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Band structure investigations of GaN films using modulation spectroscopy
Applied Surface Science 253 (2006) 246–248 www.elsevier.com/locate/apsusc
Band structure investigations of GaN films using modulation spectroscopy V.P. Makhniy a, M.M. Slyotov a, V.V. Gorley b, P.P. Horley b,*, Yu.V. Vorobiev c, J. Gonza´lez-Herna´ndez d b
a Department of Optoelectronics, Chernivtsi National University, 2 Kotsyubynsky Str., 58012 Chernivtsi, Ukraine Department of Electronics and Energy Engineering, Chernivtsi National University, 2 Kotsyubynsky Str., 58012 Chernivtsi, Ukraine c CINVESTAV-IPN, Unidad Quere´taro, Libramiento Norponiente 2000, Fracc. Real de Juiriquilla, 76230 Quere´taro, QRO, Mexico d CIMAV, Miguel de Servantes No. 120, Complejo Industrial, 31109 Chihuahua, Mexico
Available online 10 July 2006
Abstract The paper presents investigation results concerning band structure of gallium nitride and position of intrinsic and associate defect levels. Main optical characteristics (transmission, reflection and luminescence) were measured in both ordinary and l-modulation mode for epitaxy-grown GaN films, allowing to determine valence band splitting caused by spin–orbital interaction (48 meV) and crystalline field (10 meV). Analysis of photoluminescence spectra made it possible to identify main recombination mechanisms involving donor and acceptor levels formed by intrinsic point defects VN ; V 0 Ga , and their associates. # 2006 Elsevier B.V. All rights reserved. Keywords: GaN films; Modulation spectroscopy; Photoluminescence spectra
1. Introduction Significant progress of modern optoelectronics was to the great degree achieved due to different applications of III-group nitride materials [1]. One of their representatives, the gallium nitride, plays an important part being intensively used as the base material for different types of photodetectors, light emitting diodes (LED) and laser diodes [1–3]. Physical and chemical properties of GaN, as well as its technological peculiarities, correlate well with the other nitrides. At the same time, its wide band gap makes it possible to develop devices operating in green, blue and ultra-violet spectral ranges [2]. GaN-based optical and electronic device properties depend significantly on technological regimes used for the base material. Monocrystalline gallium nitride can be obtained using optimized technology [1,2,4], strongly influencing its optical properties. Analysis of the published data [1–5] proves that for any technology used, there are always present certain band structure peculiarities and crystalline lattice defects, which in different
* Corresponding author. Tel.: +380 3722 46877; fax: +380 3722 46877. E-mail address: [email protected] (P.P. Horley). 0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2006.05.075
proportion determine characteristics of the resulted material, including optical reflection, absorption and luminescence. To perform a correct analysis of the factors mentioned, one can not rely much on classical methodology, because experimentally measured GaN spectra feature in general wide bands without clearly discernible structure, significantly complicating the interpretation of possible generation–recombination mechanisms [6]. To avoid this problem, one can use modulation spectroscopy, measuring differential spectra under small periodic wavelength perturbations [7,8]. This paper is focused on investigation of GaN band structure and possible generation–recombination processes using spectral data on optical properties of the material, obtained with a modulation spectroscopy method. 2. Experimental and investigation methodology GaN films with thickness of 0.5–5 mm were grown with chloride-hydride vapor phase epitaxy (HVPE) [2,3], pyrolisys of non-organic gallium compounds (PNC) [9] and molecular beam epitaxy (MBE) [1,2] over specially processed sapphire aAl2O3 substrates [4]. Developed optimized technology [1–3,9] allowed us to obtain monocrystalline material, which was confirmed with electron topography and X-ray studies.
V.P. Makhniy et al. / Applied Surface Science 253 (2006) 246–248
247
Fig. 1. Schematic diagram of experimental setup to measure l-modulated optical photoluminescence spectra: (1) laser with its power source (2); (3) sample; (4) optical cryostat; (5,9) lenses; (6) chopper; (7) monochromator MDR-23; (8) oscillating mirror (modulator); (10) photodetector; (11) selective amplifier; (12) synchronous detector; (13) plotting device; (14) sound generator; (15) power amplifier.
