Abstract

In high-resolution transmission electron microscopy (HRTEM) images of heterostructures, it is always difficult to accurately determine the interface position and identify dislocations in a large field of view at tens to hundreds of nanometers due to the small lattice differences. However, in the heterostructure, the determination of the interface position is the key to obtain the true mismatch stress/strain field of the interface. Due to the magnifying effect of the digital moiré method on small differences, digital moiré technology was applied to determine Ge/Si heterostructure interfaces and large-area identification interface dislocations in HRTEM lattice diagrams in this study. By optimizing the frequency and angle of the reference lattice, the interface and dislocation position are clearly and intuitively displayed. How to accurately determine the position of the heterostructure interface and the dislocation of the large-area recognition interface from HRTEM images are studied through simulation experiments. The results show that when the frequency of the reference lattice and the specimen lattice are close, and the angle between them is within 10°, the position of the heterostructure interface can be accurately and intuitively determined by the naked eye according to the distortion characteristics of the moiré fringe. When the frequency of the reference lattice is 0.7 to 0.9 times of the specimen lattice, and the rotation angle is within 8°, the visually clear crossover phenomenon of the moiré fringes is used for large-area identification of interface dislocations. Using the phase measurement interface position sensitivity can reach the Å level. Using the phase-shifting digital moiré method the strain field on the dislocation core at the Ge/Si heterostructure interface and the interface stress distribution were quantitatively analyzed. Compared with the Peierls-Nabarro dislocation model and the Foreman dislocation model, Foreman's variable factor α = 4 is more suitable for describing the strain field of misfit dislocations on the Ge/Si heterostructure interface.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  5. Y. Hu, H. O. Churchill, D. J. Reilly, J. Xiang, C. M. Lieber, and C. M. Marcus, “A Ge/Si heterostructure nanowire-based double quantum dot with integrated charge sensor,” Nat. Nanotechnol. 2(10), 622–625 (2007).
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    [Crossref]
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    [Crossref]
  33. J. J. Peters, R. Beanland, M. Alexe, J. W. Cockburn, D. G. Revin, S. Y. Zhang, and A. M. Sanchez, “Artefacts in geometric phase analysis of compound materials,” Ultramicroscopy 157, 91–97 (2015).
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2019 (1)

H. Xing, Z. Gao, H. Wang, Z. Lei, L. Ma, and W. Qiu, “Digital rotation moirémethod for strain measurement based on high-resolution transmission electron microscope lattice image,” Opt. Laser. Eng. 122(2), 347–353 (2019).
[Crossref]

2018 (1)

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, and T. Sugiyama, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-fourier-transform sampling moiré method,” Jpn. J. Appl. Phys. 57(4S), 04FC04 (2018).
[Crossref]

2017 (2)

Q. H. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyashita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28(45), 455704 (2017).
[Crossref]

N. Cherkashin, T. Denneulin, and M. J. Hÿtch, “Electron microscopy by specimen design: application to strain measurements,” Sci. Rep. 7(1), 12394 (2017).
[Crossref]

2016 (1)

H. Zhang, Z. Liu, H. Wen, H. Xie, and C. Liu, “Subset geometric phase analysis method for deformation evaluation of HRTEM images,” Ultramicroscopy 171, 34–42 (2016).
[Crossref]

2015 (2)

J. J. Peters, R. Beanland, M. Alexe, J. W. Cockburn, D. G. Revin, S. Y. Zhang, and A. M. Sanchez, “Artefacts in geometric phase analysis of compound materials,” Ultramicroscopy 157, 91–97 (2015).
[Crossref]

M. Mao, A. Nie, J. Liu, H. Wang, S. X. Mao, Q. Wang, K. Li, and X.-X. Zhang, “Atomic resolution observation of conversion-type anode RuO2 during the first electrochemical lithiation,” Nanotechnology 26(12), 125404 (2015).
[Crossref]

2014 (1)

D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
[Crossref]

2013 (2)

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
[Crossref]

J. Li, C. Zhao, Y. Xing, S. Su, and B. Cheng, “Full-Field Strain Mapping at a Ge/Si Heterostructure Interface,” Materials 6(6), 2130–2142 (2013).
[Crossref]

2012 (2)

Q. Liu, C. W. Zhao, Y. M. Xing, S. J. Su, and B. W. Cheng, “Quantitative strain analysis of misfit dislocations in a Ge/Si heterostructure interface by geometric phase analysis,” Opt. Laser. Eng. 50(5), 796–799 (2012).
[Crossref]

S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51(16), 3214–3223 (2012).
[Crossref]

2010 (1)

