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Strain relaxation in InxGa1−xN epitaxial films grown coherently on GaN
Journal of Crystal Growth 249 (2003) 455–460
Strain relaxation in InxGa1xN epitaxial films grown coherently on GaN Seong-Eun Parka, Byungsung Oa,*, Cheul-Ro Leeb b
a Department of Physics, Chungnam National University, Taejon 305-764, South Korea School of Advanced Materials Engineering, RIAMD, Engineering College, Chonbuk National University, Chonju 561-756, South Korea
Received 20 October 2002; accepted 4 November 2002 Communicated by M. Schieber
Abstract The strain relaxation was investigated in Inx Ga1x N films grown pseudomorphically on GaN buffer layer. The shift of dominant peaks originated from In0:035 Ga0:965 N films which were thinner than the critical thickness was observed with the increasing film thickness. Considering the same thermal strains in all the samples, this is attributed to the relaxation of the in-plane strains that resulted from the increased common in-plane lattice constant of coherently grown-In0:035 Ga0:965 N films with the increasing thickness. r 2002 Elsevier Science B.V. All rights reserved. PACS: 81.15.Gh Keywords: A1. High resolution X-ray diffraction; Al. Stresses; Al. X-ray topography; A3. Metalorganic chemical vapor deposition; B2. Semiconducting III–V materials
1. Introduction An InGaN ternary alloy among III–V compound semiconductors has been a very interesting material because of its important role as an active layer in GaN-related optoelectronic devices. [1] In spite of a successful fabrication of photonic and electronic devices such as blue light emitting diodes and blue laser diodes, the device performances were significantly dependent on the thickness or the composition of InGaN active layers. [2] To increase the device efficiencies, many research *Corresponding author. E-mail address: [email protected] (B. O).
groups have tried to grow quantum structures such as InGaN quantum dots(QDs) and wells (QWs), in which carriers are confined in two or three directions. However, it has been complicated to design the quantum structures because of their lattice-mismatched systems which were limited by the critical thickness (CT) of the films. In InGaN/GaN quantum structures, InGaN layers generally require to be grown below the CT for achieving the best electrical and optical properties of the structures. The strains produced by the difference of the lattice constants or the thermal expansion coefficients between two materials are commonly known not to relax but to be accommodated in a pseudomorphically
0022-0248/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-0248(02)02244-3
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
grown-film. On the contrary, the strains in a thicker layer begin to relax, generating defects such as dislocations and three-dimensional growth. Recently lots of physical characteristics estimated during the pseudomorphic growth of InGaN materials have been reported. [3,4] In this work, Inx Ga1x N films thinner than the CT were grown on GaN buffer layer. The strain behavior in coherently grown-InGaN films was examined by the high-resolution X-ray diffraction (HRXRD), photoluminescence (PL), and Raman scattering (RS) measurements, respectively.
(0002) GaN InxGa1-xN/GaN Normalized intensity (a.u)
456
(0002) InGaN A B C D -600 -500 -400 -300 -200 -100
(a)
0
100
200
Rocking angle (arcsec)
2. Experimental procedure Inx Ga1x N films were grown on 1:7 mm-thick GaN buffer layers by metalorganic chemical vapor deposition (MOCVD) system. First, the GaN buffer layer was grown on (0 0 0 1) sapphire substrate at 10501C and then the substrate temperature was lowered to 8501C to grow an Inx Ga1x N film (x ¼ 0:035). The growth time of the films was varied from 20 to 80 min. The composition of Inx Ga1x N films could be predicted from that of the thicker samples grown under the same condition. The film thicknesses derived from the growth rate of 150 nm/h were in the range of 50–200 nm and could be assured by a fringe method in HRXRD rocking curves to be discussed later. The HRXRD measurements were carried out with a triple crystal diffractometer. The PL experiments were performed at room temperature (RT) using the 325 nm line of He–Cd laser as an excitation source. RS spectra were measured employing 514.5 nm Arþ laser and a backscattering geometry. The incident and out-going beams were not polarized.
3. Results and discussion Fig. 1(a) illustrates the HRXRD rocking curves from the Inx Ga1x N films grown on GaN buffer layers. The film thicknesses estimated from the growth time are 50 (sample A), 100 (sample B),
(b) Fig. 1. (a) Triple crystal rocking curves from Inx Ga1x N=GaN heterostructures with the various film thicknesses. (b) The reciprocal space map of 150 nm-thick Inx Ga1x N film.
