Nano Science and Technology Institute
MSM 99
MSM 99
Technical Proceedings of the 1999 International Conference on Modeling and Simulation of Microsystems
Chapter 12: Semiconductor Device Modeling

Three-Dimensional Multi-Grid Poisson Solver for Modeling Semiconductor Devices

Authors:S.J. Wigger, M. Saraniti and S.M. Goodnick
Affilation:Arizona State University, US
Pages:415 - 418
Keywords:semiconductor device modeling, poisson solver, multi-grid, EEPROM, Fowler-Hordheim tunneling
Abstract:In this paper, a full three-dimensional (3D), inhomogenous linear multi-grid Poisson solver is presented for application in particle-based simulation tools for devic emodeling. This algorithm represents the first such fully 3D multi-grid solver for device applications. As a test for the linear POiisson solver, a nonlinear version is developed using Newton's method and a 3D EEPROM (Electrically Erasable/Programmable Read ONly Memory) device is modeled. The solution of the nonlinear Poisson equation provides thermal equilibrium characteristics of the device. The basic functionality of an EEPTROM device can be understood with a complete electrostatic analysis, making it an ideal application for the solver. The relationship between the threshold voltage and the floating gate charge in the EEPROM device is analyzed for various geometries. The Fowler-Nordheim tunneling current density is also determined as a function of the EEPROM channel dimension.
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