From: A Collective Study on Modeling and Simulation of Resistive Random Access Memory
Model | Original I-V relationship (f_{1}) | Improved I-V using concepts from Wang and Roychowdhury^{100} |
---|---|---|
Linear ion drift [3] | f_{1} = (R_{ON} × s + R_{off} × (1 − s))^{−1} × vpn |
Can have division by zero error when s = R_{off}/(R_{on}/R_{off}). Modified equation: y = smoothclip(s − R_{off}/(R_{on} − R_{off}), smoothing) + R_{off}/(R_{on} − R_{off}) Then, f_{1} = (R_{on} × y + R_{off} × (1 − y))^{−1} × vpn |
Non-linear ion drift [46, 68] | I = s^{n}β 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. f_{1p} = A_{1} × s × safesinh(B × vpn, maxslope) f_{1n} = A_{2} × s × safesinh(B × vpn, maxslope) f_{1} = smoothswitch(f_{1n}, f_{1p}, 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() |