Computational Lithography

Appendix G

Formula Derivation in Chapter 10

The derivation of Eq. (10.18) is as follows:

(G.1)

For the OPC optimization in the first type of optical lithography system, all the entries of have real values. In addition, according to Eq. 10.7, , where . Thus,

(G.2)

The derivation of Eq. (10.19) is as follows:

(G.3)

Therefore,

(G.4)

The derivation of Eq. (10.20) is as follows:

(G.5)

Therefore,

(G.6)

The derivation of Eq. (10.21) is as follows:

(G.7)

Therefore,

(G.8)