Abstract

A reflectometer adaptable to the exit slit of a grazing-incidence monochromator is developed to investigate the optical properties of crystals or evaporated layers before exposure to air in the region 100–1000 Å (124–12.4 eV). The optical constants are determined by three methods; one of them is new and based on the state of polarization of the light emerging from the monochromator. The real and imaginary parts of the dielectric constant and the energy-loss function (−Im−1) are given for Pyrex, corundum, and ruby and for polished and cleaved crystals of LiF and CaF2. The possibility of a plasma level is discussed from experimental curves.

© 1967 Optical Society of America

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  1. M. Morlais and S. Robin, Compt. Rend. 259, 1489 (1964).
  2. J. Romand and B. Vodar, Opt. Acta 9, 371 (1962).
    [CrossRef]
  3. J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 23, 184 (1933).
    [CrossRef]
  4. G. Stéphan, J. C. Lemonnier, and S. Robin, Optica Acta 12, 345 (1965).
    [CrossRef]
  5. J. Romand and B. Vodar, Rev. Opt. (Theor. Instr.) 4, 39 (1960).
  6. Mme. S. Robin, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publishing Company, Amsterdam; John Wiley & Sons, Inc., New York, 1966), p. 202.
  7. K. Rabinovitch, L. R. Canfield, and R. P. Madden, Appl. Opt. 4, 1005 (1965).
    [CrossRef]
  8. E. Uzan, H. Damany, and J. Romand, Compt. Rend. 260, 5735 (1965).
  9. This spectral range corresponds to a sufficient polarization of the monochromatic beam.
  10. D. G. Avery, Proc. Phys. Soc. 65, 425 (1952).
    [CrossRef]
  11. W. R. Hunter, Japan J. Appl. Phys. 4, 520 (1965).
  12. T. Sasaki, H. Fukutani, K. Ishiguro, and T. Izutami, Japan J. Appl. Phys. 4, 527 (1965).
  13. C. J. Powell and J. B. Swan, Phys. Rev. 118, 640 (1960).
    [CrossRef]
  14. E. Loh, Solid-State Commun. 2, 269, (1964).
    [CrossRef]
  15. R. Kato, J. Phys. Soc. Japan 16, 1476, 2525 (1961).
    [CrossRef]
  16. A. Milgram and M. P. Givens, Phys. Rev. 125, 1506 (1962).
    [CrossRef]
  17. W. C. Walker, J. Opt. Soc. Am. 52, 223 (1962).
    [CrossRef]
  18. Cubic system Oh cleavage plane (100).
  19. C. Pradal and F. Gout, Compt. Rend. 256, 1267 (1963).
  20. P. E. Best, Proc. Phys. Soc. (London) 79, 133 (1962). Proc. Phys. Soc. (London) 80, 1308 (1962).
    [CrossRef]
  21. O. Sueoka, J. Phys. Soc. Japan 19, 2239 (1964); J. Phys. Soc. Japan 20, 2226 (1965).
    [CrossRef]
  22. R. Tousey, Phys. Rev. 50, 1057 (1936).
    [CrossRef]
  23. S. Robin-Kandare, J. Robin, and Y. Quéma, Compt. Rend. 262, B355 (1966).
  24. D. Fabre, Doctoral thesis, Paris (1964).
  25. Cubic system Oh cleavage plane (111).
  26. D. Pines and D. Bohm, Phys. Rev. 83, 221 (1951); Phys. Rev. 85, 338 (1952).
  27. C. Horie, Progr. Theor. Phys. 21, 113 (1959).
    [CrossRef]
  28. P. S. Bagus, Phys. Rev. 139, A619 (1965).
    [CrossRef]
  29. J. C. Lemonnier, G. Stéphan, and Mme S. Robin, Compt. Read. 261, 2463 (1965).
  30. H. Ehrenreich, in The Optical Properties of Solids, J. Tauc, Ed. (Academic Press Inc., New York, 1966).
  31. N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, New York, 1940).
  32. F. Stern, Solid-State Phys. 15, 299 (1963).
    [CrossRef]
  33. D. Beaglehole, Proc. Phys. Soc. (London) 87, 461 (1966).
    [CrossRef]

