Abstract

In a form analogous to the methods for the measurement of optical constants, a set of methods for the measurement of their changes is described. The methods compared measure light reflected at different angles, with different experimental arrangements; the conclusions reached are demonstrated experimentally with Ge, by electroreflectance measurements.

© 1969 Optical Society of America

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References

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  1. J. Tauc, in Progress in Semiconductors, A. F. Gibson, Ed. (Heywood, London, 1965), Vol. 9, p. 87.
  2. J. C. Phillips, in Solid State Physics, Vol. 18, F. Seitz and D. Turnbull, Eds. (Academic Press Inc., New York, 1966).
    [Crossref]
  3. H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
    [Crossref]
  4. D. G. Avery, Proc. Phys. Soc. (London) B65, 425 (1952).
  5. R. F. Potter, J. Opt. Soc. Am. 54, 904 (1964).
    [Crossref]
  6. A. Vašíček, Optics of Thin Films (North-Holland Publ. Co., Amsterdam, 1960).
  7. R. J. Archer, Manual of Ellipsometry (Gaertner Scientific Corp. Chicago, 1968).
  8. K. Vedam, W. Knausenberger, and F. Lukes, J. Opt. Soc. Am. 59, 64 (1969).
    [Crossref]
  9. B. O. Seraphin, R. B. Hess, and N. Bottka, J. Appl. Phys. 36, 2242 (1965).
    [Crossref]
  10. M. Cardona, K. L. Shaklee, and F. H. Pollak, Phys. Rev. 154, 696 (1967).
    [Crossref]
  11. W. E. Engeler, H. Fritzsche, M. Garfinkel, and J. J. Tiemann, Phys. Rev. Letters 14, 1069 (1965).
    [Crossref]
  12. G. O. Gobeli and E. O. Kane, Phys. Rev. Letters 15, 142 (1965).
    [Crossref]
  13. B. Batz, Solid State Comm. 4, 241 (1966).
    [Crossref]
  14. C. N. Berglund, J. Appl. Phys. 37, 3019 (1966).
    [Crossref]
  15. F. Lukes, private communication; see Ref. 16.
  16. J. E. Fischer and B. O. Seraphin, Solid State Comm. 5, 973 (1967).
    [Crossref]
  17. A. B. Buckman and N. M. Bashara, J. Opt. Soc. Am. 58, 700 (1968).
    [Crossref]
  18. B. Velický, Czech. J. Phys. B11, 787 (1961).
    [Crossref]
  19. A. Reisman and R. Rohr, J. Electrochem Soc. 111, 1425 (1964).
    [Crossref]
  20. R. F. Potter, Phys. Rev. 150, 562 (1966).
    [Crossref]

1969 (1)

1968 (1)

1967 (2)

M. Cardona, K. L. Shaklee, and F. H. Pollak, Phys. Rev. 154, 696 (1967).
[Crossref]

J. E. Fischer and B. O. Seraphin, Solid State Comm. 5, 973 (1967).
[Crossref]

1966 (3)

B. Batz, Solid State Comm. 4, 241 (1966).
[Crossref]

C. N. Berglund, J. Appl. Phys. 37, 3019 (1966).
[Crossref]

R. F. Potter, Phys. Rev. 150, 562 (1966).
[Crossref]

1965 (3)

W. E. Engeler, H. Fritzsche, M. Garfinkel, and J. J. Tiemann, Phys. Rev. Letters 14, 1069 (1965).
[Crossref]

G. O. Gobeli and E. O. Kane, Phys. Rev. Letters 15, 142 (1965).
[Crossref]

B. O. Seraphin, R. B. Hess, and N. Bottka, J. Appl. Phys. 36, 2242 (1965).
[Crossref]

1964 (2)

R. F. Potter, J. Opt. Soc. Am. 54, 904 (1964).
[Crossref]

A. Reisman and R. Rohr, J. Electrochem Soc. 111, 1425 (1964).
[Crossref]

1961 (1)

B. Velický, Czech. J. Phys. B11, 787 (1961).
[Crossref]

1959 (1)

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[Crossref]

1952 (1)

D. G. Avery, Proc. Phys. Soc. (London) B65, 425 (1952).

Archer, R. J.

R. J. Archer, Manual of Ellipsometry (Gaertner Scientific Corp. Chicago, 1968).

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. (London) B65, 425 (1952).

Bashara, N. M.

Batz, B.

B. Batz, Solid State Comm. 4, 241 (1966).
[Crossref]

Berglund, C. N.

C. N. Berglund, J. Appl. Phys. 37, 3019 (1966).
[Crossref]

Bottka, N.

