Abstract

A detailed study of a new method of determining the optical properties of absorbing materials is presented. It makes use of normal incidence reflectances from the specimen itself (Rs) and from the specimen coated with a transparent film of two different thicknesses but of the same refractive index (R1s and R2s) in the form of R1s/Rs and R2s/Rs. It is seen that a simple goniometer can be easily adopted for measuring the reflectance ratios over a wide spectral range. The versatility of the method has been proved by the fact that it has been successfully adopted for specimens with surface structures varying from atomically smooth to rough surfaces.

© 1981 Optical Society of America

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References

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  1. S. P. F. Humphreys-Owen, Proc. Phys. Soc. London Sect. B 77, 949 (1961).
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  3. F. Abelés, Phys. Thin Films 6, 151 (1971).
  4. O. S. Heavens, Phys. Thin Films 2, 193 (1964).
  5. J. Vincent-Geisse, N. T. Tai, J. P. Pinnan-Lucorre, Journal de Physique 28, 26 (1967).
  6. S. G. Tomlin, Thin Solid Films 13, 265 (1972).
  7. J. Tauc, A. Abraham, Czech, J. Phys. B: 19, 1246 (1969).
  8. B. O. Seraphin, H. E. Bennett, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic, New York, 1967), Vol. 3, p. 449.
  9. G. A. N. Connell, R. J. Temkin, W. Paul, Adv. Phys. 22, 643 (1973).
  10. P. Ruard, P. Bosquet, Prog. Opt. 4, 145 (1965).
  11. P. Ruard, A. Meessen, Prog. Opt. 15, 79 (1977).
  12. C. L. Nagendra, G. K. M. Thutupalli, to be published in J. Phys. D. Appl. Phys.
  13. S. G. Tomlin, Br. J. Appl. Phys. 1, 1667 (1968).
  14. H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
  15. H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963).
  16. P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  17. J. M. Eastmann, Phys. Thin Films 10, 167 (1978).
  18. J. O. Porteus, J. Opt. Soc. Am. 53, 139 (1963).
  19. H. K. Pulker, Appl. Opt. 18, 1969 (1979).
  20. B. Carnahan, J. Wilkies, Digital Computing and Numeridal Methods (Wiley, New York, 1973).
  21. C. L. Nagendra, G. K. M. Thutupalli, Accepted for publication in Vacuum.
  22. S. G. Tomlin, E. Khawaja, G. K. M. Thutupalli, J. Phys C: 9, 4334 (1976).
  23. G. K. M. Thutupalli, “Optical Properties of Some Semiconductors,” Ph.D. Thesis, U. Adelaide, Australia, 1976.
  24. E. Khawaja, S. G. Tomlin, Thin Solid Films 30, 371 (1975).
  25. H. E. Bennett, J. L. Stanford, J. Res Natl. Bur. Stand. Sect. A: 80, 643 (1976).

1979 (1)

1978 (1)

J. M. Eastmann, Phys. Thin Films 10, 167 (1978).

1977 (1)

P. Ruard, A. Meessen, Prog. Opt. 15, 79 (1977).

1976 (2)

S. G. Tomlin, E. Khawaja, G. K. M. Thutupalli, J. Phys C: 9, 4334 (1976).

H. E. Bennett, J. L. Stanford, J. Res Natl. Bur. Stand. Sect. A: 80, 643 (1976).

1975 (1)

E. Khawaja, S. G. Tomlin, Thin Solid Films 30, 371 (1975).

1973 (1)

G. A. N. Connell, R. J. Temkin, W. Paul, Adv. Phys. 22, 643 (1973).

1972 (1)

S. G. Tomlin, Thin Solid Films 13, 265 (1972).

1971 (1)

F. Abelés, Phys. Thin Films 6, 151 (1971).

1969 (1)

J. Tauc, A. Abraham, Czech, J. Phys. B: 19, 1246 (1969).

1968 (1)

S. G. Tomlin, Br. J. Appl. Phys. 1, 1667 (1968).

1967 (1)

J. Vincent-Geisse, N. T. Tai, J. P. Pinnan-Lucorre, Journal de Physique 28, 26 (1967).

1965 (1)

P. Ruard, P. Bosquet, Prog. Opt. 4, 145 (1965).

1964 (1)

O. S. Heavens, Phys. Thin Films 2, 193 (1964).

1963 (2)

J. O. Porteus, J. Opt. Soc. Am. 53, 139 (1963).

H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963).

