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Raman spectroscopy of disorder effects in AlxGa1−xN solid solutions
Materials Science and Engineering B59 (1999) 222 – 225
Raman spectroscopy of disorder effects in Alx Ga1 − x N solid solutions Valery Y. Davydov a,*, Igor N. Goncharuk a, Marina V. Baidakova a, Alexander N. Smirnov a, Arsen V. Subashiev b, Jochen Aderhold c, Jens Stemmer c, Thomas Rotter c, Dirk Uffmann c, Olga Semchinova c a
Ioffe Physicotechnical Institute, 194021 St. Petersburg, Russia b State Technical Uni6ersity, 195251 St. Petersburg, Russia c LfI, Uni6ersita¨t Hanno6er, 30167 Hanno6er, Germany
Abstract The results of Raman spectroscopic studies of the disorder effects in hexagonal Alx Ga1 − x N epitaxial layers grown by MBE and HVPE on different substrates for a large range of Al concentrations are presented. The width of the nonpolar phonon line with E2 symmetry results from the inhomogeneous broadening due to spatial fluctuations in the Al content. The abnormally small broadening of the A1(TO) polar phonon mode for x or (1 − x) 1 and the large broadening for x$ 0.5 – 0.7 are attributed to the specific frequency dependence of the density of states for the branch with the directional dispersion in pure crystals. Thus the Raman spectrum is found to be highly sensitive to the composition of Alx Ga1 − x N epitaxial layers and its inhomogeneity. It is shown that in the estimation of the crystal composition, on the basis of Raman data, the influence of the homogeneous strain effects could be excluded via measuring a linear combination of two Raman line frequencies. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Disordered systems; Inelastic light scattering; Phonons; Semiconductors
1. Introduction GaN, AlN, and their solid solutions (Alx Ga1 − x N) are known to be promising materials for microelectronics and optoelectronics. The possibility to change the band gap in a wide range of energies (from 3.4 to 6.2 eV) makes these compounds useful for fabrication of light emitters and detectors operating in the blue and near ultraviolet regions of the spectrum. Therefore it is highly important to prepare a solid solution with a strictly specified composition. Raman spectroscopy is one of the most efficient techniques used for the characterization of semiconducting materials. It is a rapid nondestructive method which can provide information with a high spatial resolution of the order of 3–5 mm. The behavior of the phonon modes in ternary Alx Ga1 − xN compounds was studied by Raman scattering in [1 –3]. The possibilities of Raman spectroscopy for the * Corresponding author. Fax: +7-812-2471017. E-mail address: [email protected] (V.Y. Davydov)
characterization of disorder effects in epitaxial layers of solid solutions of Alx Ga1 − x N will be demonstrated in this paper.
2. Experimental details The Alx Ga1 − x N layers were grown on a thin GaN layer deposited on the c-plane sapphire in a Riber 32 molecular beam epitaxy system. The chamber was equipped with a CARS25 plasma source from Oxford Applied Research to generate nitrogen radicals and conventional Knudsen cells to evaporate gallium and aluminum. After transferring into the growth chamber the sapphire substrates were heated to 530°C and exposed to the nitrogen plasma to get a more reactive surface for the nucleation step, which is essential for epitaxial growth [4]. The nucleation was done at a substrate temperature of 620°C and was directly followed by annealing under a flux of nitrogen radicals at 700°C. Thereafter, the substrate temperature was low-
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ered slightly and the growth of the nominally 40 nm thick GaN layer was performed. The growth of the Alx Ga1 − x N layers (0.5 – 0.6 mm) occurred at the same temperature. The Ga flux was kept constant throughout the process and the Al content was controlled by adjusting the Al flux. Thick Alx Ga1 − x N layers (10–20 mm) were grown on SiC and (0001) a-Al2O3 substrates using chloride-hydride-vapor-phase epitaxy (CHVPE). Raman spectra of Alx Ga1 − x N layers were measured in the back-scattering configuration at room temperature. Two directions of the incident laser beams were used: along the c-axis of the wurtzite structure (z direction) and perpendicular to it (x direction). An Ar + laser (l =488 nm) was used as a source of excitation. The structural quality of the layers and the alloy composition were controlled by X-ray diffraction and electron probe microanalysis (EPMA).
