Additive Decomposition Applied to the Semiconductor Drift-Diffusion Model

A new numerical method for semiconductor device simulation is presented. The additive decomposition method has been successfully applied to Burgers' and Navier-Stokes equations governing turbulent fluid flow by decomposing the equations into large-scale and small-scale parts without averaging. The additive decomposition (AD) technique is well suited to problems with a large range of time and/or space scales, for example, thermal-electrical simulation of power semiconductor devices with large physical size. Furthermore, AD adds a level of parallelization for improved computational efficiency. The new numerical technique has been tested on the 1-D drift-diffusion model of a p-i-n diode for reverse and forward biases. Distributions of φ, n and p have been calculated using the AD method on a coarse large-scale grid and then in parallel small-scale grid sections. The AD results agreed well with the results obtained with a traditional one-grid approach, while potentially reducing memory requirements with the new method.