Abstract

A numerical method developed previously [J. Appl. Phys. 80, 4621 (1996)] has been extended to simulate the nonnormal-incidence reflectance-difference spectroscopy and transmittance-difference spectroscopy spectra of biaxial anisotropic (xyz) multilayer systems with finite thickness. It is demonstrated that, when the principal axes of the anisotropy layer are at certain orientations, a reflectance-difference spectrum can be separated into two spectra, namely, an in-plane anisotropic spectrum and an out-of-plane anisotropic spectrum. It is shown that the separation is valid for large in-plane anisotropy, i.e., |x-y||x|, and an incident angle of 20°.

© 1998 Optical Society of America

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  1. D. E. Aspnes and A. A. Studna, Phys. Rev. Lett. 54, 1956 (1985).
    [CrossRef] [PubMed]
  2. D. E. Aspnes, J. Vac. Sci. Technol. B 3, 1498 (1985).
    [CrossRef]
  3. D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, J. Vac. Sci. Technol. A 6, 1327 (1988).
    [CrossRef]
  4. Z. Yang, G. W. Wong, I. K. Sou, and Y. H. Yeung, Appl. Phys. Lett. 66, 2235 (1995).
    [CrossRef]
  5. H. Akinaya and K. Tanaka, Appl. Surf. Sci. 82/83, 298 (1994).
    [CrossRef]
  6. T. Yasuda, D. E. Aspnes, D. R. Lee, C. H. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12, 1152 (1994).
    [CrossRef]
  7. D. E. Aspnes, Mater. Sci. Eng. B 30, 109 (1995).
    [CrossRef]
  8. I. Kamiya, D. E. Aspnes, L. T. Florez, and J. P. Harbison, Phys. Rev. B 46, 15, 894 (1992).
    [CrossRef]
  9. O. Acher, F. Omnes, and M. Razeghi, Mater. Sci. Eng. B 5, 223 (1990).
    [CrossRef]
  10. J. S. Luo, J. M. Olson, S. R. Kurtz, D. J. Arent, and K. A. Bertness, Phys. Rev. B 51, 7603 (1995).
    [CrossRef]
  11. K. Hingerl, D. E. Aspnes, I. Kamiya, and L. T. Florez, Appl. Phys. Lett. 63, 885 (1993).
    [CrossRef]
  12. K. Hingerl, D. E. Aspnes, and I. Kamiya, Surf. Sci. 287/288, 686 (1993).
    [CrossRef]
  13. S.-H. Wei and A. Zunger, Phys. Rev. B 51, 14, 110 (1995).
    [CrossRef]
  14. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  15. T.-K. Kwok and Z. Yang, J. Appl. Phys. 80, 4621 (1996).
    [CrossRef]
  16. D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
    [CrossRef]
  17. S. Adachi and T. Taguchi, Phys. Rev. B 43, 9569 (1991).
    [CrossRef]
  18. M. Schubert, Phys. Rev. B 53, 4265 (1996).
    [CrossRef]

1996 (2)

T.-K. Kwok and Z. Yang, J. Appl. Phys. 80, 4621 (1996).
[CrossRef]

M. Schubert, Phys. Rev. B 53, 4265 (1996).
[CrossRef]

1995 (4)

S.-H. Wei and A. Zunger, Phys. Rev. B 51, 14, 110 (1995).
[CrossRef]

Z. Yang, G. W. Wong, I. K. Sou, and Y. H. Yeung, Appl. Phys. Lett. 66, 2235 (1995).
[CrossRef]

D. E. Aspnes, Mater. Sci. Eng. B 30, 109 (1995).
[CrossRef]

J. S. Luo, J. M. Olson, S. R. Kurtz, D. J. Arent, and K. A. Bertness, Phys. Rev. B 51, 7603 (1995).
[CrossRef]

1994 (2)

H. Akinaya and K. Tanaka, Appl. Surf. Sci. 82/83, 298 (1994).
[CrossRef]

T. Yasuda, D. E. Aspnes, D. R. Lee, C. H. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12, 1152 (1994).
[CrossRef]

1993 (2)

K. Hingerl, D. E. Aspnes, I. Kamiya, and L. T. Florez, Appl. Phys. Lett. 63, 885 (1993).
[CrossRef]

K. Hingerl, D. E. Aspnes, and I. Kamiya, Surf. Sci. 287/288, 686 (1993).
[CrossRef]

1992 (1)

I. Kamiya, D. E. Aspnes, L. T. Florez, and J. P. Harbison, Phys. Rev. B 46, 15, 894 (1992).
[CrossRef]

1991 (1)

S. Adachi and T. Taguchi, Phys. Rev. B 43, 9569 (1991).
[CrossRef]

1990 (1)

O. Acher, F. Omnes, and M. Razeghi, Mater. Sci. Eng. B 5, 223 (1990).
[CrossRef]

1988 (1)

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, J. Vac. Sci. Technol. A 6, 1327 (1988).
[CrossRef]

1985 (2)

D. E. Aspnes and A. A. Studna, Phys. Rev. Lett. 54, 1956 (1985).
[CrossRef] [PubMed]

D. E. Aspnes, J. Vac. Sci. Technol. B 3, 1498 (1985).
[CrossRef]

1983 (1)

D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
[CrossRef]

Acher, O.

