Abstract

Low energy ion-beam sputtering of GaSb results in self-organized nanostructures with the potential of structuring large surface areas. Characterization of such nanostructures by optical methods is studied and compared to direct (local) microscopic methods. The samples consist of densely packed GaSb cones on bulk GaSb, approximately 30, 50, and 300nm in height, prepared by sputtering at normal incidence. The optical properties are studied by spectroscopic ellipsometry, in the range 0.66.5eV, and with Mueller matrix ellipsometry in the visible range, 1.462.88eV. The optical measurements are compared to direct topography measurements obtained by scanning electron microscopy, high resolution transmission electron microscopy, and atomic force microscopy. Good agreement is achieved between the two classes of methods when the experimental optical response of the short cones (<55nm) is inverted with respect to topological surface information, via a graded anisotropic effective medium model. The main topological parameter measured was the average cone height. Optical methods are shown to represent a valuable characterization tool of nanostructured surfaces, in particular when a large coverage area is desirable. Because of the fast and nondestructive properties of optical techniques, they may readily be adapted to in situ configurations.

© 2008 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th corrected ed. (Pergamon, 1980).
    [PubMed]
  2. G. Beydaghyan, C. Buzea, Y. Cui, C. Elliott, and K. Robbie, “Ex situ ellipsometric investigation of nanocolumns inclination angle of obliquely evaporated silicon thin films,” Appl. Phys. Lett. 87, 153103 (2005).
    [CrossRef]
  3. Z. P. Yang, L. Ci, J. A. Bur, S. Y. Lin, and P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446-451(2008).
    [CrossRef] [PubMed]
  4. S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
    [CrossRef] [PubMed]
  5. N. Brun, A. Lelarge, S. Le Roy, E. Søndergård, and E. Barthel are preparing a manuscript to be called “Composition of nanostructured GaSb.”
  6. M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
    [CrossRef]
  7. B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: in situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1-87(1993).
    [CrossRef]
  8. P. Hauge, “Conventions and formulas for using the Mueller-Stokes calculus in ellipsometry,” Surf. Sci. 96, 81-107(1980).
    [CrossRef]
  9. G. E. Jellison, Jr. and J. W. McCamy, “Sample depolarization effects from thin films of ZnS on GaAs as measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 61, 512-514 (1992).
    [CrossRef]
  10. R. A. Chipman, “Depolarization index and the average degree of polarization,” Appl. Opt. 44, 2490-2495 (2005).
    [CrossRef] [PubMed]
  11. D. Weaire and N. Rivier, “Soap, cells and statistics--random patterns in two dimensions,” Contemp. Phys. 25, 59-99 (1984).
    [CrossRef]
  12. C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavour 26, 79-84 (1967).
  13. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).
  14. G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190-8198 (1997).
    [CrossRef]
  15. A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Mueller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
    [CrossRef]
  16. I. S. Nerbø, M. Kildemo, S. W. Hagen, S. Leroy, and E. Søndergård, “Optical properties and characterization of tilted gasb nanocones,” (to be published).
  17. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 ev,” Phys. Rev. B 27, 985-1009(1983).
    [CrossRef]
  18. M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265-4274 (1996).
    [CrossRef]
  19. D. W. Berreman, “Optics in stratified and anisotropic media: 4×4 matrix formulation,” J. Opt. Soc. Am. 62, 502-510 (1972).
    [CrossRef]
  20. J. E. Spanier and I. P. Herman, “Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous sic films,” Phys. Rev. B 61, 10437-10450 (2000).
    [CrossRef]
  21. J. Stuke and G. Zimmerer, “Optical properties of amorphous iii-v compounds. i. Experiment,” Phys. Stat. Sol. B 49, 513-523(1972).
    [CrossRef]
  22. S. Zollner, “Model dielectric functions for native oxides on compound semiconductors,” Appl. Phys. Lett. 63, 2523-2524(1993).
    [CrossRef]

2008 (2)

Z. P. Yang, L. Ci, J. A. Bur, S. Y. Lin, and P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446-451(2008).
[CrossRef] [PubMed]

M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
[CrossRef]

2005 (2)

G. Beydaghyan, C. Buzea, Y. Cui, C. Elliott, and K. Robbie, “Ex situ ellipsometric investigation of nanocolumns inclination angle of obliquely evaporated silicon thin films,” Appl. Phys. Lett. 87, 153103 (2005).
[CrossRef]

