Abstract

CHAPTER 3. BIFURCATION ANALYSIS 64
GMRES was able to more efficiently solve the linear systems in the Householder
continuation than in the bordering method.
3.9 Results
Once the simulator was connected with LOCA, the first thing we wanted to do was
analyze the original grid Nx = 86, Nk = 72 that our project’s physicists and engi-
neers had used in reporting results to the scientific community. These results [8],
[40] reported hystersis in the current-voltage (I-V) curves and current oscillation for
some values of applied bias. Figure 3.6 shows a forward sweep in bias from V =0to
V =0.480, with increments of 0.08 taken in bias. As you can see, the I-V curve drops
suddenly at 0.318 volts to a lower curve and continues on. In the reverse bias case,
wherewestartatV =0.480 and reduce by 0.08 volts to V = 0, the I-V curve follows
out this lower branch, but does not jump up at 0.318 volts. Instead, it continues along
this lower curve, until it jumps back up to the upper curve at 0.256 volts. Figure 3.7
shows the window of voltage that creates current oscillation within the device. We
can see the oscillation onsets between 0.240 volts and 0.248 volts and turns off again
between 0.256 volts and 0.264 volts.
Using LOCA’s pseudo arc-length continuation algorithm and eigensolver, we were
able to explain why these phenomena occur. Figure 3.8 shows the I-V curve generated
by LOCA. LOCA has found two turning points: one at 0.256 volts and one at 0.318
volts. The branch connecting the two is an unstable steady-state solution branch,