Characteristics of some indirect‐gap semiconductors associated with the recombination radiation: electric constant, Debye temperature, the binding energy of exciton, the free-exciton radius, critical temperature, and concentration for formation of EHL.
Original experimental data on the recombination radiation of free excitons, the band-A of luminescence, and the recombination radiation of electron-hole liquid in a diamond have been presented. A review of the literature on the recombination radiation in diamond and its application was performed. There was no displacement of free-exciton band at 5.275 eV in the temperature range of 80–300 K. At low excitation levels, the temperature dependence of free-exciton band intensity had the maximum at ∼150 K. The band-A of luminescence, due to defects containing sp2-hybridizedcarbon bonds, is located in the spectral range 350–650 nm with a maximum at ∼440 nm and is characterized by the decay time of 8–19 m sec in the temperature range of 80–300 K. The electron-hole liquid recombination radiation in the diamond was observed at temperatures of <200 K and at peak densities of charge carriers of ≥(0.3–1.0)×1018 cm-3. Condensation of electron-hole liquid implies the displacement of the free-exciton intensity maximum on the temperature dependence to higher temperatures. The critical temperature of electron-hole liquid condensation takes values in the range of 160–220 K. The literature data on the diamond light-emitting devices are discussed.
- electron‐hole pair
- electron‐hole liquid
- electron‐hole plasma
- light‐emitting device
Recombination radiation in semiconductors appears due to radiative recombination of nonequilibrium charge carriers, which are generated in the processes of photon and high‐energy particles absorption, or are injected through the contacts . Usually, recombination luminescence is observed in the spectra of photoluminescence (PL), cathodoluminescence (CL) and electroluminescence (EL).
For simple indirect‐gap semiconductors (germanium, silicon, diamond), plasma band recombination of electron‐hole pairs (at least at low excitation levels) is not observed in the luminescence spectra. Depending on the defect‐impurity composition, temperature and density of nonequilibrium carriers, phonon components of radiative recombination bands of free (FE) and bound (BE) excitons, exciton complexes (EC), the electron‐hole liquid (EHL) and electron‐hole plasma (EHP) are observed in the luminescence spectra of the sample near the fundamental absorption edge. In the latter case, there is a bound state of nonequilibrium charge carriers arising when the Mott transition is fulfilled (phase transition of the second kind)—transition gas FE–EHP. In addition to the processes mentioned above, the radiative recombination of nonequilibrium charge carriers can occur through the impurity‐defect allowed states located in the band gap. In this case, recombination emission bands are observed in the spectral region close to the half‐width of the energy gap.
Due to the short covalent C–C bond, the low dielectric constant and high Debye temperature diamond excel other semiconductors. Table 1 shows comparative data on diamond and other semiconductor‐related recombination radiation.
|Semiconductor||Electric constant, ε||Debye temperature, T [K]||Binding energy of free exciton, Ex [meV]||Radius of|
free exciton, ax [nm]
|Critical EHL carrier density, n [cm-3]||Critical EHL temperature, T [K]|
|Silicon carbide, 3C‐SiC||9.7||1200||13.5||3||2.3×1018||41|
|Gallium phosphide, GaP||9.1||445||10||5||2.6×1018||45|
Diamond is characterized by high exciton binding energy (80.5 meV) , which corresponds to a temperature of 660°C. At room temperature, the thermal energy of the charge carriers is less than twice the binding energy of FE. At the temperature of liquid nitrogen, binding energy of FE in the diamond exceeds the thermal energy of lattice on an order of magnitude. Therefore, nonequilibrium charge carriers in diamond form FEs, because it is energetically favorable for them. These temperatures are not extremely low (helium). At the same time, the high density of trapping/recombination centers of charge carriers hinders the formation of FE. However, in the diamond samples containing the impurity‐defect centers of <1018 cm-3, nonequilibrium charge carriers being generated or injected (at small values of the electric field) form excitons, which are then involved in the radiative and nonradiative recombination, the formation of the EC, condensation and evaporation of EHL.
This chapter of the book is devoted to the review process of radiative recombination FE, EHL, and EHP bands, as well as the so‐called band‐A of luminescence. We discuss the observed effects, the outstanding issues and possible research directions.
We investigated the properties of several diamond samples, whose main characteristics are given in Table 2.
|Sign||Synthesis method||Monocrystal/polycrystalline||Size [mm]||Transparency||FE‐band||Band‐A||EHL‐band|
|C4||Natural||Mono||∅4 × 0.25||Yes||No||Strong||No|
|C5||Chemical vapor deposition (CVD)||Poly||10 × 10 × 0.5||Yes||Strong||Very weak||Strong|
|C6 (fragments)||CVD||Poly||10 × 10 × 0.1||Yes||Weak||Very weak||No|
|C10||CVD||Mono||5 × 5 × 0.25||Yes||Strong||No||Strong|
|C11||CVD||Poly||5 × 5 × 0.25||No||No||Very weak||No|
|C12||High‐pressure high‐temperature (HPHT)||Mono||5 × 5 × 0.25||Yes||Strong||No||Weak|
The densities of impurities and defects in samples were less than 1018 cm‐3. IR absorption spectra of samples did not reveal any peculiarities in one‐phonon absorption in the range of 7.5–15 microns (see Ref. ), due to the impurity‐defect centers.
IR absorption spectra were measured at room temperature (RT) using infrared spectrometer Nicolet 5700 with Fourier transformation in the spectral region from 2.5 to 15 microns. Raman spectra of samples in the wave number range of 100–3700 cm-1 were obtained at RT using the same infrared spectrometer equipped with the Raman attachment NXR FT‐Raman. Spectral resolution was 2 cm-1.
