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A class of finite element methods with averaging techniques for solving the three-dimensional drift-diffusion model in semiconductor device simulations
Zhang, Qianru1,2; Wang, Qin1,2; Zhang, Linbo1,2; Lu, Benzhuo1,2
2022-06-01
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume458Pages:24
AbstractObtaining a satisfactory numerical solution of the classical three-dimensional drift -diffusion (DD) model, widely used in semiconductor device simulations, is still challenging nowadays, especially when the convection dominates the diffusion. In this work, we propose a series of finite element schemes with different types of averaging techniques to discretize the three-dimensional continuity equations. Our methods are based on the classical finite element framework, quite different from those mixed finite element/volume methods that also employ inverse averaging techniques. At first, the Slotboom variables are employed to transform the continuity equations into self-adjoint second-order elliptic equations with exponentially behaved coefficients. Then four averaging techniques, denoted with A1-A4, are introduced to approximate the exponential coefficient with its average on every tetrahedral element of the grid. The first scheme calculates the harmonic average of the exponential coefficient on a whole tetrahedron, and the other three schemes calculate the average of the exponential coefficient on each edge of a tetrahedral element. Our methods can avoid the spurious non-physical numerical oscillations and guarantee the conservation of the computed terminal currents with a terminal current evaluation approach. In fact, these methods not only maintain numerical stability but also overcome the disadvantages of some stabilization methods that cannot guarantee the conservation of the terminal currents, such as the streamline-upwind Petrov-Galerkin (SUPG) method. Moreover, the derivation of these discretization methods does not need the dual Voronoi grid as that of the finite volume Scharfetter-Gummel (FVSG) method or other mixed finite element/volume methods with inverse averaging techniques, which greatly reduces the complexity of parallel implementations of our methods. Simulations on two realistic three-dimensional semiconductor devices are carried out to test the accuracy and stability of our methods. According to numerical results, we conclude that scheme A4 can produce more accurate numerical solutions than the other three schemes, especially when the bias applied on the electrode is high. Numerical results also show that the scheme A4 is more robust than the Zlamal finite element method [1] in high-bias cases, and it also performs better than the FVSG method and a tetrahedral mixed finite element method [2] on poor-quality grids. Scheme A4 is also employed to study rich physical properties of the n-channel MOSFET.(c) 2022 Elsevier Inc. All rights reserved.
KeywordThree-dimensional drift -diffusion model Averaging technique Finite element method Semiconductor device
DOI10.1016/j.jcp.2022.111086
Indexed BySCI
Language英语
Funding ProjectNational Key R&D Program of China[2019YFA0709600] ; National Key R&D Program of China[2019YFA0709601] ; National Natural Science Foundation of China[11771435] ; National Natural Science Foundation of China[22073110]
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000793405100007
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61394
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLu, Benzhuo
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS,ISEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Qianru,Wang, Qin,Zhang, Linbo,et al. A class of finite element methods with averaging techniques for solving the three-dimensional drift-diffusion model in semiconductor device simulations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,458:24.
APA Zhang, Qianru,Wang, Qin,Zhang, Linbo,&Lu, Benzhuo.(2022).A class of finite element methods with averaging techniques for solving the three-dimensional drift-diffusion model in semiconductor device simulations.JOURNAL OF COMPUTATIONAL PHYSICS,458,24.
MLA Zhang, Qianru,et al."A class of finite element methods with averaging techniques for solving the three-dimensional drift-diffusion model in semiconductor device simulations".JOURNAL OF COMPUTATIONAL PHYSICS 458(2022):24.
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