3. Results and discussion The hexagonal GaN, AlN, and their solid solutions (Alx Ga1 − x N) crystallize in the wurtzite structure having six optical modes (1A1(TO) +1A1(LO)+ 1E1(TO)+1E1(LO) + 2E2) active in the first-order Raman scattering. The major contribution to the Raman scattering intensity comes from the transverse polar A1(TO) and high-frequency nonpolar E2 phonon modes. The Porto notation will be used to indicate the polarization configuration used in each experiment. The A1(TO) mode was measured in the x(zz)x¯ scattering geometry (Raman spectra were taken from the edge of the layer). The E2 and A1(LO) modes were observed in the z(yy)z¯ geometry (Raman spectra were taken from the Alx Ga1 − x N layer plane). In the Alx Ga1 − x N solid solutions, the frequency of the A1(TO) phonon shifts with varying composition from 532 cm − 1 in GaN to 612 cm − 1 in AlN and exhibits a one-mode type behavior shown in Fig. 1, while the E2 phonon mode demonstrates a two-mode type behavior presented in Fig. 2 [1,2]. Large frequency shifts depending on the Al content and the one-mode type behavior are also typical of the longitudinal polar A1(LO) phonon line (from 734 cm − 1 in GaN to 890 cm − 1 in AlN). Note that the frequency position of the A1(LO) line depends not only on the Al content, but also on the concentration of free carriers in the sample which is associated with the presence of uncontrollable dopants.
3.1. Deformation effects The analysis of the Raman data and EPMA results have revealed considerably differing positions of the A1(TO) and E2 lines for the samples having the same composition and grown on different or on the identical
Fig. 1. Raman spectra for different Alx Ga1 − x N compositions obtained in the geometry corresponding to the A1(TO) and E1(LO) phonon modes. For clarity, the spectrum intensity near the E1(LO) phonon modes is doubled.
substrates. As will be shown below, this is due to the difference in residual homogeneous strains in the layers. Measurements of the deformation displacement constants of the A1(TO) and E2 lines in GaN performed in [5] have shown that their ratio is R= 0.51. A similar value R=0.55 has also been obtained in our experiments for these lines in AlN. Since the symmetry of vibrations does not change in the alloys, it can be
Fig. 2. Raman spectra for different Alx Ga1 − x N compositions obtained in the geometry corresponding to the E2 and A1(LO) phonon modes. For clarity, the spectrum intensity near the E1(LO) phonon modes is magnified. The black triangles show the position of the A1(TO) phonon symmetry line which is forbidden in this scattering geometry. The asterisks indicate the lines corresponding to the phonon modes of the sapphire substrate.
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Fig. 3. Variations in Dv=v(A1(TO))−v(E2)R as a function of x in Alx Ga1 − x N layers. The solid line corresponds to fitting with the formula v= 243 + 62x−62x 2 + 42x 3 (cm − 1).
expected that the ratio R changes only slightly with varying composition. Then the difference, Dv = v(A1(TO))− v(E2)R, depends only on the relative contents of the components in the solution and is strain-independent. The experimental values of Dv for a number of samples (grown by both the MBE and CHVPE techniques) with different contents of Al are shown in Fig. 3. The obtained data show that Dv is a smooth function of the composition of the samples grown by different techniques and on different substrates. Thus, (i) the observed random shifts of the lines in the Raman spectra of the Alx Ga1 − x N epitaxial layers are due to strain effects, and (ii) the measurements of the Dvvalues can be used for the evaluation of the composition of the Alx Ga1 − x N layers.
