Purpose: Explain the top 10 phenomena and concepts key to

Transcription

1 Basic rojection rinting (B) Modules urpose: Explain the top 10 phenomena and concepts key to understanding optical projection printing B-1: Resolution and Depth of Focus (1.5X) B-2: Bragg condition and Mask scattering (1.5X) B-3: Electric fields and Intensity (1.5X) B-4: Coupling and Standing Waves in resist (2X) B-5: artial Coherence B-6: Integral Representation of Fresnel and Fraunhoffer Each module is a min presentation of about a dozen slides. Suggested reading: Griffin: lummer, Deal and Chapter 5 Sheats and Smith: , , , , 121 Wong: 31-45, 55-58, 83

2 Qualitative Explanation of image degradation by lens Mask + 2 lens wafer plane +1 φ 0 parallel optical beam - -1 grating with θ 2 spatial frequency 1/ sin φ n n 0, ± 1, ± 2,... L S l m 2L sin φ <oflens

3 Bragg Condition Incident ray with wave fronts L S Quartz L+S sin n n Transmitted ray ϕ n ϕ n φ n Chrome Wavefronts Ray of Light Diffracted ray #3 The Bragg condition sets the diffraction angles

4 Line and Space Definition L S L+S Quartz Chrome Lens A line of chrome on the mask ositive Resist produces a line of resist remaining on the wafer L S Simulation Domain

5 Optical Reduction Ratio R M M L M +S M L M S M Quartz Dimensions on the wafer are reduced by the reduction ratio R. W L W +S W sinφ n Rsinφφ n ositive Resist L W S W Wafer Chrome Lens Rays travel at larger angles on the wafer side deof the lens. Example: The ASML 248nm exposure tool in the Microfabrication Lab has R5.

6 The Fourier Transform One Dimensional F( u) f ( ) 2πiux x e dx u is a ray direction or lens pupil location u sinφ/ Fourier spectrum of plane waves that make up the light Electric field passing through the photomask Two Dimensional F ( u, v ) f, u and v give the ray direction or lens pupil location ( x y ) e 2πi ( ux+ vy ) dxdy Smith Ch 8 in Sheats and Smith

7 Functions and Transforms rect(x) > sinc(u) sin(πu)/πu comb(x/b) > comb(bu) f g > F G comb( x / ) + ( x ) δ n f g > F G Smith Ch 8 in Sheats and Smith

8 Modular Lithography Lectures, A.R. Neureuther, Sp 2006 Electric Field Spectrum M(u) from E(x) Electric Field Spectrum M(u) from E(x) x b x t A ) ( comb rect A x m 2 / ) ( { } x comb F x rect A F x m F u M ) ( ) ( { } comb ect x m u 2 / ) ( ) ( A ( ) ( ) n u u u u c A u M sin 2 δ u 1/ Sheats and Smith Values are ½, 1/π, 1/3π, 1/5π u 0 1/

9 (Sinθ x, Sinθ x ) wave accounting system Sinθ Y σ Lens upil Sinθ MAX 1.0 Sinθ X Lens Illumination Sinθ MAX σ Location (Sinθ x, Sinθ x ) corresponds to a ray making angles θ x and θ Y with the downward z-axis

10 upil Wave Traffic: artial Coherence #4 Lens is a low pass filter of mask diffraction at Bragg angles Sinθ Y Shifted by sinφ l/ Lens upil Sinθ MAX Cone of Incident Light Some misses pupil Diffracted Orders from a mask with period Sinθ X +2 otential for entering the pupil

11 Effect of Fourier Components on aerial image 3 wave case note the zeros > perfect contrast > Contrast not such a good metric Smith Ch 8 in Sheats and Smith

12 Contrast vs. eriod Contrast 1.0 First Order Max Dead Zone Third Order Max L S 0.5 Unbalanced 3rd / Cutoff

13 upil Traffic: cut-off / σ 1+ σ 0.67 ( ) L S 0.33

14 upil Traffic: Best 1 st Order / σ 2.0 ( 1 σ ) L S 1. 0

15 upil Traffic: Adding 3rd Order 3/ σ 6.0 ( 1 σ ) L S 3. 0

16 upil Traffic: Dead Zone 3/ Extra 3 rd not matched 3 3 Extra 3 rd not matched 3 L S 1.5 Additive one sided 3 rd order complex plane wave with an imaginary part of which cannot be cancelled.