The PL spectra of diamond samples were measured at temperatures from 80 to 300 K using spectrometer Ocean Optics HR 4000 in the spectral range of 200–300 nm with spectral resolution of 0.4 nm and Stellar‐Net EPP‐2000C in the spectral range of 200–850 nm with resolution of 1.5 nm. Before measurements, diamond sample was mounted on a cooled copper holder, placed in a vacuum chamber. The sample temperature was measured with a platinum thermoresistor Heraeus Pt1000. Excitation of PL was provided by pulsed KrCl‐laser radiation (λ = 222 nm) with pulse duration 18 ns (FWHM) or ArF‐laser radiation (λ = 193 nm) with pulse duration of 8 ns (FWHM). Laser pulse energy was 30 mJ. The radiation was focused on a sample by a quartz cylindrical lens with a focal length of 65 mm. The peak intensity of the laser radiation on the surface of the sample reached 13 and 10 MW/cm2 at 222 and 193 nm, respectively. PL radiation from the opposite side of the diamond sample (excitation relative) was transported to the spectrometer through the optical fiber. The incident energy on the sample was measured by laser radiation pyroelectric sensor Ophir PE50-BB. The experimental scheme is described in detail in Ref. .
Figure 1 shows the evacuated chamber design, which was used to research the pulse PL of diamond samples at cooling from room temperature (RT) to the temperature of liquid nitrogen. The design of this camera also enables to conduct the measurement of diamond photoconductivity.
Thermal contact of the sample
The absorption of photons in the diamond sample leads to a nonuniform distribution of nonequilibrium charge carriers. Reduction in the peak intensity of the laser radiation with the depth of the sample (taking into account the reflections from the rear face) is calculated by the formula :
Profiles of charge carrier peak density over the sample thickness were calculated using the formula :
Figure 2 shows the distribution of the laser peak intensity and the peak carrier density in the sample, calculated by the formulas (1) and (2), at peak laser intensity
Thus, the photons at 222 and 193 nm created in the samples the maximum nonequilibrium charge carrier density of
CL spectra were measured using another vacuum chamber, a similar device. The camera was attached directly to the electron accelerator. The luminescence radiation of a sample was transported to a spectrometer through the optical fiber. The technique of CL measurements is described more detailed in .
3. Free exciton recombination band
In the diamonds with the densities of impurity‐defect centers of less than 1018 cm-3, the recombination FE band is characterized by considerable intensity even at RT. In Ref. , observation of the FE luminescence band of the diamond sample doped with boron at temperatures up to 277°C was reported. Presumably, in luminescence spectra of undoped ultrapure samples, the FE recombination band can be observed up to temperatures of ∼660°C.
Due to the indirect zone structure in the diamond, the FE radiative recombination arises with the generation of momentum‐conserving phonons. Recombination radiation of FEs in diamond is accompanied by the generation of the three main phonon components—the dominant TO (transverse optical phonon 141 meV) at 5.275 eV, TA (transverse acoustic phonon 87 meV) at 5.325 eV and TO+OΓ (two‐phonon process involving TO + Raman phonon 141 + 159 meV) at 5.117 eV, as shown in Figure 3. The LO‐component (longitudinal optical phonon 156 meV) at 5.254 eV is characterized by low intensity and is indistinguishable on the background of intense temperature‐broadened TO‐components at temperatures higher than 100 K .
The spectral position of the phonon component of the recombination FE band was determined by the band gap , the binding energy of FE , and the corresponding phonon energy :
Depending on experimental conditions, all three terms in the right side of the expression (3) vary slightly, causing the displacement of the spectral components.
It is known that the band gap decreases with increasing temperature due to increase in thermal energy of the atomic lattice . In Ref. , the difference between the band gap and exciton binding energy in the 80–620 K temperature range was measured by finding the position of the phonon component of exciton absorption threshold at 5.258 and 5.314 eV for several natural diamonds. In the temperature range 80–300 K, the reduction of value was ∼15 meV (see. Figure 4). According to Eq. (3), this reduction, , should cause a corresponding shift of the maxima of phonon FE component. In Ref. , the position of TO‐component maximum of FE recombination was measured in the temperature range 80–250 K for CVD diamond samples (see Figure 4). The FE band maximum shifted to shorter wavelengths by ∼16 meV as the temperature increases from 80 to 200 K. This observation contradicts to the effect of band gap reduction with increasing temperature.
We have measured the position of dominant TO‐component maximum of FE recombination depending on the temperature for the samples C10 and C12 at low level of excitation at 222 nm. The measured values are shown in Figure 4. The observed change in the maximum position of radiative FE recombination is about 3–5 meV, which lies within the measurement error, and is significantly less than one measured in . In Ref. , there was another trend of TO‐component position shifting to shorter wavelengths with increasing temperature. Thus, the data are inconsistent, and the observed phenomena deserve separate studies.
At low excitation levels, the binding energy of FE in diamond is 80.5 meV . As the FE density approaching the Mott transition level or EHL condensation critical density (phase transition of the first kind), which is characterized by a decrease in the average distance between FEs to a value = 1–2 (in FE radius size), the FE binding energy should decrease to zero . In the literature, there is no information for diamonds about the FE binding energy measurements under such conditions.
For various diamond samples with various defect‐impurity compositions, different phonon energy is mentioned for indirect optical transitions of radiative recombination. Table 3 shows the values of TA‐, TO‐, LO‐ and OΓ‐phonon energies to various literature references.
