Abstract

Progress in the field of reflective multilayer coatings for the wavelength region between 50 Å and 2000 Å is reviewed. All the coatings contain absorbing materials, absorption losses are minimized by positioning strongly absorbing materials into the nodes of the standing wave inside the coating. Above λ = 1200 Å, ideal coatings with a reflectivity approaching 100% are theoretically possible; the theoretical predictions have been confirmed for coatings up to six layers at wavelengths around 2000 Å. Below λ = 1000 Å, no absorption-free material is available that can be used as a spacer layer to cover the antinodes of the standing wave field. This limits the theoretically obtainable reflectivity. However, even at the shortest wavelength a reflectivity of 30% is still possible. Experimental results have been obtained for wavelengths between 100 Å and 200 Å for coatings up to nine layers. Discrepancies between experiment and theory can be explained as due to insufficient knowledge of the optical constants of the films used. Extensive future work on the optical constants of materials and their dependence on film thickness and deposition conditions is required for further improvement.

© 1976 Optical Society of America

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References

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  1. M. L. Perlman, E. M. Rowe, R. E. Watson, Phys. Today 27, No. 7, 30 (1974).
  2. D. L. Spears, H. I. Smith, Electron. Lett. 8, 102 (1972).
  3. R. Feder, E. Spiller, J. Topalian, J. Vac. Sci. Technol. 12, 1332 (1975).
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  5. E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).
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  7. G. Hass, W. Hunter, in Space Optics, Proceedings of ICO-IX, Santa Monica, 1972 (National Academy of Science, Washington, D.C., 1974), p. 525.
  8. E. Spiller, in Ref. 7, p. 581.
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  10. O. Wiener, Ann. Phys. 40, 203 (1890).
  11. E. Spiller, Appl. Phys. Lett. 20, 365 (1972).
  12. C. V. Shank, J. E. Bjorkholm, H. Kogelnik, Appl. Phys. Lett. 16, 395 (1971).
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  23. M. A. Spivack, Rev. Sci. Instrum. 41, 1614 (1970).

1976 (4)

E. Spiller, R. Feder, J. Topalian, E. Castellani, L. Romankiw, M. Heritage, Solid State Technol. 19, 62 (April1976).

E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).

R. P. Haelbich, C. Kunz, Opt. Commun. 17, 287 (1976).

H. J. Hagemann, W. Gudat, C. Kunz, Phys. Stat. Sol. 74, 507 (1976).

1975 (2)

H. J. Hagemann, W. Gudat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

R. Feder, E. Spiller, J. Topalian, J. Vac. Sci. Technol. 12, 1332 (1975).

1974 (3)

E. Spiller, Appl. Opt. 13, 1209 (1974).

M. L. Perlman, E. M. Rowe, R. E. Watson, Phys. Today 27, No. 7, 30 (1974).

A. Malherbe, Appl. Opt. 13, 1275 (1974).

1973 (1)

E. Spiller, Optik 39, 118 (1973).

1972 (3)

D. L. Spears, H. I. Smith, Electron. Lett. 8, 102 (1972).

E. Spiller, Appl. Phys. Lett. 20, 365 (1972).

E. T. Hutcheson, J. T. Cox, G. Hass, W. R. Hunter, Appl. Opt. 11, 1590 (1972).

1971 (1)

C. V. Shank, J. E. Bjorkholm, H. Kogelnik, Appl. Phys. Lett. 16, 395 (1971).

1970 (1)

M. A. Spivack, Rev. Sci. Instrum. 41, 1614 (1970).

1966 (1)

1960 (1)

G. Koppelmann, Ann. Phys. 7 Folge 5, 388 (1960).

1890 (1)

O. Wiener, Ann. Phys. 40, 203 (1890).

Arthur, Y. R.

A. Y. Cho, Y. R. Arthur, in Progress in Solid State Chemistry, G. Somerjai, Y. McClain, Ed. (Pergamon, New York, 1975), Vol. 10, p. 157.

Bates, B.

Bjorkholm, J. E.

C. V. Shank, J. E. Bjorkholm, H. Kogelnik, Appl. Phys. Lett. 16, 395 (1971).

Bradley, D. J.

Castellani, E.

E. Spiller, R. Feder, J. Topalian, E. Castellani, L. Romankiw, M. Heritage, Solid State Technol. 19, 62 (April1976).

Chang, L. L.

L. L. Chang, R. Ludeke, in Epitaxial Growth, Y. W. Matthews, Ed. (Academic, New York, 1975), p. 37.

Cho, A. Y.

A. Y. Cho, Y. R. Arthur, in Progress in Solid State Chemistry, G. Somerjai, Y. McClain, Ed. (Pergamon, New York, 1975), Vol. 10, p. 157.

Cox, J. T.

Eastman, D.

E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).

Feder, R.

E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).

