Abstract

Reflectance difference spectroscopy (RDS) has been used to determine piezo-optical coefficients of semiconductors above the fundamental gap. The high sensitivity of the RDS technique allows the determination of these coefficients with the use of very small uniaxial stresses (<0.05 GPa). By measurement of RDS on samples of cubic crystals under uniaxial stress along the [001] and [111] crystal directions, the piezo-optical coefficients P11-P12 and P44, respectively, were determined. Measurements on InP give results in good agreement with previously reported values obtained by ellipsometry. RDS was used successfully to determine the spectral dependence of P11-P12 in ZnSe, a II–VI semiconductor too brittle to support the stresses required for ellipsometric measurements. RDS is less sensitive than ellipsometry to the presence of surface overlayers.

© 1999 Optical Society of America

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  6. C. W. Higginbotham, M. Cardona, F. H. Pollak, “Intrinsic piezobirefringence of Ge, Si, and GaAs,” Phys. Rev. 184, 821–829 (1969).
    [Crossref]
  7. R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
    [Crossref]
  8. M. Chandrasekhar, M. H. Grimsditch, M. Cardona, “Piezobirefringence above the fundamental edge in Si,” Phys. Rev. B 18, 4301–4311 (1978).
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  9. M. H. Grimsditch, E. Kisela, M. Cardona, “Real and imaginary elasto-optic constants of silicon,” Phys. Status Solidi A 60, 135–143 (1980).
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  10. G. W. Gobeli, E. O. Kane, “Dependence of the optical constants of silicon on uniaxial stress,” Phys. Rev. Lett. 15, 142–146 (1965).
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  12. J. Musilova, “Piezoreflectance study of E1 and E2 transitions in germanium from 107 to 326 K,” Phys. Status Solidi B 101, 85–93 (1980).
    [Crossref]
  13. P. Etchegoin, J. Kircher, M. Cardona, C. Grein, “Piezo-optical response of Ge in the visible–uv range,” Phys. Rev. B 45, 11721–11735 (1992).
    [Crossref]
  14. P. Etchegoin, J. Kircher, M. Cardona, C. Grein, E. Bustarret, “Piezo-optics of GaAs,” Phys. Rev. B 46, 15139–15149 (1992).
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  15. P. Etchegoin, J. Kircher, M. Cardona, “Elasto-optical constants of Si,” Phys. Rev. B 47, 10292–10303 (1993).
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  16. D. Rönnow, P. Santos, M. Cardona, E. Anastassakis, M. Kuball, “Piezo-optics of InP in the visible–ultraviolet range,” Phys. Rev. B 57, 4432–4442 (1998).
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    [Crossref]
  22. B. Koopmans, B. Richards, P. Santos, K. Eberl, M. Cardona, “In-plane optical anisotropy of GaAs/AlAs multiple quantum wells probed by microscopic reflectance difference spectroscopy,” Appl. Phys. Lett. 69, 782–784 (1996).
    [Crossref]
  23. D. Toet, B. Koopmans, P. V. Santos, R. B. Bergmann, B. Richards, “Growth of polycrystalline silicon on glass by selective laser-induced nucleation,” Appl. Phys. Lett. 69, 3719–3721 (1996).
    [Crossref]
  24. H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
    [Crossref]
  25. B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
    [Crossref]
  26. D. E. Aspnes, “Analysis of modulation spectra of stratified media,” J. Opt. Soc. Am. 63, 1380–1390 (1973).
    [Crossref]
  27. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  28. D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327–1332 (1988).
    [Crossref]
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    [Crossref]
  36. P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
    [Crossref]
  37. S. Zollner, “Model dielectric functions for native oxides on compound semiconductors,” Appl. Phys. Lett. 63, 2523–2524 (1993).
    [Crossref]
  38. C. C. Kim, S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
    [Crossref]
  39. D. E. Aspnes, “Approximate solution of ellipsometric equations for optically biaxial crystal,” J. Opt. Soc. Am. 70, 1275–1277 (1980).
    [Crossref] [PubMed]

1998 (1)

D. Rönnow, P. Santos, M. Cardona, E. Anastassakis, M. Kuball, “Piezo-optics of InP in the visible–ultraviolet range,” Phys. Rev. B 57, 4432–4442 (1998).
[Crossref]

