A Domain Decomposition Method for Silicon Devices

By: Carlo Cercignani, Irene Gamba, Joseph W. Jerome and Chi-Wang Shu

A mesoscopic/macroscopic model for self-consistent charged transport under high field scaling conditions corresponding to drift-collisions balance was derived by Cercignani, Gamba, and Levermore in [4]. The model was summarized in relationship to semiconductors in [2]. In [3], a conceptual domain decomposition method was implemented, based upon use of the drift-diffusion model in highly-doped regions of the device, and use of the high-field model in the channel, which represents a (relatively) lightly-doped region. The hydrodynamic model was used to calibrate interior boundary conditions. The material parameters of GaAs were employed in [3]. This paper extends the approach of [3]. (1) Benchmark comparisons are described for a Silicon $n^+-n-n^+$ diode. A global kinetic model is simulated with Silicon parameters. These simulations are sensitive to the choice of mobility/relaxation. (2) An elementary global domain decomposition method is presented. Mobilities are selected consistently with respect to the kinetic model. This study underscores the significance of the asymptotic parameter defined below, as the ratio of drift and thermal velocities, as a way to measure the change in velocity scales. This parameter gauges the effectiveness of the high field model.
This paper appears in Transport Theory and Statistical Physics vol. 29 (2000), 525--536. It can be viewed in the following format: