- Email: [email protected]
GaAs quantum dot superlattice near the InAs critical thickness
ARTICLE IN PRESS Microelectronics Journal 40 (2009) 479– 482
Contents lists available at ScienceDirect
Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo
Investigation of the effect of growth interruption on the formation of InAs/GaAs quantum dot superlattice near the InAs critical thickness R.J. Kashtiban a, U. Bangert a,, M. Missous b a b
Nanostructured Materials Research Group, School of Materials, The University of Manchester, P.O. Box 88, Manchester M1 7HS, UK Microelectronics and Nanostructures Group, School of Electrical and Electronic Engineering, The University of Manchester, P.O. Box 88, Manchester M60 1QD, UK
a r t i c l e in fo
abstract
Available online 8 August 2008
Two kinds of superlattices (i) with and (ii) without growth interrupt (GI) after deposition of 1.77 monolayers (ML) of InAs on GaAs (0 0 1) were grown by solid-source molecular beam epitaxy (MBE) and assessed by transmission electron microscopy (TEM) techniques, double crystal X-ray diffraction (DCXRD) and photoluminescence (PL) measurements in order to gain an understanding of the structural and compositional properties. In case (i) formation of coherent dislocation free self-organized quantum dots (SOQDs) with 2.8–3.2 nm height and 13–16 nm lateral size was observed, whereas in case (ii) no quantum dots had formed. In order to better understand the implication of growth interruption for the formation mechanism, highly localised assessment of the composition of the QD was carried out via atomic resolution Z-contrast imaging and electron energy loss spectroscopy (EELS). & 2008 Elsevier Ltd. All rights reserved.
Keywords: Molecular beam epitaxy InAs quantum dots EELS HAADF
1. Introduction In recent years, self-organized quantum dots (SOQDs) grown using the Stranski–Krastanow (SK) method [1] have attracted great attentions because of potential applications in low threshold current quantum dot lasers with high temperature stability [2]. For device applications control of size, distribution and homogeneity of the dots, as well as defects within, are very important. A profound understanding of the formation and evolution of SOQDs and also of the early stage of the 2D–3D transition and its mechanism will enable use of the best growth condition for optimum structures. There is a general agreement that the 2D–3D transition during growth of InAs on GaAs(0 0 1) by molecular beam epitaxy (MBE) occurs within a 0.2 monolayers (ML) incremental deposition of InAs after the critical thickness (1.6–1.8 ML) has been reached [3]. A number of researchers has shown that the amount of material in the islands when the substrate temperature is more than 400 1C is greater than the amount of material deposited after 2D–3D transition and, more surprisingly, greater than the deposited InAs at 500 1C, and the only exception for this effect occurs at low deposition rates (p0.02 ML s 1) in which case the total deposited amount of materials is the same before and after the 2D–3D transition [4–6]. It has been found that the dots form a ternary alloy (InGaAs) of inhomogeneous composition [7–9]. Recently, it has been suggested that islands first nucleate at step edges as part of step
Corresponding author. Tel.: +44 161 306 3587; fax: +44 161 306 3586.
E-mail address: [email protected] (U. Bangert). 0026-2692/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.06.078
erosion, owing to Ga–In intermixing and mass transport from the substrate to the islands [10], and the total volume of dots is 4.6 times the deposition in the 1.6–1.8 ML range [3]. Most of the aforementioned investigations were performed by AFM, STM, RHEED and transmission electron microscopy (TEM); however, there are few direct investigations by high resolution STEM of the early stages of InAs pseudomorphic growth. This work tries to improve the understanding of the role of growth interrupts (GI) in the evolution of the microstructure of thin layers of InAs on GaAs (0 0 1) around the critical thickness for quantum dot formation. High angle annular dark field (HAADF)- or atomic resolution Z-contrast imaging was carried out in an aberration corrected dedicated scanning transmission electron microscope (STEM). The elemental distribution of In and Ga in the QDs was assessed by extracting maps of the relative intensity of the In–M5 absorption edge in the low-loss region of electron energy loss spectroscopy (EELS) spectra (o35 eV). For this Kramers–Kronig (K–K) analysis was employed; the imaginary part of dielectric function (e2) of the InAs/GaAs was extracted, which results in the suppression of the plasmon and hence in improved detectability of the In- (and Ga-) signal. Furthermore, in order to quantify the In content in the QDs the sample thickness is required, the latter was obtained by applying the K–K sum rule.