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling Moiré Method for Accurate Small Deformation Distribution Measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

2008 (1)

F. Hüe, M. Hÿtch, H. Bender, F. Houdellier, and A. Claverie, “Direct mapping of strain in a strained silicon transistor by high-resolution electron microscopy,” Phys. Rev. Lett. 100(15), 156602 (2008).
[Crossref]

2007 (1)

Y. Hu, H. O. Churchill, D. J. Reilly, J. Xiang, C. M. Lieber, and C. M. Marcus, “A Ge/Si heterostructure nanowire-based double quantum dot with integrated charge sensor,” Nat. Nanotechnol. 2(10), 622–625 (2007).
[Crossref]

2006 (2)

S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
[Crossref]

J. Xiang, W. Lu, Y. J. Hu, Y. Wu, H. Yan, and C. M. Lieber, “Ge/Si nanowire heterostructures as Highperformance field-effect transistors,” Nature 441(7092), 489–493 (2006).
[Crossref]

2005 (3)

N. Hirashita, N. Sugiyama, E. Toyoda, and S. Takagi, “Relaxation processes in strained Si layers on silicon-germanium- on-insulator substrates,” Appl. Phys. Lett. 86(22), 221923 (2005).
[Crossref]

R. Loo, R. Delhougne, M. Caymax, and M. Ries, “Formation of misfit dislocations at the thin strained Si∕strain-relaxed buffer interface,” Appl. Phys. Lett. 87(18), 182108 (2005).
[Crossref]

N. Cherkashin, M. J. Hÿtch, E. Snoeck, A. Claverie, J. M. Hartmann, and Y. Bogumilowicz, “Quantitative strain and stress measurements in Ge/Si dual channels grown on a Si0.5Ge0.5 virtual substrate,” Mater. Sci. Eng., B 124-125, 118–122 (2005).
[Crossref]

2004 (1)

L. Vescan and S. Wickenhauser, “Relaxation mechanism of low temperature SiGe/Si (0 0 1) buffer layers,” Solid-State Electron. 48(8), 1279–1284 (2004).
[Crossref]

2002 (2)

K. Brunner, “Si/Ge nanostructures,” Rep. Prog. Phys. 65(1), 27–72 (2002).
[Crossref]

H. Xie, A. Asundi, G. B. Chai, Y. Lu, Z. W. Zhong, and B. K. A. Ngoi, “High resolution AFM scanning Moiré method and its application to the micro-deformation in the BGA electronic package,” Microelectron. Reliab. 42(8), 1219–1227 (2002).
[Crossref]

2000 (1)

S. Mahajan, “Defects in Semiconductors and their Effects on Devices,” Acta Mater. 48(1), 137–149 (2000).
[Crossref]

1999 (1)

F. Dai and Y. Xing, “Nano-moire method,” Acta Mech. Sin. 15(3), 283–288 (1999).
[Crossref]

1994 (1)

R. Bonnet and M. Loubradou, “Atomic positions around misfit dislocations on a planar heterointerface,” Phys. Rev. B 49(20), 14397–14402 (1994).
[Crossref]

1991 (1)

1987 (1)

P. M. J. Maree, J. C. Barbour, d. V. G. F. Van, and K. L. Kavanagh, “Generation of misfit dislocations in semiconductors,” J. Appl. Phys. 62(11), 4413–4420 (1987).
[Crossref]

1958 (1)

G. A. Bassett, J. W. Menter, and D. W. Pashley, “Moiré Patterns on Electron Micrographs, and their Application to the Study of Dislocations in Metals,” Proc. R. Soc. Lond. A 246(1246), 345–368 (1958).
[Crossref]

1957 (1)

G. A. Geach and R. Phillip, “Moiré Patterns in Transmission Electron Micrographs of Sub-Boundaries of Aluminium,” Nature 179(4573), 1293 (1957).
[Crossref]

1951 (1)

A. J. Foreman, M. A. Jaswon, and J. K. Wood, “Factors controlling dislocation widths,” Proc. Phys. Soc. A 64(2), 156–163 (1951).
[Crossref]

1947 (1)

F. R. N. Nabarro, “Dislocations in a simple cubic lattice,” Proc. Phys. Soc. 59(2), 256–272 (1947).
[Crossref]

1940 (1)

R. E. Peierls, “The size of a dislocation,” Proc. Phys. Soc. 52(1), 34–37 (1940).
[Crossref]

Alexe, M.

J. J. Peters, R. Beanland, M. Alexe, J. W. Cockburn, D. G. Revin, S. Y. Zhang, and A. M. Sanchez, “Artefacts in geometric phase analysis of compound materials,” Ultramicroscopy 157, 91–97 (2015).
[Crossref]

Asayesh-Ardakani, H.

