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Residual strain and surface roughness of Si1−xGex alloy layers grown by molecular beam epitaxy on Si(001) substrate
Thin Solid Films 369 (2000) 161±166
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Residual strain and surface roughness of Si12xGex alloy layers grown by molecular beam epitaxy on Si(001) substrate C. Tatsuyama*, T. Asano, T. Nakao, H. Matada, T. Tambo, H. Ueba Department of Electrical and Electronic Engineering, Faculty of Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555, Japan
Abstract Residual strain and surface roughness of Si12xGex alloy layers grown by molecular beam epitaxy on Si(001) substrate at 5508C have been characterized by X-ray diffraction (XRD) and atomic force microscopy (AFM). Two kinds of samples were grown. One is a series of the Ê directly grown on Si(001) substrate, and the other is the Si0.7Ge0.3 alloy layers with Si12xGex alloy layers with x # 0:3 and thickness of 5000 A Ê grown on Si(001) via compositionally graded Si12yGey (0 # y # x) buffer layers. The Ge grading rate in the buffer layer, thickness of 2000 A de®ned as % Ge/mm, was ranged from 22 to 76. In the case of direct growth, the surface morphology changes from wavy ripple pattern to a cross-hatch pattern with increase in x, and island-like pattern appears at x 0:3. The residual strain decreases with increase in x, whereas the surface roughness increases with x. In the case of Si0.7Ge0.3 alloy layers grown with buffer layers, the surfaces of all samples display crosshatch pattern. The surface roughness shows maximum for a grading rate of about 35, and it decreases for both lower and higher grading rates. The residual strain also shows a similar dependence on the grading rate. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Si12 xGex alloy layers; Residual strain; Surface roughness; X-ray diffraction; Atomic force microscopy; Molecular beam epitaxy
1. Introduction Si12xGex alloy layers can grow pseudomorphically on Si substrate only up to a critical thickness depending on Ge composition x due to the lattice mismatch of 4.2% between Ge and Si. Above this critical thickness, mis®t dislocations are introduced, resulting in the lattice relaxation. However, the residual strain still remains in the grown layer, and much more thickness is required to relax completely. High density of dislocations are introduced in the relaxed alloy layers. The relaxed Si12xGex alloy layers without dislocations on Si are important as `substrates' for the subsequent growth of quantum wells and two-dimensional electron and hole structures. For this purpose, compositionally graded Si12yGey (0 # y # x) layers are widely used as buffer layers to reduce threading dislocations in the Si12xGex alloy layers [1,2]. The Si/Si12yGey(y , x) superlattices [3,4], graded superlattice [2,5], step-graded layers [6] and graded short-period (SimGen) superlattices [7] have also been used for the buffer layer. Furthermore, it has recently been reported that a thin Si layer grown at low temperature, such as 4008C, is effective as buffer layer [8].
* Corresponding author. Tel.: 181-764-45-6725; fax: 181-764-45-6697. E-mail address: [email protected] (C. Tatsuyama).
Using these buffer layers, the threading dislocation density decreases remarkably in the topmost alloy layers. However, it is well known that the surface of Si12xGex layers exhibits roughness, which also degrades the subsequently grown device quality, depending on the growth conditions and Ge composition x. In the present paper, the relation between the residual strain and surface morphology of Si12xGex alloy layers on Si(001) substrate with and without buffer layers grown by molecular beam epitaxy (MBE) is comparatively studied using X-ray diffraction (XRD) and atomic force microscopy (AFM). 2. Experimental The samples were grown on Si(001) substrate in a MBE chamber (ANELVA, E-620s) equipped with re¯ection-high energy electron diffraction (RHEED). Un-doped high purity (10-nine) Si and Ge were evaporated from an electron beam evaporator and a Knudsen cell (K-cell), respectively. Substrate was heated by a carbon heater, and the substrate temperature was measured by a W-Re thermocouple attached on the substrate holder. The growth rate Ê /s estimated by a quartz thickness monitor was about 0.5 A for Si. The base pressure was 5 £ 10 210 Torr, and the pres-
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0040-609 0(00)00798-7
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3. Experimental results and discussion 3.1. Si12xGex alloy layers grown without buffer layers
Fig. 1. XRD patterns of (a) Si12xGex alloy layer with x 0:17 grown on Si(001) substrate without buffer layer, (b) Si0.7Ge0.3 alloy layers grown on Si(001) via graded buffer layer with grading rate gr 76. The SiGe(004) peaks due to Cu Ka 1 line of alloy layers are observed at 64.422 and 68.0588, respectively. The peak position of Si(004) due to Cu Ka 1 line is 69.1328.