1996 (4)

L. F. Lastras-Martı́nez, A. Lastras-Martı́nez, “Reflectance anisotropy of GaAs(100): dislocation-induced piezo-optic effects,” Phys. Rev. B 54, 10726–10735 (1996).
[Crossref]

B. Koopmans, B. Richards, P. Santos, K. Eberl, M. Cardona, “In-plane optical anisotropy of GaAs/AlAs multiple quantum wells probed by microscopic reflectance difference spectroscopy,” Appl. Phys. Lett. 69, 782–784 (1996).
[Crossref]

D. Toet, B. Koopmans, P. V. Santos, R. B. Bergmann, B. Richards, “Growth of polycrystalline silicon on glass by selective laser-induced nucleation,” Appl. Phys. Lett. 69, 3719–3721 (1996).
[Crossref]

C. C. Kim, S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
[Crossref]

1995 (2)

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
[Crossref]

1994 (1)

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
[Crossref]

1993 (2)

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

P. Etchegoin, J. Kircher, M. Cardona, “Elasto-optical constants of Si,” Phys. Rev. B 47, 10292–10303 (1993).
[Crossref]

1992 (4)

J. Kircher, W. Böhringer, W. Dietrich, H. Hirt, P. Etchegoin, M. Cardona, “Design of a compact uniaxial stress apparatus for optical measurements,” Rev. Sci. Instrum. 63, 3733–3735 (1992).
[Crossref]

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, “Piezo-optical response of Ge in the visible–uv range,” Phys. Rev. B 45, 11721–11735 (1992).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, E. Bustarret, “Piezo-optics of GaAs,” Phys. Rev. B 46, 15139–15149 (1992).
[Crossref]

1991 (1)

B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
[Crossref]

1988 (1)

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327–1332 (1988).
[Crossref]

1985 (1)

D. E. Aspnes, “Above-bandgap optical anisotropies in cubic semiconductors: a visible–near ultraviolet probe of surfaces,” J. Vac. Sci. Technol. B 3, 1498–1506 (1985).
[Crossref]

1980 (3)

J. Musilova, “Piezoreflectance study of E1 and E2 transitions in germanium from 107 to 326 K,” Phys. Status Solidi B 101, 85–93 (1980).
[Crossref]

M. H. Grimsditch, E. Kisela, M. Cardona, “Real and imaginary elasto-optic constants of silicon,” Phys. Status Solidi A 60, 135–143 (1980).
[Crossref]

D. E. Aspnes, “Approximate solution of ellipsometric equations for optically biaxial crystal,” J. Opt. Soc. Am. 70, 1275–1277 (1980).
[Crossref] [PubMed]

1978 (1)

M. Chandrasekhar, M. H. Grimsditch, M. Cardona, “Piezobirefringence above the fundamental edge in Si,” Phys. Rev. B 18, 4301–4311 (1978).
[Crossref]

1973 (1)

1969 (2)

C. W. Higginbotham, M. Cardona, F. H. Pollak, “Intrinsic piezobirefringence of Ge, Si, and GaAs,” Phys. Rev. 184, 821–829 (1969).
[Crossref]

D. D. Sell, E. O. Kane, “Piezoreflectance of germanium from 1.9 to 2.8 eV,” Phys. Rev. 185, 1103–1114 (1969).
[Crossref]

1968 (1)

A. Feldman, D. Horowitz, “Dispersion of the piezobirefringence of GaAs,” J. Appl. Phys. 39, 5597–5599 (1968).
[Crossref]

1966 (2)

R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[Crossref]

A. Feldman, “High-stress optical birefringence in pure and degenerate n-type germanium,” Phys. Rev. 150, 748–757 (1966).
[Crossref]

1965 (1)

G. W. Gobeli, E. O. Kane, “Dependence of the optical constants of silicon on uniaxial stress,” Phys. Rev. Lett. 15, 142–146 (1965).
[Crossref]

1815 (1)

D. Brewster, “On the effects of simple pressure in producing that species of crystallization which forms two oppositely polarised images, and exhibits the complementary colours by polarised light,” Philos. Trans. R. Soc. London 105, 60–64 (1815);“On the communication of the structure of doubly refracting crystals to glass, muriate of soda, fluor spar, and other substances, by mechanical compression and dilatation,” Philos. Trans. R. Soc. London 106, 156–178 (1816).
[Crossref]

Anastassakis, E.

