Stabilized mixed finite elements for fluid models in semiconductors

Abstract.In this article we deal with the numerical simulation of semiconductor devices using the Energy-Balance (EB) transport model. This accounts for hot electrons behaviour and nonlocal effects which are of utmost relevance in the simulation of submicron devices. We propose an efficient and accurate solver for the EB equations based on the well-known Gummel’s decoupled algorithm to handle iteratively the full system, while the discretization employs cell-centred Mixed Finite Volume (MFV) methods. These are derived from the standard Raviart-Thomas (RT) finite elements of lowest degree through a suitable quadrature formula which diagonalizes the element mass matrix. Numerical results to validate the newly proposed stabilized method are reported including the simulation of a model curved p-n diode, a one-dimensional p-n diode and a realistic state-of-the-art 1 μm-channel nMOS transistor.

[1]  M. Stynes,et al.  Numerical methods for singularly perturbed differential equations : convection-diffusion and flow problems , 1996 .

[2]  Jean E. Roberts,et al.  Global estimates for mixed methods for second order elliptic equations , 1985 .

[3]  Massimo Rudan,et al.  Hydrodynamic simulation of impact-ionization effects in p-n junctions , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

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

[5]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[6]  R. R. P. Van Nooyen,et al.  A Petrov-Galerkin mixed finite element method with exponential fitting , 1995 .

[7]  Paola Pietra,et al.  New mixed finite element schemes for current continuity equations , 1990 .

[8]  S. M. Sze,et al.  Physics of semiconductor devices , 1969 .

[9]  K. Blotekjaer.  Transport equations for electrons in two-valley semiconductors , 1970 .

[10]  Joseph W. Jerome.  Analysis of Charge Transport: A Mathematical Study of Semiconductor Devices , 1995 .

[11]  P. Raviart,et al.  A mixed finite element method for 2-nd order elliptic problems , 1977 .

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

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

[14]  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..