sure was better than 1 £ 10 29 Torr during the deposition. The n-type Si wafer with resistivity of about 10 V cm was cut into 25 £ 25 mm 2 for the substrate. After the chemical cleaning, the substrate was introduced into the MBE chamber, where the substrate was annealed at 8508C for 15 min Ê thick Si at 7008C, to remove SiO2. After depositing 1000 A the substrate was further annealed at 8008C for 10 min. After these treatments, the surface exhibited a clean (2 £ 1) RHEED pattern. Two kinds of samples were grown on the Si(001) substrate at 5508C. One is a series of compositionally uniform Si12xGex alloy layers with thickness of 50008C grown without buffer layers. The Ge composition x was ranged from 0.08 to 0.30. The other is Si0.7Ge0.3 alloy layers Ê grown on compositionally graded with thickness of 2000 A SiGe buffer layers. The composition was increased monotonically from 0 at.% Ge at the beginning to 30 at.% Ge at the top of buffer layer by increasing the Ge K-cell temperature under the constant Si ¯ux. The grading rate, gr, de®ned by % Ge/mm, was ranged from 22 to 76. The Ge composition in the Si12xGex and Si0.7Ge0.3 alloy layers was estimated from the areal intensity ratio of Si 2p and Ge 3d peaks in the X-ray photoemission spectroscopy (XPS) spectra excited by Mg Ka X-rays. The residual strain in the alloy layers was determined from the XRD pattern using Cu Ka X-rays. The surface morphology was observed by AFM, and the surface roughness was characterized by root mean squared (RMS) roughness. The dislocations in the samples were observed by cross-sectional transmission electron microscope operating at 200 kV.
Ê , which correThe thickness of the samples was 5000 A sponds to the critical thickness for the ®lm with x 0:13 according to People and Bean's theory [9]. However, this thickness of all samples exceeds the critical thickness given by van de Leur et al. [10] and Fukuda et al. [11]. Fig. 1a shows the XRD pattern of Si12xGex alloy layer with x 0:17 grown on Si(001) substrate without buffer layer, where the diffraction peak corresponding to SiGe(004) due to Cu Ka 1 line is observed at 64.4228. The Si(004) peak position is 69.1328. The residual strain 1' perpendicular to the growth plane in the alloy layers is de®ned as 1' (aXPS 2 aXRD)/aXPS, where aXPS is the lattice constant of the unstrained alloy layer with Ge composition determined by XPS (assuming Vegard's law), and aXRD is the lattice constant along the growth direction of alloy layer determined by the SiGe(004) peak position due to Cu Ka 1 line. The lattice constant of Si and Ge are 5.431 and 5.658 Ê , respectively. The residual strain of the sample shown in A Fig. 1a is thus estimated to be 20.20%. The minus sign of the value of 1' means that the alloy layer is expanded in the growth direction under the compressive biaxial stress in the basal plane from the substrate. This absolute value of 1' for the sample with x 0:17 is signi®cantly smaller than the value of 20.54% expected for the pseudomorphically strained Si0.83Ge0.17 layer on Si(001) substrate. This result suggests that the alloy layer is considerably relaxed with a relaxation rate of 59%. The obtained values of 1' of several samples are plotted in Fig. 2 as a function of Ge composition x. The absolute value of 1' 20.21% of sample with x 0:08 is slightly
Fig. 2. Residual strain and root mean squared (RMS) roughness of Si12xGex alloy layers grown on Si(001) as a function of Ge composition x.