2. Experiment The samples in this study were grown on (0 0 1) GaAs substrates using a V100+ MBE system. The samples (denoted as XMBE#11 and XMBE#12, and #11 and #12 for simplicity) consist
ARTICLE IN PRESS 480
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of a 500 nm buffer layer grown at 580 1C, followed by 10 periods of a 24.5 nm thick GaAs spacer and InAs layer with a nominal thickness of 1.77 ML. The sample #12 was grown with a GI of 60 s after deposition of the InAs in each period, whereas in the sample #11 GaAs and InAs were grown continuously. The TEM diffraction-contrast images were acquired with a Philips CM20 microscope operating at 200 kV and the sample aligned with the /11 0S zone axes of GaAs parallel to the electron beam. The HREM BF and HAADF images were acquired with an aberration corrected STEM (SuperSTEM at Daresbury Laboratories) operating at 100 keV, and equipped with an UHV Enfina EEL spectrometer. A Bede double crystal X-ray diffractometer, QC200, with a source of 1.54056 A˚ wavelength of random polarisation was used for the XRD studies; a Ge crystal was the reference crystal for the GaAs substrate with all measurements taken in the (0 0 4) reflection plane geometry. Photoluminescence (PL) measurements were performed at room temperature using the Accent RPM2000 system with an InGaAs array detector and a laser source operating at 532 nm with 11 mW of power.
3. Results Fig. 1 shows the TEM images of sample #11 (without GI) and sample #12(with GI). Formation of SOQDs in sample with GI can bee seen in Fig. 1 whereas the image of the sample without GI does not reveal any contrast related to QDs. The density of SOQDs is estimated to be 1 per 1000 nm2. Our double crystal X-ray diffraction (DCXRD) investigation showed that the width of the wetting layer was 5.2 and 5.38 A˚ for samples #12 and #11, respectively. A simple explanation for the 0.18 A˚ thinner InAs wetting layer of sample #12 could be the redistribution of the material into the dots, but further investigation showed that the volume of dots was far from this amount of InAs. Conventional TEM, due to strain contrast, cannot reveal the exact dimensions of wetting layer and dots. In order to obtain atomic scale information, HAADF images were acquired in the Daresbury SuperSTEM. Fig. 2 shows an atomic resolution HAADF and BF image of a QD in sample #12. The HAADF image demonstrates that the dot height and lateral extent is 2.8–3.2 and 13–16 nm, respectively. Although small fluctuations in contrast arise partially from thickness variations or surface contamination there nevertheless appears to be some inhomogeneity of the In-distribution within the dot. It should be noted that the fading of the intensity at the dot apex is due to the
Fig. 1. Cross-sectional BF image of sample #12 (left) and sample #11 (right) in (110) orientation.
Fig. 2. HAADF image of a QD (top) and BF image of the QD (bottom).
