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GaN layers
Materials Science and Engineering B93 (2002) 163 /167 www.elsevier.com/locate/mseb
Splitting of X-ray diffraction and photoluminescence peaks in InGaN/GaN layers S. Pereira a,b,*, M.R. Correia a, E. Pereira a, K.P. O’Donnell b, R.W. Martin b, M.E. White b, E. Alves c, A.D. Sequeira c, N. Franco c b
a Departamento de Fı´sica, Universidade de Aveiro, 3810-193 Aveiro, Portugal Department of Phys. and Appl. Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, UK c Departamento de Fı´sica do ITN, E.N. 10, 2686-953 Sacave´m, Portugal
Abstract The observation of multiple, X-ray diffraction (XRD) and photoluminescence (PL) peaks in an InGaN epilayer is sometimes regarded as an indicator of phase segregation. In this report, a detailed characterisation of a InGaN/GaN bilayer by a combination of XRD and Rutherford backscattering spectrometry (RBS) shows that splitting of the XRD peak may occur in the absence of phase decomposition. An XRD reciprocal space map performed on the (105) plane shows that one component of the partially resolved InGaN double peak is almost aligned with that of the GaN buffer, indicating that part of the layer is pseudomorphic to the GaN template. From a consideration of the effect of strain on the c - and a -lattice constants, both the partially relaxed and the pseudomorphic components are shown to have the same indium content. The layer composition deduced from XRD measurements is confirmed by RBS. Depth-resolving RBS/channelling angular scans also shows that the region closer to the GaN/InGaN interface is nearly pseudomorphic to the GaN substrate, whereas the surface region is almost fully relaxed. Furthermore, PL spectroscopy shows a double peak that can be accounted for by regions of the sample under different strains. # 2002 Elsevier Science B.V. All rights reserved. Keywords: InGaN; X-ray diffraction; Rutherford backscattering; Strain; Composition; Photoluminescence
1. Introduction Group III nitride epilayers, grown by metalorganic vapour phase epitaxy (MOVPE), are currently a major topic of research due to their widespread use in light emitting diodes (LEDs) and laser diodes [1,2]. Commercial indium gallium nitride (InGaN) LEDs, developed over the last decade, enjoy unrivalled performance in the UV, blue and green spectral regions. Structural properties of InGaN materials, such as those at the heart of these devices, have been studied intensively. Some key topics under discussion include the role of composition, strain, ordering and phase separation on the optical properties [3 /6]. Misinterpretations regarding the effects of strain and composition have generated some systematic uncertainties in the literature.
* Corresponding author. Tel.: 351-918-178-065; fax: 351-234424-965. E-mail address: [email protected] (S. Pereira).
In this work we study selected InGaN films, grown in commercial nitride reactors, which show well defined double X-Ray diffraction (XRD) peaks. Using a combination of high-resolution XRD (HRXRD) and RBS/ channelling we address the origin of the double peak in terms of the composition and strain in the epilayer. The effect of such structural feature on the luminescence properties is also briefly discussed.
2. Experimental details The samples studied are nominally undoped wurtzite InGaN/GaN bilayers, grown by metal organic chemical vapour deposition (MOCVD) on Al2O3 substrates in an AIX2000/2400HT CVD reactor. HRXRD characterisation was performed using a double-crystal diffractometer. A flat Ge (444) monochromator and horizontal divergence slits select Cu Ka1 radiation. A position sensitive detector was placed at a variable distance from the sample in an achromatic geometry.
0921-5107/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 0 2 ) 0 0 0 3 9 - 9
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The instrumental resolution limit is about 30 arcs. RBS/ channelling measurements were performed with a 1-mm collimated beam of 2.0 MeV 4He ions at currents of about 5 nA. Samples were mounted on a computercontrolled two-axis goniometer with an accuracy of 9/ 0.018. The backscattered particles were detected at 1608 and close to 1808, with respect to the beam direction, using silicon surface barrier detectors located in the standard Cornell geometry. PL was excited with a He / Cd laser with the samples mounted in a closed cycle helium cryostat on an x /y /z stage and analysed with a CCD spectrograph.
