Finite-element methods in semiconductor device simulation

Application of the finite-element method for continuous time-dependent media to two-dimensional semiconductor device simulation is described. It is shown that this method guarantees exact conservation of current both locally and at the device terminals. Finite-element forms of Poisson's equation and the electron and hole current continuity equations are derived. Implementation of second order (linear triangular elements) and fourth order (Hermite bicubic elements) methods is discussed.

[1]  K. W. Morton.  Finite difference and finite element methods , 1976 .

[3]  J. Slotboom,et al.  Computer-aided two-dimensional analysis of bipolar transistors , 1973 .

[4]  M. Reiser,et al.  A two-dimensional numerical FET model for DC, AC, and large-signal analysis , 1973 .

[5]  O. Zienkiewicz.  The Finite Element Method In Engineering Science , 1971 .

[6]  W. Engl,et al.  Two-dimensional computer simulation for switching a bipolar transistor out of saturation , 1975, IEEE Transactions on Electron Devices.

[7]  G. Haddad,et al.  Finite-element simulation of GaAs MESFET's with lateral doping profiles and submicron gates , 1976, IEEE Transactions on Electron Devices.

[8]  H. Kodera,et al.  Drain conductance of junction gate FET's in the hot electron range , 1976, IEEE Transactions on Electron Devices.

[9]  W. Engl,et al.  Two-dimensional analysis of a monolithic PNP transistor , 1974 .

[10]  H. H. Heimeier.  A two-dimensional numerical analysis of a silicon N-P-N transistor , 1973 .

[11]  B. Himsworth,et al.  A two-dimensional analysis of indium phosphide junction field effect transistors with long and short channels , 1972 .

[12]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[13]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[14]  H. Saunders.  Book Reviews : NUMERICAL METHODS IN FINITE ELEMENT ANALYSIS K.-J. Bathe and E.L. Wilson Prentice-Hall, Inc, Englewood Cliffs, NJ , 1978 .

[15]  D A Calahan,et al.  Vectorized General Sparsity Algorithms with Backing Store. , 1977 .

[16]  M. Reiser.  On the stability of finite difference schemes in transient semiconductor problems , 1973 .

[17]  G. Stone.  High-Order Finite Elements for Inhomogeneous Acoustic Guiding Structures , 1973 .

[18]  L. Segerlind.  Applied Finite Element Analysis , 1976 .

[19]  R. J. Lomax,et al.  wo-dimensional finite element simulation of semiconductor devices , 1974 .

[20]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[21]  E. M. Buturla,et al.  Steady-state analysis of field effect transistors via the finite element method , 1975 .

[22]  J. Oden.  Finite Elements of Nonlinear Continua , 1971 .

[23]  H. Gummel,et al.  Large-signal analysis of a silicon Read diode oscillator , 1969 .

[24]  R. R. O'Brien,et al.  Computer aided two-dimensional analysis of the junction field-effect transistor , 1970 .