The rapid developments in semiconductor device technology have led to typical device lengths in the deca-nanometer regime. In this regime, quantum mechanical effects are sufficiently small such that carrier transport is well described using a semi-classical picture. However, macroscopic transport models such as the drift-diffusion model, which has been used in science and industry for several decades, are no longer valid and thus unable to provide additional physical insight into device operation. To recover the loss of accuracy of macroscopic transport models, the Boltzmann Transport Equation (BTE) needs to solved, which is commonly considered to be the best semi-classical description of carrier transport in semiconductor devices. Here, the distribution of carriers with respect to spatial location, momentum, and time is modeled by a distribution function. Due to the high dimensionality of the equation, direct solution approaches are limited by high memory requirements. As a consequence, the most popular solution method for the BTE is the Monte Carlo method, which has disadvantages due to its stochastic nature.
A deterministic solution approach is the Spherical Harmonics Expansion (SHE) method, which is a spectral method in momentum space obtained by expanding the distribution function into spherical harmonics. The advantage of this approach is the reduced dimensionality, since only a five-dimensional problem instead of a seven-dimensional problem needs to be solved. We extended the SHE method to unstructured grids, which led to a significant reduction of the number of unknowns in the resulting linear systems for three-dimensional device simulations.Together with recently developed adaptive expansion orders and the parallel preconditioner scheme, we carried out the first three-dimensional device simulations of a trigate transistor using the SHE method. Moreover, we managed to run our simulations on an average work station equipped with twelve Gigabytes of main memory and thus demonstrated that no supercomputers were required for the SHE method even in the case of three-dimensional device simulations.