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 robustne ss of four basic iteration methods for implementing self-consistency i n Wigner function-based quantum device simulation. These methods inclu de steady-stale Gummel, transient Gummel, steady-stale Newton, and tra nsient Newton. Ln a single mathematical framework and notation, we pre sent the numerical implementation of each of these self-consistency it eration methods. As a lest case to compare the iteration methods, we s imulate 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 danger s of this practice, and show how to take advantage of the complimentar y strengths of both steady-state and transient iteration methods where appropriate. Thus, because the steady-state methods are vastly more e fficient (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 re duced the use of the steady-stale methods in practice. On the other ha nd, 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 appr opriate for a narrower range of directed investigations where transien t effects are inherent or suspected, rather than for full I-V curve tr acts. Finally, we found the two Gummel methods to be generally prefera ble to their (theoretically more accurate) Newton counterparts, since the Gummel methods are: equally accurate in practice, while having a l ower computational cost.