R. A. Chipman, “Depolarization index and the average degree of polarization,” Appl. Opt. 44, 2490-2495 (2005).
[CrossRef] [PubMed]

2004 (1)

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Mueller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

2000 (1)

J. E. Spanier and I. P. Herman, “Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous sic films,” Phys. Rev. B 61, 10437-10450 (2000).
[CrossRef]

1999 (1)

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

1997 (1)

1996 (1)

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265-4274 (1996).
[CrossRef]

1993 (2)

S. Zollner, “Model dielectric functions for native oxides on compound semiconductors,” Appl. Phys. Lett. 63, 2523-2524(1993).
[CrossRef]

B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: in situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1-87(1993).
[CrossRef]

1992 (1)

G. E. Jellison, Jr. and J. W. McCamy, “Sample depolarization effects from thin films of ZnS on GaAs as measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 61, 512-514 (1992).
[CrossRef]

1984 (1)

D. Weaire and N. Rivier, “Soap, cells and statistics--random patterns in two dimensions,” Contemp. Phys. 25, 59-99 (1984).
[CrossRef]

1983 (1)

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 ev,” Phys. Rev. B 27, 985-1009(1983).
[CrossRef]

1980 (1)

P. Hauge, “Conventions and formulas for using the Mueller-Stokes calculus in ellipsometry,” Surf. Sci. 96, 81-107(1980).
[CrossRef]

1972 (2)

J. Stuke and G. Zimmerer, “Optical properties of amorphous iii-v compounds. i. Experiment,” Phys. Stat. Sol. B 49, 513-523(1972).
[CrossRef]

D. W. Berreman, “Optics in stratified and anisotropic media: 4×4 matrix formulation,” J. Opt. Soc. Am. 62, 502-510 (1972).
[CrossRef]

1967 (1)

C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavour 26, 79-84 (1967).

Ajayan, P. M.

Z. P. Yang, L. Ci, J. A. Bur, S. Y. Lin, and P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446-451(2008).
[CrossRef] [PubMed]

Aspnes, D. E.

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 ev,” Phys. Rev. B 27, 985-1009(1983).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Barthel, E.

N. Brun, A. Lelarge, S. Le Roy, E. Søndergård, and E. Barthel are preparing a manuscript to be called “Composition of nanostructured GaSb.”

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Bernhard, C. G.

C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavour 26, 79-84 (1967).

Berreman, D. W.

Beydaghyan, G.

G. Beydaghyan, C. Buzea, Y. Cui, C. Elliott, and K. Robbie, “Ex situ ellipsometric investigation of nanocolumns inclination angle of obliquely evaporated silicon thin films,” Appl. Phys. Lett. 87, 153103 (2005).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th corrected ed. (Pergamon, 1980).
[PubMed]

Brun, N.

N. Brun, A. Lelarge, S. Le Roy, E. Søndergård, and E. Barthel are preparing a manuscript to be called “Composition of nanostructured GaSb.”

Bur, J. A.

Z. P. Yang, L. Ci, J. A. Bur, S. Y. Lin, and P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446-451(2008).
[CrossRef] [PubMed]

Buzea, C.

G. Beydaghyan, C. Buzea, Y. Cui, C. Elliott, and K. Robbie, “Ex situ ellipsometric investigation of nanocolumns inclination angle of obliquely evaporated silicon thin films,” Appl. Phys. Lett. 87, 153103 (2005).
[CrossRef]

Chipman, R. A.

Ci, L.

Z. P. Yang, L. Ci, J. A. Bur, S. Y. Lin, and P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446-451(2008).
[CrossRef] [PubMed]

Cui, Y.

G. Beydaghyan, C. Buzea, Y. Cui, C. Elliott, and K. Robbie, “Ex situ ellipsometric investigation of nanocolumns inclination angle of obliquely evaporated silicon thin films,” Appl. Phys. Lett. 87, 153103 (2005).
[CrossRef]

Dekorsy, T.

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

Drévillon, B.

B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: in situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1-87(1993).
[CrossRef]

Elliott, C.

G. Beydaghyan, C. Buzea, Y. Cui, C. Elliott, and K. Robbie, “Ex situ ellipsometric investigation of nanocolumns inclination angle of obliquely evaporated silicon thin films,” Appl. Phys. Lett. 87, 153103 (2005).
[CrossRef]

Facsko, S.

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

Gioti, M.

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Mueller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

Hagen, S. W.

I. S. Nerbø, M. Kildemo, S. W. Hagen, S. Leroy, and E. Søndergård, “Optical properties and characterization of tilted gasb nanocones,” (to be published).

