This research will consider mathematical and numerical aspects of models describing semiconductor transport in novel device structures. Two aspects of the problems will be considered in tandem. First, increasing miniaturization results in effects which, while they can still be described by the Basic Semiconductor Equations (BSE), are intrinsically three- dimensional in nature. To address this problem, this research will develop and analyze an iterative algorithm for solution of the nonlinear BSE using a decoupling procedure based on asymptotic analysis. Secondly, miniaturization leads to physical phenomena, such as "hot electrons," which are not described by the BSE. This research will thus also consider the development and use of new model equations. This research could have a direct impact on the design of semiconductor devices and aid in the development of advanced technology.
