Two-dimensional semiconductor analysis using finite-element method

Two-dimensional simulation of semiconductor devices using a finite-element formulation is described. In the present analysis, Poisson's equation is solved by a finite-element method, based on the variational principle, and current continuity equations are solved by a method of weighted residuals. The advantage of this method is mentioned. In order to demonstrate the validity of this method, a bipolar n-p-n transistor is analyzed, considering the generation-recombination term. Not only voltage-current characteristic, but also junction capacitance and cutoff frequency are calculated. Then transistor behavior under inverse mode by using the n-type buried layer as a common emitter is discussed.

[1]  W. Read,et al.  Statistics of the Recombinations of Holes and Electrons , 1952 .

[2]  H. Gummel.  A self-consistent iterative scheme for one-dimensional steady state transistor calculations , 1964 .

[3]  David P. Kennedy,et al.  Analysis of the Impurity Atom Distribution Near the Diffusion Mask for a Planar p-n Junction , 1965, IBM J. Res. Dev..

[4]  O. Zienkiewicz,et al.  The finite element method in structural and continuum mechanics, numerical solution of problems in structural and continuum mechanics , 1967 .

[5]  H. L. Stone.  ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[6]  A. De Mari,et al.  An accurate numerical steady-state one-dimensional solution of the P-N junction , 1968 .

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

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

[9]  H. C. Poon,et al.  An integral charge control model of bipolar transistors , 1970, Bell Syst. Tech. J..

[10]  R. Berry,et al.  An Optimal Ordering of Electronic Circuit Equations for a Sparse Matrix Solution , 1971 .

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

[12]  H. S. Cabayan,et al.  Efficient Techniques for Finite Element Analysis of Electric Machines , 1973 .

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

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

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

[16]  F. Klaassen.  Device physics of integrated injection logic , 1975, IEEE Transactions on Electron Devices.

[17]  R. R. O'Brien,et al.  Two-dimensional finite element modeling of NPN devices , 1976, 1976 International Electron Devices Meeting.

[18]  J. Slotboom,et al.  The pn-product in silicon , 1977 .