150 (sample C), and 200 (sample D) nm, respectively. These values can be confirmed by a fringe method. That is, the film thickness t related to the period of Pendellosung fringes Dyf is expressed as the following [5]: t¼
l ; 2Dyf cos ys
ð1Þ
where l is the wavelength of CuKa1 radiation and ys Bragg’s angle of the substrate. For sample C and sample D, the fringes between (0 0 0 2) InGaN and (0 0 0 2) GaN peaks are clear and the periods can be found to be 110 arcsec and 80 arcsec which correspond to the thickness of 148 and 196 nm, respectively. Consequently, for sample A and sample B, the thicknesses could be thought to be
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
x ¼ 0:62x0 0:059x02 ;
ð2Þ
where x0 is the apparent composition derived from the interpolation of the values for InN and GaN binary alloys using the c-lattice constants analyzed from the separation angles between (0 0 0 2) InGaN and (0 0 0 2) GaN reflections. The In compositions determined with Eq. (2) resulted in the same value of x ¼ 0:035 for all samples in this work with the error range of 70:00020: The determined In composition is well consistent with that of our thicker film fully relaxed and grown under the same condition. Considering that all the Inx Ga1x N films had the same composition (x ¼ 0:035), the CT hc of the films could be theoretically and experimentally evaluated. The CT for the various In compositions in InGaN/GaN heterostructures are plotted in Fig. 2(a). The experimental values recently determined by other works seem to be closer to those calculated by People’s and Bean’s energy balance model [Eq. (3)] than those by Matthew’s and Blakeslee’s mechanical equilibrium model [Eq. (4) which gives the low magnitude of about an order
Critical thickness (Å)
105
104
InxGa1-xN/GaN Energy balance model Mechanical equilibrium model This work Parker et al. Reed et al.
103
102
101 0.00 (a)
0.05
0.10 0.15 In composition, x
0.20
0.25
200 InxGa1-xN/GaN x = 0.035 150 F WHM (arcsec)
almost the same as those expected by the growth rate. To determine the relaxation of the Inx Ga1x N films on the GaN buffer layers, the reciprocal space map (RSM) of 150 nm-thick Inx Ga1x N film was measured as shown in Fig. 1(b) [6]. It was found that both reciprocal lattice point of the Inx Ga1x N layer (lower side) and corresponding reciprocal lattice point of the GaN buffer layer (upper side) were on the same vertical line. This indicates that the 150 nm-thick Inx Ga1x N film was fully strained. Furthermore, our thickness ranges seem to be below the CT for In composition of less than x ¼ 0:1; considering other similar results that 225 nm-thick Inx Ga1x N films were pseudomorphically grown on GaN buffer layers at x up to 0.114 [7]. Therefore, the In composition deduced from the c-lattice constants needs to be modified because the Vegard’s law is not valid for these strained Inx Ga1x N films [8]. The In composition of the strained Inx Ga1x N films is known to be calculated as [9]
457
Theory This work 100
50
0 0.01 (b)
0.1 1 Thickness (µm)
10
Fig. 2. (a) Critical thicknesses theoretically and experimentally obtained versus In compositions in Inx Ga1x N=GaN: The experimental values measured by other groups are fitted with the dot lines, respectively. (b) FWHM of (0 0 0 2) rocking curves for In0:035 Ga0:965 N films grown on GaN buffer layer as a function of the film thickness.