Differences in phonon energies arise from different calculation methods, measurement errors and experimental conditions. Experimental conditions are the most important thing, because it is necessary to use the phonon energy as the varying values for the best fit of the experimental and calculated data. This indicates an incomplete understanding of observed phenomena.
The presence of defects and impurities in the sample increases the probability of nonradiative recombination processes of FEs. CL spectra at room temperature of two different polycrystalline CVD diamond samples C5 and C6 are shown in Figure 5. FE recombination band dominated in both spectra. The inset in Figure 5 shows the Raman spectra of several diamond samples, including C5 and C6. For comparison, the spectra of natural (C4) and CVD single crystals (C10), as well as a fully opaque CVD polycrystalline sample (C11), are presented. In contrast to sample C5, the Raman spectrum of sample C6 is characterized by high intensity “non‐diamond” bands: amorphous carbon (570–580 and 1540 cm-1), disoriented graphite (1350 cm-1) and microcrystalline diamond (1140 cm-1). These features are reflected in the intensity of FE band. Thus, the presence of large density of states of “non‐diamond” carbon increases the probability of nonradiative recombination and reduces the probability of optical transitions in FE band. Samples C5 and C6—diamonds of “optical quality”— had no measurable absorption bands in the IR range, had low intensity of luminescence band‐A (see Section 4), showed no other luminescence bands (except the band‐A and the FE band) and revealed the clear edge of fundamental absorption . In addition, sample C5 demonstrated the radiative recombination of EHL at higher excitation levels [3, 16], which will be discussed in Section 5.
The intensity of FE recombination band varies with the temperature of the sample as shown in Figure 6. At low excitation levels, this dependence has the form as shown in the inset of Figure 6 and is determined by the FE lifetime of charge carriers in diamond :
The intensity maximum of TO‐component of recombination FE band usually locates at temperature about 150 K for all diamond samples and excitation methods [12, 17, 18]. The exception is the PL at high excitation levels (see Section 5).
Thus, the FE recombination radiation in the diamond at low excitation levels has been studied quite well. However, there are following unresolved aspects: the absence of spectral shifting of dominant TO‐component, when the temperature changes; the different phonon energies of FE recombination component in different experiments; and the unknown change in FE binding energy by increasing the charge density to values ≥1019 cm-3.
4. The band‐A of luminescence
Diamond samples of any synthesis method show the blue luminescence band (350–650 nm) in the visible region of luminescence spectra. This so‐called band‐A is observed at any excitation method  (See Figures 7–9). There is a competition between the FE recombination band and band‐A . More defective samples show intense band‐A, and purer samples—intensive FE band. Thus, the centers of band‐A are effective FE radiative recombination centers.
There is no common opinion about the origin of luminescence band‐A. Initially, luminescence analysis objects of the diamond structure were natural crystals and specimens grown in conditions of high pressure and high temperature (HPHT). Such samples always contain nitrogen in significant densities (1017–1020 cm-3) in the dispersed form or in polyatomic complexes. In Ref. , it was suggested that the band‐A is the result of recombination of electrons and holes on closely spaced donor‐acceptor pairs. However, intensive band‐A was observed in samples containing impurities below 1017 cm-3 . In , band‐A has been attributed to optical transitions in N4V centers. However, a clear correlation between the intensities of the band‐A and N9 system (associated with N4V centers) has not been identified . In Refs. [8, 12, 23, 24], it has been proposed that band‐A is associated with dislocations. However, not all of the dislocations were luminesced [19, 23], a clear correlation with the type of dislocation was not observed , and band‐A radiation may come from sample areas, which are free from dislocations . Sometimes, the observed emission of band‐A appeared from a single dislocation, which has led to assume about the optical transitions in defect centers, decorating dislocation and dangling bonds in dislocations.
The development of CVD technology was enabled to receive diamond samples of large sizes (up to Ø120 × 3 mm3) . Untreated CVD diamonds contain no nitrogen with aggregation degree of more than 2, because the synthesis gas receives nitrogen from air only. The observation of band‐A in luminescence spectra of undoped CVD diamonds has led to speculation that the band‐A is a result of recombination of electron‐hole pairs on lattice defects, containing the sp2‐hybridized carbon bonds . In natural diamonds subjected to natural HPHT treatment, this type of defects exists throughout the whole volume of sample .
The band‐A is practically immeasurable in CVD single crystals . Intrinsic defects, containing sp2‐hybridized carbon bonds, are concentrated in grain boundaries of polycrystalline CVD diamonds . In Ref. , it was found that the band‐A of CVD polycrystalline diamond luminescence is observed from defective disoriented areas—grain boundaries. Calculations  showed that the grain boundaries contain ∼40% of amorphous carbon with sp3‐hybridized carbon bonds, preserving the short‐range order of diamond lattice only, ∼10% of dangling bonds and ∼30% of sp2‐hybridized carbon dimers, which create allowed states in the band gap. The radiative recombination of FEs in the spectral region of band‐A occurs through allowed states in the band gap.
In Ref. , there was competition between the FE recombination band and band‐A in the CVD diamond films. The increase in boron impurity density led to the emergence of “non‐diamond” bands in Raman spectra, reduction of FE band intensity and increase in the band‐A intensity and vice versa. The FE binding energy in the diamond is about two times higher than heat energy at room temperature. There is a competition between the processes of spontaneous FE radiative recombination and FEs capture on band‐A defects.