O. Acher, F. Omnes, and M. Razeghi, Mater. Sci. Eng. B 5, 223 (1990).
[CrossRef]

Adachi, S.

S. Adachi and T. Taguchi, Phys. Rev. B 43, 9569 (1991).
[CrossRef]

Akinaya, H.

H. Akinaya and K. Tanaka, Appl. Surf. Sci. 82/83, 298 (1994).
[CrossRef]

Arent, D. J.

J. S. Luo, J. M. Olson, S. R. Kurtz, D. J. Arent, and K. A. Bertness, Phys. Rev. B 51, 7603 (1995).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, Mater. Sci. Eng. B 30, 109 (1995).
[CrossRef]

T. Yasuda, D. E. Aspnes, D. R. Lee, C. H. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12, 1152 (1994).
[CrossRef]

K. Hingerl, D. E. Aspnes, and I. Kamiya, Surf. Sci. 287/288, 686 (1993).
[CrossRef]

K. Hingerl, D. E. Aspnes, I. Kamiya, and L. T. Florez, Appl. Phys. Lett. 63, 885 (1993).
[CrossRef]

I. Kamiya, D. E. Aspnes, L. T. Florez, and J. P. Harbison, Phys. Rev. B 46, 15, 894 (1992).
[CrossRef]

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, J. Vac. Sci. Technol. A 6, 1327 (1988).
[CrossRef]

D. E. Aspnes and A. A. Studna, Phys. Rev. Lett. 54, 1956 (1985).
[CrossRef] [PubMed]

D. E. Aspnes, J. Vac. Sci. Technol. B 3, 1498 (1985).
[CrossRef]

D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
[CrossRef]

Bertness, K. A.

J. S. Luo, J. M. Olson, S. R. Kurtz, D. J. Arent, and K. A. Bertness, Phys. Rev. B 51, 7603 (1995).
[CrossRef]

Bjorkman, C. H.

T. Yasuda, D. E. Aspnes, D. R. Lee, C. H. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12, 1152 (1994).
[CrossRef]

Florez, L. T.

K. Hingerl, D. E. Aspnes, I. Kamiya, and L. T. Florez, Appl. Phys. Lett. 63, 885 (1993).
[CrossRef]

I. Kamiya, D. E. Aspnes, L. T. Florez, and J. P. Harbison, Phys. Rev. B 46, 15, 894 (1992).
[CrossRef]

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, J. Vac. Sci. Technol. A 6, 1327 (1988).
[CrossRef]

Harbison, J. P.

I. Kamiya, D. E. Aspnes, L. T. Florez, and J. P. Harbison, Phys. Rev. B 46, 15, 894 (1992).
[CrossRef]

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, J. Vac. Sci. Technol. A 6, 1327 (1988).
[CrossRef]

Hingerl, K.

K. Hingerl, D. E. Aspnes, I. Kamiya, and L. T. Florez, Appl. Phys. Lett. 63, 885 (1993).
[CrossRef]

K. Hingerl, D. E. Aspnes, and I. Kamiya, Surf. Sci. 287/288, 686 (1993).
[CrossRef]

Kamiya, I.

K. Hingerl, D. E. Aspnes, and I. Kamiya, Surf. Sci. 287/288, 686 (1993).
[CrossRef]

K. Hingerl, D. E. Aspnes, I. Kamiya, and L. T. Florez, Appl. Phys. Lett. 63, 885 (1993).
[CrossRef]

I. Kamiya, D. E. Aspnes, L. T. Florez, and J. P. Harbison, Phys. Rev. B 46, 15, 894 (1992).
[CrossRef]

Kurtz, S. R.

J. S. Luo, J. M. Olson, S. R. Kurtz, D. J. Arent, and K. A. Bertness, Phys. Rev. B 51, 7603 (1995).
[CrossRef]

Kwok, T.-K.

T.-K. Kwok and Z. Yang, J. Appl. Phys. 80, 4621 (1996).
[CrossRef]

Lee, D. R.

T. Yasuda, D. E. Aspnes, D. R. Lee, C. H. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12, 1152 (1994).
[CrossRef]

Lucovsky, G.