are expected to be linear with respect to concentration. The experimentally observed line width changes with x are poorly approximated by a linear fit. Therefore, this mechanism is inefficient. (ii) The inhomogeneous broadening effects induced by the impurity fluctuations, similar to the mechanisms of the excitonic line broadening [6]. First of all, these effects can originate from the phonon scattering by the Gaussian local fluctuations of composition in homogeneous mixed crystal. In this case the increase in the line width is known to be described by G=c1x 2(1−x 2) and should be accompanied by a considerable asymmetry of the phonon line. This type of behavior is inconsistent with our experimental findings too. The experimental data obtained for high-quality crystals are fairly well approximated by G8 x(1− x) (see Fig. 4.). This dependence is known to originate from the inhomogeneous broadening mechanism [7] and is often observed in the excitonic luminescence spectra of AIIIBV (and Alx Ga1 − x N) mixed crystals. In the case of the excitons the dependence is typical for the local exciton line broadening due to Gaussian fluctuations in the Al (or Ga) concentration within the exciton localization radius. The same mechanism can be efficient in the case of the phonons in a crystal having the micro crystallite structure. Then the broadenings can be attributed to the content fluctuations in micro crystals. For this broadening mechanism one has: G= c2
(v a
x(1−x) 0 (x a
(1)
where a0 is the lattice parameter and c2 is a constant of the order of unity. The spatial dimension a in which phonons are confined enters Eq. (1) and, therefore, it can be extracted from the fit to the experimental data. The localization radius for the E2 phonons in Alx Ga1 − x N
3.2. Nonpolar phonon E2 line broadening In the strained layer samples there is a spread of the line broadenings for a given Al content caused by inhomogeneous deformation of the layers. This broadening is negligible in high quality samples. The Raman spectra of the GaN- and AlN-like nonpolar phonon lines with E2 symmetry in the Alx Ga1 − x N epitaxial layers exhibit substantial broadening even for crystals with a high structural quality (controlled by X-ray diffraction patterns). Broadening is a sharply rising function of the Al or Ga content at small concentrations of these components in the solid solution. The line full width at half maximum (FWHM) as a function of x for high quality layers is shown in Fig. 4. There are several mechanisms for nonpolar phonon line broadening in mixed crystals. These mechanisms lead to different concentration dependences of the FWHM: (i) Changes in the homogeneous (anharmonic) line width
Fig. 4. Dependence of the width of the upper and lower E2 lines on the Al content in Alx Ga1 − x N layers.
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tions for the polar phonon modes with a strong directional dependence for hexagonal crystals [8]. The width of the A1(LO) phonon line. The experimentally observed A1(LO) line width dependence is close to G= c3x(1− x). For the polar phonon with a small directional dispersion the main broadening mechanism is a random dipole–dipole interaction that leads to the observed FWHM dependence on x, where the coefficient c3 can be estimated using the value of the A1 mode LO-TO splitting. The estimation gives c3 $ (v 2LO − v 2TO)/vLO, which agrees fairly well with the experiment. The excess broadening of the Raman line is associated with the crystal structure imperfections, which is consistent with the X-ray diffraction data. Therefore, the FWHM of the A1(TO) phonon line can be used to estimate the structural quality of the layer. Fig. 5. Dependence of the width of the A1(TO) and A1(LO) lines on the Al content in Alx Ga1 − x N layers.
crystals is found to be a :6 – 8.5 nm. This estimate is somewhat lower than the results obtained from the X-ray data analysis. The difference can be attributed to the inhomogeneous distribution of the Al content inside a micro crystal. Additional broadening of the E2 phonon line is observed in some crystals which have larger luminescence and X-ray diffraction line widths that can be attributed to a high concentration of structural defects. Therefore, the excess broadening can be used to estimate the structural quality of layers. The width of the polar A1(TO) phonon line. The Raman spectra for the A1(TO) phonons show that the A1(TO) line width changes only slightly with a change in the Al content in mixed crystals (see the solid line in Fig. 5.). In structurally perfect crystals the line width is close to G= 7.5 cm − 1 both for x 1 and (1 − x)1, with a sharp rise near x $ 0.7. The long-wavelength vibrations of the A1(TO) symmetry with a substantial directional dispersion have an anomalously small density of states. The edge dependence of it varies from the quasi-four-dimensional (in the region x 1) to quasifive-dimensional vibrational system at (1−x) 1. As a result, in the mixed crystal A1(TO) phonons are weakly scattered by the fluctuations in x and the probability that phonons will be localized in the region of high fluctuation of x is exponentially small [8]. Therefore, the concentrational broadening of the A1(TO) line is expected to be exponentially small for all mixed crystal compositions except a small range near x =xc, where xc is estimated to be xc $0.5 – 0.7. The broadening becomes substantial when the phonon branch has small dispersion in the Brillouin zone and the density of the phonon states at the spectrum edge becomes large enough. Thus the observed dependence of FWHM for the A1(TO) line is consistent with the theoretical predic.
