Abstract

A review of the theory of absorption on microscopic and macroscopic levels is given. This theory is then applied to the absorption of UV light by diazo-type positive photoresist during exposure. A formal treatment of the properties of polychromatic light is given. Using these analyses, the effects of polychromatic exposure of a photoresist are derived. Finally, experimental verification of Beer’s law and determination of the exposure quantum efficiency of a particular photoresist is given.

© 1988 Optical Society of America

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References

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  1. D. A. Skoog, D. M. West, Fundamentals of Analytical Chemistry (Holt, Rinehart, & Winston, New York, 1976), pp. 509–510.
  2. J. M. Koyler et al., “Thermal Properties of Positive Photoresist and Their Relationship to VLSI Processing,” in Proceedings, Kodak Microelectronic Interface ’79 (Oct.1979), pp. 150–165.
  3. J. M. Shaw, M. A. Frisch, F. H. Dill, “Thermal Analysis of Positive Photoresist Films by Mass Spectrometry,” IBM J. Res. Dev. 21, 219 (1977).
    [CrossRef]
  4. F. H. Dill et al., “Characterization of Positive Photoresist,” IEEE Trans. Electron Dev. ED-22, 445 (1975).
    [CrossRef]
  5. W. J. Moore, Physical Chemistry (Prenctice Hall, Englewood Cliffs, NJ, 1972), pp. 753–755.
  6. G. Bachur, “Development of Optical Measurement and Control Systems for Photolithography,” Proc. Soc. Photo-Opt. Instrum. Eng. 80, 2 (1976).
  7. A. Minvielle, R. Rice, “Spectral Output Variations in Perkin-Elmer Micraligns,” in Proceedings, Kodak Microelectronic Interface ’79 (Oct.1979), pp. 60–65.
  8. C. A. Mack, “Analytical Expression for the Standing Wave Intensity in Photoresist,” Appl. Opt. 25, 1958 (1986).
    [CrossRef] [PubMed]
  9. J. Albers, D. B. Novotny, “Intensity Dependence of Photo-chemical Reaction Rates for Photoresists,” J. Electrochem. Soc. 127, 1400, (1980).
    [CrossRef]
  10. C. A. Mack, “PROLITH: A Comprehensive Optical Lithography Model,” Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207 (1985).
  11. Reichhold Chemicals, Inc., Warren, NJ 07060.
  12. Fairmount Chemical Co., Inc., Newark, NJ 07105.

1986

1985

C. A. Mack, “PROLITH: A Comprehensive Optical Lithography Model,” Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207 (1985).

1980

J. Albers, D. B. Novotny, “Intensity Dependence of Photo-chemical Reaction Rates for Photoresists,” J. Electrochem. Soc. 127, 1400, (1980).
[CrossRef]

1979

J. M. Koyler et al., “Thermal Properties of Positive Photoresist and Their Relationship to VLSI Processing,” in Proceedings, Kodak Microelectronic Interface ’79 (Oct.1979), pp. 150–165.

1977

J. M. Shaw, M. A. Frisch, F. H. Dill, “Thermal Analysis of Positive Photoresist Films by Mass Spectrometry,” IBM J. Res. Dev. 21, 219 (1977).
[CrossRef]

1976

G. Bachur, “Development of Optical Measurement and Control Systems for Photolithography,” Proc. Soc. Photo-Opt. Instrum. Eng. 80, 2 (1976).

1975

F. H. Dill et al., “Characterization of Positive Photoresist,” IEEE Trans. Electron Dev. ED-22, 445 (1975).
[CrossRef]

Albers, J.

J. Albers, D. B. Novotny, “Intensity Dependence of Photo-chemical Reaction Rates for Photoresists,” J. Electrochem. Soc. 127, 1400, (1980).
[CrossRef]

Bachur, G.

G. Bachur, “Development of Optical Measurement and Control Systems for Photolithography,” Proc. Soc. Photo-Opt. Instrum. Eng. 80, 2 (1976).

Dill, F. H.

J. M. Shaw, M. A. Frisch, F. H. Dill, “Thermal Analysis of Positive Photoresist Films by Mass Spectrometry,” IBM J. Res. Dev. 21, 219 (1977).
[CrossRef]

F. H. Dill et al., “Characterization of Positive Photoresist,” IEEE Trans. Electron Dev. ED-22, 445 (1975).
[CrossRef]

Frisch, M. A.

J. M. Shaw, M. A. Frisch, F. H. Dill, “Thermal Analysis of Positive Photoresist Films by Mass Spectrometry,” IBM J. Res. Dev. 21, 219 (1977).
[CrossRef]

Koyler, J. M.

