Guaranteeing charge conservation of empirically extracted Gallium Nitride (GaN) High-Electron-Mobility Transistor (HEMT) models is necessary to avoid simulation issues and artifacts in the prediction. However, dispersive effects, such as thermal and charge-trapping phenomena, may compromise the model extraction flow resulting in poor model accuracy. Although GaN HEMT models should be extracted, in principle, from an isodynamic dataset, this work deals with the systematic identification of an approximate, yet most suitable, charge-conservative empirical model from standard multi-bias S-parameters, i.e., from non-isodynamic data. Results show that the obtained model maintains a reasonable accuracy in predicting both small- and large-signal behavior, while providing the benefits of charge conservation.

High-order interpolation algorithms for charge conservation in Particle-in-Cell (PIC) simulations are presented. The methods are valid for the case that a particle trajectory is a zigzag line. The second-order and third-order algorithms which can be applied to any even-order and odd-order are discussed in this paper, respectively. Several test simulations are performed to demonstrate their validity in two-dimensional PIC code. Compared with the simulation results of one-order, high-order algorithms have advantages in computation precision and enlarging the grid scales which reduces the CPU time.

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson’s equation, or equivalently under charge conservation, the Ampère’s one, which self-consistently rules the electric field evolution. In order to ensure having proper physical solutions, it is necessary that the scheme preserves charge numerically. B-spline deposition will be used for the interpolation step. The solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure.