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MgxZn1−xO heterostructures
ARTICLE IN PRESS
Journal of Physics and Chemistry of Solids 69 (2008) 497–500 www.elsevier.com/locate/jpcs
Defect and interface studies of ZnO/MgxZn1xO heterostructures Z. Vashaeia,, T. Minegishia, H. Suzukia, M.W. Chob, T. Yaoa,b a
Center for Interdisciplinary Research, Tohoku University, Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan b Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Abstract The defect characteristics of ZnO layers grown on thin MgxZn1xO buffer layers with two different crystal structures of cubic and wurtzite are investigated by transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) and high-resolution X-ray diffraction (HRXRD). It was found that the screw dislocation density of ZnO layers grown on MgZnO-wurtzite buffer layer are lower than ZnO layers grown on MgZnO-cubic buffer layers, while the edge dislocation density in ZnO layers grown on MgZnO-wurtzite buffer layer are slightly higher than for ZnO layers grown on MgZnO-cubic buffer layers. Dislocation loop and stacking fault were observed in ZnO/MgZnO-cubic layers. r 2007 Elsevier Ltd. All rights reserved. Keywords: D. Defects
1. Introduction ZnO is a II–VI wide band gap (3.37 eV) semiconductor with a large exciton binding energy of 60 meV, which has attracted considerable attention as a promising candidate for optical and electronic device applications [1]. It is well known that the electrical and optical properties of ZnO films depend on the microstructure, and that the presence of defects and the structure of the film–substrate interface have a crucial role in device performance. Low-cost sapphire substrates have been most extensively used as a substrate for ZnO. However, the crystal quality of ZnO grown directly on (0 0 0 1) sapphire tends to be very poor due to the formation of twins caused by the large lattice and thermal mismatch [2]. In order to improve the crystal quality of ZnO layers, much effort has been devoted to seeking a suitable buffer layer for ZnO epilayers such as MgO and GaN [2–4]. Very recently, development of a Ga modified sapphire technique has also reported [5,6]. MgxZn1xO alloys, which possess rock salt cubic structures for x40.41 and hexagonal wurtzite structures for xo0.41 [7], have been of substantial interest as a barrier
Corresponding author. Tel.: +81 22 215 2074; fax: +81 22 215 2073.
E-mail address: [email protected] (Z. Vashaei). 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.07.032
for ZnO in QW structures [8]. However, there has been no report on MgZnO buffer layers for ZnO epitaxy. Therefore, this study has been devoted to the investigation of defects in ZnO layers grown on thin MgxZn1xO buffer layers with the two different crystal structures of cubic and wurtzite. The defects morphology, including dislocations, stacking faults (SF), and interface defects, was investigated by transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) and highresolution X-ray diffraction (HRXRD). 2. Experimental The samples were grown on Al2O3 (0 0 0 1) substrates by plasma-assisted molecular beam epitaxy (P-MBE). Substrate pretreatments were performed in a sequence of chemical etching, annealing, and O-plasma pre-exposure. A few-nm-thick MgO buffer layer followed by a 5-nmthick MgxZn1xO layer were deposited at 550 1C followed by annealing at 800 1C. Then, ZnO layers were grown at a low temperature of 550 1C for 20 min followed by annealing and high-temperature growth at 800 1C. Two sets of samples with different crystal structures of MgxZn1xO buffer layer were prepared. In Sample A, the buffer layer was cubic-MgxZn1xO (xffi0.75) while sample B was grown on a wurtzite-MgxZn1xO (xffi0.25) buffer layer.
