Abstract

The enhanced second-harmonic (SH) generation from Si (111) stripes induced by external cylindrical strain is investigated. The dependence of the intensity of the strain-induced SH on the sample azimuth shows that the Si under cylindrical strain has 3m symmetry, which is similar to that of the Si (111) surface. Further studies indicate that the intensity of the enhanced SH is a quadratic function of the cylindrical strain within the magnitude that the Si stripe can bear. For the p-polarized and s-polarized SH, the intensities are, respectively, enhanced by 47.9% and 13% at ϵ0=2.93×104. The enhancement of SH is due to the contributions from the strain-induced second-order nonlinear susceptibility χstrain(2) to the bulk dipole.

© 2009 Optical Society of America

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  1. H. W. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
    [CrossRef]
  2. D. Xiao, E. Ramsay, D. T. Reid, B. Offenbeck, and N. Weber, Appl. Phys. Lett. 88, 114107 (2006).
    [CrossRef]
  3. E. D. Mishina, N. Tanimura, S. Nakabayashi, O. A. Aktsipetrov, and M. C. Downer, Jpn. J. Appl. Phys., Part 1 42, 6731 (2003).
    [CrossRef]
  4. O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
    [CrossRef]
  5. G. Lüpke, D. J. Bottomley, and H. M. van Driel, Phys. Rev. B 47, 10389 (1993).
    [CrossRef]
  6. W. Daum, H. J. Krause, U. Reichel, and H. Ibach, Phys. Rev. Lett. 71, 1234 (1993).
    [CrossRef] [PubMed]
  7. H. Hirayama and K. Watanabe, Phys. Rev. B 51, 14717 (1995).
    [CrossRef]
  8. N. Hayazawa, M. Motohashi, Y. Saito, and S. Kawata, Appl. Phys. Lett. 86, 263114 (2005).
    [CrossRef]
  9. J. Y. Huang, Jpn. J. Appl. Phys., Part 1 33, 3878 (1994).
    [CrossRef]
  10. S. V. Govorkov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, Appl. Phys. A 50, 439 (1990).
    [CrossRef]
  11. E. Liarokapis, D. Papadimitriou, J. Rumberg, and W. Richter, Phys. Status Solidi B 211, 309 (1999).
    [CrossRef]
  12. D. Papadimitriou and W. Richter, Phys. Rev. B 72, 075212 (2005).
    [CrossRef]
  13. G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (IPST, 1974).
  14. S. V. Govorkov, V. I. Emel'yanov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, J. Opt. Soc. Am. B 6, 1117 (1989).
    [CrossRef]
  15. E. Liarokapis and W. Richter, Meas. Sci. Technol. 3, 347 (1992).
    [CrossRef]
  16. J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
    [CrossRef]
  17. V. I. Emelyanov, N. I. Koroteev, and V. V. Yakovlev, Opt. Spectrosc. 62, 701 (1987).

2006 (1)

D. Xiao, E. Ramsay, D. T. Reid, B. Offenbeck, and N. Weber, Appl. Phys. Lett. 88, 114107 (2006).
[CrossRef]

2005 (2)

N. Hayazawa, M. Motohashi, Y. Saito, and S. Kawata, Appl. Phys. Lett. 86, 263114 (2005).
[CrossRef]

D. Papadimitriou and W. Richter, Phys. Rev. B 72, 075212 (2005).
[CrossRef]

2003 (1)

E. D. Mishina, N. Tanimura, S. Nakabayashi, O. A. Aktsipetrov, and M. C. Downer, Jpn. J. Appl. Phys., Part 1 42, 6731 (2003).
[CrossRef]

1999 (2)

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

E. Liarokapis, D. Papadimitriou, J. Rumberg, and W. Richter, Phys. Status Solidi B 211, 309 (1999).
[CrossRef]

1995 (1)

H. Hirayama and K. Watanabe, Phys. Rev. B 51, 14717 (1995).
[CrossRef]

1994 (1)

J. Y. Huang, Jpn. J. Appl. Phys., Part 1 33, 3878 (1994).
[CrossRef]

1993 (2)

G. Lüpke, D. J. Bottomley, and H. M. van Driel, Phys. Rev. B 47, 10389 (1993).
[CrossRef]

W. Daum, H. J. Krause, U. Reichel, and H. Ibach, Phys. Rev. Lett. 71, 1234 (1993).
[CrossRef] [PubMed]

1992 (1)

E. Liarokapis and W. Richter, Meas. Sci. Technol. 3, 347 (1992).
[CrossRef]

1990 (1)

S. V. Govorkov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, Appl. Phys. A 50, 439 (1990).
[CrossRef]

1989 (1)

1987 (2)

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

V. I. Emelyanov, N. I. Koroteev, and V. V. Yakovlev, Opt. Spectrosc. 62, 701 (1987).

1983 (1)

H. W. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

Aktsipetrov, O. A.