3. Results and discussion Fig. 1 presents a v /2u HRXRD map of an InGaN/ GaN(001)/Al2O3(001) sample, which shows, in addition to the well separated GaN and InGaN (002) diffraction peaks, a splitting of the InGaN peak. Note the use of the three-index notation for directions and planes of the hexagonal system: (hkl ) is equivalent to the four-index notation (hkil ), with i / /(h/k ). Two diffraction peaks corresponding to the InGaN layer can be clearly observed in addition to the GaN peak at 2u /34.558. The diffraction peak at higher angle is broader. Considerable peak broadening along v , observed in the (002) map, is a typical feature for nitride layers and indicates a mosaic structure of the epilayer. The width of the peaks in a v scan is particularly sensitive to mosaic spread and is normally used as a figure of merit for the crystalline quality. A u /2u scan on the (006) reflection, shown in Fig. 2, provides improved resolution of the doublet. Combining Bragg’s law with the expression for the inter-planar spacing in hexagonal structures, the lattice constant in the growth direction is found to be c /l +l/
Fig. 1. v /2u map around the GaN and InGaN (002) diffraction peaks for one of the layers under study. The v u line corresponds to a u /2u scan.
Fig. 2. u /2u scan on the InGaN (006) reflections fitted to two Voigt functions.
(2 sin uB), for any allowed (00l ) reflection of X-rays of wavelength l . For this layer, two values for the InGaN lattice parameters cInGaN(1) /5.286 and cInGaN(2) / 5.255, are calculated directly from the XRD peak positions in Fig. 1. Some caution is required when interpreting the X-ray profile from InGaN layers. In some cases confusion has arisen between the (101) diffraction peak from metallic Indium, appearing in some high In content layers due to In droplet formation [7], and that corresponding to pure InN, which has been reported as experimental evidence of phase separation [8], predicted to occur in InGaN [6]. However, we observe no additional diffraction peaks, from metallic Indium (101), at 2u :/32.968, or pure InN, at 2u :/31.338, in the present InGaN samples. On the other hand the presence of double peaks in the diffraction profile has often been interpreted as an indication of partial phase segregation, attributed to the presence of InGaN ‘micro-regions’ of different In content [9 /11]. Composition estimations in these sub-regions frequently rely on the assumption of total strain relaxation and direct application of Vegard’s law, which states that the lattice constants of a relaxed ternary compound scale linearly with composition [12]. In the present case, let us consider the two peaks as ‘belonging to’ regions (1) and (2). Under the assumption, described above, each measured lattice parameter, cInGaN(1,2), could be used to directly estimate the indium mole fractions x (1) and x (2). Using this approach, the two regions would have x(1) /0.180 and x (2) /0.129. However, as discussed previously by some of the present authors [13], biaxially strained wurtzite structures suffer distortion of the hexagonal unit cell; in consequence, the procedure discussed above tends to overestimate the In content of layers that are not fully relaxed. The magnitude of the error depends on the relaxation degree of the layer, and can only be
S. Pereira et al. / Materials Science and Engineering B93 (2002) 163 /167
evaluated if the in-plane lattice constant or the actual composition is known. Information on the crystal structure and strain of an epitaxial film can be obtained by performing a reciprocal space map (RSM) on an asymmetric reflection. Additionally, the out-of-plane (c ) and in-plane (a ) lattice constants of the hexagonal structure can be measured and a direct comparison of the position of GaN and InGaN diffraction peaks in the RS can be performed. A RSM of the InGaN/GaN structure under study, measured around the (105) reflection, is shown in Fig. 3. The RSM confirms that two peaks compose the diffraction profile of the InGaN film. Additionally, we can note that one of them is nearly aligned with the GaN diffraction maximum along Qx , the reciprocal space vector in the plane of the layers. From this, it is apparent that one of the sub-regions, InGaN(1), has practically the same in-plane lattice constant as the underlying GaN buffer layer. This InGaN region has a higher outof-plane lattice constant cInGaN(1), as seen by the peak position relative to Qz . On the other hand, the second diffraction peak corresponds to a larger value of a / aInGaN(2) and a smaller value of c /cInGaN(2). From the asymmetric scan, the lattice constants aInGaN(1) /3.186 and aInGaN(2) /3.220, are determined. When both a - and c- are known, the sample strain can be taken into account in estimates of the composition [14]. From the definition of Poisson’s ratio, we find [cInGaN c0 (x)]2
C13 (x)c0 (x) C33 (x)a0 (x)
[aInGaN a0 (x)] 0
(1)
where cInGaN and aInGaN are the measured lattice parameters, c0 and a0 are the relaxed parameters predicted by Vegard’s law and Ci;j (x) are elastic
Fig. 3. (105) reciprocal space map of the InGaN/GaN layer. The abscissa (Qx ) and the ordinate (Qz ) are proportional to 2/â3a and 5/c , respectively.
