Abstract

We describe a new method for obtaining the optical constants of a material based upon measurement of the relative derivative of reflectance with angle of incidence (1/R)(dR/dθ). The systematic optical errors in this system were reduced to about 5 × 10−4 rad−1. The relative accuracy in (1/R)(dR/dθ) was then typically five times better than the relative accuracy in the optical absorptance (1 − R0) measured in a standard reflectometer. Systematic calibration errors were comparable with those for a reflectometer and were about 0.6%. Used in conjunction with a normal incidence reflectometer, the system provides the optical constants of materials in regions where the reflectivity is not high. When the reflectivity approaches unity, as it does for metals in the ir, the measured quantity (for light of both polarizations) becomes proportional to (1 − R0) and may be used to measure the absorptance of a sample with an accuracy of about 3%.

© 1972 Optical Society of America

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References

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  1. T. S. Robinson, Proc. Phys. Soc. (London) B65, 910 (1952); J. C. Phillips, Solid State Phys. 18, 56 (1966).
  2. J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 222 (1955).
  3. S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969).
    [CrossRef]
  4. J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
    [CrossRef]
  5. D. K. Burge, H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).
    [CrossRef]
  6. D. Beaglehole, Appl. Opt. 7, 2218 (1968).
    [CrossRef] [PubMed]
  7. M. Theye, Phys. Rev. 2, 3060 (1970); Ph.D. Thesis, Paris (1968).
    [CrossRef]
  8. We used unannealed films evaporated at 10−6Torr while Theye used well-annealed films evaporated at 10−10Torr. As shown by Theye in Ref. 7, vacuum conditions and annealing can have a large effect upon the properties of semitransparent films, and we might also expect the properties of opaque films to be somewhat affected by the same factors.

1970 (1)

M. Theye, Phys. Rev. 2, 3060 (1970); Ph.D. Thesis, Paris (1968).
[CrossRef]

1969 (1)

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

1968 (1)

1964 (1)

1955 (1)

J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 222 (1955).

1952 (1)

T. S. Robinson, Proc. Phys. Soc. (London) B65, 910 (1952); J. C. Phillips, Solid State Phys. 18, 56 (1966).

1943 (1)

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
[CrossRef]

Beaglehole, D.

Beattie, J. R.

J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 222 (1955).

Bennett, H. E.

Bock, R. O.

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
[CrossRef]

Burge, D. K.

Collins, J. R.

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
[CrossRef]

Conn, G. K. T.

J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 222 (1955).

Jasperson, S. N.

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Robinson, T. S.

T. S. Robinson, Proc. Phys. Soc. (London) B65, 910 (1952); J. C. Phillips, Solid State Phys. 18, 56 (1966).

Schnatterly, S. E.

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Theye, M.

M. Theye, Phys. Rev. 2, 3060 (1970); Ph.D. Thesis, Paris (1968).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Philos. Mag. (1)

J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 222 (1955).

Phys. Rev. (1)

M. Theye, Phys. Rev. 2, 3060 (1970); Ph.D. Thesis, Paris (1968).
[CrossRef]

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

T. S. Robinson, Proc. Phys. Soc. (London) B65, 910 (1952); J. C. Phillips, Solid State Phys. 18, 56 (1966).

Rev. Sci. Instrum. (2)

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
[CrossRef]

Other (1)

We used unannealed films evaporated at 10−6Torr while Theye used well-annealed films evaporated at 10−10Torr. As shown by Theye in Ref. 7, vacuum conditions and annealing can have a large effect upon the properties of semitransparent films, and we might also expect the properties of opaque films to be somewhat affected by the same factors.

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Figures (8)

Fig. 1
Fig. 1

Contours of constant G(θ) and R0 plotted vs 1 and 2 for 60° angle of incidence.

Fig. 2
Fig. 2

Contours of constant normal incidence reflectivity −R0 and constant reflectivity of p-polarized light at 60° angle of incidence −Rp plotted vs 1 and 2.

Fig. 3
Fig. 3

Contours of constant G(θ) and R0 plotted vs 1 and 2 for 75° angle of incidence.

Fig. 4
Fig. 4

Contours of constant G(θ) and R0 plotted vs 1 and 2 for 45° angle of incidence.

Fig. 5
Fig. 5

Sample mount with magnet, pickup coil, and driving coil.

Fig. 6
Fig. 6

The optical system.

Fig. 7
Fig. 7

The normal incidence absorptivity, 1 − R0 (——) and G(θ) (---) at 60° angle of incidence measured for gold. (Note the change of scale for the longer wavelengths.)

Fig. 8
Fig. 8

The continuous line with representative error bars shows the dielectric constant of a gold film. Circles show values from M. Theye.7

Tables (3)

Tables Icon

Table I Errors in 1 and 2 in Percent Introduced by a 1% Error in Parameters R0, G(θ), Rp(θ), (Rp/Rs) and by an Error of 0.01 rad in Δa

Tables Icon

Table II Effects of an Oxide Film in Percent on the Parameters and on the Dielectric Constant (t/λ = 1/4000 and n = 2.3)a

Tables Icon

Table III Errors in 1 and 2 in Percent due to the Limits of Accuracy of the Three Methods Considereda

Equations (8)

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R s = | r s | 2 with r s = ( sin 2 θ ) 1 2 cos θ ( sin 2 θ ) 1 2 + cos θ ,
R p = | r p | 2 with r p = ( sin 2 θ ) 1 2 cos θ ( sin 2 θ ) 1 2 + cos θ .
1 R s d R s d θ = 4 Re [ sin θ ( sin 2 θ ) 1 2 ] ,
1 R p d R p d θ = 4 Re { sin θ ( sin 2 θ ) 1 2 · 1 1 sin 2 θ [ 1 + ( 1 / ) ] . }
G ( θ ) = [ ( 1 / R s ) ( d R s / d θ ) ( 1 / R p ) ( d R p / d θ ) ] .
( 1 / R s ) ( d R s / d θ ) 2 sin θ [ 2 / ( | 1 | 3 2 ) ] ,
( 1 / R p ) ( d R p / d θ ) [ ( 2 sin θ ) / cos 2 θ ] [ 2 / ( | 1 | 3 2 ) ] .
R 0 exp = R 0 ( 1 n 1 , 2 n 1 ) + R 0 ( 1 n 1 , 2 n 1 ) 1 Δ 1 n + R 0 ( 1 n 1 , 2 n 1 ) 2 Δ 2 n , G exp = G ( 1 n 1 , 2 n 1 ) + G ( 1 n 1 , 2 n 1 ) 1 Δ 1 n + G ( 1 n 1 , 2 n 1 ) 2 Δ 2 n .

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