Abstract

When a thin dielectric film placed between two semi-infinite media is irradiated with monochromatic plane waves, a standing wave is produced in the film. An analytical expression for the standing wave intensity within the film is derived. This expression is then expanded to include the effects of other dielectric films on either side of the film or an inhomogeneous film. Applications of these expressions are given for photolithographic modeling.

© 1986 Optical Society of America

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References

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  1. S. Middlehoek, “Projection Masking, Thin Photoresist Layers and Interference Effects,” IBM J. Res. Dev. 14, 117 (Mar.1970).
  2. J. E. Korka, “Standing Waves in Photoresists,” Appl. Opt. 9, 969 (1970).
  3. D. F. Ilten, K. V. Patel, “Standing Wave Effects in Photoresist Exposure,” Image Technol. 9 (Feb/Mar.1971).
  4. D. W. Widmann, “Quantitative Evaluation of Photoresist Patterns in the 1-μm Range,” Appl. Opt. 14, 931 (1975).
  5. F. H. Dill, “Optical Lithography,” Trans. Electron Dev. ED-22, 440 (July1975).
  6. B. F. Griffing, P. R. West, “Contrast Enhanced Lithography,” Solid State Tech. 28, 152 (May1985).
  7. C. A. Mack, “PROLITH: A Comprehensive Optical Lithography Model,” Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207 (1985).
  8. P. H. Berning, “Theory and Calculations of Optical Thin Films,” Physics of Thin Films, George Hass, Ed. (Academic, New York, 1963), pp. 69–121.

1985 (2)

B. F. Griffing, P. R. West, “Contrast Enhanced Lithography,” Solid State Tech. 28, 152 (May1985).

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

1975 (2)

F. H. Dill, “Optical Lithography,” Trans. Electron Dev. ED-22, 440 (July1975).

D. W. Widmann, “Quantitative Evaluation of Photoresist Patterns in the 1-μm Range,” Appl. Opt. 14, 931 (1975).

1971 (1)

D. F. Ilten, K. V. Patel, “Standing Wave Effects in Photoresist Exposure,” Image Technol. 9 (Feb/Mar.1971).

1970 (2)

S. Middlehoek, “Projection Masking, Thin Photoresist Layers and Interference Effects,” IBM J. Res. Dev. 14, 117 (Mar.1970).

J. E. Korka, “Standing Waves in Photoresists,” Appl. Opt. 9, 969 (1970).

Berning, P. H.

P. H. Berning, “Theory and Calculations of Optical Thin Films,” Physics of Thin Films, George Hass, Ed. (Academic, New York, 1963), pp. 69–121.

Dill, F. H.

F. H. Dill, “Optical Lithography,” Trans. Electron Dev. ED-22, 440 (July1975).

Griffing, B. F.

B. F. Griffing, P. R. West, “Contrast Enhanced Lithography,” Solid State Tech. 28, 152 (May1985).

Ilten, D. F.

D. F. Ilten, K. V. Patel, “Standing Wave Effects in Photoresist Exposure,” Image Technol. 9 (Feb/Mar.1971).

Korka, J. E.

Mack, C. A.

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

Middlehoek, S.

S. Middlehoek, “Projection Masking, Thin Photoresist Layers and Interference Effects,” IBM J. Res. Dev. 14, 117 (Mar.1970).

Patel, K. V.

D. F. Ilten, K. V. Patel, “Standing Wave Effects in Photoresist Exposure,” Image Technol. 9 (Feb/Mar.1971).

West, P. R.

B. F. Griffing, P. R. West, “Contrast Enhanced Lithography,” Solid State Tech. 28, 152 (May1985).

Widmann, D. W.

Appl. Opt. (2)

IBM J. Res. Dev. (1)

S. Middlehoek, “Projection Masking, Thin Photoresist Layers and Interference Effects,” IBM J. Res. Dev. 14, 117 (Mar.1970).

Image Technol. (1)

D. F. Ilten, K. V. Patel, “Standing Wave Effects in Photoresist Exposure,” Image Technol. 9 (Feb/Mar.1971).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

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

Solid State Tech. (1)

B. F. Griffing, P. R. West, “Contrast Enhanced Lithography,” Solid State Tech. 28, 152 (May1985).

Trans. Electron Dev. (1)

F. H. Dill, “Optical Lithography,” Trans. Electron Dev. ED-22, 440 (July1975).

Other (1)

P. H. Berning, “Theory and Calculations of Optical Thin Films,” Physics of Thin Films, George Hass, Ed. (Academic, New York, 1963), pp. 69–121.

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Figures (3)

Fig. 1
Fig. 1

Geometry used in the derivation of the standing wave intensity.

Fig. 2
Fig. 2

Standing wave intensity within a photoresist film at the start of exposure (calculated using the parameters given in Table I) The intensity shown is relative to the incident intensity I0.

Fig. 3
Fig. 3

Predicted resist profile using the standing wave intensity shown in Fig. 2 (calculated using the model PROLITH7).