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constants linearly interpolated from the binary values [15]. Of the three possible solutions of the resulting cubic equation, only one is physically acceptable (0 B/x B/1). In addition to the measured lattice parameters cInGaN(1,2) and aInGaN(1,2), the input parameters necessary to complete the calculation are the GaN (cGaN / 0.51850, aGaN /0.31892 nm) [16] and InN (cInN / 0.57033, aInN /0.35378 nm) [17] relaxed lattice constants, and the elastic constants [18] (c13 /103 and c33 / 405 Gpa) for GaN and (c13 /92 and c33 /224 Gpa) InN. Solving Eq. (1) yields values of x (1) /0.119 and x (2) /0.118. It is interesting to note that if the state of strain of each sub-region is properly taken into account, the value of x obtained is actually the same, within the error limits of such an estimate (9/0.01). Therefore, it is clear that the two sub-regions co-existing in the InGaN layer (and showing distinct XRD peaks) correspond, in fact, to regions with the same In content under different states of strain. In order to measure the In content directly, free from the effects of strain, and to gain an insight about the distinctive structural features of this sample, a supplementary characterisation of the sample was performed by RBS/channelling. RBS allows an accurate determination of the In mole fraction (x ) with depth resolution. Determination of x in InGaN layers by RBS does not require any standards as we measure only the ratio of In/ Ga signals. Random (38 off axis) and 0001-aligned RBS spectra from the InGaN/GaN bilayer are shown in Fig. 4a. Simulation of the random spectrum using RUMP [19], reveals an InGaN layer thickness of 1809/10 nm and a composition, x /0.1199/0.005. The value for x determined by RBS is in very good agreement with the XRD estimate. The simulation also indicates that the In content is uniform over depth, a circumstance not always verified for InGaN layers [20]. Although the determination of composition by RBS is insensitive to the state of strain in a sample, the channelling effect, in which particles are steered along atomic rows, can be used to measure strain with depth resolution in epitaxial layers. Depth resolution is attained by energy selection of the backscattered particles. Angular scans were performed from 001 towards the 101 axis in the (1 /20) plane. In the RBS spectra corresponding to the InGaN layer, two integration regions, corresponding to In and Ga atoms at 0/90 and 90/180 nm depths, were used. For the 001 axis all three channelling dips have the same angular position, as shown in Fig. 4b. The angular position of the 101 axis with respect to the 001 axis is a function of the lattice constants c - and a - of the wurtzite structure as seen in the inset of the figure. It is rather interesting to note in Fig. 4b that the position of the InGaN 101 dip changes with depth. Fepi values of 46.609/0.05 and 46.909/0.058 for the InGaN layer at the
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Fig. 5. Photoluminescence spectrum excited with a He /Cd laser acquired at 14 K.
under different degrees of strain can explain the observed splitting, with the lower energy peak corresponding to the relaxed region and the higher energy to the strained one. Details about the influence of strain on the PL peak position are currently under investigation and will be discussed elsewhere.