Natural samples (e.g., C4), containing a small amount of N2 defects, exhibit intensive band‐A of luminescence in the spectral range of 350–650 nm (see Figure 7). The luminescence spectra of polycrystalline CVD samples of “optical quality” contain the dominant FE recombination band at 235.2 nm. At the same time, the band‐A is characterized by low intensity (see Figures 8 and 9).
The natural diamonds and synthetic samples, which were subjected to HPHT treatment, demonstrate the band‐A of luminescence that overlapped the bands of other defects . These defects (N3V, N2V and NV centers) show vibronic bands of luminescence with the zero‐phonon lines (ZPL) at 415, 503 and 575 nm, respectively. For this reason, the integrated luminescence spectra of the diamonds in the visible region can have multiple peaks and exhibit shifts from sample to sample. Figure 7 shows the CL and PL spectra of the natural type IIa specimen (C4). CL was excited by electron beam with pulse duration of 0.1, 2 and 4 ns; for PL excitation, the pulsed laser radiation at 222 nm with a pulse duration of 18 ns (FWHM) was used. Besides band‐A, the luminescence spectra exhibit the so‐called N3 system with ZPL at 415.2 nm due to N3V centers.
Measurements of luminescence spectra with time resolution allow to resolve the band‐A and superimposed bands in time. Figure 10 shows the change in the CL spectrum of natural sample C4 in time. The CL spectrum in the maximum of optical signal consisted of system N3 with ZFL 415.2 nm and its phonon replicas (427, 438, 450 and 463 nm), and the wide anti‐Stokes (with respect to the ZPL) component at 350–410 nm. At 30 ns after starting of excitation pulse, the CL intensity decreased by seven times, the position of the ZPL and phonon replicas did not change, and anti‐Stokes luminescence component drastically decreased. At 2 ms after starting of excitation pulse, the ZPL 415.2 nm and its phonon replicas completely disappeared, and the intensity was reduced by three orders of magnitude, maximum shifted to 450–480 nm.
Thus, the band‐A is characterized by prolonged weak emission in the 350–650 nm range with decay time 8–9 ms at room temperature, as shown in Figure 11. At temperature ∼80 K of diamond sample, the decay time increased up to 18–19 ms [7, 29]. The temperature dependence of the band‐A was investigated in detail earlier . The sample heating from 30 to 110°C resulted in complete quenching of the band‐A. In Ref. , the observation of band‐A at temperatures up to 125°C was reported. So the activation energy of nonradiative recombination of band‐A centers is about 35 meV.
The observed temperature quenching of band‐A in nonradiative recombination processes showed the complex structure of energy levels of corresponding defects. Temperature quenching was observed at temperatures above 80 K. There are no references in the available literature about the dependence of band‐A intensity at temperature less than 80 K.
Thus, the experimental data indicate that the recombination band‐A of luminescence in the diamond is due to the intrinsic defects of the diamond lattice, containing the sp2‐hybridized carbon bonds. The lifetime of the metastable excited level centers of band‐A is ∼8–19 ms in the temperature range 300–80 K. The activation energy of temperature quenching of band‐A is ≥35 meV. At the same time, the atomic structure and the position of energy levels of band‐A centers are not known exactly. Research in this area will improve the understanding of defect formation in diamond and advance in the synthesis of ultra‐pure diamond samples for optoelectronic applications.
5. Electron‐hole liquid recombination band
The electron‐hole liquid (EHL) is a condensed state of FE gas in semiconductors . For the condensation of EHL, it is necessary to provide the temperature below the critical point and high charge carrier density. The EHL exists in the form of droplets with size 10-8–10-4 m depending on the material. The lifetime of the EHL is determined by the charge carrier lifetime and the processes of droplet condensation/evaporation. The EHL is observed in PL and CL spectra in the form of recombination band shifted toward longer wavelengths relative to FE recombination band.
EHL properties in germanium and silicon are well understood . For them, the critical constitute 6.7 K and 24.5 K, respectively. Diamond is the third one‐component indirect‐gap semiconductor. Due to the high FE binding energy of 80.5 meV and the high Debye temperature of 1860 K, the critical temperature of EHL existence in diamond is more than 160 K [31–33].
The first reports on the EHL observation in diamond have been made quite recently [33, 34] as improving CVD synthesis technology. Observation of EHL in luminescence spectra of natural diamonds (as well as FEs) is difficult because of high level of doping with nitrogen . These defect centers act as nonradiative (NS, N2, N4V) and radiative (N3V, N2V, NV, sp2‐bonds) centers of FE recombination. Currently, the EHL properties in diamond attract some interest [3, 35].
The observation of EHL recombination band in CL spectra of the diamond is complicated by heating the area of electron beam exposure. An accelerated electron generates tens‐thousands of “hot” electron‐hole pairs, which then thermalize in cascades of phonon emission, causing the heating of lattice and the “phonon wind,” making difficulties to EHL condensation. In CL spectra, the EHL recombination band is observed in the form of low‐intensity band at 5.16–5.23 eV range and between TO‐ and TO+OΓ‐components of FE recombination band (see Figure 12, CVD sample C5). In addition to this work in the available literature, it was reported only once about the EHL recombination band in CL spectra of the HPHT IIa type (pure) and IIb type (doped with boron) diamonds .
The excitation of nonequilibrium charge carriers by laser radiation provides less heating of the lattice, as an absorbed photon produces an electron‐hole pair. Moreover, if the excitation of nonequilibrium carriers by laser radiation takes place at the fundamental absorption edge, the generated carriers will have a minimum excess energy, and consequently, less laser energy is converted to the lattice heating and the “phonon wind.”