pyramidal shape and hence decreasing (increasing) amount of In (Ga) in the atomic columns. Areas of the wetting layer on either side (particularly on the left) of the QD are darker than the area joining the base of the dot; this may be due to the preferable migration of In adatoms from the wetting layer to steps at the island. This type of distribution of In around the QDs has been suggested as a result of the formation of dots on the top edge of steps and subsequent erosion of steps by the evolving dot [3,10]. Contrast profile investigation showed that the bottom interface of the wetting layer its sharper then the top interface, possibly caused by interdiffusion with Ga as a result of migration of In toward QDs. The observation of diffuse wetting layer interfaces of sample #12 is confirmed by the weak PL emission at 912 nm related to wetting layer, accompanied by a strong emission from the QDs at 1162, in comparison with the strong 922 nm emission of the wetting layer of sample #11. The QD emission is very broad, indicating a variation in QD sizes and/or the dot composition. In order to assess the composition of the QDs, EELS was performed. Fig. 3 presents an intensity map of the In–M4,5 absorption edge obtained from an EEL spectrum image [11] of a QD, where the In signal was extracted following K–K analysis [12]. The contrast of the map is represented on the temperature scale with blue/black signifying low, and yellow/white high In concentration. The occurrence of slight compositional fluctuations within the dot appears to be confirmed at first sight, although quantitation would require rigorous modelling. The wetting layer adjacent to the dot appears to be ‘pinched off’, confirming the hypothesis that the In diffuses from some distance away into the dots thereby depleting the wetting layer. We applied the K–K sum role routine to obtain a value of 80 nm for the absolute thickness of sample #12 in the region of the above images. Assuming a pyramid-shaped dot [13] and using QD dimensions as derived, e.g., from Fig. 2, the volume of the dot is 260 nm3. From TEM images, we furthermore derive a dot density of 1 per 1000 nm2; hence the dot volume is about 3–4 times the amount of the differences between the volumes of the wetting layers in the samples #11 and #12. This discrepancy in volume can
ARTICLE IN PRESS R.J. Kashtiban et al. / Microelectronics Journal 40 (2009) 479–482
481
Fig. 4. HREM BF (top) and atomic resolution HAADF (bottom) image of a quantum well in sample #11. The arrows indicate atomic steps in the bottom interface.
Fig. 3. In signal intensity in a QD extracted after K–K analysis and NLLS fitting of an EEL spectrum image.
be explained by additional material participating in the formation of QDs originating from the GaAs spacer layers as a result of In segregation, thereby forming a ternary alloy of InGaAs within the dots. Fig. 4 shows BF and HAADF lattice images of a quantum well in sample #11. The Z-contrast indicates that wells and interfaces are far from monoatomically flat and abrupt: the bottom interface has numerous atomic steps and the top interface is additionally diffuse. PL indicates that there are possibly QDs in the uncapped top layer, which would have formed after growth stopped in a similar fashion as the dots in each layer of sample #12 have formed after a GI. This is demonstrated in the HERM BF and HAADF images and the intensity map of the M4,5 In-edge in Fig. 5, which reveal, indeed, the existence of small dots in the top InAs layer.
4. Conclusion We investigated the early stage of the formation of InAs/GaAs SOQDs after applying GI for 60 s just before the critical thickness for the 2D–3D transition was reached. This suggests an upper limit for the diffusion length of In adatoms on the surface. These segregate to step edges which acts as sinks. The increases the strain in these areas and strain relief by the diffusion of Ga adatoms from the substrate leads to erosion at the edges of islands
Fig. 5. HREM BF STEM image (top) of the uncapped top quantum well in sample #11 together with the intensity map of the In M4,5 edge. The construction of the contrast map is explained in the text. The STEM image is brought to focus at the location of the dot.
and evolution of dots of an InGaAs alloy with inhomogeneous composition. Without GI, the immediate growth of GaAs after InAs inhibits diffusion and segregation of In adatoms, and In–Ga intermixing leads to reduction of the strain in the wetting layer. In support of the above conclusions, the atomic resolution HAADF lattice images of nominal 1.77 ML InAs in superlattices without apparent dot formation suggest considerable roughness on the scale of 1–2 ML and step separations of 10 nm.