J. M. Koyler et al., “Thermal Properties of Positive Photoresist and Their Relationship to VLSI Processing,” in Proceedings, Kodak Microelectronic Interface ’79 (Oct.1979), pp. 150–165.

Mack, C. A.

C. A. Mack, “Analytical Expression for the Standing Wave Intensity in Photoresist,” Appl. Opt. 25, 1958 (1986).
[CrossRef] [PubMed]

C. A. Mack, “PROLITH: A Comprehensive Optical Lithography Model,” Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207 (1985).

Minvielle, A.

A. Minvielle, R. Rice, “Spectral Output Variations in Perkin-Elmer Micraligns,” in Proceedings, Kodak Microelectronic Interface ’79 (Oct.1979), pp. 60–65.

Moore, W. J.

W. J. Moore, Physical Chemistry (Prenctice Hall, Englewood Cliffs, NJ, 1972), pp. 753–755.

Novotny, D. B.

J. Albers, D. B. Novotny, “Intensity Dependence of Photo-chemical Reaction Rates for Photoresists,” J. Electrochem. Soc. 127, 1400, (1980).
[CrossRef]

Rice, R.

A. Minvielle, R. Rice, “Spectral Output Variations in Perkin-Elmer Micraligns,” in Proceedings, Kodak Microelectronic Interface ’79 (Oct.1979), pp. 60–65.

Shaw, J. M.

J. M. Shaw, M. A. Frisch, F. H. Dill, “Thermal Analysis of Positive Photoresist Films by Mass Spectrometry,” IBM J. Res. Dev. 21, 219 (1977).
[CrossRef]

Skoog, D. A.

D. A. Skoog, D. M. West, Fundamentals of Analytical Chemistry (Holt, Rinehart, & Winston, New York, 1976), pp. 509–510.

West, D. M.

D. A. Skoog, D. M. West, Fundamentals of Analytical Chemistry (Holt, Rinehart, & Winston, New York, 1976), pp. 509–510.

Appl. Opt.

IBM J. Res. Dev.

J. M. Shaw, M. A. Frisch, F. H. Dill, “Thermal Analysis of Positive Photoresist Films by Mass Spectrometry,” IBM J. Res. Dev. 21, 219 (1977).
[CrossRef]

IEEE Trans. Electron Dev.

F. H. Dill et al., “Characterization of Positive Photoresist,” IEEE Trans. Electron Dev. ED-22, 445 (1975).
[CrossRef]

J. Electrochem. Soc.

J. Albers, D. B. Novotny, “Intensity Dependence of Photo-chemical Reaction Rates for Photoresists,” J. Electrochem. Soc. 127, 1400, (1980).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

C. A. Mack, “PROLITH: A Comprehensive Optical Lithography Model,” Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207 (1985).

G. Bachur, “Development of Optical Measurement and Control Systems for Photolithography,” Proc. Soc. Photo-Opt. Instrum. Eng. 80, 2 (1976).

Proceedings, Kodak Microelectronic Interface ’79

J. M. Koyler et al., “Thermal Properties of Positive Photoresist and Their Relationship to VLSI Processing,” in Proceedings, Kodak Microelectronic Interface ’79 (Oct.1979), pp. 150–165.

Other

D. A. Skoog, D. M. West, Fundamentals of Analytical Chemistry (Holt, Rinehart, & Winston, New York, 1976), pp. 509–510.

W. J. Moore, Physical Chemistry (Prenctice Hall, Englewood Cliffs, NJ, 1972), pp. 753–755.

Reichhold Chemicals, Inc., Warren, NJ 07060.

Fairmount Chemical Co., Inc., Newark, NJ 07105.

A. Minvielle, R. Rice, “Spectral Output Variations in Perkin-Elmer Micraligns,” in Proceedings, Kodak Microelectronic Interface ’79 (Oct.1979), pp. 60–65.

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Figures (5)

Fig. 1
Fig. 1

Photoresist absorption parameters A and B as a function of wavelength for AZ1350J.

Fig. 2
Fig. 2

Geometry used to compare macroscopic and microscopic absorption.

Fig. 3
Fig. 3

Typical mercury arc lamp spectrum and a detector response curve.

Fig. 4
Fig. 4

Part of the mercury arc lamp spectrum that is seen by the detector in Fig. 3.

Fig. 5
Fig. 5

Verification of Beer’s law for an experimental positive photoresist.