Hartnagel, H. L.

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

Hauge, P.

P. Hauge, “Conventions and formulas for using the Mueller-Stokes calculus in ellipsometry,” Surf. Sci. 96, 81-107(1980).
[CrossRef]

Herman, I. P.

J. E. Spanier and I. P. Herman, “Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous sic films,” Phys. Rev. B 61, 10437-10450 (2000).
[CrossRef]

Holt, L.

M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
[CrossRef]

Jellison, G. E.

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190-8198 (1997).
[CrossRef]

G. E. Jellison, Jr. and J. W. McCamy, “Sample depolarization effects from thin films of ZnS on GaAs as measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 61, 512-514 (1992).
[CrossRef]

Kildemo, M.

M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
[CrossRef]

I. S. Nerbø, M. Kildemo, S. W. Hagen, S. Leroy, and E. Søndergård, “Optical properties and characterization of tilted gasb nanocones,” (to be published).

Koerdt, C.

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

Kurz, H.

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

Laskarakis, A.

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Mueller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

Le Roy, S.

N. Brun, A. Lelarge, S. Le Roy, E. Søndergård, and E. Barthel are preparing a manuscript to be called “Composition of nanostructured GaSb.”

Lelarge, A.

N. Brun, A. Lelarge, S. Le Roy, E. Søndergård, and E. Barthel are preparing a manuscript to be called “Composition of nanostructured GaSb.”

Leroy, S.

I. S. Nerbø, M. Kildemo, S. W. Hagen, S. Leroy, and E. Søndergård, “Optical properties and characterization of tilted gasb nanocones,” (to be published).

Lin, S. Y.

Z. P. Yang, L. Ci, J. A. Bur, S. Y. Lin, and P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446-451(2008).
[CrossRef] [PubMed]

Logothetidis, S.

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Mueller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

McCamy, J. W.

G. E. Jellison, Jr. and J. W. McCamy, “Sample depolarization effects from thin films of ZnS on GaAs as measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 61, 512-514 (1992).
[CrossRef]

Modine, F. A.

Nerbø, I. S.

M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
[CrossRef]

I. S. Nerbø, M. Kildemo, S. W. Hagen, S. Leroy, and E. Søndergård, “Optical properties and characterization of tilted gasb nanocones,” (to be published).

Pavlopoulou, E.

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Mueller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

Rivier, N.

D. Weaire and N. Rivier, “Soap, cells and statistics--random patterns in two dimensions,” Contemp. Phys. 25, 59-99 (1984).
[CrossRef]

Robbie, K.

G. Beydaghyan, C. Buzea, Y. Cui, C. Elliott, and K. Robbie, “Ex situ ellipsometric investigation of nanocolumns inclination angle of obliquely evaporated silicon thin films,” Appl. Phys. Lett. 87, 153103 (2005).
[CrossRef]

Schubert, M.

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265-4274 (1996).
[CrossRef]

Simonsen, I.

M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
[CrossRef]

Søndergård, E.

M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
[CrossRef]

I. S. Nerbø, M. Kildemo, S. W. Hagen, S. Leroy, and E. Søndergård, “Optical properties and characterization of tilted gasb nanocones,” (to be published).

N. Brun, A. Lelarge, S. Le Roy, E. Søndergård, and E. Barthel are preparing a manuscript to be called “Composition of nanostructured GaSb.”

Spanier, J. E.

J. E. Spanier and I. P. Herman, “Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous sic films,” Phys. Rev. B 61, 10437-10450 (2000).
[CrossRef]

Stachakovsky, M.

M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
[CrossRef]

Studna, A. A.

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 ev,” Phys. Rev. B 27, 985-1009(1983).
[CrossRef]

Stuke, J.

J. Stuke and G. Zimmerer, “Optical properties of amorphous iii-v compounds. i. Experiment,” Phys. Stat. Sol. B 49, 513-523(1972).
[CrossRef]

Trappe, C.

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

Vogt, A.

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

Weaire, D.

D. Weaire and N. Rivier, “Soap, cells and statistics--random patterns in two dimensions,” Contemp. Phys. 25, 59-99 (1984).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th corrected ed. (Pergamon, 1980).
[PubMed]

Yang, Z. P.

Z. P. Yang, L. Ci, J. A. Bur, S. Y. Lin, and P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446-451(2008).
[CrossRef] [PubMed]

Zimmerer, G.

