Continuation methods in semiconductor device simulation

Predictor-corrector continuation methods for characterizing the voltage-current (V, I) behavior of semiconductor devices are presented. Numerical simulations of some complex CMOS structures demonstrate the efficacy of continuation methods; in particular, it is possible to accurately determine the limit points of certain (V, I) curves, corresponding to latchup triggering and holding points. Continuation techniques, coupled with grid adaption, provide substantial improvement in computational efficiency over previous approaches and are well suited to deal with multivalued current responses.

[1]  Hans D. Mittelmann,et al.  Continuation and multi-grid for nonlinear elliptic systems , 1986 .

[2]  Mark R. Pinto,et al.  Computation of steady-state CMOS latchup characteristics , 1988, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[3]  M. S. Mock,et al.  Analysis of mathematical models of semiconductors devices , 1983 .

[4]  D. Rose,et al.  Global approximate Newton methods , 1981 .

[5]  Coupled and decoupled algorithms for semiconductor simulation , 1985 .

[6]  C.S. Rafferty,et al.  Iterative Methods in Semiconductor Device Simulation , 1985, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[7]  M.R. Pinto,et al.  An efficient numerical model of CMOS latch-up , 1983, IEEE Electron Device Letters.

[8]  R. Bank,et al.  Some a posteriori error estimators for elliptic partial differential equations , 1985 .

[9]  Christian A. Ringhofer,et al.  Computation of Current-Voltage Characteristics in a Semiconductor Device using Arc-length Continuation , 1983 .

[10]  Werner C. Rheinboldt,et al.  Solution Fields of Nonlinear Equations and Continuation Methods , 1980 .

[11]  Wolfgang Hackbusch,et al.  Multigrid Methods II , 1986 .

[12]  W. Rheinboldt.  On the computation of multi-dimensional solution manifolds of parametrized equations , 1988 .

[13]  Randolph E. Bank,et al.  Transient simulation of silicon devices and circuits , 1985 .

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

[15]  H. Schwetlick,et al.  Ein lokal überlinear konvergentes Verfahren zur Bestimmung von Rückkehrpunkten implizit definierter Raumkurven , 1982 .

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

[17]  Randolph E. Bank,et al.  A-posteriori error estimates. Adaptive local mesh refinement and multigrid iteration , 1986 .

[18]  T. Chan.  Deflation Techniques and Block-Elimination Algorithms for Solving Bordered Singular Systems , 1984 .

[19]  Randolph E. Bank,et al.  Semiconductor device simulation , 1983 .

[20]  D.J. Rose,et al.  CAzM: A circuit analyzer with macromodeling , 1983, IEEE Transactions on Electron Devices.

[21]  Randolph E. Bank,et al.  Numerical Methods for Semiconductor Device Simulation , 1983 .

[22]  Seymour V. Parter.  A POSTERIORI ERROR ESTIMATES , 1975 .

[23]  A. De Mari,et al.  An accurate numerical one-dimensional solution of the p-n junction under arbitrary transient conditions , 1967 .

[24]  E. Grosse,et al.  Aspects of Computational Circuit Analysis , 1986 .

[25]  Andrea Demari.  Erratum: Accurate numerical solution of the one-dimensional p-n junction in steady state , 1967 .

[26]  S. M. Sze,et al.  Physics of semiconductor devices , 1969 .