1961 (2)

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).

S. P. F. Humphreys-Owen, Proc. Phys. Soc. London Sect. B 77, 949 (1961).

Abelés, F.

F. Abelés, Phys. Thin Films 6, 151 (1971).

Abraham, A.

J. Tauc, A. Abraham, Czech, J. Phys. B: 19, 1246 (1969).

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).

Beckmann, P.

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Bennett, H. E.

H. E. Bennett, J. L. Stanford, J. Res Natl. Bur. Stand. Sect. A: 80, 643 (1976).

H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963).

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).

B. O. Seraphin, H. E. Bennett, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic, New York, 1967), Vol. 3, p. 449.

Bosquet, P.

P. Ruard, P. Bosquet, Prog. Opt. 4, 145 (1965).

Carnahan, B.

B. Carnahan, J. Wilkies, Digital Computing and Numeridal Methods (Wiley, New York, 1973).

Connell, G. A. N.

G. A. N. Connell, R. J. Temkin, W. Paul, Adv. Phys. 22, 643 (1973).

Eastmann, J. M.

J. M. Eastmann, Phys. Thin Films 10, 167 (1978).

Heavens, O. S.

O. S. Heavens, Phys. Thin Films 2, 193 (1964).

Humphreys-Owen, S. P. F.

S. P. F. Humphreys-Owen, Proc. Phys. Soc. London Sect. B 77, 949 (1961).

Khawaja, E.

S. G. Tomlin, E. Khawaja, G. K. M. Thutupalli, J. Phys C: 9, 4334 (1976).

E. Khawaja, S. G. Tomlin, Thin Solid Films 30, 371 (1975).

Meessen, A.

P. Ruard, A. Meessen, Prog. Opt. 15, 79 (1977).

Nagendra, C. L.

C. L. Nagendra, G. K. M. Thutupalli, to be published in J. Phys. D. Appl. Phys.

C. L. Nagendra, G. K. M. Thutupalli, Accepted for publication in Vacuum.

Paul, W.

G. A. N. Connell, R. J. Temkin, W. Paul, Adv. Phys. 22, 643 (1973).

Pinnan-Lucorre, J. P.

J. Vincent-Geisse, N. T. Tai, J. P. Pinnan-Lucorre, Journal de Physique 28, 26 (1967).

Porteus, J. O.

J. O. Porteus, J. Opt. Soc. Am. 53, 139 (1963).

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).

Pulker, H. K.

Ruard, P.

P. Ruard, A. Meessen, Prog. Opt. 15, 79 (1977).

P. Ruard, P. Bosquet, Prog. Opt. 4, 145 (1965).

Seraphin, B. O.

B. O. Seraphin, H. E. Bennett, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic, New York, 1967), Vol. 3, p. 449.

Spizzichino, A.

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Stanford, J. L.

H. E. Bennett, J. L. Stanford, J. Res Natl. Bur. Stand. Sect. A: 80, 643 (1976).

Tai, N. T.

J. Vincent-Geisse, N. T. Tai, J. P. Pinnan-Lucorre, Journal de Physique 28, 26 (1967).

Tauc, J.

J. Tauc, A. Abraham, Czech, J. Phys. B: 19, 1246 (1969).

Temkin, R. J.

G. A. N. Connell, R. J. Temkin, W. Paul, Adv. Phys. 22, 643 (1973).

Thutupalli, G. K. M.

S. G. Tomlin, E. Khawaja, G. K. M. Thutupalli, J. Phys C: 9, 4334 (1976).

G. K. M. Thutupalli, “Optical Properties of Some Semiconductors,” Ph.D. Thesis, U. Adelaide, Australia, 1976.

C. L. Nagendra, G. K. M. Thutupalli, Accepted for publication in Vacuum.

C. L. Nagendra, G. K. M. Thutupalli, to be published in J. Phys. D. Appl. Phys.

Tomlin, S. G.

S. G. Tomlin, E. Khawaja, G. K. M. Thutupalli, J. Phys C: 9, 4334 (1976).

E. Khawaja, S. G. Tomlin, Thin Solid Films 30, 371 (1975).

S. G. Tomlin, Thin Solid Films 13, 265 (1972).

S. G. Tomlin, Br. J. Appl. Phys. 1, 1667 (1968).

Vincent-Geisse, J.