B. O. Seraphin, R. B. Hess, and N. Bottka, J. Appl. Phys. 36, 2242 (1965).
[Crossref]

Buckman, A. B.

Cardona, M.

M. Cardona, K. L. Shaklee, and F. H. Pollak, Phys. Rev. 154, 696 (1967).
[Crossref]

Engeler, W. E.

W. E. Engeler, H. Fritzsche, M. Garfinkel, and J. J. Tiemann, Phys. Rev. Letters 14, 1069 (1965).
[Crossref]

Fischer, J. E.

J. E. Fischer and B. O. Seraphin, Solid State Comm. 5, 973 (1967).
[Crossref]

Fritzsche, H.

W. E. Engeler, H. Fritzsche, M. Garfinkel, and J. J. Tiemann, Phys. Rev. Letters 14, 1069 (1965).
[Crossref]

Garfinkel, M.

W. E. Engeler, H. Fritzsche, M. Garfinkel, and J. J. Tiemann, Phys. Rev. Letters 14, 1069 (1965).
[Crossref]

Gobeli, G. O.

G. O. Gobeli and E. O. Kane, Phys. Rev. Letters 15, 142 (1965).
[Crossref]

Hess, R. B.

B. O. Seraphin, R. B. Hess, and N. Bottka, J. Appl. Phys. 36, 2242 (1965).
[Crossref]

Kane, E. O.

G. O. Gobeli and E. O. Kane, Phys. Rev. Letters 15, 142 (1965).
[Crossref]

Knausenberger, W.

Lukes, F.

Philipp, H. R.

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[Crossref]

Phillips, J. C.

J. C. Phillips, in Solid State Physics, Vol. 18, F. Seitz and D. Turnbull, Eds. (Academic Press Inc., New York, 1966).
[Crossref]

Pollak, F. H.

M. Cardona, K. L. Shaklee, and F. H. Pollak, Phys. Rev. 154, 696 (1967).
[Crossref]

Potter, R. F.

Reisman, A.

A. Reisman and R. Rohr, J. Electrochem Soc. 111, 1425 (1964).
[Crossref]

Rohr, R.

A. Reisman and R. Rohr, J. Electrochem Soc. 111, 1425 (1964).
[Crossref]

Seraphin, B. O.

J. E. Fischer and B. O. Seraphin, Solid State Comm. 5, 973 (1967).
[Crossref]

B. O. Seraphin, R. B. Hess, and N. Bottka, J. Appl. Phys. 36, 2242 (1965).
[Crossref]

Shaklee, K. L.

M. Cardona, K. L. Shaklee, and F. H. Pollak, Phys. Rev. 154, 696 (1967).
[Crossref]

Taft, E. A.

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[Crossref]

Tauc, J.

J. Tauc, in Progress in Semiconductors, A. F. Gibson, Ed. (Heywood, London, 1965), Vol. 9, p. 87.

Tiemann, J. J.

W. E. Engeler, H. Fritzsche, M. Garfinkel, and J. J. Tiemann, Phys. Rev. Letters 14, 1069 (1965).
[Crossref]

Vašícek, A.

A. Vašíček, Optics of Thin Films (North-Holland Publ. Co., Amsterdam, 1960).

Vedam, K.

Velický, B.

B. Velický, Czech. J. Phys. B11, 787 (1961).
[Crossref]

Czech. J. Phys. (1)

B. Velický, Czech. J. Phys. B11, 787 (1961).
[Crossref]

J. Appl. Phys. (2)

C. N. Berglund, J. Appl. Phys. 37, 3019 (1966).
[Crossref]

B. O. Seraphin, R. B. Hess, and N. Bottka, J. Appl. Phys. 36, 2242 (1965).
[Crossref]

J. Electrochem Soc. (1)

A. Reisman and R. Rohr, J. Electrochem Soc. 111, 1425 (1964).
[Crossref]

J. Opt. Soc. Am. (3)

Phys. Rev. (3)

R. F. Potter, Phys. Rev. 150, 562 (1966).
[Crossref]

M. Cardona, K. L. Shaklee, and F. H. Pollak, Phys. Rev. 154, 696 (1967).
[Crossref]

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[Crossref]

Phys. Rev. Letters (2)

W. E. Engeler, H. Fritzsche, M. Garfinkel, and J. J. Tiemann, Phys. Rev. Letters 14, 1069 (1965).
[Crossref]

G. O. Gobeli and E. O. Kane, Phys. Rev. Letters 15, 142 (1965).
[Crossref]

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

D. G. Avery, Proc. Phys. Soc. (London) B65, 425 (1952).

Solid State Comm. (2)

