Browsing by Author "Chen, RC"

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A quantum corrected energy-transport model for nanoscale semiconductor devices
(2005-03-20)
Chen, RC
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
An energy transport model coupled with the density gradient method as quantum mechanical corrections is proposed and numerically investigated. This new model is comprehensive in both physical and mathematical aspects. It is capable of describing hot electron transport as well as significant quantum mechanical effects for advanced devices with dimensions comparable to the de Broglie wave-length. The model is completely self-adjoint for all state variables and hence provides many appealing mathematical features such as global convergence, fast iterative solution, and highly parallelizable. Numerical simulations on diode and MOSFET with the gate length down to 34 nm using this model have been performed and compared with that using the classical transport model. It is shown that the I V characteristics of this short-channel device is significantly corrected by the density-gradient equations with current drive reduced by up to 60% comparing with that of the classical model along. Moreover, a 2D quantum layer, which is only a fraction of the length scale of inversion layer, is also effectively captured by this new model with very fine mesh near the interface produced by an adaptive finite element method. (c) 2004 Elsevier Inc. All rights reserved.
An iterative method for adaptive finite element solutions of an energy transport model of semiconductor devices
(2003-08-10)
Chen, RC
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A self-adjoint formulation of the energy transport model of semiconductor devices is proposed. This new formulation leads to symmetric and monotonic properties of the resulting system of nonlinear algebraic equations from an adaptive finite element approximation of the model. A node-by-node iterative method is then presented for solving the system. This is a globally convergent method that does not require the assembly of the global matrix system and full Jacobian matrices. An adaptive algorithm implementing this method is described in detail to illustrate the main features of this paper, namely, adaptation, node-by-node calculation, and global convergence. Numerical results of simulations on deep-submicron diode and MOSFET device structures are given to demonstrate the accuracy and efficiency of the algorithm. (C) 2003 Elsevier Science B.V. All rights reserved.
Monotone iterative methods for the adaptive finite element solution of semiconductor equations
(2003-10-15)
Chen, RC
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
Picard, Gauss-Seidel, and Jacobi monotone iterative methods are presented and analyzed for the adaptive finite element solution of semiconductor equations in terms of the Slotboom variables. The adaptive meshes are generated by the 1-irregular mesh refinement scheme. Based on these unstructured meshes and a corresponding modification of the Scharfetter-Gummel discretization scheme, it is shown that the resulting finite element stiffness matrix is an M-matrix which together with the Shockley-Read-Hall model for the generation-recombination rate leads to an existence-uniqueness-comparison theorem with simple upper and lower solutions as initial iterates. Numerical results of simulations on a MOSFET device model are given to illustrate the accuracy and efficiency of the adaptive and monotone properties of the present methods. (C) 2003 Elsevier B.V. All rights reserved.
Object-oriented programming of adaptive finite element and finite volume methods
(1996-10-01)
Liu, JL
;
Lin, IJ
;
Shih, MZ
;
Chen, RC
;
Hsieh, MC
This article describes an object-oriented implementation of the finite element method and the finite volume method in a unified adaptive system using the programming language C++. The system applies to various types of mathematical model problems. Traditionally, different numerical methods for different types of problems are implemented independently by procedural languages such as C and Fortran. Moreover, adaptive analysis programs are more complicated than nonadaptive programs. Nevertheless, these methods share many common properties such as linear system solvers, data structures, a posteriori error analyses, and refinement processes. Some advantageous features of object-oriented programming are demonstrated through the integration of these properties in the adaptive system. New data types of objects specific to adaptive methods are also introduced. The system is well-structured, extendable, and maintainable due mainly to the nature of encapsulation and inheritance of object-oriented programming.
Object-oriented programming of adaptive finite element and finite volume methods
(1996-10-01)
Liu, JL
;
Lin, IJ
;
Shih, MZ
;
Chen, RC
;
Hsieh, MC
This article describes an object-oriented implementation of the finite element method and the finite volume method in a unified adaptive system using the programming language C++. The system applies to various types of mathematical model problems. Traditionally, different numerical methods for different types of problems are implemented independently by procedural languages such as C and Fortran. Moreover, adaptive analysis programs are more complicated than nonadaptive programs. Nevertheless, these methods share many common properties such as linear system solvers, data structures, a posteriori error analyses, and refinement processes. Some advantageous features of object-oriented programming are demonstrated through the integration of these properties in the adaptive system. New data types of objects specific to adaptive methods are also introduced. The system is well-structured, extendable, and maintainable due mainly to the nature of encapsulation and inheritance of object-oriented programming.