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
[Crossref]

Asundi, A.

H. Xie, A. Asundi, G. B. Chai, Y. Lu, Z. W. Zhong, and B. K. A. Ngoi, “High resolution AFM scanning Moiré method and its application to the micro-deformation in the BGA electronic package,” Microelectron. Reliab. 42(8), 1219–1227 (2002).
[Crossref]

A. Asundi and K. H. Yung, “Phase-shifting and logical moiré,” J. Opt. Soc. Am. A 8(10), 1591–1600 (1991).
[Crossref]

Barbour, J. C.

P. M. J. Maree, J. C. Barbour, d. V. G. F. Van, and K. L. Kavanagh, “Generation of misfit dislocations in semiconductors,” J. Appl. Phys. 62(11), 4413–4420 (1987).
[Crossref]

Bassett, G. A.

G. A. Bassett, J. W. Menter, and D. W. Pashley, “Moiré Patterns on Electron Micrographs, and their Application to the Study of Dislocations in Metals,” Proc. R. Soc. Lond. A 246(1246), 345–368 (1958).
[Crossref]

Beanland, R.

J. J. Peters, R. Beanland, M. Alexe, J. W. Cockburn, D. G. Revin, S. Y. Zhang, and A. M. Sanchez, “Artefacts in geometric phase analysis of compound materials,” Ultramicroscopy 157, 91–97 (2015).
[Crossref]

Bender, H.

F. Hüe, M. Hÿtch, H. Bender, F. Houdellier, and A. Claverie, “Direct mapping of strain in a strained silicon transistor by high-resolution electron microscopy,” Phys. Rev. Lett. 100(15), 156602 (2008).
[Crossref]

Bogumilowicz, Y.

N. Cherkashin, M. J. Hÿtch, E. Snoeck, A. Claverie, J. M. Hartmann, and Y. Bogumilowicz, “Quantitative strain and stress measurements in Ge/Si dual channels grown on a Si0.5Ge0.5 virtual substrate,” Mater. Sci. Eng., B 124-125, 118–122 (2005).
[Crossref]

Bonnet, R.

R. Bonnet and M. Loubradou, “Atomic positions around misfit dislocations on a planar heterointerface,” Phys. Rev. B 49(20), 14397–14402 (1994).
[Crossref]

Bonzom, R.

S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
[Crossref]

Brunner, K.

K. Brunner, “Si/Ge nanostructures,” Rep. Prog. Phys. 65(1), 27–72 (2002).
[Crossref]

Caymax, M.

S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
[Crossref]

R. Loo, R. Delhougne, M. Caymax, and M. Ries, “Formation of misfit dislocations at the thin strained Si∕strain-relaxed buffer interface,” Appl. Phys. Lett. 87(18), 182108 (2005).
[Crossref]

Chai, G. B.

H. Xie, A. Asundi, G. B. Chai, Y. Lu, Z. W. Zhong, and B. K. A. Ngoi, “High resolution AFM scanning Moiré method and its application to the micro-deformation in the BGA electronic package,” Microelectron. Reliab. 42(8), 1219–1227 (2002).
[Crossref]

Cheng, B.

J. Li, C. Zhao, Y. Xing, S. Su, and B. Cheng, “Full-Field Strain Mapping at a Ge/Si Heterostructure Interface,” Materials 6(6), 2130–2142 (2013).
[Crossref]

Cheng, B. W.

Q. Liu, C. W. Zhao, Y. M. Xing, S. J. Su, and B. W. Cheng, “Quantitative strain analysis of misfit dislocations in a Ge/Si heterostructure interface by geometric phase analysis,” Opt. Laser. Eng. 50(5), 796–799 (2012).
[Crossref]

Cheng, Y.

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
[Crossref]

Cherkashin, N.

N. Cherkashin, T. Denneulin, and M. J. Hÿtch, “Electron microscopy by specimen design: application to strain measurements,” Sci. Rep. 7(1), 12394 (2017).
[Crossref]

N. Cherkashin, M. J. Hÿtch, E. Snoeck, A. Claverie, J. M. Hartmann, and Y. Bogumilowicz, “Quantitative strain and stress measurements in Ge/Si dual channels grown on a Si0.5Ge0.5 virtual substrate,” Mater. Sci. Eng., B 124-125, 118–122 (2005).
[Crossref]

Churchill, H. O.

