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Tensor Mobility Model of Shockley Equations

K. Matsuda
Naruto University of Education, JP

Keywords: mobility, Shockley equations, MEMS

Mobilities usually used in Shockley equations of conventional device simulators are scalar. However, the scalar mobility is inconvenience in anisotropic transport simulation, such as MEMS simulations, Hall effect simulations, where the magnitude of mobility depends on crystallographic direction. As is known from the consideration on crystallographic symmetry, the mobility is a second-rank tensor. Moreover, the mobility should be expressed as a fourth-rank tensor when strain or magnetic field is applied. The author has ever proposed a tensor mobility notation in MEMS simulation [1]. In the present work, the tensor mobility model is introduced in the Shockley equations. Optimum set of device equations should be comprised of Maxwell equations, Boltzmann equations and Schrodinger equations [2]. For simplify the optimum set of device equations, Maxwell equations are replaced by Poisson equation and Boltzmann equations are replaced by the equation of continuity and the equation of current. As computer processor performance becomes increased, the simplified equations should be replaced by the optimum ones as much as possible. Recently, Monte Carlo method has been used for hot carriers transport in small size devices. For low field transport, Kubo-Greenwood formula is used in this work, instead of the mobility in continuity equation. Because of this formula, tensor expressions for the mobility are obtained. Sharfetter-Gummel discretization is rewritten by taking the tensor mobility into account. As an example, two-dimensional MEMS simulation is presented. [1] K. Matsuda and Y. Kanda, ''Implementation of Strain Induced Effects in Sensor Device Simulation,'' Tech. Proc. of the Second International Conference on MSM, San Juan, USA, April 19-21, 1999, pp.431-434. [2] K. Hess, ''Advanced Theory of Semiconductor Devices,'' IEEE Press, 1999.

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