E. Spiller, R. Feder, J. Topalian, E. Castellani, L. Romankiw, M. Heritage, Solid State Technol. 19, 62 (April1976).

R. Feder, E. Spiller, J. Topalian, J. Vac. Sci. Technol. 12, 1332 (1975).

Gudat, W.

E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).

H. J. Hagemann, W. Gudat, C. Kunz, Phys. Stat. Sol. 74, 507 (1976).

H. J. Hagemann, W. Gudat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

Haelbich, R. P.

R. P. Haelbich, C. Kunz, Opt. Commun. 17, 287 (1976).

Hagemann, H. J.

H. J. Hagemann, W. Gudat, C. Kunz, Phys. Stat. Sol. 74, 507 (1976).

H. J. Hagemann, W. Gudat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

Hass, G.

E. T. Hutcheson, J. T. Cox, G. Hass, W. R. Hunter, Appl. Opt. 11, 1590 (1972).

G. Hass, W. Hunter, in Space Optics, Proceedings of ICO-IX, Santa Monica, 1972 (National Academy of Science, Washington, D.C., 1974), p. 525.

Heritage, M.

E. Spiller, R. Feder, J. Topalian, E. Castellani, L. Romankiw, M. Heritage, Solid State Technol. 19, 62 (April1976).

Hunter, W.

G. Hass, W. Hunter, in Space Optics, Proceedings of ICO-IX, Santa Monica, 1972 (National Academy of Science, Washington, D.C., 1974), p. 525.

Hunter, W. R.

Hutcheson, E. T.

Kogelnik, H.

C. V. Shank, J. E. Bjorkholm, H. Kogelnik, Appl. Phys. Lett. 16, 395 (1971).

Koppelmann, G.

G. Koppelmann, Ann. Phys. 7 Folge 5, 388 (1960).

Kunz, C.

R. P. Haelbich, C. Kunz, Opt. Commun. 17, 287 (1976).

H. J. Hagemann, W. Gudat, C. Kunz, Phys. Stat. Sol. 74, 507 (1976).

H. J. Hagemann, W. Gudat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

Ludeke, R.

L. L. Chang, R. Ludeke, in Epitaxial Growth, Y. W. Matthews, Ed. (Academic, New York, 1975), p. 37.

Malherbe, A.

Perlman, M. L.

M. L. Perlman, E. M. Rowe, R. E. Watson, Phys. Today 27, No. 7, 30 (1974).

Romankiw, L.

E. Spiller, R. Feder, J. Topalian, E. Castellani, L. Romankiw, M. Heritage, Solid State Technol. 19, 62 (April1976).

Rowe, E. M.

M. L. Perlman, E. M. Rowe, R. E. Watson, Phys. Today 27, No. 7, 30 (1974).

Samson, J. A. R.

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967).

Sayre, D.

E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).

Shank, C. V.

C. V. Shank, J. E. Bjorkholm, H. Kogelnik, Appl. Phys. Lett. 16, 395 (1971).

Smith, H. I.

D. L. Spears, H. I. Smith, Electron. Lett. 8, 102 (1972).

Spears, D. L.

D. L. Spears, H. I. Smith, Electron. Lett. 8, 102 (1972).

Spiller, E.

E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).

E. Spiller, R. Feder, J. Topalian, E. Castellani, L. Romankiw, M. Heritage, Solid State Technol. 19, 62 (April1976).

R. Feder, E. Spiller, J. Topalian, J. Vac. Sci. Technol. 12, 1332 (1975).

E. Spiller, Appl. Opt. 13, 1209 (1974).

E. Spiller, Optik 39, 118 (1973).

E. Spiller, Appl. Phys. Lett. 20, 365 (1972).

E. Spiller, in Ref. 7, p. 581.

Spivack, M. A.

M. A. Spivack, Rev. Sci. Instrum. 41, 1614 (1970).

Topalian, J.

E. Spiller, R. Feder, J. Topalian, E. Castellani, L. Romankiw, M. Heritage, Solid State Technol. 19, 62 (April1976).

E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).

R. Feder, E. Spiller, J. Topalian, J. Vac. Sci. Technol. 12, 1332 (1975).

Watson, R. E.

M. L. Perlman, E. M. Rowe, R. E. Watson, Phys. Today 27, No. 7, 30 (1974).

Wiener, O.

