Abstract : As the feature size of modern integrated circuits goes to nanometer-scale, the design and analysis of integrated circuits become complicated. Quantum mechanical phenomena become prominent in numerical simulations of semiconductor device. At the same time, rigorous computational lithography beyond Kirchhoff approximation becomes more important, but are too resource intensive to use for full chip applications. Efficient and accurate numerical simulation of device and lithography continues to be a challenge. We are concerned with the numerical modeling of semiconductor devices simulation and electromagnetic computation in lithography. Of particular interest to this minisymposium are recent advances on general numerical methods.
Organizer(s) : Junqing Chen,Tao Cui,Wenhao Lu ,Weiying Zheng
[01756] Arbitrarily high order finite element methods for arbitrarily shaped domains with automatic mesh generation
Format : Talk at Waseda University
Author(s) :
Zhiming Chen (Chinese Academy of Sciences)
Abstract : We consider high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. Numerical examples are presented to illustrate the competitive performance of the method. This talk is based on a joint work with Yong Liu.
[01921] An iterative method for inverse lithography problem with TV regularization
Format : Talk at Waseda University
Author(s) :
Junqing Chen (Tsinghua University)
Abstract : I will introduce an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms. In the framework of ADMM method, the optimization problem is divided into several subproblems. Each of the subproblems can be solved efficiently. The convergence analysis is given. Some numerical examples are shown to illustrate the effectiveness of the method.
[03833] A SOURCE TRANFER DOMAIN DECOMPOSITION METHOD FOR MAXWELL’S EQUATIONS
Format : Talk at Waseda University
Author(s) :
TAO CUI (NCMIS, LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
ZIMING WANG (School of Mathematical Sciences, University of Chinese Academy of Sciences)
XUESHUANG XIANG (Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology)
Abstract : In this paper, we develop an efficient solver for the Maxwell’s equations in unbounded domain by extending the source transfer domain decomposition method (STDDM) proposed by Chen et al. Through the analysis of the fundamental solution of the Maxwell’s equations, the convergence of STDDM is proved for the case of constant wave number. Numerical experiments are included, demonstrating that the proposed method can be used as an efficient preconditioner in the preconditioned GMRES method for solving the PML equation of the Maxwell’s equations with constant and heterogeneous wave numbers, including an example for lithography.
[01824] Numerical simulation for quantum transports in nano-semiconductor device
Format : Talk at Waseda University
Author(s) :
Haiyan Jiang (Beijing Institute of Technology)
tiao Lu (Peking University)
Weitong Zhang (Peking University)
Abstract : We develop a new hybrid scheme for the coupled systems of quantum transport in nano-semiconductor device. Sinc-Galerkin method is used to solve the time-dependent Wigner equation numerically with the spectral convergence of the cardinal sine basis function solution of Wigner function in velocity space. A second-order semi-implicit time integration scheme is designed for the Wigner-Poisson equations (TWPEs). The numerical method is applied to study a double-barrier resonant tunneling diode (RTD), Error estimation, stability, and convergence are also investigated concretely. Numerical experiments validate the theoretical results and present the reliability and efficiency of the proposed algorithm to simulate quantum effects.
[01985] An efficient iterative scheme for the coupled Schrödinger-Poisson equations
Format : Talk at Waseda University
Author(s) :
Wenhao Lu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Abstract : We propose an efficient iterative scheme for solving the coupled Schrödinger-Poisson equations in three-dimensions. In this scheme, the series of electron densities is truncated to a sum of finite terms, and only a finite number of eigenvalues are computed at each iteration step. The convergence analysis is also presented. We present numerical results that demonstrate the properties of the proposed scheme.
[01922] Dispersion Analysis of CIP-FEM for Helmholtz Equation
Format : Talk at Waseda University
Author(s) :
Haijun Wu (Nanjing University)
Yu Zhou (Nanjing University)
Abstract : When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number $k$ increases, known as `pollution effect' which is directly related to the phase difference between the exact and numerical solutions, caused by the numerical dispersion. In this paper, we propose a dispersion analysis for the continuous interior penalty finite element method (CIP-FEM) and derive an explicit formula of the penalty parameter for the $p^{\rm th}$ order CIP-FEM on tensor product (Cartesian) meshes, with which the phase difference is reduced from $\mathcal{O}\big(k(kh)^{2p}\big)$ to $\mathcal{O}\big(k(kh)^{2p+2}\big)$. Extensive numerical tests show that the pollution error of the CIP-FE solution is also reduced by two orders in $kh$ with the same penalty parameter.
[01779] Efficient Simulation Algorithm for FinFET and Gate-All-Around FET
Format : Talk at Waseda University
Author(s) :
Lang Zeng (Beihang University)
Abstract : In this talk, our self-developed device simulator based on the framework of Mode space method will be introduced which can accurately and efficiently simulate the current characteristic of FinFET and GAA FET. In our hybrid framework, the 3D device is divided into 2D cross-sectional direction with closed boundary condition and 1D transport direction with open boundary condition. Our simulator is designed by modular concept that different physical models can be picked and combined freely.
[01757] A finite element method for the Schr\"{o}dinger-Poisson model
Format : Talk at Waseda University
Author(s) :
Weiying Zheng (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Abstract : We propose a finite element method for solving the coupled Schr$\ddot{\rm o}$dinger-Poisson equations in three-dimensions. The series of electron density is truncated into the sum of finite terms. Sharp estimates are proved for both the truncation error and the finite element discretization error. A robust iterative scheme is proposed to solve the nonlinearly coupled problem.
