Abstract

The optical constants (n, k) of single crystalline InBi have been determined using a two-angle method applying Fresnel’s equations. The complex dielectric constant was then calculated using the relation ∊* = ∊1 − i∊2, where ∊1 = n2k2 and ∊2 = 2nk. Assuming a free-electron model, the volume plasma resonance energy was found from the crossover position of the n and k curves to be 10.3 eV. The energy loss functions − Im[1/∊] and − Im[1/(∊ + 1)], which have been interpreted as having maxima at the volume and surface plasma frequencies, respectively, when interband transitions are not significant, were plotted using the n and k data. These values were in general agreement with those obtained from the crossover point on the n and k curves and from the Ritchie relation Es=Ev/2.

© 1976 Optical Society of America

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References

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  1. W. P. Binnie, Acta Crystallogr. 9, 686 (1956).
    [Crossref]
  2. E. S. Makarov, Dokl. Akad. Nauk. SSSR 59, 899 (1948).
  3. O. Henry and E. Badwick, Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.)2159 (1947); Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.) 14, 23 (1947).
  4. E. A. Peretti and S. C. Carapella, Trans. Am. Soc. Met. 41, 947 (1949).
  5. Sizuo Asanabe, Mem. Fac. Sci. Kyusyu Univ. Ser. B 2, 82 (1956).
  6. Y. Shapira, S. J. Williamson, and S. Fishler, Phys. Rev. 44, 715 (1966).
    [Crossref]
  7. R. Th, W. Meyer, J. J. A. Hofmans, and A. R. DeVroomen, J. Phys. Chem. Solids 35, 307 (1974).
    [Crossref]
  8. R. B. Lal, H. U. Walter, and J. H. Davis, Bul. Am. Phys. Soc. 17, 520 (1972).
  9. R. B. Lal, J. H. Davis, and B. E. Powell, J. Less-Common Met. 27, 367 (1972).
    [Crossref]
  10. R. Tousey, J. Opt. Soc. Am. 29, 235 (1939).
    [Crossref]
  11. A. Matsui and W. C. Walker, J. Opt. Soc. Am. 60, 64 (1970).
    [Crossref]
  12. R. P. Madden, in Physics of Thin Films, Vol. 1, edited by G. Hass (Academic, New York, 1963), Chap. III.
  13. Grant R. Fowles, Introduction to Modern Optics (Holt, Rinehart and Winston, New York, 1968), Chap. 5.
  14. F. Seitz, The Modern Theory of Solids (McGraw-Hill, New York, 1940), Chap. 17.
  15. H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959).
    [Crossref]
  16. H. Fröhlich and R. L. Platzman, Phys. Rev. 92, 1152 (1953).
    [Crossref]
  17. H. Fröhlich and H. Pelzer, Proc. Phys. Soc. London Ser. A 68, 525 (1955).
    [Crossref]
  18. C. J. Powell, J. Opt. Soc. Am. 59, 738 (1969).
    [Crossref]
  19. R. H. Ritchie, Phys. Rev. 106, 874 (1957).
    [Crossref]

1974 (1)

R. Th, W. Meyer, J. J. A. Hofmans, and A. R. DeVroomen, J. Phys. Chem. Solids 35, 307 (1974).
[Crossref]

1972 (2)

R. B. Lal, H. U. Walter, and J. H. Davis, Bul. Am. Phys. Soc. 17, 520 (1972).

R. B. Lal, J. H. Davis, and B. E. Powell, J. Less-Common Met. 27, 367 (1972).
[Crossref]

1970 (1)

1969 (1)

1966 (1)

Y. Shapira, S. J. Williamson, and S. Fishler, Phys. Rev. 44, 715 (1966).
[Crossref]

1959 (1)

H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959).
[Crossref]

1957 (1)

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[Crossref]

1956 (2)

W. P. Binnie, Acta Crystallogr. 9, 686 (1956).
[Crossref]

Sizuo Asanabe, Mem. Fac. Sci. Kyusyu Univ. Ser. B 2, 82 (1956).

1955 (1)

H. Fröhlich and H. Pelzer, Proc. Phys. Soc. London Ser. A 68, 525 (1955).
[Crossref]

1953 (1)

H. Fröhlich and R. L. Platzman, Phys. Rev. 92, 1152 (1953).
[Crossref]

1949 (1)

E. A. Peretti and S. C. Carapella, Trans. Am. Soc. Met. 41, 947 (1949).

1948 (1)

E. S. Makarov, Dokl. Akad. Nauk. SSSR 59, 899 (1948).

1947 (1)

O. Henry and E. Badwick, Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.)2159 (1947); Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.) 14, 23 (1947).

