Abstract

Variable-angle spectroscopic ellipsometry was used to determine nondestructively the porosity depth profile and thickness of thin porous silicon layers produced by anodization of p +-doped silicon wafers. A porosity graded-layer model is presented and used in the analysis of the material. In the porosity graded-layer model an inhomogeneous layer is built up by several thin sublayers with the porosity changing slightly from one sublayer to the next. Results from the ellipsometry analysis and from transmission electron microscopy reveal inhomogeneous layers whose porosity and thereby optical properties change with their depth in the layers.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  27. G. Parjadis de Larvière, J. M. Frigerio, J. Rivory, F. Abelès, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry,” Appl. Opt. 31, 6056–6061 (1992).
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    [CrossRef]

1997 (2)

A. G. Cullis, L. T. Canham, P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

L. M. Madsen, L. Weaver, S. N. Jacobsen, “Influence of material properties on TEM specimen preparation of thin films,” Microsc. Res. Technol. 36, 354–361 (1997).
[CrossRef]

1996 (3)

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

L. A. A. Pettersson, S. Zangooie, R. Bjorklund, H. Arwin, “Microstructural analysis and modelling of thin porous silicon layers with variable angle spectroscopic ellipsometry,” Mater. Res. Soc. Symp. Proc. 431, 259–264 (1996).
[CrossRef]

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

1995 (2)

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

B. Hamilton, “Porous silicon,” Semicond. Sci. Technol. 10, 1187–1207 (1995).
[CrossRef]

1994 (2)

L. H. Qin, Y. D. Zheng, R. Zhang, S. L. Gu, H. T. Shi, D. Feng, “Ellipsometric studies of porous silicon,” Appl Phys. A 58, 163–165 (1994).
[CrossRef]

A. Larré, A. Halimaoui, F. Glowacki, F. Ferrieu, Y. Campidelli, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultra high vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

1993 (6)

U. Rossow, H. Münder, M. Thönissen, W. Theiss, “Characterisation of porous silicon layers by spectroscopic ellipsometry,” J. Lumin. 57, 205–209 (1993).
[CrossRef]

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

C. Pickering, L. T. Canham, D. Brumhead, “Spectroscopic ellipsometry characterisation of light-emitting porous silicon,” Appl. Surf. Sci. 63, 22–26 (1993).
[CrossRef]

G. E. Jellison, “Data analysis for spectroscopic ellipsometry,” Thin Solid Films 234, 416–422 (1993).
[CrossRef]

J. P. McCaffrey, “Improved TEM samples of semiconductors prepared by a small-angle cleavage technique,” Microsc. Res. Tech. 21, 180–184 (1993).
[CrossRef]

1992 (6)

G. E. Jellison, “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41–47 (1992).
[CrossRef]

G. Parjadis de Larvière, J. M. Frigerio, J. Rivory, F. Abelès, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry,” Appl. Opt. 31, 6056–6061 (1992).
[CrossRef]

R. L. Smith, S. D. Collins, “Porous silicon formation mechanisms,” J. Appl. Phys. 71, R1–R22 (1992).
[CrossRef]

P. C. Searson, J. M. Macaulay, S. M. Prokes, “The formation, morphology, and optical properties of porous silicon,” J. Electrochem. Soc. 139, 3373–3378 (1992).
[CrossRef]

F. Ferrieu, A. Halimaoui, D. Bensahel, “Optical characterisation of porous silicon layers by spectrometric ellipsometry in the 1.5–5 eV range,” Solid State Commun. 84, 293–296 (1992).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

1991 (1)

1990 (1)

1985 (1)

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985).
[CrossRef]

1984 (1)

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon,” J. Phys. C 17, 6535–6552 (1984).
[CrossRef]

1935 (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalisher Konstanten vor heterogenen Substanzen,” Ann. Phys. (Leipzig) 24, 636–679 (1935).

Abelès, F.

Andrzejak, C.

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Arwin, H.

L. A. A. Pettersson, S. Zangooie, R. Bjorklund, H. Arwin, “Microstructural analysis and modelling of thin porous silicon layers with variable angle spectroscopic ellipsometry,” Mater. Res. Soc. Symp. Proc. 431, 259–264 (1996).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).

Badoz, P. A.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Bársony, I.

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).

Beale, M. I. J.

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985).
[CrossRef]

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon,” J. Phys. C 17, 6535–6552 (1984).
[CrossRef]

Bensahel, D.