ARTICLE IN PRESS Z. Vashaei et al. / Journal of Physics and Chemistry of Solids 69 (2008) 497–500
498
Hereafter, for convenience, we call cubic-MgxZn1xO, MgZnO(c), and wurtzite-MgxZn1xO, MgZnO(w). HRXRD experiments were carried out with a Philips, X’ Pert-MRD diffractometer. Cross-section TEM specimens were prepared by conventional techniques consisting of mechanical polishing, dimpling, and Ar ion milling. Defects were investigated using a JEOL-2000EX II TEM operated at 200 kV. The interface study was performed by HRTEM observation using a JEOL JEM-ARM 1250 electron microscope operated at 1250 kV and a JEOL 3010 at 300 kV. 3. Results and discussion Fig. 1 shows XRD o-rocking curves of ZnO(0 0 0 2) and (1 0 1¯ 1) f-scan for both samples A and B. Basically, screw dislocations contribute to broaden the out-of-plane rocking curve, whereas broadening of asymmetry f-scan such as (1 0 1¯ 0) is attributed to edge dislocations. The narrow full-width at half-maximum (FWHM) value of the ZnO(0 0 0 2) diffraction peak of sample B, which is as
small as 10 arcsec in comparison with 576 arcsec for sample A (Fig. 1(a)), indicates a low density of dislocations with a screw component. However, as Fig. 1(b) shows, the FWHM value of ZnO(1 0 1¯ 1) f-scan peak for sample B is a little smaller than that of sample A, suggesting fewer pure-edge dislocations. To get more insight into the nature of the defects in both samples, TEM dislocation observation was carried out. Fig. 2(a, b) and (c, d) shows cross-section TEM (XTEM) micrographs of the ZnO/Mg0.75 Zn0.25O(c) (sample A) and ZnO/Mg0.25 Zn0.75O(w) (sample B), respectively. The samples were observed near the [1 1 2¯ 0] zone axis under the bright field condition with g ¼ [0 0 0 2] (images (a) and (c)) and weak-beam condition with g ¼ [1 0 1¯ 0] (images (b) and (c)), which make screw and edge components of dislocations visible, respectively. Fig. 2(a and c) clearly shows that the screw-type threading dislocation (TD) density in sample A is higher than in sample B, which confirms the XRD results. It should be noted that in the XTEM micrograph of sample A, mixed TDs are also observable in addition to edge
Fig. 1. XRD o-rocking curves of ZnO(0 0 0 2) (a) and f-scan of ZnO(1 0 1¯ 1) (b) diffraction peaks.
Fig. 2. XTEM images of ZnO layers grown on Mg0.75Zn0.25O(c)/c-sapphire (a, b) and Mg0.25Zn0.75O(w)/c-sapphire (c, d). Bright-field condition with g ¼ [0 0 0 2] was used for (a, c) and weak-beam condition with g ¼ (1 0 1¯ 0) was used for (b, d).
ARTICLE IN PRESS Z. Vashaei et al. / Journal of Physics and Chemistry of Solids 69 (2008) 497–500
and screw TDs, while no mixed TDs were observed in sample B. Screw dislocations with opposite Burgers vectors can be paired to form dislocation loops as is observed in Fig. 2(a). This feature is an effect of the cubic structure of the MgZnO buffer layer, which has a different dislocation slip system from a hexagonal crystal structure. The same features have been reported in previous reports about ZnO grown on c-sapphire with an ultra-thin Ga wetting layer [6] and silicon delta-doped GaN grown on Si(1 1 1) [9]. XTEM results confirm the XRD results that for both samples the majority of TDs are edge-type dislocations with Burgers vectors 1/3/1 1 2¯ 0S. The same features were reported for ZnO on c-sapphire with a MgO buffer layer [10]. However, XTEM results confirm the lower edge-type TD density for sample A than sample B as XRD results show. By observing several pictures, the average TD Table 1 Dislocation densities in ZnO/Mg0.75Zn0.25O(c)/c-sapphire (sample A) and ZnO/Mg0.25Zn0.75O(w)/c-sapphire (sample B) Samples
ZnO/Mg0.75Zn0.25O(c) ZnO/Mg0.25Zn0.75O(w)
Dislocation Screw (cm2)
Edge (cm2)
Mixed (cm2)
1.97 109 9.14 106
3.20 109 4.94 109
1.35 109 –
499
Fig. 4. HRTEM image of ZnO/Mg0.25Zn0.75O(w)/c-sapphire near the interface.
