge role in food processing, transformation, and preparation adding to the competition against industrial and domestic water use [33]. Even though food processing uses much less water than primary production, this part of the food system requires water that is of high-quality standards and that does not pose any health and safety risks on both human and ecosystem health.
There is also a drive toward introducing water-use efficiency, reducing pollution impacts from processing industries [34]. Poor quality water used in food processing can lead to food-borne disease such as diarrhea and other diseases that contribute to malnutrition. The unsafe food creates a vicious circle of diseases affecting particularly the more vulnerable populations that include children, the elderly, and the sick [33].
Priority must be given to encouraging greater efficiency of water use and the development of integrated water management plans [30]. The shortage of food production due to water scarcity calls the need to manage every water drop to attain food security and food safety in Africa. This raises awareness that water for agricultural production is a pressing issue.
It has been noted that agricultural developments require a consistent and sustainable provision of large quantities of good quality water for food security [35]. The present situation is a clear sign that previous potential solutions to solving Africa’s food insecurity have not received the most needed attention when defining development goals on the continent. Societies depend on water availability to meet a wide range of needs including water for irrigation, domestic, and industrial use.
Poverty and water are inextricably intertwined. Food security cannot be achieved without tackling water issues since lack of safe water underpins food insecurity. Countries continue to invest in the protection and management of water resources to continue deriving benefits for improved living standards. Undoubtedly, major water investments in agriculture are necessary toward meeting food production needs [35]. Crucial role players are needed to put together efforts to conserve water for a food secure world.
4.1 Water scarcity impacts on food security
Many Africans depend on aquatic and riparian plants and animals as an important source of food for both humans and livestock. These include fish, shellfish, bait, edible plants, and grazing. In addition, some areas such as wetlands and floodplains across Africa may be used for the cultivation of food crops. In this way, these riparian areas contribute to food security and livelihoods. These services are of particular importance to poor communities [36].
Nonetheless, the provision of reliable sources of water whether for small-scale water for food processing or large-scale water for irrigation is necessary to move beyond subsistence farming toward a more food secure continent [37]. The availability of water allows farmers to continue growing crops of high value such as vegetables, which are highly sensitive to water stress periods [38].
Although quality of water is crucial for peoples’ nutrition and water availability for food security in developing countries [39], water investments have been rapidly declining. While irrigation has a high potential for environmental damages or disturbances, it has contributed positively to poverty eradication [39]. Irrigated agriculture has benefited both rural and urban poor by lowering food prices [39]. The availability of water for irrigation means less people fall below the poverty line, and that poor communities, women in particular, also benefit greatly from irrigation as a major source of water for most of their domestic uses, fishing, small and/or informal businesses [39].
Nonetheless, small-scale water availability can impact on food security positively. The availability of water for small-scale harvesting has a huge effect on incomes and food security in developing and poorest communities. Major water investments will have more drastic and positive impacts on the poorest communities, where the majority of people live on less than US$1 on a daily basis [39].
Existing challenges between water availability, quality, and sustainable agriculture linkages must be explored and be made explicit in planning potential agriculture-based strategies for improving food security. The need for fresh clean water is, however, threatened by the changing quantity and quality of the freshwater resources on which people depend for survival. The need for clean water is also linked to adequate sanitation and improved health [14]. Proper sanitation helps to protect water sources from bacterial, viral, and protozoal agents that cause water-related diseases. The concern for many is how can water quality be attained?
5. Water quality management
As much as water is an essential component of life, it is a hotbed for carriers of many diseases caused by consuming unclean water. Access to safe drinking-water, sanitation, and hygiene (WASH) services is an important element of food security and has a positive impact on nutrition [40]. A number of approaches are used to assess water pollution effects on the ecosystems which have a direct contribution to food security and nutrition.
A common approach is to use chemical indicators to measure the concentration of chemicals or toxicants within a water body using either water samples or direct in-stream measurement of the water source using water samples as (chemical indicators). If the chemicals within the water are in exceedance with acceptable limits, that water system is regarded as polluted and not fit for human consumption. Biomonitoring can also be used to assess water quality by examining the presence or absence of certain species or organisms in a water body [41].