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Acknowledgements The authors are grateful to Dr. A. Harvey from Manchester Materials Science Centre and Dr. M. Gass from superSTEM laboratory for their TEM and STEM assistance. References [1] I.N. Stranski, L. Krastanow, Akad. Weiss. Lit. Mainz Math.-Natur Kl., 1939. [2] Y. Arakawa, H. Sakaki, Appl. Phys. Lett. 40 (11) (1982) 939. [3] E. Placidi, F. Arciprete, M. Fanfoni, F. Patella, E. Orsini, A. Balzarotti, J. Phys.: Condens. Matter 19 (2007) 225006. [4] B.A. Joyce, J.L. Sudijono, J.G. Belk, H. Yamaguchi, X.M. Zhang, H.T. Dobbs, A. Zangwill, D.D. Vvedensky, T.S. Jones, Jpn. J. Appl. Phys. 36 (1997) 4111.
[5] P.B. Joyce, T.J. Krzyzewski, G. R Bell, T.S. Jones, S. Malik, D. Childs, R. Murray, Phys. Rev. B 62 (16) (2000) 10891. [6] P.B. Joyce, T.J. Krzyzewski, G.R. Bell, B.A. Joyce, T.S. Jones, Phys. Rev. B 58 (24) (1998) R15981. [7] N. Grandjean, J. Massies, O. Tottereau, Phys. Rev. B 55 (16) (1997) R10189. [8] I. Kegel, T.H. Metzger, A. Lorke, J. Peisl, J. Stangl, G. Bauer, J.M. Garcia, P.M. Petroff, Phys. Rev. Lett. 85 (8) (2000) 1694. [9] A. Rosenauer, D. Gerthsen, D. Dyck, M. VanArzberger, G. Bhm, G. Abstreiter, Phys. Rev. B 64 (24) (2001) 245334. [10] A.G. Cullis, D.J. Norris, T. Walther, M.A. Migliorato, M. Hopkinson, Phys. Rev. B 66 (8) (2002) 081305. [11] J.A. Hunt, D.B. Williams, Ultramicroscopy 38 (1) (1991) 47. [12] M.H. Gass, A.J. Papworth, T.J. Bullough, P.R. Chalker, Ultramicroscopy 101 (2–4) (2004) 257. [13] P. Wang, A.L. Bleloch, M. Falke, P.J. Goodhew, J. Ng, M. Missous, Appl. Phys. Lett. 89 (7) (2006).
Contents lists available at ScienceDirect
Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo
Investigation of the effect of growth interruption on the formation of InAs/GaAs quantum dot superlattice near the InAs critical thickness R.J. Kashtiban a, U. Bangert a,, M. Missous b a b
Nanostructured Materials Research Group, School of Materials, The University of Manchester, P.O. Box 88, Manchester M1 7HS, UK Microelectronics and Nanostructures Group, School of Electrical and Electronic Engineering, The University of Manchester, P.O. Box 88, Manchester M60 1QD, UK
a r t i c l e in fo
abstract
Available online 8 August 2008
Two kinds of superlattices (i) with and (ii) without growth interrupt (GI) after deposition of 1.77 monolayers (ML) of InAs on GaAs (0 0 1) were grown by solid-source molecular beam epitaxy (MBE) and assessed by transmission electron microscopy (TEM) techniques, double crystal X-ray diffraction (DCXRD) and photoluminescence (PL) measurements in order to gain an understanding of the structural and compositional properties. In case (i) formation of coherent dislocation free self-organized quantum dots (SOQDs) with 2.8–3.2 nm height and 13–16 nm lateral size was observed, whereas in case (ii) no quantum dots had formed. In order to better understand the implication of growth interruption for the formation mechanism, highly localised assessment of the composition of the QD was carried out via atomic resolution Z-contrast imaging and electron energy loss spectroscopy (EELS). & 2008 Elsevier Ltd. All rights reserved.