4. Conclusions The frequencies and the FWHM of the Raman-active long-wavelength phonons have been measured in the whole composition range of Alx Ga1 − x N epitaxial layers grown on different substrates. It is shown that the errors in the estimates of the ctystal composition caused by homogeneous strain effects could be eliminated by using a linear combination of two Raman line frequencies. We show that the behavior of the line widths of the phonons with different symmetries can be attributed to different mechanisms of the inhomogeneous line broadening induced by the disorder effects.
Acknowledgements VYuD, ING, MVB, ANS, and AVS appreciate the support of the Ministry of Sciences of Russia, Programme ‘Physics of Solid State Nanostructures’, grant 97-1035 and grant 97-1091.
References [1] A. Cros, H. Angerer, O. Ambacher, M. Stutzmann, R. Hopler, T. Metzger, Solid State Commun. 104 (1997) 35. [2] F. Demangeot, J. Groenen, J. Frandon, et al., MRS Int. J. Nitride Semicond. Res. 2 (1997) 40. [3] L. Bergman, M.D. Bremser, W.G. Perry, R.F. Davis, M. Dutta, R.J. Nemanich, Appl. Phys. Lett. 71 (1997) 2157. [4] S. Yoshida, S. Misawa, S. Gonda, J. Appl. Phys. 53 (1982) 6844. [5] V.Y. Davydov, N.S. Averkiev, I.N. Goncharuk, et al., J. Appl. Phys. 82 (1997) 5097. [6] A.L. Efros, M.E. Raikh, in: R.J. Elliott, I.P. Ipatova (Eds.), Optical Properties of Mixed Crystals, Elseiver Science, Amsterdam, 1988, p. 135. [7] E.F. Schubert, E.O. Gobel, Y. Horikoshi, K. Ploog, H.G. Queisser, Phys. Rev. B 30 (1984) 813. [8] I.P. Ipatova, V.A. Shchukin, JETPh 97 (1990) 990.
Raman spectroscopy of disorder effects in Alx Ga1 − x N solid solutions Valery Y. Davydov a,*, Igor N. Goncharuk a, Marina V. Baidakova a, Alexander N. Smirnov a, Arsen V. Subashiev b, Jochen Aderhold c, Jens Stemmer c, Thomas Rotter c, Dirk Uffmann c, Olga Semchinova c a
Ioffe Physicotechnical Institute, 194021 St. Petersburg, Russia b State Technical Uni6ersity, 195251 St. Petersburg, Russia c LfI, Uni6ersita¨t Hanno6er, 30167 Hanno6er, Germany
Abstract The results of Raman spectroscopic studies of the disorder effects in hexagonal Alx Ga1 − x N epitaxial layers grown by MBE and HVPE on different substrates for a large range of Al concentrations are presented. The width of the nonpolar phonon line with E2 symmetry results from the inhomogeneous broadening due to spatial fluctuations in the Al content. The abnormally small broadening of the A1(TO) polar phonon mode for x or (1 − x) 1 and the large broadening for x$ 0.5 – 0.7 are attributed to the specific frequency dependence of the density of states for the branch with the directional dispersion in pure crystals. Thus the Raman spectrum is found to be highly sensitive to the composition of Alx Ga1 − x N epitaxial layers and its inhomogeneity. It is shown that in the estimation of the crystal composition, on the basis of Raman data, the influence of the homogeneous strain effects could be excluded via measuring a linear combination of two Raman line frequencies. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Disordered systems; Inelastic light scattering; Phonons; Semiconductors
1. Introduction GaN, AlN, and their solid solutions (Alx Ga1 − x N) are known to be promising materials for microelectronics and optoelectronics. The possibility to change the band gap in a wide range of energies (from 3.4 to 6.2 eV) makes these compounds useful for fabrication of light emitters and detectors operating in the blue and near ultraviolet regions of the spectrum. Therefore it is highly important to prepare a solid solution with a strictly specified composition. Raman spectroscopy is one of the most efficient techniques used for the characterization of semiconducting materials. It is a rapid nondestructive method which can provide information with a high spatial resolution of the order of 3–5 mm. The behavior of the phonon modes in ternary Alx Ga1 − xN compounds was studied by Raman scattering in [1 –3]. The possibilities of Raman spectroscopy for the * Corresponding author. Fax: +7-812-2471017. E-mail address: [email protected] (V.Y. Davydov)
characterization of disorder effects in epitaxial layers of solid solutions of Alx Ga1 − x N will be demonstrated in this paper.