Investigation of GaN band structure was carried out using spectroscopic data on transmission Tv, reflection Rv and photoluminescence Nv, measured with multi-function equipment schematically depicted in Fig. 1 [6]. Changeable illumination sources and variable sample position (before or after diffraction monochromator MDR-23) allowed us to measure different spectra with the same photodetector FEU-79 (Fig. 1.10). Photoluminescence measurements were performed under LGI-21 laser illumination, characterized with the wavelength lmax 0.337 mm. Transmission (Tv) and reflection (Rv) studies were carried out using halogen lamp, positioning the sample as it is shown in Fig. 1 for Rv measurements, and before the lens 9 and photodetector 10 to obtain Tv spectra. The samples were put in the optical cryostat 4 with electronic thermoregulation system, which allowed to perform measurements in wide temperature ranges of 77– 500 K with 0.5 K precision. Special movable frame holding non-selectively reflecting mirror 8 was used to perform wavelength modulation and record differential spectra. When the modulator was turned off, the equipment allows measurements of ordinary spectra according to standard methodology, using the chopper 6 (Fig. 1). l-modulated spectra T 0 v ; R0 v and N 0 v , were measured under periodic oscillation of modulator mirror with a frequency v0 = 30 Hz; second derivative of photoluminescence N 00 v was obtained at double frequency 2v0. All the measurements were performed using synchronous detection system; resulting spectral data were post-processed, involving correction using device-specific error function. Multi-functionality of measuring equipment allowed to investigate different optical processes in the material studied under similar conditions, ensuring proper comparison and simplifying interpretation of experimental data. 3. Results and discussion Small periodic perturbations used in a modulation spectroscopy method result in much sharper differential spectral curves [7,8], revealing details unobservable in ordinary absorption, reflection and photoluminescence measurements. Our experimental data of differential T 0 v R0 v and N 00 v , spectra correlated well between each other and allowed to determine
Fig. 2. Spectra of l-modulated reflection (1) and transmission (2) of non-doped gallium nitride layers at T = 300 K. The inset shows band diagram of GaN in the vicinity of G-point.
main band parameters and investigate possible recombination phenomena, determining properties of non-doped GaN. Differential reflection spectrum R0 v , shown in Fig. 2, feature three distinct minima A, B and C. The position of the most prominent A-minimum corresponds to the band gap Eg = 3.42 eV of monocrystalline GaN [1,5]. The presence of two other minima can be explained by optical transitions involving valence subbands EVB and EVC (inset to Fig. 2), formed under the influence of crystalline field Dcr and spin–orbital Dso splitting, characteristic to wurtzite-lattice GaN [4]. Numerical values of Dcr and Dso for gallium nitride in the vicinity of G-point, still lack exact definition. Our experimental data on l-modulated reflection yielded transition energies DEAB ffi 10 meV, DEBC ffi 38 meV, correlating well with theoretical estimations [5] and allowing to obtain valence band splitting parameters for GaN as Dcr ffi 10 meV and Dso ffi 48 meV. Investigation of ordinary GaN transmission spectra did not revealed new information on parameters of deeper sub-bands because of large absorption coefficient of GaN. The general shape of Tv curve was smooth, without any prominent details, featuring abrupt decrease at photon energies close to Eg. On the contrary, lmodulated transmission spectra (Fig. 2) shows three peaks A, D, and E. The position of peak A confirms the material band gap value of Eg = 3.42 eV, obtained from R0 v studies. Two other smaller peaks appearing in Fig. 2 at hv ¼ 3:375 and 3:28 eV, corresponding to photon energies hv < Eg , have different nature. Position of peak D correlates well with depth of donor centers, created with nitrogen vacancy VN ; in similar way, peak E represents association centers ðVN V 0 Ga Þ [9]. Further studies of l-modulated photoluminescence (Fig. 3), confirmed this suggestion. In general, luminescence spectrum of non-doped GaN films at 300 K is by characterized with wide structureless band in ultra-violet spectral range with 3:1 eV ¼ hv ¼ 3:55 eV (Fig. 3, curve 1). As it was shown by previous investigation, this luminescence is determined by defects of crystalline structure, namely single-charged vacancies of nitrogen VN and gallium
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V.P. Makhniy et al. / Applied Surface Science 253 (2006) 246–248
one can estimate the possibility of associative center formation [9], assuming wave functions overlap for donor–acceptor pair components if they are situated closer than of ˚ . Resulting photon energy in this case Ri = (Rd + Ra) ffi 33 A will be equal to [12]: hv ¼ Eg Ed Ea þ
Fig. 3. Ordinary (1) and l-modulated photoluminescence spectrum measured at double frequency (2) for non-doped gallium nitride films.