Another approach that is used to assess water pollution is ecotoxicology. An investigation is conducted to examine responses of insects, fish, and other invertebrates to a chemical or stressor as biological indicators of water quality [42]. Thus, polluted aquatic systems may not adequately support the provision of fish and insects as food for humans. Similarly, necessary microbes that support plant growth in soils may not thrive in polluted environments, thereby affecting food security.
Without good quality water, the lives of millions of people especially young children are at risk of dying from preventable diseases caused by poor water, and a lack of sanitation and hygiene. There is a growing interest to better understand and measure the effect of programs and approaches not only directed toward improving water management in agriculture and food production but also to include integrated approach to implementing safe water and adequate sanitation [40]. Approaches and practices for ongoing efforts to better link WASH and nutrition programs integrating WASH into food security and nutrition programs are discussed in the following section.
5.1 Water, sanitation, and hygiene (WASH) programs and food security
The World Health Organization [43] report defines drinking water as water with acceptable quality in terms of its chemical, bacteriological, and physical parameters for safe human consumption. Estimates indicate that about 80% of all sicknesses and diseases on a global scale are linked to consumption of unclean and unsafe water and poor sanitation.
However, the quality of any water is influenced by both natural and human factors [44]. Without human influences, water quality would be determined by natural factors and/or processes such as bedrock minerals, deposition of dust, natural leaching of soil minerals and organic matter, and biological processes, among others. Water quality is determined by using water quality guidelines or standards to make a comparison between the physical and chemical characteristics of water samples. The guidelines and standards are developed to ensure the safe consumption of water and protection of ecosystems.
Africa with its soaring human population continues to experience a decline in water quality [43, 44]. Adequate water, sanitation, and hygiene are essential components for reducing poverty, illness, and death and bring about an improved socio-economic development. Poor WASH programs expose people to water-borne diseases, resulting in death and disabilities in certain cases [44]. The United Nations International Children’s Emergency Fund (UNICEF) report revealed that the absence of toilets results in the contamination of water resources, while a lack of clean water impedes on basic hygiene [45]. However, increasing WASH programs have led to increased access to adequate drinking water sources and improved sanitation globally since 1990 [43].
To explore how WASH programs could improve the water and sanitation conditions for poor and developing countries across Africa, it is important to define hygiene and sanitation. Peal et al. [46] defined “sanitation” as the treatment and management of human excreta from coming into contact with humans, while “hygiene” is a required action to avoid the transmission of diseases within and between different communities. WASH programs are vital for helping people avoid contaminating water sources, which in turn improves their access and the overall food safety and security.
WASH programs also help to improve water quality for adequate food production due to their design nature, whereby communities work together to disseminate WASH information for a more collaborative program and implementation [46]. Here, practitioners work together with communities and local authorities to deliver the components of the WASH program on-site. This is complemented by practitioners revisiting the communities or distributing surveys for monitoring and evaluation purpose. Therefore, WASH program approaches have the potential to improve food security within the poor and developing African countries.
6. Effects of water pollution on food security
Water pollution is the building up of one or more substances in water to an extent that they cause water-related problems for people and animals [47]. It is a complex problem that is underpinned by many causes, which makes it difficult to solve. Increasing human population continues to exert immense pressure on the world’s water resources [29]. Both urbanization and industrial revolutions have exacerbated water pollution through effluent and untreated wastewater discharges.
Irrigated agriculture has resulted in increased salinity of freshwater bodies as salts are flushed out from soils [48]. When farmers fertilize their fields or control insects using herbicides, the chemicals used get washed away as salts through surface run-off into nearby water systems. Toxic chemicals released into the atmosphere by industries can also enter into water systems as acid rain [49].
