Abstract

The generation of periodic surface corrugations by ion-beam milling and chemical etching of grating relief patterns in photoresist is analyzed. A general treatment is developed for gratings of any desired period on substrates of arbitrary reflectivity, but particular emphasis is given to the generation of gratings with deep grooves and fine periods (Λ < 3000 Å) on GaAs. Analysis of the intensity distribution in photoresist for both p- and s-polarized incident beams reveals that the standing waves generated by reflection from the substrate are diminished for p-polarized beams, but the existence of a displaced grating for certain ranges of substrate reflectivity and angle of incidence severely limits groove depth in resist. The requirements are given for the establishment of an intensity maximum at the photoresist–substrate interface, a condition desired for subsequent chemical etching. It is shown further that the alternative use of a quarterwave intermediate oxide layer to achieve this condition on GaAs results in a lower limit being imposed on grating period. Constant-intensity contours approximating the groove profiles in resist demonstrate that an imbalance in incident beam intensity may lead to severing of the resist stripes, and the dependence of this phenomenon on substrate reflectivity is determined. For beams of equal intensity, a similar phenomenon occurs with increasing reflectivity of the substrate. The transfer of a grating relief pattern to the substrate by ion-beam milling is treated by considering the erosion profiles produced by ion bombardment. This analysis is used to examine the influence of milling geometry on the depth and shape of the groove. Although the ion-beam milling rate of GaAs is several times greater than AZ-1350 photoresist, it is shown that the groove aspect ratio (depth/period) in GaAs can be no more than about 1.2, a figure that is obtained, surprisingly, by milling at the angle of maximum removal rate of photoresist. For a metal substrate, the groove aspect ratio decreases with increasing grating period. For gratings produced by chemical etch, the problem of the weakly exposed layer of resist adjacent to the substrate is solved by using a combination of ion-beam milling and chemical etching. Using a preferential chemical etch with a sufficiently slow etch rate, gratings with well-defined planar features, a period ∼2500 Å, and a groove aspect ratio >0.6 have been produced on GaAs.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
    [CrossRef]
  2. C. V. Shank, R. V. Schmidt, B. I. Miller, Appl. Phys. Lett. 25, 200 (1974).
    [CrossRef]
  3. R. D. Burnham, D. R. Scifres, W. Streifer, IEEE J. Quantum Electron. QE-11, 439 (1975).
    [CrossRef]
  4. F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
    [CrossRef]
  5. H. C. Casey, S. Somekh, M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).
    [CrossRef]
  6. D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 27, 295 (1975).
    [CrossRef]
  7. M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
    [CrossRef]
  8. M. Nakamura, K. Aiki, J. Umeda, A. Yariv, Appl. Phys. Lett. 27, 403 (1975).
    [CrossRef]
  9. W. Ng, H. W. Yen, A. Katzir, I. Samid, A. Yariv, Opt. Commun. 18, 215 (1976).
    [CrossRef]
  10. D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 25, 203 (1974).
    [CrossRef]
  11. M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
    [CrossRef]
  12. D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
    [CrossRef]
  13. Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
    [CrossRef]
  14. V. N. Lukyanov, N. V. Shelkov, S. D. Yakubovitch, Sov. J. Quantum Electron. 5, 99 (1975).
    [CrossRef]
  15. M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
    [CrossRef]
  16. H. Kogelnik, T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).
  17. D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
    [CrossRef]
  18. R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651 (1974).
    [CrossRef]
  19. S. Somekh, A. Yariv, Appl. Phys. Lett 21, 140 (1972).
    [CrossRef]
  20. See, for example, F. H. Dill, IEEE Trans. Electron Devices ED-22, 440 (1975).
    [CrossRef]
  21. F. H. Dill, W. P. Hornberger, P. S. Hauge, J. M. Shaw, IEEE Trans Electron Devices 22, 445 (1975).
    [CrossRef]
  22. Differentiation of I∥g/I∥m with respect to c reveals that maximum grating contrast is obtained when beam intensities are equal. (I∥g is the maximum groove intensity; I∥m the intensity midway between grooves.)
  23. The quartz uv objectives were made by Carl Zeiss, Inc. We have found that these lenses deteriorate when used to transmit a laser beam of only a few mW at 3250 Å.
  24. T. Aoyagi, Y. Aoyagi, S. Namba, Appl. Phys. Lett. 29, 303 (1976).
    [CrossRef]
  25. S. Somekh, H. C. Casey, Appl. Opt. 16, 126 (1977).
    [CrossRef] [PubMed]
  26. S. Iida, K. Ito, J. Electrochem. Soc. 118, 768 (1971).
    [CrossRef]
  27. See, e.g., E. G. Spencer, P. H. Schmidt, J. Vac. Sci. Technol. 8, 552 (1971).
    [CrossRef]
  28. H. L. Garvin, E. Garmire, S. Somekh, H. Stoll, A. Yariv, Appl Opt. 12, 455 (1973).
    [CrossRef] [PubMed]
  29. W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
    [CrossRef]
  30. S. Somekh, H. C. Casey, Appl. Opt. 16, 126 (1977).
    [CrossRef] [PubMed]
  31. M. J. Beesley, J. G. Castledine, Appl Opt. 9, 2720 (1970).
    [CrossRef] [PubMed]
  32. D. J. Barber, F. C. Frank, M. Moss, J. W. Steeds, I. S. T. Tsong, J. Mater. Sci. 8, 1030 (1973).
    [CrossRef]
  33. J. P. Ducommun, M. Cantagrel, M. Marchal, J. Mater. Sci. 9, 725 (1974).
    [CrossRef]
  34. J. P. Ducommun, M. Cantagrel, M. Moulin, J. Mater. Sci. 10, 52 (1975).
    [CrossRef]
  35. Y. Tarui, Y. Komiya, Y. Harada, J. Electrochem. Soc. 118, 118 (1971).
    [CrossRef]
  36. R. A. Logan, B. Schwartz, W. J. Sundberg, J. Electrochem. Soc. 120, 1385 (1973).
    [CrossRef]
  37. L. Comerford, P. Zory, Appl. Phys. Lett. 25, 208 (1974).
    [CrossRef]
  38. W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
    [CrossRef]
  39. W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 596 (1976).
    [CrossRef]
  40. J. L. Merz, R. A. Logan, J. Appl. Phys. 47, 3503 (1976).
    [CrossRef]
  41. R. C. Miller, W. A. Nordland, R. A. Logan, L. F. Johnson, J. Appl. Phys. (to be published).
  42. W. T. Tsang, Appl Opt. 16, 1918 (1977).
    [CrossRef] [PubMed]
  43. See, e.g., F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, IEEE Trans Electron Devices 22, 456 (1975).
    [CrossRef]
  44. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), Chap. 13.
  45. R. E. Morrison, Phys Rev. 124, 1314 (1961).
    [CrossRef]