Fig. 4. (a) Random, aligned, and simulated RBS spectra from an In0.12Ga0.88N/GaN/Al2O3(0001) sample. Vertical arrows indicate the scattering energies of the different chemical elements. Horizontal arrows indicate the depth location in the sample. (b) Angular RBS/ channelling scans, corresponding to the GaN buffer layer and the InGaN layer at the indicated depths, along the (1 20) plane from the 001 to the 101 crystal axis. The inset shows the angular dependence of the crystal axis on the wurtzite lattice constants.
stated depths were measured. The tetragonal distortion, o T, defined in Ref. [21], can be deduced from the RBS/ channelling study: the values are /0.859/0.10% for the region closer to the GaN/InGaN interface and /0.019/ 0.10% for the near-surface region, respectively. Therefore the surface region can be considered fully relaxed within the resolution of the RBS angular scans, whereas the near interface region is highly strained. The negative values for o T indicate that the InGaN layer is under tensile strain along the growth direction, as would be expected. The measured values of o T at the examined depths show that InGaN regions at different depths are under different states of strain. This is the origin of the double XRD peak. A low temperature photoluminescence spectrum of the sample under study is shown in Fig. 5. A double luminescence peak related to the InGaN bandedge emission can be observed in the PL spectrum. The low energy band centred on /2.2 eV is defectrelated luminescence (yellow band). The two regions
4. Conclusion The results presented here show that a double peak observed in the XRD and PL profile of an InGaN epilayer with constant In content over depth may be accounted for by a discrete strain variation. As an InGaN layer grows, the elastic strain energy increases. Beyond a critical layer thickness, when no more strain can be accommodated by the lattice, misfit dislocations form and the InGaN film relaxes. The presence of the double PL and XRD peaks can be unrelated to phase separation.
Acknowledgements Se´rgio Pereira acknowledges financial support from Fundac¸a˜o para a Cieˆncia e Tecnologia (SFRH/BD/859/ 2000). We thank Dr Patricia Kidd (Philips Analytical Research Centre) for useful discussions and AIXTRON for providing the samples.
References [1] B. Gil (Ed.), Group III Nitride Semiconductor Compounds, Physics and Applications. Series on Semiconductor Science and Technology, vol. 6, Oxford Science Publications, Oxford, 1998. [2] S. Nakamura, J. Cryst. Growth 202 (1999) 290.
S. Pereira et al. / Materials Science and Engineering B93 (2002) 163 /167 [3] K.P. O’Donnell, Phys. Stat. Sol. (A) 183 (2001) 117. [4] M.E. Aumer, S.F. LeBoeuf, S.M. Bedair, M. Smith, J.Y. Lin, H.X. Jiang, Appl. Phys. Lett. 77 (2000) 821. [5] A.F. Wright, K. Leung, M. Van Schilfgaarde, Appl. Phys. Lett. 78 (2001) 189. [6] I. Ho, G.B. Stringfellow, Appl. Phys. Lett. 68 (1996) 2701. [7] A. Krost, J. Bla¨sing, H. Protzmann, M. Lu¨nenbu¨rger, M. Heuken, Appl. Phys. Lett. 76 (2000) 1395. [8] D. Doppalapudi, S.N. Basu, K.F. Ludwig, T.D. Moustakas, Jr, J. Appl. Phys. 84 (1998) 1389. [9] N.A. El-Masry, E.L. Piner, S.X. Liu, S.M. Bedair, Appl. Phys. Lett. 72 (1998) 40. [10] Y.-T. Moon, D.-J. Kim, K.-M. Song, I.-H. Lee, M.-S. Yi, D.Y. Noh, C.-J. Choi, T.-Y. Seong, S.-J. Park, Phys. Stat. Sol. (B) 216 (1999) 167. [11] D. Rudolff, Phys. Stat. Sol. (B) 216 (1999) 315. [12] L. Vegard, Z. Phys. 5 (1921) 17.
