Table 3.

Improved I-V relationships of the various models

Model	Original I-V relationship (f1)	Improved I-V using concepts from Wang and Roychowdhury100
Linear ion drift [3]	f1 = (RON × s + Roff × (1 − s))−1 × vpn	Can have division by zero error when s = Roff/(Ron/Roff). Modified equation: y = smoothclip(s − Roff/(Ron − Roff), smoothing) + Roff/(Ron − Roff) Then, f1 = (Ron × y + Roff × (1 − y))−1 × vpn
Non-linear ion drift [46, 68]	I = snβ sinh(α × vpn) + χ(exp(γ × vpn) − 1)	sinh can be changed to safesinh(), exponential function to safeexp()
Yakopcic [73, 74]	$I\left(t\right)=\left\{\begin{array}{c}{A}_1\times s\times sinh\left(\mathit{\text{Bvpn}}\right),\mathit{vpn}\ge 0\\ A_2\times s\times sinh\left(\mathit{\text{Bvpn}}\right),\mathit{vpn}<0\end{array}\right.$	sinh is changed to safesinh(). The function is then smoothed. f1p = A1 × s × safesinh(B × vpn, maxslope) f1n = A2 × s × safesinh(B × vpn, maxslope) f1 = smoothswitch(f1n, f1p, vpn, smoothing)
TEAM/VTEAM [75–77]	$v\left(t\right)=R_{\mathrm{ON}}{e}^{\left(\lambda /x_{\mathrm{off}}-x_{\mathrm{on}}\right)\left(x-x_{\mathrm{on}}\right)}\times i\left(t\right)$	The exponential function is changed to safeexp()
ASU/Stanford [78–81]	$I\left(g,V\right)=I_{0}exp\left(\frac{-g}{g_0}\right)sinh\left(\frac{V}{V_0}\right)$	The gap is expressed using s: gap = s ×  min  gap + (1 − s) × maxgap Then sinh is changed to safesinh(), exponential function to safeexp()