J. Vincent-Geisse, N. T. Tai, J. P. Pinnan-Lucorre, Journal de Physique 28, 26 (1967).

Wilkies, J.

B. Carnahan, J. Wilkies, Digital Computing and Numeridal Methods (Wiley, New York, 1973).

Adv. Phys. (1)

G. A. N. Connell, R. J. Temkin, W. Paul, Adv. Phys. 22, 643 (1973).

Appl. Opt. (1)

Br. J. Appl. Phys. (1)

S. G. Tomlin, Br. J. Appl. Phys. 1, 1667 (1968).

Czech, J. Phys. B: (1)

J. Tauc, A. Abraham, Czech, J. Phys. B: 19, 1246 (1969).

J. Opt. Soc. Am. (3)

J. Phys C: (1)

S. G. Tomlin, E. Khawaja, G. K. M. Thutupalli, J. Phys C: 9, 4334 (1976).

J. Res Natl. Bur. Stand. Sect. A: (1)

H. E. Bennett, J. L. Stanford, J. Res Natl. Bur. Stand. Sect. A: 80, 643 (1976).

Journal de Physique (1)

J. Vincent-Geisse, N. T. Tai, J. P. Pinnan-Lucorre, Journal de Physique 28, 26 (1967).

Phys. Thin Films (3)

F. Abelés, Phys. Thin Films 6, 151 (1971).

O. S. Heavens, Phys. Thin Films 2, 193 (1964).

J. M. Eastmann, Phys. Thin Films 10, 167 (1978).

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

S. P. F. Humphreys-Owen, Proc. Phys. Soc. London Sect. B 77, 949 (1961).

Prog. Opt. (2)

P. Ruard, P. Bosquet, Prog. Opt. 4, 145 (1965).

P. Ruard, A. Meessen, Prog. Opt. 15, 79 (1977).

Thin Solid Films (2)

S. G. Tomlin, Thin Solid Films 13, 265 (1972).

E. Khawaja, S. G. Tomlin, Thin Solid Films 30, 371 (1975).

Other (7)

G. K. M. Thutupalli, “Optical Properties of Some Semiconductors,” Ph.D. Thesis, U. Adelaide, Australia, 1976.

B. Carnahan, J. Wilkies, Digital Computing and Numeridal Methods (Wiley, New York, 1973).

C. L. Nagendra, G. K. M. Thutupalli, Accepted for publication in Vacuum.

B. O. Seraphin, H. E. Bennett, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic, New York, 1967), Vol. 3, p. 449.

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

C. L. Nagendra, G. K. M. Thutupalli, to be published in J. Phys. D. Appl. Phys.

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

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Figures (13)

Fig. 1
Fig. 1

Reflectance ratios for the hypothetical system for thicknesses d1 = 90.0 nm and d2 = 150.0 nm.

Fig. 2
Fig. 2

Dispersion curve and associated inadmissible solutions for the hypothetical system.

Fig. 3
Fig. 3

Effect of overestimated and underestimated thickness (d1) on the dispersion curve (91,150 and 89,150 thickness combinations).

Fig. 4
Fig. 4

Effect of overestimated and underestimated thickness (d2) on the dispersion curve (90,149 and 90,151 thickness combinations).

Fig. 5
Fig. 5

Nature of dispersion curve when both the thicknesses (d1 and d2) are overestimated (91,151) and underestimated (89,149).

Fig. 6
Fig. 6

Nature of dispersion curve when thickness (d1,d2) deviations are in opposite directions (91,149 and 89,151).

Fig. 7
Fig. 7

Schematic diagram of the experimental setup.

Fig. 8
Fig. 8

Reflectance ratios for a germanium sample with an atomically smooth surface and coated with tantalum pentoxide films with two different thicknesses.

Fig. 9
Fig. 9

Dispersion curve and its associated inadmissible solutions. Cross bars represent probable deviations in the refractive index.

Fig. 10
Fig. 10

Absorption index values for germanium.

Fig. 11
Fig. 11

Reflectance values for a germanium sample (rough surface) and coated with tantalum pentoxide films.