A. Larré, A. Halimaoui, F. Glowacki, F. Ferrieu, Y. Campidelli, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultra high vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

F. Ferrieu, A. Halimaoui, D. Bensahel, “Optical characterisation of porous silicon layers by spectrometric ellipsometry in the 1.5–5 eV range,” Solid State Commun. 84, 293–296 (1992).
[CrossRef]

Berbezier, I.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Berger, M. G.

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Billat, S.

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

Bjorklund, R.

L. A. A. Pettersson, S. Zangooie, R. Bjorklund, H. Arwin, “Microstructural analysis and modelling of thin porous silicon layers with variable angle spectroscopic ellipsometry,” Mater. Res. Soc. Symp. Proc. 431, 259–264 (1996).
[CrossRef]

Bomchil, G.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalisher Konstanten vor heterogenen Substanzen,” Ann. Phys. (Leipzig) 24, 636–679 (1935).

Brumhead, D.

C. Pickering, L. T. Canham, D. Brumhead, “Spectroscopic ellipsometry characterisation of light-emitting porous silicon,” Appl. Surf. Sci. 63, 22–26 (1993).
[CrossRef]

Calcott, P. D. J.

A. G. Cullis, L. T. Canham, P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

Campidelli, Y.

A. Larré, A. Halimaoui, F. Glowacki, F. Ferrieu, Y. Campidelli, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultra high vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Canham, L. T.

A. G. Cullis, L. T. Canham, P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

C. Pickering, L. T. Canham, D. Brumhead, “Spectroscopic ellipsometry characterisation of light-emitting porous silicon,” Appl. Surf. Sci. 63, 22–26 (1993).
[CrossRef]

Carniglia, C. K.

Collins, S. D.

R. L. Smith, S. D. Collins, “Porous silicon formation mechanisms,” J. Appl. Phys. 71, R1–R22 (1992).
[CrossRef]

Cullis, A. G.

A. G. Cullis, L. T. Canham, P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

de Larvière, G. Parjadis

Eickhoff, T.

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Feng, D.

L. H. Qin, Y. D. Zheng, R. Zhang, S. L. Gu, H. T. Shi, D. Feng, “Ellipsometric studies of porous silicon,” Appl Phys. A 58, 163–165 (1994).
[CrossRef]

Ferrieu, F.

A. Larré, A. Halimaoui, F. Glowacki, F. Ferrieu, Y. Campidelli, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultra high vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

F. Ferrieu, A. Halimaoui, D. Bensahel, “Optical characterisation of porous silicon layers by spectrometric ellipsometry in the 1.5–5 eV range,” Solid State Commun. 84, 293–296 (1992).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

Fried, M.

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

Frigerio, J. M.

Frohnhoff, S.

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

Frotscher, U.

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

Garchery, L.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Glowacki, F.

A. Larré, A. Halimaoui, F. Glowacki, F. Ferrieu, Y. Campidelli, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultra high vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Greef, R.

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985).
[CrossRef]

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon,” J. Phys. C 17, 6535–6552 (1984).
[CrossRef]

Gu, S. L.

L. H. Qin, Y. D. Zheng, R. Zhang, S. L. Gu, H. T. Shi, D. Feng, “Ellipsometric studies of porous silicon,” Appl Phys. A 58, 163–165 (1994).
[CrossRef]

Halimaoui, A.

A. Larré, A. Halimaoui, F. Glowacki, F. Ferrieu, Y. Campidelli, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultra high vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

F. Ferrieu, A. Halimaoui, D. Bensahel, “Optical characterisation of porous silicon layers by spectrometric ellipsometry in the 1.5–5 eV range,” Solid State Commun. 84, 293–296 (1992).
[CrossRef]

Hamilton, B.

B. Hamilton, “Porous silicon,” Semicond. Sci. Technol. 10, 1187–1207 (1995).
[CrossRef]

Herino, R.

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Jacobsen, S. N.

L. M. Madsen, L. Weaver, S. N. Jacobsen, “Influence of material properties on TEM specimen preparation of thin films,” Microsc. Res. Technol. 36, 354–361 (1997).
[CrossRef]

Jellison, G. E.

