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

DOI: 10.1007/978-3-540-71992-2_84

ABSTRACT 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.

  • Source
    [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. · 1.58 Impact Factor
  • Source
    [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; · 1.30 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A nanoscale double-gate MOSFET is simulated with an energy-transport subband model for semiconductors formulated starting from the moment system derived from the Schrödinger–Poisson–Boltzmann equations. The system is closed on the basis of the maximum entropy principle and includes scattering of electrons with acoustic and non-polar optical phonons. The proposed expression of the entropy combines quantum effects and semiclassical transport by weighting the contribution of each subband with the square modulus of the envelope functions arising from the Schrödinger–Poisson subsystem. The simulations show that the model is able to capture the relevant confining and transport features and assess the robustness of the numerical scheme.
    Continuum Mechanics and Thermodynamics 01/2011; 24(4-6). · 1.09 Impact Factor