Comparison of self-consistency iteration options for the Wigner function method of quantum device simulation

In the present work, we compare the efficiency, accuracy, and robustness of four basic iteration methods for implementing self-consistency in Wigner function-based quantum device simulation. These methods include steady-stale Gummel, transient Gummel, steady-stale Newton, and transient Newton. Ln a single mathematical framework and notation, we present the numerical implementation of each of these self-consistency iteration methods. As a lest case to compare the iteration methods, we simulate the current-voltage (I-V) curve of a resonant tunneling diode. Standard practice ibr this task has been to rely solely on either st steady-state or a transient iteration method. We illustrate the dangers of this practice, and show how to take advantage of the complimentary strengths of both steady-state and transient iteration methods where appropriate. Thus, because the steady-state methods are vastly more efficient (i.e., have a much lower computational cost), and are usually equal in accuracy to the transient methods, the former are preferable for wide-ranging initial device investigations such as tracing the I-V curve. Implementation difficulties which we address here may have reduced the use of the steady-stale methods in practice. On the other hand, the transient methods are inherently more robust and accurate (i.e., they reliably and correctly reproduce device;physics), However, the high computational cost of the transient methods makes them more appropriate for a narrower range of directed investigations where transient effects are inherent or suspected, rather than for full I-V curve tracts. Finally, we found the two Gummel methods to be generally preferable to their (theoretically more accurate) Newton counterparts, since the Gummel methods are: equally accurate in practice, while having a lower computational cost.