Y. Hu, H. O. Churchill, D. J. Reilly, J. Xiang, C. M. Lieber, and C. M. Marcus, “A Ge/Si heterostructure nanowire-based double quantum dot with integrated charge sensor,” Nat. Nanotechnol. 2(10), 622–625 (2007).
[Crossref]

Claverie, A.

F. Hüe, M. Hÿtch, H. Bender, F. Houdellier, and A. Claverie, “Direct mapping of strain in a strained silicon transistor by high-resolution electron microscopy,” Phys. Rev. Lett. 100(15), 156602 (2008).
[Crossref]

N. Cherkashin, M. J. Hÿtch, E. Snoeck, A. Claverie, J. M. Hartmann, and Y. Bogumilowicz, “Quantitative strain and stress measurements in Ge/Si dual channels grown on a Si0.5Ge0.5 virtual substrate,” Mater. Sci. Eng., B 124-125, 118–122 (2005).
[Crossref]

Cockburn, J. W.

J. J. Peters, R. Beanland, M. Alexe, J. W. Cockburn, D. G. Revin, S. Y. Zhang, and A. M. Sanchez, “Artefacts in geometric phase analysis of compound materials,” Ultramicroscopy 157, 91–97 (2015).
[Crossref]

Conard, T.

S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
[Crossref]

Dai, F.

F. Dai and Y. Xing, “Nano-moire method,” Acta Mech. Sin. 15(3), 283–288 (1999).
[Crossref]

Delhougne, R.

R. Loo, R. Delhougne, M. Caymax, and M. Ries, “Formation of misfit dislocations at the thin strained Si∕strain-relaxed buffer interface,” Appl. Phys. Lett. 87(18), 182108 (2005).
[Crossref]

Denneulin, T.

N. Cherkashin, T. Denneulin, and M. J. Hÿtch, “Electron microscopy by specimen design: application to strain measurements,” Sci. Rep. 7(1), 12394 (2017).
[Crossref]

Dong, C.

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
[Crossref]

Elshocht, S. V.

S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
[Crossref]

Foreman, A. J.

A. J. Foreman, M. A. Jaswon, and J. K. Wood, “Factors controlling dislocation widths,” Proc. Phys. Soc. A 64(2), 156–163 (1951).
[Crossref]

Fujigaki, M.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling Moiré Method for Accurate Small Deformation Distribution Measurement,” Exp. Mech. 50(4), 501–508 (2010).
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A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
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H. Xing, Z. Gao, H. Wang, Z. Lei, L. Ma, and W. Qiu, “Digital rotation moirémethod for strain measurement based on high-resolution transmission electron microscope lattice image,” Opt. Laser. Eng. 122(2), 347–353 (2019).
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S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
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N. Cherkashin, M. J. Hÿtch, E. Snoeck, A. Claverie, J. M. Hartmann, and Y. Bogumilowicz, “Quantitative strain and stress measurements in Ge/Si dual channels grown on a Si0.5Ge0.5 virtual substrate,” Mater. Sci. Eng., B 124-125, 118–122 (2005).
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S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
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J. Xiang, W. Lu, Y. J. Hu, Y. Wu, H. Yan, and C. M. Lieber, “Ge/Si nanowire heterostructures as Highperformance field-effect transistors,” Nature 441(7092), 489–493 (2006).
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F. Hüe, M. Hÿtch, H. Bender, F. Houdellier, and A. Claverie, “Direct mapping of strain in a strained silicon transistor by high-resolution electron microscopy,” Phys. Rev. Lett. 100(15), 156602 (2008).
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S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
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A. J. Foreman, M. A. Jaswon, and J. K. Wood, “Factors controlling dislocation widths,” Proc. Phys. Soc. A 64(2), 156–163 (1951).
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P. M. J. Maree, J. C. Barbour, d. V. G. F. Van, and K. L. Kavanagh, “Generation of misfit dislocations in semiconductors,” J. Appl. Phys. 62(11), 4413–4420 (1987).
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Q. H. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyashita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28(45), 455704 (2017).
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H. Xing, Z. Gao, H. Wang, Z. Lei, L. Ma, and W. Qiu, “Digital rotation moirémethod for strain measurement based on high-resolution transmission electron microscope lattice image,” Opt. Laser. Eng. 122(2), 347–353 (2019).
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S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
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D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
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J. Li, C. Zhao, Y. Xing, S. Su, and B. Cheng, “Full-Field Strain Mapping at a Ge/Si Heterostructure Interface,” Materials 6(6), 2130–2142 (2013).
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M. Mao, A. Nie, J. Liu, H. Wang, S. X. Mao, Q. Wang, K. Li, and X.-X. Zhang, “Atomic resolution observation of conversion-type anode RuO2 during the first electrochemical lithiation,” Nanotechnology 26(12), 125404 (2015).
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Li, Q.

