10.2.1 Coherence Length

In the open Schrödinger equation we assume incoming waves with infinite coherence length. In the discrete Wigner equation the coherence length had to be introduced for purely numerical reasons and only in a second step was given a physical interpretation. The coherence length is a parameter which is not available in the QTBM. To compare with results from the QTBM we have to look at the limit $L_{\mathrm{coh}} \rightarrow \infty$.

In favor of the Wigner function method we note that physically a finite coherence length is more adequate. Results from elementary tunneling theory using Schrödinger formulations tend to overestimate the peak to valley ratio [Fre90], [RFK89].

A small change in the coherence length can already have a significant effect on the peak to valley ratio. This is shown in figure 10.4, where the coherence length is increased from $34$ to $62$ $\mathrm{nm}$ for a resonant tunneling diode [KKNS03] which leads to a 50 percent increase in the peak to valley ratio.

Figure 10.4: Effect of the coherence length in Wigner simulations