Tables (2)

Tables Icon

Table I Measured and Calculated Parameters for an Experimental Photoresist

Tables Icon

Table II Absorption and Exposure Parameters for Commercial Photoresists

Equations (64)

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d I d z = - α I ,
I ( z ) = I 0 exp ( - α z ) ,
I ( z ) = I 0 exp ( - abs ) ,
n = n - i K .
α = 4 π K / λ .
α solution = a c ,
α T = j = 1 N a j c j .
I A i I A T = ( a i c i α T ) ,
α = a M M + a P P + a R R + a S S .
P = M 0 - M .
α = A m + B ,
α exposed = B .
α umexposed = A + B .
α diff = α umexposed - α exposed = A .
M UV P .
Δ Φ M = N M B E ( λ ) J ( λ ) d λ ,
Φ M = N M 0 B E ( λ ) J ( λ ) d λ .
I A M = ( I 0 - I T ) ( a M M α ) .
Δ Φ M = λ S h c ( I 0 - I T ) ( a M M α ) ,
λ S h c ( I 0 - I T ) ( a M M α ) = N M B E ( λ ) J ( λ ) d λ .
a M M λ N A h c α ( I 0 - I T Δ z ) = M B E ( λ ) J ( λ ) d λ .
lim Δ z 0 ( I 0 - I T Δ z ) = - d I d z = α I .
a M λ N A h c M J ( λ ) d λ = M B E ( λ ) J ( λ ) d λ .
B E ( λ ) = a M λ N A h c .
B E ( λ ) = ( 4 π ( M W ) M ρ M N A h c ) K M .
A E ( λ ) = 8 π h c 2 n 2 λ 5 B E ( λ ) .
A E = 8 π c n 2 N A 0 a M λ 4 d λ .
I T = 0 J ( λ ) d λ .
I ( λ 0 ) = 0 t ( λ ) J ( λ ) d λ ,
I ( λ 0 ) = T J ( λ 0 ) Δ λ .
I R ( λ 0 ) I ( λ 0 ) / I ( 365 nm ) = J ( λ 0 ) / ( 365 nm ) ,
J ( λ ) = I R ( λ ) J ( 365 nm ) .
I M = 0 S D ( λ ) J ( λ ) d λ ,
I M = J ( 365 nm ) 0 S D ( λ ) I R ( λ ) d λ ,
J ( λ ) = I M I R ( λ ) 0 S D ( λ ) I R ( λ ) d λ .
I T = I M 0 I R ( λ ) d λ 0 S D ( λ ) I R ( λ ) d λ .
I T ( z ) = 0 J ( z , λ ) d λ .
J ( z , λ ) = J 0 ( λ ) T 12 exp [ - α ( λ ) z ] ,
I T ( z ) = I M T 12 0 exp [ - α ( λ ) z ] I R ( λ ) d λ 0 S D ( λ ) I R ( λ ) d λ .
I T ( z ) = I 0 exp ( - α z ) ,
I 0 = I M T 12 0 I R ( λ ) d λ 0 S D ( λ ) I R ( λ ) d λ .
J ( z , λ ) = J 0 ( λ ) T 12 exp ( - i k z ) + ρ 23 t D 2 exp ( i k z ) 2 1 + ρ 12 ρ 23 τ D 2 2 ,
M k 2 k 1 M * k 3 P ,
d M d t = k 2 M * - k 1 M , d M * d t = k 1 M - ( k 2 + k 3 ) M * , d P d t = k 3 M * .
M ( t = 0 ) = M 0 , M * ( t = 0 ) = P ( t = 0 ) = 0.
d M * d t = 0.
d M d t = - K M ,
K = k 1 k 3 k 2 + k 3 .
M = M 0 exp ( - K t ) .
Φ = molecules of M converted to M * number of photons aborbed by M ,
d M * d t ( generated ) = M 0 Φ ( λ ) B E ( λ ) J ( λ ) d λ .
k 1 = 0 Φ ( λ ) B E ( λ ) J ( λ ) d λ .
M * k 2 M ,
k 2 = A E + k q + 0 B E ( λ ) J ( λ ) d λ ,
k 2 = A E .
K = 0 C ( λ ) J ( λ ) d λ ,
C ( λ ) = k 3 Φ ( λ ) B E ( λ ) A E + k 3 Φ T ( λ ) B E ( λ ) ,
M = M 0 exp [ - t 0 C ( λ ) J ( λ ) d λ ] .
M = M 0 exp - ( C I t ) .
Φ T ( λ ) = N A h c C ( λ ) a M ( λ ) λ .
I eff ( z ) = 0 S R ( λ ) J ( z , λ ) d λ ,
S R ( λ ) = Φ T ( λ ) a M ( λ ) M = N A h c M C ( λ ) λ .
m = exp ( - C eff I M t ) ,
C eff = 0 C ( λ ) I R ( λ ) d λ 0 S D ( λ ) I R ( λ ) d λ .

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