E. D. Mishina, N. Tanimura, S. Nakabayashi, O. A. Aktsipetrov, and M. C. Downer, Jpn. J. Appl. Phys., Part 1 42, 6731 (2003).
[CrossRef]

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Anderson, M. H.

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Bir, G. L.

G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (IPST, 1974).

Bottomley, D. J.

G. Lüpke, D. J. Bottomley, and H. M. van Driel, Phys. Rev. B 47, 10389 (1993).
[CrossRef]

Dadap, J. I.

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Daum, W.

W. Daum, H. J. Krause, U. Reichel, and H. Ibach, Phys. Rev. Lett. 71, 1234 (1993).
[CrossRef] [PubMed]

Downer, M. C.

E. D. Mishina, N. Tanimura, S. Nakabayashi, O. A. Aktsipetrov, and M. C. Downer, Jpn. J. Appl. Phys., Part 1 42, 6731 (2003).
[CrossRef]

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Emelyanov, V. I.

V. I. Emelyanov, N. I. Koroteev, and V. V. Yakovlev, Opt. Spectrosc. 62, 701 (1987).

Emel'yanov, V. I.

Fedyanin, A. A.

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Govorkov, S. V.

S. V. Govorkov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, Appl. Phys. A 50, 439 (1990).
[CrossRef]

S. V. Govorkov, V. I. Emel'yanov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, J. Opt. Soc. Am. B 6, 1117 (1989).
[CrossRef]

Hayazawa, N.

N. Hayazawa, M. Motohashi, Y. Saito, and S. Kawata, Appl. Phys. Lett. 86, 263114 (2005).
[CrossRef]

Heinz, T. F.

H. W. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

Hirayama, H.

H. Hirayama and K. Watanabe, Phys. Rev. B 51, 14717 (1995).
[CrossRef]

Huang, J. Y.

J. Y. Huang, Jpn. J. Appl. Phys., Part 1 33, 3878 (1994).
[CrossRef]

Ibach, H.

W. Daum, H. J. Krause, U. Reichel, and H. Ibach, Phys. Rev. Lett. 71, 1234 (1993).
[CrossRef] [PubMed]

Kawata, S.

N. Hayazawa, M. Motohashi, Y. Saito, and S. Kawata, Appl. Phys. Lett. 86, 263114 (2005).
[CrossRef]

Koroteev, N. I.

S. V. Govorkov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, Appl. Phys. A 50, 439 (1990).
[CrossRef]

S. V. Govorkov, V. I. Emel'yanov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, J. Opt. Soc. Am. B 6, 1117 (1989).
[CrossRef]

V. I. Emelyanov, N. I. Koroteev, and V. V. Yakovlev, Opt. Spectrosc. 62, 701 (1987).

Krause, H. J.

W. Daum, H. J. Krause, U. Reichel, and H. Ibach, Phys. Rev. Lett. 71, 1234 (1993).
[CrossRef] [PubMed]

Liarokapis, E.

E. Liarokapis, D. Papadimitriou, J. Rumberg, and W. Richter, Phys. Status Solidi B 211, 309 (1999).
[CrossRef]

E. Liarokapis and W. Richter, Meas. Sci. Technol. 3, 347 (1992).
[CrossRef]

Lüpke, G.

G. Lüpke, D. J. Bottomley, and H. M. van Driel, Phys. Rev. B 47, 10389 (1993).
[CrossRef]

Melnikov, A. V.

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Mishina, E. D.

E. D. Mishina, N. Tanimura, S. Nakabayashi, O. A. Aktsipetrov, and M. C. Downer, Jpn. J. Appl. Phys., Part 1 42, 6731 (2003).
[CrossRef]

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Motohashi, M.

N. Hayazawa, M. Motohashi, Y. Saito, and S. Kawata, Appl. Phys. Lett. 86, 263114 (2005).
[CrossRef]

Nakabayashi, S.