1977

1976

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 596 (1976).
[CrossRef]

J. L. Merz, R. A. Logan, J. Appl. Phys. 47, 3503 (1976).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
[CrossRef]

T. Aoyagi, Y. Aoyagi, S. Namba, Appl. Phys. Lett. 29, 303 (1976).
[CrossRef]

W. Ng, H. W. Yen, A. Katzir, I. Samid, A. Yariv, Opt. Commun. 18, 215 (1976).
[CrossRef]

1975

R. D. Burnham, D. R. Scifres, W. Streifer, IEEE J. Quantum Electron. QE-11, 439 (1975).
[CrossRef]

F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[CrossRef]

H. C. Casey, S. Somekh, M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 27, 295 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, Appl. Phys. Lett. 27, 403 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[CrossRef]

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

V. N. Lukyanov, N. V. Shelkov, S. D. Yakubovitch, Sov. J. Quantum Electron. 5, 99 (1975).
[CrossRef]

See, for example, F. H. Dill, IEEE Trans. Electron Devices ED-22, 440 (1975).
[CrossRef]

F. H. Dill, W. P. Hornberger, P. S. Hauge, J. M. Shaw, IEEE Trans Electron Devices 22, 445 (1975).
[CrossRef]

J. P. Ducommun, M. Cantagrel, M. Moulin, J. Mater. Sci. 10, 52 (1975).
[CrossRef]

See, e.g., F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, IEEE Trans Electron Devices 22, 456 (1975).
[CrossRef]

1974

L. Comerford, P. Zory, Appl. Phys. Lett. 25, 208 (1974).
[CrossRef]

J. P. Ducommun, M. Cantagrel, M. Marchal, J. Mater. Sci. 9, 725 (1974).
[CrossRef]

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651 (1974).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 25, 203 (1974).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
[CrossRef]

C. V. Shank, R. V. Schmidt, B. I. Miller, Appl. Phys. Lett. 25, 200 (1974).
[CrossRef]

1973

H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
[CrossRef]

D. J. Barber, F. C. Frank, M. Moss, J. W. Steeds, I. S. T. Tsong, J. Mater. Sci. 8, 1030 (1973).
[CrossRef]

R. A. Logan, B. Schwartz, W. J. Sundberg, J. Electrochem. Soc. 120, 1385 (1973).
[CrossRef]

H. L. Garvin, E. Garmire, S. Somekh, H. Stoll, A. Yariv, Appl Opt. 12, 455 (1973).
[CrossRef] [PubMed]

1972

S. Somekh, A. Yariv, Appl. Phys. Lett 21, 140 (1972).
[CrossRef]

1971

S. Iida, K. Ito, J. Electrochem. Soc. 118, 768 (1971).
[CrossRef]

See, e.g., E. G. Spencer, P. H. Schmidt, J. Vac. Sci. Technol. 8, 552 (1971).
[CrossRef]

Y. Tarui, Y. Komiya, Y. Harada, J. Electrochem. Soc. 118, 118 (1971).
[CrossRef]

1970

M. J. Beesley, J. G. Castledine, Appl Opt. 9, 2720 (1970).
[CrossRef] [PubMed]

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

H. Kogelnik, T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

1961

R. E. Morrison, Phys Rev. 124, 1314 (1961).
[CrossRef]

Aiki, K.

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, Appl. Phys. Lett. 27, 403 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
[CrossRef]

Alferov, Zh. I.

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

Andreyev, V. M.

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

Aoyagi, T.

T. Aoyagi, Y. Aoyagi, S. Namba, Appl. Phys. Lett. 29, 303 (1976).
[CrossRef]

Aoyagi, Y.

T. Aoyagi, Y. Aoyagi, S. Namba, Appl. Phys. Lett. 29, 303 (1976).
[CrossRef]

Barber, D. J.