An increase in water salinity negatively impacts on the survival of aquatic macroinvertebrates, while some crops become intolerant to high soil salinities if thresholds are exceeded [50]. As a consequence, soil productivity is affected and can lead to low crop production and food insecurity. It is therefore clear that low crop production is not only an issue in semi-arid regions but also areas that receive plenteous rainfall.
Thompson and Darwish [49] argued that the poor quality of water has a direct impact on food security, with metals detected in some edible food in China, posing a high health-related risk to consumers. If pollution effects are properly monitored using the approaches outlined above, Africa can produce quality food for its citizens. However, the UNICEF [45] report outlines the importance of educating people on water quality issues as another approach to solving water pollution.
Further, strict environmental laws are necessary to minimize water pollution. For example, environmental reports indicate that the “polluter pays” principle is effective in tackling pollution [49]. The polluter principle makes it less expensive for humans to behave in an environmental cautious and/or responsible manner. It is sad, to note, however, that some countries considered to have the best water laws in Africa and beyond, such as South Africa [51], are still struggling to deal with historical water quality issues that subsequently impact on their food security. Further, unstable countries due to political reasons such as Libya would greatly be affected by food insecurities considering their dry nature. The water quality of both countries is discussed in the following sections.
6.1 South Africa: a country with poor water quality
South Africa has sufficient water to meet all the needs of the country until the year 2025 and beyond [37]. However, the country is faced with challenges related to water quality, which impedes on food production to meet people’s demand for food. Poor water quality renders water unusable. Changes in agricultural practices and the expansion of urban settlements have a serious effect on the quality of water [37]. Furthermore, acid mine drainage (AMD), pesticides from agricultural practices, unmonitored sewerage systems, domestic water usage like washing clothes on the river and dumping waste in water sources in some areas of the country, and salinization from the weathering of minerals all pollute water [42, 52, 53]. Once water is polluted, it may be difficult and extremely expensive to redress, particularly in the case of underground water, which may affect agricultural production in terms of excessive salts on the soil and usable water for food production. It is thus important to note that good water quality would be suitable for food production to ensure food security.
6.2 Libya: a country in a political crisis
Libya has a rapid growing demand for freshwater availability while the water supply is limited [54]. The issue of severe water deficits as a result of nonending water demands in Libya has become more problematic for the increasing population under low rainfall, which is a result of climate change. Furthermore, the country has been experiencing high rates of pollution and depletion due to water resource unavailability. This has had major impacts on Libya’s economy and social and environmental resistance capacity.
Considering that Libya is one of the driest countries on a global scale with high temperatures, meeting and maintaining acceptable living standards for the future is extremely difficult, especially in relation to food security. Food sufficiency remains uncertain in Libya due to its political instability coupled with poor water quality and soaring human population [54]. The country is likely to experience severe and most devastating situations and high risks of food insecurity and malnutrition with current political instabilities.
7. Water and food safety
This section discusses the relationship between water and food safety. Water is seen as an essential component in the food chain, starting from production, processing, and eventually consumption. In addition, water pollution has historically impacted on food safety, which constitutes an important threat to human health, food, and nutritional security. In most sub-Sahara African countries, food safety problems vary in nature, severity, and extent. These challenges are often exacerbated by the effect of climate change and natural disasters such as floods and hurricanes, whereby food may become contaminated by surface water that has itself been contaminated by sewage and wastewaters. It is well documented that flood waters often pick up large quantities of wastes and pathogenic bacteria from farms, sewer systems, latrines, and septic tanks. Overcrowding of the survivors after disasters may aggravate the situation, particularly if sanitary conditions are poor.
Any breakdown in vital services, such as water supply or electricity, also adversely affects the quality of food. In the absence of electricity, cold storage may be more difficult, if not impossible, and foods may be subject to bacterial growth. This may be obtained at any stage of the food chain, from production to consumption. Lack of safe drinking water and sanitation hampers the hygienic preparation of food and increases the risk of food contamination.