E. D. Mishina, N. Tanimura, S. Nakabayashi, O. A. Aktsipetrov, and M. C. Downer, Jpn. J. Appl. Phys., Part 1 42, 6731 (2003).
[CrossRef]

Offenbeck, B.

D. Xiao, E. Ramsay, D. T. Reid, B. Offenbeck, and N. Weber, Appl. Phys. Lett. 88, 114107 (2006).
[CrossRef]

Papadimitriou, D.

D. Papadimitriou and W. Richter, Phys. Rev. B 72, 075212 (2005).
[CrossRef]

E. Liarokapis, D. Papadimitriou, J. Rumberg, and W. Richter, Phys. Status Solidi B 211, 309 (1999).
[CrossRef]

Petrov, G. I.

S. V. Govorkov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, Appl. Phys. A 50, 439 (1990).
[CrossRef]

S. V. Govorkov, V. I. Emel'yanov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, J. Opt. Soc. Am. B 6, 1117 (1989).
[CrossRef]

Pikus, G. E.

G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (IPST, 1974).

Ramsay, E.

D. Xiao, E. Ramsay, D. T. Reid, B. Offenbeck, and N. Weber, Appl. Phys. Lett. 88, 114107 (2006).
[CrossRef]

Reichel, U.

W. Daum, H. J. Krause, U. Reichel, and H. Ibach, Phys. Rev. Lett. 71, 1234 (1993).
[CrossRef] [PubMed]

Reid, D. T.

D. Xiao, E. Ramsay, D. T. Reid, B. Offenbeck, and N. Weber, Appl. Phys. Lett. 88, 114107 (2006).
[CrossRef]

Richter, W.

D. Papadimitriou and W. Richter, Phys. Rev. B 72, 075212 (2005).
[CrossRef]

E. Liarokapis, D. Papadimitriou, J. Rumberg, and W. Richter, Phys. Status Solidi B 211, 309 (1999).
[CrossRef]

E. Liarokapis and W. Richter, Meas. Sci. Technol. 3, 347 (1992).
[CrossRef]

Rubtsov, A. N.

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Rumberg, J.

E. Liarokapis, D. Papadimitriou, J. Rumberg, and W. Richter, Phys. Status Solidi B 211, 309 (1999).
[CrossRef]

Saito, Y.

N. Hayazawa, M. Motohashi, Y. Saito, and S. Kawata, Appl. Phys. Lett. 86, 263114 (2005).
[CrossRef]

Shen, Y. R.

H. W. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

Shumay, I. L.

S. V. Govorkov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, Appl. Phys. A 50, 439 (1990).
[CrossRef]

S. V. Govorkov, V. I. Emel'yanov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, J. Opt. Soc. Am. B 6, 1117 (1989).
[CrossRef]

Sipe, J. E.

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Tanimura, N.

E. D. Mishina, N. Tanimura, S. Nakabayashi, O. A. Aktsipetrov, and M. C. Downer, Jpn. J. Appl. Phys., Part 1 42, 6731 (2003).
[CrossRef]

ter Beek, M.

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Tom, H. W. K.

H. W. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

van Driel, H. M.

G. Lüpke, D. J. Bottomley, and H. M. van Driel, Phys. Rev. B 47, 10389 (1993).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Watanabe, K.

H. Hirayama and K. Watanabe, Phys. Rev. B 51, 14717 (1995).
[CrossRef]

Weber, N.

D. Xiao, E. Ramsay, D. T. Reid, B. Offenbeck, and N. Weber, Appl. Phys. Lett. 88, 114107 (2006).
[CrossRef]

Wilson, P. T.

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Xiao, D.

D. Xiao, E. Ramsay, D. T. Reid, B. Offenbeck, and N. Weber, Appl. Phys. Lett. 88, 114107 (2006).
[CrossRef]

Xu, X. F.

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

Yakovlev, V. V.

S. V. Govorkov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, Appl. Phys. A 50, 439 (1990).
[CrossRef]

S. V. Govorkov, V. I. Emel'yanov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, J. Opt. Soc. Am. B 6, 1117 (1989).
[CrossRef]

V. I. Emelyanov, N. I. Koroteev, and V. V. Yakovlev, Opt. Spectrosc. 62, 701 (1987).

Appl. Phys. A (1)

S. V. Govorkov, N. I. Koroteev, G. I. Petrov, I. L. Shumay, and V. V. Yakovlev, Appl. Phys. A 50, 439 (1990).
[CrossRef]

Appl. Phys. Lett. (2)

D. Xiao, E. Ramsay, D. T. Reid, B. Offenbeck, and N. Weber, Appl. Phys. Lett. 88, 114107 (2006).
[CrossRef]

N. Hayazawa, M. Motohashi, Y. Saito, and S. Kawata, Appl. Phys. Lett. 86, 263114 (2005).
[CrossRef]

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys., Part 1 (2)

J. Y. Huang, Jpn. J. Appl. Phys., Part 1 33, 3878 (1994).
[CrossRef]

E. D. Mishina, N. Tanimura, S. Nakabayashi, O. A. Aktsipetrov, and M. C. Downer, Jpn. J. Appl. Phys., Part 1 42, 6731 (2003).
[CrossRef]

Meas. Sci. Technol. (1)

E. Liarokapis and W. Richter, Meas. Sci. Technol. 3, 347 (1992).
[CrossRef]

Opt. Spectrosc. (1)

V. I. Emelyanov, N. I. Koroteev, and V. V. Yakovlev, Opt. Spectrosc. 62, 701 (1987).

Phys. Rev. B (5)

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

D. Papadimitriou and W. Richter, Phys. Rev. B 72, 075212 (2005).
[CrossRef]

O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov, M. H. Anderson, P. T. Wilson, M. ter Beek, X. F. Xu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).
[CrossRef]

G. Lüpke, D. J. Bottomley, and H. M. van Driel, Phys. Rev. B 47, 10389 (1993).
[CrossRef]

H. Hirayama and K. Watanabe, Phys. Rev. B 51, 14717 (1995).
[CrossRef]

Phys. Rev. Lett. (2)

H. W. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

W. Daum, H. J. Krause, U. Reichel, and H. Ibach, Phys. Rev. Lett. 71, 1234 (1993).
[CrossRef] [PubMed]

Phys. Status Solidi B (1)

E. Liarokapis, D. Papadimitriou, J. Rumberg, and W. Richter, Phys. Status Solidi B 211, 309 (1999).
[CrossRef]

Other (1)

G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (IPST, 1974).

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Figures (4)

Fig. 1
Fig. 1

(a) Left, schematic diagram of the experimental setup for SHG measurements. The two rectangles are the polarizer and analyzer, respectively. Right, schematic structure of the uniaxial strain equipment. J 0 , h, and 2 a are the central deformation, thickness, and length of the sample, respectively. (b) Strain along stripes of thickness h calculated from the central deformation J 0 . Data points are experimentally obtained by measuring the radius of curvature. (c) Object assemblage of the uniaxial strain device and experimental setup.

Fig. 2
Fig. 2

The p-polarized SHG intensity from the unstrained and strained Si (111) surface for s-polarized excitation as a function of the sample rotation angle ϕ. Curve A is obtained from the unstrained Si surface. The corresponding strain values with curves B and C are 2.93 × 10 4 and 5.86 × 10 4 , respectively.

Fig. 3
Fig. 3

The s-polarized SHG intensity from unstrained and strained Si (111) surfaces for s-polarized excitation as a function of the sample rotation angle ϕ. Curve A is obtained from the unstrained Si surface. The corresponding strain values with curves B and C are 2.93 × 10 4 and 5.86 × 10 4 , respectively.

Fig. 4
Fig. 4

Intensity of the p-polarized and s-polarized SH signals from reflected Si surface as a function of the strain. The solid curves A and B are fitted, and the fitting functions can be expressed as I s p = 4.8773 × 10 6 ϵ 0 2 + 0.0006 × 10 6 ϵ 0 for the p-polarized SH signal and I s s = 8.0749 × 10 5 ϵ 0 2 + 0.0022 × 10 5 ϵ 0 for the s-polarized SH signal, respectively.

Equations (4)

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

I s p ( 2 ω ) | a s , p + c s , p cos ( 3 ϕ ) | 2 ,
I s s ( 2 ω ) | b s , s sin 3 ϕ | 2 ,
E s p ( 2 ω ) i χ z y y ( 2 ) , strain + a ζ ,
χ z y y ( 2 ) , strain ( esu ) = 1.03 × 10 6 ϵ 0 .

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