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Formation of Ge self-assembled quantum dots on a SixGe1−x buffer layer
Applied Surface Science 252 (2005) 1476–1480 www.elsevier.com/locate/apsusc
Formation of Ge self-assembled quantum dots on a SixGe1x buffer layer Hyungjun Kim a, Chansun Shin b, Joonyeon Chang c,* a
b
Department of Electrical Engineering, University of California Los Angeles, Los Angeles, CA 90095-1595, USA Nuclear Materials Technology Development, Korea Atomic Energy Research Institute, Daejeon 305-353, Republic of Korea c Nano Device Research Center, Korea Institute of Science and Technology, P.O. Box 131, Chongryang, Seoul 136-791, Republic of Korea Received 10 July 2004; received in revised form 12 January 2005; accepted 22 February 2005 Available online 23 May 2005
Abstract Ge self-assembled quantum dots (SAQDs) grown on a relaxed Si0.75Ge0.25 buffer layer were observed using an atomic force microscopy (AFM) and a transmission electron microscopy (TEM). The effect of buried misfit dislocations on the formation and the distribution of Ge SAQDs was extensively investigated. The Burgers vector determination of each buried dislocation using the gb = 0 invisibility criterion with plane-view TEM micrographs shows that Ge SAQDs grow at specific positions related to the Burgers vectors of buried dislocations. The measurement of the lateral distance between a SAQD and the corresponding misfit dislocation with plane-view and cross-sectional TEM images reveals that SAQDs form at the intersections of the top surface with the slip planes of misfit dislocations. The stress field on the top surface due to misfit dislocations is computed, and it is found that the strain energy of the misfit dislocations provides the preferential formation sites for Ge SAQDs nucleation. # 2005 Elsevier B.V. All rights reserved. PACS: 85.30.V; 81.15.H; 61.16.B Keywords: Ge self-assembled quantum dots; Molecular beam epitaxy (MBE); Transmission electron microscopy (TEM)
1. Introduction Semiconductor quantum dots (QDs) in heteroepitaxial systems have been attractive because of their extensive optoelectronic applications such as lasers and photodetectors [1,2]. Carriers in QDs are confined * Corresponding author. Tel.: +82 2 958 6822; fax: +82 2 958 6851. E-mail address: [email protected] (J. Chang).
three dimensionally, and thus the optoelectronic properties of QDs are different from those of bulk materials, quantum wells and quantum wires. The shape and the size of QDs are important parameters in determining their optoelectronic properties [3,4]. Size and shape uniformity of QDs should be well controlled for enhanced performance of devices. Ge self-assembled quantum dots (SAQDs) on Si have served as a simple model system because the system consists of two components. Buried misfit
0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.02.141
H. Kim et al. / Applied Surface Science 252 (2005) 1476–1480
dislocations formed between a Si substrate and a SiGe buffer layer have been interesting because it can be employed as a tool to control the distribution of Ge SAQDs. The previous work [5] shows that the distribution of Ge SAQDs can be controlled by the density of the buried dislocation networks. The work of Kim et al. [6] pointed out that there exist three different types of effective sites for the nucleation and growth of Ge SAQDs: (i) the intersection of two perpendicular buried dislocations, (ii) a single dislocation line and (iii) the region beyond one diffusion length away from any dislocation. According to the work, the density of Ge adatoms increases homogeneously on a Si substrate at the beginning of deposition. After the initial stage of low Ge coverage, Ge adatoms diffuse to the effective sites due to the fact that the lattice constant of the locally strained effective sites are close to that of Ge. Consequently, Ge adatoms dwell longer at the effective sites, and form Ge SAQDs [7]. In this work, we observed the regular distribution of Ge SAQDs grown on a relaxed Si0.75Ge0.25 buffer layer causing low density of misfit dislocations to investigate the spatial relationship between misfit dislocations and preferential formation sites of SAQDs. The Burgers vector of each buried misfit dislocation is carefully determined with plane-view TEM. The preferential formation sites of Ge SAQDs are observed with crosssectional TEM micrographs. We have paid attention to the strain energy of the buried misfit dislocation network observed in TEM micrographs.
