Commun. Comput. Phys., 10 (2011), pp. 305-338.

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

Tiao Lu 1, Gang Du 2, Xiaoyan Liu 2, Pingwen Zhang 1*

1 School of Mathematical Sciences, LMAM and CAPT, Peking University, Beijing 100871, China.
2 Institute of Microelectronics, Peking University, Beijing 100871, China.

Received 7 November 2009; Accepted (in revised version) 26 November 2010
Available online 27 April 2011


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.

AMS subject classifications: 35Q20, 35Q40, 65Z05

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Key words: Double gate MOSFET, multi subband Boltzmann transport equation, 2D electron gas, deterministic solver, PFC method.

*Corresponding author.
Email: (T. Lu), (G. Du), (X. Liu), (P. Zhang)

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