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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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References

[1] Ben Abdallah, N., Cáceres, M. J., Carrillo, J. A., and Vecil, F., A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs, J. Comput. Phys., 228 (2009), 6553–6571.CrossRefGoogle Scholar
[2] Ando, T., Fowler, Alan B., and Stern, F., Electronic properties of two-dimensional systems, Rev. Mod. Phys., 54 (1982), 437–672.CrossRefGoogle Scholar
[3] Bertrand, G., Deleonibus, S., Previtali, B., Guegan, G., Jehl, X., Sanquer, M., and Balestra, F., Towards the limits of conventional MOSFETs: case of sub 30nm NMOS devices, Solid. State. Electron., 48 (2004), 505–509.CrossRefGoogle Scholar
[4] Bouchut, F., Golse, F., and Pulvirenti, M., Kinetic Equations and Asymptotic Theory, Gauthier Villars, Paris, 2000.Google Scholar
[5] Carrillo, J. A., Gamba, I. M., Majorana, A., and Shu, Chi-Wang, A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods, J. Comput. Phys., 184 (2003), 498–525.CrossRefGoogle Scholar
[6] Datta, S., Nanoscale device modeling: the Greens function method, Superlattice. Microst., 28 (2000), 253–278.CrossRefGoogle Scholar
[7] Datta, S., Quantum Transport: Atom to Transistor, Cambridge Univ. Press, Cambridge, U.K, 2005.CrossRefGoogle Scholar
[8] Delaurens, F. and Mustieles, F. J., A deterministic particle method for solving kinetic transport equations: the semiconductor Botzmann equation case, SIMA J. Appl. Math., 52 (1992), 973–998.Google Scholar
[9] Do, V. Nam, Dollfus, P., and Lien Nguyen, V., Transport and noise in resonant tunneling diode using self-consistent green function calculation, J. Appl. Phys., 100 (2006), 093705–093711.CrossRefGoogle Scholar
[10] Fatemi, E. and Odeh, F., Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices, J. Comput. Phys., 108 (1993), 209–217.CrossRefGoogle Scholar
[11] Fijalkow, E., A numerical solution to the Vlasov equation, Comput. Phys. Commun., 116 (1999), 319–328.Google Scholar
[12] Filbet, F. and Russo, G., High order numerical methods for the space non-homogeneous Boltz-mann equation, J. Comput. Phys., 186 (2003), 457–480.CrossRefGoogle Scholar
[13] Filbet, F. and Sonnendrucker, E., Comparison of eulerian vlasov solvers, Comput. Phys. Commun., 150 (2003), 247–266.CrossRefGoogle Scholar
[14] Filbet, F., Sonnendrìcker, E., and Bertrand, P., Conservative numerical schemes for the Vlasov equation, J. Comput. Phys., 172 (2001), 166–187.CrossRefGoogle Scholar
[15] Granzner, R., Polyakov, V. M., Schwierz, F., Kittler, M., and T, Doll, On the suitability of DD and HD models for the simulation of nanometer double-gate MOSFETs, Phys. E., 19 (2002), 33–38.Google Scholar
[16] Heroux, M. A., Willenbring, J. M., and Heaphy, R., Trilinos developers guide, Technical Report SAND2003-1898, Sandia National Laboratories, 2003.Google Scholar
[17] Lake, R., Klimeck, G., Bowen, R. C., and Jovanovic, D., Single and multiband modeling of quantum electron transport through layered semiconductor devices, J. Appl. Phys., 81 (1997), 7845–7869.CrossRefGoogle Scholar
[18] Majorana, A. and Pidatella, R. M., A finite difference scheme solving the Boltzmann-Poisson system for semiconductor devices, J. Comput. Phys., 174 (2001), 649–668.CrossRefGoogle Scholar
[19] Ren, Z. B., Nanoscale MOSFETs: Physics, Simulation, and Design, PhD thesis, Purdue University, West Lafayette, IN, (2001).Google Scholar
[20] Ren, Z., Venugopal, R., Goasguen, S., Datta, S., and Lundstrom, M. S., nanoMOS 2.5: a two-dimensional simulator for quantum transport in double-gate MOSFETs, IEEE Trans. Electron. Devices., 50 (2003), 1914–1924.Google Scholar
[21] Rhew, J.-H., Ren, Z., and Lundstrom, M. S., A numerical stduy of ballistic transport in a nanoscale MOSFET, Solid. State. Electron., 46 (2002), 1899–1906.CrossRefGoogle Scholar
[22] Smirnov, S., Physical Modeling of Electron Transport in Strained Silicon and Silicon Germanium, PhD thesis, Fakultät für Elektrotechnik und Informationstechnik, von, Wien, Österreich, 2003.Google Scholar
[23] Strang, G., Onthe construction and comparison of difference schemes, SIAM J. Numer. Anal., 5(1968), 506–517.CrossRefGoogle Scholar
[24] Sverdlov, V., Ungersboeck, E., Kosina, H., and Selberherr, S., Current transport models for nanoscale semiconductor devices, Mat. Sc. Eng. R., 58 (2008), 228–270.Google Scholar
[25] Ventura, D., Gnudi, A., Baccarani, G., and Odeh, F., Multidimensional spherical harmonics expansion of Boltzmann equation for transport in semiconductors, Appl. Math. Lett., 5 (1992), 85–90.CrossRefGoogle Scholar