2. Experimental procedure ˚ thick Si0.75Ge0.25 layer was grown on a Si An 800 A (0 0 1) substrate at 550 8C. A Si0.75Ge0.25 layer is under compression as grown, which makes the surface ˚ thick Si cap layer was of the layer wrinkle. A 100 A deposited on a Si0.75Ge0.25 layer at 600 8C subsequently to keep the surface of a Si0.75Ge0.25 layer flat by equilibrating the stress state. The buffer layer consisting of a Si0.75Ge0.25 layer and a Si cap layer was annealed at 700 8C for 30 min afterward. The postgrowth annealing resulted in approximately 10% relaxation of the buffer layer. The composition of the relaxed buffer layer was found to generate misfit dislocations with a relatively large separation distance.
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Ge dots were nucleated on both a Si (0 0 1) substrate ˚ thick Ge and a Si (0 0 1) with the buffer layer. A 4.5 A layer was deposited first on Si at 280 8C so as to minimize alloying between Si and Ge dots [8]. Ge dots were grown subsequently at 650 8C with a constant ˚ /s. All epitaxial layers were grown growth rate of 0.05 A using a molecular beam epitaxy (MBE, Riber EVA32). The size and the shape of nucleated SAQDs were characterized using a Park Scientific atomic force microscopy (AFM) in contact mode. TEM specimens for (0 0 1) plane-view and h1 1 0i cross-sectional observations were prepared by chemical thinning in a room-temperature HF/HNO3 solution and by ionbeam thinning using a Gatan 660 Ion-Beam thinner with a cold stage respectively. TEM micrographs were taken with a Philips CM30 and a JEOL 2000FX transmission electron microscopy. Buried misfit dislocations and the nucleation sites of Ge SAQDs were observed with plane-view and cross-sectional TEM images. The Burgers vector of each dislocation was determined by the gb = 0 invisibility criterion.
3. Results and discussion Fig. 1 shows AFM morphologies of Ge SAQDs grown on two different types of substrates. In the case of Ge SAQDs nucleated on a Si (0 0 1) substrate (Fig. 1(a)), Ge dots are distributed randomly. Ge SAQDs grown on the relaxed buffer layer (Fig. 1(b)), however, are well aligned along two orthogonal lines. The relaxed buffer layer provides preferential formation sites of Ge SAQDs. It was also observed that the buffer layer promotes the formation of Ge SAQDs. A plane-view TEM image corresponding to Fig. 1(b) is shown in Fig. 2(a). Lines represent misfit dislocations nucleated at the interface between the relaxed buffer layer and a Si (0 0 1) substrate, and small dots are Ge SAQDs. The misfit dislocation lines are found to be generated along two orthogonal lines of [1 1 0] and ½1 1¯ 0 in order to accommodate the lattice mismatch between the substrate and a partially relaxed Si0.75Ge0.25 layer. The composition of the buffer layer induces relatively large separation distance of a few hundred nanometers between adjacent misfit dislocations. The density of misfit dislocations can be easily controlled by changing the composition x of SixGe1x because the lattice parameter of Ge is 4% larger than
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Fig. 2. (a) A (0 0 1) plane-view TEM micrograph of Ge SAQDs grown on the relaxed Si0.75Ge0.25 buffer layer. The projection of the Burgers vector of each misfit dislocation is marked as arrows. (b) A schematic view of a [1, 1, 0] misfit dislocation line and the four possible Burgers vectors on two {1 1 1} planes.
Fig. 1. AFM images of Ge SAQDs showing different mode of distribution depending on the presence of a buried misfit dislocation network.