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[13] S. Pereira, M.R. Correia, T. Monteiro, E. Pereira, E. Alves, A.D. Sequeira, N. Franco, Appl. Phys. Lett. 78 (2001) 2137. [14] M. Schuster, P.O. Gervais, B. Jobst, W. Ho¨sler, R. Averbeck, H. Riechert, A. Iberl, R. Sto¨mmer, J. Phys. D: Appl. Phys. 32 (1999) A56. [15] S. Pereira, M.R. Correia, E. Pereira, C. Trager-Cowan, F. Sweeney, P.R. Edwards, K.P. O’Donnell, E. Alves, A.D. Sequeira, N. Franco, Mater. Res. Soc. Proc. 639 (2000) G3.52. [16] T. Detchprohm, K. Hiramatsu, K. Itoh, I. Akasaki, Jpn. J. Appl. Phys. 31 (1992) L1454. [17] W. Paszkowicz, Powder Diffraction 14 (1999) 258. [18] A.F. Wright, J. Appl. Phys. 82 (1997) 2833. [19] L.R. Doolittle, Nucl. Inst. Methods B 9 (1985) 344. [20] S. Pereira, M.R. Correia, E. Pereira, K.P. O’Donnell, C. TragerCowan, F. Sweeney, E. Alves, Phys. Rev. B 64 (2001) 205311. [21] M.F. Wu, A. Vantomme, S.M. Hogg, G. Langouche, W. Van der Stricht, K. Jacobs, I. Moerman, Appl. Phys. Lett. 74 (1999) 365.
Splitting of X-ray diffraction and photoluminescence peaks in InGaN/GaN layers S. Pereira a,b,*, M.R. Correia a, E. Pereira a, K.P. O’Donnell b, R.W. Martin b, M.E. White b, E. Alves c, A.D. Sequeira c, N. Franco c b
a Departamento de Fı´sica, Universidade de Aveiro, 3810-193 Aveiro, Portugal Department of Phys. and Appl. Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, UK c Departamento de Fı´sica do ITN, E.N. 10, 2686-953 Sacave´m, Portugal
Abstract The observation of multiple, X-ray diffraction (XRD) and photoluminescence (PL) peaks in an InGaN epilayer is sometimes regarded as an indicator of phase segregation. In this report, a detailed characterisation of a InGaN/GaN bilayer by a combination of XRD and Rutherford backscattering spectrometry (RBS) shows that splitting of the XRD peak may occur in the absence of phase decomposition. An XRD reciprocal space map performed on the (105) plane shows that one component of the partially resolved InGaN double peak is almost aligned with that of the GaN buffer, indicating that part of the layer is pseudomorphic to the GaN template. From a consideration of the effect of strain on the c - and a -lattice constants, both the partially relaxed and the pseudomorphic components are shown to have the same indium content. The layer composition deduced from XRD measurements is confirmed by RBS. Depth-resolving RBS/channelling angular scans also shows that the region closer to the GaN/InGaN interface is nearly pseudomorphic to the GaN substrate, whereas the surface region is almost fully relaxed. Furthermore, PL spectroscopy shows a double peak that can be accounted for by regions of the sample under different strains. # 2002 Elsevier Science B.V. All rights reserved. Keywords: InGaN; X-ray diffraction; Rutherford backscattering; Strain; Composition; Photoluminescence
1. Introduction Group III nitride epilayers, grown by metalorganic vapour phase epitaxy (MOVPE), are currently a major topic of research due to their widespread use in light emitting diodes (LEDs) and laser diodes [1,2]. Commercial indium gallium nitride (InGaN) LEDs, developed over the last decade, enjoy unrivalled performance in the UV, blue and green spectral regions. Structural properties of InGaN materials, such as those at the heart of these devices, have been studied intensively. Some key topics under discussion include the role of composition, strain, ordering and phase separation on the optical properties [3 /6]. Misinterpretations regarding the effects of strain and composition have generated some systematic uncertainties in the literature.