D. J. Barber, F. C. Frank, M. Moss, J. W. Steeds, I. S. T. Tsong, J. Mater. Sci. 8, 1030 (1973).
[CrossRef]

Beesley, M. J.

M. J. Beesley, J. G. Castledine, Appl Opt. 9, 2720 (1970).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), Chap. 13.

Burnham, R. D.

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 27, 295 (1975).
[CrossRef]

R. D. Burnham, D. R. Scifres, W. Streifer, IEEE J. Quantum Electron. QE-11, 439 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 25, 203 (1974).
[CrossRef]

Cantagrel, M.

J. P. Ducommun, M. Cantagrel, M. Moulin, J. Mater. Sci. 10, 52 (1975).
[CrossRef]

J. P. Ducommun, M. Cantagrel, M. Marchal, J. Mater. Sci. 9, 725 (1974).
[CrossRef]

Casey, H. C.

Castledine, J. G.

M. J. Beesley, J. G. Castledine, Appl Opt. 9, 2720 (1970).
[CrossRef] [PubMed]

Comerford, L.

L. Comerford, P. Zory, Appl. Phys. Lett. 25, 208 (1974).
[CrossRef]

Dakss, M. L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Dill, F. H.

See, e.g., F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, IEEE Trans Electron Devices 22, 456 (1975).
[CrossRef]

F. H. Dill, W. P. Hornberger, P. S. Hauge, J. M. Shaw, IEEE Trans Electron Devices 22, 445 (1975).
[CrossRef]

See, for example, F. H. Dill, IEEE Trans. Electron Devices ED-22, 440 (1975).
[CrossRef]

Ducommun, J. P.

J. P. Ducommun, M. Cantagrel, M. Moulin, J. Mater. Sci. 10, 52 (1975).
[CrossRef]

J. P. Ducommun, M. Cantagrel, M. Marchal, J. Mater. Sci. 9, 725 (1974).
[CrossRef]

Flanders, D. C.

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651 (1974).
[CrossRef]

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Frank, F. C.

D. J. Barber, F. C. Frank, M. Moss, J. W. Steeds, I. S. T. Tsong, J. Mater. Sci. 8, 1030 (1973).
[CrossRef]

Garmire, E.

H. L. Garvin, E. Garmire, S. Somekh, H. Stoll, A. Yariv, Appl Opt. 12, 455 (1973).
[CrossRef] [PubMed]

H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
[CrossRef]

Garvin, H. L.

H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
[CrossRef]

H. L. Garvin, E. Garmire, S. Somekh, H. Stoll, A. Yariv, Appl Opt. 12, 455 (1973).
[CrossRef] [PubMed]

Gurevich, S. A.

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

Harada, Y.

Y. Tarui, Y. Komiya, Y. Harada, J. Electrochem. Soc. 118, 118 (1971).
[CrossRef]

Hauge, P. S.

F. H. Dill, W. P. Hornberger, P. S. Hauge, J. M. Shaw, IEEE Trans Electron Devices 22, 445 (1975).
[CrossRef]

Heidrich, P. F.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Hornberger, W. P.

F. H. Dill, W. P. Hornberger, P. S. Hauge, J. M. Shaw, IEEE Trans Electron Devices 22, 445 (1975).
[CrossRef]

Iida, S.

S. Iida, K. Ito, J. Electrochem. Soc. 118, 768 (1971).
[CrossRef]

Ilegems, M.

H. C. Casey, S. Somekh, M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).
[CrossRef]

Ito, K.

S. Iida, K. Ito, J. Electrochem. Soc. 118, 768 (1971).
[CrossRef]

Johnson, L. F.

R. C. Miller, W. A. Nordland, R. A. Logan, L. F. Johnson, J. Appl. Phys. (to be published).

Katzir, A.

W. Ng, H. W. Yen, A. Katzir, I. Samid, A. Yariv, Opt. Commun. 18, 215 (1976).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
[CrossRef]

Kazarinov, R. F.

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

Kogelnik, H.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

H. Kogelnik, T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

Komiya, Y.

Y. Tarui, Y. Komiya, Y. Harada, J. Electrochem. Soc. 118, 118 (1971).
[CrossRef]

Kuhn, L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Larionov, V. M.

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

Logan, R. A.

J. L. Merz, R. A. Logan, J. Appl. Phys. 47, 3503 (1976).
[CrossRef]

F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[CrossRef]

R. A. Logan, B. Schwartz, W. J. Sundberg, J. Electrochem. Soc. 120, 1385 (1973).
[CrossRef]

R. C. Miller, W. A. Nordland, R. A. Logan, L. F. Johnson, J. Appl. Phys. (to be published).

Lukyanov, V. N.

V. N. Lukyanov, N. V. Shelkov, S. D. Yakubovitch, Sov. J. Quantum Electron. 5, 99 (1975).
[CrossRef]

Marchal, M.

J. P. Ducommun, M. Cantagrel, M. Marchal, J. Mater. Sci. 9, 725 (1974).
[CrossRef]

Merz, J. L.

J. L. Merz, R. A. Logan, J. Appl. Phys. 47, 3503 (1976).
[CrossRef]

Miller, B. I.

C. V. Shank, R. V. Schmidt, B. I. Miller, Appl. Phys. Lett. 25, 200 (1974).
[CrossRef]

Miller, R. C.

R. C. Miller, W. A. Nordland, R. A. Logan, L. F. Johnson, J. Appl. Phys. (to be published).

Mizerov, M. N.