1939 (1)

Asanabe, Sizuo

Sizuo Asanabe, Mem. Fac. Sci. Kyusyu Univ. Ser. B 2, 82 (1956).

Badwick, E.

O. Henry and E. Badwick, Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.)2159 (1947); Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.) 14, 23 (1947).

Binnie, W. P.

W. P. Binnie, Acta Crystallogr. 9, 686 (1956).
[Crossref]

Carapella, S. C.

E. A. Peretti and S. C. Carapella, Trans. Am. Soc. Met. 41, 947 (1949).

Cohen, M. H.

H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959).
[Crossref]

Davis, J. H.

R. B. Lal, J. H. Davis, and B. E. Powell, J. Less-Common Met. 27, 367 (1972).
[Crossref]

R. B. Lal, H. U. Walter, and J. H. Davis, Bul. Am. Phys. Soc. 17, 520 (1972).

DeVroomen, A. R.

R. Th, W. Meyer, J. J. A. Hofmans, and A. R. DeVroomen, J. Phys. Chem. Solids 35, 307 (1974).
[Crossref]

Ehrenreich, H.

H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959).
[Crossref]

Fishler, S.

Y. Shapira, S. J. Williamson, and S. Fishler, Phys. Rev. 44, 715 (1966).
[Crossref]

Fowles, Grant R.

Grant R. Fowles, Introduction to Modern Optics (Holt, Rinehart and Winston, New York, 1968), Chap. 5.

Fröhlich, H.

H. Fröhlich and H. Pelzer, Proc. Phys. Soc. London Ser. A 68, 525 (1955).
[Crossref]

H. Fröhlich and R. L. Platzman, Phys. Rev. 92, 1152 (1953).
[Crossref]

Henry, O.

O. Henry and E. Badwick, Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.)2159 (1947); Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.) 14, 23 (1947).

Hofmans, J. J. A.

R. Th, W. Meyer, J. J. A. Hofmans, and A. R. DeVroomen, J. Phys. Chem. Solids 35, 307 (1974).
[Crossref]

Lal, R. B.

R. B. Lal, H. U. Walter, and J. H. Davis, Bul. Am. Phys. Soc. 17, 520 (1972).

R. B. Lal, J. H. Davis, and B. E. Powell, J. Less-Common Met. 27, 367 (1972).
[Crossref]

Madden, R. P.

R. P. Madden, in Physics of Thin Films, Vol. 1, edited by G. Hass (Academic, New York, 1963), Chap. III.

Makarov, E. S.

E. S. Makarov, Dokl. Akad. Nauk. SSSR 59, 899 (1948).

Matsui, A.

Meyer, W.

R. Th, W. Meyer, J. J. A. Hofmans, and A. R. DeVroomen, J. Phys. Chem. Solids 35, 307 (1974).
[Crossref]

Pelzer, H.

H. Fröhlich and H. Pelzer, Proc. Phys. Soc. London Ser. A 68, 525 (1955).
[Crossref]

Peretti, E. A.

E. A. Peretti and S. C. Carapella, Trans. Am. Soc. Met. 41, 947 (1949).

Platzman, R. L.

H. Fröhlich and R. L. Platzman, Phys. Rev. 92, 1152 (1953).
[Crossref]

Powell, B. E.

R. B. Lal, J. H. Davis, and B. E. Powell, J. Less-Common Met. 27, 367 (1972).
[Crossref]

Powell, C. J.

Ritchie, R. H.

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[Crossref]

Seitz, F.

F. Seitz, The Modern Theory of Solids (McGraw-Hill, New York, 1940), Chap. 17.

Shapira, Y.

Y. Shapira, S. J. Williamson, and S. Fishler, Phys. Rev. 44, 715 (1966).
[Crossref]

Th, R.

R. Th, W. Meyer, J. J. A. Hofmans, and A. R. DeVroomen, J. Phys. Chem. Solids 35, 307 (1974).
[Crossref]

Tousey, R.

Walker, W. C.

Walter, H. U.

R. B. Lal, H. U. Walter, and J. H. Davis, Bul. Am. Phys. Soc. 17, 520 (1972).

Williamson, S. J.