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smaller than the expected value of 20.26% for the completely strained layer, suggesting the partial relaxation of the alloy layer (relaxation rate of 19%). The residual strain decreases with increase in x, and becomes almost zero at x 0:3 (relaxation rate of 100%). AFM images of the samples are shown in Fig. 3. The scanning area is 10 £ 10 mm 2 and the vertical scale has been enhanced by a factor of 1000 to emphasize the surface undulations. The sides of these ®gures are parallel to [100] and [010] directions, respectively. On the surface of the sample with x 0:08 (Fig. 3a), wavy undulation aligned
163
along the [100] direction is observed. The amplitude and frequency of the undulation are about 1.2 nm and 0.5 mm, respectively. Cullis et al. [12,13] and Dutartre et al. [14] ascribed the surface ripples aligned along [100] direction to the lowering of the system free energy by partial elastic strain relief due to oscillatory lattice plane distortion. Even though the present undulation is quite different in shape from ripples reported by them, these undulations should be due to the large residual strain in the ®lm as observed by XRD. Furthermore, a few light ridges running parallel to [110] and [110] directions are also seen. These ridges may
Fig. 3. Evolution of AFM images of Si12xGex alloy layers grown on Si(001) substrate without buffer layers depending on the Ge composition x, (a) x 0:08, (b) x 0:14, (c) x 0:17, (d) x 0:19, (e) x 0:27, (f) x 0:30. The sides of these ®gures are parallel to [100] and [010] directions, respectively.
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be an indication of the formation of cross hatch. Formation of the cross hatch is considered due to the mis®t dislocations [15±19]. The appearance of cross-hatch pattern is thus consistent with reduced residual strain obtained by XRD measurement. According to People and Bean's theory [9], the critical thickness of alloy layer with x 0:08 is about 1.5 mm. Therefore, the strain relaxation starts to occur for the ®lms with thickness much smaller than the critical thickness expected by People and Bean's theory. The critical thickness would be very sensitive to the growth conditions,
such as growth temperature and growth rate. Our present results seem to support the smaller critical thickness given by van de Leur et al. [10] or Fukuda et al. [11]. On the surface of sample with x 0:17 (Fig. 3c), the undulations running parallel to [110] and [110] directions are observed all over the surface. Since this sample contains large residual strain, it may be considered that this is a cross-hatch pattern due to the generation of mis®t dialocations strongly in¯uenced by the strain. On the surface of sample with x 0:19 (Fig. 3d), the cross-hatch pattern with long-range order
Fig. 4. AFM images of Si0.7Ge0.3 alloy layers grown on Si(001) via graded buffer layer. The grading rate gr de®ned by % Ge/mm of buffer layer for each sample is (a) gr 76, (b) gr 59, (c) gr 48, (d) gr 39, (e) gr 22. The sides of these ®gures are parallel to [100] and [010] directions, respectively.
C. Tatsuyama et al. / Thin Solid Films 369 (2000) 161±166
covers all the surface, suggesting the generation of a lot of mis®t dislocations, resulting in the strain relaxation. In fact, the value of 1' of this sample is 0.15%, which is much smaller than the expected value for a strained layer (0.61%). Sample with x 0:27 (Fig. 3e) also shows a lot of cross hatches. In the case of sample with x 0:3 (Fig. 3f), irregular island-like structures appear, and cross-hatch pattern is no more seen. The surface roughness expressed by root mean squared (RMS) roughness is plotted in Fig. 2 as a function of Ge composition x in Si12xGex. It is found that RMS roughness increases monotonically with x, and reaches about 2.4 nm at x 0:3. Xie et al. [20] claimed that the pronounced surface roughness occurs for ®lms under compressive strain exceeding 1.4%. However, from our results, it is clear that the roughness can be observed for ®lms with strain less than 1%. 3.2. Si0.7Ge0.3 alloy layers grown on buffer layers Ê were grown Si0.7Ge0.3 alloy layers with thickness 2000 A on the compositionally graded SiGe buffer layers on Si(001) substrate. AFM images of all samples show cross-hatch patterns with long-range order aligned along [110] and [110] directions with a period of ridge and trough of 0.6±0.8 mm as shown in Fig. 4. The period slightly decreases with increase in grading rate. Fig. 5 plots RMS roughness over 20 £ 20 mm 2 AFM images as a function of Ge grading rate (gr) of the buffer layer. The residual strain 1' in the alloy layers estimated by XRD measurement (see Fig. 1b) is also plotted in Fig. 5. In strong contrast to the alloy layers grown without buffer layers, both change in similar manner with grading
