A Frequency- and Space-Domain Series-Expansion Approach for Efficient Numerical Modeling of Semiconductor Devices

In this paper, an approach is described that combines frequency-domain Fourier series expansion and space-domain polynomial expansion of the physical quantities inside the semiconductor, for an efficient numerical modeling of high-frequency active devices, based on the solution of the physical transport equations in the semiconductor. The unknowns of the problem are the coefficients of the expansions of the physical quantities in the device channel: electrostatic potential and electron density, velocity, and energy. 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-difference approaches. Moreover, the frequency-domain technique eliminates the need for time-to-frequency transforms for a spectral solution and allows for the easy inclusion of frequency-dependent parameters of the semiconductor that are particularly important at very high frequencies (e.g., dielectric constant). In addition, the coupling with an 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-2-D 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 with a standard Harmonic Balance formulation.