that of Si. Ge SAQDs are found to be well aligned to the buried misfit dislocation lines, and it should be noted that Ge SAQDs form at a certain distance from the misfit dislocation lines. The Burgers vector of each dislocation in Fig. 2(a) was determined by the gb = 0 invisibility criterion ¯ 1 3 1; ¯ 1 1 1¯ and with four different g vectors i.e., 1¯ 3 1; ¯1 1 1: ¯ The Burgers vector of each dislocation line is projected on the (0 0 1) plane and represented by arrows in Fig. 2(a). It is assumed that all the Burgers vectors make an acute angle with the [0 0 1] direction. The slip system of the diamond structure such as Si and Ge is h1 1 0i{1 1 1}, and misfit dislocations on the interface between a Si (0 0 1) substrate and a relaxed SiGe layer are known to be a mixed edge-screw type
with the Burgers vector oriented 608 from a dislocation line direction [9,10] as observed in this work. Fig. 2(b) represents a schematic diagram of a ½1¯ 1 0 misfit dislocation line lying on a (0 0 1) plane and the four possible Burgers vectors. The slip plane is ¯ plane, which is inclined to either (1 1 1) or ð1 1 1Þ (0 0 1) plane with an angle of 54.78. From the determination of the Burgers vector, it is found that Ge SAQDs are nucleated at one side of the buried misfit dislocation, which is offset to the corresponding Burgers vector direction. The position of one array of SAQDs is marked by a dashed line in Fig. 2(a) along the corresponding [1 1 0] dislocation line. In order to investigate the relationship between buried misfit dislocation network and preferential formation sites of Ge SAQDs rigorously, h1 1 0i crosssectional TEM micrographs are examined. Fig. 3(a) shows such a cross-sectional micrograph viewed along [1 1 0], in which misfit dislocations are indicated by arrows. The average distance between a dislocation
H. Kim et al. / Applied Surface Science 252 (2005) 1476–1480
Fig. 3. (a) A [1 1 0] cross-sectional TEM micrograph. White arrows represent buried misfit dislocations. (b) A schematic view of a Ge SAQD and the corresponding misfit dislocation.
line and a Ge SAQD in Fig. 3(a) is found to be ˚ . The distance agrees well to the lateral 650 13 A distance between a misfit dislocation and the position where the slip plane of the dislocation intersects the ˚ thick buffer layer as shown in top surface of the 900 A Fig. 3(b). Ge SAQDs thus grow at the specific positions where the slip planes of buried dislocations intersect with the top surface. This fact suggests that the distribution of Ge SAQDs can be manipulated by utilizing a buried misfit dislocation network. A two-dimensional array of long straight dislocations with the same configuration as shown in Fig. 2(a) is constructed in order to compute the elastic stress field of the array of dislocation lines. The stress field due to a dislocation line is calculated using the Li’s formula [11] under the assumption of isotropic linear elasticity, and the image stress field due to the free surface is computed using the method of Gosling and Willis [12]. The strain energy is computed assuming Hookean elasticity. The array of misfit dislocations and the corresponding strain energy per unit volume on the top surface are shown in Fig. 4. The unit strain energy is normalized by mb/{4p(1 n)} with m and n being the shear modulus and the Poisson’s ratio of the buffer layer respectively. The maximum value of the normalized strain energy is
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Fig. 4. The contour of the computed unit strain energy on the top surface: solid lines represent underlying misfit dislocation lines and dotted lines indicate the intersections between the slip planes of the dislocations and the top surface. The Burgers vector of each dislocation line is also marked (minimum, maximum and the number of contour levels: 3 107, 4.5 106, 11).
4.76 106. The contour of the normalized unit strain energy shows that the region of the maximum strain energy is offset to the intersection line of each slip plane, where Ge SAQDs form preferentially as observed experimentally. Ross [13] showed that the nucleation of Ge SAQDs occurs approximately at the point of the maximum tensile strain (exx + eyy) due to a single dislocation. In the case of a dislocation network comprising several perpendicular misfit dislocations, however, the nucleation sites of Ge SAQDs are not always corresponding to the region of the maximum tensile strain of the dislocation network involved. The strain energy of buried dislocations is likely to be an important factor for the distribution of Ge SAQDs, and SAQDs are nucleated on the top surface by reducing the strain energy due to buried misfit dislocations. Based on the results, it is concluded that the intersection of two perpendicular buried dislocations is energetically most favorable site for the formation of Ge SAQDs among three effective sites proposed in [6].
4. Summary Systematic AFM and TEM observations were performed to investigate the relationship between
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misfit dislocations and the distribution of Ge SAQDs. Ge SAQDs form randomly on a Si (0 0 1) substrate, whereas they are nucleated along misfit dislocations buried in a relaxed Si0.75Ge0.25 buffer layer. Both plane-view and cross-sectional TEM images clearly show that Ge SAQDs grow at specific positions where the slip planes of misfit dislocations intersect with the surface of the buffer layer. The computation of the stress field of the buried misfit dislocation network observed experimentally shows that the location of Ge SAQDs is well aligned with the region of the maximum strain energy due to the dislocation network. This result implies that a uniform distribution of Ge SAQDs can be successfully achieved by utilizing a uniform network of misfit dislocations generated in a partially relaxed SiGe buffer layer.