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rate, indicating the intimate correlation between residual strain and surface roughness. For low grading rate, gr, they increase with grading rate, and show maximum at about 35% grading rate, above which they decrease for further increase in grading rate. The maximum value of RMS roughness is about 2.8 nm at 35% grading rate, which is slightly larger than the value for directly grown Ê (see Fig. alloy layer with x 0:3 and thickness of 5000 A 2). At low grading rate, the thickness of buffer layers is much larger than the critical thickness [15], resulting in the generation of a lot of dislocations leading to decrease in the residual strain. However, the dislocations are swept out from the edge of ®lm due to the slip on the {111} grid planes, resulting in the decrease of the surface roughness. The large thickness of the buffer layer for low grading rates would also play a role in the smoothing of the surface. At higher grading rate, a lot of dislocations are easily introduced due to the decrease in critical thickness as in the case of directly grown layer, which leads to the decrease in residual strain albeit the thickness is small. It is surprising that RMS roughness shows smaller values such as 1.1 nm for higher grading rates. According to Fitzgerald et al. [15], an increased grading rate enhances the surface roughness because dislocations are located closer to the surface. This is the case for grading rates lower than about 35% Ge/mm. However, in the present experiment, the surface roughness decreases for the grading rates over 35. As observed from the XTEM images of these samples(data are not shown), the dislocations are injected deep into the substrate, which may be the origin of the surface smoothing. These results imply that rather high grading rates such as 60% Ge/mm may be promising for the buffer layers, which is very important for the practical use. In fact, LeGoues et al. [2] have reported very low densities of threading dislocations by growing rather sharply graded layers (50% Ge/mm) at low temperature such as 5008C. They did not discuss in detail the surface roughening depending on the grading rates. The increase in the growth temperature signi®cantly enhances the surface roughness. In fact, the RMS values for graded layers with ®nal Ge composition of x 0:3 reported by Hsu et al. [16] are greater than the present values by about a factor of four, where the growth was performed at 9008C. 4. Conclusion
Fig. 5. Residual strain and root mean squared (RMS) roughness of Si0.7Ge0.3 alloy layers grown on Si(001) via graded buffer layer as a function of Ge grading rate (gr) of buffer layer.
Residual strain and surface roughness of Si12xGex (0 , x % 0:3) alloy layers grown by molecular beam epitaxy on Si(001) substrate at 5508C with and without compositionally graded buffer layers have been compared using XRD and AFM results. In the case of the growth without buffer layers, the surface morphology of the samples changed from wavy ripple pattern to a crosshatch pattern with increase in x, and, at x 0:3, the surface exhibited island-like pattern. The residual strain decreased with increase in x, whereas RMS roughness increased
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monotonically with x. In the case of Si0.7Ge0.3 alloy layers grown on buffer layers, the surfaces of all samples displayed cross-hatch pattern. The residual strain and RMS roughness showed similar dependence on grading rate with maximum at about 35% Ge/mm, suggesting a strong correlation between residual strain and surface morphology. References [1] E.A. Fitzgerald, Y.H. Xie, M.L. Green, et al., Phys. Lett. 59 (1991) 811. [2] F.K. LeGoues, B.S. Meyerson, J.F. Morar, Phys. Rev. Lett. 66 (1991) 2903. [3] P.J. Wang, B.S. Meyerson, K. Ismail, F.F. Fang, J. Nocera, MRS. Symp. Proc. 220 (1991) 403. [4] R. Hull, J.C. Bean, R.E. Leibenguth, D.J. Werder, J. Appl. Phys. 65 (1989) 4723. [5] B.S. Meyerson, K.J. Uram, F.K. LeGoues, Appl. Phys. Lett. 53 (1988) 2555. [6] P.M. Mooney, J.L. Jordan-Sweet, K. Ismail, J.O. Chu, R.M. Feensta, F.K. Legoues, Appl. Phys. Lett. 67 (1995) 2373. [7] T. Obata, K. Komeda, T. Nakao, H. Ueba, C. Tatsuyama, J. Appl. Phys. 81 (1997) 199.
[8] C.S. Peng, Z.Y. Zhao, H. Chen, et al., Phys. Lett. 72 (1998) 3160. [9] R. People, J.C. Bean, Appl. Phys. Lett. 47 (1985) 322. [10] R.H.M. van de Leur, A.J.G. Schellingerhout, F. Tuinstra, J.E. Mooij, J. Appl. Phys. 64 (1988) 3043. [11] Y. Fukuda, Y. Kohama, Y. Ohmachi, Jpn. J. Appl. Phys. 29 (1990) L20. [12] A.G. Cullis, D.J. Robbins, A.J. Pidduck, P.W. Smith, J. Cryst. Growth 123 (1992) 333. [13] A.G. Cullis, D.J. Robbins, S.J. Barnett, A.J. Pidduck, J. Vac. Sci. Technol. A 12 (1994) 1924. [14] D. Dutartre, P. Warren, F. Chollet, F. Gisbert, M. Berenguer, I. Berbezier, J. Cryst. Growth 142 (1994) 78. [15] E.A. Fitzgerald, Y.H. Xie, D. Monroe, J. Vac, et al., Sci. Technol. B 10 (1992) 1807. [16] J.W.P. Hsu, E.A. Fitzgerald, Y.H. Xie, P.J. Silverman, M.J. Cardillo, Appl. Phys. Lett. 61 (1992) 1293. [17] S. Yu Shiryaev, F. Jensen, J.W. Petersen, Appl. Phys. Lett. 64 (1994) 3305. [18] M.A. Lutz, R.M. Feenstra, F.K. LeGoues, P.M. Mooney, J.O. Dhu, Appl. Phys. Lett. 66 (1995) 724. [19] M. Albrecht, S. Christiansen, J. Michler, Appl. Phys. Lett. 67 (1995) 1232. [20] Y.H. Xie, G.H. Gilmer, C. Roland, et al., Rev. Lett. 73 (1994) 3006.
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Residual strain and surface roughness of Si12xGex alloy layers grown by molecular beam epitaxy on Si(001) substrate C. Tatsuyama*, T. Asano, T. Nakao, H. Matada, T. Tambo, H. Ueba Department of Electrical and Electronic Engineering, Faculty of Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555, Japan
Abstract Residual strain and surface roughness of Si12xGex alloy layers grown by molecular beam epitaxy on Si(001) substrate at 5508C have been characterized by X-ray diffraction (XRD) and atomic force microscopy (AFM). Two kinds of samples were grown. One is a series of the Ê directly grown on Si(001) substrate, and the other is the Si0.7Ge0.3 alloy layers with Si12xGex alloy layers with x # 0:3 and thickness of 5000 A Ê grown on Si(001) via compositionally graded Si12yGey (0 # y # x) buffer layers. The Ge grading rate in the buffer layer, thickness of 2000 A de®ned as % Ge/mm, was ranged from 22 to 76. In the case of direct growth, the surface morphology changes from wavy ripple pattern to a cross-hatch pattern with increase in x, and island-like pattern appears at x 0:3. The residual strain decreases with increase in x, whereas the surface roughness increases with x. In the case of Si0.7Ge0.3 alloy layers grown with buffer layers, the surfaces of all samples display crosshatch pattern. The surface roughness shows maximum for a grading rate of about 35, and it decreases for both lower and higher grading rates. The residual strain also shows a similar dependence on the grading rate. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Si12 xGex alloy layers; Residual strain; Surface roughness; X-ray diffraction; Atomic force microscopy; Molecular beam epitaxy
1. Introduction Si12xGex alloy layers can grow pseudomorphically on Si substrate only up to a critical thickness depending on Ge composition x due to the lattice mismatch of 4.2% between Ge and Si. Above this critical thickness, mis®t dislocations are introduced, resulting in the lattice relaxation. However, the residual strain still remains in the grown layer, and much more thickness is required to relax completely. High density of dislocations are introduced in the relaxed alloy layers. The relaxed Si12xGex alloy layers without dislocations on Si are important as `substrates' for the subsequent growth of quantum wells and two-dimensional electron and hole structures. For this purpose, compositionally graded Si12yGey (0 # y # x) layers are widely used as buffer layers to reduce threading dislocations in the Si12xGex alloy layers [1,2]. The Si/Si12yGey(y , x) superlattices [3,4], graded superlattice [2,5], step-graded layers [6] and graded short-period (SimGen) superlattices [7] have also been used for the buffer layer. Furthermore, it has recently been reported that a thin Si layer grown at low temperature, such as 4008C, is effective as buffer layer [8].
* Corresponding author. Tel.: 181-764-45-6725; fax: 181-764-45-6697. E-mail address: [email protected] (C. Tatsuyama).