Fig. 12
Fig. 12

Comparison of dispersion curves obtained by Tomlin's and present methods.

Fig. 13
Fig. 13

Comparison of absorption index values obtained by Tomlin's and present method.

Tables (1)

Tables Icon

Table 1 Nature Of Breaks In Dispersion Curve For Different Thickness Combinations

Equations (15)

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R = ( n n 0 ) 2 + k 2 ( n + n 0 ) 2 + k 2 ,
R 1 = { ( n 0 2 + n 1 2 ) ( n 1 2 + n 2 + k 2 ) + ( n 0 2 n 1 2 ) [ ( n 1 2 n 2 k 2 ) cos 2 X 1 + 2 n 1 k sin 2 X 1 ] 4 n 0 n 1 2 n } { ( n 0 2 + n 1 2 ) ( n 1 2 + n 2 + k 2 ) + ( n 0 2 n 1 2 ) [ ( n 1 2 n 2 k 2 ) cos 2 X 1 + 2 n 1 k sin 2 X 1 ] 4 n 0 n 1 2 n } ,
R s R = exp ( 4 π n 0 σ λ ) 2 + [ 1 exp ( 4 π n 0 σ λ ) 2 ] × [ 1 exp 2 ( π σ α m λ ) 2 ] ,
R cs R 1 = exp ( 4 π n 0 σ λ ) 2 ,
R 1 s R 1 = exp ( 4 π n 0 σ λ ) 2 + [ 1 exp ( 4 π σ n 0 λ ) 2 ] × [ 1 exp 2 ( π σ α m λ ) 2 ] ,
R 1 s R s = { ( n 0 2 + n 1 2 ) ( n 1 2 + n 2 + k 2 ) + ( n 0 2 n 1 2 ) [ ( n 1 2 n 2 k 2 ) cos 2 X 1 + 2 n 1 k sin 2 X 1 ] 4 n 0 n 1 2 n } [ ( n + n 0 ) 2 + k 2 ] { ( n 0 2 + n 1 2 ) ( n 1 2 + n 2 + k 2 ) + ( n 0 2 n 1 2 ) [ ( n 1 2 n 2 k 2 ) cos 2 X 1 + 2 n 1 k sin 2 X 1 ] 4 n 0 n 1 2 n } [ ( n n 0 ) 2 + k 2 ] .
R 2 s R s = R 2 R .
n i + 1 = n i + f 2 × f 1 k f 1 × f 2 k f 1 n × f 2 k f 2 n × f 1 k ,
k i + 1 = k i + f 2 × f 1 n f 1 × f 2 n f 2 n × f 1 k f 1 n × f 2 k f 1 , f 2 , f 1 n , f 1 k , f 2 n , and f 2 k .
Δ n = Δ ( R 1 s / R s ) k ( R 2 s / R s ) Δ ( R 2 s / R s ) ( R 1 s / R s ) n ( R 1 s / R s ) k ( R 2 s / R s ) k ( R 1 s / R s ) n ( R 2 s / R s ) ,
Δ k = Δ ( R 2 s / R s ) n ( R 1 s / R s ) Δ ( R 1 s / R s ) n ( R 2 s / R s ) n ( R 1 s / R s ) k ( R 2 s / R s ) k ( R 1 s / R s ) n ( R 2 s / R s ) ,
n ( R 1 s / R s ) , k ( R 1 s / R s ) , n ( R 2 s / R s ) , k ( R 2 s / R s )
f 1 = ( p 1 y ) ( R 1 s R s ) ( p 1 + y ) R , f 2 = ( p 2 y ) ( R 2 s R s ) ( p 2 + y ) R ,
p 1 = ( n 0 2 + n 1 2 ) ( n 1 2 + n 2 + k 2 ) + ( n 0 2 n 1 2 ) [ ( n 1 2 n 2 k 2 ) cos 2 X 1 + 2 n 1 k sin 2 X 1 ] , p 2 = ( n 0 2 + n 1 2 ) ( n 1 2 + n 2 + k 2 ) + ( n 0 2 n 1 2 ) [ ( n 1 2 n 2 k 2 ) cos 2 X 2 + 2 n 1 k sin 2 X 2 ] , y = 4 n 0 n 1 2 n .
f 1 n , f 2 n , f 1 k , f 2 k

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