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

Morikawa, T.

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
[CrossRef]

Morrison, R. E.

R. E. Morrison, Phys Rev. 124, 1314 (1961).
[CrossRef]

Moss, M.

D. J. Barber, F. C. Frank, M. Moss, J. W. Steeds, I. S. T. Tsong, J. Mater. Sci. 8, 1030 (1973).
[CrossRef]

Moulin, M.

J. P. Ducommun, M. Cantagrel, M. Moulin, J. Mater. Sci. 10, 52 (1975).
[CrossRef]

Nakamura, M.

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, Appl. Phys. Lett. 27, 403 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
[CrossRef]

H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
[CrossRef]

Namba, S.

T. Aoyagi, Y. Aoyagi, S. Namba, Appl. Phys. Lett. 29, 303 (1976).
[CrossRef]

Neureuther, A. R.

See, e.g., F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, IEEE Trans Electron Devices 22, 456 (1975).
[CrossRef]

Ng, W.

W. Ng, H. W. Yen, A. Katzir, I. Samid, A. Yariv, Opt. Commun. 18, 215 (1976).
[CrossRef]

Nordland, W. A.

R. C. Miller, W. A. Nordland, R. A. Logan, L. F. Johnson, J. Appl. Phys. (to be published).

Portnoy, E. L.

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

Reinhart, F. K.

F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[CrossRef]

Samid, I.

W. Ng, H. W. Yen, A. Katzir, I. Samid, A. Yariv, Opt. Commun. 18, 215 (1976).
[CrossRef]

Schmidt, P. H.

See, e.g., E. G. Spencer, P. H. Schmidt, J. Vac. Sci. Technol. 8, 552 (1971).
[CrossRef]

Schmidt, R. V.

C. V. Shank, R. V. Schmidt, B. I. Miller, Appl. Phys. Lett. 25, 200 (1974).
[CrossRef]

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651 (1974).
[CrossRef]

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Schwartz, B.

R. A. Logan, B. Schwartz, W. J. Sundberg, J. Electrochem. Soc. 120, 1385 (1973).
[CrossRef]

Scifres, D. R.

R. D. Burnham, D. R. Scifres, W. Streifer, IEEE J. Quantum Electron. QE-11, 439 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 27, 295 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 25, 203 (1974).
[CrossRef]

Scott, B. A.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Shank, C. V.

F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[CrossRef]

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651 (1974).
[CrossRef]

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

C. V. Shank, R. V. Schmidt, B. I. Miller, Appl. Phys. Lett. 25, 200 (1974).
[CrossRef]

Shaw, J. M.

F. H. Dill, W. P. Hornberger, P. S. Hauge, J. M. Shaw, IEEE Trans Electron Devices 22, 445 (1975).
[CrossRef]

Shelkov, N. V.

V. N. Lukyanov, N. V. Shelkov, S. D. Yakubovitch, Sov. J. Quantum Electron. 5, 99 (1975).
[CrossRef]

Somekh, S.

S. Somekh, H. C. Casey, Appl. Opt. 16, 126 (1977).
[CrossRef] [PubMed]

S. Somekh, H. C. Casey, Appl. Opt. 16, 126 (1977).
[CrossRef] [PubMed]

H. C. Casey, S. Somekh, M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).
[CrossRef]

H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
[CrossRef]

H. L. Garvin, E. Garmire, S. Somekh, H. Stoll, A. Yariv, Appl Opt. 12, 455 (1973).
[CrossRef] [PubMed]

S. Somekh, A. Yariv, Appl. Phys. Lett 21, 140 (1972).
[CrossRef]

Sosnowski, T. P.

H. Kogelnik, T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

Spencer, E. G.

See, e.g., E. G. Spencer, P. H. Schmidt, J. Vac. Sci. Technol. 8, 552 (1971).
[CrossRef]

Standley, R. D.

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651 (1974).
[CrossRef]

Steeds, J. W.

D. J. Barber, F. C. Frank, M. Moss, J. W. Steeds, I. S. T. Tsong, J. Mater. Sci. 8, 1030 (1973).
[CrossRef]

Stoll, H.

H. L. Garvin, E. Garmire, S. Somekh, H. Stoll, A. Yariv, Appl Opt. 12, 455 (1973).
[CrossRef] [PubMed]

Streifer, W.

R. D. Burnham, D. R. Scifres, W. Streifer, IEEE J. Quantum Electron. QE-11, 439 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 27, 295 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 25, 203 (1974).
[CrossRef]

Sundberg, W. J.

R. A. Logan, B. Schwartz, W. J. Sundberg, J. Electrochem. Soc. 120, 1385 (1973).
[CrossRef]

Tarui, Y.

Y. Tarui, Y. Komiya, Y. Harada, J. Electrochem. Soc. 118, 118 (1971).
[CrossRef]

Tsang, W. T.

W. T. Tsang, Appl Opt. 16, 1918 (1977).
[CrossRef] [PubMed]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 596 (1976).
[CrossRef]

Tsong, I. S. T.

D. J. Barber, F. C. Frank, M. Moss, J. W. Steeds, I. S. T. Tsong, J. Mater. Sci. 8, 1030 (1973).
[CrossRef]

Tuttle, J. A.

See, e.g., F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, IEEE Trans Electron Devices 22, 456 (1975).
[CrossRef]

Umeda, J.