* Corresponding author. Tel.: 351-918-178-065; fax: 351-234424-965. E-mail address: [email protected] (S. Pereira).
In this work we study selected InGaN films, grown in commercial nitride reactors, which show well defined double X-Ray diffraction (XRD) peaks. Using a combination of high-resolution XRD (HRXRD) and RBS/ channelling we address the origin of the double peak in terms of the composition and strain in the epilayer. The effect of such structural feature on the luminescence properties is also briefly discussed.
2. Experimental details The samples studied are nominally undoped wurtzite InGaN/GaN bilayers, grown by metal organic chemical vapour deposition (MOCVD) on Al2O3 substrates in an AIX2000/2400HT CVD reactor. HRXRD characterisation was performed using a double-crystal diffractometer. A flat Ge (444) monochromator and horizontal divergence slits select Cu Ka1 radiation. A position sensitive detector was placed at a variable distance from the sample in an achromatic geometry.
0921-5107/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 0 2 ) 0 0 0 3 9 - 9
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The instrumental resolution limit is about 30 arcs. RBS/ channelling measurements were performed with a 1-mm collimated beam of 2.0 MeV 4He ions at currents of about 5 nA. Samples were mounted on a computercontrolled two-axis goniometer with an accuracy of 9/ 0.018. The backscattered particles were detected at 1608 and close to 1808, with respect to the beam direction, using silicon surface barrier detectors located in the standard Cornell geometry. PL was excited with a He / Cd laser with the samples mounted in a closed cycle helium cryostat on an x /y /z stage and analysed with a CCD spectrograph.
3. Results and discussion Fig. 1 presents a v /2u HRXRD map of an InGaN/ GaN(001)/Al2O3(001) sample, which shows, in addition to the well separated GaN and InGaN (002) diffraction peaks, a splitting of the InGaN peak. Note the use of the three-index notation for directions and planes of the hexagonal system: (hkl ) is equivalent to the four-index notation (hkil ), with i / /(h/k ). Two diffraction peaks corresponding to the InGaN layer can be clearly observed in addition to the GaN peak at 2u /34.558. The diffraction peak at higher angle is broader. Considerable peak broadening along v , observed in the (002) map, is a typical feature for nitride layers and indicates a mosaic structure of the epilayer. The width of the peaks in a v scan is particularly sensitive to mosaic spread and is normally used as a figure of merit for the crystalline quality. A u /2u scan on the (006) reflection, shown in Fig. 2, provides improved resolution of the doublet. Combining Bragg’s law with the expression for the inter-planar spacing in hexagonal structures, the lattice constant in the growth direction is found to be c /l +l/
Fig. 1. v /2u map around the GaN and InGaN (002) diffraction peaks for one of the layers under study. The v u line corresponds to a u /2u scan.
Fig. 2. u /2u scan on the InGaN (006) reflections fitted to two Voigt functions.