Keywords: Molecular beam epitaxy InAs quantum dots EELS HAADF
1. Introduction In recent years, self-organized quantum dots (SOQDs) grown using the Stranski–Krastanow (SK) method [1] have attracted great attentions because of potential applications in low threshold current quantum dot lasers with high temperature stability [2]. For device applications control of size, distribution and homogeneity of the dots, as well as defects within, are very important. A profound understanding of the formation and evolution of SOQDs and also of the early stage of the 2D–3D transition and its mechanism will enable use of the best growth condition for optimum structures. There is a general agreement that the 2D–3D transition during growth of InAs on GaAs(0 0 1) by molecular beam epitaxy (MBE) occurs within a 0.2 monolayers (ML) incremental deposition of InAs after the critical thickness (1.6–1.8 ML) has been reached [3]. A number of researchers has shown that the amount of material in the islands when the substrate temperature is more than 400 1C is greater than the amount of material deposited after 2D–3D transition and, more surprisingly, greater than the deposited InAs at 500 1C, and the only exception for this effect occurs at low deposition rates (p0.02 ML s 1) in which case the total deposited amount of materials is the same before and after the 2D–3D transition [4–6]. It has been found that the dots form a ternary alloy (InGaAs) of inhomogeneous composition [7–9]. Recently, it has been suggested that islands first nucleate at step edges as part of step
Corresponding author. Tel.: +44 161 306 3587; fax: +44 161 306 3586.
E-mail address: [email protected] (U. Bangert). 0026-2692/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.06.078
erosion, owing to Ga–In intermixing and mass transport from the substrate to the islands [10], and the total volume of dots is 4.6 times the deposition in the 1.6–1.8 ML range [3]. Most of the aforementioned investigations were performed by AFM, STM, RHEED and transmission electron microscopy (TEM); however, there are few direct investigations by high resolution STEM of the early stages of InAs pseudomorphic growth. This work tries to improve the understanding of the role of growth interrupts (GI) in the evolution of the microstructure of thin layers of InAs on GaAs (0 0 1) around the critical thickness for quantum dot formation. High angle annular dark field (HAADF)- or atomic resolution Z-contrast imaging was carried out in an aberration corrected dedicated scanning transmission electron microscope (STEM). The elemental distribution of In and Ga in the QDs was assessed by extracting maps of the relative intensity of the In–M5 absorption edge in the low-loss region of electron energy loss spectroscopy (EELS) spectra (o35 eV). For this Kramers–Kronig (K–K) analysis was employed; the imaginary part of dielectric function (e2) of the InAs/GaAs was extracted, which results in the suppression of the plasmon and hence in improved detectability of the In- (and Ga-) signal. Furthermore, in order to quantify the In content in the QDs the sample thickness is required, the latter was obtained by applying the K–K sum rule.
2. Experiment The samples in this study were grown on (0 0 1) GaAs substrates using a V100+ MBE system. The samples (denoted as XMBE#11 and XMBE#12, and #11 and #12 for simplicity) consist
ARTICLE IN PRESS 480
R.J. Kashtiban et al. / Microelectronics Journal 40 (2009) 479–482
of a 500 nm buffer layer grown at 580 1C, followed by 10 periods of a 24.5 nm thick GaAs spacer and InAs layer with a nominal thickness of 1.77 ML. The sample #12 was grown with a GI of 60 s after deposition of the InAs in each period, whereas in the sample #11 GaAs and InAs were grown continuously. The TEM diffraction-contrast images were acquired with a Philips CM20 microscope operating at 200 kV and the sample aligned with the /11 0S zone axes of GaAs parallel to the electron beam. The HREM BF and HAADF images were acquired with an aberration corrected STEM (SuperSTEM at Daresbury Laboratories) operating at 100 keV, and equipped with an UHV Enfina EEL spectrometer. A Bede double crystal X-ray diffractometer, QC200, with a source of 1.54056 A˚ wavelength of random polarisation was used for the XRD studies; a Ge crystal was the reference crystal for the GaAs substrate with all measurements taken in the (0 0 4) reflection plane geometry. Photoluminescence (PL) measurements were performed at room temperature using the Accent RPM2000 system with an InGaAs array detector and a laser source operating at 532 nm with 11 mW of power.
