Abstract

Strained silicon is a versatile new type of material, which has found application in microelectronics and integrated optics in the last years. Unlike ordinary silicon, it does not possess a centrosymmetric lattice structure. This allows for stimulation of nonlinear optical processes that involve second-order nonlinear susceptibility. Here, the dependence of the nonlinear susceptibility on the applied strain by means of reflected second-harmonic generation is investigated. This surface-sensitive technique is suitable for the investigation of bulk silicon strained by a layer of thermal oxide. The obtained relation between applied stress and susceptibility enhancement is compared to theoretical prediction based on an analytical model for the deformed silicon orbital. The knowledge of the stress-susceptibility dependence can be used to develop suitable photonic devices that benefit from second-order nonlinear processes in silicon.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Jalali, Nat. Photonics 1, 193 (2007).
    [CrossRef]
  2. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
    [CrossRef] [PubMed]
  3. N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, Appl. Phys. Lett. 94, 091116 (2009).
    [CrossRef]
  4. 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]
  5. J. Y. Huang, Jpn. J. Appl. Phys. 33, 3878 (1994).
    [CrossRef]
  6. E. M. Lifshitz, A. M. Kosevich, L. P. Kitaevskii, and L. D. Landau, Theory of Elasticity (Elsevier, 2007).
  7. T. Emoto, K. Akimoto, Y. Ishikawa, A. Ichimiya, and A. Tanikawa, Thin Solid Films 369, 281 (2000).
    [CrossRef]
  8. J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
    [CrossRef]
  9. A. Rumpel, B. Manschwetus, G. Lilienkamp, H. Schmidt, and W. Daum, Phys. Rev. B 74, 081303 (2006).
    [CrossRef]
  10. G. Janssen, M. Abdalla, F. van Keulen, B. Pujada, and B. van Venrooy, Thin Solid Films 517, 1858 (2009).
    [CrossRef]
  11. Y. Q. An, Ph.D. thesis (University of Colorado, 2003).
  12. D. E. Aspnes, Properties of Crystalline Silicon (INSPEC, 1999).
  13. H. A. Naseem, M. S. Haque, and W. D. Brown, in Silicon Nitride and Silicon Dioxide Thin Insulating Films (The Electrochemical Society, 1997).
  14. E. Kobeda and E. A. Irene, J. Vac. Sci. Technol. B 7, 163 (1989).
    [CrossRef]

2009 (2)

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, Appl. Phys. Lett. 94, 091116 (2009).
[CrossRef]

G. Janssen, M. Abdalla, F. van Keulen, B. Pujada, and B. van Venrooy, Thin Solid Films 517, 1858 (2009).
[CrossRef]

2007 (1)

B. Jalali, Nat. Photonics 1, 193 (2007).
[CrossRef]

2006 (2)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

A. Rumpel, B. Manschwetus, G. Lilienkamp, H. Schmidt, and W. Daum, Phys. Rev. B 74, 081303 (2006).
[CrossRef]

2000 (1)

T. Emoto, K. Akimoto, Y. Ishikawa, A. Ichimiya, and A. Tanikawa, Thin Solid Films 369, 281 (2000).
[CrossRef]

1994 (1)

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

1989 (2)

1987 (1)

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

Abdalla, M.

G. Janssen, M. Abdalla, F. van Keulen, B. Pujada, and B. van Venrooy, Thin Solid Films 517, 1858 (2009).
[CrossRef]

Akimoto, K.

T. Emoto, K. Akimoto, Y. Ishikawa, A. Ichimiya, and A. Tanikawa, Thin Solid Films 369, 281 (2000).
[CrossRef]

An, Y. Q.

Y. Q. An, Ph.D. thesis (University of Colorado, 2003).

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Aspnes, D. E.

D. E. Aspnes, Properties of Crystalline Silicon (INSPEC, 1999).

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Borel, P. I.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Brown, W. D.

H. A. Naseem, M. S. Haque, and W. D. Brown, in Silicon Nitride and Silicon Dioxide Thin Insulating Films (The Electrochemical Society, 1997).

Daum, W.

A. Rumpel, B. Manschwetus, G. Lilienkamp, H. Schmidt, and W. Daum, Phys. Rev. B 74, 081303 (2006).
[CrossRef]

Emel'yanov, V. I.

Emoto, T.

T. Emoto, K. Akimoto, Y. Ishikawa, A. Ichimiya, and A. Tanikawa, Thin Solid Films 369, 281 (2000).
[CrossRef]

Fage-Pedersen, J.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Frandsen, L. H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Govorkov, S. V.

Hansen, O.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Haque, M. S.

H. A. Naseem, M. S. Haque, and W. D. Brown, in Silicon Nitride and Silicon Dioxide Thin Insulating Films (The Electrochemical Society, 1997).

Hon, N. K.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, Appl. Phys. Lett. 94, 091116 (2009).
[CrossRef]

Huang, J. Y.

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

Ichimiya, A.

T. Emoto, K. Akimoto, Y. Ishikawa, A. Ichimiya, and A. Tanikawa, Thin Solid Films 369, 281 (2000).
[CrossRef]

Irene, E. A.

E. Kobeda and E. A. Irene, J. Vac. Sci. Technol. B 7, 163 (1989).
[CrossRef]

Ishikawa, Y.

T. Emoto, K. Akimoto, Y. Ishikawa, A. Ichimiya, and A. Tanikawa, Thin Solid Films 369, 281 (2000).
[CrossRef]

Jacobsen, R. S.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Jalali, B.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, Appl. Phys. Lett. 94, 091116 (2009).
[CrossRef]

B. Jalali, Nat. Photonics 1, 193 (2007).
[CrossRef]

Janssen, G.

G. Janssen, M. Abdalla, F. van Keulen, B. Pujada, and B. van Venrooy, Thin Solid Films 517, 1858 (2009).
[CrossRef]

Kitaevskii, L. P.

E. M. Lifshitz, A. M. Kosevich, L. P. Kitaevskii, and L. D. Landau, Theory of Elasticity (Elsevier, 2007).

Kobeda, E.

E. Kobeda and E. A. Irene, J. Vac. Sci. Technol. B 7, 163 (1989).
[CrossRef]

Koroteev, N. I.

Kosevich, A. M.

E. M. Lifshitz, A. M. Kosevich, L. P. Kitaevskii, and L. D. Landau, Theory of Elasticity (Elsevier, 2007).

Kristensen, M.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Landau, L. D.

E. M. Lifshitz, A. M. Kosevich, L. P. Kitaevskii, and L. D. Landau, Theory of Elasticity (Elsevier, 2007).

Lavrinenko, A. V.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Lifshitz, E. M.

E. M. Lifshitz, A. M. Kosevich, L. P. Kitaevskii, and L. D. Landau, Theory of Elasticity (Elsevier, 2007).

Lilienkamp, G.

A. Rumpel, B. Manschwetus, G. Lilienkamp, H. Schmidt, and W. Daum, Phys. Rev. B 74, 081303 (2006).
[CrossRef]

Manschwetus, B.

A. Rumpel, B. Manschwetus, G. Lilienkamp, H. Schmidt, and W. Daum, Phys. Rev. B 74, 081303 (2006).
[CrossRef]

Moss, D. J.

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

Moulin, G.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Naseem, H. A.

H. A. Naseem, M. S. Haque, and W. D. Brown, in Silicon Nitride and Silicon Dioxide Thin Insulating Films (The Electrochemical Society, 1997).

Ou, H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Petrov, G. I.

Peucheret, C.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Pujada, B.

G. Janssen, M. Abdalla, F. van Keulen, B. Pujada, and B. van Venrooy, Thin Solid Films 517, 1858 (2009).
[CrossRef]

Rumpel, A.

A. Rumpel, B. Manschwetus, G. Lilienkamp, H. Schmidt, and W. Daum, Phys. Rev. B 74, 081303 (2006).
[CrossRef]

Schmidt, H.

A. Rumpel, B. Manschwetus, G. Lilienkamp, H. Schmidt, and W. Daum, Phys. Rev. B 74, 081303 (2006).
[CrossRef]

Shumay, I. L.

Sipe, J. E.

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

Solli, D. R.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, Appl. Phys. Lett. 94, 091116 (2009).
[CrossRef]

Tanikawa, A.

T. Emoto, K. Akimoto, Y. Ishikawa, A. Ichimiya, and A. Tanikawa, Thin Solid Films 369, 281 (2000).
[CrossRef]

Tsia, K. K.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, Appl. Phys. Lett. 94, 091116 (2009).
[CrossRef]

van Driel, H. M.

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

van Keulen, F.

G. Janssen, M. Abdalla, F. van Keulen, B. Pujada, and B. van Venrooy, Thin Solid Films 517, 1858 (2009).
[CrossRef]

van Venrooy, B.

G. Janssen, M. Abdalla, F. van Keulen, B. Pujada, and B. van Venrooy, Thin Solid Films 517, 1858 (2009).
[CrossRef]

Yakovlev, V. V.

Zsigri, B.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, Appl. Phys. Lett. 94, 091116 (2009).
[CrossRef]

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

J. Vac. Sci. Technol. B (1)

E. Kobeda and E. A. Irene, J. Vac. Sci. Technol. B 7, 163 (1989).
[CrossRef]

Jpn. J. Appl. Phys. (1)

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

Nat. Photonics (1)

B. Jalali, Nat. Photonics 1, 193 (2007).
[CrossRef]

Nature (1)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, Nature 441, 199 (2006).
[CrossRef] [PubMed]

Phys. Rev. B (2)

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

A. Rumpel, B. Manschwetus, G. Lilienkamp, H. Schmidt, and W. Daum, Phys. Rev. B 74, 081303 (2006).
[CrossRef]

Thin Solid Films (2)

G. Janssen, M. Abdalla, F. van Keulen, B. Pujada, and B. van Venrooy, Thin Solid Films 517, 1858 (2009).
[CrossRef]

T. Emoto, K. Akimoto, Y. Ishikawa, A. Ichimiya, and A. Tanikawa, Thin Solid Films 369, 281 (2000).
[CrossRef]

Other (4)

Y. Q. An, Ph.D. thesis (University of Colorado, 2003).

D. E. Aspnes, Properties of Crystalline Silicon (INSPEC, 1999).

H. A. Naseem, M. S. Haque, and W. D. Brown, in Silicon Nitride and Silicon Dioxide Thin Insulating Films (The Electrochemical Society, 1997).

E. M. Lifshitz, A. M. Kosevich, L. P. Kitaevskii, and L. D. Landau, Theory of Elasticity (Elsevier, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Experimental setup for measuring the dependence of the SHG's reflected signal on the azimuthal angle Φ. The stress σ ( z ) is mediated into the substrate by a thermal silicon oxide layer with the stress level σ 0 .

Fig. 2
Fig. 2

Azimuthal dependence of the second harmonic intensity. The dots represent measured values. The solid line is a least-square fit of Eq. (3) to the measurements.

Fig. 3
Fig. 3

Enhancement of the second-order susceptibility components a p p and c p p , respectively, depending on the applied stress. The fit (solid line) shows a linear dependence as predicted in [4, 5].

Tables (1)

Tables Icon

Table 1 Comparison of Different Results for the Strain Enhancement of Tensorial Components of χ ( 2 )

Equations (3)

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

σ ( z ) = σ 0 exp ( z d ) ,
χ def ( 2 ) σ 0 d .
I p p SHG | a p p + c p p cos ( 3 ϕ ) | 2 I p , 0 2 ,

Metrics