(2 sin uB), for any allowed (00l ) reflection of X-rays of wavelength l . For this layer, two values for the InGaN lattice parameters cInGaN(1) /5.286 and cInGaN(2) / 5.255, are calculated directly from the XRD peak positions in Fig. 1. Some caution is required when interpreting the X-ray profile from InGaN layers. In some cases confusion has arisen between the (101) diffraction peak from metallic Indium, appearing in some high In content layers due to In droplet formation [7], and that corresponding to pure InN, which has been reported as experimental evidence of phase separation [8], predicted to occur in InGaN [6]. However, we observe no additional diffraction peaks, from metallic Indium (101), at 2u :/32.968, or pure InN, at 2u :/31.338, in the present InGaN samples. On the other hand the presence of double peaks in the diffraction profile has often been interpreted as an indication of partial phase segregation, attributed to the presence of InGaN ‘micro-regions’ of different In content [9 /11]. Composition estimations in these sub-regions frequently rely on the assumption of total strain relaxation and direct application of Vegard’s law, which states that the lattice constants of a relaxed ternary compound scale linearly with composition [12]. In the present case, let us consider the two peaks as ‘belonging to’ regions (1) and (2). Under the assumption, described above, each measured lattice parameter, cInGaN(1,2), could be used to directly estimate the indium mole fractions x (1) and x (2). Using this approach, the two regions would have x(1) /0.180 and x (2) /0.129. However, as discussed previously by some of the present authors [13], biaxially strained wurtzite structures suffer distortion of the hexagonal unit cell; in consequence, the procedure discussed above tends to overestimate the In content of layers that are not fully relaxed. The magnitude of the error depends on the relaxation degree of the layer, and can only be
S. Pereira et al. / Materials Science and Engineering B93 (2002) 163 /167
evaluated if the in-plane lattice constant or the actual composition is known. Information on the crystal structure and strain of an epitaxial film can be obtained by performing a reciprocal space map (RSM) on an asymmetric reflection. Additionally, the out-of-plane (c ) and in-plane (a ) lattice constants of the hexagonal structure can be measured and a direct comparison of the position of GaN and InGaN diffraction peaks in the RS can be performed. A RSM of the InGaN/GaN structure under study, measured around the (105) reflection, is shown in Fig. 3. The RSM confirms that two peaks compose the diffraction profile of the InGaN film. Additionally, we can note that one of them is nearly aligned with the GaN diffraction maximum along Qx , the reciprocal space vector in the plane of the layers. From this, it is apparent that one of the sub-regions, InGaN(1), has practically the same in-plane lattice constant as the underlying GaN buffer layer. This InGaN region has a higher outof-plane lattice constant cInGaN(1), as seen by the peak position relative to Qz . On the other hand, the second diffraction peak corresponds to a larger value of a / aInGaN(2) and a smaller value of c /cInGaN(2). From the asymmetric scan, the lattice constants aInGaN(1) /3.186 and aInGaN(2) /3.220, are determined. When both a - and c- are known, the sample strain can be taken into account in estimates of the composition [14]. From the definition of Poisson’s ratio, we find [cInGaN c0 (x)]2
C13 (x)c0 (x) C33 (x)a0 (x)
[aInGaN a0 (x)] 0
(1)
where cInGaN and aInGaN are the measured lattice parameters, c0 and a0 are the relaxed parameters predicted by Vegard’s law and Ci;j (x) are elastic
Fig. 3. (105) reciprocal space map of the InGaN/GaN layer. The abscissa (Qx ) and the ordinate (Qz ) are proportional to 2/â3a and 5/c , respectively.