J. Stuke and G. Zimmerer, “Optical properties of amorphous iii-v compounds. i. Experiment,” Phys. Stat. Sol. B 49, 513-523(1972).
[CrossRef]

Zollner, S.

S. Zollner, “Model dielectric functions for native oxides on compound semiconductors,” Appl. Phys. Lett. 63, 2523-2524(1993).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

S. Zollner, “Model dielectric functions for native oxides on compound semiconductors,” Appl. Phys. Lett. 63, 2523-2524(1993).
[CrossRef]

G. Beydaghyan, C. Buzea, Y. Cui, C. Elliott, and K. Robbie, “Ex situ ellipsometric investigation of nanocolumns inclination angle of obliquely evaporated silicon thin films,” Appl. Phys. Lett. 87, 153103 (2005).
[CrossRef]

G. E. Jellison, Jr. and J. W. McCamy, “Sample depolarization effects from thin films of ZnS on GaAs as measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 61, 512-514 (1992).
[CrossRef]

Contemp. Phys. (1)

D. Weaire and N. Rivier, “Soap, cells and statistics--random patterns in two dimensions,” Contemp. Phys. 25, 59-99 (1984).
[CrossRef]

Endeavour (1)

C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavour 26, 79-84 (1967).

J. Opt. Soc. Am. (1)

Nano Lett. (1)

Z. P. Yang, L. Ci, J. A. Bur, S. Y. Lin, and P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446-451(2008).
[CrossRef] [PubMed]

Phys. Rev. B (3)

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 ev,” Phys. Rev. B 27, 985-1009(1983).
[CrossRef]

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265-4274 (1996).
[CrossRef]

J. E. Spanier and I. P. Herman, “Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous sic films,” Phys. Rev. B 61, 10437-10450 (2000).
[CrossRef]

Phys. Stat. Sol C (1)

M. Kildemo, I. S. Nerbø, E. Søndergård, L. Holt, I. Simonsen, and M. Stachakovsky, “Optical response of nanostructured gasb,” Phys. Stat. Sol C 5, 1382-1385 (2008).
[CrossRef]

Phys. Stat. Sol. B (1)

J. Stuke and G. Zimmerer, “Optical properties of amorphous iii-v compounds. i. Experiment,” Phys. Stat. Sol. B 49, 513-523(1972).
[CrossRef]

Prog. Cryst. Growth Charact. (1)

B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: in situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1-87(1993).
[CrossRef]

Science (1)

S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, “Formation of ordered nanoscale semiconductor dots by ion sputtering,” Science 285, 1551-1553(1999).
[CrossRef] [PubMed]

Surf. Sci. (1)

P. Hauge, “Conventions and formulas for using the Mueller-Stokes calculus in ellipsometry,” Surf. Sci. 96, 81-107(1980).
[CrossRef]

Thin Solid Films (1)

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Mueller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

Other (4)

I. S. Nerbø, M. Kildemo, S. W. Hagen, S. Leroy, and E. Søndergård, “Optical properties and characterization of tilted gasb nanocones,” (to be published).

N. Brun, A. Lelarge, S. Le Roy, E. Søndergård, and E. Barthel are preparing a manuscript to be called “Composition of nanostructured GaSb.”

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

M. Born and E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th corrected ed. (Pergamon, 1980).
[PubMed]

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Figures (9)

Fig. 1
Fig. 1

SEM images of GaSb nanocones.(a) Sample A at normal beam incidence, (b) tilted sample A. Sample D is also depicted at (c) normal beam incidence and (d) tilted beam incidence.

Fig. 2
Fig. 2

High resolution TEM images of GaSb nanocones (sample A). Figure (a) shows several cones while figure (b) shows one individual cone in greater detail. The lighter part of the image is the amorphous adhesive used in the sample preparation. The crystalline cones appear darker and in (b) the atomic column spacing at the 110 GaSb zone-axis orientation is clearly visible. The approximately 5 nm layer of amorphous GaSb oxide is visible as a shadow around the cones that has slightly darker contrast than the adhesive.

Fig. 3
Fig. 3

Ellipsometric intensities I s = m 43 , I c = m 33 , of plane GaSb with 7 nm oxide, short nanostructured cones, samples A, B, and C (approximately 50 nm high cones), and sample D (approximately 300 nm cones).

Fig. 4
Fig. 4

Reflectance ( M 11 ) of nanostructured GaSb cones, for sample C (approximately 36 nm high cones) and D (approximately 300 nm high cones). As a reference, the reflectance of a clean GaSb surface with oxide is also included.