The threshold laser intensity for the observation of EHL recombination band in the PL spectra depends on the fundamental properties of the material, as well as the impurity‐defective composition of a particular sample. The higher the recombination center density in the sample is, the higher the threshold intensity to compensate the exciton recombination should be. On the other hand, some impurity‐defect centers can act as condensation nuclei of EHL drops, which should reduce the threshold intensity, as condensation on the irregularities is thermodynamically favorable than the condensation in the homogeneous vapor [13, 37].
Figure 13 shows the PL spectra of polycrystalline diamond sample C5 in the temperature range 90–235 K with excitation at 222 nm with peak intensity of 3 MW/cm2 . The EHL recombination band is observed in the form of long‐wavelength shoulder (5.2–5.16 eV) of TO‐component of FE band. The EHL recombination radiation arises from the central regions of crystallites, but not from the crystallite boundaries. Figure 14 shows a micrograph of sample C5 with magnification ×4. Crystallite sizes range from 50 to 400 microns, which is significantly higher than the FE diffusion length in diamond (1–10 microns) at RT [21, 39, 40].
For a single‐crystal sample C10 with excitation at 222 nm, the threshold intensity of EHL recombination band was about 7 MW/cm2, which is more than two times higher than the threshold intensity for sample C5. The reason for this effect has not yet been established.
In addition to changing the threshold intensity for observation EHL recombination radiation from sample to sample due to its different impurity‐defective structure, the threshold intensity also depends on the excitation wavelength. As mentioned above, the higher photon energy of excitation exceeds the band gap, and more laser energy is converted into thermal energy of lattice. The spectra of edge luminescence of the sample C10 are shown in Figures 15 and 16 with excitation at 222 and 193 nm, respectively. Spectra are marked with numbers, which correspond to the peak intensity of laser radiation in units of MW/cm2.
According to the expression (2) at 222 nm excitation with peak intensities of 7, 10 and 13 MW/cm2, the peak densities of non‐equilibrium carriers were (0.72, 1.04 and 1.35)×1018 cm-3, respectively. At 193 nm excitation with peak intensities of 5 and 10 MW/cm2, the peak densities were (3.47 and 6.94)×1018 cm-3, respectively. Thus, for comparable peak densities, the PL spectra, shown in Figures 15 and 16, were significantly different.
At 222 nm excitation with the peak intensity 7 MW/cm2, the FE recombination band was observed only at temperatures of 81 and 298 K in the PL spectrum (see Figure 15). At 298 K, there was a considerable thermal broadening of the FE band components. At 10 MW/cm2 on the long‐wavelength edge of the TO‐component of FE band, the shoulder appeared due to the EHL radiative recombination (and EC, possibly). When the peak intensity achieved of 13 MW/cm2 and the sample temperature was 81 K, the EHL band was expressed explicitly as the TO‐component at 5.16–5.22 eV and the TO+OΓ‐component at 5.0–5.09 eV. There was possible contribution of TA‐component in the spectral range of 5.18–5.26 eV and of EC band in the spectral range of 5.20–5.26 eV. The broadening of short‐wavelength edge of TO‐component of FE band at 81 K in the spectral range of 5.18–5.34 eV was also due to the contribution of TA‐component of EHL band. At the temperature of 298 K, the short‐wavelength edge of TO‐component of FE band practically did not change with increasing of laser intensity. Note that at the temperatures of liquid nitrogen and of RT, the long‐wavelength shoulder of TO‐component of FE band was presented in the PL spectrum. At RT, this broadening cannot be described in terms of thermal broadening.
Figure 16 shows the PL spectra excited at 193 nm with a peak intensity of 5 and 10 MW/cm2 for temperatures 83 and 297 K. At 193 nm PL excitation, the peak density of electron‐hole pairs was higher by 3–10 times than at 222 nm excitation. The radiation at 193 nm is absorbed in layer ∼13 μm. It was an order of magnitude less than that at 222 nm excitation. However, at 193 nm excitation the PL spectra at 83 K showed a smaller contribution EHL recombination band than at 222 nm excitation. At excitation on the same wavelength, the charge carrier density increase was resulted in the increase in the contribution of the EHL band. Presumably, there is a high density of structural defects in a surface layer, which are nonradiative recombination centers. It results in an increase in threshold FE density for EHL condensation. At the same time, the envelope of PL spectra essentially unchanged at RT with different peak intensities. Unlike excitation at 222 nm in PL spectra at 193 nm excitation, “tails” in the spectral region of <5.08 eV were observed that for the case of silicon was attributed to the EHP recombination .
Figure 17 shows the edge luminescence spectra of the HPHT single crystal C12 at 222 nm excitation. The EHL recombination band was not expressed clearly, and FE band was three times less intensive with the same peak intensities as for sample C10. The spectrum envelopes did not change during the peak intensity growth for both temperatures. This indicates a much greater density of nonradiative recombination centers in the sample C12, as compared to C10, which makes it difficult for EHL condensation in sample C12.
The EHL condensation was evident also in the temperature dependence of intensity of the dominant TO‐component of FE recombination band, as shown in Figure 18. In conditions where condensation EHL was insignificant, the maximum of temperature dependence of FE band intensity was close to 150 K (see Figure 18 for C10, 7 MW/cm2). The peak position arises from the FE lifetime temperature dependence (Eq. 4). As the EHL band intensity increases with the increase in laser intensity (10 MW/cm2), the additional maximum appeared at 190–220 K on the temperature dependence. As the intensity increases further (13 MW/cm2), the maximum at 190–220 K becomes dominant.
