Effects of Quantum-Well Base Geometry on Optoelectronic Characteristics of Transistor Laser

Since the discovery of the transistor, the base current (minority carrier recombination) has been the key to the device operation. Among all developments through which Bipolar Junction Transistors (BJT) have progressed, the most innovating modification may be the replacement of the homojunction emitter material by a larger-energy-gap material, thus forming a Heterojunction Bipolar Transistor (HBT). In a silicon bipolar junction transistor, both homo and hetero structures, the base current is dissipated as heat, i.e. through nonradiative recombination, but can yield substantial radiative recombination for a directbandgap semiconductor like GaAs. Thus we can reinvent the base region and its mechanism (i.e. carrier recombination and transport function) to decrease current gain significantly and achieve stimulated recombination. Researches on III–V high-current-density high-speed HBT, revealed the ability of the transistor to operate electrically and optically in the same time. The modified transistor, called in literature as light emitting transistor (LET), works as a three port device with an electrical and an optical outputs (Feng et al. 2004a). Further improvements including wavelength tunability obtained by incorporating a place for better carrier confinement, called a Quantum-Well (QW) (Feng et al. 2004b). Carrier recombination in quantum well (QW) can be modified with a reflecting cavity changing the optoelectronic properties of QWLET (Walter et al. 2004). Room temperature continuous wave operation of such a device at GHz develops a novel three-terminal device, called a HBT Transistor Laser (HBTL) or briefly TL, in which laser emission produces by stimulated recombination (Feng et al. 2005). In the TL, the usual transistor electrical collector is accompanied with an optical collector, i.e. the above mentioned QW, inserted in the base region of the HBT. Stimulated recombination, unique in the TL, causes “compression” in the collector I-V characteristics and decrease in gain. Combined functionality of an HBT, i.e. amplification of a weak electrical signal, and that of a diode laser, i.e. generating laser emission, is observed in the TL. In other words, a modulating base current leads to modulated signals of the laser output power and collector current. It raises the possibility of replacing some metal wiring between components on a circuit board or wafer chip with optical interconnections, thus providing more flexibility and capability in optoelectronic integrated circuits (OEIC) (Feng et al. 2006a). It has been planned that TL is appropriate for telecommunication and other applications because of its capability of achieving a large optical bandwidth (BW) and a


TL structure
The device studied here is based on n-p-n heterojunction bipolar transistor (n-InGaP/ p-GaAs +InGaAs quantum well/n-GaAs).The epitaxial structure of the crystal used for the HBTL, demonstrated in Fig. 1, consist of a 5000 Å n-type heavily doped GaAs buffer layer, followed by three layers of n-type forming the bottom cladding layers.These layers are followed by an n-type subcollector layer, a 600 Å undoped GaAs collector layer, and an 880 Å p-type GaAs base layer (the active layer), which includes (in the base region) a 120 Å InGaAs QW (designed for ≈1000 nm).The base area is ≈ 4000 m 2 and we can treat the QW base region as three distinct subregions: Two 10 19 cm −3 doped GaAs regions and one 160Å undoped InGaAs QW within them.The epitaxial HBTL structure is completed with the growth of the n-type emitter and upper cladding layers.Finally, the HBTL structure is capped with a 1000 Å heavily doped n-type GaAs contact layer.The HBTL fabrication www.intechopen.comEffects of Quantum-Well Base Geometry on Optoelectronic Characteristics of Transistor Laser 257 process utilizes eight mask layers for three wet chemical etching steps, three dry (plasma) etching steps, and three metallization steps for top-side contacts.The HBTL sample is cleaved front-to-back using conventional etching methods to a length of 150µm between Fabry-Perot facets.Detailed fabrication process of HBTL has been described in (Chan et al., 2006;Feng et al., 2005;Feng et al., 2006a).Although other device structures like Tunnel Junction Transistor Laser (TJTL) (Feng et al., 2009), VSCEL (Shi et al., 2008), Heterojunction Field effect (HFETL) (Suzuki et al., 1990) and Distributed Feedback Transistor Laser (DFBTL) (Dixon, 2010) have been proposed in the literature, we focus solely on Heterostructure Bipolar Junction transistors.