Food safety has become a constant global concern apart from affecting human health; factors such as international trade and food security are also influenced. Consequently, most research institutions, healthcare institutions, and governments of several African countries have conducted comprehensive studies on the effect of water on food safety in various production chains. According to a recent study, the main water issues that affect food safety in low income countries include bacterial pathogens, followed by pesticide residues and healthy diet [40]. Although the reported evidence of food-borne disease is still limited, the known incidences of food borne disease in low income countries such as sub-Saharan African largely emanate from three major sources, namely biological hazards and chemical and physical contamination.
7.1 Biological water contaminants
Water and food contaminated by microorganisms are major contributing factors for the emerging diarrheal diseases in the developing countries, and over 1 billion children under the age of 5 years are affected worldwide [26]. The high prevalence of deaths related to food and water contamination in developing countries could be attributed to several factors. For example, in many African countries, milk and dairy production constitute an important source of livelihoods for most peasant and smallholder farmers. Furthermore, animal production has become part of agricultural diversification strategy for most African countries in an attempt to ensure food security. The intensification of animal production has also generated a considerable impact on the environment considering the fact that milk provides suitable condition for the growth of different kinds of microorganisms, and microbial hazards are the most important concern within the dairy industry.
Biological agents associated with water contamination that have an impact on food safety include enteric pathogens such as bacteria, viruses, and protozoa. A study conducted in North-West Province of South Africa reported that multi-drug resistant Staphylococcus aureus strains were detected in samples of raw, bulk, and pasteurized milk [43]. Other common biological contaminants are Escherichia coli. The E. coli bacteria belong to the intestinal microbiota of humans and animals and are generally not harmful. Certain E. coli strains, however, harbor virulence factors and can cause intestinal and extra-intestinal diseases. For example, Shiga toxin-producing Escherichia coli zoonotic bacteria have globally been associated with various foods of animal origin, especially beef and sheep meat [40].
Apart from animal product contamination, biological contaminants may also occur in crop products. Foodborne outbreaks from fruit and vegetable produce have caused economic loss, food wastage and loss confidence regarding the safety of fresh produce from most African countries. Studies on the safety of fresh produce have identified water as one of the key risk factors that contribute to contamination of the farm produce. Indeed, studies have shown that most foodborne diseases are caused by consumption of fresh, perishable foods sold in informal markets [44].
7.2 Chemical hazards
Generally, mycotoxins, heavy metals, and over-application of fertilizers and pesticides are considered to be the most important chemical factors impacting on food safety in most developing countries including the African region [45]. In nature, thousands of mycotoxins occur but only a few of them present significant food safety challenges.
Mycotoxins are secondary metabolites mainly produced by fungal species from the Aspergillus, Penicillium, and Fusarium genera. They often develop during production, harvest, and storage of grains and nuts in the presence of water [45]. In the food production process, mycotoxins are among the most potent mutagenic and carcinogenic substances known. Ingestion of mycotoxins poses chronic health risks such as hepatotoxicity, genotoxicity, suppression of immunity, estrogenicity, nephrotoxicity, teratogenicity, and carcinogenic effects [44].
The adverse health effects of mycotoxins are compounded by the fact that they are not completely eliminated during food processing operations and can contaminate finished processed food products [55]. The presence of mycotoxins, particularly the aflatoxins, has generated a lot of interest in the food products from African countries. The work by Maxwell (1998) evaluated the presence of aflatoxins in human body fluids and tissues in relation to child health in the tropics. The findings showed that in Ghana, Kenya, Nigeria, and Sierra Leone, 25% of cord blood samples contained aflatoxins, ranging from 7 ng/L to 65 μg/L. The major classes of aflatoxins that were identified in the African countries include B1 and M1. Figure 1 shows the chemical structures of the most prevalent aflatoxins in African countries.
Figure 1.
Chemical structures of aflatoxins prevalent in African countries.