Tables (1)

Tables Icon

Table I Typical Parameters for Photoresist Projection Printing. λ = 436 nm

Equations (28)

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E z ( x , y , z ) = E I ( x , y ) τ 12 exp ( - i k 2 z ) + ρ 23 τ D 2 exp ( i k 2 z ) 1 + ρ 12 ρ 23 τ D 2 ,
I ( z ) = I 0 T 12 exp ( - a z ) 1 + g ( D - z ) + ρ 23 2 exp [ - a 2 ( D - z ) ] 1 + ρ 12 g ( D ) + ρ 12 2 ρ 23 2 exp ( - a 2 D ) ,
E 2 ( x , y , z ) = E I ( x , y ) τ 12 exp ( - i k 2 z ) + ρ 23 τ D 2 2 exp ( i k 2 z ) 1 + ρ 12 ρ 23 τ D 2 2 ,
ρ 23 = n 2 - n 3 X 3 n 2 + n 3 X 3 , X 3 = 1 - ρ 34 τ D 3 2 1 + ρ 34 τ D 3 2 , ρ 34 = n 3 - n 4 X 4 n 3 + n 4 X 4 , X m = 1 - ρ m , m + 1 τ D m 2 1 + ρ m , m + 1 τ D m 2 , ρ m , m + 1 = n m - n m + 1 n m + n m + 1 , τ D j = exp ( - i k j D j ) ;
E j ( x , y , z ) = E I ( eff ) τ j - 1 j * exp ( - i k j z j ) + ρ j , j + 1 τ D j 2 exp ( i k j z j ) 1 + ρ j - 1 , j * ρ j , j + 1 τ D j 2 ,
ρ j - 1 , j * = n j - 1 Y j - 1 - n j n j - 1 Y j - 1 + n j ; Y j - 1 = 1 + ρ j - 2 , j - 1 * τ D j - 1 2 1 - ρ j - 2 , j - 1 * τ D j - 1 2 ; ρ 23 * = n 2 Y 2 - n 3 n 2 Y 2 + n 3 ; Y 2 = 1 + ρ 12 τ D 2 2 1 - ρ 12 τ D 2 2 ; ρ 12 = n 1 - n 2 n 1 + n 2 ; E I ( eff ) = E I τ 12 τ D 2 1 + ρ 12 τ D 2 2 τ 23 * τ D 3 1 + ρ 23 * τ D 3 2 τ j - 2 , j - 1 * τ D j - 1 1 + ρ j - 2 , j - 1 * τ D j - 1 2 ;
A ( z ) = 0 z α ( z ) d z .
I ( z ) = I 0 T 12 exp [ - A ( z ) ] 1 + g ( D - z ) + ρ 23 2 exp [ - 2 A ( D - z ) ] 1 + ρ 23 g ( D ) + ρ 12 2 ρ 23 2 exp [ - 2 A ( D ) ] ,
α ( z ) = A m ( z ) + B ,
m ( z ) = exp [ - c I ( z ) t ] ,
E j ( x , y , z ) = E ( x , y ) [ A j exp ( - i k j z ) + B j exp ( i k j z ) ] ,
H j ( x , y , z ) = 1 η j E ( x , y ) [ A j exp ( - i k j z ) - B j exp ( i k j z ) ] ,
E 1 ( x , y , 0 ) = E 2 ( x , y , 0 ) ,
H 1 ( x , y , 0 ) = H 2 ( x , y , 0 ) ,
E 2 ( x , y , D ) = E 3 ( x , y , D ) ,
H 2 ( x , y , D ) = H 3 ( x , y , D ) .
A 1 + B 1 = A 2 + B 2 ,
n 1 ( A 1 - B 1 ) = n 2 ( A 2 + B 2 ) ,
A 2 exp ( - i k 2 D ) + B 2 exp ( i k 2 D ) = A 3 exp ( - i k 3 D ) ,
n 2 [ A 2 exp ( - i k 2 D ) - B 2 exp ( i k 2 D ) ] = n 3 A 3 exp ( - i k 3 D ) .
E 2 ( x , y , z ) = E I ( x , y ) τ 12 exp ( - i k 2 z ) + ρ 23 τ D 2 exp ( i k 2 z ) 1 + ρ 12 ρ 23 τ D 2 ,
E 0 ( z ) = E I τ 12 exp ( i k 2 z ) ,
E 1 ( z ) = ρ 23 E 0 ( D ) exp [ i k 2 ( z - D ) ] = E I ρ 23 τ 12 τ D 2 exp ( i k 2 z ) .
E 2 ( z ) = E I ρ 21 ρ 23 τ 12 τ D 2 exp ( - i k 2 z ) .
E 3 ( z ) = E I ρ 21 ρ 23 2 τ 12 τ D 4 exp ( i k 2 z ) , E 4 ( z ) = E I ρ 21 2 ρ 23 2 τ 12 τ D 4 exp ( - i k 2 z ) ,
E T ( z ) = E I τ 12 [ exp ( - i k 2 z ) + ρ 23 τ D 2 exp ( i k 2 z ) ] S ,
S = 1 / ( 1 - ρ 21 ρ 23 τ D 2 ) = 1 / ( 1 + ρ 12 ρ 23 τ D 2 ) .
E T ( x , y , z ) = E I ( x , y ) τ 12 exp ( - i k 2 z ) + ρ 23 τ D 2 exp ( i k 2 z ) 1 + ρ 12 ρ 23 τ D 2 ,

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