1966 (2)

S. Robin-Kandare, J. Robin, and Y. Quéma, Compt. Rend. 262, B355 (1966).

D. Beaglehole, Proc. Phys. Soc. (London) 87, 461 (1966).
[CrossRef]

1965 (7)

P. S. Bagus, Phys. Rev. 139, A619 (1965).
[CrossRef]

J. C. Lemonnier, G. Stéphan, and Mme S. Robin, Compt. Read. 261, 2463 (1965).

G. Stéphan, J. C. Lemonnier, and S. Robin, Optica Acta 12, 345 (1965).
[CrossRef]

K. Rabinovitch, L. R. Canfield, and R. P. Madden, Appl. Opt. 4, 1005 (1965).
[CrossRef]

E. Uzan, H. Damany, and J. Romand, Compt. Rend. 260, 5735 (1965).

W. R. Hunter, Japan J. Appl. Phys. 4, 520 (1965).

T. Sasaki, H. Fukutani, K. Ishiguro, and T. Izutami, Japan J. Appl. Phys. 4, 527 (1965).

1964 (3)

M. Morlais and S. Robin, Compt. Rend. 259, 1489 (1964).

E. Loh, Solid-State Commun. 2, 269, (1964).
[CrossRef]

O. Sueoka, J. Phys. Soc. Japan 19, 2239 (1964); J. Phys. Soc. Japan 20, 2226 (1965).
[CrossRef]

1963 (2)

C. Pradal and F. Gout, Compt. Rend. 256, 1267 (1963).

F. Stern, Solid-State Phys. 15, 299 (1963).
[CrossRef]

1962 (4)

P. E. Best, Proc. Phys. Soc. (London) 79, 133 (1962). Proc. Phys. Soc. (London) 80, 1308 (1962).
[CrossRef]

A. Milgram and M. P. Givens, Phys. Rev. 125, 1506 (1962).
[CrossRef]

W. C. Walker, J. Opt. Soc. Am. 52, 223 (1962).
[CrossRef]

J. Romand and B. Vodar, Opt. Acta 9, 371 (1962).
[CrossRef]

1961 (1)

R. Kato, J. Phys. Soc. Japan 16, 1476, 2525 (1961).
[CrossRef]

1960 (2)

J. Romand and B. Vodar, Rev. Opt. (Theor. Instr.) 4, 39 (1960).

C. J. Powell and J. B. Swan, Phys. Rev. 118, 640 (1960).
[CrossRef]

1959 (1)

C. Horie, Progr. Theor. Phys. 21, 113 (1959).
[CrossRef]

1952 (1)

D. G. Avery, Proc. Phys. Soc. 65, 425 (1952).
[CrossRef]

1951 (1)

D. Pines and D. Bohm, Phys. Rev. 83, 221 (1951); Phys. Rev. 85, 338 (1952).

1936 (1)

R. Tousey, Phys. Rev. 50, 1057 (1936).
[CrossRef]

1933 (1)

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. 65, 425 (1952).
[CrossRef]

Bagus, P. S.

P. S. Bagus, Phys. Rev. 139, A619 (1965).
[CrossRef]

Beaglehole, D.

D. Beaglehole, Proc. Phys. Soc. (London) 87, 461 (1966).
[CrossRef]

Best, P. E.

P. E. Best, Proc. Phys. Soc. (London) 79, 133 (1962). Proc. Phys. Soc. (London) 80, 1308 (1962).
[CrossRef]

Bohm, D.

D. Pines and D. Bohm, Phys. Rev. 83, 221 (1951); Phys. Rev. 85, 338 (1952).

Canfield, L. R.

Damany, H.

E. Uzan, H. Damany, and J. Romand, Compt. Rend. 260, 5735 (1965).

Edlén, B.

Ehrenreich, H.

H. Ehrenreich, in The Optical Properties of Solids, J. Tauc, Ed. (Academic Press Inc., New York, 1966).

Fabre, D.

D. Fabre, Doctoral thesis, Paris (1964).

Fukutani, H.

T. Sasaki, H. Fukutani, K. Ishiguro, and T. Izutami, Japan J. Appl. Phys. 4, 527 (1965).

Givens, M. P.

