A Kinetic Monte Carlo Model for Stochastic Switching in Monolayer MoS2 RRAMs

We construct a kinetic Monte Carlo (kMC) model to simulate the impact of stochastic multi-hotspot chalcogen-mediated switching on the $I$ - $V$ characteristics and associated variability in monolayer MoS ${ }_{2}$ RRAMs. The designed physics-informed rate equations capture the abrupt and gradual (with electric field) SET and RESET, respectively and enable the extraction of key material parameters. The calibrated model yields an excellent fit with experimental $I-V$ and replicates the large cycle-to-cycle (C2C) variability (coefficient of variance, $\sigma / \mu>0.5)$. Next, we examine the controlled annihilation of hotspots in the RESET process, using DC and pulsed biasing schemes - thereby tuning the statistical parameters of HRS variability at runtime. The change in the mean ($\mu \sim 30-600 \mathrm{M} \Omega$) and coefficient of variance ($\sigma / \mu \sim 1-4$) in HRS variability obtained by tuning the stop voltage in the RESET cycle ($~_{~}{ }_{\text {stop }}$) is limited. However, the pulsed biasing scheme allows a much larger control over $\left(\mu \sim 10^{3}\right.$ to $\left.10^{9} \Omega\right)$ and $\left(\sigma / \mu \sim 10^{-2}\right.$ to $\left.10^{1}\right)$, by adjusting the pulse height $\left(V_{p}\right)$, duration $\left(t_{p w}\right)$, and number of pulses $\left(\mathbf{N}_{\mathbf{p}}\right)$. Finally, the promise of these devices as tunable stochastic sources is illustrated using a $n: n(n=8-256)$ challenge response pair (CRP) based physically unclonable function (PUF). These PUFs demonstrate state-of-the-art inter- and intra-Hamming distance, and the degree of stochasticity is validated using Shannon entropy and NIST SP 800-22 tests.