Abstract

We performed a study of the in-plane birefringence of anisotropically nanostructured Si layers, which exhibit a greater difference in the main value of the anisotropic refractive index than that of natural birefringent crystals. The anisotropy parameters were found to be strongly dependent on the typical size of the Si nanowires used to assemble the layers. This finding opens the possibility of an application of birefringent Si retarders to a wide spectral range for control of the polarization state of light.

© 2001 Optical Society of America

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References

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  1. C. F. Klingshirn, Semiconductor Optics (Springer-Verlag, Berlin, 1997).
  2. P. Etchegoin, J. Kircher, and M. Cardona, Phys. Rev. B 47, 16 (1993).
    [CrossRef]
  3. A. A. Sirenko, P. Etchegoin, A. Fainstein, K. Eberl, and M. Cardona, Phys. Rev. B 60, 8253 (1999).
    [CrossRef]
  4. H. A. Lorentz, Collected Papers (Nijhoff, Dordrecht, The Netherlands, 1936), Vol. II, p. 79.
  5. S. H. A. Lorentz, Collected Papers (Nijhoff, Dordrecht, The Netherlands, 1936), Vol. III, p. 314.
  6. J. Pastrnak and K. Vedam, Phys. Rev. B 3, 2567 (1971).
    [CrossRef]
  7. A. G. Cullis, L. T. Canham, and P. D. J. Calcott, J. Appl. Phys. 82, 909 (1997).
    [CrossRef]
  8. D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B 215, 871 (1999).
    [CrossRef]
  9. A. G. Cullis and L. T. Canham, Nature 353, 335 (1991).
    [CrossRef]
  10. D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
    [CrossRef]
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  12. I. Mihalcescu, G. Lerondel, and R. Romestain, Thin Solid Films 297, 245 (1997).
    [CrossRef]
  13. S. F. Chuang, S. D. Collins, and R. L. Smith, Appl. Phys. Lett. 55, 675 (1989).
    [CrossRef]
  14. L. Bergmann, Lehrbuch der Experimentalphysik: Optik (de Gruyter, Berlin, 1978).
  15. D. A. G. Bruggeman, Ann. Phys. 24, 636 (1935).
    [CrossRef]

1999 (2)

A. A. Sirenko, P. Etchegoin, A. Fainstein, K. Eberl, and M. Cardona, Phys. Rev. B 60, 8253 (1999).
[CrossRef]

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

1997 (2)

I. Mihalcescu, G. Lerondel, and R. Romestain, Thin Solid Films 297, 245 (1997).
[CrossRef]

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, J. Appl. Phys. 82, 909 (1997).
[CrossRef]

1995 (1)

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

1993 (1)

P. Etchegoin, J. Kircher, and M. Cardona, Phys. Rev. B 47, 16 (1993).
[CrossRef]

1991 (1)

A. G. Cullis and L. T. Canham, Nature 353, 335 (1991).
[CrossRef]

1989 (1)

S. F. Chuang, S. D. Collins, and R. L. Smith, Appl. Phys. Lett. 55, 675 (1989).
[CrossRef]

1971 (1)

J. Pastrnak and K. Vedam, Phys. Rev. B 3, 2567 (1971).
[CrossRef]

1935 (1)

D. A. G. Bruggeman, Ann. Phys. 24, 636 (1935).
[CrossRef]

Ben-Chorin, M.

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

Bergmann, L.

L. Bergmann, Lehrbuch der Experimentalphysik: Optik (de Gruyter, Berlin, 1978).

Bruggeman, D. A. G.

D. A. G. Bruggeman, Ann. Phys. 24, 636 (1935).
[CrossRef]

Calcott, P. D. J.

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, J. Appl. Phys. 82, 909 (1997).
[CrossRef]

Canham, L. T.

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, J. Appl. Phys. 82, 909 (1997).
[CrossRef]

A. G. Cullis and L. T. Canham, Nature 353, 335 (1991).
[CrossRef]

Cardona, M.