A. Milgram and M. P. Givens, Phys. Rev. 125, 1506 (1962).
[CrossRef]

Gout, F.

C. Pradal and F. Gout, Compt. Rend. 256, 1267 (1963).

Gurney, R. W.

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, New York, 1940).

Horie, C.

C. Horie, Progr. Theor. Phys. 21, 113 (1959).
[CrossRef]

Hunter, W. R.

W. R. Hunter, Japan J. Appl. Phys. 4, 520 (1965).

Ishiguro, K.

T. Sasaki, H. Fukutani, K. Ishiguro, and T. Izutami, Japan J. Appl. Phys. 4, 527 (1965).

Izutami, T.

T. Sasaki, H. Fukutani, K. Ishiguro, and T. Izutami, Japan J. Appl. Phys. 4, 527 (1965).

Kato, R.

R. Kato, J. Phys. Soc. Japan 16, 1476, 2525 (1961).
[CrossRef]

Lemonnier, J. C.

J. C. Lemonnier, G. Stéphan, and Mme S. Robin, Compt. Read. 261, 2463 (1965).

G. Stéphan, J. C. Lemonnier, and S. Robin, Optica Acta 12, 345 (1965).
[CrossRef]

Loh, E.

E. Loh, Solid-State Commun. 2, 269, (1964).
[CrossRef]

Mack, J. E.

Madden, R. P.

Milgram, A.

A. Milgram and M. P. Givens, Phys. Rev. 125, 1506 (1962).
[CrossRef]

Morlais, M.

M. Morlais and S. Robin, Compt. Rend. 259, 1489 (1964).

Mott, N. F.

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, New York, 1940).

Pines, D.

D. Pines and D. Bohm, Phys. Rev. 83, 221 (1951); Phys. Rev. 85, 338 (1952).

Powell, C. J.

C. J. Powell and J. B. Swan, Phys. Rev. 118, 640 (1960).
[CrossRef]

Pradal, C.

C. Pradal and F. Gout, Compt. Rend. 256, 1267 (1963).

Quéma, Y.

S. Robin-Kandare, J. Robin, and Y. Quéma, Compt. Rend. 262, B355 (1966).

Rabinovitch, K.

Robin, J.

S. Robin-Kandare, J. Robin, and Y. Quéma, Compt. Rend. 262, B355 (1966).

Robin, Mme S.

J. C. Lemonnier, G. Stéphan, and Mme S. Robin, Compt. Read. 261, 2463 (1965).

Robin, Mme. S.

Mme. S. Robin, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publishing Company, Amsterdam; John Wiley & Sons, Inc., New York, 1966), p. 202.

Robin, S.

G. Stéphan, J. C. Lemonnier, and S. Robin, Optica Acta 12, 345 (1965).
[CrossRef]

M. Morlais and S. Robin, Compt. Rend. 259, 1489 (1964).

Robin-Kandare, S.

S. Robin-Kandare, J. Robin, and Y. Quéma, Compt. Rend. 262, B355 (1966).

Romand, J.

E. Uzan, H. Damany, and J. Romand, Compt. Rend. 260, 5735 (1965).

J. Romand and B. Vodar, Opt. Acta 9, 371 (1962).
[CrossRef]

J. Romand and B. Vodar, Rev. Opt. (Theor. Instr.) 4, 39 (1960).

Sasaki, T.

T. Sasaki, H. Fukutani, K. Ishiguro, and T. Izutami, Japan J. Appl. Phys. 4, 527 (1965).

Stehn, J. R.

Stéphan, G.

J. C. Lemonnier, G. Stéphan, and Mme S. Robin, Compt. Read. 261, 2463 (1965).

G. Stéphan, J. C. Lemonnier, and S. Robin, Optica Acta 12, 345 (1965).
[CrossRef]

Stern, F.

F. Stern, Solid-State Phys. 15, 299 (1963).
[CrossRef]

Sueoka, O.

O. Sueoka, J. Phys. Soc. Japan 19, 2239 (1964); J. Phys. Soc. Japan 20, 2226 (1965).
[CrossRef]

Swan, J. B.