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
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Y. Hu, H. O. Churchill, D. J. Reilly, J. Xiang, C. M. Lieber, and C. M. Marcus, “A Ge/Si heterostructure nanowire-based double quantum dot with integrated charge sensor,” Nat. Nanotechnol. 2(10), 622–625 (2007).
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J. Xiang, W. Lu, Y. J. Hu, Y. Wu, H. Yan, and C. M. Lieber, “Ge/Si nanowire heterostructures as Highperformance field-effect transistors,” Nature 441(7092), 489–493 (2006).
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H. Zhang, Z. Liu, H. Wen, H. Xie, and C. Liu, “Subset geometric phase analysis method for deformation evaluation of HRTEM images,” Ultramicroscopy 171, 34–42 (2016).
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Liu, J.

M. Mao, A. Nie, J. Liu, H. Wang, S. X. Mao, Q. Wang, K. Li, and X.-X. Zhang, “Atomic resolution observation of conversion-type anode RuO2 during the first electrochemical lithiation,” Nanotechnology 26(12), 125404 (2015).
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Q. Liu, C. W. Zhao, Y. M. Xing, S. J. Su, and B. W. Cheng, “Quantitative strain analysis of misfit dislocations in a Ge/Si heterostructure interface by geometric phase analysis,” Opt. Laser. Eng. 50(5), 796–799 (2012).
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H. Zhang, Z. Liu, H. Wen, H. Xie, and C. Liu, “Subset geometric phase analysis method for deformation evaluation of HRTEM images,” Ultramicroscopy 171, 34–42 (2016).
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R. Loo, R. Delhougne, M. Caymax, and M. Ries, “Formation of misfit dislocations at the thin strained Si∕strain-relaxed buffer interface,” Appl. Phys. Lett. 87(18), 182108 (2005).
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J. P. Hirth, J. Lothe, and T. Mura, Theory of Dislocations, (2 edition. Wiley, 1982).

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J. Xiang, W. Lu, Y. J. Hu, Y. Wu, H. Yan, and C. M. Lieber, “Ge/Si nanowire heterostructures as Highperformance field-effect transistors,” Nature 441(7092), 489–493 (2006).
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H. Xie, A. Asundi, G. B. Chai, Y. Lu, Z. W. Zhong, and B. K. A. Ngoi, “High resolution AFM scanning Moiré method and its application to the micro-deformation in the BGA electronic package,” Microelectron. Reliab. 42(8), 1219–1227 (2002).
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H. Xing, Z. Gao, H. Wang, Z. Lei, L. Ma, and W. Qiu, “Digital rotation moirémethod for strain measurement based on high-resolution transmission electron microscope lattice image,” Opt. Laser. Eng. 122(2), 347–353 (2019).
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M. Mao, A. Nie, J. Liu, H. Wang, S. X. Mao, Q. Wang, K. Li, and X.-X. Zhang, “Atomic resolution observation of conversion-type anode RuO2 during the first electrochemical lithiation,” Nanotechnology 26(12), 125404 (2015).
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Mao, S. X.

M. Mao, A. Nie, J. Liu, H. Wang, S. X. Mao, Q. Wang, K. Li, and X.-X. Zhang, “Atomic resolution observation of conversion-type anode RuO2 during the first electrochemical lithiation,” Nanotechnology 26(12), 125404 (2015).
[Crossref]

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Y. Hu, H. O. Churchill, D. J. Reilly, J. Xiang, C. M. Lieber, and C. M. Marcus, “A Ge/Si heterostructure nanowire-based double quantum dot with integrated charge sensor,” Nat. Nanotechnol. 2(10), 622–625 (2007).
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P. M. J. Maree, J. C. Barbour, d. V. G. F. Van, and K. L. Kavanagh, “Generation of misfit dislocations in semiconductors,” J. Appl. Phys. 62(11), 4413–4420 (1987).
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A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
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G. A. Bassett, J. W. Menter, and D. W. Pashley, “Moiré Patterns on Electron Micrographs, and their Application to the Study of Dislocations in Metals,” Proc. R. Soc. Lond. A 246(1246), 345–368 (1958).
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S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
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Miyashita, N.

Q. H. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyashita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28(45), 455704 (2017).
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S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling Moiré Method for Accurate Small Deformation Distribution Measurement,” Exp. Mech. 50(4), 501–508 (2010).
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Mura, T.

J. P. Hirth, J. Lothe, and T. Mura, Theory of Dislocations, (2 edition. Wiley, 1982).

Muramatsu, T.

