Highly Controllable Probabilistic Bits Leveraging Instability of SiO_x-Based Threshold Switching Devices for Probabilistic Computing

We demonstrate probabilistic bits (P-bits) with a novel $\mathrm{Ti} / \mathrm{SiO}_{\mathrm{x}} / \mathrm{Ti}$ stack, which is a fundamental building block for probabilistic computing. Nanoscale $\mathrm{SiO}_{\mathbf{x}}$ devices typically exhibit threshold switching (TS) characteristics, generating reliable voltage oscillations at a given input voltage ($V_{\mathrm {{i n}}}$) pulse. Here, we introduce a chemically reactive Ti scavenging layer at the interface between the electrode and SiO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> to promote the instability of TS, causing variation. This leads to the random voltage oscillation with the unexpected failure to represent the data ‘ 1 ’, enabling stochastic P-bit operation. More importantly, the $\mathrm{SiO}_{\mathbf{x}}$ film sandwiched with Ti layers at both interfaces allows the probability of data ‘ 1 ’ $\left(\mathrm{P}_{1}\right)$ to be precisely controlled as a function of $V_{\text {in }}$. This results in a sigmoidal $P_{1}$ curve over a wide range of $V_{\text {in }}$ greater than 1.4 V. Therefore, leveraging the developed $\mathrm{SiO}_{\mathrm{x}}$-based P -bit can speed up the algorithm for finding the optimal path in the vehicle routing problem, which is verified through MATLAB simulation.