C. J. Powell and J. B. Swan, Phys. Rev. 118, 640 (1960).
[CrossRef]

Tousey, R.

R. Tousey, Phys. Rev. 50, 1057 (1936).
[CrossRef]

Uzan, E.

E. Uzan, H. Damany, and J. Romand, Compt. Rend. 260, 5735 (1965).

Vodar, B.

J. Romand and B. Vodar, Opt. Acta 9, 371 (1962).
[CrossRef]

J. Romand and B. Vodar, Rev. Opt. (Theor. Instr.) 4, 39 (1960).

Walker, W. C.

Appl. Opt. (1)

Compt. Read. (1)

J. C. Lemonnier, G. Stéphan, and Mme S. Robin, Compt. Read. 261, 2463 (1965).

Compt. Rend. (4)

C. Pradal and F. Gout, Compt. Rend. 256, 1267 (1963).

S. Robin-Kandare, J. Robin, and Y. Quéma, Compt. Rend. 262, B355 (1966).

E. Uzan, H. Damany, and J. Romand, Compt. Rend. 260, 5735 (1965).

M. Morlais and S. Robin, Compt. Rend. 259, 1489 (1964).

J. Opt. Soc. Am. (2)

J. Phys. Soc. Japan (2)

R. Kato, J. Phys. Soc. Japan 16, 1476, 2525 (1961).
[CrossRef]

O. Sueoka, J. Phys. Soc. Japan 19, 2239 (1964); J. Phys. Soc. Japan 20, 2226 (1965).
[CrossRef]

Japan J. Appl. Phys. (2)

W. R. Hunter, Japan J. Appl. Phys. 4, 520 (1965).

T. Sasaki, H. Fukutani, K. Ishiguro, and T. Izutami, Japan J. Appl. Phys. 4, 527 (1965).

Opt. Acta (1)

J. Romand and B. Vodar, Opt. Acta 9, 371 (1962).
[CrossRef]

Optica Acta (1)

G. Stéphan, J. C. Lemonnier, and S. Robin, Optica Acta 12, 345 (1965).
[CrossRef]

Phys. Rev. (5)

C. J. Powell and J. B. Swan, Phys. Rev. 118, 640 (1960).
[CrossRef]

A. Milgram and M. P. Givens, Phys. Rev. 125, 1506 (1962).
[CrossRef]

R. Tousey, Phys. Rev. 50, 1057 (1936).
[CrossRef]

D. Pines and D. Bohm, Phys. Rev. 83, 221 (1951); Phys. Rev. 85, 338 (1952).

P. S. Bagus, Phys. Rev. 139, A619 (1965).
[CrossRef]

Proc. Phys. Soc. (1)

D. G. Avery, Proc. Phys. Soc. 65, 425 (1952).
[CrossRef]

Proc. Phys. Soc. (London) (2)

D. Beaglehole, Proc. Phys. Soc. (London) 87, 461 (1966).
[CrossRef]

P. E. Best, Proc. Phys. Soc. (London) 79, 133 (1962). Proc. Phys. Soc. (London) 80, 1308 (1962).
[CrossRef]

Progr. Theor. Phys. (1)

C. Horie, Progr. Theor. Phys. 21, 113 (1959).
[CrossRef]

Rev. Opt. (Theor. Instr.) (1)

J. Romand and B. Vodar, Rev. Opt. (Theor. Instr.) 4, 39 (1960).

Solid-State Commun. (1)

E. Loh, Solid-State Commun. 2, 269, (1964).
[CrossRef]

Solid-State Phys. (1)

F. Stern, Solid-State Phys. 15, 299 (1963).
[CrossRef]

Other (7)

H. Ehrenreich, in The Optical Properties of Solids, J. Tauc, Ed. (Academic Press Inc., New York, 1966).

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, New York, 1940).

D. Fabre, Doctoral thesis, Paris (1964).

Cubic system Oh cleavage plane (111).

Cubic system Oh cleavage plane (100).

Mme. S. Robin, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publishing Company, Amsterdam; John Wiley & Sons, Inc., New York, 1966), p. 202.

This spectral range corresponds to a sufficient polarization of the monochromatic beam.