G. E. Jellison, “Data analysis for spectroscopic ellipsometry,” Thin Solid Films 234, 416–422 (1993).
[CrossRef]

G. E. Jellison, “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41–47 (1992).
[CrossRef]

G. E. Jellison, “Use of the biased estimator in the interpretation of spectroscopic ellipsometry data,” Appl. Opt. 30, 3354–3360 (1991).
[CrossRef] [PubMed]

Krüger, M.

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

Lambert, B.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Larré, A.

A. Larré, A. Halimaoui, F. Glowacki, F. Ferrieu, Y. Campidelli, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultra high vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Ligeon, M.

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Lohner, T.

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

Lüth, H.

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Macaulay, J. M.

P. C. Searson, J. M. Macaulay, S. M. Prokes, “The formation, morphology, and optical properties of porous silicon,” J. Electrochem. Soc. 139, 3373–3378 (1992).
[CrossRef]

Madsen, L. M.

L. M. Madsen, L. Weaver, S. N. Jacobsen, “Influence of material properties on TEM specimen preparation of thin films,” Microsc. Res. Technol. 36, 354–361 (1997).
[CrossRef]

McCaffrey, J. P.

J. P. McCaffrey, “Improved TEM samples of semiconductors prepared by a small-angle cleavage technique,” Microsc. Res. Tech. 21, 180–184 (1993).
[CrossRef]

Münder, H.

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

U. Rossow, H. Münder, M. Thönissen, W. Theiss, “Characterisation of porous silicon layers by spectroscopic ellipsometry,” J. Lumin. 57, 205–209 (1993).
[CrossRef]

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Pearson, P. J.

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985).
[CrossRef]

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon,” J. Phys. C 17, 6535–6552 (1984).
[CrossRef]

Perret, P.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Petrik, P.

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

Pettersson, L. A. A.

L. A. A. Pettersson, S. Zangooie, R. Bjorklund, H. Arwin, “Microstructural analysis and modelling of thin porous silicon layers with variable angle spectroscopic ellipsometry,” Mater. Res. Soc. Symp. Proc. 431, 259–264 (1996).
[CrossRef]

Pickering, C.

C. Pickering, L. T. Canham, D. Brumhead, “Spectroscopic ellipsometry characterisation of light-emitting porous silicon,” Appl. Surf. Sci. 63, 22–26 (1993).
[CrossRef]

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985).
[CrossRef]

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon,” J. Phys. C 17, 6535–6552 (1984).
[CrossRef]

Piel, J. P.

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

Polgár, O.

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

Prokes, S. M.

P. C. Searson, J. M. Macaulay, S. M. Prokes, “The formation, morphology, and optical properties of porous silicon,” J. Electrochem. Soc. 139, 3373–3378 (1992).
[CrossRef]

Qin, L. H.

L. H. Qin, Y. D. Zheng, R. Zhang, S. L. Gu, H. T. Shi, D. Feng, “Ellipsometric studies of porous silicon,” Appl Phys. A 58, 163–165 (1994).
[CrossRef]

Regolini, J. L.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Richter, W.

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Rivory, J.

Robbins, D. J.

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985).
[CrossRef]

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon,” J. Phys. C 17, 6535–6552 (1984).
[CrossRef]

Rossow, U.

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

U. Rossow, H. Münder, M. Thönissen, W. Theiss, “Characterisation of porous silicon layers by spectroscopic ellipsometry,” J. Lumin. 57, 205–209 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Sagnes, I.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Searson, P. C.

P. C. Searson, J. M. Macaulay, S. M. Prokes, “The formation, morphology, and optical properties of porous silicon,” J. Electrochem. Soc. 139, 3373–3378 (1992).
[CrossRef]

Shi, H. T.

L. H. Qin, Y. D. Zheng, R. Zhang, S. L. Gu, H. T. Shi, D. Feng, “Ellipsometric studies of porous silicon,” Appl Phys. A 58, 163–165 (1994).
[CrossRef]

Smith, R. L.

R. L. Smith, S. D. Collins, “Porous silicon formation mechanisms,” J. Appl. Phys. 71, R1–R22 (1992).
[CrossRef]

Stehle, J. L.

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

Theiss, W.

U. Rossow, H. Münder, M. Thönissen, W. Theiss, “Characterisation of porous silicon layers by spectroscopic ellipsometry,” J. Lumin. 57, 205–209 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

Thönissen, M.

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

U. Rossow, H. Münder, M. Thönissen, W. Theiss, “Characterisation of porous silicon layers by spectroscopic ellipsometry,” J. Lumin. 57, 205–209 (1993).
[CrossRef]

Vázsonyi, É.