Charge analysis
The three-terminal TL is fundamentally different from a diode laser (single p-n junction), i.e. a two-terminal device, where the injection current is carried totally by recombination.There is no third terminal and collector current "competition".In TL the collector current I C (I E =I B +I C ) is the fraction of emitter current "collected" at the reverse-biased base collector junction, with the remainder I B supplying base recombination radiation.We show here that the carrier lifetime can be extracted from the HBT I-V characteristics, thus allowing the intrinsic optical frequency response of the TL to be derived by modifying the coupled carrier-photon rate equations.

Carrier dynamics
Being an essential feature of transistor operation, QW-base recombination of electron-hole supported by the base current I B causes photon generation while carrier injection into the base region is provided by the emitter current I E .Solving the continuity equation for the above mentioned three regions of QW-base, expressed in equations 1 and 2 for base bulk and QW region respectively, can shape distribution of base injected electrons from emitter.
Where n=n(x,t) is the base electron distribution and the quantities τ bulk and τ qw are the recombination lifetimes in the GaAs and in the InGaAs QW, respectively.Sudden decrease in τ qw at lasing threshold is a result of faster recombination rate in the QW thus base carrier tilt at emitter is intensified compared to spontaneous emission.The term n/τ qw in equation 2 represents for spontaneous and stimulated photon generation and coupling of the optical field into the device operation.The bulk lifetime, τ bulk , in the GaAs layer with 10 19 doping is approximated as 193 ps.Uniform diffusion constant, D≈26 cm 2 /s, is assumed throughout the base region and diffusion current, I=qAD∂n/∂x, is supposed continuous across the GaAs/InGaAs-QW/GaAs interface.The position of QW, W EQW , is assessed here by its central location distance from the emitter-base interface and is the variable parameter during analysis of section 5 where the effect of QW position will be investigated.
Zero charge density at collector-base junction and ∂n/∂t=0 form the initial conditions for the continuity equations 1 and 2. The calculated charge distribution for increasing base current (I B ) corresponding to the I-V characteristics of HBTL are shown plotted in Fig. 2. The device currents are then calculated from common formula for diffusion current.Deviation from triangular approximation is observed in Fig. 2 and the profile is inclined more steeply upward near the emitter-base interface due to faster recombination in QW compared with the bulk base and reduced base width (W QW <W EC ).At the lasing threshold, τ qw decreases abruptly agreeing with stim < spon as stimulated recombination speeds up the overall rate of recombination in the QW.Consequently, the emitter-end "tilt" of the carrier population is more noticeable beyond the threshold.

Charge control model
Charge control model for TL consists of superposition of two different triangular charge populations named as Q 1 and Q 2 (Feng et al., 2007).As TL integrates two distinguish operations, i.e.HBT electrical and semiconductor diode laser optical outputs, it might be supposed as a two-collector device.One is the base-collector junction and the other is QW called correspondingly electrical and optical collector.In the model of charge control Q 1 and Q 2 are responsible for transporting minority carriers to the QW (for optical operation) and keeping transport of carriers to the electrical collector (for electrical operation) respectively.Q 1 and Q 2 are obtained from carrier density profile, Fig. 3 and calculated so that Where n 1 and n 2 are extracted from bias data, i.e. emitter base bias voltage ( BE ) and I C , so that ( n 1 + n 2 ) exhibits total carrier density at the emitter-base interface.Deriving I C and I B from I-V characteristics of TL (W EQW =590 Å), we can estimate Q 1 and Q 2 as Where t,1 is the transient time from emitter to QW and t,2 is the transient time across the entire base (W B =880Å) and calculated as below.
Two base carrier populations, Q 1 and Q 2 , are combined to form the overall effective base recombination lifetime, B , of the entire base population which is expressed as Since bulk >> t,1 , B ≈(1+Q 2 /Q 1 ).t,1 .Beyond the lasing threshold, B decreases when stimulated emission accelerates the overall rate of recombination in the base of the TL.This is obvious in the steeper slope of the Q 1 population, transporting a larger proportion of the base carriers to a faster ( B,stim ) optical collector (QW), leading to a shorter overall base recombination lifetime, B , and decreased gain .B values for charge density distributions near the threshold and beyond, plotted in Fig. 4 of (Feng et al., 2007).

