Karl Rupp MSc Dipl.-Ing. Dr.techn. Publications

Semiconductor device simulation relies on solving the most accurate models available and is commonly constrained by the computational budget of a single machine. The recent shift from purely two-dimensional to fully three-dimensional device layouts, however, entails a much higher computational cost for simulations of the same accuracy – typically orders of magnitude.
A reduction in the accuracy to fit the same computational budget is highly undesirable from an engineering point of view. Instead, accuracy can be preserved by increasing the computational budget beyond what is provided by a single machine through a distributed simulation on a compute cluster or on a supercomputer, such as the Vienna Scientific Cluster.
In our current research, we focus on numerically solving the Boltzmann transport equation (BTE), which is commonly considered to be the best semiclassical description of charge transport in semiconductors. The most widely used method for solving the BTE is the so-called Monte Carlo method. Unfortunately, the stochastic nature of the Monte Carlo method results in a poor scaling of accuracy with available computational resources. For a twofold increase in accuracy, four times the computational resources are required. Thus, simulations using the Monte Carlo method provide only limited gains in accuracy when run on a supercomputer instead of a single machine.
A better alternative for the solution of the BTE on supercomputers is the deterministic spherical harmonics expansion method. With a proper choice of algorithms for the spherical harmonics expansion method, a twofold increase in accuracy can be achieved with a twofold increase in computational resources. To achieve this linear relation of accuracy and computational resources, we conducted research into better discretizations and scalable linear and nonlinear solvers. Fig. 1 depicts one of our research results, wherein we identified a block structure of the system matrix based on trajectories of charge carriers in free flight and proposed a parallel preconditioner exploiting the block structure.
Ultimately, we aim to be the first to compute deterministic large-scale solutions of the BTE. Our simulations will provide unprecedented accuracy for three-dimensional device simulations and offer new insights into urgent modeling and engineering challenges, such as hot carrier degradation.

Fig. 1: Trajectories of charge carriers in free flight lead to a block structure of the system matrix. Each trajectory corresponds to charge carriers with the same discrete constant total energy and is represented by one block in the system matrix. The blocks are coupled by inelastic scattering processes and can be processed in parallel.