Acknowledgements This work was supported by ‘‘Korea Institute of Science of Technology Vision 21st program and R&D Program for NT-IT Fusion Strategy of Advanced Technologies’’. The authors are grateful to
Dr. M. Fivel from GPM2, Institut national polytechnique de Grenoble (France) for helpful discussions on the computation of image stresses.
References [1] K. Eberl, Phys. World 9 (1997) 47. [2] Zh.I. Alferov, Phys. Scripta 68 (1996) 32. [3] R. Leon, S. Farard, D. Leonard, J.L. Merz, P.M. Petroff, Appl. Phys. Lett. 67 (1995) 521. [4] A.A. Seraphin, E. Werwa, K.D. Kolenbrabder, J. Mater. Res. 12 (1997) 3386. [5] H.J. Kim, J.Y. Chang, Y.H. Xie, J. Cryst. Growth 247 (2003) 251. [6] H.J. Kim, Z.M. Zhao, Y.H. Xie, Phys. Rev. B 68 (2003) 205312. [7] H.J. Kim, Z.M. Zhao, J. Liu, V. Ozolins, J.Y. Chang, Y.H. Xie, J. Appl. Phys. 95 (2004) 6065. [8] E.A. Fitzgerald, Mater. Sci. Rep. 7 (1991) 87. [9] J.C. Bean, R. Hull, Scripta Metall. Mater. 27 (1992) 663. [10] H.J. Kim, Y.H. Xie, Appl. Phys. Lett. 79 (2001) 263. [11] J.C.M. Li, Phil. Mag. 10 (1964) 1097. [12] T.J. Gosling, J.R. Willis, J. Mech. Phys. Solids 42 (1994) 1199. [13] F.M. Ross, IBM J. Res. Dev. 44 (2000) 489.
Formation of Ge self-assembled quantum dots on a SixGe1x buffer layer Hyungjun Kim a, Chansun Shin b, Joonyeon Chang c,* a
b
Department of Electrical Engineering, University of California Los Angeles, Los Angeles, CA 90095-1595, USA Nuclear Materials Technology Development, Korea Atomic Energy Research Institute, Daejeon 305-353, Republic of Korea c Nano Device Research Center, Korea Institute of Science and Technology, P.O. Box 131, Chongryang, Seoul 136-791, Republic of Korea Received 10 July 2004; received in revised form 12 January 2005; accepted 22 February 2005 Available online 23 May 2005
Abstract Ge self-assembled quantum dots (SAQDs) grown on a relaxed Si0.75Ge0.25 buffer layer were observed using an atomic force microscopy (AFM) and a transmission electron microscopy (TEM). The effect of buried misfit dislocations on the formation and the distribution of Ge SAQDs was extensively investigated. The Burgers vector determination of each buried dislocation using the gb = 0 invisibility criterion with plane-view TEM micrographs shows that Ge SAQDs grow at specific positions related to the Burgers vectors of buried dislocations. The measurement of the lateral distance between a SAQD and the corresponding misfit dislocation with plane-view and cross-sectional TEM images reveals that SAQDs form at the intersections of the top surface with the slip planes of misfit dislocations. The stress field on the top surface due to misfit dislocations is computed, and it is found that the strain energy of the misfit dislocations provides the preferential formation sites for Ge SAQDs nucleation. # 2005 Elsevier B.V. All rights reserved. PACS: 85.30.V; 81.15.H; 61.16.B Keywords: Ge self-assembled quantum dots; Molecular beam epitaxy (MBE); Transmission electron microscopy (TEM)
1. Introduction Semiconductor quantum dots (QDs) in heteroepitaxial systems have been attractive because of their extensive optoelectronic applications such as lasers and photodetectors [1,2]. Carriers in QDs are confined * Corresponding author. Tel.: +82 2 958 6822; fax: +82 2 958 6851. E-mail address: [email protected] (J. Chang).
three dimensionally, and thus the optoelectronic properties of QDs are different from those of bulk materials, quantum wells and quantum wires. The shape and the size of QDs are important parameters in determining their optoelectronic properties [3,4]. Size and shape uniformity of QDs should be well controlled for enhanced performance of devices. Ge self-assembled quantum dots (SAQDs) on Si have served as a simple model system because the system consists of two components. Buried misfit
0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.02.141
H. Kim et al. / Applied Surface Science 252 (2005) 1476–1480
dislocations formed between a Si substrate and a SiGe buffer layer have been interesting because it can be employed as a tool to control the distribution of Ge SAQDs. The previous work [5] shows that the distribution of Ge SAQDs can be controlled by the density of the buried dislocation networks. The work of Kim et al. [6] pointed out that there exist three different types of effective sites for the nucleation and growth of Ge SAQDs: (i) the intersection of two perpendicular buried dislocations, (ii) a single dislocation line and (iii) the region beyond one diffusion length away from any dislocation. According to the work, the density of Ge adatoms increases homogeneously on a Si substrate at the beginning of deposition. After the initial stage of low Ge coverage, Ge adatoms diffuse to the effective sites due to the fact that the lattice constant of the locally strained effective sites are close to that of Ge. Consequently, Ge adatoms dwell longer at the effective sites, and form Ge SAQDs [7]. In this work, we observed the regular distribution of Ge SAQDs grown on a relaxed Si0.75Ge0.25 buffer layer causing low density of misfit dislocations to investigate the spatial relationship between misfit dislocations and preferential formation sites of SAQDs. The Burgers vector of each buried misfit dislocation is carefully determined with plane-view TEM. The preferential formation sites of Ge SAQDs are observed with crosssectional TEM micrographs. We have paid attention to the strain energy of the buried misfit dislocation network observed in TEM micrographs.
2. Experimental procedure ˚ thick Si0.75Ge0.25 layer was grown on a Si An 800 A (0 0 1) substrate at 550 8C. A Si0.75Ge0.25 layer is under compression as grown, which makes the surface ˚ thick Si cap layer was of the layer wrinkle. A 100 A deposited on a Si0.75Ge0.25 layer at 600 8C subsequently to keep the surface of a Si0.75Ge0.25 layer flat by equilibrating the stress state. The buffer layer consisting of a Si0.75Ge0.25 layer and a Si cap layer was annealed at 700 8C for 30 min afterward. The postgrowth annealing resulted in approximately 10% relaxation of the buffer layer. The composition of the relaxed buffer layer was found to generate misfit dislocations with a relatively large separation distance.
1477
Ge dots were nucleated on both a Si (0 0 1) substrate ˚ thick Ge and a Si (0 0 1) with the buffer layer. A 4.5 A layer was deposited first on Si at 280 8C so as to minimize alloying between Si and Ge dots [8]. Ge dots were grown subsequently at 650 8C with a constant ˚ /s. All epitaxial layers were grown growth rate of 0.05 A using a molecular beam epitaxy (MBE, Riber EVA32). The size and the shape of nucleated SAQDs were characterized using a Park Scientific atomic force microscopy (AFM) in contact mode. TEM specimens for (0 0 1) plane-view and h1 1 0i cross-sectional observations were prepared by chemical thinning in a room-temperature HF/HNO3 solution and by ionbeam thinning using a Gatan 660 Ion-Beam thinner with a cold stage respectively. TEM micrographs were taken with a Philips CM30 and a JEOL 2000FX transmission electron microscopy. Buried misfit dislocations and the nucleation sites of Ge SAQDs were observed with plane-view and cross-sectional TEM images. The Burgers vector of each dislocation was determined by the gb = 0 invisibility criterion.
