Efficient Frequency Domain plus Spatial Expansion Method For Semiconductor Devices Modeling

Abstract

We here present a method that combines frequency-domain Fourier series expansion and space-domain polynomial expansion of the physical quantities inside the semiconductor, for an efficient numerical modelling of high-frequency active devices, based on the solution of the physical transport equations in the semiconductor. The frequency- and space-domain expansions drastically reduce the number of time and space sampling points where the equations are computed, greatly reducing the computational burden with respect to classical finite-differences approaches. Moreover, the frequency-domain technique eliminates the need for time-to-frequency transforms for a spectral solution, and allows easy inclusion of frequency-dependent parameters of the semiconductor especially important at very high frequencies (e.g. dielectric constant). Also the coupling with a EM program, for a global modeling simulator, becomes straightforward, due to the reduced interconnection nodes with the physical simulator. A demonstrator for PC implementing a quasi-2D model with a hydrodynamic formulation with the first three moments of Boltzmann's Transport Equation is given, and its results are compared with a standard finite-difference time-domain approach and measured results.