D. Rönnow, P. Santos, M. Cardona, E. Anastassakis, M. Kuball, “Piezo-optics of InP in the visible–ultraviolet range,” Phys. Rev. B 57, 4432–4442 (1998).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327–1332 (1988).
[Crossref]

D. E. Aspnes, “Above-bandgap optical anisotropies in cubic semiconductors: a visible–near ultraviolet probe of surfaces,” J. Vac. Sci. Technol. B 3, 1498–1506 (1985).
[Crossref]

D. E. Aspnes, “Approximate solution of ellipsometric equations for optically biaxial crystal,” J. Opt. Soc. Am. 70, 1275–1277 (1980).
[Crossref] [PubMed]

D. E. Aspnes, “Analysis of modulation spectra of stratified media,” J. Opt. Soc. Am. 63, 1380–1390 (1973).
[Crossref]

Azzam, R. M. A.

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

Bashara, N. M.

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

Bechstedt, F.

P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
[Crossref]

Bergmann, R. B.

D. Toet, B. Koopmans, P. V. Santos, R. B. Bergmann, B. Richards, “Growth of polycrystalline silicon on glass by selective laser-induced nucleation,” Appl. Phys. Lett. 69, 3719–3721 (1996).
[Crossref]

Böhringer, W.

J. Kircher, W. Böhringer, W. Dietrich, H. Hirt, P. Etchegoin, M. Cardona, “Design of a compact uniaxial stress apparatus for optical measurements,” Rev. Sci. Instrum. 63, 3733–3735 (1992).
[Crossref]

Brewster, D.

D. Brewster, “On the effects of simple pressure in producing that species of crystallization which forms two oppositely polarised images, and exhibits the complementary colours by polarised light,” Philos. Trans. R. Soc. London 105, 60–64 (1815);“On the communication of the structure of doubly refracting crystals to glass, muriate of soda, fluor spar, and other substances, by mechanical compression and dilatation,” Philos. Trans. R. Soc. London 106, 156–178 (1816).
[Crossref]

Burns, M.

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
[Crossref]

Bustarret, E.

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, E. Bustarret, “Piezo-optics of GaAs,” Phys. Rev. B 46, 15139–15149 (1992).
[Crossref]

Cardona, M.

D. Rönnow, P. Santos, M. Cardona, E. Anastassakis, M. Kuball, “Piezo-optics of InP in the visible–ultraviolet range,” Phys. Rev. B 57, 4432–4442 (1998).
[Crossref]

B. Koopmans, B. Richards, P. Santos, K. Eberl, M. Cardona, “In-plane optical anisotropy of GaAs/AlAs multiple quantum wells probed by microscopic reflectance difference spectroscopy,” Appl. Phys. Lett. 69, 782–784 (1996).
[Crossref]

P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, “Elasto-optical constants of Si,” Phys. Rev. B 47, 10292–10303 (1993).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, E. Bustarret, “Piezo-optics of GaAs,” Phys. Rev. B 46, 15139–15149 (1992).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, “Piezo-optical response of Ge in the visible–uv range,” Phys. Rev. B 45, 11721–11735 (1992).
[Crossref]

J. Kircher, W. Böhringer, W. Dietrich, H. Hirt, P. Etchegoin, M. Cardona, “Design of a compact uniaxial stress apparatus for optical measurements,” Rev. Sci. Instrum. 63, 3733–3735 (1992).
[Crossref]

M. H. Grimsditch, E. Kisela, M. Cardona, “Real and imaginary elasto-optic constants of silicon,” Phys. Status Solidi A 60, 135–143 (1980).
[Crossref]

M. Chandrasekhar, M. H. Grimsditch, M. Cardona, “Piezobirefringence above the fundamental edge in Si,” Phys. Rev. B 18, 4301–4311 (1978).
[Crossref]

C. W. Higginbotham, M. Cardona, F. H. Pollak, “Intrinsic piezobirefringence of Ge, Si, and GaAs,” Phys. Rev. 184, 821–829 (1969).
[Crossref]

M. Cardona, in Light Scattering in Solids II, M. Cardona, G. Güntherodt, eds. (Springer, Berlin, 1982), p. 19.

Chandrasekhar, H. R.