3. Results and discussion Fig. 1 shows AFM morphologies of Ge SAQDs grown on two different types of substrates. In the case of Ge SAQDs nucleated on a Si (0 0 1) substrate (Fig. 1(a)), Ge dots are distributed randomly. Ge SAQDs grown on the relaxed buffer layer (Fig. 1(b)), however, are well aligned along two orthogonal lines. The relaxed buffer layer provides preferential formation sites of Ge SAQDs. It was also observed that the buffer layer promotes the formation of Ge SAQDs. A plane-view TEM image corresponding to Fig. 1(b) is shown in Fig. 2(a). Lines represent misfit dislocations nucleated at the interface between the relaxed buffer layer and a Si (0 0 1) substrate, and small dots are Ge SAQDs. The misfit dislocation lines are found to be generated along two orthogonal lines of [1 1 0] and ½1 1¯ 0 in order to accommodate the lattice mismatch between the substrate and a partially relaxed Si0.75Ge0.25 layer. The composition of the buffer layer induces relatively large separation distance of a few hundred nanometers between adjacent misfit dislocations. The density of misfit dislocations can be easily controlled by changing the composition x of SixGe1x because the lattice parameter of Ge is 4% larger than
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H. Kim et al. / Applied Surface Science 252 (2005) 1476–1480
Fig. 2. (a) A (0 0 1) plane-view TEM micrograph of Ge SAQDs grown on the relaxed Si0.75Ge0.25 buffer layer. The projection of the Burgers vector of each misfit dislocation is marked as arrows. (b) A schematic view of a [1, 1, 0] misfit dislocation line and the four possible Burgers vectors on two {1 1 1} planes.
Fig. 1. AFM images of Ge SAQDs showing different mode of distribution depending on the presence of a buried misfit dislocation network.
that of Si. Ge SAQDs are found to be well aligned to the buried misfit dislocation lines, and it should be noted that Ge SAQDs form at a certain distance from the misfit dislocation lines. The Burgers vector of each dislocation in Fig. 2(a) was determined by the gb = 0 invisibility criterion ¯ 1 3 1; ¯ 1 1 1¯ and with four different g vectors i.e., 1¯ 3 1; ¯1 1 1: ¯ The Burgers vector of each dislocation line is projected on the (0 0 1) plane and represented by arrows in Fig. 2(a). It is assumed that all the Burgers vectors make an acute angle with the [0 0 1] direction. The slip system of the diamond structure such as Si and Ge is h1 1 0i{1 1 1}, and misfit dislocations on the interface between a Si (0 0 1) substrate and a relaxed SiGe layer are known to be a mixed edge-screw type
with the Burgers vector oriented 608 from a dislocation line direction [9,10] as observed in this work. Fig. 2(b) represents a schematic diagram of a ½1¯ 1 0 misfit dislocation line lying on a (0 0 1) plane and the four possible Burgers vectors. The slip plane is ¯ plane, which is inclined to either (1 1 1) or ð1 1 1Þ (0 0 1) plane with an angle of 54.78. From the determination of the Burgers vector, it is found that Ge SAQDs are nucleated at one side of the buried misfit dislocation, which is offset to the corresponding Burgers vector direction. The position of one array of SAQDs is marked by a dashed line in Fig. 2(a) along the corresponding [1 1 0] dislocation line. In order to investigate the relationship between buried misfit dislocation network and preferential formation sites of Ge SAQDs rigorously, h1 1 0i crosssectional TEM micrographs are examined. Fig. 3(a) shows such a cross-sectional micrograph viewed along [1 1 0], in which misfit dislocations are indicated by arrows. The average distance between a dislocation
H. Kim et al. / Applied Surface Science 252 (2005) 1476–1480
Fig. 3. (a) A [1 1 0] cross-sectional TEM micrograph. White arrows represent buried misfit dislocations. (b) A schematic view of a Ge SAQD and the corresponding misfit dislocation.
