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A Finite Volume Method for the Multi Subband Boltzmann Equation with Realistic 2D Scattering in Double Gate MOSFETs

Published online by Cambridge University Press:  20 August 2015

Tiao Lu ,
Gang Du ,
Xiaoyan Liu  and
Pingwen Zhang
Tiao Lu*
Affiliation:
School of Mathematical Sciences, LMAM and CAPT, Peking University, Beijing 100871, China
Gang Du*
Affiliation:
Institute of Microelectronics, Peking University, Beijing 100871, China
Xiaoyan Liu*
Affiliation:
Institute of Microelectronics, Peking University, Beijing 100871, China
Pingwen Zhang*
Affiliation:
School of Mathematical Sciences, LMAM and CAPT, Peking University, Beijing 100871, China
*
Email:tlu@math.pku.edu.cn
Email:gangdu@pku.edu.cn
Email:xyliu@ime.pku.edu.cn
Corresponding author.Email:pzhang@math.pku.edu.cn
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Abstract

We propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation (MSBTE) for the two dimensional (2D) electron gas in double gate metal oxide semiconductor field effect transistors (MOSFETs) with flared out source/drain contacts. A realistic model with six-valleys of the conduction band of silicon and both intra-valley and inter-valley phonon-electron scattering is solved. We propose a second order finite volume method based on the positive and flux conservative (PFC) method to discretize the Boltzmann transport equations (BTEs). The transport part of the BTEs is split into two problems. One is a 1D transport problem in the position space, and the other is a 2D transport problem in the wavevector space. In order to reduce the splitting error, the 2D transport problem in the wavevector space is solved directly by using the PFC method instead of splitting into two 1D problems. The solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristic is investigated. Comparison of the numerical results with ballistic solutions show that the scattering influence is not ignorable even when the size of a nanoscale semiconductor device goes to the scale of the electron mean free path.

Keywords

35Q2035Q4065Z05Double gate MOSFETmulti subband Boltzmann transport equation2D electron gasdeterministic solverPFC method
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 2 , August 2011 , pp. 305 - 338
Copyright
Copyright © Global Science Press Limited 2011

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