densities were determined and the results are summarized in Table 1. Fig. 3(a) shows an HRTEM image along the [1 1 2¯ 0] zone axis taken of the hetero interfaces of sample A. The ZnO/MgZnO(c) interface is not completely smooth due to the 3D-growth mode of MgZnO(c) as was confirmed by RHEED patterns during growth (not shown). No ZnO with a cubic structure near the MgZnO(c) layer is observed. The squares show the area with partial dislocations that terminate SF. To reduce contrast inhomogeniety, a small section marked with 1 containing a partial dislocation, is Fourier filtered using only the {0 0 0 2} and {1 1¯ 0 0} reflections. Fig. 3(b) shows the filtered image and illustrates the Burgers circuit. Two low-energy SF types with different stacking sequences are favorable in a hexagonal structure [11]. The observed Burgers vector projection is compatible with a Frank partial dislocation with Burgers vector b ¼ 1/6/2 2¯ 0 3S (Fig. 3(c)). The corresponding stacking fault type is characterized by AaBbAaBbAa|CcAaCcAa (the large and small letters denote the cation and anion sites, respectively). The most probable model for generation of such SF is the condensation of vacancies or interstitial, which leads to a missing or additional (0 0 0 2) plane [12]. Fig. 4 represents an HRTEM image taken near the interface of sample B under the [1 1 2¯ 0] zone axis. A noticeable aspect is the undistinguishable interface between ZnO and MgZnO(w) which is evidence of a good lattice match. 4. Conclusions
Fig. 3. HRTEM micrograph of ZnO/Mg0.75Zn0.25O(c)/c-sapphire near the interface (a). Fourier-filtered HRTEM image of a partial dislocation from the region marked by the square in (a) accompanied by Burgers circuit (b). Illustration of the Burgers vector corresponding to a SF (c).
In summary, we characterized the defect structure of ZnO films grown on MgZnO(c) and MgZnO(w) layers by TEM and XRD. It was found that ZnO layers grown on MgZnO(w) buffer layers have much lower screw-type TD density than those grown on MgZnO(c), while they have a slightly larger edge-type TD density than ZnO layer grown on MgZnO(c) buffer. Mixed-type TDs and dislocation loops were observed in ZnO layers grown on MgZnO(c).
ARTICLE IN PRESS 500
Z. Vashaei et al. / Journal of Physics and Chemistry of Solids 69 (2008) 497–500
HRTEM observation demonstrated the SFs formation near the ZnO/MgZnO(c) heterointerface. No mixed-type TDs and SFs were observed in ZnO layers grown on MgZnO(w). References [1] Y. Chen, D.M. Bagnall, H.J. Koh, K.T. Park, K. Hiraga, Z. Zhu, T. Yao, J. Appl. Phys. 84 (1998) 3912. [2] Y. Chen, H.J. Ko, S.K. Hong, T. Yao, Appl. Phys. Lett. 76 (2000) 559. [3] A. Setiawan, H.J. Ko, S.K. Hong, Y. Chen, T. Yao, Thin Solid Films 445 (2003) 213. [4] S.K. Hong, H.J. Ko, Y. Chen, T. Yao, J. Cryst. Growth 209 (2000) 537.
[5] H.P. Sun, X.Q. Pan, X.L. Du, Z.X. Mei, Z.Q. Zeng, Q.K. Xue, Appl. Phys. Lett. 85 (2004) 4385. [6] Y. Wang, X.L. Du, Z.X. Mei, Z.Q. Zeng, Q.Y. Xu, Q.K. Xue, Z. Zhang, J. Cryst. Growth 273 (2004) 100. [7] Z. Vashaei, T. Minegishi, H. Suzuki, T. Hanada, M.W. Cho, T. Yao, A. Setiawan, J. Appl. Phys. 98 (2005) 054911. [8] T. Makino, Y. Segawa, M. Kawasaki, H. Koinuma, Semicond. Sci. Technol. 20 (2005) S78. [9] O. Contreras, F.A. Ponce, J. Christen, A. Dadgar, A. Krost, Appl. Phys. Lett. 81 (2002) 4712. [10] A. Setiawan, Z. Vashaei, M.W. Cho, T. Yao, H. Kato, M. Sano, K. Miyamoto, I. Yonenaga, H.J. Ko, J. Appl. Phys. 96 (2004) 3763. [11] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley, New York, 1982, p. 354. [12] D. Gerthsen, D. Litvinov, Th. Gruber, C. Kirchner, A. Waag, Appl. Phys. Lett. 81 (2002) 3972.