compared with the former [10,11]. ð1 nðxÞÞB hc hc ¼ ln ; 2 B ð1 þ nðxÞÞ32pf ðxÞ B hc ln hc ¼ þ1 ; ð1 þ nðxÞÞ4pf ðxÞ B
ð3Þ
ð4Þ
where p Bffiffiffi is Burger’s vector expressed as aInGaN = 2; nðxÞ Poisson’s ratio, and f ðxÞ the
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
458
lattice mismatch. From these results, the film thickness in this work was considered to be below both the theoretical and experimental critical thickness. Fig. 2(b) shows the relationship between the theoretical and the experimental FWHM of In0:035 Ga0:965 N rocking curves and the thickness of the films in InGaN/GaN heterostructures. When a film is coherently grown on a substrate accommodating a lattice mismatch, the FWHM of the film is theoretically given by [12] Dy ¼
l sin o ; t sin 2y
ð5Þ
where o is the reflection angle. Though there are the slight differences below the thickness of 150 nm, our results are well below the theoretical values. These support that all the In0:035 Ga0:965 N films were grown below the CT. Fig. 3 represents the PL spectra which shifted towards the lower energies with the increasing film thickness. The position of the strong and narrow band-edge (BE) emission of Inx Ga1x N corresponding to the radiative decay of bound excitons seems to depend on the film thickness. As the thickness of Inx Ga1x N films increased from 50 to 200 nm, the BE emissions shifted from 3.280 to 3.272 eV. To analyze the PL emissions at RT for
the strained Inx Ga1x N films, the following expression related to both the band gap energy and the In composition of Inx Ga1x N alloy was used [13] Eg ¼ 3:42 3:93x
ðeVÞ:
Note that the shift difference of about 8 meV is larger than that of 1.5 meV calculated with the composition variation (70:00020) in the HRXRD experiments. This suggests that the slight composition variation can be negligible and the redshift of the BE emissions was attributed to the strain relaxation in In0:035 Ga0:965 N films [14,15]. In addition, the (0 0 0 2) InGaN reflection peaks in HRXRD spectra shifted from 366.0 to 362.1 arcsec towards the relaxing strain as shown in Fig. 1. This behavior is comparable with other works that the reflection peak of strained InGaAs layers in InGaAs/GaAs structures has shifted towards that of GaAs buffer layers with the increasing thickness of the InGaAs layers due to the strain relaxation [16]. Note that the full-width at half-maximum (FWHM) for the symmetric (0 0 0 2) reflection of the hexagonal Inx Ga1x N alloys became narrower from 171 to 73 arcsec with the increasing thickness. This indicates that the thicker InGaN films, the better the crystal quality of the films due to the strain relaxation.
In0.035Ga0.965N/GaN
Normalized PL intensity (a.u.)
In0.035Ga0.965N/GaN
Intensity (a.u.)
E2(high) = 569.8
D
cm-1 InGaN-related Eg(s)
D C B A
C B A 3.0
ð6Þ
1.7 µm-thick GaN
3.1
3.2
3.3
3.4
3.5
Energy (eV) Fig. 3. Band-edge emission of the different thickIn0:035 Ga0:965 N films measured in PL at room temperature.
560
565
570 575 Raman shift (cm-1)
Fig. 4. Raman scattering spectra In0:035 Ga0:965 N=GaN heterostructures.
580 obtained
585 in
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
Fig. 4 exhibits the shifting phonon modes in RS measurements. It was well known that the phonon modes shifted towards different directions according to the induced strain types in the film like the PL results [17]. The dominant phonon peaks shifted from 572.3 to 571:7 cm1 with the increasing thickness of the films. In comparison with the Raman scattering spectra of a 1:7 mm-thick GaN layer without an InGaN upper layer, these phonon modes peaking around 572 cm1 were attributed to In0:035 Ga0:965 N films and the small phonon peaks at 569:8 cm1 were thought to be the high frequency E2 modes of GaN buffer layers. The redshift of 2:2 cm1 in the peak position of the InGaN-related phonon modes with the increasing thickness supports that the strains could relax in these coherently grown-Inx Ga1x N films. The experimental and theoretical values obtained in this work are listed in Table 1. In general, the strains produced in a film due to the different physical parameters of a substrate keep constant up to its CT and begin to relax over the CT, generating dislocations. However, the results taken in this work were quite different from the conventional works, for the strain relaxation happened even during the pseudomorphic growth. These strain relaxations in coherently grown-InGaN films on GaN buffer layers can be explained with several possibilities. Firstly, there is a thermal strain induced by the difference of the thermal expansion coefficients (TEC) between InGaN and GaN materials. Assuming that the TEC of Inx Ga1x N changes linearly with the composition, that of 5:53 106 was employed for In0:035 Ga0:965 N films in this work. The calculated thermal strains were the same as 4:94 105 in all samples. This indicates