T. Yasuda, D. E. Aspnes, D. R. Lee, C. H. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12, 1152 (1994).
[CrossRef]

Luo, J. S.

J. S. Luo, J. M. Olson, S. R. Kurtz, D. J. Arent, and K. A. Bertness, Phys. Rev. B 51, 7603 (1995).
[CrossRef]

Olson, J. M.

J. S. Luo, J. M. Olson, S. R. Kurtz, D. J. Arent, and K. A. Bertness, Phys. Rev. B 51, 7603 (1995).
[CrossRef]

Omnes, F.

O. Acher, F. Omnes, and M. Razeghi, Mater. Sci. Eng. B 5, 223 (1990).
[CrossRef]

Razeghi, M.

O. Acher, F. Omnes, and M. Razeghi, Mater. Sci. Eng. B 5, 223 (1990).
[CrossRef]

Schubert, M.

M. Schubert, Phys. Rev. B 53, 4265 (1996).
[CrossRef]

Sou, I. K.

Z. Yang, G. W. Wong, I. K. Sou, and Y. H. Yeung, Appl. Phys. Lett. 66, 2235 (1995).
[CrossRef]

Studna, A. A.

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, J. Vac. Sci. Technol. A 6, 1327 (1988).
[CrossRef]

D. E. Aspnes and A. A. Studna, Phys. Rev. Lett. 54, 1956 (1985).
[CrossRef] [PubMed]

D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
[CrossRef]

Taguchi, T.

S. Adachi and T. Taguchi, Phys. Rev. B 43, 9569 (1991).
[CrossRef]

Tanaka, K.

H. Akinaya and K. Tanaka, Appl. Surf. Sci. 82/83, 298 (1994).
[CrossRef]

Wei, S.-H.

S.-H. Wei and A. Zunger, Phys. Rev. B 51, 14, 110 (1995).
[CrossRef]

Wong, G. W.

Z. Yang, G. W. Wong, I. K. Sou, and Y. H. Yeung, Appl. Phys. Lett. 66, 2235 (1995).
[CrossRef]

Yang, Z.

T.-K. Kwok and Z. Yang, J. Appl. Phys. 80, 4621 (1996).
[CrossRef]

Z. Yang, G. W. Wong, I. K. Sou, and Y. H. Yeung, Appl. Phys. Lett. 66, 2235 (1995).
[CrossRef]

Yasuda, T.

T. Yasuda, D. E. Aspnes, D. R. Lee, C. H. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12, 1152 (1994).
[CrossRef]

Yeung, Y. H.

Z. Yang, G. W. Wong, I. K. Sou, and Y. H. Yeung, Appl. Phys. Lett. 66, 2235 (1995).
[CrossRef]

Zunger, A.

S.-H. Wei and A. Zunger, Phys. Rev. B 51, 14, 110 (1995).
[CrossRef]

Appl. Phys. Lett. (2)

Z. Yang, G. W. Wong, I. K. Sou, and Y. H. Yeung, Appl. Phys. Lett. 66, 2235 (1995).
[CrossRef]

K. Hingerl, D. E. Aspnes, I. Kamiya, and L. T. Florez, Appl. Phys. Lett. 63, 885 (1993).
[CrossRef]

Appl. Surf. Sci. (1)

H. Akinaya and K. Tanaka, Appl. Surf. Sci. 82/83, 298 (1994).
[CrossRef]

J. Appl. Phys. (1)

T.-K. Kwok and Z. Yang, J. Appl. Phys. 80, 4621 (1996).
[CrossRef]

J. Vac. Sci. Technol. A (2)

T. Yasuda, D. E. Aspnes, D. R. Lee, C. H. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12, 1152 (1994).
[CrossRef]

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, J. Vac. Sci. Technol. A 6, 1327 (1988).
[CrossRef]

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

D. E. Aspnes, J. Vac. Sci. Technol. B 3, 1498 (1985).
[CrossRef]

Mater. Sci. Eng. B (2)

O. Acher, F. Omnes, and M. Razeghi, Mater. Sci. Eng. B 5, 223 (1990).
[CrossRef]

D. E. Aspnes, Mater. Sci. Eng. B 30, 109 (1995).
[CrossRef]

Phys. Rev. B (6)

I. Kamiya, D. E. Aspnes, L. T. Florez, and J. P. Harbison, Phys. Rev. B 46, 15, 894 (1992).
[CrossRef]

J. S. Luo, J. M. Olson, S. R. Kurtz, D. J. Arent, and K. A. Bertness, Phys. Rev. B 51, 7603 (1995).
[CrossRef]

D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
[CrossRef]

S. Adachi and T. Taguchi, Phys. Rev. B 43, 9569 (1991).
[CrossRef]

M. Schubert, Phys. Rev. B 53, 4265 (1996).
[CrossRef]

S.-H. Wei and A. Zunger, Phys. Rev. B 51, 14, 110 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

D. E. Aspnes and A. A. Studna, Phys. Rev. Lett. 54, 1956 (1985).
[CrossRef] [PubMed]

Surf. Sci. (1)

K. Hingerl, D. E. Aspnes, and I. Kamiya, Surf. Sci. 287/288, 686 (1993).
[CrossRef]

Other (1)

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

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Figures (6)

Fig. 1
Fig. 1

(a) Real part and (b) imaginary part of the numerical RDS spectra generated at ϕ=0° and different incident angles θa.

