# 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] $$I(t)=\left\{\begin{array}{c}{A}_1\times s\times \sinh (Bvpn),\kern0.5em vpn\ge 0\\ {}{A}_2\times s\times \sinh (Bvpn),\kern2.25em vpn<0\end{array}\right.$$ 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 [75,76,77] $$v(t)={R}_{\mathrm{ON}}{e}^{\left(\lambda /{x}_{\mathrm{off}}-{x}_{\mathrm{on}}\right)\left(x-{x}_{\mathrm{on}}\right)}\times i(t)$$ The exponential function is changed to safeexp()
ASU/Stanford [78,79,80,81] $$I\left(g,V\right)={I}_0\exp \left(\frac{-g}{g_0}\right)\sinh \left(\frac{V}{V_0}\right)$$ The gap is expressed using s:
gap = s ×  min  gap + (1 − s) × maxgap
Then sinh is changed to safesinh(), exponential function to safeexp()