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constants linearly interpolated from the binary values [15]. Of the three possible solutions of the resulting cubic equation, only one is physically acceptable (0 B/x B/1). In addition to the measured lattice parameters cInGaN(1,2) and aInGaN(1,2), the input parameters necessary to complete the calculation are the GaN (cGaN / 0.51850, aGaN /0.31892 nm) [16] and InN (cInN / 0.57033, aInN /0.35378 nm) [17] relaxed lattice constants, and the elastic constants [18] (c13 /103 and c33 / 405 Gpa) for GaN and (c13 /92 and c33 /224 Gpa) InN. Solving Eq. (1) yields values of x (1) /0.119 and x (2) /0.118. It is interesting to note that if the state of strain of each sub-region is properly taken into account, the value of x obtained is actually the same, within the error limits of such an estimate (9/0.01). Therefore, it is clear that the two sub-regions co-existing in the InGaN layer (and showing distinct XRD peaks) correspond, in fact, to regions with the same In content under different states of strain. In order to measure the In content directly, free from the effects of strain, and to gain an insight about the distinctive structural features of this sample, a supplementary characterisation of the sample was performed by RBS/channelling. RBS allows an accurate determination of the In mole fraction (x ) with depth resolution. Determination of x in InGaN layers by RBS does not require any standards as we measure only the ratio of In/ Ga signals. Random (38 off axis) and 0001-aligned RBS spectra from the InGaN/GaN bilayer are shown in Fig. 4a. Simulation of the random spectrum using RUMP [19], reveals an InGaN layer thickness of 1809/10 nm and a composition, x /0.1199/0.005. The value for x determined by RBS is in very good agreement with the XRD estimate. The simulation also indicates that the In content is uniform over depth, a circumstance not always verified for InGaN layers [20]. Although the determination of composition by RBS is insensitive to the state of strain in a sample, the channelling effect, in which particles are steered along atomic rows, can be used to measure strain with depth resolution in epitaxial layers. Depth resolution is attained by energy selection of the backscattered particles. Angular scans were performed from 001 towards the 101 axis in the (1 /20) plane. In the RBS spectra corresponding to the InGaN layer, two integration regions, corresponding to In and Ga atoms at 0/90 and 90/180 nm depths, were used. For the 001 axis all three channelling dips have the same angular position, as shown in Fig. 4b. The angular position of the 101 axis with respect to the 001 axis is a function of the lattice constants c - and a - of the wurtzite structure as seen in the inset of the figure. It is rather interesting to note in Fig. 4b that the position of the InGaN 101 dip changes with depth. Fepi values of 46.609/0.05 and 46.909/0.058 for the InGaN layer at the
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Fig. 5. Photoluminescence spectrum excited with a He /Cd laser acquired at 14 K.
under different degrees of strain can explain the observed splitting, with the lower energy peak corresponding to the relaxed region and the higher energy to the strained one. Details about the influence of strain on the PL peak position are currently under investigation and will be discussed elsewhere.
Fig. 4. (a) Random, aligned, and simulated RBS spectra from an In0.12Ga0.88N/GaN/Al2O3(0001) sample. Vertical arrows indicate the scattering energies of the different chemical elements. Horizontal arrows indicate the depth location in the sample. (b) Angular RBS/ channelling scans, corresponding to the GaN buffer layer and the InGaN layer at the indicated depths, along the (1 20) plane from the 001 to the 101 crystal axis. The inset shows the angular dependence of the crystal axis on the wurtzite lattice constants.
stated depths were measured. The tetragonal distortion, o T, defined in Ref. [21], can be deduced from the RBS/ channelling study: the values are /0.859/0.10% for the region closer to the GaN/InGaN interface and /0.019/ 0.10% for the near-surface region, respectively. Therefore the surface region can be considered fully relaxed within the resolution of the RBS angular scans, whereas the near interface region is highly strained. The negative values for o T indicate that the InGaN layer is under tensile strain along the growth direction, as would be expected. The measured values of o T at the examined depths show that InGaN regions at different depths are under different states of strain. This is the origin of the double XRD peak. A low temperature photoluminescence spectrum of the sample under study is shown in Fig. 5. A double luminescence peak related to the InGaN bandedge emission can be observed in the PL spectrum. The low energy band centred on /2.2 eV is defectrelated luminescence (yellow band). The two regions
4. Conclusion The results presented here show that a double peak observed in the XRD and PL profile of an InGaN epilayer with constant In content over depth may be accounted for by a discrete strain variation. As an InGaN layer grows, the elastic strain energy increases. Beyond a critical layer thickness, when no more strain can be accommodated by the lattice, misfit dislocations form and the InGaN film relaxes. The presence of the double PL and XRD peaks can be unrelated to phase separation.
Acknowledgements Se´rgio Pereira acknowledges financial support from Fundac¸a˜o para a Cieˆncia e Tecnologia (SFRH/BD/859/ 2000). We thank Dr Patricia Kidd (Philips Analytical Research Centre) for useful discussions and AIXTRON for providing the samples.
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