Accelerating the transient simulation of semiconductor devices using filter-bank transforms

Abstract

Simulation of high frequency semiconductor devices, where non-local and hot carrier transport cannot be ignored, requires solution of Poisson's equation and at least the first three moments of the Boltzmann transport equation (hydrodynamic transport model). These equations form non-linear, coupled and time-dependent partial differential equations. One of the most efficient solvers of such system of equations is decoupled solver. In conventional decoupled methods, the fully implicit, semi-implicit and explicit methods are used to solve the equations. In fully or semi-implicit schemes, the method is unconditionally stable for any Δt or for very large Δt compared to explicit scheme. Thus, these schemes are very suitable and efficient for transient simulations. But, using these techniques leads to a large system of linear equations. Here for the first time, a filter bank-based preconditioning method is used to facilitate the iterative solution of this system. This method provides efficient preconditioners for matrices arising from discretizing of the PDEs, using finite difference techniques. Numerical results show that the condition number and iteration number are significantly reduced. The most important advantage of this preconditioner is its low computational complexity which can be reduced to O(N). Copyright © 2006 John Wiley & Sons, Ltd.