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F. R. N. Nabarro, “Dislocations in a simple cubic lattice,” Proc. Phys. Soc. 59(2), 256–272 (1947).
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H. Xie, A. Asundi, G. B. Chai, Y. Lu, Z. W. Zhong, and B. K. A. Ngoi, “High resolution AFM scanning Moiré method and its application to the micro-deformation in the BGA electronic package,” Microelectron. Reliab. 42(8), 1219–1227 (2002).
[Crossref]

Nie, A.

M. Mao, A. Nie, J. Liu, H. Wang, S. X. Mao, Q. Wang, K. Li, and X.-X. Zhang, “Atomic resolution observation of conversion-type anode RuO2 during the first electrochemical lithiation,” Nanotechnology 26(12), 125404 (2015).
[Crossref]

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
[Crossref]

Pashley, D. W.

G. A. Bassett, J. W. Menter, and D. W. Pashley, “Moiré Patterns on Electron Micrographs, and their Application to the Study of Dislocations in Metals,” Proc. R. Soc. Lond. A 246(1246), 345–368 (1958).
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J. J. Peters, R. Beanland, M. Alexe, J. W. Cockburn, D. G. Revin, S. Y. Zhang, and A. M. Sanchez, “Artefacts in geometric phase analysis of compound materials,” Ultramicroscopy 157, 91–97 (2015).
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Phillip, R.

G. A. Geach and R. Phillip, “Moiré Patterns in Transmission Electron Micrographs of Sub-Boundaries of Aluminium,” Nature 179(4573), 1293 (1957).
[Crossref]

Qiu, W.

H. Xing, Z. Gao, H. Wang, Z. Lei, L. Ma, and W. Qiu, “Digital rotation moirémethod for strain measurement based on high-resolution transmission electron microscope lattice image,” Opt. Laser. Eng. 122(2), 347–353 (2019).
[Crossref]

Reilly, D. J.

Y. Hu, H. O. Churchill, D. J. Reilly, J. Xiang, C. M. Lieber, and C. M. Marcus, “A Ge/Si heterostructure nanowire-based double quantum dot with integrated charge sensor,” Nat. Nanotechnol. 2(10), 622–625 (2007).
[Crossref]

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J. J. Peters, R. Beanland, M. Alexe, J. W. Cockburn, D. G. Revin, S. Y. Zhang, and A. M. Sanchez, “Artefacts in geometric phase analysis of compound materials,” Ultramicroscopy 157, 91–97 (2015).
[Crossref]

Ri, S.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, and T. Sugiyama, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-fourier-transform sampling moiré method,” Jpn. J. Appl. Phys. 57(4S), 04FC04 (2018).
[Crossref]

Q. H. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyashita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28(45), 455704 (2017).
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S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51(16), 3214–3223 (2012).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling Moiré Method for Accurate Small Deformation Distribution Measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

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R. Loo, R. Delhougne, M. Caymax, and M. Ries, “Formation of misfit dislocations at the thin strained Si∕strain-relaxed buffer interface,” Appl. Phys. Lett. 87(18), 182108 (2005).
[Crossref]

Sanchez, A. M.

J. J. Peters, R. Beanland, M. Alexe, J. W. Cockburn, D. G. Revin, S. Y. Zhang, and A. M. Sanchez, “Artefacts in geometric phase analysis of compound materials,” Ultramicroscopy 157, 91–97 (2015).
[Crossref]

Schwingenschlögl, U.

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
[Crossref]

Snoeck, E.

N. Cherkashin, M. J. Hÿtch, E. Snoeck, A. Claverie, J. M. Hartmann, and Y. Bogumilowicz, “Quantitative strain and stress measurements in Ge/Si dual channels grown on a Si0.5Ge0.5 virtual substrate,” Mater. Sci. Eng., B 124-125, 118–122 (2005).
[Crossref]

Steenbergen, J. V.

S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
[Crossref]

Su, S.

J. Li, C. Zhao, Y. Xing, S. Su, and B. Cheng, “Full-Field Strain Mapping at a Ge/Si Heterostructure Interface,” Materials 6(6), 2130–2142 (2013).
[Crossref]

Su, S. J.

Q. Liu, C. W. Zhao, Y. M. Xing, S. J. Su, and B. W. Cheng, “Quantitative strain analysis of misfit dislocations in a Ge/Si heterostructure interface by geometric phase analysis,” Opt. Laser. Eng. 50(5), 796–799 (2012).
[Crossref]

Sugiyama, N.