B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
[Crossref]

Chandrasekhar, M.

B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
[Crossref]

M. Chandrasekhar, M. H. Grimsditch, M. Cardona, “Piezobirefringence above the fundamental edge in Si,” Phys. Rev. B 18, 4301–4311 (1978).
[Crossref]

Cohen, M. G.

R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[Crossref]

Dietrich, W.

J. Kircher, W. Böhringer, W. Dietrich, H. Hirt, P. Etchegoin, M. Cardona, “Design of a compact uniaxial stress apparatus for optical measurements,” Rev. Sci. Instrum. 63, 3733–3735 (1992).
[Crossref]

Dixon, R. W.

R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[Crossref]

Eberl, K.

B. Koopmans, B. Richards, P. Santos, K. Eberl, M. Cardona, “In-plane optical anisotropy of GaAs/AlAs multiple quantum wells probed by microscopic reflectance difference spectroscopy,” Appl. Phys. Lett. 69, 782–784 (1996).
[Crossref]

Esser, N.

P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
[Crossref]

Etchegoin, P.

P. Etchegoin, J. Kircher, M. Cardona, “Elasto-optical constants of Si,” Phys. Rev. B 47, 10292–10303 (1993).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, E. Bustarret, “Piezo-optics of GaAs,” Phys. Rev. B 46, 15139–15149 (1992).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, “Piezo-optical response of Ge in the visible–uv range,” Phys. Rev. B 45, 11721–11735 (1992).
[Crossref]

J. Kircher, W. Böhringer, W. Dietrich, H. Hirt, P. Etchegoin, M. Cardona, “Design of a compact uniaxial stress apparatus for optical measurements,” Rev. Sci. Instrum. 63, 3733–3735 (1992).
[Crossref]

Feldman, A.

A. Feldman, D. Horowitz, “Dispersion of the piezobirefringence of GaAs,” J. Appl. Phys. 39, 5597–5599 (1968).
[Crossref]

A. Feldman, “High-stress optical birefringence in pure and degenerate n-type germanium,” Phys. Rev. 150, 748–757 (1966).
[Crossref]

Florez, L. T.

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327–1332 (1988).
[Crossref]

Gao, G. B.

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
[Crossref]

Gobeli, G. W.

G. W. Gobeli, E. O. Kane, “Dependence of the optical constants of silicon on uniaxial stress,” Phys. Rev. Lett. 15, 142–146 (1965).
[Crossref]

Grein, C.

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, “Piezo-optical response of Ge in the visible–uv range,” Phys. Rev. B 45, 11721–11735 (1992).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, E. Bustarret, “Piezo-optics of GaAs,” Phys. Rev. B 46, 15139–15149 (1992).
[Crossref]

Grimsditch, M. H.

M. H. Grimsditch, E. Kisela, M. Cardona, “Real and imaginary elasto-optic constants of silicon,” Phys. Status Solidi A 60, 135–143 (1980).
[Crossref]

M. Chandrasekhar, M. H. Grimsditch, M. Cardona, “Piezobirefringence above the fundamental edge in Si,” Phys. Rev. B 18, 4301–4311 (1978).
[Crossref]

Groenen, J.

P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
[Crossref]

Gunshor, R. L.

B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
[Crossref]

Harbison, J. P.

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327–1332 (1988).
[Crossref]

Higginbotham, C. W.

C. W. Higginbotham, M. Cardona, F. H. Pollak, “Intrinsic piezobirefringence of Ge, Si, and GaAs,” Phys. Rev. 184, 821–829 (1969).
[Crossref]

Hirt, H.

J. Kircher, W. Böhringer, W. Dietrich, H. Hirt, P. Etchegoin, M. Cardona, “Design of a compact uniaxial stress apparatus for optical measurements,” Rev. Sci. Instrum. 63, 3733–3735 (1992).
[Crossref]

Hoffman, H.-J.

H.-J. Hoffman, in The Properties of Optical Glass (Springer, Heidelberg, 1995), Chap. 2.4.

