A wavelet method to solve high-dimensional transport equations in semiconductor devices

This paper reports the first numerical solver for the Boltzmann transport equation (BTE) that uses wavelets as basis functions. The main advantage of wavelets is that they offer modern compression and adaptation techniques that could cope with the “curse of dimensionality” of the 6-dimensional phase space. An adequate numerical method for the BTE has been developed which combines a conservative discontinuous Galerkin (DG) formulation with a Multi-Wavelets (MW) basis. NIN device simulations in a 3-dimensional phase space prove that the DG formulation performs well together with MWs. On the other hand, it shows that MWs provide a very efficient basis for the BTE. The number of degrees of freedom can be compressed to about 1–10% in comparison to other modern solvers. Even greater advantages are expected for higher-dimensional phase spaces.