N. Hirashita, N. Sugiyama, E. Toyoda, and S. Takagi, “Relaxation processes in strained Si layers on silicon-germanium- on-insulator substrates,” Appl. Phys. Lett. 86(22), 221923 (2005).
[Crossref]

Sugiyama, T.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, and T. Sugiyama, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-fourier-transform sampling moiré method,” Jpn. J. Appl. Phys. 57(4S), 04FC04 (2018).
[Crossref]

Suguro, K.

Q. H. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyashita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28(45), 455704 (2017).
[Crossref]

Takagi, S.

N. Hirashita, N. Sugiyama, E. Toyoda, and S. Takagi, “Relaxation processes in strained Si layers on silicon-germanium- on-insulator substrates,” Appl. Phys. Lett. 86(22), 221923 (2005).
[Crossref]

Tao, R.

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
[Crossref]

Toyoda, E.

N. Hirashita, N. Sugiyama, E. Toyoda, and S. Takagi, “Relaxation processes in strained Si layers on silicon-germanium- on-insulator substrates,” Appl. Phys. Lett. 86(22), 221923 (2005).
[Crossref]

Tsuda, H.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, and T. Sugiyama, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-fourier-transform sampling moiré method,” Jpn. J. Appl. Phys. 57(4S), 04FC04 (2018).
[Crossref]

Q. H. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyashita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28(45), 455704 (2017).
[Crossref]

Van, d. V. G. F.

P. M. J. Maree, J. C. Barbour, d. V. G. F. Van, and K. L. Kavanagh, “Generation of misfit dislocations in semiconductors,” J. Appl. Phys. 62(11), 4413–4420 (1987).
[Crossref]

Vandervorst, W.

S. V. Elshocht, M. Caymax, T. Conard, S. D. Gendt, I. Hoflijk, M. Houssa, F. Leys, R. Bonzom, B. D. Jaeger, J. V. Steenbergen, W. Vandervorst, M. Heyns, and M. Meuris, “Study of CVD high-k gate oxides on high-mobility Ge and Ge/Si substrates,” Thin Solid Films 508(1-2), 1–5 (2006).
[Crossref]

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L. Vescan and S. Wickenhauser, “Relaxation mechanism of low temperature SiGe/Si (0 0 1) buffer layers,” Solid-State Electron. 48(8), 1279–1284 (2004).
[Crossref]

Wang, H.

H. Xing, Z. Gao, H. Wang, Z. Lei, L. Ma, and W. Qiu, “Digital rotation moirémethod for strain measurement based on high-resolution transmission electron microscope lattice image,” Opt. Laser. Eng. 122(2), 347–353 (2019).
[Crossref]

M. Mao, A. Nie, J. Liu, H. Wang, S. X. Mao, Q. Wang, K. Li, and X.-X. Zhang, “Atomic resolution observation of conversion-type anode RuO2 during the first electrochemical lithiation,” Nanotechnology 26(12), 125404 (2015).
[Crossref]

Wang, H.-T.

A. Nie, L.-Y. Gan, Y. Cheng, H. Asayesh-Ardakani, Q. Li, C. Dong, R. Tao, F. Mashayek, H.-T. Wang, and U. Schwingenschlögl, “Atomic-scale observation of lithiation reaction front in nanoscale SnO2 materials,” ACS Nano 7(7), 6203–6211 (2013).
[Crossref]

Wang, Q.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, and T. Sugiyama, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-fourier-transform sampling moiré method,” Jpn. J. Appl. Phys. 57(4S), 04FC04 (2018).
[Crossref]

M. Mao, A. Nie, J. Liu, H. Wang, S. X. Mao, Q. Wang, K. Li, and X.-X. Zhang, “Atomic resolution observation of conversion-type anode RuO2 during the first electrochemical lithiation,” Nanotechnology 26(12), 125404 (2015).
[Crossref]

Wang, Q. H.

Q. H. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyashita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28(45), 455704 (2017).
[Crossref]

Wang, R.

D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
[Crossref]

Wen, H.

H. Zhang, Z. Liu, H. Wen, H. Xie, and C. Liu, “Subset geometric phase analysis method for deformation evaluation of HRTEM images,” Ultramicroscopy 171, 34–42 (2016).
[Crossref]

Wickenhauser, S.

L. Vescan and S. Wickenhauser, “Relaxation mechanism of low temperature SiGe/Si (0 0 1) buffer layers,” Solid-State Electron. 48(8), 1279–1284 (2004).
[Crossref]

Wood, J. K.

A. J. Foreman, M. A. Jaswon, and J. K. Wood, “Factors controlling dislocation widths,” Proc. Phys. Soc. A 64(2), 156–163 (1951).
[Crossref]

Wu, D.