M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, Appl. Phys. Lett. 27, 403 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
[CrossRef]

Walker, E. J.

See, e.g., F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, IEEE Trans Electron Devices 22, 456 (1975).
[CrossRef]

Wang, S.

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 596 (1976).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), Chap. 13.

Yakubovitch, S. D.

V. N. Lukyanov, N. V. Shelkov, S. D. Yakubovitch, Sov. J. Quantum Electron. 5, 99 (1975).
[CrossRef]

Yariv, A.

W. Ng, H. W. Yen, A. Katzir, I. Samid, A. Yariv, Opt. Commun. 18, 215 (1976).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, Appl. Phys. Lett. 27, 403 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
[CrossRef]

H. L. Garvin, E. Garmire, S. Somekh, H. Stoll, A. Yariv, Appl Opt. 12, 455 (1973).
[CrossRef] [PubMed]

H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
[CrossRef]

S. Somekh, A. Yariv, Appl. Phys. Lett 21, 140 (1972).
[CrossRef]

Yen, H. W.

W. Ng, H. W. Yen, A. Katzir, I. Samid, A. Yariv, Opt. Commun. 18, 215 (1976).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
[CrossRef]

H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
[CrossRef]

Zory, P.

L. Comerford, P. Zory, Appl. Phys. Lett. 25, 208 (1974).
[CrossRef]

Appl Opt.

M. J. Beesley, J. G. Castledine, Appl Opt. 9, 2720 (1970).
[CrossRef] [PubMed]

W. T. Tsang, Appl Opt. 16, 1918 (1977).
[CrossRef] [PubMed]

H. L. Garvin, E. Garmire, S. Somekh, H. Stoll, A. Yariv, Appl Opt. 12, 455 (1973).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett

S. Somekh, A. Yariv, Appl. Phys. Lett 21, 140 (1972).
[CrossRef]

Appl. Phys. Lett.

T. Aoyagi, Y. Aoyagi, S. Namba, Appl. Phys. Lett. 29, 303 (1976).
[CrossRef]

L. Comerford, P. Zory, Appl. Phys. Lett. 25, 208 (1974).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 596 (1976).
[CrossRef]

F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[CrossRef]

H. C. Casey, S. Somekh, M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 27, 295 (1975).
[CrossRef]

C. V. Shank, R. V. Schmidt, B. I. Miller, Appl. Phys. Lett. 25, 200 (1974).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, Appl. Phys. Lett. 27, 403 (1975).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 25, 203 (1974).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Yariv, H. W. Yen, T. Morikawa, Appl. Phys. Lett. 25, 487 (1974).
[CrossRef]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651 (1974).
[CrossRef]

W. T. Tsang, S. Wang, Appl. Phys. Lett. 28, 44 (1976).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

IEEE J. Quantum Electron.

Zh. I. Alferov, V. M. Andreyev, S. A. Gurevich, R. F. Kazarinov, V. M. Larionov, M. N. Mizerov, E. L. Portnoy, IEEE J. Quantum Electron. QE-11, 449 (1975).
[CrossRef]

R. D. Burnham, D. R. Scifres, W. Streifer, IEEE J. Quantum Electron. QE-11, 439 (1975).
[CrossRef]

M. Nakamura, K. Aiki, J. Umeda, A. Katzir, A. Yariv, H. W. Yen, IEEE J. Quantum Electron. QE-11, 436 (1975).
[CrossRef]

IEEE Trans Electron Devices

F. H. Dill, W. P. Hornberger, P. S. Hauge, J. M. Shaw, IEEE Trans Electron Devices 22, 445 (1975).
[CrossRef]

See, e.g., F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, IEEE Trans Electron Devices 22, 456 (1975).
[CrossRef]

IEEE Trans. Electron Devices

See, for example, F. H. Dill, IEEE Trans. Electron Devices ED-22, 440 (1975).
[CrossRef]

J. Appl. Phys.

J. L. Merz, R. A. Logan, J. Appl. Phys. 47, 3503 (1976).
[CrossRef]

J. Electrochem. Soc.

Y. Tarui, Y. Komiya, Y. Harada, J. Electrochem. Soc. 118, 118 (1971).
[CrossRef]

R. A. Logan, B. Schwartz, W. J. Sundberg, J. Electrochem. Soc. 120, 1385 (1973).
[CrossRef]

S. Iida, K. Ito, J. Electrochem. Soc. 118, 768 (1971).
[CrossRef]

J. Mater. Sci.

D. J. Barber, F. C. Frank, M. Moss, J. W. Steeds, I. S. T. Tsong, J. Mater. Sci. 8, 1030 (1973).
[CrossRef]

J. P. Ducommun, M. Cantagrel, M. Marchal, J. Mater. Sci. 9, 725 (1974).
[CrossRef]

J. P. Ducommun, M. Cantagrel, M. Moulin, J. Mater. Sci. 10, 52 (1975).
[CrossRef]

J. Vac. Sci. Technol.

See, e.g., E. G. Spencer, P. H. Schmidt, J. Vac. Sci. Technol. 8, 552 (1971).
[CrossRef]

Opt. Commun.

H. W. Yen, M. Nakamura, E. Garmire, S. Somekh, A. Yariv, H. L. Garvin, Opt. Commun. 9, 35 (1973).
[CrossRef]

W. Ng, H. W. Yen, A. Katzir, I. Samid, A. Yariv, Opt. Commun. 18, 215 (1976).
[CrossRef]

Phys Rev.