Journal of Physics and Chemistry of Solids 69 (2008) 497–500 www.elsevier.com/locate/jpcs
Defect and interface studies of ZnO/MgxZn1xO heterostructures Z. Vashaeia,, T. Minegishia, H. Suzukia, M.W. Chob, T. Yaoa,b a
Center for Interdisciplinary Research, Tohoku University, Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan b Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Abstract The defect characteristics of ZnO layers grown on thin MgxZn1xO buffer layers with two different crystal structures of cubic and wurtzite are investigated by transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) and high-resolution X-ray diffraction (HRXRD). It was found that the screw dislocation density of ZnO layers grown on MgZnO-wurtzite buffer layer are lower than ZnO layers grown on MgZnO-cubic buffer layers, while the edge dislocation density in ZnO layers grown on MgZnO-wurtzite buffer layer are slightly higher than for ZnO layers grown on MgZnO-cubic buffer layers. Dislocation loop and stacking fault were observed in ZnO/MgZnO-cubic layers. r 2007 Elsevier Ltd. All rights reserved. Keywords: D. Defects
1. Introduction ZnO is a II–VI wide band gap (3.37 eV) semiconductor with a large exciton binding energy of 60 meV, which has attracted considerable attention as a promising candidate for optical and electronic device applications [1]. It is well known that the electrical and optical properties of ZnO films depend on the microstructure, and that the presence of defects and the structure of the film–substrate interface have a crucial role in device performance. Low-cost sapphire substrates have been most extensively used as a substrate for ZnO. However, the crystal quality of ZnO grown directly on (0 0 0 1) sapphire tends to be very poor due to the formation of twins caused by the large lattice and thermal mismatch [2]. In order to improve the crystal quality of ZnO layers, much effort has been devoted to seeking a suitable buffer layer for ZnO epilayers such as MgO and GaN [2–4]. Very recently, development of a Ga modified sapphire technique has also reported [5,6]. MgxZn1xO alloys, which possess rock salt cubic structures for x40.41 and hexagonal wurtzite structures for xo0.41 [7], have been of substantial interest as a barrier
Corresponding author. Tel.: +81 22 215 2074; fax: +81 22 215 2073.
E-mail address: [email protected] (Z. Vashaei). 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.07.032
for ZnO in QW structures [8]. However, there has been no report on MgZnO buffer layers for ZnO epitaxy. Therefore, this study has been devoted to the investigation of defects in ZnO layers grown on thin MgxZn1xO buffer layers with the two different crystal structures of cubic and wurtzite. The defects morphology, including dislocations, stacking faults (SF), and interface defects, was investigated by transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) and highresolution X-ray diffraction (HRXRD). 2. Experimental The samples were grown on Al2O3 (0 0 0 1) substrates by plasma-assisted molecular beam epitaxy (P-MBE). Substrate pretreatments were performed in a sequence of chemical etching, annealing, and O-plasma pre-exposure. A few-nm-thick MgO buffer layer followed by a 5-nmthick MgxZn1xO layer were deposited at 550 1C followed by annealing at 800 1C. Then, ZnO layers were grown at a low temperature of 550 1C for 20 min followed by annealing and high-temperature growth at 800 1C. Two sets of samples with different crystal structures of MgxZn1xO buffer layer were prepared. In Sample A, the buffer layer was cubic-MgxZn1xO (xffi0.75) while sample B was grown on a wurtzite-MgxZn1xO (xffi0.25) buffer layer.
