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

Journal Article · Sun Jun 20 00:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.02.002· OSTI ID:21333912

Duan, Chen ^[1]; Guowei, Wei ^[1]

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1. Department of Mathematics, Michigan State University, East Lansing, MI 48824 (United States)

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 two-scale 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.

• OSTI ID: 21333912
• Journal Information: Journal of Computational Physics, Vol. 229, Issue 12; Other Information: DOI: 10.1016/j.jcp.2010.02.002; PII: S0021-9991(10)00075-6; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
COMPUTERIZED SIMULATION
CONVERGENCE
DECOMPOSITION
DELTA FUNCTION
DIRICHLET PROBLEM
ELECTRIC POTENTIAL
ELECTRON DENSITY
ELECTRONIC EQUIPMENT
ELECTRONIC STRUCTURE
ELECTRONS
ELECTROSTATICS
GREEN FUNCTION
INTEGRATED CIRCUITS
MATHEMATICAL MODELS
MINIATURIZATION
MOSFET
OPTIMIZATION
OXIDES
POISSON EQUATION
QUANTUM MECHANICS
RANDOMNESS
SCHROEDINGER EQUATION
SEMICONDUCTOR MATERIALS
THREE-DIMENSIONAL CALCULATIONS
TRANSPORT THEORY