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Computation lithography: virtual reality and virtual virtuality

Edmund Y. Lam and Alfred K. K. Wong

Open Access Open Access

Abstract

Computation lithography is enabled by a combination of physical understanding, mathematical abstraction, and implementation simplification. An application in the virtual world of computation lithography can be a virtual reality or a virtual virtuality depending on its engineering sensible-ness and technical feasibility. Examples under consideration include design-for-manufacturability and inverse lithography.

©2009 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Illustration of a projection microlithography exposure system [26].

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Fig. 2.
Fig. 2. An example of inverse lithography with no regularization.

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Fig. 3.
Fig. 3. An example of inverse lithography designed for robustness against defocus.

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Fig. 4.
Fig. 4. The reality-virtuality space of computation lithography (not to scale).

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Equations (10)

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I xy = ∫+ ∫−∞ ∫∞ ∫ w (x−x′o,y−y′o;x−x″o,y−y″o) O (x′o,y′o) O* (x″o,y″o) d x′o d y′o d x″o d y″o ,
where w (x′o,y′o;x″o,y″o) =J (x′o−x″o,y′o−y″o) H (x′o,y′o)H*(x″o,y″o),
J (x′o−x″o,y′o−y″o) is the mutual intensity ,
H xy is the optical system transfer function ,
O xy is the mask transmittance ,
I ( x , y ) ≊ ∑k=1Kλk ∣ ∫∫−∞+∞φk(x−x′,y−y′) O ( x ′ , y ′ ) dx ′ d y ′ ∣2 .
I xy ≅ ∑k=1K∣ ∑n=1Ntfg [ψk(x−x1(n),y−y1(n))−ψk(x−x2(n),y−y1(n))+
ψk(x−x2(n),y−y2(n))−ψk(x−x1(n),y−y2(n))] ∣2 ,
Oopt xy =argOxymin∈{0,1} Σx,y[11+exp{−a(∣Hxy⊗Oxy∣2−tr)}−Îxy]2
Oopt xy =argOxymin∈{0,1} ℰβ{Σx,y[11+exp{−a(∣Hxy⊗Oxy∣2−tr)}−Îxy]2},
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