Mathematical properties of a kinetic transport model for carriers and phonons in semiconductors

Galler, Martin; Schürrer, Ferdinand

doi:10.1007/s00033-007-4119-1

Cited by 1 publication

(1 citation statement)

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“…Recently, Cheng et al have constructed a discontinuous Galerkin solver for Boltzmann-Poisson systems in double-gate MOSFETs [19]. Moreover, the Bloch-Boltzmann Peierl equation can be used for the transport of electrons and polar optical phonons in periodic settings [38, 39]. Other density matrix methods, such as the Master equation [48, 35], describe the time evolution of the probability function.…”

Section: Introductionmentioning

confidence: 99%

Modeling and simulation of electronic structure, material interface and random doping in nano-electronic devices

Chen

Wei

2010

Journal of Computational Physics

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The miniaturization of nano-scale electronic devices, such as metal oxide semiconductor field effect transistors (MOSFETs), has given rise to a pressing demand in the new theoretical understanding and practical tactic for dealing with quantum mechanical effects in integrated circuits. Modeling and simulation of this class of problems have emerged as an important topic in applied and computational mathematics. This work presents mathematical models and computational algorithms for the simulation of nano-scale MOSFETs. We introduce a unified twoscale energy functional to describe the electrons and the continuum electrostatic potential of the nano-electronic device. This framework enables us to put microscopic and macroscopic descriptions in an equal footing at nano scale. By optimization of the energy functional, we derive consistently-coupled Poisson-Kohn-Sham equations. Additionally, layered structures are crucial to the electrostatic and transport properties of nano transistors. A material interface model is proposed for more accurate description of the electrostatics governed by the Poisson equation. Finally, a new individual dopant model that utilizes the Dirac delta function is proposed to understand the random doping effect in nano electronic devices. Two mathematical algorithms, the matched interface and boundary (MIB) method and the Dirichlet-to-Neumann mapping (DNM) technique, are introduced to improve the computational efficiency of nano-device simulations. Electronic structures are computed via subband decomposition and the transport properties, such as the I-V curves and electron density, are evaluated via the non-equilibrium Green's functions (NEGF) formalism. Two distinct device configurations, a double-gate MOSFET and a four-gate MOSFET, are considered in our three-dimensional numerical simulations. For these devices, the current fluctuation and voltage threshold lowering effect induced by the discrete dopant model are explored. Numerical convergence and model well-posedness are also investigated in the present work.

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