A Domain Decomposition Method for Silicon Devices

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]. • 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. • 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 η 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. Acknowledgments: The first author is supported by M.U.R.S.T. of Italy. The second author is supported by the National Science Foundation under grant DMS-9623037. The third author is supported by the National Science Foundation under grants DMS-9424464 and DMS-9704458. The fourth author is supported by the National Science Foundation under grant ECS-9627849 and the Army Research Office under grant DAAG55-97-1-0318. ∗Politecnico di Milano, 20133 Milano, Italy. tel: 0039-2-23994557, Fax: 0039-2-23994568, email: [email protected] †Department of Mathematics and Texas Institute of Computational and Applied Mathematics, University of Texas, Austin, TX 78712. tel: (512) 471-7150, Fax: (512) 471-9038, email: [email protected] ‡Department of Mathematics, Northwestern University, Evanston, IL 60208. tel: (847) 491-5575, Fax: (847) 491-8906, email: [email protected]; corresponding author. §Division of Applied Mathematics, Brown University, Providence, RI 02912. tel: (401) 863-2549, Fax: (401) 863-1355, email: [email protected]