line and a Ge SAQD in Fig. 3(a) is found to be ˚ . The distance agrees well to the lateral 650 13 A distance between a misfit dislocation and the position where the slip plane of the dislocation intersects the ˚ thick buffer layer as shown in top surface of the 900 A Fig. 3(b). Ge SAQDs thus grow at the specific positions where the slip planes of buried dislocations intersect with the top surface. This fact suggests that the distribution of Ge SAQDs can be manipulated by utilizing a buried misfit dislocation network. A two-dimensional array of long straight dislocations with the same configuration as shown in Fig. 2(a) is constructed in order to compute the elastic stress field of the array of dislocation lines. The stress field due to a dislocation line is calculated using the Li’s formula [11] under the assumption of isotropic linear elasticity, and the image stress field due to the free surface is computed using the method of Gosling and Willis [12]. The strain energy is computed assuming Hookean elasticity. The array of misfit dislocations and the corresponding strain energy per unit volume on the top surface are shown in Fig. 4. The unit strain energy is normalized by mb/{4p(1 n)} with m and n being the shear modulus and the Poisson’s ratio of the buffer layer respectively. The maximum value of the normalized strain energy is
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Fig. 4. The contour of the computed unit strain energy on the top surface: solid lines represent underlying misfit dislocation lines and dotted lines indicate the intersections between the slip planes of the dislocations and the top surface. The Burgers vector of each dislocation line is also marked (minimum, maximum and the number of contour levels: 3 107, 4.5 106, 11).
4.76 106. The contour of the normalized unit strain energy shows that the region of the maximum strain energy is offset to the intersection line of each slip plane, where Ge SAQDs form preferentially as observed experimentally. Ross [13] showed that the nucleation of Ge SAQDs occurs approximately at the point of the maximum tensile strain (exx + eyy) due to a single dislocation. In the case of a dislocation network comprising several perpendicular misfit dislocations, however, the nucleation sites of Ge SAQDs are not always corresponding to the region of the maximum tensile strain of the dislocation network involved. The strain energy of buried dislocations is likely to be an important factor for the distribution of Ge SAQDs, and SAQDs are nucleated on the top surface by reducing the strain energy due to buried misfit dislocations. Based on the results, it is concluded that the intersection of two perpendicular buried dislocations is energetically most favorable site for the formation of Ge SAQDs among three effective sites proposed in [6].
4. Summary Systematic AFM and TEM observations were performed to investigate the relationship between
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misfit dislocations and the distribution of Ge SAQDs. Ge SAQDs form randomly on a Si (0 0 1) substrate, whereas they are nucleated along misfit dislocations buried in a relaxed Si0.75Ge0.25 buffer layer. Both plane-view and cross-sectional TEM images clearly show that Ge SAQDs grow at specific positions where the slip planes of misfit dislocations intersect with the surface of the buffer layer. The computation of the stress field of the buried misfit dislocation network observed experimentally shows that the location of Ge SAQDs is well aligned with the region of the maximum strain energy due to the dislocation network. This result implies that a uniform distribution of Ge SAQDs can be successfully achieved by utilizing a uniform network of misfit dislocations generated in a partially relaxed SiGe buffer layer.
Acknowledgements This work was supported by ‘‘Korea Institute of Science of Technology Vision 21st program and R&D Program for NT-IT Fusion Strategy of Advanced Technologies’’. The authors are grateful to
Dr. M. Fivel from GPM2, Institut national polytechnique de Grenoble (France) for helpful discussions on the computation of image stresses.
References [1] K. Eberl, Phys. World 9 (1997) 47. [2] Zh.I. Alferov, Phys. Scripta 68 (1996) 32. [3] R. Leon, S. Farard, D. Leonard, J.L. Merz, P.M. Petroff, Appl. Phys. Lett. 67 (1995) 521. [4] A.A. Seraphin, E. Werwa, K.D. Kolenbrabder, J. Mater. Res. 12 (1997) 3386. [5] H.J. Kim, J.Y. Chang, Y.H. Xie, J. Cryst. Growth 247 (2003) 251. [6] H.J. Kim, Z.M. Zhao, Y.H. Xie, Phys. Rev. B 68 (2003) 205312. [7] H.J. Kim, Z.M. Zhao, J. Liu, V. Ozolins, J.Y. Chang, Y.H. Xie, J. Appl. Phys. 95 (2004) 6065. [8] E.A. Fitzgerald, Mater. Sci. Rep. 7 (1991) 87. [9] J.C. Bean, R. Hull, Scripta Metall. Mater. 27 (1992) 663. [10] H.J. Kim, Y.H. Xie, Appl. Phys. Lett. 79 (2001) 263. [11] J.C.M. Li, Phil. Mag. 10 (1964) 1097. [12] T.J. Gosling, J.R. Willis, J. Mech. Phys. Solids 42 (1994) 1199. [13] F.M. Ross, IBM J. Res. Dev. 44 (2000) 489.