B. Batz, Solid State Comm. 4, 241 (1966).
[Crossref]

J. E. Fischer and B. O. Seraphin, Solid State Comm. 5, 973 (1967).
[Crossref]

Other (5)

A. Vašíček, Optics of Thin Films (North-Holland Publ. Co., Amsterdam, 1960).

R. J. Archer, Manual of Ellipsometry (Gaertner Scientific Corp. Chicago, 1968).

F. Lukes, private communication; see Ref. 16.

J. Tauc, in Progress in Semiconductors, A. F. Gibson, Ed. (Heywood, London, 1965), Vol. 9, p. 87.

J. C. Phillips, in Solid State Physics, Vol. 18, F. Seitz and D. Turnbull, Eds. (Academic Press Inc., New York, 1966).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1

The dependence of Idc, (dI/dn)2/Idc, (dI/dk)2/Idc, and IR on angle of incidence in the PS arrangement for P = 0°, 30°, 60°, 90° and where n2 = 5.0, k2 = 2.0, n1 = 2.0, n0 = 1.3, d1 = 50 Å, Δn2 = 0.1, and Δk2 = 0.1. The magnitudes are given in relative units of the same scale.

Fig. 2
Fig. 2

The ideal-case graphical solution of Δn2 and Δk2 using different values of P at a fixed angle of incidence ϕ = 70° for the PS, PSA (A = 30°), PQSA (A = 30°, Q = 45°) arrangements (assumed values: n2 = 5.0, k2 = 2.0, n0 = 1.3, d1 = 50 Å, Δn2 = 0.1, Δk2 = 0.1).

Fig. 3
Fig. 3

The ideal-case graphical solution of Δn2 and Δk2 using different angles of incidence for the PS, PSA (A = 30°), and PQSA (A =30°, Q = 45°) arrangements (assumed values: n2 = 5.0, k2 = 2.0, n0 = 1.3, d1 = 50 Å, Δn2 = 0.1, Δk2 = 0.1).

Fig. 4
Fig. 4

The dependence of IR, Iac, and Idc on the position of P for the PS (ϕ = 60°), PSA (ϕ = 60°, A = 30°), and PQSA (ϕ = 80°, A = 30°, ϕ = 45°) arrangements (assumed values: n2 = 5.0, k2 = 2.0, n0 = 1.3, d1 = 50 Å, Δn2 = 0.1, Δk2 = 0.1). The magnitudes are given in relative units.

Fig. 5
Fig. 5

The experimental arrangement.

Fig. 6
Fig. 6

IR as a function of wavelength as measured on Ge using the PS arrangement with P = 0°, 45°, and 90°.

Fig. 7
Fig. 7

IR as a function of wavelength as measured on Ge using the PQSA arrangement with Q = 45°, A = 45°, and P = 0°, 45°, and 90°.

Fig. 8
Fig. 8

Δ1 and Δ2 as a function of wavelength as computed from data measured using the PS (fixed ϕ = 70°02′, variable P = 0°, 45°, 90°), PQSA (fixed ϕ = 70°02′, Q = 45°, A = 45°, variable P = 0°, 45°, 90°), and PQSA (fixed P = 90°, Q = 45°, A = 45°, variable ϕ = 70°02′, 82°57′) arrangements, as shown in descending order.

Fig. 9
Fig. 9

Δ1 as a function of wavelength as computed using various assumed values of film thickness d1 (where actual d1 = 50 Å) for the PS and PQSA (Q = 45°, A = 45°) arrangements for ϕ = 70°02′.

Equations (4)

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Δ I = ( I / n 2 ) Δ n 2 + ( I / k 2 ) Δ k 2 ,
I D C = K ( R s sin 2 P + R p cos 2 P ) ,
I D C = K [ R s sin 2 P sin 2 A + R p cos 2 P cos 2 A + 1 2 ( R s R p ) 1 2 cos Δ sin 2 P sin 2 A ] ,
I D C = K { cos 2 ( P - Q ) [ R p cos 2 A cos 2 Q + R s sin 2 A sin 2 Q ] + sin 2 ( P - Q ) [ R p cos 2 A cos 2 Q + R s sin 2 A sin 2 Q ] + 1 2 cos δ sin 2 ( P - Q ) sin 2 Q [ R s sin 2 A - R p cos 2 A ] + 1 2 ( R p R s ) 1 2 sin 2 A [ cos Δ sin 2 Q cos 2 ( P - Q ) + sin 2 ( P - Q ) ( cos 2 Q cos ( δ + Δ ) - sin 2 Q cos ( δ - Δ ) ) ] } ,