ARTICLE IN PRESS Z. Vashaei et al. / Journal of Physics and Chemistry of Solids 69 (2008) 497–500
498
Hereafter, for convenience, we call cubic-MgxZn1xO, MgZnO(c), and wurtzite-MgxZn1xO, MgZnO(w). HRXRD experiments were carried out with a Philips, X’ Pert-MRD diffractometer. Cross-section TEM specimens were prepared by conventional techniques consisting of mechanical polishing, dimpling, and Ar ion milling. Defects were investigated using a JEOL-2000EX II TEM operated at 200 kV. The interface study was performed by HRTEM observation using a JEOL JEM-ARM 1250 electron microscope operated at 1250 kV and a JEOL 3010 at 300 kV. 3. Results and discussion Fig. 1 shows XRD o-rocking curves of ZnO(0 0 0 2) and (1 0 1¯ 1) f-scan for both samples A and B. Basically, screw dislocations contribute to broaden the out-of-plane rocking curve, whereas broadening of asymmetry f-scan such as (1 0 1¯ 0) is attributed to edge dislocations. The narrow full-width at half-maximum (FWHM) value of the ZnO(0 0 0 2) diffraction peak of sample B, which is as
small as 10 arcsec in comparison with 576 arcsec for sample A (Fig. 1(a)), indicates a low density of dislocations with a screw component. However, as Fig. 1(b) shows, the FWHM value of ZnO(1 0 1¯ 1) f-scan peak for sample B is a little smaller than that of sample A, suggesting fewer pure-edge dislocations. To get more insight into the nature of the defects in both samples, TEM dislocation observation was carried out. Fig. 2(a, b) and (c, d) shows cross-section TEM (XTEM) micrographs of the ZnO/Mg0.75 Zn0.25O(c) (sample A) and ZnO/Mg0.25 Zn0.75O(w) (sample B), respectively. The samples were observed near the [1 1 2¯ 0] zone axis under the bright field condition with g ¼ [0 0 0 2] (images (a) and (c)) and weak-beam condition with g ¼ [1 0 1¯ 0] (images (b) and (c)), which make screw and edge components of dislocations visible, respectively. Fig. 2(a and c) clearly shows that the screw-type threading dislocation (TD) density in sample A is higher than in sample B, which confirms the XRD results. It should be noted that in the XTEM micrograph of sample A, mixed TDs are also observable in addition to edge
Fig. 1. XRD o-rocking curves of ZnO(0 0 0 2) (a) and f-scan of ZnO(1 0 1¯ 1) (b) diffraction peaks.
Fig. 2. XTEM images of ZnO layers grown on Mg0.75Zn0.25O(c)/c-sapphire (a, b) and Mg0.25Zn0.75O(w)/c-sapphire (c, d). Bright-field condition with g ¼ [0 0 0 2] was used for (a, c) and weak-beam condition with g ¼ (1 0 1¯ 0) was used for (b, d).
ARTICLE IN PRESS Z. Vashaei et al. / Journal of Physics and Chemistry of Solids 69 (2008) 497–500
and screw TDs, while no mixed TDs were observed in sample B. Screw dislocations with opposite Burgers vectors can be paired to form dislocation loops as is observed in Fig. 2(a). This feature is an effect of the cubic structure of the MgZnO buffer layer, which has a different dislocation slip system from a hexagonal crystal structure. The same features have been reported in previous reports about ZnO grown on c-sapphire with an ultra-thin Ga wetting layer [6] and silicon delta-doped GaN grown on Si(1 1 1) [9]. XTEM results confirm the XRD results that for both samples the majority of TDs are edge-type dislocations with Burgers vectors 1/3/1 1 2¯ 0S. The same features were reported for ZnO on c-sapphire with a MgO buffer layer [10]. However, XTEM results confirm the lower edge-type TD density for sample A than sample B as XRD results show. By observing several pictures, the average TD Table 1 Dislocation densities in ZnO/Mg0.75Zn0.25O(c)/c-sapphire (sample A) and ZnO/Mg0.25Zn0.75O(w)/c-sapphire (sample B) Samples
ZnO/Mg0.75Zn0.25O(c) ZnO/Mg0.25Zn0.75O(w)
Dislocation Screw (cm2)
Edge (cm2)
Mixed (cm2)
1.97 109 9.14 106
3.20 109 4.94 109
1.35 109 –
499
Fig. 4. HRTEM image of ZnO/Mg0.25Zn0.75O(w)/c-sapphire near the interface.
