Hendrik Leenders, Paul Luckner, Tobias Linn, Christoph Jungemann
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A Godunov-type stabilization scheme for the Boltzmann transport equation of III-V devices with a 3D k-space
This paper presents a deterministic approach for solving the Boltzmann transport equation (BTE) together with the Poisson equation (PE) for III-V semiconductor devices with a three-dimensional \({\textbf {k}}\)-space. The BTE is stabilized using Godunov’s scheme, whose linearity in the distribution function simplifies the application of the Newton–Raphson method to the coupled discrete BTE and PE. The formulation of the discrete equations ensures the nonnegativity of the distribution function regardless of the scattering rate, which can include the Pauli exclusion principle, and exhibits excellent numerical stability under steady state as well as transient conditions. In the latter case, both implicit and explicit time integration methods can be used and even slow processes (e.g., recombination) can be handled using this approach. In addition, the direct solution of the BTE can be easily extended to the small-signal case for arbitrary frequencies. Exemplary BTE results are shown for a GaAs \({\textrm{N}}^{+}{\textrm{NN}}^{+}\)-structure, revealing, inter alia, that the approximations of the drift-diffusion model can fail for large built-in fields in III-V devices.
期刊介绍:
he Journal of Computational Electronics brings together research on all aspects of modeling and simulation of modern electronics. This includes optical, electronic, mechanical, and quantum mechanical aspects, as well as research on the underlying mathematical algorithms and computational details. The related areas of energy conversion/storage and of molecular and biological systems, in which the thrust is on the charge transport, electronic, mechanical, and optical properties, are also covered.
In particular, we encourage manuscripts dealing with device simulation; with optical and optoelectronic systems and photonics; with energy storage (e.g. batteries, fuel cells) and harvesting (e.g. photovoltaic), with simulation of circuits, VLSI layout, logic and architecture (based on, for example, CMOS devices, quantum-cellular automata, QBITs, or single-electron transistors); with electromagnetic simulations (such as microwave electronics and components); or with molecular and biological systems. However, in all these cases, the submitted manuscripts should explicitly address the electronic properties of the relevant systems, materials, or devices and/or present novel contributions to the physical models, computational strategies, or numerical algorithms.