V 0 Ga [9], forming donor and acceptor states taking part in luminescence phenomena either as separate centers or donor– acceptor pairs, formed by defect complexes ðVN V 0 Ga Þ. In general case, detection of corresponding bands is a complicated task, requiring special temperature studies to determine energy position of recombination center and investigation of excitation level L influence on the shape of spectral curve, carrying out corresponding analytical calculations using Alentsev–Fok method [10,11]. Wavelength modulation makes it possible to discern composing sub-bands in photoluminescence spectrum of nondoped GaN films. Experimental studies of the second derivative N 00 v reveals fine structure (Fig. 3, curve 2) with wide peak A, relatively narrow minima D, F and complex formation of several minima E. As it was expected, minima of second derivative correlate well with local maxima of ordinary Nv spectrum. Performing analysis of N 00 v features observed, one can find their connection with GaN defect subsystem. According to Lambe–Klick model, recombination involving free hole and bounded electron at donor level VN will result in light emission with photon energy corresponding to D-band. In similar way, component F is caused by recombination of free electrons with localized holes at acceptor levels V 0 Ga according to Klasens model [12], proving our assumption about high importance of intrinsic point defects—nitrogen and gallium vacancies forming donor and acceptor centers. The nature of complex E-band with greater semi-width and clearly defined inner structure can be explained with possible formation of donor–acceptor pairs from oppositely charged nitrogen and gallium vacancies, if the latter becomes situated at certain distance Ri between each other or closer. Considering Bohr radius estimation for donors (Rd) and acceptors (Ra) [12]: 1 mn;p ; (1) Rd;a ¼ 0:53e m0
e2 ; 4pee0 Ri
(2)
which in our case for Ed = 0.042 eV, Ea = 0.24 eV and e = 9.6 can be estimated as 3.18 eV for suggested Ri and 3.35 eV for ˚ (GaN lattice constant). The energies obtained corRi = 5.6 A relate well with experimental data, almost coinciding with limits of complex band E. Its four distinct minima at 3.32, 3.28, 3.25 and 3.21 eV, to our opinion, can be explained by the presence of associates with different distances Ri between the components. Luminescence at photon energies greater than Eg (Fig. 3, Aband) may appear as a result of inter-band transitions. Estimating luminescence energy resulting from inter-band recombination as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hv Eg 2 N v eðhvÞ hv Eg exp (3) kT for GaN band gap value Eg = 3.42 eV, positive correspondence with experimental data is obtained. 4. Conclusions Using l-modulation spectroscopy for investigation of reflection, transmission and luminescence spectra allowed determine characteristic peculiarities of non-doped GaN band diagram, caused by splitting of valence band into two sub-bands under action of crystalline field potential and spin–orbital interaction. Modulated transmission and photoluminescence spectra revealed information about intrinsic point defects VN and V 0 Ga , forming local donor and acceptor states and associative centers ðVN V 0 Ga Þ leading to different generation–recombination processes in addition to ordinary inter-band transitions. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
P. Kung, M. Razeghi, Opto-Electron. Rev. 8 (2000) 201. F.A. Ponce, D.P. Bouz, Nature 386 (1997) 351. Bo Monemar, J. Cryst. Growth 189/190 (1998) 1. W.A. Melton, J.I. Pankove, J. Cryst. Growth 178 (1997) 168. G.D. Chen, M. Smith, J.Y. Liu, H.X. Jiang, S.-H. Wei, M. Asif Khan, C.J. Sun, Appl. Phys. Lett. 68 (1996) 2784. V.P. Makhniy, M.M. Slyotov, E.V. Stets, I.V. Tkachenko, V.V. Gorley, P.P. Horley, Thin Solid Films 450 (2004) 222. M. Cardona, Modulation Spectroscopy, Mir, Moscow, 1972, p. 416. V.P. Makhniy, Principles of Modulation Spectroscopy, Ruta, Chernivtsi, 2001, p. 102. A.V. Dobrynin, M.M. Slyotov, V.V. Smirnov, J. Appl. Spectrosc. 55 (1991) 861. M.V. Fok, Tr. FIAN USSR 59 (1972) 3. A.N. Geogrobiani, A.N. Gruzintsev, Yu.V. Ozerov, I.M. Tiginyanu, Tr. FIAN USSR 163 (1985) 39. V.V. Serdyuk, Yu.F. Vaksman, Luminescence of Semiconductors, Vyshcha shkola, Kiev, 1988, p. 200.