459
that the same thermal strains did not contribute to the redshift of the dominant peaks in each measurement. Next, it is assumed that the in-plane strains relaxed as the common in-plane lattice constants between InGaN layers and GaN buffer layer increased with the increasing thickness during the pseudomorphic growth. This is similar to other works that GaN and AlN have relaxed with the same in-plane lattice constant below the CT of the GaN in GaN/AlN structures [18]. The common in-plane lattice constant a0 is expressed by [19] a0 ¼
KL hL =aL þ KS hS =aS KL hL =a2L þ KS hS =a2S
ð7Þ
where KL ðKS Þ is the elastic constant of the layer(substrate), aL ðaS Þ the fully relaxed lattice constant of the layer(substrate), and hL ðhS Þ the thickness of the layer(substrate), respectively. The elastic constant K is given by K ¼ 2mð1 þ nÞ=ð1 nÞ with the shear modulus m and Poisson’s ratio n of the layer. In this calculation, KL ¼ 726 GPa; KS ¼ 712 GPa; ( and aS ¼ 3:1890 A ( were employed, aL ¼ 3:2013 A, respectively [20]. As a result, it is thought that the increased a0 ( with the increasing from 3.1894 to 3.1903 A thickness resulted in the strain relaxation in In0:035 Ga0:965 N films grown coherently on a GaN buffer layer. In addition, it was reported that the stresses generated in the films from the beginning of the pseudomorphic growth have been varied with the increasing thickness of the AlN layers in Al/Si heterostructures [21]. This suggests that the stress induced in the film during the pseudomorpic growth might not keep constant but vary.
Table 1 The values taken in this work are listed as a function of the film thickness
50 nm 100 nm 150 nm 200 nm
(0 0 0 2) InGaN peak (arcsec)
HRXRD FWHM (arcsec)
Band-edge emission (eV)
Raman shift (cm1 )
Thermal strain (105 )
In-plane strain ð103 Þ
366.0 365.2 364.3 362.1
171 121 91 73
3.280 3.276 3.275 3.272
572.3 572.1 572.0 571.7
4.94 4.94 4.94 4.94
3.73 3.62 3.52 3.43
460
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
4. Conclusions The strain relaxation in In0:035 Ga0:965 N films thinner than the CT was investigated. As the film thicknesses were increased within the CT, the FWHM of (0 0 0 2) InGaN reflection peaks became narrower in HRXRD measurements and the BE emissions and the phonon modes of In0:035 Ga0:965 N films shifted towards the lower energies in both PL and RS experiments, respectively. From the shift of the peaks observed in all measurements, it is suggested that the common inplane lattice constants between InGaN layers and GaN buffer layers increased with the increasing thickness. As a result, the increased lattice constants are considered to give rise to the strain relaxations in In0:035 Ga0:965 N epitaxial films thinner than the critical thickness.
Acknowledgements This work was supported by Korea Research Foundation Grant (KRF-2001-015-DP0189).
References [1] S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, Appl. Phys. Lett. 70 (1997) 1417.
[2] Y. Kawaguchi, M. Shimizu, K. Hiramatsu, N. Sawaki, MRS Symp. Proc. 449 (1997) 89. [3] L. Gorgens, O. Ambacher, M. Stutzmann, C. Miskys, F. Scholz, J. Off, Appl. Phys. Lett. 76 (2000) 577. [4] C.A. Parker, J.C. Roberts, S.M. Bedair, M.J. Reed, S.X. Liu, N.A. El-Masry, Appl. Phys. Lett. 75 (1999) 2776. [5] J. Kervarec, M. Baudet, J. Caulet, P. Auvray, J.Y. Emey, A. Regreny, J. Appl. Cryst. 