R. E. Morrison, Phys Rev. 124, 1314 (1961).
[CrossRef]

Sov. J. Quantum Electron.

V. N. Lukyanov, N. V. Shelkov, S. D. Yakubovitch, Sov. J. Quantum Electron. 5, 99 (1975).
[CrossRef]

Other

R. C. Miller, W. A. Nordland, R. A. Logan, L. F. Johnson, J. Appl. Phys. (to be published).

Differentiation of I∥g/I∥m with respect to c reveals that maximum grating contrast is obtained when beam intensities are equal. (I∥g is the maximum groove intensity; I∥m the intensity midway between grooves.)

The quartz uv objectives were made by Carl Zeiss, Inc. We have found that these lenses deteriorate when used to transmit a laser beam of only a few mW at 3250 Å.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), Chap. 13.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (26)

Fig. 1
Fig. 1

Diagram of incident and reflected waves (displaced for clarity) at photoresist–substrate boundary showing positive directions of p-polarized components.

Fig. 2
Fig. 2

The dependence of the reflectivity at the photoresist (AZ-1350)–GaAs interface on angle of incidence (λ0 = 3250 Å) (See Appendix B).

Fig. 3
Fig. 3

Grating groove intensity within a 2500-Å film of AZ-1350 photoresist on GaAs at angles of incidence in photoresist of 21° and 48° (corresponding to second- and first-order gratings for GaAs lasers). λ0 = 3250 Å, and the intensity of each s-polarized beam is A2.

Fig. 4
Fig. 4

The limit on beam intensity ratio vs substrate reflectivity (see text).

Fig. 5
Fig. 5

Constant-intensity contours for a 2600-Å period grating in a 2500-Å thick film of photoresist on GaAs. The incident beams are of equal intensity, and the contour labeled b shows the profile produced when development is sufficient to just reach the substrate.

Fig. 6
Fig. 6

The same as Fig. 5 but with a beam intensity ratio of c2 = 2.

Fig. 7
Fig. 7

The same as Fig. 5 but with a beam intensity ratio of 3.3.

Fig. 8
Fig. 8

The same as Fig. 5 but with a beam intensity ratio of 4.

Fig. 9
Fig. 9

Grating relief pattern in photoresist on a GaAs substrate. The period is 2600 Å, and 900 Å of resist remains in the groove. Magnification 50k×.

Fig. 10
Fig. 10

Constant-intensity contours just reaching the substrate for a 2600-Å grating on substrates of reflectivity R = 0.01, 0.3, 0.5, and 0.8. The photoresist thickness is 2500 Å, the incident beams are of equal intensity, and the substrates are all of higher refractive index than the resist.

Fig. 11
Fig. 11

SEM photograph of groove profile in photoresist on an aluminum film substrate. The grating period is 5000 Å, and 1700 Å of resist remains in the grooves. Steps appear at heights corresponding approximately to ½-wavelength intervals from the substrate. Magnification 45 k×.

Fig. 12
Fig. 12

Constant-intensity contour just reaching the substrate for a first-order grating in photoresist on GaAs. The incident beams are of equal intensity.

Fig. 13
Fig. 13

The dependence of the restricted range for p-polarized beams on angle of incidence in photoresist and substrate reflection coefficient. The dashed line shows the magnitude of the reflection coefficient for GaAs.

Fig. 14
Fig. 14

Location of grating antinodes in photoresist at angles of incidence corresponding to P, Q,…, in Fig. 13. The beams are p- polarized, and the size of the dots indicate antinode intensity.

Fig. 15
Fig. 15

Experimental arrangement for interferometric exposure of photoresist.

Fig. 16
Fig. 16

Chemically etched grating showing the result of spatial variation in incident beam intensity with the single spatial filter arrangement (Λ = 2580 Å).

Fig. 17
Fig. 17

Ion-beam milling rates of GaAs and AZ-1350 photoresist vs angle of incidence (taken from Somekh and Casey30).

Fig. 18
Fig. 18

The evolution of a sinusoidal grating profile in photoresist subjected to ion-beam milling: (a) grating depth d < Λ; (b) d > Λ (after Ducommun et al.33).

Fig. 19
Fig. 19

Erosion of grating profile in photoresist under ion-beam milling, showing the trajectory of facet erosion V(θp) and the true erosion rate relative to the substrate VN.

Fig. 20
Fig. 20

Ion-beam milling parallel to the grooves in photoresist with the substrate tilted at an angle ϕ (see text).

Fig. 21
Fig. 21

Erosion of photoresist and groove development in GaAs under ion-beam milling at tilt angles of (a) 35° and (b) 60°.

Fig. 22
Fig. 22

Erosion of grating profile not developed down to the substrate for tilt angles of (a) ϕ = 58°, (b) ϕ = 62°.

Fig. 23
Fig. 23

SEM photograph of grating in resist on GaAs, ion-beam milled at 58° tilt. Λ = 2600 Å.

Fig. 24
Fig. 24

SEM photographs of the development of chemically etched rectangular grooves along the [010] direction on the (100) plane of GaAs. Ion-beam milling (to reach the substrate) at a tilt angle ϕ = 50° has produced shallow facets on the photoresist remaining between the grooves. The etch times are 30 sec, 40 sec, and 60 sec for (a)–(c). A = 2580 Å; magnification 50 k×.