Band structure investigations of GaN films using modulation spectroscopy V.P. Makhniy a, M.M. Slyotov a, V.V. Gorley b, P.P. Horley b,*, Yu.V. Vorobiev c, J. Gonza´lez-Herna´ndez d b
a Department of Optoelectronics, Chernivtsi National University, 2 Kotsyubynsky Str., 58012 Chernivtsi, Ukraine Department of Electronics and Energy Engineering, Chernivtsi National University, 2 Kotsyubynsky Str., 58012 Chernivtsi, Ukraine c CINVESTAV-IPN, Unidad Quere´taro, Libramiento Norponiente 2000, Fracc. Real de Juiriquilla, 76230 Quere´taro, QRO, Mexico d CIMAV, Miguel de Servantes No. 120, Complejo Industrial, 31109 Chihuahua, Mexico
Available online 10 July 2006
Abstract The paper presents investigation results concerning band structure of gallium nitride and position of intrinsic and associate defect levels. Main optical characteristics (transmission, reflection and luminescence) were measured in both ordinary and l-modulation mode for epitaxy-grown GaN films, allowing to determine valence band splitting caused by spin–orbital interaction (48 meV) and crystalline field (10 meV). Analysis of photoluminescence spectra made it possible to identify main recombination mechanisms involving donor and acceptor levels formed by intrinsic point defects VN ; V 0 Ga , and their associates. # 2006 Elsevier B.V. All rights reserved. Keywords: GaN films; Modulation spectroscopy; Photoluminescence spectra
1. Introduction Significant progress of modern optoelectronics was to the great degree achieved due to different applications of III-group nitride materials [1]. One of their representatives, the gallium nitride, plays an important part being intensively used as the base material for different types of photodetectors, light emitting diodes (LED) and laser diodes [1–3]. Physical and chemical properties of GaN, as well as its technological peculiarities, correlate well with the other nitrides. At the same time, its wide band gap makes it possible to develop devices operating in green, blue and ultra-violet spectral ranges [2]. GaN-based optical and electronic device properties depend significantly on technological regimes used for the base material. Monocrystalline gallium nitride can be obtained using optimized technology [1,2,4], strongly influencing its optical properties. Analysis of the published data [1–5] proves that for any technology used, there are always present certain band structure peculiarities and crystalline lattice defects, which in different
* Corresponding author. Tel.: +380 3722 46877; fax: +380 3722 46877. E-mail address: [email protected] (P.P. Horley). 0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2006.05.075
proportion determine characteristics of the resulted material, including optical reflection, absorption and luminescence. To perform a correct analysis of the factors mentioned, one can not rely much on classical methodology, because experimentally measured GaN spectra feature in general wide bands without clearly discernible structure, significantly complicating the interpretation of possible generation–recombination mechanisms [6]. To avoid this problem, one can use modulation spectroscopy, measuring differential spectra under small periodic wavelength perturbations [7,8]. This paper is focused on investigation of GaN band structure and possible generation–recombination processes using spectral data on optical properties of the material, obtained with a modulation spectroscopy method. 2. Experimental and investigation methodology GaN films with thickness of 0.5–5 mm were grown with chloride-hydride vapor phase epitaxy (HVPE) [2,3], pyrolisys of non-organic gallium compounds (PNC) [9] and molecular beam epitaxy (MBE) [1,2] over specially processed sapphire aAl2O3 substrates [4]. Developed optimized technology [1–3,9] allowed us to obtain monocrystalline material, which was confirmed with electron topography and X-ray studies.
V.P. Makhniy et al. / Applied Surface Science 253 (2006) 246–248
247
Fig. 1. Schematic diagram of experimental setup to measure l-modulated optical photoluminescence spectra: (1) laser with its power source (2); (3) sample; (4) optical cryostat; (5,9) lenses; (6) chopper; (7) monochromator MDR-23; (8) oscillating mirror (modulator); (10) photodetector; (11) selective amplifier; (12) synchronous detector; (13) plotting device; (14) sound generator; (15) power amplifier.