2. Experimental details The Alx Ga1 − x N layers were grown on a thin GaN layer deposited on the c-plane sapphire in a Riber 32 molecular beam epitaxy system. The chamber was equipped with a CARS25 plasma source from Oxford Applied Research to generate nitrogen radicals and conventional Knudsen cells to evaporate gallium and aluminum. After transferring into the growth chamber the sapphire substrates were heated to 530°C and exposed to the nitrogen plasma to get a more reactive surface for the nucleation step, which is essential for epitaxial growth [4]. The nucleation was done at a substrate temperature of 620°C and was directly followed by annealing under a flux of nitrogen radicals at 700°C. Thereafter, the substrate temperature was low-
0921-5107/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 9 8 ) 0 0 3 7 0 - 5
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ered slightly and the growth of the nominally 40 nm thick GaN layer was performed. The growth of the Alx Ga1 − x N layers (0.5 – 0.6 mm) occurred at the same temperature. The Ga flux was kept constant throughout the process and the Al content was controlled by adjusting the Al flux. Thick Alx Ga1 − x N layers (10–20 mm) were grown on SiC and (0001) a-Al2O3 substrates using chloride-hydride-vapor-phase epitaxy (CHVPE). Raman spectra of Alx Ga1 − x N layers were measured in the back-scattering configuration at room temperature. Two directions of the incident laser beams were used: along the c-axis of the wurtzite structure (z direction) and perpendicular to it (x direction). An Ar + laser (l =488 nm) was used as a source of excitation. The structural quality of the layers and the alloy composition were controlled by X-ray diffraction and electron probe microanalysis (EPMA).
3. Results and discussion The hexagonal GaN, AlN, and their solid solutions (Alx Ga1 − x N) crystallize in the wurtzite structure having six optical modes (1A1(TO) +1A1(LO)+ 1E1(TO)+1E1(LO) + 2E2) active in the first-order Raman scattering. The major contribution to the Raman scattering intensity comes from the transverse polar A1(TO) and high-frequency nonpolar E2 phonon modes. The Porto notation will be used to indicate the polarization configuration used in each experiment. The A1(TO) mode was measured in the x(zz)x¯ scattering geometry (Raman spectra were taken from the edge of the layer). The E2 and A1(LO) modes were observed in the z(yy)z¯ geometry (Raman spectra were taken from the Alx Ga1 − x N layer plane). In the Alx Ga1 − x N solid solutions, the frequency of the A1(TO) phonon shifts with varying composition from 532 cm − 1 in GaN to 612 cm − 1 in AlN and exhibits a one-mode type behavior shown in Fig. 1, while the E2 phonon mode demonstrates a two-mode type behavior presented in Fig. 2 [1,2]. Large frequency shifts depending on the Al content and the one-mode type behavior are also typical of the longitudinal polar A1(LO) phonon line (from 734 cm − 1 in GaN to 890 cm − 1 in AlN). Note that the frequency position of the A1(LO) line depends not only on the Al content, but also on the concentration of free carriers in the sample which is associated with the presence of uncontrollable dopants.
3.1. Deformation effects The analysis of the Raman data and EPMA results have revealed considerably differing positions of the A1(TO) and E2 lines for the samples having the same composition and grown on different or on the identical
Fig. 1. Raman spectra for different Alx Ga1 − x N compositions obtained in the geometry corresponding to the A1(TO) and E1(LO) phonon modes. For clarity, the spectrum intensity near the E1(LO) phonon modes is doubled.
substrates. As will be shown below, this is due to the difference in residual homogeneous strains in the layers. Measurements of the deformation displacement constants of the A1(TO) and E2 lines in GaN performed in [5] have shown that their ratio is R= 0.51. A similar value R=0.55 has also been obtained in our experiments for these lines in AlN. Since the symmetry of vibrations does not change in the alloys, it can be
Fig. 2. Raman spectra for different Alx Ga1 − x N compositions obtained in the geometry corresponding to the E2 and A1(LO) phonon modes. For clarity, the spectrum intensity near the E1(LO) phonon modes is magnified. The black triangles show the position of the A1(TO) phonon symmetry line which is forbidden in this scattering geometry. The asterisks indicate the lines corresponding to the phonon modes of the sapphire substrate.
