Time-domain Coupled Full Maxwell- and Drift-diffsion-solver for Simulating Scanning Microwave Microscopy of Semiconductors

This paper presents a transient electromagnetic Maxwell solver (MS), a transient
semiconductor Poisson-Drift-Dffusion (PDD) solver, and their numerical coupling. The proposed
numerical solution schemes are based on Finite Element Method (FEM). Due to the solvers
complexity it is important to carefully examine the obtained initial results. Therefore, a simple
1D pn junction diode illuminated by an external electromagnetic plane wave is considered, as the
stationary solutions of this structure such as the depletion width, built-in voltage, and carrier
concentration distribution can be analytically obtained. The presented initially obtained transient
results converge well to the analytic stationary solutions. The electromagnetic waves reflected
from a diode with zero bias and 0.8V bias structure reveal a small signal di®erence within a
wide frequency range, which is an encouraging initial step towards more realistic simulations of
scanning microwave microscopy structures and arrangements. The extension of the presented
field formulations and numerical methods to 2D and 3D problems is straightforward.