A. A. Sirenko, P. Etchegoin, A. Fainstein, K. Eberl, and M. Cardona, Phys. Rev. B 60, 8253 (1999).
[CrossRef]

P. Etchegoin, J. Kircher, and M. Cardona, Phys. Rev. B 47, 16 (1993).
[CrossRef]

Chuang, S. F.

S. F. Chuang, S. D. Collins, and R. L. Smith, Appl. Phys. Lett. 55, 675 (1989).
[CrossRef]

Collins, S. D.

S. F. Chuang, S. D. Collins, and R. L. Smith, Appl. Phys. Lett. 55, 675 (1989).
[CrossRef]

Cullis, A. G.

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, J. Appl. Phys. 82, 909 (1997).
[CrossRef]

A. G. Cullis and L. T. Canham, Nature 353, 335 (1991).
[CrossRef]

Diener, J.

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

Eberl, K.

A. A. Sirenko, P. Etchegoin, A. Fainstein, K. Eberl, and M. Cardona, Phys. Rev. B 60, 8253 (1999).
[CrossRef]

Efros, Al.

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

Etchegoin, P.

A. A. Sirenko, P. Etchegoin, A. Fainstein, K. Eberl, and M. Cardona, Phys. Rev. B 60, 8253 (1999).
[CrossRef]

P. Etchegoin, J. Kircher, and M. Cardona, Phys. Rev. B 47, 16 (1993).
[CrossRef]

Fainstein, A.

A. A. Sirenko, P. Etchegoin, A. Fainstein, K. Eberl, and M. Cardona, Phys. Rev. B 60, 8253 (1999).
[CrossRef]

Gippius, A.

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

Heckler, H.

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

Kircher, J.

P. Etchegoin, J. Kircher, and M. Cardona, Phys. Rev. B 47, 16 (1993).
[CrossRef]

Klingshirn, C. F.

C. F. Klingshirn, Semiconductor Optics (Springer-Verlag, Berlin, 1997).

Koch, F.

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

Kovalev, D.

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

Landau, L. D.

E. M. Lifshitz, L. P. Pitaevskii, and L. D. Landau, Electrodynamics of Continuous Media (Elsevier, New York, 1985).

Lerondel, G.

I. Mihalcescu, G. Lerondel, and R. Romestain, Thin Solid Films 297, 245 (1997).
[CrossRef]

Lifshitz, E. M.

E. M. Lifshitz, L. P. Pitaevskii, and L. D. Landau, Electrodynamics of Continuous Media (Elsevier, New York, 1985).

Lorentz, H. A.

H. A. Lorentz, Collected Papers (Nijhoff, Dordrecht, The Netherlands, 1936), Vol. II, p. 79.

Lorentz, S. H. A.

S. H. A. Lorentz, Collected Papers (Nijhoff, Dordrecht, The Netherlands, 1936), Vol. III, p. 314.

Mihalcescu, I.

I. Mihalcescu, G. Lerondel, and R. Romestain, Thin Solid Films 297, 245 (1997).
[CrossRef]

Pastrnak, J.

J. Pastrnak and K. Vedam, Phys. Rev. B 3, 2567 (1971).
[CrossRef]

Pitaevskii, L. P.

E. M. Lifshitz, L. P. Pitaevskii, and L. D. Landau, Electrodynamics of Continuous Media (Elsevier, New York, 1985).

Polisski, G.

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

Romestain, R.

I. Mihalcescu, G. Lerondel, and R. Romestain, Thin Solid Films 297, 245 (1997).
[CrossRef]

Rosen, M.

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

Sirenko, A. A.

A. A. Sirenko, P. Etchegoin, A. Fainstein, K. Eberl, and M. Cardona, Phys. Rev. B 60, 8253 (1999).
[CrossRef]

Smith, R. L.