Fig. 25
Fig. 25

SEM photographs of the development of chemically etched V-grooves along the [ 01 1 ¯ ] direction on GaAs (100). The etch times are 15 sec, 30 sec, 60 sec, and 90 sec for (a)–(d). Λ = 2580 Å, and the magnification is 50 k× for (a)–(c), 45 k× for (d).

Fig. 26
Fig. 26

Undercutting of resist in the removal of a quarterwave oxide layer by an isotropic chemical etch.

Equations (45)

Equations on this page are rendered with MathJax. Learn more.

A x = A cos θ 1 exp ( i α i ) , A y = A exp ( i α i ) , A z = A sin θ 1 exp ( i α i ) , B x = B cos θ 1 exp ( i β i ) , B y = B exp ( i β i ) , B z = B sin θ 1 exp ( i β i ) ,
α i = ω t K x sin θ 1 + K z cos θ 1 δ , β i = ω t + K x sin θ 1 + K z cos θ 1 + δ , K = ( 2 π n 1 ) / λ 0 , 2 δ = phase difference between A ̅ and B ̅ at the origin .
A x r = r A cos θ 1 exp ( i α r ) , A y r = r A exp ( i α r ) , A z r = r A sin θ 1 exp ( i α r ) , B x r = r B cos θ 1 exp ( i β r ) , B y r = r B exp ( i β r ) , B z r = r B sin θ 1 exp ( i β r ) ,
α r = ω t K x sin θ 1 K z cos θ 1 δ , β r = ω t + K x sin θ 1 K z cos θ 1 + δ ,
r = n 2 cos θ 1 n 1 cos θ 2 n 2 cos θ 1 + n 1 cos θ 2 r = n 1 cos θ 1 n 2 cos θ 2 n 2 cos θ 1 + n 2 cos θ 2 .
E x = A x + A x r + B x + B x r = ( r 1 ) ( A B ) cos θ 1 exp ( i α i ) + 2 ( r 1 ) B cos θ 1 cos ( K x sin θ 1 ) exp [ i ( ω t + K z cos θ 1 ) ] + 2 r ( A B ) cos θ 1 sin ( K z sin θ 1 ) × exp [ i ( ω t K x sin θ 1 π 2 ) ] + 4 r B cos θ 1 cos ( K x sin θ 1 ) sin ( K z cos θ 1 ) exp [ i ( ω t π 2 ) ] ,
E y = A y + A y r + B y + B y r = 1 ( 1 + r ) ( A B ) exp ( i α i ) + 2 ( 1 + r ) B cos ( K x sin θ 1 ) exp [ i ( ω t + K z cos θ 1 ) ] + 2 r ( A B ) sin ( K z cos θ 1 ) exp [ i ( ω t + K x sin θ 1 π 2 ) ] + 4 r B cos ( K x sin θ 1 ) sin ( K z cos θ 1 ) exp [ i ( ω t π 2 ) ] ,
E z = A z + A z r + B z + B z r = ( r 1 ) ( A B ) sin θ 1 exp ( i α i ) + 2 ( r 1 ) B sin θ 1 sin ( K x sin θ 1 ) exp [ i ( ω t + K z cos θ 1 π 2 ) ] 2 r ( A B ) sin θ 1 cos ( K z cos θ 1 ) exp [ i ( ω t K x sin θ 1 ) ] 4 r B sin θ 1 sin ( K x sin θ 1 ) cos ( K z cos θ 1 ) exp [ i ( ω t π 2 ) ] .
E y E y * = A 2 + r 2 A 2 + B 2 + r 2 B 2 + 2 ( 1 + r 2 ) A B cos ( 2 K x sin θ 1 ) + 2 ( r A 2 + r B 2 ) cos ( 2 K z cos θ 1 ) + 4 r A B cos ( 2 K x sin θ 1 ) cos ( 2 k z cos θ 1 ) ,
E x E x * + E z E z * = A 2 + r 2 A 2 + B 2 + r 2 B 2 + 2 ( 1 + r 2 ) A B ( 1 2 sin 2 θ 1 ) cos ( 2 K x sin θ 1 ) 2 ( r A 2 + r B 2 ) ( 1 2 sin 2 θ 1 ) cos ( 2 K z cos θ 1 ) 4 r A B cos ( 2 K x sin θ 1 ) cos ( 2 k z cos θ 1 ) .
I n 1 2 8 π ( E x E x * + E z E z * ) , I = n 1 2 8 π E y E y * .
X = ( m λ 0 ) / ( 2 n 1 sin θ 1 ) , m = 0 , 1 , 2 , . . . .
z cos θ 1 = ( 2 m + 1 ) [ λ 0 / ( 4 n 1 ) ] , m = 0 , 1 , 2 , . . . ,