17 (1984) 196. [6] D.K. Bowen, B.K. Tanner, High Resolution X-ray Diffractometry and Topography, Taylor and Francis, London, 1998, pp. 153–157. [7] L.T. Romano, B.S. Krusor, M.D. McCluskey, D.P. Bour, K. Nauka, Appl. Phys. Lett. 73 (1998) 1757. [8] T. Takeuchi, H. Takeuchi, S. Sota, H. Sakai, H. Amano, I. Akasaki, Jpn. J. Appl. Phys., Part 2 36 (1997) L177. [9] H. Amano, T. Takeuchi, S. Sota, H. Sakai, I. Akasaki, MRS Symp. Proc. 449 (1997) 1143. [10] R. People, J.C. Bean, Appl. Phys. Lett. 47 (1985) 322. [11] J.W. Matthews, S. Mader, T.B. Light, J. Appl. Phys. 41 (1974) 3800. [12] W.J. Bartels, J. Vac. Sci. Technol. B 1 (1983) 338. [13] M.D. McCluskey, C.G. Van de Walle, C.P. Master, L.T. Romano, N.M. Johnson, Appl. Phys. Lett. 72 (1998) 2725. [14] D.C. Reynolds, D.C. Look, B. Jogai, J.E. Hoelscher, R.E. Sherriff, R.J. Molnar, J. Appl. Phys. 88 (2000) 1460. [15] A. Shikanai, T. Azuhata, T. Sota, S. Chichibu, A. Kuramata, K. Horino, S. Nakamura, J. Appl. Phys. 81 (1997) 417. [16] P.J. Orders, B.F. Usher, Appl. Phys. Lett. 50 (1987) 980. [17] M. Klose, N. Wieser, G. C. Rohr, R. Dassow, F. Scholz, J. Off, J. Crystal Growth 189/190 (1998) 634. [18] C. Kim, I.K. Robinson, J. Myoung, K.H. Shim, K. Kim, J. Appl. Phys. 85 (1999) 4040. [19] F.Y. Huang, Appl. Phys. Lett. 76 (2000) 3046. [20] A.F. Wright, J. Appl. Phys. 82 (1997) 2833. [21] W.J. Meng, J.A. Sell, T.A. Perry, L.E. Rehn, P.M. Baldo, J. Appl. Phys. 75 (1994) 3446.
Strain relaxation in InxGa1xN epitaxial films grown coherently on GaN Seong-Eun Parka, Byungsung Oa,*, Cheul-Ro Leeb b
a Department of Physics, Chungnam National University, Taejon 305-764, South Korea School of Advanced Materials Engineering, RIAMD, Engineering College, Chonbuk National University, Chonju 561-756, South Korea
Received 20 October 2002; accepted 4 November 2002 Communicated by M. Schieber
Abstract The strain relaxation was investigated in Inx Ga1x N films grown pseudomorphically on GaN buffer layer. The shift of dominant peaks originated from In0:035 Ga0:965 N films which were thinner than the critical thickness was observed with the increasing film thickness. Considering the same thermal strains in all the samples, this is attributed to the relaxation of the in-plane strains that resulted from the increased common in-plane lattice constant of coherently grown-In0:035 Ga0:965 N films with the increasing thickness. r 2002 Elsevier Science B.V. All rights reserved. PACS: 81.15.Gh Keywords: A1. High resolution X-ray diffraction; Al. Stresses; Al. X-ray topography; A3. Metalorganic chemical vapor deposition; B2. Semiconducting III–V materials
1. Introduction An InGaN ternary alloy among III–V compound semiconductors has been a very interesting material because of its important role as an active layer in GaN-related optoelectronic devices. [1] In spite of a successful fabrication of photonic and electronic devices such as blue light emitting diodes and blue laser diodes, the device performances were significantly dependent on the thickness or the composition of InGaN active layers. [2] To increase the device efficiencies, many research *Corresponding author. E-mail address: [email protected] (B. O).
groups have tried to grow quantum structures such as InGaN quantum dots(QDs) and wells (QWs), in which carriers are confined in two or three directions. However, it has been complicated to design the quantum structures because of their lattice-mismatched systems which were limited by the critical thickness (CT) of the films. In InGaN/GaN quantum structures, InGaN layers generally require to be grown below the CT for achieving the best electrical and optical properties of the structures. The strains produced by the difference of the lattice constants or the thermal expansion coefficients between two materials are commonly known not to relax but to be accommodated in a pseudomorphically
0022-0248/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-0248(02)02244-3
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
grown-film. On the contrary, the strains in a thicker layer begin to relax, generating defects such as dislocations and three-dimensional growth. Recently lots of physical characteristics estimated during the pseudomorphic growth of InGaN materials have been reported. [3,4] In this work, Inx Ga1x N films thinner than the CT were grown on GaN buffer layer. The strain behavior in coherently grown-InGaN films was examined by the high-resolution X-ray diffraction (HRXRD), photoluminescence (PL), and Raman scattering (RS) measurements, respectively.