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Fig. 3. Variations in Dv=v(A1(TO))−v(E2)R as a function of x in Alx Ga1 − x N layers. The solid line corresponds to fitting with the formula v= 243 + 62x−62x 2 + 42x 3 (cm − 1).
expected that the ratio R changes only slightly with varying composition. Then the difference, Dv = v(A1(TO))− v(E2)R, depends only on the relative contents of the components in the solution and is strain-independent. The experimental values of Dv for a number of samples (grown by both the MBE and CHVPE techniques) with different contents of Al are shown in Fig. 3. The obtained data show that Dv is a smooth function of the composition of the samples grown by different techniques and on different substrates. Thus, (i) the observed random shifts of the lines in the Raman spectra of the Alx Ga1 − x N epitaxial layers are due to strain effects, and (ii) the measurements of the Dvvalues can be used for the evaluation of the composition of the Alx Ga1 − x N layers.
are expected to be linear with respect to concentration. The experimentally observed line width changes with x are poorly approximated by a linear fit. Therefore, this mechanism is inefficient. (ii) The inhomogeneous broadening effects induced by the impurity fluctuations, similar to the mechanisms of the excitonic line broadening [6]. First of all, these effects can originate from the phonon scattering by the Gaussian local fluctuations of composition in homogeneous mixed crystal. In this case the increase in the line width is known to be described by G=c1x 2(1−x 2) and should be accompanied by a considerable asymmetry of the phonon line. This type of behavior is inconsistent with our experimental findings too. The experimental data obtained for high-quality crystals are fairly well approximated by G8 x(1− x) (see Fig. 4.). This dependence is known to originate from the inhomogeneous broadening mechanism [7] and is often observed in the excitonic luminescence spectra of AIIIBV (and Alx Ga1 − x N) mixed crystals. In the case of the excitons the dependence is typical for the local exciton line broadening due to Gaussian fluctuations in the Al (or Ga) concentration within the exciton localization radius. The same mechanism can be efficient in the case of the phonons in a crystal having the micro crystallite structure. Then the broadenings can be attributed to the content fluctuations in micro crystals. For this broadening mechanism one has: G= c2
(v a
x(1−x) 0 (x a
(1)
where a0 is the lattice parameter and c2 is a constant of the order of unity. The spatial dimension a in which phonons are confined enters Eq. (1) and, therefore, it can be extracted from the fit to the experimental data. The localization radius for the E2 phonons in Alx Ga1 − x N
3.2. Nonpolar phonon E2 line broadening In the strained layer samples there is a spread of the line broadenings for a given Al content caused by inhomogeneous deformation of the layers. This broadening is negligible in high quality samples. The Raman spectra of the GaN- and AlN-like nonpolar phonon lines with E2 symmetry in the Alx Ga1 − x N epitaxial layers exhibit substantial broadening even for crystals with a high structural quality (controlled by X-ray diffraction patterns). Broadening is a sharply rising function of the Al or Ga content at small concentrations of these components in the solid solution. The line full width at half maximum (FWHM) as a function of x for high quality layers is shown in Fig. 4. There are several mechanisms for nonpolar phonon line broadening in mixed crystals. These mechanisms lead to different concentration dependences of the FWHM: (i) Changes in the homogeneous (anharmonic) line width
Fig. 4. Dependence of the width of the upper and lower E2 lines on the Al content in Alx Ga1 − x N layers.
