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DTRAN A One Dimensional Program for Time and Frequency Domain Analysis of Transistors and Other Semiconductor Devices

IP.com Disclosure Number: IPCOM000074711D
Original Publication Date: 1971-Jun-01
Included in the Prior Art Database: 2005-Feb-23
Document File: 3 page(s) / 115K

Publishing Venue

IBM

Related People

Cooley, JW: AUTHOR [+2]

Abstract

DTRAN is a program for solving in one space dimension (e.g., Fig. 1) and time or frequency, the three coupled nonlinear PDE (partial differential equations) which describe semiconductor devices with arbitrarily specified impurity profiles (e.g., Fig. 2). These PDE are a) Poisson's equation, b) and c) hole and electron continuity equations. Solution of these equations allows a user to predict from theory the behavior of a proposed or exact semiconductor device. DTRAN, with the novel nine-diagonal band matrix formulation described below, uses (centered) three-point differences on a nonuniform space grid and implicit (backward) two-point differences on a nonuniform and variable time grid.

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DTRAN A One Dimensional Program for Time and Frequency Domain Analysis of Transistors and Other Semiconductor Devices

DTRAN is a program for solving in one space dimension (e.g., Fig. 1) and time or frequency, the three coupled nonlinear PDE (partial differential equations) which describe semiconductor devices with arbitrarily specified impurity profiles (e.g., Fig. 2). These PDE are a) Poisson's equation, b) and c) hole and electron continuity equations. Solution of these equations allows a user to predict from theory the behavior of a proposed or exact semiconductor device. DTRAN, with the novel nine-diagonal band matrix formulation described below, uses (centered) three-point differences on a nonuniform space grid and implicit (backward) two-point differences on a nonuniform and variable time grid. In frequency domain analysis, instead of being discretized, the time derivative operator, d/dt, is replaced by j omega where j = square root of -1, and omega is the angular or radian frequency. In equilibrium (DC) or time domain (transient) analysis the output consists of device terminal characteristics as well as internal distributions such as hole and electron densities, electric fields, etc. as function of distance and time. In frequency domain (AC) analysis, the terminal characteristics are output in the form of a complex, frequency dependent port immitance matrix and internal distributions are available as functions of distance and frequency. The frequency anal...