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

Vincent, G.

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

Weaver, L.

L. M. Madsen, L. Weaver, S. N. Jacobsen, “Influence of material properties on TEM specimen preparation of thin films,” Microsc. Res. Technol. 36, 354–361 (1997).
[CrossRef]

Zangooie, S.

L. A. A. Pettersson, S. Zangooie, R. Bjorklund, H. Arwin, “Microstructural analysis and modelling of thin porous silicon layers with variable angle spectroscopic ellipsometry,” Mater. Res. Soc. Symp. Proc. 431, 259–264 (1996).
[CrossRef]

Zhang, R.

L. H. Qin, Y. D. Zheng, R. Zhang, S. L. Gu, H. T. Shi, D. Feng, “Ellipsometric studies of porous silicon,” Appl Phys. A 58, 163–165 (1994).
[CrossRef]

Zheng, Y. D.

L. H. Qin, Y. D. Zheng, R. Zhang, S. L. Gu, H. T. Shi, D. Feng, “Ellipsometric studies of porous silicon,” Appl Phys. A 58, 163–165 (1994).
[CrossRef]

Ann. Phys. (Leipzig) (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalisher Konstanten vor heterogenen Substanzen,” Ann. Phys. (Leipzig) 24, 636–679 (1935).

Appl Phys. A (1)

L. H. Qin, Y. D. Zheng, R. Zhang, S. L. Gu, H. T. Shi, D. Feng, “Ellipsometric studies of porous silicon,” Appl Phys. A 58, 163–165 (1994).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. Larré, A. Halimaoui, F. Glowacki, F. Ferrieu, Y. Campidelli, D. Bensahel, “In situ spectroscopic ellipsometry of porous silicon layers annealed under ultra high vacuum,” Appl. Phys. Lett. 65, 1566–1568 (1994).
[CrossRef]

Appl. Surf. Sci. (4)

H. Münder, M. G. Berger, H. Lüth, U. Rossow, U. Frotscher, W. Richter, R. Herino, M. Ligeon, “The influence of nanocrystals on the dielectric function of porous silicon,” Appl. Surf. Sci. 63, 57–61 (1993).
[CrossRef]

G. Bomchil, A. Halimaoui, I. Sagnes, P. A. Badoz, I. Berbezier, P. Perret, B. Lambert, G. Vincent, L. Garchery, J. L. Regolini, “Porous silicon: material properties, visible photo- and electroluminescence,” Appl. Surf. Sci. 65/66, 394–407 (1993).

C. Pickering, L. T. Canham, D. Brumhead, “Spectroscopic ellipsometry characterisation of light-emitting porous silicon,” Appl. Surf. Sci. 63, 22–26 (1993).
[CrossRef]

H. Münder, C. Andrzejak, M. G. Berger, T. Eickhoff, H. Lüth, W. Theiss, U. Rossow, W. Richter, R. Herino, M. Ligeon, “Optical characterization of porous silicon layers formed on heavily p-doped substrates,” Appl. Surf. Sci. 56/58, 6–10 (1992).
[CrossRef]

J. Appl. Phys. (3)

R. L. Smith, S. D. Collins, “Porous silicon formation mechanisms,” J. Appl. Phys. 71, R1–R22 (1992).
[CrossRef]

A. G. Cullis, L. T. Canham, P. D. J. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

M. Thönissen, S. Billat, M. Krüger, H. Lüth, M. G. Berger, U. Frotscher, U. Rossow, “Depth inhomogeneity of porous silicon layers,” J. Appl. Phys. 80, 2990–2993 (1996).
[CrossRef]

J. Electrochem. Soc. (1)

P. C. Searson, J. M. Macaulay, S. M. Prokes, “The formation, morphology, and optical properties of porous silicon,” J. Electrochem. Soc. 139, 3373–3378 (1992).
[CrossRef]

J. Lumin. (1)

U. Rossow, H. Münder, M. Thönissen, W. Theiss, “Characterisation of porous silicon layers by spectroscopic ellipsometry,” J. Lumin. 57, 205–209 (1993).
[CrossRef]

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

J. Phys. C (1)

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon,” J. Phys. C 17, 6535–6552 (1984).
[CrossRef]

Mater. Res. Soc. Symp. Proc. (1)