O. Wiener, Ann. Phys. 40, 203 (1890).

Ann. Phys. (1)

O. Wiener, Ann. Phys. 40, 203 (1890).

Ann. Phys. 7 Folge (1)

G. Koppelmann, Ann. Phys. 7 Folge 5, 388 (1960).

Appl. Opt. (4)

Appl. Phys. Lett. (2)

E. Spiller, Appl. Phys. Lett. 20, 365 (1972).

C. V. Shank, J. E. Bjorkholm, H. Kogelnik, Appl. Phys. Lett. 16, 395 (1971).

Electron. Lett. (1)

D. L. Spears, H. I. Smith, Electron. Lett. 8, 102 (1972).

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. (1)

R. Feder, E. Spiller, J. Topalian, J. Vac. Sci. Technol. 12, 1332 (1975).

Opt. Commun. (1)

R. P. Haelbich, C. Kunz, Opt. Commun. 17, 287 (1976).

Optik (1)

E. Spiller, Optik 39, 118 (1973).

Phys. Stat. Sol. (1)

H. J. Hagemann, W. Gudat, C. Kunz, Phys. Stat. Sol. 74, 507 (1976).

Phys. Today (1)

M. L. Perlman, E. M. Rowe, R. E. Watson, Phys. Today 27, No. 7, 30 (1974).

Rev. Sci. Instrum. (1)

M. A. Spivack, Rev. Sci. Instrum. 41, 1614 (1970).

Science (1)

E. Spiller, R. Feder, J. Topalian, D. Eastman, W. Gudat, D. Sayre, Science 191, 1172 (1976).

Solid State Technol. (1)

E. Spiller, R. Feder, J. Topalian, E. Castellani, L. Romankiw, M. Heritage, Solid State Technol. 19, 62 (April1976).

Other (5)

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967).

G. Hass, W. Hunter, in Space Optics, Proceedings of ICO-IX, Santa Monica, 1972 (National Academy of Science, Washington, D.C., 1974), p. 525.

E. Spiller, in Ref. 7, p. 581.

L. L. Chang, R. Ludeke, in Epitaxial Growth, Y. W. Matthews, Ed. (Academic, New York, 1975), p. 37.

A. Y. Cho, Y. R. Arthur, in Progress in Solid State Chemistry, G. Somerjai, Y. McClain, Ed. (Pergamon, New York, 1975), Vol. 10, p. 157.

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Figures (8)

Fig. 1
Fig. 1

Intensity distribution within and in front of five-layer reflecting coatings: (a) lossless quarter wave stack of materials with different refractive indices; (b) optimized coating of one absorbing and one non absorbing material with the same refractive index. Light is incident from the right.

Fig. 2
Fig. 2

Normal incidence reflectivity for periodic structures of period λ/2, where an absorbing material with k = 0.5 alternates with a non-absorbing material vs the number of periods in the structure. The parameter d is the thickness of the absorber material. Dashed curves: optimal thickness dopt of the absorber and highest reflectivity obtainable (from Ref. 11).

Fig. 3
Fig. 3

Vector diagram for the reflectivity of a single absorbing film surrounded by material of smaller absorption and about the same refractive index.

Fig. 4
Fig. 4

Measured values of the absorption of six-layer coatings plotted against their reflectivity and compared to the same curve for a single Al film (from Ref. 13).

Fig. 5
Fig. 5

Transmission vs wavelength for a two cavity interference filter for λ = 1216 Å (from A. Malherbe, Ref. 17).

Fig. 6
Fig. 6

Calculated reflectivity as a function of wavelength of mirror coatings for the xuv region. The thickness of the layers counted from the substrate are (in Å) (a) 61.4, 40.3, 66.6, 33.4, 71.9, 28.9, 75.2, 26, 77.5, 24.7; (b) 98.9, 51.9, 101.9, 45, 112.5, 38.3, 116.4, 34.9, 119.8, 34; (c) 198.4, 100.3, 237.9, 61, 250.3, 48.7, 257.7, 42.8, 262.8, 36.6, 268, 32.7, 269.4, 32.8. The optical constants used for the substrate are (a) n = 0.95, k = 0.08; (b) n = 0.89, k = 0.092; (c) n = 0.85, k = 0.47. The last layer of each coating (i.e., the first layer toward the incident light) is always a layer of the material with the high k (from Ref. 8).

Fig. 7
Fig. 7

Measured reflectivity R of a nine-layer mirror coating of Au and C at an angle of incidence of 15° compared with the measured (dash) and calculated (dash–dot) reflectivity of an opaque Au film (from R. P. Haelbich and C. Kunz, Ref. 18).

Fig. 8
Fig. 8

Calculated normal incidence reflectivity for an optimized reflective coating of Au and C vs the number of layers in the coating and required thickness of each gold film for λ = 46 Å.

Equations (3)

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r = n ^ 1 - n ^ 2 n ^ 1 + n ^ 2 = n 1 2 + k 1 2 - ( n 2 2 + k 2 2 ) + 2 i ( n 1 k 2 - n 2 k 1 ) ( n 1 + n 2 ) 2 + ( k 1 + k 2 ) 2
tan ϕ = 2 ( n 1 k 2 - n 2 k 1 ) n 1 2 + k 1 2 - ( n 2 2 + k 2 2 ) .
r total = r front + r back

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