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Talk Abstract
Multiscale Problems in Semiconductor Processing

Avner Friedman
Regents' Professor, School of Mathematics
Director, Minnesota Center for Industrial Mathematics
University of Minnesota

In the processing of semiconductors one encounters the problem of disparity of scales; the controling tools are on the order of several centimeters, while the physical parameters of the transistors on the wafer vary on the submicron scale. This situation makes standard numerical schemes, such as finite differences, infeasible. One possible approach is by homogenization. The talk will describe joint work with Bei Hu on how the problem is homogenized; we shall describe results concerning the free boundary problem of the growing semiconductor film, and how to control the microscale features by the (macroscopic) control functions.

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