Device optoelectronic characteristics
Among several characteristics, either optical or electrical, of the TL, small signal optical frequency response and current gain are most interesting.The reason arises from the fact that the TL needs suitable optoelectronic characteristics to be incorporated in an Optoelectronic Integrated Circuit (OEIC).The intrinsic frequency response of the TL can be improved towards 100 GHz owing to carrier lifetime determined by a thin base and the ability of the TL to inject and withdraw stored charge within picoseconds (forcing recombination to compete with E-C transport).Methods are required to improve the optical bandwidth to equalize both bandwidths as much as possible.The following describes a brief analysis of these characteristics.

Small-signal analysis of optical frequency response
When integrated over the entire base width, continuity equations ( 1) and ( 2) can result in an approximation for optical frequency response.The result for the TL is a modification of the coupled carrier-photon equations, formulated by Statz & deMars (Feng et al., 2007) which is expressed as Where N≈(Q 1 +Q 2 )/q is the total base minority carrier population, is the photon group velocity, is the optical confinement factor of active medium (i.e.QW), P is the photon lifetime, g is the gain per unit length of the active medium, and N p is the total generated photon number.The small signal optical frequency response is obtained as below Where P m (ω) is the modulated photon density, I B (ω) is the modulated base current and b is the optical confinement factor of the waveguide.The natural frequency and damping ratio are: , .
For ζ≤0.7 the resonance frequency and bandwidth are: While these values for ζ≥0.7 are expressed as: We can obtain P from the common equation: For cleaved cavity laser of lengths L=150 and 400( m) with R 1 =R 2 =0.32 and a photon absorption factor ( ) of 5cm -1 , the approximate photon lifetime are P =1.5 and 3.6(ps) respectively.It should be noticed that we neglect the capture and escape lifetimes in this small signal analysis.Optical gain is also assumed independent on photon and carrier populations.Although the difference in final results is negligible, an interested reader can refer to (Faraji et al., 2009) for more information.
In equations ( 13) and ( 14) the parameter B,spon is a specific value of overall base recombination lifetime, B , evaluated in spontaneous emission region at lasing threshold.According to Fig. 4 of (Feng et al.,2007) (not shown here) this value for a TL with W EQW =590Å is about 2.5ps.
Under bias condition such that I B =33mA (I B /I B,th =1.5), small signal optical frequency response for two TL with above mentioned cavity length is sketched in Fig. 4. For comparison, the curve also contains optical response of an ordinary diode laser (DL) with a large base recombination lifetime of B,spon =100ps.When compared with traditional diode laser, fast modulation response of TL is due to this difference in their optical frequency response which suffers a resonance peak in low frequencies in the case of diode laser.The very short effective carrier lifetime of a TL, i.e. the same order of magnitude as the cavity photon lifetime, results in a near unity resonance peak and provides in effect a significantly larger bandwidth , which is typically not available when the bandwidth is limited by carrier-photon density resonance, as in a diode with a large carrier lifetime (0.1-1ns).We see that by charge analysis, if a QW base HBT is capable of laser operation, its "speed" of operation is not affected by common recombination, and the limitation of spatial charge "pileup" as in a diode, but by the base dynamics of charge transport described in this section.Indeed, only fast recombination is able to compete with fast collection of carriers.

