Expedited Award for Novel Research: Analytical Methods for VLSI Semiconductor Device Design

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The Principal Investigator proposes to carry out new mathematical analyses of the basic nonlinear partial differential equations and boundary conditions, that define the operation of a large class of VLSI semiconductor devices. The Principal Investigator proposes to utilize state of the art advances in the theory of nonlinear partial differential equations to create and analyze new procedures to handle problems in both two and (short channel) three spatial dimensions in device design without leading to the usual numerical divergences of conventional algorithms. Moreover, the Principal Investigator proposes to investigate analytically several new important effects that appear as the miniaturization process proceeds to chips at the submicron level (e.g. electronic instabilities, and parameter dependence), which seems to lead to bifurcation phenomena.