Note that for the C12 sample (Figure 18), the temperature dependences were differed. The FE band intensity remained practically unchanged in the temperature range of 130–190 K, i.e., the temperature maximum has been extended essentially, in contrast to the dependencies for the sample C10. With an increase in the peak laser intensity from 10 to 13 MW/cm2, the FE recombination intensity remained approximately unchanged. The additional maximum at 190–220 K was not clearly manifested.
When EHL droplet size increases, the FE density decreases due to their loss in the process of EHL condensation (FE intensity maximum shifts on the temperature dependence);
The FE condensation can take place up to temperatures of ∼220 K (EHL or EHP according to Mott);
The interaction cross‐section of nonradiative recombination centers with EHL drops is higher than with FEs (no intensity increase for sample C12 with the peak laser intensity increase from 10 to 13 MW/cm2).
The plot of phase diagram of electron‐hole system in the diamond as the temperature dependence on the charge carrier density is an important problem, which is not completely solved yet. The results of the plot of phase diagram are summarized in Figure 19. Experimental data and theoretical models were used in [14, 41, 42].
The experimental data [14, 42] were approximated (white squares in Figure 19) in the model of a degenerate plasma with the critical temperature = 173 K and the critical density = 4.05 1019 cm-3 (curve 1‐1 in Figure 19) and in the model of simple liquid near the critical point with the critical temperature = 173 K and the charge carrier density at the absolute zero of temperature = 1.0×1020 cm-3 (curve 2‐1 in Figure 19). Note that in [14, 42] the PL excitation of diamond samples was provided by laser radiation with duration of 5–8 ns at FWHM.
In Refs.  and , the model of a degenerate plasma was used also with the critical temperature = 160 K and the critical density = 3.33×1019 cm-3 (curve 1‐2 in Figure 19) and the model of simple liquid near the critical point  with a critical value temperature = 160 K and the charge carrier density at the absolute zero of temperature = 1.0×1020 cm-3 (curve 2‐2 in Figure 19). In Ref. , the laser pulses with subpicosecond duration (200 fs) were used for PL excitation. These experimental data (white circles in Figure 8) were obtained not only for right side of the phase diagram at densities higher than the critical, but at densities less than densities of the Mott transition. In Thomas‐Fermi approximation, the Mott transition has a threshold (curve 3 in Figure 19), but in Debye‐Huckel approximation the Mott transition criterion increases monotonically with the FE density (curve 4 in Figure 19).
Note that the values of the experimental densities in Figure 19 were obtained [14, 33, 42] through the form factors analysis of spectral components. But the density range of 4.1×1018–6.0×1019 cm-3 was not investigated.
Black rhombs in Figure 19 mark two sets of critical temperature and density for the EHL condensation. Different values of these quantities define the different calculated values in a degenerate plasma model and a phenomenological model of the gas‐liquid transition (curves 1‐1, 1‐2, 2‐1, 2‐2 in Figure 19). As shown in Figure 20, the several different values of critical temperature and density for the EHL condensation were defined or calculated for the diamond [16, 31–33] and other semiconductors [30, 32]. Furthermore, in  it was postulated that the critical temperature for the EHL condensation is in the range of 180–207 K at PL excitation by laser pulses of nanosecond duration. At the same time, in Ref. , the EHL was observed at temperatures below 120 K at PL excitation by subpicosecond laser pulses. Note that the critical EHL condensation temperatures were determined from the shapes of PL spectra, but the EHL critical densities were the calculated parameters. Significant differences between the nanosecond PL excitation [14, 42] and the femtosecond PL excitation [32, 33, 43] were caused by:
Different modes of excitation—stationary and pulsed, respectively. At the stationary mode of excitation, the pulse duration is significantly longer than the lifetime of EHL drops (less than 1 ns), which leads to the nucleation of drops during the excitation pulse. At the pulsed mode of excitation, the duration of laser radiation is shorter in three orders of magnitude than the lifetime of EHL drops, so the PL spectra of EHL recombination display drops formed around the same time.
Different peak intensities of laser excitation—a few to tens of MW/cm2 at the stationary mode and a few to tens of GW/cm2 at the pulsed mode. The peak intensity of laser radiation of gigawatt level leads to the generation of electron‐hole plasma with an initial density of more than 1020 cm-3 and causes the lattice heating due to the thermalization process of hot carriers and to the Auger recombination. This heating leads to a decrease in the critical temperature for the EHL condensation. For example, the authors of  were forced to use the understated initial FE density of 1018 cm-3 to perform calculations.
Different excitation wavelengths—218–220 and 215 nm, respectively. Due to the sharp increase in the absorption coefficient at the fundamental absorption edge of diamond , the shorter wavelengths are characterized by the thinner diamond layer in which absorption occurs. Therefore, at the same radiation intensity the shortwave radiation creates the higher initial FE density (see Figure 2). Moreover, the FE generation by shortwave photons creates “hot” carriers, which transmit more energy to the diamond lattice in the thermalization process, and it reduces the critical temperature.
As it can be seen from Figure 19, the modeling of phase diagram of gas FE‐EHL in the diamond describes satisfactorily the right branch, whereas, for the left branch the used models do not give a close description of experimental curves. The Mott criterion in Debye‐Huckel approximation describes most closely the boundary of FE gas existence (left branch of the phase diagram) at the FE densities of (1–4)×1018 cm-3. The values of critical temperatures and densities of experimental data of this work are marked as white triangles in Figure 19. Note that we have obtained the charge carrier densities according to expressions (1) and (2), but the values of critical temperature were taken from the positions of maxima on the temperature dependences of FE intensity (Figure 18).