Horowitz, D.

A. Feldman, D. Horowitz, “Dispersion of the piezobirefringence of GaAs,” J. Appl. Phys. 39, 5597–5599 (1968).
[Crossref]

Kane, E. O.

D. D. Sell, E. O. Kane, “Piezoreflectance of germanium from 1.9 to 2.8 eV,” Phys. Rev. 185, 1103–1114 (1969).
[Crossref]

G. W. Gobeli, E. O. Kane, “Dependence of the optical constants of silicon on uniaxial stress,” Phys. Rev. Lett. 15, 142–146 (1965).
[Crossref]

Kim, C. C.

C. C. Kim, S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
[Crossref]

Kircher, J.

P. Etchegoin, J. Kircher, M. Cardona, “Elasto-optical constants of Si,” Phys. Rev. B 47, 10292–10303 (1993).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, E. Bustarret, “Piezo-optics of GaAs,” Phys. Rev. B 46, 15139–15149 (1992).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, “Piezo-optical response of Ge in the visible–uv range,” Phys. Rev. B 45, 11721–11735 (1992).
[Crossref]

J. Kircher, W. Böhringer, W. Dietrich, H. Hirt, P. Etchegoin, M. Cardona, “Design of a compact uniaxial stress apparatus for optical measurements,” Rev. Sci. Instrum. 63, 3733–3735 (1992).
[Crossref]

Kisela, E.

M. H. Grimsditch, E. Kisela, M. Cardona, “Real and imaginary elasto-optic constants of silicon,” Phys. Status Solidi A 60, 135–143 (1980).
[Crossref]

Kobayashi, M.

B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
[Crossref]

Koopmans, B.

D. Toet, B. Koopmans, P. V. Santos, R. B. Bergmann, B. Richards, “Growth of polycrystalline silicon on glass by selective laser-induced nucleation,” Appl. Phys. Lett. 69, 3719–3721 (1996).
[Crossref]

B. Koopmans, B. Richards, P. Santos, K. Eberl, M. Cardona, “In-plane optical anisotropy of GaAs/AlAs multiple quantum wells probed by microscopic reflectance difference spectroscopy,” Appl. Phys. Lett. 69, 782–784 (1996).
[Crossref]

Kuball, M.

D. Rönnow, P. Santos, M. Cardona, E. Anastassakis, M. Kuball, “Piezo-optics of InP in the visible–ultraviolet range,” Phys. Rev. B 57, 4432–4442 (1998).
[Crossref]

Lastras-Marti´nez, A.

L. F. Lastras-Martı́nez, A. Lastras-Martı́nez, “Reflectance anisotropy of GaAs(100): dislocation-induced piezo-optic effects,” Phys. Rev. B 54, 10726–10735 (1996).
[Crossref]

Lastras-Marti´nez, L. F.

L. F. Lastras-Martı́nez, A. Lastras-Martı́nez, “Reflectance anisotropy of GaAs(100): dislocation-induced piezo-optic effects,” Phys. Rev. B 54, 10726–10735 (1996).
[Crossref]

Lin, M. E.

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
[Crossref]

Meyne, C.

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

Morkoc, H.

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
[Crossref]

Müller, A. B.

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

Musilova, J.

J. Musilova, “Piezoreflectance study of E1 and E2 transitions in germanium from 107 to 326 K,” Phys. Status Solidi B 101, 85–93 (1980).
[Crossref]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, Oxford, UK, 1976).

Ploska, K.

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

Pollak, F. H.

C. W. Higginbotham, M. Cardona, F. H. Pollak, “Intrinsic piezobirefringence of Ge, Si, and GaAs,” Phys. Rev. 184, 821–829 (1969).
[Crossref]

Pristovsek, M.

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

Ramdas, A. K.

B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
[Crossref]

Richards, B.

B. Koopmans, B. Richards, P. Santos, K. Eberl, M. Cardona, “In-plane optical anisotropy of GaAs/AlAs multiple quantum wells probed by microscopic reflectance difference spectroscopy,” Appl. Phys. Lett. 69, 782–784 (1996).
[Crossref]

D. Toet, B. Koopmans, P. V. Santos, R. B. Bergmann, B. Richards, “Growth of polycrystalline silicon on glass by selective laser-induced nucleation,” Appl. Phys. Lett. 69, 3719–3721 (1996).
[Crossref]

Richter, W.