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tions for the polar phonon modes with a strong directional dependence for hexagonal crystals [8]. The width of the A1(LO) phonon line. The experimentally observed A1(LO) line width dependence is close to G= c3x(1− x). For the polar phonon with a small directional dispersion the main broadening mechanism is a random dipole–dipole interaction that leads to the observed FWHM dependence on x, where the coefficient c3 can be estimated using the value of the A1 mode LO-TO splitting. The estimation gives c3 $ (v 2LO − v 2TO)/vLO, which agrees fairly well with the experiment. The excess broadening of the Raman line is associated with the crystal structure imperfections, which is consistent with the X-ray diffraction data. Therefore, the FWHM of the A1(TO) phonon line can be used to estimate the structural quality of the layer. Fig. 5. Dependence of the width of the A1(TO) and A1(LO) lines on the Al content in Alx Ga1 − x N layers.
crystals is found to be a :6 – 8.5 nm. This estimate is somewhat lower than the results obtained from the X-ray data analysis. The difference can be attributed to the inhomogeneous distribution of the Al content inside a micro crystal. Additional broadening of the E2 phonon line is observed in some crystals which have larger luminescence and X-ray diffraction line widths that can be attributed to a high concentration of structural defects. Therefore, the excess broadening can be used to estimate the structural quality of layers. The width of the polar A1(TO) phonon line. The Raman spectra for the A1(TO) phonons show that the A1(TO) line width changes only slightly with a change in the Al content in mixed crystals (see the solid line in Fig. 5.). In structurally perfect crystals the line width is close to G= 7.5 cm − 1 both for x 1 and (1 − x)1, with a sharp rise near x $ 0.7. The long-wavelength vibrations of the A1(TO) symmetry with a substantial directional dispersion have an anomalously small density of states. The edge dependence of it varies from the quasi-four-dimensional (in the region x 1) to quasifive-dimensional vibrational system at (1−x) 1. As a result, in the mixed crystal A1(TO) phonons are weakly scattered by the fluctuations in x and the probability that phonons will be localized in the region of high fluctuation of x is exponentially small [8]. Therefore, the concentrational broadening of the A1(TO) line is expected to be exponentially small for all mixed crystal compositions except a small range near x =xc, where xc is estimated to be xc $0.5 – 0.7. The broadening becomes substantial when the phonon branch has small dispersion in the Brillouin zone and the density of the phonon states at the spectrum edge becomes large enough. Thus the observed dependence of FWHM for the A1(TO) line is consistent with the theoretical predic.
4. Conclusions The frequencies and the FWHM of the Raman-active long-wavelength phonons have been measured in the whole composition range of Alx Ga1 − x N epitaxial layers grown on different substrates. It is shown that the errors in the estimates of the ctystal composition caused by homogeneous strain effects could be eliminated by using a linear combination of two Raman line frequencies. We show that the behavior of the line widths of the phonons with different symmetries can be attributed to different mechanisms of the inhomogeneous line broadening induced by the disorder effects.
Acknowledgements VYuD, ING, MVB, ANS, and AVS appreciate the support of the Ministry of Sciences of Russia, Programme ‘Physics of Solid State Nanostructures’, grant 97-1035 and grant 97-1091.
References [1] A. Cros, H. Angerer, O. Ambacher, M. Stutzmann, R. Hopler, T. Metzger, Solid State Commun. 104 (1997) 35. [2] F. Demangeot, J. Groenen, J. Frandon, et al., MRS Int. J. Nitride Semicond. Res. 2 (1997) 40. [3] L. Bergman, M.D. Bremser, W.G. Perry, R.F. Davis, M. Dutta, R.J. Nemanich, Appl. Phys. Lett. 71 (1997) 2157. [4] S. Yoshida, S. Misawa, S. Gonda, J. Appl. Phys. 53 (1982) 6844. [5] V.Y. Davydov, N.S. Averkiev, I.N. Goncharuk, et al., J. Appl. Phys. 82 (1997) 5097. [6] A.L. Efros, M.E. Raikh, in: R.J. Elliott, I.P. Ipatova (Eds.), Optical Properties of Mixed Crystals, Elseiver Science, Amsterdam, 1988, p. 135. [7] E.F. Schubert, E.O. Gobel, Y. Horikoshi, K. Ploog, H.G. Queisser, Phys. Rev. B 30 (1984) 813. [8] I.P. Ipatova, V.A. Shchukin, JETPh 97 (1990) 990.