Adaptive Multiscale Modeling of Polymeric Materials used in Semiconductor Manufacturing
P.T. Bauman, S. Prudhomme, J. Tinsley Oden
The University of Texas at Austin, US
Keywords: multiscale modeling, error estimation, adaptivity, polymers, semiconductor manufacturing
Abstract:A molecular model is used to simulate the deformation of materials used in the fabrication of semiconductor devices. An algorithm is used that leads to a complex molecular model of polymer materials designed to produce an etch barrier, a critical component in imprint lithography. Each application of this polymerization process leads to one realization of a lattice-type, molecular statics model of a polymer. To reduce the size and complexity of this model, a sequence of coarser surrogate models is generated. This multiscale model involves a combination of the molecular model and a nonlinear hyperelastic continuum model. The coupling is based on the so-called Arlequin method. Furthermore, adjoint-based error estimates in local quantities of interest are constructed to estimate the error due to the approximation of the particle model by the coupled multiscale model. These error estimates are used to construct an adaptive algorithm in order to reduce the error in the quantity of interest. There are two major conclusions of this study: 1. an effective multiscale model that couples particle and continuum models can be constructed as a suitable surrogate 2. an estimate of the error can be computed with sufficient accuracy to produce effective multiscale modeling procedures.