Thus, the study of the EHL properties in the diamond has not yet responded to the key issues related to the conditions of condensation, evaporation and recombination. It remains still unclear what values of critical temperature and charge carrier density take place, and what their dependences on the impurity‐defective composition of samples, the excitation energy of particles and the duration of excitation pulses are like. The phase diagram of EHL existence requires the additional data in the density range of 4.0×1018–6.0×1019 cm-3. An important aspect is to determine the temperature dependence of intensities of TA‐ and TO+OΓ‐components of EHL recombination band. Does EC band give a contribution to PL spectra (their position, intensity)? In addition, there are two different concentrated states of nonequilibrium charge carriers in the diamond—EHL and EHP—which can have the same densities under certain conditions. So, the question arises: what are the differences between these two states?
6. Applications of recombination radiation in the diamond
The most obvious application of recombination radiation in the diamond is producing of light emitting devices (LED) based on diamond. The recombination radiation in the luminescence spectrum of diamond is located in the spectral range of 230–245 nm near the fundamental absorption edge (225 nm) (see Section 3). The band‐A of luminescence is located in the blue region of the visible spectrum with the maximum at 440 nm and has the recombination origin (see Section 4).
The LED's operating principle is based on the phenomenon of electroluminescence (EL)‐radiative recombination of electron‐hole pairs injected through contacts. The problem of making ohmic contacts to the diamond is solved in general . Typically, the ohmic contacts to the diamond consist of three‐layer metal deposition: carbide‐former metal (Ti, Ta, Mo, W, Cr), interdiffusion‐blocking layer (Pt) and protective/mounting layer (Au).
The first reports on EL in diamond were about semiconductor IIb type samples which were naturally doped with boron. The impurity of boron is an acceptor in diamond with an activation energy of 0.38 eV. In Ref. , the observation of the blue EL band of natural diamond sample with the maximum at 440 nm (the spectrum is not given) was reported. The EL was observed only at one polarity of bias of 50–100 B. In Ref. , a broadband EL (see Figure 21) was observed for several natural diamonds, presumably of IIb type (only a small fraction of the samples gave EL). In addition to the blue band with the maximum at 440 nm, the EL spectra of samples showed a broadband with several local maxima in the range from 500 to 650 nm. The green band of EL is appeared in the EL spectrum with a significant delay (tens of minutes). In general, the EL has demonstrated strong intensity fluctuations and has quenched when sample was cooled to a temperature below 100 K. This fact involves hopping conduction. In Ref. , the production of LED based on natural and HPHT diamonds was reported. The p‐ and n‐types of conductivity were created by ion implantation of boron and lithium, respectively. The emission spectrum of resulting p‐n transition is shown in Figure 22. The intensity of this transition decreases to zero with increasing temperature from -200 to 300°С, i.e., the band‐A of luminescence took place.
The development of CVD‐diamond synthesis and the ability to create p‐ (boron) and n‐ (0.47 eV phosphorus, lithium 0.29 eV) types of sample conductivity during the synthesis or during the subsequent ion implantation have led to reports on the EL research of CVD diamonds and the creation of LED based on various types of light‐emitting junctions in diamond [48–62]. The voltage of only tens of volts was used.
In 2002, the first reports on diamond LED development, emitting in the UVC range at 235 nm, appeared. In Ref. , a diamond LED p‐n junction was reported. The spectrum of LED emitted radiation is shown in Figure 22. The FE emission at 235 nm was characterized by intensity of an order of magnitude less than the intensity of band‐A. So, the low intensity of FE band indicates the unsatisfactory quality of doped layers. In Ref. , a similar device showed the same characteristics: the presence of FE peak at 235 nm and the intense band‐A.
In Refs.  and , the three‐layer structure diamond:N‐diamond:Ce‐SiO2 was studied. The EL spectrum showed the presence of wide and narrow bands in the spectral region 300–630 nm, arising from the band‐A, transitions in cesium atoms and nitrogen complexes. The monotonically decreasing tail was observed from 630 nm to the IR region. This structure demonstrated the brightness of 3.5 cd/m2 at RT and voltage of 150 V. In Ref. , the p‐n junction was formed in a CVD single crystal by ion implantation of boron and lithium with subsequent ion implantation of xenon. The resulting device demonstrated the EL broadband in the spectral region from 450 to 850 nm at voltage 100 V and RT. There were the vibronic system of Xe centers with ZPL at 812.5 nm and the weak emission of N‐V centers with ZPL at 575 nm.
In Ref. , a diamond‐based p‐i‐p structure was described, which showed the EL emission at 235 nm. Later the same group produced a p‐i‐p‐i‐p device emitting FE recombination band . In Ref. , a p‐i‐n transition doped with boron and phosphorus diamond layers was reported. At voltages of ±15 V, the p‐i‐n transition showed the dominant FE band at 235 nm, but the band‐A was suppressed. In Ref. , the С‐Si heterojunction demonstrated the red EL at RT. In Ref. , by ion implantation of B, As and P the p+‐p‐n structure was fabricated, which was based on p‐type HPHT diamond. At RT the p+‐p‐n structure demonstrated the effect of superluminescence in the spectral region of band‐A. In Ref. , the p‐C/n‐AlN‐heterojunction showed the dominant FE recombination band at 235 nm in the diamond layer. In  the p‐i‐n structure based on boron and phosphorus (ion implanted) CVD diamond layers showed the EL of N‐V defects at 575 nm. The authors of  suggested the method of creating graphite electrodes buried in a CVD diamond volume by the action of a focused MeV‐ion beam (He+). In the EL spectrum, there were the band‐A, the ZPL at 575 nm of N‐V centers, ZPL at 536.3 and 560.5 nm centers associated with helium and the broadband at 740 nm of Si‐V or V centers.