L. A. A. Pettersson, S. Zangooie, R. Bjorklund, H. Arwin, “Microstructural analysis and modelling of thin porous silicon layers with variable angle spectroscopic ellipsometry,” Mater. Res. Soc. Symp. Proc. 431, 259–264 (1996).
[CrossRef]

Microsc. Res. Tech. (1)

J. P. McCaffrey, “Improved TEM samples of semiconductors prepared by a small-angle cleavage technique,” Microsc. Res. Tech. 21, 180–184 (1993).
[CrossRef]

Microsc. Res. Technol. (1)

L. M. Madsen, L. Weaver, S. N. Jacobsen, “Influence of material properties on TEM specimen preparation of thin films,” Microsc. Res. Technol. 36, 354–361 (1997).
[CrossRef]

Opt. Mater. (1)

G. E. Jellison, “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41–47 (1992).
[CrossRef]

Semicond. Sci. Technol. (1)

B. Hamilton, “Porous silicon,” Semicond. Sci. Technol. 10, 1187–1207 (1995).
[CrossRef]

Solid State Commun. (1)

F. Ferrieu, A. Halimaoui, D. Bensahel, “Optical characterisation of porous silicon layers by spectrometric ellipsometry in the 1.5–5 eV range,” Solid State Commun. 84, 293–296 (1992).
[CrossRef]

Thin Solid Films (4)

M. Fried, T. Lohner, O. Polgár, P. Petrik, É. Vázsonyi, I. Bársony, J. P. Piel, J. L. Stehle, “Characterization of different porous silicon structures by spectroscopic ellipsometry,” Thin Solid Films 276, 223–227 (1996).
[CrossRef]

U. Rossow, U. Frotscher, M. Thönissen, M. G. Berger, S. Frohnhoff, H. Münder, W. Richter, “Influence of the formation conditions on the microstructure of porous silicon layers studied by spectroscopic ellipsometry,” Thin Solid Films 255, 5–8 (1995).
[CrossRef]

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985).
[CrossRef]

G. E. Jellison, “Data analysis for spectroscopic ellipsometry,” Thin Solid Films 234, 416–422 (1993).
[CrossRef]

Other (2)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).

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Figures (8)

Fig. 1
Fig. 1

Schematic representation of the porosity graded-layer models used for inhomogeneous PS layers divided into N sublayers (slices).

Fig. 2
Fig. 2

Fitted porosity graded-depth profiles for a 141.5-nm-thick PS layer for models A and B. Model A represents a porosity graded-layer model with discrete nodes, and model B a porosity graded-layer model with a continuous function as the porosity profile.

Fig. 3
Fig. 3

Penetration depth versus wavelength for c-Si and PS, i.e., EMA mixtures of c-Si and voids, for porosity from 10% to 80%.

Fig. 4
Fig. 4

Measured spectroscopic ellipsometry data (a) ψ and (b) Δ versus wavelength (solid curves) at 55°–75° angle of incidence (in steps of 5°) for a 141.5-nm-thick PS layer. Best fit data for model A, i.e., the graded layer model with discrete nodes, are represented by circles. The best fit at 65° angles of incidence for only one single effective medium layer representing the PS layer is also shown (dashed curves).

Fig. 5
Fig. 5

Quality of model fit, ξ, as given by Eq. (1) versus the total number of layers for models A and B in the porosity graded-layer model applied to a 141.5-nm PS layer.

Fig. 6
Fig. 6

a, Cross-sectional transmission electron microscopy image and b, corresponding selected area electron diffraction pattern of the 141.5-nm PS layer.

Fig. 7
Fig. 7

High-resolution electron microscopy images of the 141.5-nm PS layer: a, top surface region and b, substrate region.

Fig. 8
Fig. 8

(a) Refractive index and (b) extinction coefficient versus wavelength and position in a 141.5-nm-thick PS layer calculated from a porosity graded-layer model.

Equations (5)

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

ξ 2 = 1 2 η - μ i = 1 N ψ i mod - ψ i exp σ ψ , i exp 2 + Δ i mod - Δ i exp σ Δ , i exp 2 ,
i = 1 m   f i ñ i 2 - ñ 2 ñ i 2 + 2 ñ 2 = 0 ,
i = 1 m   f i = 1 ,
Porosity = f void   in   percent = 100   ñ Si 2 - ñ 2 1 + 2 ñ 2 3 ñ 2 ñ Si 2 - 1 ,
α = 4 π k λ ,

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