Journal of Computational Physics
SIAM Journal on Numerical Analysis
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
Journal of Scientific Computing
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
A coupled Schrödinger drift-diffusion model for quantum semiconductor device simulations
Journal of Computational Physics
Journal of Computational Physics
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
Journal of Computational Physics
Subband decomposition approach for the simulation of quantum electron transport in nanostructures
Journal of Computational Physics
Quantum-corrected drift-diffusion models for transport in semiconductor devices
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Accurate calculation of Green's function of the Schrödinger equation in a block layered potential
Journal of Computational Physics
An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes
Journal of Computational Physics
2D numerical simulation of the MEP energy-transport model with a finite difference scheme
Journal of Computational Physics
Journal of Computational Physics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
An accelerated algorithm for 2D simulations of the quantum ballistic transport in nanoscale MOSFETs
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
Convective scheme solution of the Boltzmann transport equation for nanoscale semiconductor devices
Journal of Computational Physics
Journal of Computational Physics
Efficient solution of the Schroedinger-Poisson equations in layered semiconductor devices
Journal of Computational Physics
Parameter-free effective potential method for use in particle-based device simulations
IEEE Transactions on Nanotechnology
IEEE Transactions on Nanotechnology
Three-Dimensional Simulation of One-Dimensional Transport in Silicon Nanowire Transistors
IEEE Transactions on Nanotechnology
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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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 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.