(0002) GaN InxGa1-xN/GaN Normalized intensity (a.u)
456
(0002) InGaN A B C D -600 -500 -400 -300 -200 -100
(a)
0
100
200
Rocking angle (arcsec)
2. Experimental procedure Inx Ga1x N films were grown on 1:7 mm-thick GaN buffer layers by metalorganic chemical vapor deposition (MOCVD) system. First, the GaN buffer layer was grown on (0 0 0 1) sapphire substrate at 10501C and then the substrate temperature was lowered to 8501C to grow an Inx Ga1x N film (x ¼ 0:035). The growth time of the films was varied from 20 to 80 min. The composition of Inx Ga1x N films could be predicted from that of the thicker samples grown under the same condition. The film thicknesses derived from the growth rate of 150 nm/h were in the range of 50–200 nm and could be assured by a fringe method in HRXRD rocking curves to be discussed later. The HRXRD measurements were carried out with a triple crystal diffractometer. The PL experiments were performed at room temperature (RT) using the 325 nm line of He–Cd laser as an excitation source. RS spectra were measured employing 514.5 nm Arþ laser and a backscattering geometry. The incident and out-going beams were not polarized.
3. Results and discussion Fig. 1(a) illustrates the HRXRD rocking curves from the Inx Ga1x N films grown on GaN buffer layers. The film thicknesses estimated from the growth time are 50 (sample A), 100 (sample B),
(b) Fig. 1. (a) Triple crystal rocking curves from Inx Ga1x N=GaN heterostructures with the various film thicknesses. (b) The reciprocal space map of 150 nm-thick Inx Ga1x N film.
150 (sample C), and 200 (sample D) nm, respectively. These values can be confirmed by a fringe method. That is, the film thickness t related to the period of Pendellosung fringes Dyf is expressed as the following [5]: t¼
l ; 2Dyf cos ys
ð1Þ
where l is the wavelength of CuKa1 radiation and ys Bragg’s angle of the substrate. For sample C and sample D, the fringes between (0 0 0 2) InGaN and (0 0 0 2) GaN peaks are clear and the periods can be found to be 110 arcsec and 80 arcsec which correspond to the thickness of 148 and 196 nm, respectively. Consequently, for sample A and sample B, the thicknesses could be thought to be
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
x ¼ 0:62x0 0:059x02 ;
ð2Þ
where x0 is the apparent composition derived from the interpolation of the values for InN and GaN binary alloys using the c-lattice constants analyzed from the separation angles between (0 0 0 2) InGaN and (0 0 0 2) GaN reflections. The In compositions determined with Eq. (2) resulted in the same value of x ¼ 0:035 for all samples in this work with the error range of 70:00020: The determined In composition is well consistent with that of our thicker film fully relaxed and grown under the same condition. Considering that all the Inx Ga1x N films had the same composition (x ¼ 0:035), the CT hc of the films could be theoretically and experimentally evaluated. The CT for the various In compositions in InGaN/GaN heterostructures are plotted in Fig. 2(a). The experimental values recently determined by other works seem to be closer to those calculated by People’s and Bean’s energy balance model [Eq. (3)] than those by Matthew’s and Blakeslee’s mechanical equilibrium model [Eq. (4) which gives the low magnitude of about an order
Critical thickness (Å)
105
104
InxGa1-xN/GaN Energy balance model Mechanical equilibrium model This work Parker et al. Reed et al.
103
102
101 0.00 (a)
0.05
0.10 0.15 In composition, x
0.20
0.25
200 InxGa1-xN/GaN x = 0.035 150 F WHM (arcsec)
almost the same as those expected by the growth rate. To determine the relaxation of the Inx Ga1x N films on the GaN buffer layers, the reciprocal space map (RSM) of 150 nm-thick Inx Ga1x N film was measured as shown in Fig. 1(b) [6]. It was found that both reciprocal lattice point of the Inx Ga1x N layer (lower side) and corresponding reciprocal lattice point of the GaN buffer layer (upper side) were on the same vertical line. This indicates that the 150 nm-thick Inx Ga1x N film was fully strained. Furthermore, our thickness ranges seem to be below the CT for In composition of less than x ¼ 0:1; considering other similar results that 225 nm-thick Inx Ga1x N films were pseudomorphically grown on GaN buffer layers at x up to 0.114 [7]. Therefore, the In composition deduced from the c-lattice constants needs to be modified because the Vegard’s law is not valid for these strained Inx Ga1x N films [8]. The In composition of the strained Inx Ga1x N films is known to be calculated as [9]
457
Theory This work 100
50
0 0.01 (b)
0.1 1 Thickness (µm)
10
Fig. 2. (a) Critical thicknesses theoretically and experimentally obtained versus In compositions in Inx Ga1x N=GaN: The experimental values measured by other groups are fitted with the dot lines, respectively. (b) FWHM of (0 0 0 2) rocking curves for In0:035 Ga0:965 N films grown on GaN buffer layer as a function of the film thickness.