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J. Xiang, W. Lu, Y. J. Hu, Y. Wu, H. Yan, and C. M. Lieber, “Ge/Si nanowire heterostructures as Highperformance field-effect transistors,” Nature 441(7092), 489–493 (2006).
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H. Zhang, Z. Liu, H. Wen, H. Xie, and C. Liu, “Subset geometric phase analysis method for deformation evaluation of HRTEM images,” Ultramicroscopy 171, 34–42 (2016).
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Figures (9)

Fig. 1.
Fig. 1. Rotating moiré, (a) simulated lattice structure with different frequency; (b) θ = 5°, fr = 0.115; (c) θ = 5°, fr = 0.125; (d) θ = 5°, fr = 0.135. (e) θ = 1°, fr = 0.130; (f) θ = 5°, fr = 0.130; (g) θ = 10°, fr = 0.130 ; (h) θ = 15°, fr = 0.130.
Fig. 2.
Fig. 2. (a) Four-step phase-shifted moiré fringe patterns extracted from Fig. 1(d); (b) wrapped phase field; (c) gradient line obtained from the phase field.
Fig. 3.
Fig. 3. (a) Three white boxes A, B, and C are the dislocation locations generated by the software, (b) and (c) different angles of rotational moiré fringes formed by the reference lattice and the specimen lattice, the white square is the location of the moiré fringe intersection.
Fig. 4.
Fig. 4. (a) HRTEM image of Si/Ge heterostructure, the yellow area is the interface between Si and Ge; (b) reference lattice parallel to the Si/Ge heterostructure (11-1) crystal face; (c) interface on moiré fringe; (d) real interface on Si/Ge heterojunction HRTEM image.
Fig. 5.
Fig. 5. (a) HRTEM images of Ge/Si heterostructure; (b) rotation moiré formed by the reference lattice and the specimen lattice.
Fig. 6.
Fig. 6. (a) HRTEM image of Ge/Si heterostructure interface; (b) Fourier transform of (a); (d) burgers vector with sampling moiré.
Fig. 7.
Fig. 7. (a) HRTEM image of Ge/Si heterostructure interface; (b) digital moiré fringe patterns; (c) fringe patterns extracted from (b).
Fig. 8.
Fig. 8. Experimental and theoretical strain fields: (a) experimental strain field; (b) strain field of P-N dislocation model; (c) - (k) strain field of Foreman dislocation model, with α ranging from 2 to 10, respectively.
Fig. 9.
Fig. 9. Interfacial strain and stress of Ge/Si heterostructure: (a) intercepted Ge/Si heterostructure interface; (b) strain field in the horizontal direction; (c) stress profile corresponding to the dash-dotted line in (b).

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

I s ( x , y ) = N s 0 + N s 1 cos ( 2 π p s y + φ s )
I r ( x , y ) = N r 0 + N r 1 cos ( 2 π p r y + φ r )
I = I r I s = N r 0 + N r 1 sin ( 2 π p r y + φ r ) N s 0 N s 1 sin ( 2 π p s y + φ s )
1 δ = 1 p r 1 p s
I N 0 + N 1 cos ( 2 π δ y + φ 0 )
I n N 0 + N 1 c o s ( 2 π δ y + φ 0 + i π 2 ) , ( n = 1 , 2 , 3 , 4 ; i = 0 , 1 , 2 , 3 )
φ ( x , y ) = arctan I 4 ( x , y ) I 2 ( x , y ) I 1 ( x , y ) I 3 ( x , y )
{ u x = u r cos α 1 + u n cos α 2 u y = u r sin α 1 + u n sin α 2
{ ε x = u x / x ε y = u y / y
σ x = E 1 v 2 ( ε x + v ε y )
{ δ 1 = p r p s 1 p s 1 2 + p r 2 2 p r p s 1 cos θ 1 tan β 1 = p r sin θ 1 p s 1 p r cos θ 1
{ δ 2 = p r p s 2 p s 2 2 + p r 2 2 p r p s 2 cos θ 2 tan β 2 = p r sin θ 2 p s 2 p r cos θ 2
Δ β = β 2 β 1 = arc tan p r sin θ 2 p s 2 p r cos θ 2 arc tan p r sin θ 1 p s 1 p r cos θ 1
θ 2 = θ 1 = θ
Δ β = β 2 β 1 = arc tan p s 1 sin θ + p s 2 sin θ p s 1 p s 2 p r + p r p s 1 cos θ p s 2 cos θ
Δ β = β 2 β 1 = arc tan sin θ 1 cos θ

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