About the dependence of the convergence of Gummel’s algorithm and its linear variants on the device geometry
Rainer Sawatzki · Birkhäuser Basel eBooks · 1990
The convergence of Gummel’algorithm is known for sufficiently small currents or sufficiently small MOSFET-devices. We take a closer look at the dependence of the convergence of Gummel’s algorithm and two linear variants on the device geometry. Using spectral analysis we give a sufficient condition for local convergence, where the geometry enters as the smallest eigenvalue of a certain general eigenvalue problem. Estimating the eigenvalue with a maximum principle yields an upper limit for the size of the device which guarantees local convergence of all of the three algorithms. Finally we compare à priori estimates with the computed eigenvalues.