Using these buffer layers, the threading dislocation density decreases remarkably in the topmost alloy layers. However, it is well known that the surface of Si12xGex layers exhibits roughness, which also degrades the subsequently grown device quality, depending on the growth conditions and Ge composition x. In the present paper, the relation between the residual strain and surface morphology of Si12xGex alloy layers on Si(001) substrate with and without buffer layers grown by molecular beam epitaxy (MBE) is comparatively studied using X-ray diffraction (XRD) and atomic force microscopy (AFM). 2. Experimental The samples were grown on Si(001) substrate in a MBE chamber (ANELVA, E-620s) equipped with re¯ection-high energy electron diffraction (RHEED). Un-doped high purity (10-nine) Si and Ge were evaporated from an electron beam evaporator and a Knudsen cell (K-cell), respectively. Substrate was heated by a carbon heater, and the substrate temperature was measured by a W-Re thermocouple attached on the substrate holder. The growth rate Ê /s estimated by a quartz thickness monitor was about 0.5 A for Si. The base pressure was 5 £ 10 210 Torr, and the pres-
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0040-609 0(00)00798-7
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3. Experimental results and discussion 3.1. Si12xGex alloy layers grown without buffer layers
Fig. 1. XRD patterns of (a) Si12xGex alloy layer with x 0:17 grown on Si(001) substrate without buffer layer, (b) Si0.7Ge0.3 alloy layers grown on Si(001) via graded buffer layer with grading rate gr 76. The SiGe(004) peaks due to Cu Ka 1 line of alloy layers are observed at 64.422 and 68.0588, respectively. The peak position of Si(004) due to Cu Ka 1 line is 69.1328.
sure was better than 1 £ 10 29 Torr during the deposition. The n-type Si wafer with resistivity of about 10 V cm was cut into 25 £ 25 mm 2 for the substrate. After the chemical cleaning, the substrate was introduced into the MBE chamber, where the substrate was annealed at 8508C for 15 min Ê thick Si at 7008C, to remove SiO2. After depositing 1000 A the substrate was further annealed at 8008C for 10 min. After these treatments, the surface exhibited a clean (2 £ 1) RHEED pattern. Two kinds of samples were grown on the Si(001) substrate at 5508C. One is a series of compositionally uniform Si12xGex alloy layers with thickness of 50008C grown without buffer layers. The Ge composition x was ranged from 0.08 to 0.30. The other is Si0.7Ge0.3 alloy layers Ê grown on compositionally graded with thickness of 2000 A SiGe buffer layers. The composition was increased monotonically from 0 at.% Ge at the beginning to 30 at.% Ge at the top of buffer layer by increasing the Ge K-cell temperature under the constant Si ¯ux. The grading rate, gr, de®ned by % Ge/mm, was ranged from 22 to 76. The Ge composition in the Si12xGex and Si0.7Ge0.3 alloy layers was estimated from the areal intensity ratio of Si 2p and Ge 3d peaks in the X-ray photoemission spectroscopy (XPS) spectra excited by Mg Ka X-rays. The residual strain in the alloy layers was determined from the XRD pattern using Cu Ka X-rays. The surface morphology was observed by AFM, and the surface roughness was characterized by root mean squared (RMS) roughness. The dislocations in the samples were observed by cross-sectional transmission electron microscope operating at 200 kV.
Ê , which correThe thickness of the samples was 5000 A sponds to the critical thickness for the ®lm with x 0:13 according to People and Bean's theory [9]. However, this thickness of all samples exceeds the critical thickness given by van de Leur et al. [10] and Fukuda et al. [11]. Fig. 1a shows the XRD pattern of Si12xGex alloy layer with x 0:17 grown on Si(001) substrate without buffer layer, where the diffraction peak corresponding to SiGe(004) due to Cu Ka 1 line is observed at 64.4228. The Si(004) peak position is 69.1328. The residual strain 1' perpendicular to the growth plane in the alloy layers is de®ned as 1' (aXPS 2 aXRD)/aXPS, where aXPS is the lattice constant of the unstrained alloy layer with Ge composition determined by XPS (assuming Vegard's law), and aXRD is the lattice constant along the growth direction of alloy layer determined by the SiGe(004) peak position due to Cu Ka 1 line. The lattice constant of Si and Ge are 5.431 and 5.658 Ê , respectively. The residual strain of the sample shown in A Fig. 1a is thus estimated to be 20.20%. The minus sign of the value of 1' means that the alloy layer is expanded in the growth direction under the compressive biaxial stress in the basal plane from the substrate. This absolute value of 1' for the sample with x 0:17 is signi®cantly smaller than the value of 20.54% expected for the pseudomorphically strained Si0.83Ge0.17 layer on Si(001) substrate. This result suggests that the alloy layer is considerably relaxed with a relaxation rate of 59%. The obtained values of 1' of several samples are plotted in Fig. 2 as a function of Ge composition x. The absolute value of 1' 20.21% of sample with x 0:08 is slightly
Fig. 2. Residual strain and root mean squared (RMS) roughness of Si12xGex alloy layers grown on Si(001) as a function of Ge composition x.