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

Rockwell, B.

B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
[Crossref]

Rönnow, D.

D. Rönnow, P. Santos, M. Cardona, E. Anastassakis, M. Kuball, “Piezo-optics of InP in the visible–ultraviolet range,” Phys. Rev. B 57, 4432–4442 (1998).
[Crossref]

Santos, P.

D. Rönnow, P. Santos, M. Cardona, E. Anastassakis, M. Kuball, “Piezo-optics of InP in the visible–ultraviolet range,” Phys. Rev. B 57, 4432–4442 (1998).
[Crossref]

B. Koopmans, B. Richards, P. Santos, K. Eberl, M. Cardona, “In-plane optical anisotropy of GaAs/AlAs multiple quantum wells probed by microscopic reflectance difference spectroscopy,” Appl. Phys. Lett. 69, 782–784 (1996).
[Crossref]

Santos, P. V.

D. Toet, B. Koopmans, P. V. Santos, R. B. Bergmann, B. Richards, “Growth of polycrystalline silicon on glass by selective laser-induced nucleation,” Appl. Phys. Lett. 69, 3719–3721 (1996).
[Crossref]

P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
[Crossref]

Schmidt, W. G.

P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
[Crossref]

Scholz, S. M.

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

Sell, D. D.

D. D. Sell, E. O. Kane, “Piezoreflectance of germanium from 1.9 to 2.8 eV,” Phys. Rev. 185, 1103–1114 (1969).
[Crossref]

Sivananthan, S.

C. C. Kim, S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
[Crossref]

Strite, S.

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
[Crossref]

Studna, A. A.

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327–1332 (1988).
[Crossref]

Sverdlov, B.

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
[Crossref]

Toet, D.

D. Toet, B. Koopmans, P. V. Santos, R. B. Bergmann, B. Richards, “Growth of polycrystalline silicon on glass by selective laser-induced nucleation,” Appl. Phys. Lett. 69, 3719–3721 (1996).
[Crossref]

Westwood, D. I.

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

Wethkamp, T.

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

Williams, R. H.

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

Woolf, D. A.

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

Zahn, D. R. T.

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

Zettler, J.-T.

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

Zollner, S.

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

Zorn, M.

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

Appl. Phys. Lett. (5)

R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[Crossref]

J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska, W. Richter, “Growth oscillations with monolayer periodicity monitored by ellipsometry during metalorganic vapor phase epitaxy of GaAs(001),” Appl. Phys. Lett. 67, 3783 (1995).
[Crossref]

B. Koopmans, B. Richards, P. Santos, K. Eberl, M. Cardona, “In-plane optical anisotropy of GaAs/AlAs multiple quantum wells probed by microscopic reflectance difference spectroscopy,” Appl. Phys. Lett. 69, 782–784 (1996).
[Crossref]

D. Toet, B. Koopmans, P. V. Santos, R. B. Bergmann, B. Richards, “Growth of polycrystalline silicon on glass by selective laser-induced nucleation,” Appl. Phys. Lett. 69, 3719–3721 (1996).
[Crossref]

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

J. Appl. Phys. (2)

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, M. Burns, “Large-bandgap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies,” J. Appl. Phys. 76, 1363–1398 (1994).
[Crossref]

A. Feldman, D. Horowitz, “Dispersion of the piezobirefringence of GaAs,” J. Appl. Phys. 39, 5597–5599 (1968).
[Crossref]

J. Opt. Soc. Am. (2)

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

D. E. Aspnes, J. P. Harbison, A. A. Studna, L. T. Florez, “Application of reflectance difference spectroscopy to molecular-beam epitaxy growth of GaAs and AlAs,” J. Vac. Sci. Technol. A 6, 1327–1332 (1988).
[Crossref]

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

S. M. Scholz, A. B. Müller, W. Richter, D. R. T. Zahn, D. I. Westwood, D. A. Woolf, R. H. Williams, “Analysis of molecular-beam epitaxial growth of InAs on GaAs(100) by reflection anisotropy spectroscopy,” J. Vac. Sci. Technol. B 10, 1710–1715 (1992).
[Crossref]