Investigation of GaN band structure was carried out using spectroscopic data on transmission Tv, reflection Rv and photoluminescence Nv, measured with multi-function equipment schematically depicted in Fig. 1 [6]. Changeable illumination sources and variable sample position (before or after diffraction monochromator MDR-23) allowed us to measure different spectra with the same photodetector FEU-79 (Fig. 1.10). Photoluminescence measurements were performed under LGI-21 laser illumination, characterized with the wavelength lmax 0.337 mm. Transmission (Tv) and reflection (Rv) studies were carried out using halogen lamp, positioning the sample as it is shown in Fig. 1 for Rv measurements, and before the lens 9 and photodetector 10 to obtain Tv spectra. The samples were put in the optical cryostat 4 with electronic thermoregulation system, which allowed to perform measurements in wide temperature ranges of 77– 500 K with 0.5 K precision. Special movable frame holding non-selectively reflecting mirror 8 was used to perform wavelength modulation and record differential spectra. When the modulator was turned off, the equipment allows measurements of ordinary spectra according to standard methodology, using the chopper 6 (Fig. 1). l-modulated spectra T 0 v ; R0 v and N 0 v , were measured under periodic oscillation of modulator mirror with a frequency v0 = 30 Hz; second derivative of photoluminescence N 00 v was obtained at double frequency 2v0. All the measurements were performed using synchronous detection system; resulting spectral data were post-processed, involving correction using device-specific error function. Multi-functionality of measuring equipment allowed to investigate different optical processes in the material studied under similar conditions, ensuring proper comparison and simplifying interpretation of experimental data. 3. Results and discussion Small periodic perturbations used in a modulation spectroscopy method result in much sharper differential spectral curves [7,8], revealing details unobservable in ordinary absorption, reflection and photoluminescence measurements. Our experimental data of differential T 0 v R0 v and N 00 v , spectra correlated well between each other and allowed to determine
Fig. 2. Spectra of l-modulated reflection (1) and transmission (2) of non-doped gallium nitride layers at T = 300 K. The inset shows band diagram of GaN in the vicinity of G-point.
main band parameters and investigate possible recombination phenomena, determining properties of non-doped GaN. Differential reflection spectrum R0 v , shown in Fig. 2, feature three distinct minima A, B and C. The position of the most prominent A-minimum corresponds to the band gap Eg = 3.42 eV of monocrystalline GaN [1,5]. The presence of two other minima can be explained by optical transitions involving valence subbands EVB and EVC (inset to Fig. 2), formed under the influence of crystalline field Dcr and spin–orbital Dso splitting, characteristic to wurtzite-lattice GaN [4]. Numerical values of Dcr and Dso for gallium nitride in the vicinity of G-point, still lack exact definition. Our experimental data on l-modulated reflection yielded transition energies DEAB ffi 10 meV, DEBC ffi 38 meV, correlating well with theoretical estimations [5] and allowing to obtain valence band splitting parameters for GaN as Dcr ffi 10 meV and Dso ffi 48 meV. Investigation of ordinary GaN transmission spectra did not revealed new information on parameters of deeper sub-bands because of large absorption coefficient of GaN. The general shape of Tv curve was smooth, without any prominent details, featuring abrupt decrease at photon energies close to Eg. On the contrary, lmodulated transmission spectra (Fig. 2) shows three peaks A, D, and E. The position of peak A confirms the material band gap value of Eg = 3.42 eV, obtained from R0 v studies. Two other smaller peaks appearing in Fig. 2 at hv ¼ 3:375 and 3:28 eV, corresponding to photon energies hv < Eg , have different nature. Position of peak D correlates well with depth of donor centers, created with nitrogen vacancy VN ; in similar way, peak E represents association centers ðVN V 0 Ga Þ [9]. Further studies of l-modulated photoluminescence (Fig. 3), confirmed this suggestion. In general, luminescence spectrum of non-doped GaN films at 300 K is by characterized with wide structureless band in ultra-violet spectral range with 3:1 eV ¼ hv ¼ 3:55 eV (Fig. 3, curve 1). As it was shown by previous investigation, this luminescence is determined by defects of crystalline structure, namely single-charged vacancies of nitrogen VN and gallium
248
V.P. Makhniy et al. / Applied Surface Science 253 (2006) 246–248
one can estimate the possibility of associative center formation [9], assuming wave functions overlap for donor–acceptor pair components if they are situated closer than of ˚ . Resulting photon energy in this case Ri = (Rd + Ra) ffi 33 A will be equal to [12]: hv ¼ Eg Ed Ea þ
Fig. 3. Ordinary (1) and l-modulated photoluminescence spectrum measured at double frequency (2) for non-doped gallium nitride films.