densities were determined and the results are summarized in Table 1. Fig. 3(a) shows an HRTEM image along the [1 1 2¯ 0] zone axis taken of the hetero interfaces of sample A. The ZnO/MgZnO(c) interface is not completely smooth due to the 3D-growth mode of MgZnO(c) as was confirmed by RHEED patterns during growth (not shown). No ZnO with a cubic structure near the MgZnO(c) layer is observed. The squares show the area with partial dislocations that terminate SF. To reduce contrast inhomogeniety, a small section marked with 1 containing a partial dislocation, is Fourier filtered using only the {0 0 0 2} and {1 1¯ 0 0} reflections. Fig. 3(b) shows the filtered image and illustrates the Burgers circuit. Two low-energy SF types with different stacking sequences are favorable in a hexagonal structure [11]. The observed Burgers vector projection is compatible with a Frank partial dislocation with Burgers vector b ¼ 1/6/2 2¯ 0 3S (Fig. 3(c)). The corresponding stacking fault type is characterized by AaBbAaBbAa|CcAaCcAa (the large and small letters denote the cation and anion sites, respectively). The most probable model for generation of such SF is the condensation of vacancies or interstitial, which leads to a missing or additional (0 0 0 2) plane [12]. Fig. 4 represents an HRTEM image taken near the interface of sample B under the [1 1 2¯ 0] zone axis. A noticeable aspect is the undistinguishable interface between ZnO and MgZnO(w) which is evidence of a good lattice match. 4. Conclusions
Fig. 3. HRTEM micrograph of ZnO/Mg0.75Zn0.25O(c)/c-sapphire near the interface (a). Fourier-filtered HRTEM image of a partial dislocation from the region marked by the square in (a) accompanied by Burgers circuit (b). Illustration of the Burgers vector corresponding to a SF (c).
In summary, we characterized the defect structure of ZnO films grown on MgZnO(c) and MgZnO(w) layers by TEM and XRD. It was found that ZnO layers grown on MgZnO(w) buffer layers have much lower screw-type TD density than those grown on MgZnO(c), while they have a slightly larger edge-type TD density than ZnO layer grown on MgZnO(c) buffer. Mixed-type TDs and dislocation loops were observed in ZnO layers grown on MgZnO(c).
ARTICLE IN PRESS 500
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HRTEM observation demonstrated the SFs formation near the ZnO/MgZnO(c) heterointerface. No mixed-type TDs and SFs were observed in ZnO layers grown on MgZnO(w). References [1] Y. Chen, D.M. Bagnall, H.J. Koh, K.T. Park, K. Hiraga, Z. Zhu, T. Yao, J. Appl. Phys. 84 (1998) 3912. [2] Y. Chen, H.J. Ko, S.K. Hong, T. Yao, Appl. Phys. Lett. 76 (2000) 559. [3] A. Setiawan, H.J. Ko, S.K. Hong, Y. Chen, T. Yao, Thin Solid Films 445 (2003) 213. [4] S.K. Hong, H.J. Ko, Y. Chen, T. Yao, J. Cryst. Growth 209 (2000) 537.
[5] H.P. Sun, X.Q. Pan, X.L. Du, Z.X. Mei, Z.Q. Zeng, Q.K. Xue, Appl. Phys. Lett. 85 (2004) 4385. [6] Y. Wang, X.L. Du, Z.X. Mei, Z.Q. Zeng, Q.Y. Xu, Q.K. Xue, Z. Zhang, J. Cryst. Growth 273 (2004) 100. [7] Z. Vashaei, T. Minegishi, H. Suzuki, T. Hanada, M.W. Cho, T. Yao, A. Setiawan, J. Appl. Phys. 98 (2005) 054911. [8] T. Makino, Y. Segawa, M. Kawasaki, H. Koinuma, Semicond. Sci. Technol. 20 (2005) S78. [9] O. Contreras, F.A. Ponce, J. Christen, A. Dadgar, A. Krost, Appl. Phys. Lett. 81 (2002) 4712. [10] A. Setiawan, Z. Vashaei, M.W. Cho, T. Yao, H. Kato, M. Sano, K. Miyamoto, I. Yonenaga, H.J. Ko, J. Appl. Phys. 96 (2004) 3763. [11] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley, New York, 1982, p. 354. [12] D. Gerthsen, D. Litvinov, Th. Gruber, C. Kirchner, A. Waag, Appl. Phys. Lett. 81 (2002) 3972.