S. F. Chuang, S. D. Collins, and R. L. Smith, Appl. Phys. Lett. 55, 675 (1989).
[CrossRef]

Tikhodeev, S. G.

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

Vedam, K.

J. Pastrnak and K. Vedam, Phys. Rev. B 3, 2567 (1971).
[CrossRef]

Ann. Phys. (1)

D. A. G. Bruggeman, Ann. Phys. 24, 636 (1935).
[CrossRef]

Appl. Phys. Lett. (2)

S. F. Chuang, S. D. Collins, and R. L. Smith, Appl. Phys. Lett. 55, 675 (1989).
[CrossRef]

D. Kovalev, M. Ben-Chorin, J. Diener, F. Koch, Al. Efros, M. Rosen, A. Gippius, and S. G. Tikhodeev, Appl. Phys. Lett. 67, 1585 (1995).
[CrossRef]

J. Appl. Phys. (1)

A. G. Cullis, L. T. Canham, and P. D. J. Calcott, J. Appl. Phys. 82, 909 (1997).
[CrossRef]

Nature (1)

A. G. Cullis and L. T. Canham, Nature 353, 335 (1991).
[CrossRef]

Phys. Rev. B (3)

J. Pastrnak and K. Vedam, Phys. Rev. B 3, 2567 (1971).
[CrossRef]

P. Etchegoin, J. Kircher, and M. Cardona, Phys. Rev. B 47, 16 (1993).
[CrossRef]

A. A. Sirenko, P. Etchegoin, A. Fainstein, K. Eberl, and M. Cardona, Phys. Rev. B 60, 8253 (1999).
[CrossRef]

Phys. Status Solidi B (1)

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

Thin Solid Films (1)

I. Mihalcescu, G. Lerondel, and R. Romestain, Thin Solid Films 297, 245 (1997).
[CrossRef]

Other (5)

E. M. Lifshitz, L. P. Pitaevskii, and L. D. Landau, Electrodynamics of Continuous Media (Elsevier, New York, 1985).

L. Bergmann, Lehrbuch der Experimentalphysik: Optik (de Gruyter, Berlin, 1978).

C. F. Klingshirn, Semiconductor Optics (Springer-Verlag, Berlin, 1997).

H. A. Lorentz, Collected Papers (Nijhoff, Dordrecht, The Netherlands, 1936), Vol. II, p. 79.

S. H. A. Lorentz, Collected Papers (Nijhoff, Dordrecht, The Netherlands, 1936), Vol. III, p. 314.

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Figures (4)

Fig. 1
Fig. 1

HR TEM image of the surface of a highly doped (110) porous Si layer (resistivity, 1 mΩ cm; etching-current density, 30 mA/cm2). The texture shows a preferential alignment of the pores and Si rods along the 11¯0 crystallographic direction.

Fig. 2
Fig. 2

Electron diffraction pattern of a highly doped (110) porous Si layer (resistivity, 1 mΩ cm; etching-current density, 30 mA/cm2). The spots have an ellipsoidal shape, with their longer axes oriented in the 001 crystallographic direction.

Fig. 3
Fig. 3

Ratio of the intensities of light polarized perpendicularly and parallel with respect to the incident beam transmitted through a 103μm-thick birefringent porous Si layer (resistivity, 50 mΩ cm; etching-current density, 30 mA/cm2). The phase shift between the projections of the electric field vector along the axes of the main refractive indices after the light passed the porous layer is indicated.

Fig. 4
Fig. 4

Spectral dependence of the anisotropy parameter, Δn=n11¯0-n001, for samples prepared from (110)-oriented Si with different doping levels. The largest anisotropy is found for the strongly doped sample (resistivity, 1 mΩ cm). Typical sizes of the Si nanowires are indicated. Square, 38 Ω cm; triangles, 50 mΩ cm; circles, 1 mΩ cm; etching-current density for all layers, 30 mA/cm2.

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