A Deterministic Solver to the Boltzmann-Poisson System Including Quantization Effects for Silicon-MOSFETs

DOI: 10.1007/978-3-540-71992-2_84


We present a deterministic solver to the Boltzmann-Poisson system for simulating the electron transport in silicon MOSFETs.
This system consists of the Boltzmann transport equations (BTEs) for free electrons and for the twodimensional electron gas
(2DEG) formed at the Si/SiO2 interface. Moreover, the Poisson equation is coupled to the BTEs. Eigenenergies and wave functions
of the 2DEG are dynamically calculated from the Schrödinger-Poisson system. Numerical studies prove the applicability and
the efficiency of the proposed numerical technique for simulating ultrasmall semiconductor devices.

5 Reads
  • Source
    • "The direct simulation of such a complex model is very expensive from a computational point of view (see [11] [12] [13] [14] [15] for the case of a DG-MOSFET) and not useful for computer aided design (CAD) purposes. Consequently it could be desirable "
    [Show abstract] [Hide abstract]
    ABSTRACT: An energy-transport model based on the maximum entropy principle is derived for the simulation of a nanoscale metal-oxide-semiconductor field-effect transistor (MOSFET). The presence of both 3D and 2D electron gas is included along with the quantization in the transversal direction with respect to the oxide at the gate which gives rise to a subband decomposition of the electron energy. Both intra- and interparticle scatterings between the 2D and 3D electron gas are considered. In particular, a fictitious transition from the 3D to the 2D electrons and vice versa is introduced by adapting the approach used in [M. V. Fischetti and S. E. Laux, Phys. Rev. B, 48 (1993), pp. 2244–2274] in the context of a Monte Carlo simulation.
    SIAM Journal on Applied Mathematics 07/2013; 73(4):1439–1459. DOI:10.1137/120893483 · 1.43 Impact Factor
  • Source
    • "A complete description of quantum confinement is obtained by solving the system (1)–(3) (see for example [13] [14] [15]), but this is a daunting computational task. Therefore simpler macroscopic models are looked for CAD purposes. "
    [Show abstract] [Hide abstract]
    ABSTRACT: A nanoscale double-gate MOSFET is simulated with an energy-transport subband model for semiconductors including the effects of non-parabolicity by means of the Kane dispersion relation. The closure relations are derived on the basis of the maximum entropy principle and all the relevant scattering mechanisms of electrons with acoustic and non polar optical phonons are taken into account. The model is shown to form a system of nonlinear parabolic partial differential equations. The results of the simulations validate the robustness of the numerical scheme and the accuracy of the model. In particular, the importance of taking into account the non-parabolicity is assessed, since a relevant difference in the currents is obtained in comparison with the parabolic band case.
    Mathematical and Computer Modelling 07/2013; 58(1-2):321-343. DOI:10.1016/j.mcm.2012.11.007 · 1.41 Impact Factor
  • Source
    • "Stochastic solutions based on MC simulations can be found for example in [4]. A recent deterministic solver has been developed in [5]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: Quantum corrections to the hydrodynamical model of semiconductor based on the maximum entropy principle are obtained at 2 order with a Chapmann-Enskog expansion in the high field approximation, modeling the 2 part of the collision term in a relaxation form. Limiting energy-transport and drift-diffusion models are deduced.
    Journal of Mathematical Physics 03/2007; 48(12). DOI:10.1063/1.2819600 · 1.24 Impact Factor
Show more

Similar Publications