compared with the former [10,11]. ð1 nðxÞÞB hc hc ¼ ln ; 2 B ð1 þ nðxÞÞ32pf ðxÞ B hc ln hc ¼ þ1 ; ð1 þ nðxÞÞ4pf ðxÞ B
ð3Þ
ð4Þ
where p Bffiffiffi is Burger’s vector expressed as aInGaN = 2; nðxÞ Poisson’s ratio, and f ðxÞ the
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
458
lattice mismatch. From these results, the film thickness in this work was considered to be below both the theoretical and experimental critical thickness. Fig. 2(b) shows the relationship between the theoretical and the experimental FWHM of In0:035 Ga0:965 N rocking curves and the thickness of the films in InGaN/GaN heterostructures. When a film is coherently grown on a substrate accommodating a lattice mismatch, the FWHM of the film is theoretically given by [12] Dy ¼
l sin o ; t sin 2y
ð5Þ
where o is the reflection angle. Though there are the slight differences below the thickness of 150 nm, our results are well below the theoretical values. These support that all the In0:035 Ga0:965 N films were grown below the CT. Fig. 3 represents the PL spectra which shifted towards the lower energies with the increasing film thickness. The position of the strong and narrow band-edge (BE) emission of Inx Ga1x N corresponding to the radiative decay of bound excitons seems to depend on the film thickness. As the thickness of Inx Ga1x N films increased from 50 to 200 nm, the BE emissions shifted from 3.280 to 3.272 eV. To analyze the PL emissions at RT for
the strained Inx Ga1x N films, the following expression related to both the band gap energy and the In composition of Inx Ga1x N alloy was used [13] Eg ¼ 3:42 3:93x
ðeVÞ:
Note that the shift difference of about 8 meV is larger than that of 1.5 meV calculated with the composition variation (70:00020) in the HRXRD experiments. This suggests that the slight composition variation can be negligible and the redshift of the BE emissions was attributed to the strain relaxation in In0:035 Ga0:965 N films [14,15]. In addition, the (0 0 0 2) InGaN reflection peaks in HRXRD spectra shifted from 366.0 to 362.1 arcsec towards the relaxing strain as shown in Fig. 1. This behavior is comparable with other works that the reflection peak of strained InGaAs layers in InGaAs/GaAs structures has shifted towards that of GaAs buffer layers with the increasing thickness of the InGaAs layers due to the strain relaxation [16]. Note that the full-width at half-maximum (FWHM) for the symmetric (0 0 0 2) reflection of the hexagonal Inx Ga1x N alloys became narrower from 171 to 73 arcsec with the increasing thickness. This indicates that the thicker InGaN films, the better the crystal quality of the films due to the strain relaxation.
In0.035Ga0.965N/GaN
Normalized PL intensity (a.u.)
In0.035Ga0.965N/GaN
Intensity (a.u.)
E2(high) = 569.8
D
cm-1 InGaN-related Eg(s)
D C B A
C B A 3.0
ð6Þ
1.7 µm-thick GaN
3.1
3.2
3.3
3.4
3.5
Energy (eV) Fig. 3. Band-edge emission of the different thickIn0:035 Ga0:965 N films measured in PL at room temperature.
560
565
570 575 Raman shift (cm-1)
Fig. 4. Raman scattering spectra In0:035 Ga0:965 N=GaN heterostructures.