Fig. 2
Fig. 2

(a) Real part and (b) imaginary part of the numerical TDS spectra generated at ϕ=0° and different incident angles θa.

Fig. 3
Fig. 3

(a) Real part and (b) imaginary part of the numerical RDS spectra generated at ϕ=tan-1(1/cos θa) and different incident angles θa.

Fig. 4
Fig. 4

(a) Real part and (b) imaginary part of the numerical TDS spectra generated at ϕ=tan-1(1/cos θa) and different incident angles θa.

Fig. 5
Fig. 5

(a) Real part and (b) imaginary part of the numerical RDS spectra of Fig. 1 after the spectra of Fig. 3 are subtracted; the spectrum is generated at ϕ=0° and θa=0°.

Fig. 6
Fig. 6

(a) Real part and (b) imaginary part of the numerical TDS spectra of Fig. 2 after the spectra of Fig. 4 are subtracted; the spectrum is generated at ϕ=0° and θa=0°.

Equations (39)

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

Ψn=PnΨn-1,
P=exp[i(ω/c)Dd].
z Ψ=i ωc DΨ,
exp[i(ωd/c)D]I+i(ωd/c)D,
Δrr=4πidna(xx-yy)λ(s-a),
r=Zrso+roa1+Zrsoroa,
Δrro=Δrrd(rsoroa+Z-1)(Zrso+roa)(rsoroa+1)(rso+roa),
AfaBfa=Dfa-1DoPoDo-1DiPiDi-1DsPsDs-1DbaAbaBba.
Pα=exp(iφα)00exp(-iφα),
Dα=11nα cos θα-nα cos θαswave,
Dα=cos θαcos θαnα-nαpwave.
Δrr=2(rs-rp)rs+rp,Δtt=2(ts-tp)ts+tp.
AfasBfasAfapBfap=Dfa-1DoPoDo-1DiPiDi-1DsPsDs-1Dba×CbaOEbaOCbaEEbaE.
εx cos2 ϕ+εy sin2 ϕcos ϕ sin ϕ(εx-εy)0cos ϕ sin ϕ(εx-εy)εy cos2 ϕ+εx sin2 ϕ000εz.
Di=11ns cos θs-ns cos θsswave,
Di=cos θpcos θpnp-nppwave,
Pi=exp(i2πns cos θsdi/λ)00exp(-i2πns cos θsdi/λ)swave,
Pi=exp(i2πnp cos θpdi/λ)00exp(-i2πnp cos θpdi/λ)pwave.
ns=nix,
np=(niy)2-(no)2 sin2 θoniyniz2-11/2;
ns=niy,
np=(nix)2-(no)2 sin2 θonixniz2-11/2,
E=Ass+App=Asy+Ap cos θax-Ap sin θaz.
ns=nix,
np=(nix)2-(no)2 sin2 θonixniz2-11/2.
ns=niy,
np=(niy)2-(no)2 sin2 θoniyniz2-11/2.
nix=(εZnSe+ε1+ε2+ε3)1/2,
niy=(εZnSe+ε2)1/2,niz=(εZnSe)1/2,
ε1=A1E1-ω-iΓ1,
ε2=A2E2-ω-iΓ2,
ε3=A3E3-ω-iΓ3
E1=2.0eV,E2=3.00eV,E3=4.00eV;
Γ1=0.03,Γ2=0.06,Γ3=0.03,
A1=0.4,A2=6.0,A3=0.8.
Δrr ϕ=0°θa20°=Δrr ϕ=0°θa=0°+Δrr ϕ=tan-1(1/cos θa)θa20°,
Δtt ϕ=0°θa20°=Δtt ϕ=0°θa=0°+Δtt ϕ=tan-1(1/cos θa)θa20°.
Δrr ϕ=90°θa20°=Δrr ϕ=90°θa=0°+Δrr ϕ=tan-1(1/cos θa)±90°θa20°,
Δtt ϕ=90°θa20°=Δtt ϕ=90°θa=0°+Δtt ϕ=tan-1(1/cos θa)±90°θa20°.

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