Robust Numerical Solver for Nonlinear Semiconductor Problems

In this work, we develop a numerical solver, efficiently and robustly treating highly nonlinear semiconductor device problems. Beyond the capabilities of commercial tools, the solver can compute the time-domain capacitance and the spectrum of the device current. The solver is based on the finite element method (FEM) and employs the successive under-relaxation scheme. Its capability has been assessed and validated in a study of an axisymmetric metal-oxide–semiconductor (MOS) structure, presenting an archetypal scanning microwave microscopy (SMM) calibration sample, with both n- and p-doped semiconductors, including different excitation sources. Excellent agreement was obtained, when testing the tool against features of a commercial tool. By computing the capacitance for the applied low-frequency (LF) bias, combined with a high-frequency (HF) probe signal, the spectrum of the current flowing in the structure was evaluated, revealing mix-product components. This allowed us to verify the solver against measurements, resulting in a very good agreement.