Current gain
Thanks to special features of QW incorporated in its base region, the most recent form of laser, the Transistor Laser, govern carrier recombination and hence electrical current gain , = I C / I B .This gain therefore becomes a crucial parameter in both transistor and laser operations of TL.As previously mentioned, stimulated emission, an extra feature of transistor, makes the collector I-V characteristics "compressed" and decreases .The gain value for both the transistor laser and an ordinary HBT (i.e. a Q-spoiled TL) was demonstrated in Fig. 6 of (Walter et al., 2006).Charge control analysis can be utilized in conjunction with these values of current gain to determine the TL terminal currents and estimate base transit and recombination lifetimes.Conversely, one can calculate theoretically for a TL as described below.The base and collector currents and the static common-emitter current gain are given for an HBT as where Q B is the charge stored in the base, B is the base recombination lifetime, and t is the base transit time.For the same HBT with a quantum well inserted in the base, a QWHBT, the base current and current gain can be modified and expressed as where QW is the recombination lifetime of the quantum well while BQW is the effective recombination lifetime of the base and quantum well.For an QWHBT transistor laser with stimulated base recombination, a QWHBTL, the base current and current gain can be further modified and expressed as where TL is the effective base recombination lifetime of the transistor laser including st , the stimulated recombination lifetime.

QW-base geometry effects
Since the first report of successful operation of TL, a number of publications reported different material combinations (Dixon et al., 2006) The electron recombination plays an important role in determining the base current due to spontaneous and stimulated emission in the QW, so that the electronic characteristics of the TL have a strong dependence on its laser operation.This is proved by the decrease in the electrical gain = I C / I B due to enhanced carrier recombination in the base region when stimulated emission occurs.According to the model described in section 4, effects of geometrical parameters of QW-base on small signal optical frequency response and current gain should be significant.In other words optoelectronic characteristics of TL are directly affected by parameters like QW position in the base (W EQW ), well width (W QW ) (and barrier width in the case of multiple quantum-wells TL), number of QWs, base width (W B ), etc.For instance, TL characteristics depend on the relative position of QW because of the quasilinear density profile of the base minority carriers (Fig. 2).Although, the mentioned first order model of charge control does not distinguish between bulk and QW carriers, TL characteristics dependency on QW and base width are still acceptable.Herein, we utilize analysis described in section before to model the effect of QW position on optical bandwidth and current gain of TL.As a goal, we look for an enhanced performance for the TL by "restructuring" it.

QW location effect
Being integrated inside the base region of the TL, the quantum-well structural parameters have certainly significant influence on both optical and electrical properties of TL, e.g. gain and bandwidth for optical and electrical outputs.This subsection is dedicated to the mentioned effects while other parameters will be studied later.

Carrier profile
According to the model, constant base-emitter voltage and collector current makes ( n 1 + n 2 ), n 1 , Q 2 unchanged.Altering the position of QW within the base can therefore change Q 1 , i.e. portion of carriers responsible for lasing.The new values for Q 1 and t,1 (base transit time) when QW moves are as below , * , , ⁄ , , , , * , , ⁄ For the TL described in previous sections we may set W EQW,old =590Å.As a result, minority carrier profile of base region solved analytically for W EQW =150 Å is sketched in Fig. 5. Also Fig. 6 demonstrates the modified charge control model.Displacement of QW position, W EQW , towards emitter can cause two noteworthy effects simultaneously.First, B falls due to reduction of Q 1 while Q 2 is constant.Second, in accordance to the diffusion formula for I E and Fig. 6, I E would increase significantly as a result of steeper charge density profile at the base emitter interface.These conditions make base current (I B ) to rise abruptly beyond the threshold current (22 mA).Due to (Kaatuzian, 2005) the threshold current is constant during this movement of QW.In other words, moving the QW in this direction decreases the electrons which are "trapped" and recombined with holes within it.Thus more carriers are allocated to electrical operation and fewer involved in light generation, i.e. fewer photons created within the well.This phenomenon, exhibited by animation in Fig. 7, means that carriers arrive sooner at QW.As a result of "faster rich time" of minority carriers to the well, it is predicted that both B and decreases drastically (by about 4 or 5 times for B ).

