Investigation of numerical algorithms in semiconductor device simulation

Abstract The algorithms used in semiconductor device simulation are investigated. Inversion algorithms, such as SOR, SI, generalized ICCG and Crout methods are compared in terms of convergency and required computer resources for various devices and bias conditions. For linearization of the basic equations, a quasi-coupled method is also compared with Gummel's conventional decoupled method. Numerical experimentation shows that even the SOR method, which has the slowest convergency among these algorithms, efficiently provides good results when used properly. Moreover, the quasi-coupled method is also effective in linearizing the basic equations for transient analysis or high bias conditions without a significant increase in the required memory. Consequently, a properly used simulator having several algorithms is shown to be necessary for two- and three-dimensional analysis. Furthermore, guidelines for applying these numerical algorithms effectively are described in detail.

[1]  W. Fichtner,et al.  Numerical methods for semiconductor device simulation , 1983, IEEE Transactions on Electron Devices.

[2]  T. Sudo,et al.  Two-dimensional semiconductor analysis using finite-element method , 1979, IEEE Transactions on Electron Devices.

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

[4]  T. Sudo,et al.  Threshold-voltage analysis of short- and narrow-channel MOSFET's by three-dimensional computer simulation , 1982, IEEE Transactions on Electron Devices.

[5]  S. Horiguchi,et al.  A three-dimensional analysis of semiconductor devices , 1982, IEEE Transactions on Electron Devices.

[6]  K. Kato,et al.  Analysis of Kink Characteristics in Silicon-on-Insulator MOSFET's Using Two-Carrier Modeling , 1985, IEEE Journal of Solid-State Circuits.

[7]  R.W. Dutton,et al.  Modeling of the silicon integrated-circuit design and manufacturing process , 1983, IEEE Transactions on Electron Devices.

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

[9]  Naoyuki Shigyo,et al.  Analysis of an anomalous subthreshold current in a fully recessed oxide MOSFET using a three-dimensional device simulator , 1985 .

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

[11]  J. Meijerink,et al.  An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix , 1977 .

[12]  L. F. Wagner,et al.  Generalised ICCG method for solution of asymmetric, sparse, linear systems of discretised semiconductor device equations , 1982 .

[13]  E. M. Buturla,et al.  Finite-element analysis of semiconductor devices: the FIELDAY program , 1981 .

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

[15]  Ken Yamaguchi,et al.  A time-dependent and two-dimensional numerical model for MOSFET device operation , 1983 .

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

[17]  W. L. Engl,et al.  High injection in a two-dimensional transistor , 1974 .

[18]  N. Kotani,et al.  A numerical analysis of avalanche breakdown in short-channel MOSFETs , 1981 .

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

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

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

[22]  S. Asai,et al.  Analytical models of threshold voltage and breakdown voltage of short-channel MOSFETs derived from two-dimensional analysis , 1979, IEEE Journal of Solid-State Circuits.

[23]  M. S. Mock,et al.  A time-dependent numerical model of the insulated-gate field-effect transistor , 1981 .

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

[25]  Y. Aoki,et al.  Three-dimensional device simulator Caddeth with highly convergent matrix solution algorithms , 1985, IEEE Transactions on Electron Devices.

[26]  H. Kitazawa,et al.  An accurate design method of bipolar devices using a two-dimensional device simulator , 1981, IEEE Transactions on Electron Devices.

[27]  T. Wada,et al.  Modification of ICCG method for application to semiconductor device simulators , 1982 .

[28]  D.H. Navon,et al.  Two-dimensional carrier flow in a transistor structure under nonisothermal conditions , 1976, IEEE Transactions on Electron Devices.