An iterative method for adaptive finite element solutions of an energy transport model of semiconductor devices

A self-adjoint formulation of the energy transport model of semiconductor devices is proposed. This new formulation leads to symmetric and monotonic properties of the resulting system of nonlinear algebraic equations from an adaptive finite element approximation of the model. A node-by-node iterative method is then presented for solving the system. This is a globally convergent method that does not require the assembly of the global matrix system and full Jacobian matrices. An adaptive algorithm implementing this method is described in detail to illustrate the main features of this paper, namely, adaptation, node-by-node calculation, and global convergence. Numerical results of simulations on deep-submicron diode and MOSFET device structures are given to demonstrate the accuracy and efficiency of the algorithm.

[1]  Walter H. Ku,et al.  Two-dimensional semiconductor device analysis based on new finite-element discretization employing the S-G scheme , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[2]  C. Schmeiser,et al.  Semiconductor equations , 1990 .

[3]  Donald J. Rose,et al.  Numerical methods for the hydrodynamic device model: subsonic flow , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[4]  Jinn-Liang Liu,et al.  On Weak Residual Error Estimation , 1996, SIAM J. Sci. Comput..

[5]  Ansgar Jüngel,et al.  Numerical Discretization of Energy-Transport Models for Semiconductors with Nonparabolic Band Structure , 2000, SIAM J. Sci. Comput..

[6]  Y. Apanovich,et al.  Steady-state and transient analysis of submicron devices using energy balance and simplified hydrodynamic models , 1994, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[7]  Riccardo Sacco,et al.  Mixed finite volume methods for semiconductor device simulation , 1997 .

[8]  Massimo Rudan,et al.  Numerical solution of the hydrodynamic model for a one-dimensional semiconductor device , 1987 .

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

[10]  Tien-Sheng Chao,et al.  A new parallel adaptive finite volume method for the numerical simulation of semiconductor devices , 2001 .

[11]  Jerry G. Fossum,et al.  Simplified energy-balance model for pragmatic multi-dimensional device simulation , 1997 .

[12]  Roberto Guerrieri,et al.  A new discretization strategy of the semiconductor equations comprising momentum and energy balance , 1988, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[13]  S. Selberherr,et al.  A singular perturbation approach for the analysis of the fundamental semiconductor equations , 1983, IEEE Transactions on Electron Devices.

[14]  I. Babuska,et al.  Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods , 1983 .

[15]  K. Singhal,et al.  A consistent nonisothermal extension of the Scharfetter—Gummel stable difference approximation , 1985, IEEE Electron Device Letters.

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

[17]  Leszek Demkowicz,et al.  Toward a universal h-p adaptive finite element strategy , 1989 .

[18]  M. Fortin,et al.  Simulation of the hydrodynamic model of semiconductor devices by a finite element method , 1996 .

[19]  H. Grubin.  The physics of semiconductor devices , 1979, IEEE Journal of Quantum Electronics.

[20]  Riccardo Sacco,et al.  Exponentially Fitted Mixed Finite Volumes for Energy Balance Models in Semiconductor Device Simulation , 1998 .

[21]  A. Marrocco,et al.  Simulation de modèles energy transport à l'aide des éléments finis mixtes , 1996 .

[22]  Thomas I. Seidman,et al.  Iterative scheme for computer simulation of semiconductor devices , 1972 .

[23]  S. Selberherr,et al.  Finite boxes—A generalization of the finite-difference method suitable for semiconductor device simulation , 1983, IEEE Transactions on Electron Devices.

[24]  Joseph W. Jerome,et al.  CONSISTENCY OF SEMICONDUCTOR MODELING: AN EXISTENCE/STABILITY ANALYSIS FOR THE STATIONARY VAN ROOSBROECK SYSTEM* , 1985 .

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

[26]  Chi-Wang Shu,et al.  Transport effects and characteristic modes in the modeling and simulation of submicron devices , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[27]  Kincho H. Law,et al.  A finite element formulation for the hydrodynamic semiconductor device equations , 1993 .

[28]  Andreas Schenk,et al.  Advanced Physical Models for Silicon Device Simulation , 2004 .

[29]  R. E. Thomas,et al.  Carrier mobilities in silicon empirically related to doping and field , 1967 .

[30]  Wolfgang Fichtner,et al.  An adaptive grid refinement strategy for the drift-diffusion equations , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[31]  Cedric Lab,et al.  An energy‐transport model for semiconductor heterostructure devices: application to AlGaAs/GaAs MODFETs , 1999 .

[32]  S. Selberherr.  Analysis and simulation of semiconductor devices , 1984 .

[33]  Ren-Chuen Chen,et al.  Object-oriented programming of adaptive finite element and finite volume methods , 1996 .

[34]  K. Brennan,et al.  Hydrodynamic Simulation of Semiconductor Devices , 1997 .

[35]  Siegfried Selberherr,et al.  MINIMOS—A two-dimensional MOS transistor analyzer , 1980 .

[36]  Ting-Wei Tang,et al.  Extension of the Scharfetter—Gummel algorithm to the energy balance equation , 1984 .

[37]  Paola Pietra,et al.  Two-dimensional exponential fitting and applications to drift-diffusion models , 1989 .

[38]  Antonio Gnudi,et al.  Numerical modeling of advanced semiconductor devices , 1992, IBM J. Res. Dev..

[39]  C. V. Pao.  Block monotone iterative methods for numerical solutions of nonlinear elliptic equations , .

[40]  S. M. Sze,et al.  Modern semiconductor device physics , 1997 .