D. E. Aspnes, “Above-bandgap optical anisotropies in cubic semiconductors: a visible–near ultraviolet probe of surfaces,” J. Vac. Sci. Technol. B 3, 1498–1506 (1985).
[Crossref]

Philos. Trans. R. Soc. London (1)

D. Brewster, “On the effects of simple pressure in producing that species of crystallization which forms two oppositely polarised images, and exhibits the complementary colours by polarised light,” Philos. Trans. R. Soc. London 105, 60–64 (1815);“On the communication of the structure of doubly refracting crystals to glass, muriate of soda, fluor spar, and other substances, by mechanical compression and dilatation,” Philos. Trans. R. Soc. London 106, 156–178 (1816).
[Crossref]

Phys. Rev. (3)

C. W. Higginbotham, M. Cardona, F. H. Pollak, “Intrinsic piezobirefringence of Ge, Si, and GaAs,” Phys. Rev. 184, 821–829 (1969).
[Crossref]

A. Feldman, “High-stress optical birefringence in pure and degenerate n-type germanium,” Phys. Rev. 150, 748–757 (1966).
[Crossref]

D. D. Sell, E. O. Kane, “Piezoreflectance of germanium from 1.9 to 2.8 eV,” Phys. Rev. 185, 1103–1114 (1969).
[Crossref]

Phys. Rev. B (9)

L. F. Lastras-Martı́nez, A. Lastras-Martı́nez, “Reflectance anisotropy of GaAs(100): dislocation-induced piezo-optic effects,” Phys. Rev. B 54, 10726–10735 (1996).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, “Piezo-optical response of Ge in the visible–uv range,” Phys. Rev. B 45, 11721–11735 (1992).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, C. Grein, E. Bustarret, “Piezo-optics of GaAs,” Phys. Rev. B 46, 15139–15149 (1992).
[Crossref]

P. Etchegoin, J. Kircher, M. Cardona, “Elasto-optical constants of Si,” Phys. Rev. B 47, 10292–10303 (1993).
[Crossref]

D. Rönnow, P. Santos, M. Cardona, E. Anastassakis, M. Kuball, “Piezo-optics of InP in the visible–ultraviolet range,” Phys. Rev. B 57, 4432–4442 (1998).
[Crossref]

M. Chandrasekhar, M. H. Grimsditch, M. Cardona, “Piezobirefringence above the fundamental edge in Si,” Phys. Rev. B 18, 4301–4311 (1978).
[Crossref]

P. V. Santos, N. Esser, J. Groenen, M. Cardona, W. G. Schmidt, F. Bechstedt, “Hydrogen interaction with Sb-terminated GaAs and InP (110) surfaces,” Phys. Rev. B 52, 17379–17385 (1995).
[Crossref]

C. C. Kim, S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
[Crossref]

B. Rockwell, H. R. Chandrasekhar, M. Chandrasekhar, A. K. Ramdas, M. Kobayashi, R. L. Gunshor, “Pressure tuning of strains in semiconductor heterostructures: (ZnSe epilayer)/(GaAs epilayer),” Phys. Rev. B 44, 11307–11314 (1991).
[Crossref]

Phys. Rev. Lett. (1)

G. W. Gobeli, E. O. Kane, “Dependence of the optical constants of silicon on uniaxial stress,” Phys. Rev. Lett. 15, 142–146 (1965).
[Crossref]

Phys. Status Solidi A (1)

M. H. Grimsditch, E. Kisela, M. Cardona, “Real and imaginary elasto-optic constants of silicon,” Phys. Status Solidi A 60, 135–143 (1980).
[Crossref]

Phys. Status Solidi B (1)

J. Musilova, “Piezoreflectance study of E1 and E2 transitions in germanium from 107 to 326 K,” Phys. Status Solidi B 101, 85–93 (1980).
[Crossref]

Rev. Sci. Instrum. (1)

J. Kircher, W. Böhringer, W. Dietrich, H. Hirt, P. Etchegoin, M. Cardona, “Design of a compact uniaxial stress apparatus for optical measurements,” Rev. Sci. Instrum. 63, 3733–3735 (1992).
[Crossref]

Other (10)

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

Oriel model 7340, Oriel Corporation, Stratford, Conn. 06447.