Small-signal optical frequency response
Calculating the optical frequency response of transistor laser in 4.1, one can sketch the response for different QW locations.Table 1 shows the simulation results of device parameters for different QW locations through the base region while Fig. 10 and Fig. 11 show optical response and bandwidth dependence on QW location, respectively.As it is obvious from the values for simulated ζ, all of them exceed 0.7 and no resonance peak, the limiting factor for diode lasers, occurs due to QW dislocation through such a thin base layer.
Non unity resonance peak in diode lasers with a large carrier lifetime (0.1 -1 ns), sets limit on f -3db and restricts performance of diode laser.Increase in optical bandwidth (f -3db ) is a direct result of sliding the QW toward collector.At the first glance opposite direction of increase for f -3db and τ B,spon is confusing and seems mistaken.However, it would be clear if we sketch the f -3db versus τ B,spon (using approximation of f -3db by equation 18).As Fig. 12 demonstrates, the bandwidth rises abnormally with τ B,spon increases while reach a peak at about B,spon =3.37 ps and then decreases.This fact shines a novel idea that there may be an optimum point for QW to be located in order to maximize the optical bandwidth.Utilizing this figure in conjunction with calculated τ B,spon , one can move the QW toward collector to W EQW =730Å to achieve maximum optical bandwidth (~54 GHz, taking into account the error due to approximate equation).As a result, the QW should be placed closed to collector as much as possible in order to achieve the maximum bandwidth.Fig. 11.QW location effect on optical bandwidth; an HBTL with well near its collector has larger optical bandwidth while electrical bandwidth is the same.

Current gain
We predicted previously that optical bandwidth increment would be at cost of sacrificing the current gain ( ).Further investigation of QW effect on TL optoelectronic characteristics, this time electrical, leads in an interesting result that matures the previous founding.
Collector current gain for an HBTL was calculated in subsection 4.2 in equations ( 24) and ( 25).As a result of QW movement towards collector, simulation at constant bias currents shows that τ TL and consequently β declines.Fig. 13 shows this change in optical bandwidth and current gain versus displacement of QW while bias voltage, i.e. v be , forces base current to be constant at I B =33mA for W EQW =590 Å.This bias enforcement does not disturb generality of the simulation results.
The opposite dependence of BW and to W EQW , is a trade-off between TL optoelectronic characteristics.Other experimental and theoretical works proved the described "trade-off" between and f -3db as well (Then et al.,2009(Then et al., ),(faraji et al., 2009)).They also predict analytically the above mentioned direct dependence of f -3db on τ B,spon .In (Then et al., 2008) the authors utilized an auxiliary base signal to enhance the optical bandwidth.As a merge of their work and the present analysis we can find the optimum place for QW that leads to better results for both and f -3db of a TL.It means we can use both method, i.e. auxiliary base signal and QW dislocation method, simultaneously.A suggestion for finding an "optimum" QW location consists of two steps .First we focus on and make it larger by locating the QW close to emitter, e.g.W EQW <300 Å, which results in BW<43 GHz.Then we use auxiliary AC bias signal to trade some gain for BW.It should be noted that less than unity is not generally accepted if TL is supposed to work as an electrical amplifier.