Heavy metals have also contributed negatively to the food safety status in most African countries. As such, human exposure to heavy metals in Africa has become a major health risk and has received the attention of national and international environmentalists [47]. Rapid population growth, increasing urbanization, and the increasing appearance of slums and townships as a consequence of poor planning coupled with increasing industrial activities are some of the major factors that have contributed to the accumulation of heavy metals in food products. Africa has large deposits of mineral resources, and mining activities have increased with poor environmental regulations and compliance. Thus, heavy metals have constituted agents of toxic pollution of water, air, soil, and food products.
An environmental assessment report by the United Nations Environment Programme (UNEP) released in 2011, showed that drinking water, air, and agricultural soil in 10 communities from southeastern Nigeria contained over 900 times permissible levels of hydrocarbon and heavy metals [47]. The report further indicated that heavy metal pollution is a continental public health challenge in the sub-Saharan African region. Another study conducted in the Democratic Republic of Congo showed a 43-fold increase in the urinary concentration of cadmium, cobalt, lead, and uranium in human subjects including children living in mining areas compared to controls [56]. The increase in the levels of the heavy metals was largely attributed to ingestion of contaminated food products and water with toxic chemical compounds. The increasing negative effects on food safety from water and soil pollution have, therefore, potentially put more people at risk of carcinogenic diseases, particularly in food producing areas.
8. Conclusion
Water is the most vital natural resource on the planet that many life forms depend on for survival. This chapter has shown how population growth, competition for water across sectors, and the exposure to infectious agents or toxic chemicals pose a serious threat to water security, food security, and human existence. There is increased pressure on all sectors to minimize water use by considering more efficient use of water and alternative sources of water. This is only possible if the normative criteria of the human right to safe drinking water which are accessibility, availability, and quality are enforced to ensure that all current and foreseeable water demands highlighted under SDG 6 are met. Little promising progress has been achieved, but much work still has to be done to make water sustainability a reality before the SDG target date of 2030. The present status of water potential in Africa suggests that synergies that adopt sharing of expertise, experiences, knowledge, analytical capabilities, and optimizing mechanisms for greater food safety assurance and awareness by looking at both chemical and microbial hazards in foods should be promoted in the continent.
\n',keywords:"agriculture, availability, contaminants, ecosystems, food security, health, pollution, safety, sanitation, scarcity, water quality, water",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/67624.pdf",chapterXML:"https://mts.intechopen.com/source/xml/67624.xml",downloadPdfUrl:"/chapter/pdf-download/67624",previewPdfUrl:"/chapter/pdf-preview/67624",totalDownloads:381,totalViews:0,totalCrossrefCites:0,dateSubmitted:"March 6th 2019",dateReviewed:"May 11th 2019",datePrePublished:"July 15th 2019",datePublished:"January 20th 2021",dateFinished:"June 11th 2019",readingETA:"0",abstract:"Water plays an important role in food security and provides the basis for healthy ecosystems and human well-being. The relationship between water and food production is key to creating resilient and sustainable food systems. This chapter will discuss the effects of water quality and scarcity with respect to food security in Africa. The effects of water availability and its usage in the African landscape and how this has impacted food security will be highlighted. Lastly, issues concerning water pollution and food safety will be tackled to identify knowledge gaps that impede food security in Africa in its efforts toward attaining the United Nations Sustainable Development Goals.