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smaller than the expected value of 20.26% for the completely strained layer, suggesting the partial relaxation of the alloy layer (relaxation rate of 19%). The residual strain decreases with increase in x, and becomes almost zero at x 0:3 (relaxation rate of 100%). AFM images of the samples are shown in Fig. 3. The scanning area is 10 £ 10 mm 2 and the vertical scale has been enhanced by a factor of 1000 to emphasize the surface undulations. The sides of these ®gures are parallel to [100] and [010] directions, respectively. On the surface of the sample with x 0:08 (Fig. 3a), wavy undulation aligned
163
along the [100] direction is observed. The amplitude and frequency of the undulation are about 1.2 nm and 0.5 mm, respectively. Cullis et al. [12,13] and Dutartre et al. [14] ascribed the surface ripples aligned along [100] direction to the lowering of the system free energy by partial elastic strain relief due to oscillatory lattice plane distortion. Even though the present undulation is quite different in shape from ripples reported by them, these undulations should be due to the large residual strain in the ®lm as observed by XRD. Furthermore, a few light ridges running parallel to [110] and [110] directions are also seen. These ridges may
Fig. 3. Evolution of AFM images of Si12xGex alloy layers grown on Si(001) substrate without buffer layers depending on the Ge composition x, (a) x 0:08, (b) x 0:14, (c) x 0:17, (d) x 0:19, (e) x 0:27, (f) x 0:30. The sides of these ®gures are parallel to [100] and [010] directions, respectively.
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C. Tatsuyama et al. / Thin Solid Films 369 (2000) 161±166
be an indication of the formation of cross hatch. Formation of the cross hatch is considered due to the mis®t dislocations [15±19]. The appearance of cross-hatch pattern is thus consistent with reduced residual strain obtained by XRD measurement. According to People and Bean's theory [9], the critical thickness of alloy layer with x 0:08 is about 1.5 mm. Therefore, the strain relaxation starts to occur for the ®lms with thickness much smaller than the critical thickness expected by People and Bean's theory. The critical thickness would be very sensitive to the growth conditions,
such as growth temperature and growth rate. Our present results seem to support the smaller critical thickness given by van de Leur et al. [10] or Fukuda et al. [11]. On the surface of sample with x 0:17 (Fig. 3c), the undulations running parallel to [110] and [110] directions are observed all over the surface. Since this sample contains large residual strain, it may be considered that this is a cross-hatch pattern due to the generation of mis®t dialocations strongly in¯uenced by the strain. On the surface of sample with x 0:19 (Fig. 3d), the cross-hatch pattern with long-range order
Fig. 4. AFM images of Si0.7Ge0.3 alloy layers grown on Si(001) via graded buffer layer. The grading rate gr de®ned by % Ge/mm of buffer layer for each sample is (a) gr 76, (b) gr 59, (c) gr 48, (d) gr 39, (e) gr 22. The sides of these ®gures are parallel to [100] and [010] directions, respectively.
