A SHOCK-TRACKING ALGORITHM FOR SURFACE EVOLUTION UNDER REACTIVE-ION ETCHING

被引：58

作者：

HAMAGUCHI, S ^{[1
]}

DALVIE, M ^{[1
]}

FAROUKI, RT ^{[1
]}

SETHURAMAN, S ^{[1
]}

机构：

[1] NYU,COURANT INST MATH SCI,NEW YORK,NY 10012

来源：

JOURNAL OF APPLIED PHYSICS | 1993年 / 74卷 / 08期

关键词：

D O I：

10.1063/1.354282

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

A new algorithm that determines the evolution of a surface eroding under reactive-ion etching is presented. The surface motion is governed by both the Hamilton-Jacobi equation and the entropy condition for a given etch rate. The trajectories of ''shocks'' and ''rarefaction waves'' are then directly tracked, and thus this method may be regarded as a generalization of the method of characteristics. This allows slope discontinuities to be accurately calculated without artificial diffusion. The algorithm is compared with ''geometric'' surface evolution methods, such as the line-segment method.

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页码：5172 / 5184

页数：13

相关论文

共 17 条

[1] RANDOM CHOICE METHODS WITH APPLICATIONS TO REACTING GAS-FLOW [J].

CHORIN, AJ .

JOURNAL OF COMPUTATIONAL PHYSICS, 1977, 25 (03) :253-272

[2]

CRANDALL MG, 1984, MATH COMPUT, V43, P1, DOI 10.1090/S0025-5718-1984-0744921-8

[3] SOME PROPERTIES OF VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].

CRANDALL, MG ;

EVANS, LC ;

LIONS, PL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 282 (02) :487-502

[4] VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].

CRANDALL, MG ;

LIONS, PL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 277 (01) :1-42

[5] FLUX CONSIDERATIONS IN THE COUPLING OF MONTE-CARLO PLASMA SHEATH SIMULATIONS WITH FEATURE EVOLUTION MODELS [J].

DALVIE, M ;

FAROUKI, RT ;

HAMAGUCHI, S .

IEEE TRANSACTIONS ON ELECTRON DEVICES, 1992, 39 (05) :1090-1099

[6]

FICHTNER W, 1988, VLSI TECHNOLOGY

[7] SOLUTIONS IN LARGE FOR NONLINEAR HYPERBOLIC SYSTEMS OF EQUATIONS [J].

GLIMM, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1965, 18 (04) :697-&

[8] LINE-PROFILE RESIST DEVELOPMENT SIMULATION TECHNIQUES [J].

JEWETT, RE ;

HAGOUEL, PI ;

NEUREUTHER, AR ;

VANDUZER, T .

POLYMER ENGINEERING AND SCIENCE, 1977, 17 (06) :381-384

[9] KINETIC-THEORY OF BOMBARDMENT INDUCED INTERFACE EVOLUTION [J].

JURGENSEN, CW ;

SHAQFEH, ESG .

JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B, 1989, 7 (06) :1488-1492

[10] THE APPLICATION OF THE HUYGENS PRINCIPLE TO SURFACE EVOLUTION IN INHOMOGENEOUS, ANISOTROPIC AND TIME-DEPENDENT SYSTEMS [J].

KATARDJIEV, IV ;

CARTER, G ;

NOBES, MJ .

JOURNAL OF PHYSICS D-APPLIED PHYSICS, 1989, 22 (12) :1813-1824