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/67624",risUrl:"/chapter/ris/67624",signatures:"Nokuthula Vilakazi, Kumbukani Nyirenda and Emmanuel Vellemu",book:{id:"8063",title:"Food Security in Africa",subtitle:null,fullTitle:"Food Security in Africa",slug:"food-security-in-africa",publishedDate:"January 20th 2021",bookSignature:"Barakat Mahmoud",coverURL:"https://cdn.intechopen.com/books/images_new/8063.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"92016",title:"Dr.",name:"Barakat",middleName:null,surname:"Mahmoud",slug:"barakat-mahmoud",fullName:"Barakat Mahmoud"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"298005",title:"Dr.",name:"Nokuthula",middleName:null,surname:"Vilakazi",fullName:"Nokuthula Vilakazi",slug:"nokuthula-vilakazi",email:"nokuthula.vilakazi@up.ac.za",position:null,institution:null},{id:"298042",title:"Dr.",name:"Kumbukani",middleName:null,surname:"Nyirenda",fullName:"Kumbukani Nyirenda",slug:"kumbukani-nyirenda",email:"knyirenda@medcol.mw",position:null,institution:null},{id:"298043",title:"Dr.",name:"Emmanuel",middleName:null,surname:"Vellemu",fullName:"Emmanuel Vellemu",slug:"emmanuel-vellemu",email:"evellemu@must.ac.mw",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Water and human survival",level:"1"},{id:"sec_2_2",title:"2.1 Water challenges affecting human survival",level:"2"},{id:"sec_4",title:"3. Global distribution of water",level:"1"},{id:"sec_4_2",title:"3.1 Agriculture",level:"2"},{id:"sec_5_2",title:"3.2 Industry",level:"2"},{id:"sec_6_2",title:"3.3 Domestic",level:"2"},{id:"sec_8",title:"4. Water in food security",level:"1"},{id:"sec_8_2",title:"4.1 Water scarcity impacts on food security",level:"2"},{id:"sec_10",title:"5. Water quality management",level:"1"},{id:"sec_10_2",title:"5.1 Water, sanitation, and hygiene (WASH) programs and food security",level:"2"},{id:"sec_12",title:"6. Effects of water pollution on food security",level:"1"},{id:"sec_12_2",title:"6.1 South Africa: a country with poor water quality",level:"2"},{id:"sec_13_2",title:"6.2 Libya: a country in a political crisis",level:"2"},{id:"sec_15",title:"7. Water and food safety",level:"1"},{id:"sec_15_2",title:"7.1 Biological water contaminants",level:"2"},{id:"sec_16_2",title:"7.2 Chemical hazards",level:"2"},{id:"sec_18",title:"8. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Global Water Partnership (GWP). Global Water Partnership Strategy 2009-2013. Stockholm, Sweden; 2009'},{id:"B2",body:'UN Water. Integrated Monitoring Guide for SDG 6: Targets and Global Indicators. 2017. pp. 1-26'},{id:"B3",body:'United Nations. Consultation Background Document 1 Global Health and Foreign Policy: Strategic Opportunities and Challenges; 2009'},{id:"B4",body:'Millennium Ecosystems Assessment (MEA). Ecosystems and Human Well-Being: Current State and Trends: Dryland Systems; 2005'},{id:"B5",body:'Millennium Ecosystem Assessment (MEA). Fresh Water; Washington, DC; 2005'},{id:"B6",body:'Douglas I. Reference Module in Earth Systems and Environmental Sciences; Elsevier; 2015'},{id:"B7",body:'NHMRC. Water, Australia; 2006'},{id:"B8",body:'Zimmerman M, Snow B. An Introduction to Nutrition. Vol. 1.0; 2012'},{id:"B9",body:'Jéquier E, Constant F. Water as an essential nutrient: The physiological basis of hydration. European Journal of Clinical Nutrition. 2010;64(2):115-123'},{id:"B10",body:'Kleiner SM. Water. Journal of the American Dietetic Association. 1999;99(2):200-206'},{id:"B11",body:'Lang F, Waldegger S. Regulating Cell Volume [Online]. 