z cos θ 1 = m [ λ 0 / ( 2 n 1 ) ] , m = 0 , 1 , 2 , . . .
I g ( z max ) ( 1 + c ) 2 ( 1 + | r | ) 2 A 2 ,
I g ( z min ) ( 1 + c ) 2 ( 1 | r | ) 2 A 2 .
I g ( 1 + c ) 2 [ A 2 + r 2 A 2 + 2 r A 2 cos ( 2 K z cos θ 1 ) ] , I m ( 1 c ) 2 [ A 2 + r 2 A 2 + 2 r A 2 cos ( 2 K z cos θ 1 ) ] ,
I g I m = ( 1 + c ) 2 ( 1 c ) 2 .
I m ( z max ) ( 1 c ) 2 ( 1 + | r | ) 2 A 2 , I g ( z min ) ( 1 + c ) 2 ( 1 | r | ) 2 A 2 ,
I ( 1 + c 2 ) ( 1 + r 2 ) A 2 + 2 β c A 2 cos ( 2 K x sin θ 1 ) 2 δ A 2 cos ( 2 K z cos θ 1 ) ,
β = ( 1 + r 2 ) ( 1 2 sin 2 θ 1 ) 2 r cos ( 2 K z cos θ 1 ) , δ = ( 1 + c 2 ) r ( 1 2 sin 2 θ 1 ) ,
2 r cos ( 2 K z cos θ 1 ) < ( 1 + r 2 ) ( 1 2 sin 2 θ 1 )
sin θ 1 < 1 2 1 | r | ( 1 + r 2 ) 1 / 2 .
2 r cos ( 2 K z cos θ 1 ) > ( 1 + r 2 ) ( 1 2 sin 2 θ 1 )
sin θ 1 > 1 2 1 + | r | ( 1 + r 2 ) 1 / 2 .
I g ( z max ) I g ( z min ) = 1 + r 2 + 2 γ 1 | r | 1 + r 2 2 γ 1 | r | ,
γ 1 = ( 1 + c ) 2 2 ( 1 + c 2 ) sin 2 θ 1 ( 1 + c ) 2 4 c sin 2 θ 1 .
I g ( z max ) I g ( z min ) = ( 1 + | r | 1 | r | ) 2 .
I g ( z max ) I g ( z min ) = 1 + r 2 2 γ 2 | r | 1 + r 2 + 2 γ 2 | r | ,
γ 2 = ( 1 c ) 2 2 ( 1 + c 2 ) sin 2 θ 1 ( 1 c ) 2 + 4 c sin 2 θ 1 .
I g ( z max ) I g ( z min ) = ( 1 + | r | 1 | r | ) 2 .
V N = V ( θ p ) cos θ p = V ( θ p ) cos 60 ° = 2 V ( θ p ) .
cos θ ( ϕ ) = ( cos ψ ) / ( cos ϕ ) .
θ ( ϕ ) = cos 1 ( cos 60 ° cos 35 ° ) = 52.4 ° .
V N ( resist ) = V ( ψ ) cos θ ( ϕ ) ,
V N ( resist ) = 900 Å / min cos 52.4 ° 1480 Å / min .
V N ( GaAs ) = V ( θ p ) GaAs = 1520 A ˚ / min .
A exp ( α 2 h z cos θ 1 )
r A exp ( α 2 h + z cos θ 1 )
I ( A 2 + B 2 ) exp ( α h z cos θ 1 ) [ 1 + r 2 exp ( 2 α z cos θ 1 ) ] + 2 A B exp ( α h z cos θ 1 ) [ 1 + r 2 exp ( 2 α z cos θ 1 ) ] × cos ( 2 K x sin θ 1 ) + 2 ( r A 2 + r B 2 ) × exp ( α h cos θ 1 ) cos ( 2 K z cos θ 1 ) + 4 r A B × exp ( α h cos θ 1 ) cos ( 2 K x sin θ 1 ) cos ( 2 K z cos θ 1 ) ,
I ( A 2 + B 2 ) exp ( α h z cos θ 1 ) [ 1 + r 2 exp ( 2 α z cos θ 1 ) ] + 2 A B exp ( α h z cos θ 1 ) [ 1 + r 2 exp ( 2 α z cos θ 1 ) ] × ( 1 2 sin 2 θ 1 ) cos ( 2 K x sin θ 1 ) 2 ( r A 2 + r B 2 ) × exp ( α h cos θ 1 ) ( 1 2 sin 2 θ 1 ) cos ( 2 K z cos θ 1 ) × 4 r A B exp ( α h cos θ 1 ) cos ( 2 K z sin θ 1 ) cos ( 2 K z cos θ 1 ) .
R = ( n 1 cos θ 1 u 2 ) 2 + υ 2 2 ( n 1 cos θ 1 + u 2 ) 2 + υ 2 2 ,
R = [ n 2 2 ( 1 k 2 2 ) cos θ 1 n 1 u 2 ] 2 + ( 2 n 2 2 k 2 cos θ 1 n 1 υ 2 ) 2 [ n 2 2 ( 1 k 2 2 ) cos θ 1 + n 1 u 2 ] 2 + ( 2 n 2 2 k 2 cos θ 1 + n 1 υ 2 ) 2 ,
2 u 2 2 = n 2 2 ( 1 k 2 2 ) n 1 2 sin 2 θ 1 + { [ n 2 2 ( 1 k 2 2 ) n 1 2 sin 2 θ 1 ] 2 + 4 n 2 4 k 2 2 } 1 / 2 , 2 υ 2 2 = [ n 2 2 ( 1 k 2 2 ) n 1 2 sin 2 θ 1 ] + { [ n 2 2 ( 1 k 2 2 ) n 1 2 sin 2 θ 1 ] 2 + 4 n 2 4 k 2 2 } 1 / 2 .
n ̅ 2 cos θ 2 = u 2 + i υ 2 ,

Metrics