Acquiring Knowledge of the Ideas: A Study of the Methods in by Kang Chen, Von Ludwig Chen

By Kang Chen, Von Ludwig Chen

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Example text

Uc is displacement at the membrane center (reprinted from Chiba and Okada 1991 with permission from the American Vacuum Society) Because the membrane’s thickness is small relative to the mask window size, the mask membrane was assumed to be only in a plane stress. 48) 46 2 X-ray Lithography  xy = 2(1 + v) Cu Cv + =  xy . 49) Using a finite element program (MSC/NASTRAN), temperature distributions, thermal stresses, and strains and thermal displacements in a silicontungsten (Si-W) mask structure were presented.

The numerical method for solving Eqs. 5) is based on a hybrid finite element and the generalized Marchuk splitting scheme (Dai and Nassar, 1997b). A domain decomposition algorithm is used with a parallel Gaussian elimination technique to obtain the solution. The finite element is applied first to the circular pattern in the xy cross section. 6) presents the finite element mesh in the first quadrant. 14) with T (x, y, z) = 0 at the side wall. 15) where v(x, y) is a function on the Sobolov space H01 (Chandrupatla and Belegundu, 1991).

1 mm for the adiabatic condition. The present model can be extended to deal with a circular mask pattern on the resist, as is seen in Fig. 5). The numerical method for solving Eqs. 5) is based on a hybrid finite element and the generalized Marchuk splitting scheme (Dai and Nassar, 1997b). A domain decomposition algorithm is used with a parallel Gaussian elimination technique to obtain the solution. The finite element is applied first to the circular pattern in the xy cross section. 6) presents the finite element mesh in the first quadrant.

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