1997. Available from: https://studylib.net/doc/7645794/regulating-cell-volume [Accessed: May 5, 2019]'},{id:"B12",body:'Mudambi S. Fundamentals of Foods, Nutrition and Diet Therapy. 5th ed. New Age International Pty Ltd Publishers; 2007. p. 128-135'},{id:"B13",body:'McNeil VH, Cox ME. Defining the climatic signal in stream salinity trends using the Interdecadal Pacific Oscillation and its rate of change. Hydrology and Earth System Sciences. 2007;11(4):1295-1307'},{id:"B14",body:'Gleick PH. Basic water requirements for human activities: Meeting basic needs. Water International. 1996;21(2):83-92'},{id:"B15",body:'Portis AJ, Sundaram CP. Diagnosis and initial management of kidney stones. American Family Physician. 2001;63(7):1329-1338'},{id:"B16",body:'Howard G, Bartram J. Sanitation and Health Programme; 2003'},{id:"B17",body:'Suting BM. Assessing the knowledge regarding environmental sanitation and its impact on health among the people in a selected rural community of Meghalaya. The Nursing Journal of India. 2016;107(4):153-155'},{id:"B18",body:'Muller M, Schreiner B, Smith L, Van Koppen B, Sally H, Aliber M, et al. Water Security in South Africa. Development Planning Division. Working Paper Series. No. 12; 2009'},{id:"B19",body:'UNICEF. Progress on Drinking Water, Sanitation and Hygiene Update and SDG Baselines 2017 Launch version July 12 Main Report; 2017'},{id:"B20",body:'Mekonnen MM, Hoekstra AY. Four billion people facing severe water scarcity. Science Advances. 2016;2(2):e1500323'},{id:"B21",body:'OECD. Agriculture Policy Notes; OECD [Online]. Available from: http://www.oecd.org/tad/agriculture-policy-notes.htm [Accessed: May 5, 2019]'},{id:"B22",body:'Gleick PH. The World’s Water. Volume 8: The Biennial Report On Freshwater Resources. 2014;8'},{id:"B23",body:'Shiklomanov IA. World Water Resources a New Appraisal and Assessment for the 21st Century a Summary of the Monograph World Water Resources Prepared in the Framework of The International Hydrological Programme. 1991;25'},{id:"B24",body:'Cosgrove WJ, Loucks DP. Water management: Current and future challenges and research directions. Water Resources Research. 2015;51:4823-4839'},{id:"B25",body:'Strzepek K, Boehlert B. Competition for water for the food system. Philosophical Transactions of the Royal Society B. 2010;365(1554):2927-2940'},{id:"B26",body:'Ritchie H, Roser M. Water Use and Sanitation, Our World Data; 2017'},{id:"B27",body:'Grey D, Sadoff CW. Sink or Swim? Water Security for Growth and Development'},{id:"B28",body:'Lal R. World water resources and achieving water security. Agronomy Journal. 2015;107(4):1526'},{id:"B29",body:'Mabhaudhi T, Chibarabada T, Modi A, Mabhaudhi T, Chibarabada T, Modi A. Water-food-nutrition-health nexus: Linking water to improving food, nutrition and health in Sub-Saharan Africa. International Journal of Environmental Research and Public Health. 2016;13(1):107'},{id:"B30",body:'Senker P. Foresight: The future of food and farming, final project report. Prometheus. 2011;29(3):309-313'},{id:"B31",body:'Davies WJ, Zhang J, Yang J, Dodd IC. Novel crop science to improve yield and resource use efficiency in water-limited agriculture. The Journal of Agricultural Science. 2011;149(S1):123-131'},{id:"B32",body:'Earle A. The Role of Virtual Water in Food Security in Southern Africa; 2001'},{id:"B33",body:'H. Level Panel of Experts on Food Security. The High Level Panel of Experts on Food Security and Nutrition Nutrition and Food Systems; 2017'},{id:"B34",body:'Newborne P, Mason N. The private Sector’s contribution to water management: Re-examining corporate Purposes and company roles. Water Alternatives. 2012;5(30):603-618'},{id:"B35",body:'Elhassadi A. Pollution of water resources from industrial effluents: a case study—Benghazi, Libya. Desalination. 