3. Results Fig. 1 shows the TEM images of sample #11 (without GI) and sample #12(with GI). Formation of SOQDs in sample with GI can bee seen in Fig. 1 whereas the image of the sample without GI does not reveal any contrast related to QDs. The density of SOQDs is estimated to be 1 per 1000 nm2. Our double crystal X-ray diffraction (DCXRD) investigation showed that the width of the wetting layer was 5.2 and 5.38 A˚ for samples #12 and #11, respectively. A simple explanation for the 0.18 A˚ thinner InAs wetting layer of sample #12 could be the redistribution of the material into the dots, but further investigation showed that the volume of dots was far from this amount of InAs. Conventional TEM, due to strain contrast, cannot reveal the exact dimensions of wetting layer and dots. In order to obtain atomic scale information, HAADF images were acquired in the Daresbury SuperSTEM. Fig. 2 shows an atomic resolution HAADF and BF image of a QD in sample #12. The HAADF image demonstrates that the dot height and lateral extent is 2.8–3.2 and 13–16 nm, respectively. Although small fluctuations in contrast arise partially from thickness variations or surface contamination there nevertheless appears to be some inhomogeneity of the In-distribution within the dot. It should be noted that the fading of the intensity at the dot apex is due to the
Fig. 1. Cross-sectional BF image of sample #12 (left) and sample #11 (right) in (110) orientation.
Fig. 2. HAADF image of a QD (top) and BF image of the QD (bottom).
pyramidal shape and hence decreasing (increasing) amount of In (Ga) in the atomic columns. Areas of the wetting layer on either side (particularly on the left) of the QD are darker than the area joining the base of the dot; this may be due to the preferable migration of In adatoms from the wetting layer to steps at the island. This type of distribution of In around the QDs has been suggested as a result of the formation of dots on the top edge of steps and subsequent erosion of steps by the evolving dot [3,10]. Contrast profile investigation showed that the bottom interface of the wetting layer its sharper then the top interface, possibly caused by interdiffusion with Ga as a result of migration of In toward QDs. The observation of diffuse wetting layer interfaces of sample #12 is confirmed by the weak PL emission at 912 nm related to wetting layer, accompanied by a strong emission from the QDs at 1162, in comparison with the strong 922 nm emission of the wetting layer of sample #11. The QD emission is very broad, indicating a variation in QD sizes and/or the dot composition. In order to assess the composition of the QDs, EELS was performed. Fig. 3 presents an intensity map of the In–M4,5 absorption edge obtained from an EEL spectrum image [11] of a QD, where the In signal was extracted following K–K analysis [12]. The contrast of the map is represented on the temperature scale with blue/black signifying low, and yellow/white high In concentration. The occurrence of slight compositional fluctuations within the dot appears to be confirmed at first sight, although quantitation would require rigorous modelling. The wetting layer adjacent to the dot appears to be ‘pinched off’, confirming the hypothesis that the In diffuses from some distance away into the dots thereby depleting the wetting layer. We applied the K–K sum role routine to obtain a value of 80 nm for the absolute thickness of sample #12 in the region of the above images. Assuming a pyramid-shaped dot [13] and using QD dimensions as derived, e.g., from Fig. 2, the volume of the dot is 260 nm3. From TEM images, we furthermore derive a dot density of 1 per 1000 nm2; hence the dot volume is about 3–4 times the amount of the differences between the volumes of the wetting layers in the samples #11 and #12. This discrepancy in volume can
ARTICLE IN PRESS R.J. Kashtiban et al. / Microelectronics Journal 40 (2009) 479–482
481
Fig. 4. HREM BF (top) and atomic resolution HAADF (bottom) image of a quantum well in sample #11. The arrows indicate atomic steps in the bottom interface.
Fig. 3. In signal intensity in a QD extracted after K–K analysis and NLLS fitting of an EEL spectrum image.
be explained by additional material participating in the formation of QDs originating from the GaAs spacer layers as a result of In segregation, thereby forming a ternary alloy of InGaAs within the dots. Fig. 4 shows BF and HAADF lattice images of a quantum well in sample #11. The Z-contrast indicates that wells and interfaces are far from monoatomically flat and abrupt: the bottom interface has numerous atomic steps and the top interface is additionally diffuse. PL indicates that there are possibly QDs in the uncapped top layer, which would have formed after growth stopped in a similar fashion as the dots in each layer of sample #12 have formed after a GI. This is demonstrated in the HERM BF and HAADF images and the intensity map of the M4,5 In-edge in Fig. 5, which reveal, indeed, the existence of small dots in the top InAs layer.