Fig. 5
Fig. 5

Degree of nonblock diagonality (A, as defined in Eq. (6) for various samples, as a function of azimuth sample rotation, for E p h = 2.75 eV . The sample denoted tilted cones consisted of cones tilted 45 ° from the surface normal (approximately 30 nm high), while the other samples have cones pointing normal to the surface.

Fig. 6
Fig. 6

Degree of polarization P, as calculated from the PMSE measurements by Eq. (4), for the nanostructured GaSb samples. The bottom figure shows P for the short cone samples: A, B, and C, while the top figure shows P for the long cones of sample D. The depolarization index D P , calculated from the Mueller matrix in the visible range, is also shown for the long cones in the top figure.

Fig. 7
Fig. 7

Parameters used in the graded effective medium model. h is the total height, s is the thickness of the coating of amorphous material and oxide, D 1 and D 2 are the lower and upper diameters of the crystalline core.

Fig. 8
Fig. 8

Simulated and experimental ellipsometric intensities I s = m 43 and I c = m 33 , for sample A (top) and sample B (bottom). The filled squares and filled triangles are the measured I s and I c , respectively. The solid lines are the simulated values calculated from the fitted model, with parameters defined in Fig. 7 (sample A: χ 2 = 2.6 , sample B: χ 2 = 12.4 ). For sample A, simpler models with only crystalline material in the effective medium layer have also been included for comparison. The lines marked by crosses (+) are for a model made by treating the cones as cylinders ( χ 2 = 118 ), the lines marked by circles (○) are for a graded model as described in Fig. 7, but with no coating of oxide and amorphous material ( χ 2 = 61.7 ).

Fig. 9
Fig. 9

Simulated and experimental ellipsometric intensities I s = m 43 and I c = m 33 , for sample C (top). The filled squares and filled triangles are the measured I s and I c , respectively. The solid lines are the simulated values calculated from the fitted model, with parameters defined in Fig. 7 (sample C: χ 2 = 1.1 ). The bottom figure depicts the measured reflectance R = ( | r s s | 2 + | r p p | 2 ) / 2 [filled squares for sample C, filled triangles for GaSb with native oxide layer)], and simulated reflectance, calculated from the fitted model.

Tables (3)

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Table 1 Sputtering Conditions and Definition of the Samples

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Table 2 Results of AFM, TEM, and SEM Studies of GaSb Nanocone Samples

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Table 3 Resulting Parameters from Fitting the Optical Models to the Ellipsometric Data

Equations (14)

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I s = m 43 = sin 2 Ψ sin Δ ,
I c = m 33 = sin 2 Ψ cos Δ ,
I c 2 = m 12 = cos 2 Ψ .
P = I s 2 + I c 2 + I c 2 2 .
D P = i , j M i j 2 M 11 2 3 M 11 ,
A = ( m 13 2 + m 14 2 + m 23 2 + m 24 2 + m 31 2 + m 32 2 + m 41 2 + m 42 2 m 11 2 + m 12 2 + m 21 2 + m 22 2 + m 33 2 + m 34 2 + m 43 2 + m 44 2 ) 1 / 2 ,
f c Ga Sb ϵ c Ga Sb ϵ i i ϵ i i + L i ( ϵ c Ga Sb ϵ i i ) + f coat ϵ coat ϵ i i ϵ i i + L i ( ϵ coat ϵ i i ) + f void ϵ void ϵ i i ϵ i i + L i ( ϵ void ϵ i i ) = 0 ,
f a Ga Sb ϵ a Ga Sb ϵ coat ϵ coat + 2 ϵ a Ga Sb + f oxide ϵ oxide ϵ coat ϵ coat + 2 ϵ oxide = 0.
I s = 2   Im ( r p p r s s * + r p s r s p * ) | r s s | 2 + | r p p | 2 + | r s p | 2 + | r p s | 2 ,
I c = 2   Re ( r p p r s s * + r p s r s p * ) | r s s | 2 + | r p p | 2 + | r s p | 2 + | r p s | 2 .
χ 2 = 1 2 N M + 1 i = 1 N [ ( I s i mod - I s i exp ) 2 σ s i 2 + ( I c i mod I c i exp ) 2 σ c i 2 ] ,
d ( n ) = D 1 D 1 D 2 N 1 n ,
f c Ga Sb ( n ) = π 12 d 2 ( n ) ,
f coat ( n ) = 2 π 3 [ d ( n ) s + s 2 ] .

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