Y. Shapira, S. J. Williamson, and S. Fishler, Phys. Rev. 44, 715 (1966).
[Crossref]

Acta Crystallogr. (1)

W. P. Binnie, Acta Crystallogr. 9, 686 (1956).
[Crossref]

Bul. Am. Phys. Soc. (1)

R. B. Lal, H. U. Walter, and J. H. Davis, Bul. Am. Phys. Soc. 17, 520 (1972).

Dokl. Akad. Nauk. SSSR (1)

E. S. Makarov, Dokl. Akad. Nauk. SSSR 59, 899 (1948).

J. Less-Common Met. (1)

R. B. Lal, J. H. Davis, and B. E. Powell, J. Less-Common Met. 27, 367 (1972).
[Crossref]

J. Opt. Soc. Am. (3)

J. Phys. Chem. Solids (1)

R. Th, W. Meyer, J. J. A. Hofmans, and A. R. DeVroomen, J. Phys. Chem. Solids 35, 307 (1974).
[Crossref]

Mem. Fac. Sci. Kyusyu Univ. Ser. B (1)

Sizuo Asanabe, Mem. Fac. Sci. Kyusyu Univ. Ser. B 2, 82 (1956).

Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.) (1)

O. Henry and E. Badwick, Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.)2159 (1947); Met. Technol. (Am. Inst. Met. Eng. Tech. Pub.) 14, 23 (1947).

Phys. Rev. (4)

Y. Shapira, S. J. Williamson, and S. Fishler, Phys. Rev. 44, 715 (1966).
[Crossref]

H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959).
[Crossref]

H. Fröhlich and R. L. Platzman, Phys. Rev. 92, 1152 (1953).
[Crossref]

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[Crossref]

Proc. Phys. Soc. London Ser. A (1)

H. Fröhlich and H. Pelzer, Proc. Phys. Soc. London Ser. A 68, 525 (1955).
[Crossref]

Trans. Am. Soc. Met. (1)

E. A. Peretti and S. C. Carapella, Trans. Am. Soc. Met. 41, 947 (1949).

Other (3)

R. P. Madden, in Physics of Thin Films, Vol. 1, edited by G. Hass (Academic, New York, 1963), Chap. III.

Grant R. Fowles, Introduction to Modern Optics (Holt, Rinehart and Winston, New York, 1968), Chap. 5.

F. Seitz, The Modern Theory of Solids (McGraw-Hill, New York, 1940), Chap. 17.

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Figures (5)

FIG. 1
FIG. 1

Sample chamber illustrating sample mounted on end of positioning rod, light path from monochromator, and light pipe coupled to photomultiplier tube.

FIG. 2
FIG. 2

Reflectance for 70° and 20° incidence of single crystalline InBi over the wavelength range 40–360 nm.

FIG. 3
FIG. 3

The optical constants n and k of InBi over the wavelength range 40–360 nm.

FIG. 4
FIG. 4

The real (∊1) and imaginary (∊2) components of the complex dielectric constant on InBi over the wavelength range 40–360 nm.

FIG. 5
FIG. 5

The energy loss functions, − Im[1/∊] and − Im[1/(∊ + 1)], for InBi over the wavelength range 40–360 nm.

Equations (7)

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R = a 2 + b 2 - 2 a cos θ + cos 2 θ a 2 + b 2 + 2 a cos θ + cos 2 θ , R = R a 2 + b 2 - 2 a sin θ tan θ + sin 2 θ tan 2 θ a 2 + b 2 + 2 a sin θ tan θ + sin 2 θ tan 2 θ ,
2 a 2 = [ ( n 2 - k 2 - sin 2 θ ) 2 + 4 n 2 k 2 ] 1 / 2 + ( n 2 - k 2 - sin 2 θ ) , 2 b 2 = [ ( n 2 - k 2 - sin 2 θ ) 2 + 4 n 2 k 2 ] 1 / 2 - ( n 2 - k 2 - sin 2 θ ) .
* = 1 - ω p 2 ω 2 + i ω / τ - j = 1 n f j ω p 2 ω 2 - ω j 2 + i ω / τ j .
= 1 - ω p 2 ω 2 + i ω / τ = 1 - ω p 2 ω 2 + τ - 2 - i ω p 2 ω 2 + τ - 2 1 ω τ .
1 = n 2 - k 2 = 1 - ω p 2 / ( ω 2 + τ - 2 ) ,
2 = 2 n k = [ ω p 2 / ( ω 2 + τ - 2 ) ] ( 1 / ω τ ) .
1 = n 2 - k 2 = 1 - ω p 2 / ω 2 .