580 obtained
585 in
S.-E. Park et al. / Journal of Crystal Growth 249 (2003) 455–460
Fig. 4 exhibits the shifting phonon modes in RS measurements. It was well known that the phonon modes shifted towards different directions according to the induced strain types in the film like the PL results [17]. The dominant phonon peaks shifted from 572.3 to 571:7 cm1 with the increasing thickness of the films. In comparison with the Raman scattering spectra of a 1:7 mm-thick GaN layer without an InGaN upper layer, these phonon modes peaking around 572 cm1 were attributed to In0:035 Ga0:965 N films and the small phonon peaks at 569:8 cm1 were thought to be the high frequency E2 modes of GaN buffer layers. The redshift of 2:2 cm1 in the peak position of the InGaN-related phonon modes with the increasing thickness supports that the strains could relax in these coherently grown-Inx Ga1x N films. The experimental and theoretical values obtained in this work are listed in Table 1. In general, the strains produced in a film due to the different physical parameters of a substrate keep constant up to its CT and begin to relax over the CT, generating dislocations. However, the results taken in this work were quite different from the conventional works, for the strain relaxation happened even during the pseudomorphic growth. These strain relaxations in coherently grown-InGaN films on GaN buffer layers can be explained with several possibilities. Firstly, there is a thermal strain induced by the difference of the thermal expansion coefficients (TEC) between InGaN and GaN materials. Assuming that the TEC of Inx Ga1x N changes linearly with the composition, that of 5:53 106 was employed for In0:035 Ga0:965 N films in this work. The calculated thermal strains were the same as 4:94 105 in all samples. This indicates
459
that the same thermal strains did not contribute to the redshift of the dominant peaks in each measurement. Next, it is assumed that the in-plane strains relaxed as the common in-plane lattice constants between InGaN layers and GaN buffer layer increased with the increasing thickness during the pseudomorphic growth. This is similar to other works that GaN and AlN have relaxed with the same in-plane lattice constant below the CT of the GaN in GaN/AlN structures [18]. The common in-plane lattice constant a0 is expressed by [19] a0 ¼
KL hL =aL þ KS hS =aS KL hL =a2L þ KS hS =a2S
ð7Þ
where KL ðKS Þ is the elastic constant of the layer(substrate), aL ðaS Þ the fully relaxed lattice constant of the layer(substrate), and hL ðhS Þ the thickness of the layer(substrate), respectively. The elastic constant K is given by K ¼ 2mð1 þ nÞ=ð1 nÞ with the shear modulus m and Poisson’s ratio n of the layer. In this calculation, KL ¼ 726 GPa; KS ¼ 712 GPa; ( and aS ¼ 3:1890 A ( were employed, aL ¼ 3:2013 A, respectively [20]. As a result, it is thought that the increased a0 ( with the increasing from 3.1894 to 3.1903 A thickness resulted in the strain relaxation in In0:035 Ga0:965 N films grown coherently on a GaN buffer layer. In addition, it was reported that the stresses generated in the films from the beginning of the pseudomorphic growth have been varied with the increasing thickness of the AlN layers in Al/Si heterostructures [21]. This suggests that the stress induced in the film during the pseudomorpic growth might not keep constant but vary.
Table 1 The values taken in this work are listed as a function of the film thickness
50 nm 100 nm 150 nm 200 nm
(0 0 0 2) InGaN peak (arcsec)
HRXRD FWHM (arcsec)
Band-edge emission (eV)
Raman shift (cm1 )
Thermal strain (105 )
In-plane strain ð103 Þ
366.0 365.2 364.3 362.1
171 121 91 73
3.280 3.276 3.275 3.272
572.3 572.1 572.0 571.7
4.94 4.94 4.94 4.94
3.73 3.62 3.52 3.43
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4. Conclusions The strain relaxation in In0:035 Ga0:965 N films thinner than the CT was investigated. As the film thicknesses were increased within the CT, the FWHM of (0 0 0 2) InGaN reflection peaks became narrower in HRXRD measurements and the BE emissions and the phonon modes of In0:035 Ga0:965 N films shifted towards the lower energies in both PL and RS experiments, respectively. From the shift of the peaks observed in all measurements, it is suggested that the common inplane lattice constants between InGaN layers and GaN buffer layers increased with the increasing thickness. As a result, the increased lattice constants are considered to give rise to the strain relaxations in In0:035 Ga0:965 N epitaxial films thinner than the critical thickness.
Acknowledgements This work was supported by Korea Research Foundation Grant (KRF-2001-015-DP0189).
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