We note that due to the superior thermal conductivity (higher than of copper in 5 times), the diamond samples are used also as passive heat sinks for LEDs based on other semiconductor materials [61, 62].
At the time being diamond LEDs are not widely used. The main reason is the need to improve the quality of the diamond structures. Another reason-the fundamental: diamond is a semiconductor with indirect‐band structure, which reduces the efficiency of FE radiative recombination. At the same time, theoretical searches of ways to overcome the fundamental limitations of the diamond as a material for LEDs are being conducted. In  it was proposed to change the band structure of diamond to the direct‐gap by using the linear compression of ∼4% or lattice deformation by high doses of radiation damage. In  it was suggested to generate picosecond high‐power pulses at 235 nm by using the superluminescence in diamond‐cooperative spontaneous FE radiative recombination. The superluminescence is possible to be created in a ring resonator. At this condition, the Mott transition is not achieved.
Thus, the recombination radiation of diamond in the FE band (235 nm) or the band‐A (400–650 nm) may be applied in LEDs. Despite the fact that the EHL is an interesting phenomenon in terms of quantum effects, its practical use as a radiation source or any other thing has not been found. The situation is the same for all semiconductors. At the same time, diamond has a highest critical temperature of EHL condensation (>160 K), which still gives hope for the practical application.
In Ref. , the strengthening of photoconductivity in the CVD diamond under conditions of EHL existing was reported. Unlike a single FE, drops of EHL are not electrically neutral particle clusters. Due to the different work function of electrons and holes (due to the different effective masses), the EHL drops have a noncompensated surface charge . Consequently, the EHL drops may drift in the electric field and participate in the photocurrent. One can assume that the EHL drops in diamond could be used as controlled sources of photons, dynamic quantum dots, etc.
This chapter provides the original experimental data on the recombination radiation of natural and synthetic diamonds and the overview of the literature about.
The FE recombination radiation in the diamond is observed in CL, PL and EL spectra in the shape of the four‐component band containing TA‐, TO‐, LO‐ and TO+OΓ‐components at 5.325, 5.275, 5.254 and 5.117 eV, respectively. The “non‐diamond” carbon phase and impurity‐defect centers have the negative effect on the intensity of FE recombination band. The spectral position of FE band maximum at 5.275 eV did not change within the measurement error in the temperature range of 80–300 K, which contradicts the phenomenon of band gap decreasing with the increase in temperature. At low excitation levels, the temperature dependence of the FE recombination band intensity has the maximum at ∼150 K, which is in agreement with published data. The band‐A, caused by intrinsic defects of the structure containing the sp2‐hybridized carbon bonds, is located in the spectral range of 350–650 nm with the maximum at about 440 nm and is characterized by the decay time of 8–19 ms in the temperature range of 80–300 K. The band‐A reflects the perfection degree of diamond sample, i.e., the higher the band‐A intensity is, the greater the structure defect density is. There is a competition between the band‐A and FE recombination band in diamond. The emission spectrum of the band‐A may be imposed by vibronic bands of N3V, N2V, NV centers, which are characterized by decay times in the nanosecond time range. Therefore, the measurement of luminescence emission spectra with time resolution allows to separate in time the spectra of band‐A and other structural defects.
The recombination radiation of EHL drops in diamond is observed in CL and PL spectra at temperatures ≤200 K and peak carrier densities ≥(0.3–1.0)×1018 cm-3. The EHL band consists of three phonon components: TA, TO and TO+OΓ at 5.249, 5.211 and 5.075 eV, respectively. The dominant TO‐component of EHL band begins to appear in the form of long‐wavelength shoulder of TO‐component of FE band when the charge carrier density reaches the critical value. A further increase in carrier density leads to an increase in EHL band intensity. The surface layer of diamond sample is more defective than the inner volume. Therefore, the absorption of exciting radiation in a thin layer hampers EHL condensation compared with volume absorption. The EHL condensation results in displacement of FE band intensity maximum on the temperature dependence to higher temperatures up to 220 K, which can be interpreted as a decline of excitons in the EHL condensation process at lower temperatures. In this context, the critical temperature of EHL condensation is not established and, presumably, takes values in the range of 160–220 K. In this regard, the phase diagram of EHL existence requires clarification.
Currently, fabricated LEDs based on p‐n, p‐i‐n, p‐i‐p and other junctions in diamond structures have showed the possibility of spontaneous emission in the UV range at 235 nm and in the visible range of 400–800 nm. However, the diamond LEDs do not satisfy the requirements of efficiency and emission brightness. The main reason is the indirect‐band zone structure of diamond, which leads to a long FE lifetime and low efficiency of the three‐particle radiative recombination. To overcome this fundamental limitation, it was suggested to use the local deformation of the crystal, resulting in direct‐gap zone structure in diamond and the superluminescence in the ring resonator. The prospect of finding the solution to increase the efficiency and the emission brightness of the diamond‐based LEDs is associated with the possibility of obtaining the compact devices that are emitting in the UV‐C spectrum.
This report was prepared with the support of the Russian Foundation for Basic Research, Project No. 14‐02‐31132.
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