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Figures (14)

Fig. 1
Fig. 1

Reflectometer a: fixed part, b: rotatable part, c: sample holder, e: lateral aperture, M: monochromator, pm1: rotating photomultiplier, pm2: monitoring photomultiplier, and pm3: photomultiplier without window used for transmittance measurements.

Fig. 2
Fig. 2

Degree of polarization of monochromatic light.

Fig. 3
Fig. 3

Reflectance of Pyrex for an incidence angle φ=60° R1: reflectance maximum obtained when the incidence plane is horizontal. R2: reflectance minimum obtained when the incidence plane is vertical. RM: averaged value corresponding to the reflectance of natural light.

Fig. 4
Fig. 4

Reflectance at quasinormal incidence R20°, real (1) and imaginary (2) parts of the dielectric constant and loss function for Pyrex glass.

Fig. 5
Fig. 5

Reflectance at quasinormal incidence R20° and real (1) and imaginary (2) parts of the dielectric constant for corundum.

Fig. 6
Fig. 6

Loss function for corundum (full line) and loss of energy of electrons traversing a thin film of Al2O3 (dotted curve) found by Powell and Swan.13 Right-hand scale is given in arbitrary units.

Fig. 7
Fig. 7

Reflectance at 20° incidence, real and imaginary parts of the dielectric constant and loss function for ruby with 1.4% Cr.

Fig. 8
Fig. 8

Reflectance of LiF. Curve A—cleaved specimen, 20° incidence, curve B—polished specimen, 20° incidence, curve C—results of Kato,15 curve D—results of Walker,17 curve E—cleaved specimen, 60° incidence.

Fig. 9
Fig. 9

Real (1) and imaginary (2) parts of the dielectric constants of LiF.

Fig. 10
Fig. 10

Loss function (−Im −1) for LiF, – – – – electron energy losses results of Best (B.),20 · · · · electron losses results of Pradal and Gout (P.G.),19 × × electron energy losses maxima obtained by Sueoka (S.).21

Fig. 11
Fig. 11

Reflectance of CaF2. Dotted curve for polished specimen at quasinormal incidence. R20° cleaved specimen, 20° incidence and R60° cleaved specimen, 60° incidence.

Fig. 12
Fig. 12

CaF2: —— imaginary (2) part of the dielectric constant, – – – – real (1) part of the dielectric constant, and · · · · loss function −Im −1.

Fig. 13
Fig. 13

Illustration of sum rules for LiF.

Fig. 14
Fig. 14

Illustration of sum rules for CaF2.

Tables (2)

Tables Icon

Table I Displacement of the first reflectance maximum vs Cr+++ concentration in Al2O3.

Tables Icon

Table II Comparison of uv and electron energy losses in CaF2.

Equations (10)

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P = ( I V - I H ) / ( I V + I H ) ,
R 1 = 1 2 [ R p ( 1 - P ) + R s ( 1 + P ) ] R 2 = 1 2 [ R p ( 1 + P ) + R s ( 1 - P ) ] .
R p R s = R 1 - R 2 - P ( R 1 + R 2 ) R 2 - R 1 - P ( R 1 + R 2 ) R s = R 2 - R 1 + P ( R 1 + R 2 ) 2 P .
p 2 - q 2 = n 2 - k 2 - sin 2 φ p q = n k ,
p = 1 2 cos φ ( cos 2 φ - sin 2 φ t g 2 φ ) ( R s - R p ) ( 1 - R s ) ( R p + R s ) ( R s - 1 ) + 2 cos 2 φ R s ( 1 - R p ) q 2 = 2 p cos φ ( R s + 1 ) / ( 1 - R s ) - p 2 - cos 2 φ ,
n 2 = 1 2 ( p 2 - q 2 + sin 2 φ ) + [ 1 4 ( p 2 - q 2 + sin 2 φ ) 2 + p 2 q 2 ] 1 2 k = p q / n .
1 = n 2 - k 2             and             2 = 2 n k .
eff = 1 + 2 π 0 2 ω d ω .
0 ω 0 ω 2 d ω = π N e 2 2 m 0 N eff ,
2 π P 0 ω 2 ω 2 - ω 0 2 d ω = ( N e 2 / m 0 ) ( 1 / ω 0 2 ) .