Numerical Boltzmann

The main objective of the Numerical Boltzmann approach is to perform device modeling by self-consistent solution of the Poisson and Boltzmann transport equations. In contrast to the hydrodynamic and drift-diffusion methods, the Numerical Boltzmann approach gives the distribution function for the entire device, as well as current-voltage characteristics. The Numerical Boltzmann approach gives almost as much information as Monte Carlo simulations, but is orders of magnitude faster and is not susceptible to statistical noise. It is thus ideal for modeling hot-electron effects including oxide degradation and EPROM programming. In addition, it does not rely on mobility models, and therefore will not be susceptible to problems defining mobility for deep-submicron devices. We first presented the approach as a simple, efficient method of solving the Boltzmann equation for a homogeneous silicon slab. Since that time, it has grown into a robust and efficient method for calculating the momentum distribution function for an entire MOSFET. The Numerical Boltzmann approach is especially useful for applications in reliability, EPROM's, and very short channel devices, where the drift-diffusion, and hydrodynamic models may not provide sufficient information.

Electron distribution function along the channel 0.0013um below the interface

K. A. Hennacy, Y.-J. Wu, N. Goldsman, I. D. Mayergoyz, "Deterministic MOSFET Simulation Using a Generalized Spherical Harmonic Expansion of the Boltzmann Equation," Solid-State Electronics, vol. 38, pp. 1495-1498, 1995. J. Stanley and N. Goldsman, "Full-Zone Dispersion Relations in Si Using Schur Complement Decomposition," Physical Review B, vol. 51, no. 8, pp. 4931-4939, 1995. Y.-J. Wu, K. Hennacy, N. Goldsman, and I. Mayergoyz, "Two Dimensional Submicron MOSFET Simulation Using Generalized Expansion Method and Fixed Point Iteration Technique to the Boltzmann Transport Equation," in International Symposium on VLSI Technology, Systems, and Applications, pp. 122-125, 1995. W. Liang, Y.-J. Wu, K. Hennacy, S. Singh, N. Goldsman, and I. Mayergoyz, "2-D MOSFET Simulation by Self-consistent Solution of the Boltzmann and Poisson Equations Using a Generalized Spherical Harmonic Expansion," in Simulation of Semiconductor Devices and Processes, (Wien, New York), pp. 122-125, Springer-Verlag, 1995. Y.-J. Wu and N. Goldsman, "Deterministic Modeling of Impact Ionization with a Random-k Approximation and the Solution of the Multi-Band Boltzmann Transport Equation," Journal of Applied Physics, vol. 78, no. 8, 1995. W. Liang, N. Goldsman, and I. Mayergoyz, "A new self-consistent 2D device simulator based on deterministic solution of the Boltzmann, Poisson and hole-continuity equations," Proceedings of the Fourth International Workshop on Computational Electronics, 1995. S. Singh, N. Goldsman, and I. Mayergoyz, "A self-consistent solution of the multi-band Boltzmann, Poisson and hole-continuity equations," Proceedings of the Fourth International Workshop on Computational Electronics, 1995. W. Liang, N. Goldsman, and I. Mayergoyz, "2-dimensional MOSFET modeling including surface effects and impact ionization by self-consistent solution of the Boltzmann, Poisson and hole-continuity equations," IEEE Transactions on Elec. Dev. S. Singh, N. Goldsman, and I. Mayergoyz, "Modeling multi-band effects in silicon by self-consistent solution of the Boltzmann transport and Poisson equations," Solid-State Electronics. W.-C. Liang, Y.-J. Wu, K. Hannacy, S. Singh, N. Goldsman, and I. Mayergoyz, "2-dimensional MOSFET analysis including impact ionization by self-consistent solution of the Boltzmann transport and Poisson equations using a generalized spherical harmonic expansion method," in Hot Carriers in Semiconductors , pp. 483-487, 1996.