2008;222(1-3):286-293'},{id:"B36",body:'Department of Water Affairs (DWA). Resource Directed Management of Water Quality: Planning Level Review of Water Quality in South Africa, Sub-seriesWQP No. 2.0; Pretoria, South Africa; 2011'},{id:"B37",body:'McLachlan M, Thorne J, Battersby-Lennard J, Drimie S, Fincham R, Frayne B, et al. Seeding change: A proposal for renewal in the South African food system. Development Planning Division. Working Paper Series No. 16. 2009'},{id:"B38",body:'Molden DJ, Fraiture C. Investing in Water for Food, Ecosystems and Livelihoods. Sri Lanka; 2004'},{id:"B39",body:'Rijsberman FR. Water scarcity: Fact or fiction? Agricultural Water Management. 2006;80(1-3):5-22'},{id:"B40",body:'Uyttendaele M, Franz E, Schlüter O. Food safety, a global challenge. International Journal of Environmental Research and Public Health. 2015;13(1):1-6'},{id:"B41",body:'Odume ON. An Evaluation of Macroinvertebrate-Based Biomonitoring and Ecotoxicological Assessments of Deteriorating Environmental Water Quality in the Swartkops River, South Africa. Rhodes University; 2014'},{id:"B42",body:'Mensah PK. Environmental Water Quality Management of Glyphosate-Based Herbicides in South Africa. Rhodes University; 2012'},{id:"B43",body:'Akindolire M, Babalola O, Ateba C. Detection of antibiotic resistant Staphylococcus aureus from milk: A public health implication. International Journal of Environmental Research and Public Health. 2015;12(9):10254-10275'},{id:"B44",body:'Marin S, Ramos AJ, Cano-Sancho G, Sanchis V. Mycotoxins: Occurrence, toxicology, and exposure assessment. Food and Chemical Toxicology. 2013;60:218-237'},{id:"B45",body:'Smith M-C, Madec S, Coton E, Hymery N. Natural co-occurrence of mycotoxins in foods and feeds and their in vitro combined toxicological effects. Toxins. 2016;8(4):94'},{id:"B46",body:'Peal A, Evans B, van der Voorden C. Hygiene and Sanitation Software: An Overview of Approaches. Geneva; 2010'},{id:"B47",body:'United Nations Environment Programme (UNEP). Global Drylands: A UN System-Wide Response; 2011'},{id:"B48",body:'Eerkes-Medrano D, Thompson RC, Aldridge DC. Microplastics in freshwater systems: A review of the emerging threats, identification of knowledge gaps and prioritisation of research needs. Water Research. 2015;75:63-82'},{id:"B49",body:'Thompson LA, Darwish WS. Environmental chemical contaminants in food: Review of a global problem. Journal of Toxicology. 2019;2019:1-14'},{id:"B50",body:'Vellemu EC, Mensah PK, Griffin N, Odume ON. Derivation of scenario-specific water quality guidelines for acid mine drainage in South Africa, using a risk-based approach. African Journal of Aquatic Science. 2018;43(1):51-58'},{id:"B51",body:'Griffin NJ, Palmer CG. Draft Report on the Status and Trends of Selected Water Quality Parameters in the Olifants River. Grahamstown; 2015'},{id:"B52",body:'McCarthy TS. The impact of acid mine drainage in South Africa. South African Journal of Science. 2011;107(5-6):01-07'},{id:"B53",body:'Vellemu EC, Mensah PK, Griffin NJ, Odume ON. Sensitivity of the mayfly Adenophlebia auriculata (Ephemeroptera: Leptophlebiidae) to MgSO4 and Na2SO4. Physics and Chemistry of the Earth, Parts A/B/C. 2017;100:81-85'},{id:"B54",body:'Wheida E, Verhoeven R. An alternative solution of the water shortage problem in Libya. Water Resources Management. 2007;21(6):961-982'},{id:"B55",body:'Bullerman LB, Bianchini A. Stability of mycotoxins during food processing. International Journal of Food Microbiology. 2007;119(1-2):140-146'},{id:"B56",body:'Fasinu P, Orisakwe OE. Heavy metal pollution in sub-Saharan Africa and possible implications in cancer epidemiology. Asian Pacific Journal of Cancer Prevention. 2013;14(6):3393-3402'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Nokuthula Vilakazi",address:"nokuthula.vilakazi@fabi.up.ac.za",affiliation:'
Future Africa, University of Pretoria, South Africa
Future Africa, University of Pretoria, South Africa
Department of Water Resources Management, Malawi University of Science and Technology, Malawi
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