V 0 Ga [9], forming donor and acceptor states taking part in luminescence phenomena either as separate centers or donor– acceptor pairs, formed by defect complexes ðVN V 0 Ga Þ. In general case, detection of corresponding bands is a complicated task, requiring special temperature studies to determine energy position of recombination center and investigation of excitation level L influence on the shape of spectral curve, carrying out corresponding analytical calculations using Alentsev–Fok method [10,11]. Wavelength modulation makes it possible to discern composing sub-bands in photoluminescence spectrum of nondoped GaN films. Experimental studies of the second derivative N 00 v reveals fine structure (Fig. 3, curve 2) with wide peak A, relatively narrow minima D, F and complex formation of several minima E. As it was expected, minima of second derivative correlate well with local maxima of ordinary Nv spectrum. Performing analysis of N 00 v features observed, one can find their connection with GaN defect subsystem. According to Lambe–Klick model, recombination involving free hole and bounded electron at donor level VN will result in light emission with photon energy corresponding to D-band. In similar way, component F is caused by recombination of free electrons with localized holes at acceptor levels V 0 Ga according to Klasens model [12], proving our assumption about high importance of intrinsic point defects—nitrogen and gallium vacancies forming donor and acceptor centers. The nature of complex E-band with greater semi-width and clearly defined inner structure can be explained with possible formation of donor–acceptor pairs from oppositely charged nitrogen and gallium vacancies, if the latter becomes situated at certain distance Ri between each other or closer. Considering Bohr radius estimation for donors (Rd) and acceptors (Ra) [12]: 1 mn;p ; (1) Rd;a ¼ 0:53e m0
e2 ; 4pee0 Ri
(2)
which in our case for Ed = 0.042 eV, Ea = 0.24 eV and e = 9.6 can be estimated as 3.18 eV for suggested Ri and 3.35 eV for ˚ (GaN lattice constant). The energies obtained corRi = 5.6 A relate well with experimental data, almost coinciding with limits of complex band E. Its four distinct minima at 3.32, 3.28, 3.25 and 3.21 eV, to our opinion, can be explained by the presence of associates with different distances Ri between the components. Luminescence at photon energies greater than Eg (Fig. 3, Aband) may appear as a result of inter-band transitions. Estimating luminescence energy resulting from inter-band recombination as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hv Eg 2 N v eðhvÞ hv Eg exp (3) kT for GaN band gap value Eg = 3.42 eV, positive correspondence with experimental data is obtained. 4. Conclusions Using l-modulation spectroscopy for investigation of reflection, transmission and luminescence spectra allowed determine characteristic peculiarities of non-doped GaN band diagram, caused by splitting of valence band into two sub-bands under action of crystalline field potential and spin–orbital interaction. Modulated transmission and photoluminescence spectra revealed information about intrinsic point defects VN and V 0 Ga , forming local donor and acceptor states and associative centers ðVN V 0 Ga Þ leading to different generation–recombination processes in addition to ordinary inter-band transitions. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
P. Kung, M. Razeghi, Opto-Electron. Rev. 8 (2000) 201. F.A. Ponce, D.P. Bouz, Nature 386 (1997) 351. Bo Monemar, J. Cryst. Growth 189/190 (1998) 1. W.A. Melton, J.I. Pankove, J. Cryst. Growth 178 (1997) 168. G.D. Chen, M. Smith, J.Y. Liu, H.X. Jiang, S.-H. Wei, M. Asif Khan, C.J. Sun, Appl. Phys. Lett. 68 (1996) 2784. V.P. Makhniy, M.M. Slyotov, E.V. Stets, I.V. Tkachenko, V.V. Gorley, P.P. Horley, Thin Solid Films 450 (2004) 222. M. Cardona, Modulation Spectroscopy, Mir, Moscow, 1972, p. 416. V.P. Makhniy, Principles of Modulation Spectroscopy, Ruta, Chernivtsi, 2001, p. 102. A.V. Dobrynin, M.M. Slyotov, V.V. Smirnov, J. Appl. Spectrosc. 55 (1991) 861. M.V. Fok, Tr. FIAN USSR 59 (1972) 3. A.N. Geogrobiani, A.N. Gruzintsev, Yu.V. Ozerov, I.M. Tiginyanu, Tr. FIAN USSR 163 (1985) 39. V.V. Serdyuk, Yu.F. Vaksman, Luminescence of Semiconductors, Vyshcha shkola, Kiev, 1988, p. 200.