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covers all the surface, suggesting the generation of a lot of mis®t dislocations, resulting in the strain relaxation. In fact, the value of 1' of this sample is 0.15%, which is much smaller than the expected value for a strained layer (0.61%). Sample with x 0:27 (Fig. 3e) also shows a lot of cross hatches. In the case of sample with x 0:3 (Fig. 3f), irregular island-like structures appear, and cross-hatch pattern is no more seen. The surface roughness expressed by root mean squared (RMS) roughness is plotted in Fig. 2 as a function of Ge composition x in Si12xGex. It is found that RMS roughness increases monotonically with x, and reaches about 2.4 nm at x 0:3. Xie et al. [20] claimed that the pronounced surface roughness occurs for ®lms under compressive strain exceeding 1.4%. However, from our results, it is clear that the roughness can be observed for ®lms with strain less than 1%. 3.2. Si0.7Ge0.3 alloy layers grown on buffer layers Ê were grown Si0.7Ge0.3 alloy layers with thickness 2000 A on the compositionally graded SiGe buffer layers on Si(001) substrate. AFM images of all samples show cross-hatch patterns with long-range order aligned along [110] and [110] directions with a period of ridge and trough of 0.6±0.8 mm as shown in Fig. 4. The period slightly decreases with increase in grading rate. Fig. 5 plots RMS roughness over 20 £ 20 mm 2 AFM images as a function of Ge grading rate (gr) of the buffer layer. The residual strain 1' in the alloy layers estimated by XRD measurement (see Fig. 1b) is also plotted in Fig. 5. In strong contrast to the alloy layers grown without buffer layers, both change in similar manner with grading
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rate, indicating the intimate correlation between residual strain and surface roughness. For low grading rate, gr, they increase with grading rate, and show maximum at about 35% grading rate, above which they decrease for further increase in grading rate. The maximum value of RMS roughness is about 2.8 nm at 35% grading rate, which is slightly larger than the value for directly grown Ê (see Fig. alloy layer with x 0:3 and thickness of 5000 A 2). At low grading rate, the thickness of buffer layers is much larger than the critical thickness [15], resulting in the generation of a lot of dislocations leading to decrease in the residual strain. However, the dislocations are swept out from the edge of ®lm due to the slip on the {111} grid planes, resulting in the decrease of the surface roughness. The large thickness of the buffer layer for low grading rates would also play a role in the smoothing of the surface. At higher grading rate, a lot of dislocations are easily introduced due to the decrease in critical thickness as in the case of directly grown layer, which leads to the decrease in residual strain albeit the thickness is small. It is surprising that RMS roughness shows smaller values such as 1.1 nm for higher grading rates. According to Fitzgerald et al. [15], an increased grading rate enhances the surface roughness because dislocations are located closer to the surface. This is the case for grading rates lower than about 35% Ge/mm. However, in the present experiment, the surface roughness decreases for the grading rates over 35. As observed from the XTEM images of these samples(data are not shown), the dislocations are injected deep into the substrate, which may be the origin of the surface smoothing. These results imply that rather high grading rates such as 60% Ge/mm may be promising for the buffer layers, which is very important for the practical use. In fact, LeGoues et al. [2] have reported very low densities of threading dislocations by growing rather sharply graded layers (50% Ge/mm) at low temperature such as 5008C. They did not discuss in detail the surface roughening depending on the grading rates. The increase in the growth temperature signi®cantly enhances the surface roughness. In fact, the RMS values for graded layers with ®nal Ge composition of x 0:3 reported by Hsu et al. [16] are greater than the present values by about a factor of four, where the growth was performed at 9008C. 4. Conclusion
Fig. 5. Residual strain and root mean squared (RMS) roughness of Si0.7Ge0.3 alloy layers grown on Si(001) via graded buffer layer as a function of Ge grading rate (gr) of buffer layer.
Residual strain and surface roughness of Si12xGex (0 , x % 0:3) alloy layers grown by molecular beam epitaxy on Si(001) substrate at 5508C with and without compositionally graded buffer layers have been compared using XRD and AFM results. In the case of the growth without buffer layers, the surface morphology of the samples changed from wavy ripple pattern to a crosshatch pattern with increase in x, and, at x 0:3, the surface exhibited island-like pattern. The residual strain decreased with increase in x, whereas RMS roughness increased
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monotonically with x. In the case of Si0.7Ge0.3 alloy layers grown on buffer layers, the surfaces of all samples displayed cross-hatch pattern. The residual strain and RMS roughness showed similar dependence on grading rate with maximum at about 35% Ge/mm, suggesting a strong correlation between residual strain and surface morphology. References [1] E.A. Fitzgerald, Y.H. Xie, M.L. Green, et al., Phys. Lett. 59 (1991) 811. [2] F.K. LeGoues, B.S. Meyerson, J.F. Morar, Phys. Rev. Lett. 66 (1991) 2903. [3] P.J. Wang, B.S. Meyerson, K. Ismail, F.F. Fang, J. Nocera, MRS. Symp. Proc. 220 (1991) 403. [4] R. Hull, J.C. Bean, R.E. Leibenguth, D.J. Werder, J. Appl. Phys. 65 (1989) 4723. [5] B.S. Meyerson, K.J. Uram, F.K. LeGoues, Appl. Phys. Lett. 53 (1988) 2555. [6] P.M. Mooney, J.L. Jordan-Sweet, K. Ismail, J.O. Chu, R.M. Feensta, F.K. Legoues, Appl. Phys. Lett. 67 (1995) 2373. [7] T. Obata, K. Komeda, T. Nakao, H. Ueba, C. Tatsuyama, J. Appl. Phys. 81 (1997) 199.
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