Quantum-well width
Being an optical collector, the QW plays a significant role as it governs both optical and electrical characteristics of TL.Among QW-base geometry parameters, other than QW location, one can investigate the width of QW incorporated within the base region.For instance, we can change the well width while other geometrical parameters, like QW location, are left unchanged in order to examine how the optical frequency response and current gain alter.Base minority carrier recombination lifetime was calculated before as in equation ( 9) which was an independent function of well width.Charge control model and charge analysis based on this model, described in previous sections, should be completed in order to do this analysis.The base carrier lifetime, B , can be written as below (Then et al., 2007c) Where th is the thermal velocity of carriers, N r is the density of possible recombination sites and is the cross section of carrier capture. is a measure of the region that an electron has the possibility to capture and recombine with a hole and is proportional to well width (W QW ).In the other hand, N r depends on the hole concentration, i.e.N A of the base region.So we can evaluate B as where G is a proportionality factor defined by other geometrical properties of the base.Using this equation one can extract base recombination lifetime of base minority carriers for different base doping densities.Calculations exhibit an indirect relation between B and well width, agreeing with a larger QW width enhancing the capture cross section for electrons.Moreover, the larger N A , the greater the recombination and hence the smaller B .
The results for optical frequency response based on Statz-deMars equations of section 4 can be utilized to evaluate the optical properties of a TL for varying well width.Indeed, equations ( 13) and ( 14) require B,spon not B , as described above, therefore threshold current should be calculated for different QW widths.An expression for base threshold current of TL is as below where n 0 is minority carrier density in steady-state (under dc base current density of J 0 ), τ cap is the electron capture time by QW (not included in charge control model for simplicity), τ qw is the QW recombination lifetime of electron and rb0 is the bulk lifetime (or direct recombination lifetime outside the well, also ignored in our model).The base geometry factor, , gives the fraction of the base charge captured in the QW and defines as (Zhang & Leburton, 2009) where W qw is the QW width, the factor we investigate here, W b is the base width and x qw is the QW location, similar but not equal to previously defined parameter of W EQW .By setting all the constants, one can calculate B,spon and then small-signal optical frequency response and bandwidth of TL for a range of QW widths.Optimization is also possible like what we did for QW location.

Conclusion and future prospects
An analytical simulation was performed to predict dependence of TL optoelectronic characteristics on QW position in order to find a possible optimum place for QW.Simulated base recombination lifetime of HBTL for different QW positions exhibited an increase in optical bandwidth QW moved towards the collector within the base.Further investigations of optical response prove the possibility of a maximum optical bandwidth of about 54GHz in WEQW≈730 Å.Since no resonance peak occurred in optical frequency response, the bandwidth is not limited in this method.In addition, the current gain decreased when QW moved in the direction of collector.The above mentioned gain-bandwidth trade-off between optoelectronic parameters of TL was utilized together with other experimental methods reported previously to find a QW position for more appropriate performance.The investigated transistor laser has an electrical bandwidth of more than 100GHz.Thus the structure can be modified, utilizing the displacement method reported in this paper, to equalize optical and electrical cut-off frequencies as much as possible.
In previous sections we consider the analysis of a single quantum well (SQW) where there is just one QW incorporated within the base region.This simplifies the modelling and mathrelated processes.In practice, SQWTL has not sufficient optical gain and may suffer thermal heating which requires additional heat sink.Modifications needed to model a multiple QW transistor laser (MQWTL).First one should rewrite the rate equations of coupled carrier and photon for separate regions between wells.Solving these equations and link them by applying initial conditions, i.e. continuity of current and carrier concentrations, is the next step.In addition to multiple capture and escape lifetime of carriers, tunnelling of the 2dimensional carriers to the adjacent wells should be considered.For wide barriers one may use carrier transport across the barriers instead the mentioned tunnelling.Simulation results

Fig. 1 .
Fig. 1.Epitaxial structure of heterojunction bipolar Transistor Laser (HBTL).A QW is incorporated within the base to improve the recombination efficiency.

Fig. 2 .
Fig. 2. Calculated minority carrier distribution for increasing I B corresponding to the I-V characteristics.The shape tilts inside the QW due to faster recombination and reduced base width.

Fig. 3 .
Fig. 3. Charge Control Model illustrates the role of Q 1 and Q 2 triangles in the entire base carrier distribution.Large amount of carriers enter the base while a little of them survive to the collector.

Fig. 5 .
Fig. 5. Calculated minority carrier distribution for QW moved toward emitter; the profile deviates more from triangular form of regular HBT.

Fig. 9
Fig. 9. 3-D scheme of base recombination lifetime ( B ) versus I B and W EQW placed in different positions through the base.

Table 1 .
Simulated device parameters for different W EQW ; No resonance peak due to QW movement when ≥0.7.