Hamamatsu C2177-01, Hamamatsu Photonics K.K. 325-6 Sunayama-cho, Hamamatsu, Shizuoka, Japan.

Spex model 1680, Spex Industries, Edison, N.J. 08820.

Hinds PEM-90 with an I/FS50 optical head, Hinds Instruments, Hillsboro, Oreg. 97124.

Kepco model 2000B, Kepco Inc., 131-38 Sanford Avenue, Flushing, N.Y. 11352.

EG & G model 5210, EG & G Princeton Applied Research, 45 William Street, Wellesley, Mass. 02181.

M. Cardona, in Light Scattering in Solids II, M. Cardona, G. Güntherodt, eds. (Springer, Berlin, 1982), p. 19.

H.-J. Hoffman, in The Properties of Optical Glass (Springer, Heidelberg, 1995), Chap. 2.4.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, Oxford, UK, 1976).

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Figures (6)

Fig. 1
Fig. 1

Optical setup of the RDS system used to measure piezo-optical coefficients of semiconductors above E0. A, analyzer; P, polarizer; S, sample; PEM, photoelastic modulator; PMT, photomultiplier; L, laser used for alignment; I, irises; Sc, screen; X, applied uniaxial stress; and , dielectric function parallel and perpendicular to the stress X, respectively.

Fig. 2
Fig. 2

(a) Real and (b) imaginary parts of the reflectance difference Δr/r¯ versus photon energy for InP, as measured at several uniaxial stresses X  [111] [0 (solid curves), -0.096 GPa (dotted curves), -0.19 GPa (short-dashed curves), -0.30 GPa (long-dashed curves), and -0.40 GPa (dotted–dashed curves)]. (c) Change in Δr/r¯ per unit stress. The data in (c) were obtained from straight-line fits of the data in (a) and (b).

Fig. 3
Fig. 3

Pseudodielectric function 〈〉 of InP, as measured with ellipsometry. Data from a sample cleaved and measured under ultrahigh-vacuum conditions (Ref. 36) are shown (solid curves) together with data corrected (dotted curves) and uncorrected (dotted–dashed curves) for the presence of an oxide overlayer.

Fig. 4
Fig. 4

(a) Real and (b) imaginary parts of the piezo-optical coefficient P44 of InP, as obtained from RDS. The data that were corrected (solid curves) and uncorrected (dotted curves) for a surface overlayer are given, as well as those obtained by using the uncorrected pseudodielectric function 〈〉 in Fig. 3 (dotted–dashed curves). Data obtained from ellipsometry (Ref. 16) are also shown (circles).

Fig. 5
Fig. 5

(a) Real and (b) imaginary parts of the reflectance difference Δr/r¯ versus photon energy for ZnSe, as measured at several uniaxial stresses X  [001] [0 (solid curves), -0.011 GPa (dotted curves), -0.021 GPa (short-dashed curves), -0.027 GPa (long-dashed curves), and -0.033 GPa (dotted–dashed curves)]. (c) Change in Δr/r¯ per unit change in stress for ZnSe. The data in (c) were obtained from straight-line fits of the data in (a) and (b).

Fig. 6
Fig. 6

Real (solid curve) and imaginary (dotted curve) parts of the piezo-optical coefficient P11-P12, as obtained from RDS. Also shown is the Kramers–Kronig transform of the imaginary part of P11-P12 (dotted–dashed curve). The values for the E1 and E1+Δ1 transitions marked by arrows are from Ref. 38.

Equations (7)

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

P11-P12=δ (-)δX  [001],
P44=δ (-)δX  [111],
P11+2P12=δ (+2)δX  [001]=δ (+2)δX  [111],
-=(-1) Δrr¯,
-=(+f)2f[r1+r2 exp(-i2β)][1+r1r2 exp(-i2β)](1-r12)exp(-i2β)Δrr,
ΔV(t)V=2-ImΔrr¯-2apJ1(δr)sin(ωt)+2ReΔrr¯+2ΔP+2ΔCJ2(δr)cos(2ωt),
Re[Pij(ω)]=-2πP ω Im[Pij(ω)]ω2-ω2dω+C,

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