4. Conclusion We investigated the early stage of the formation of InAs/GaAs SOQDs after applying GI for 60 s just before the critical thickness for the 2D–3D transition was reached. This suggests an upper limit for the diffusion length of In adatoms on the surface. These segregate to step edges which acts as sinks. The increases the strain in these areas and strain relief by the diffusion of Ga adatoms from the substrate leads to erosion at the edges of islands
Fig. 5. HREM BF STEM image (top) of the uncapped top quantum well in sample #11 together with the intensity map of the In M4,5 edge. The construction of the contrast map is explained in the text. The STEM image is brought to focus at the location of the dot.
and evolution of dots of an InGaAs alloy with inhomogeneous composition. Without GI, the immediate growth of GaAs after InAs inhibits diffusion and segregation of In adatoms, and In–Ga intermixing leads to reduction of the strain in the wetting layer. In support of the above conclusions, the atomic resolution HAADF lattice images of nominal 1.77 ML InAs in superlattices without apparent dot formation suggest considerable roughness on the scale of 1–2 ML and step separations of 10 nm.
ARTICLE IN PRESS 482
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Acknowledgements The authors are grateful to Dr. A. Harvey from Manchester Materials Science Centre and Dr. M. Gass from superSTEM laboratory for their TEM and STEM assistance. References [1] I.N. Stranski, L. Krastanow, Akad. Weiss. Lit. Mainz Math.-Natur Kl., 1939. [2] Y. Arakawa, H. Sakaki, Appl. Phys. Lett. 40 (11) (1982) 939. [3] E. Placidi, F. Arciprete, M. Fanfoni, F. Patella, E. Orsini, A. Balzarotti, J. Phys.: Condens. Matter 19 (2007) 225006. [4] B.A. Joyce, J.L. Sudijono, J.G. Belk, H. Yamaguchi, X.M. Zhang, H.T. Dobbs, A. Zangwill, D.D. Vvedensky, T.S. Jones, Jpn. J. Appl. Phys. 36 (1997) 4111.
[5] P.B. Joyce, T.J. Krzyzewski, G. R Bell, T.S. Jones, S. Malik, D. Childs, R. Murray, Phys. Rev. B 62 (16) (2000) 10891. [6] P.B. Joyce, T.J. Krzyzewski, G.R. Bell, B.A. Joyce, T.S. Jones, Phys. Rev. B 58 (24) (1998) R15981. [7] N. Grandjean, J. Massies, O. Tottereau, Phys. Rev. B 55 (16) (1997) R10189. [8] I. Kegel, T.H. Metzger, A. Lorke, J. Peisl, J. Stangl, G. Bauer, J.M. Garcia, P.M. Petroff, Phys. Rev. Lett. 85 (8) (2000) 1694. [9] A. Rosenauer, D. Gerthsen, D. Dyck, M. VanArzberger, G. Bhm, G. Abstreiter, Phys. Rev. B 64 (24) (2001) 245334. [10] A.G. Cullis, D.J. Norris, T. Walther, M.A. Migliorato, M. Hopkinson, Phys. Rev. B 66 (8) (2002) 081305. [11] J.A. Hunt, D.B. Williams, Ultramicroscopy 38 (1) (1991) 47. [12] M.H. Gass, A.J. Papworth, T.J. Bullough, P.R. Chalker, Ultramicroscopy 101 (2–4) (2004) 257. [13] P. Wang, A.L. Bleloch, M. Falke, P.J. Goodhew, J. Ng, M. Missous, Appl. Phys. Lett. 89 (7) (2006).