Sigmoid Probabilistic Bits Using SiOₓ Threshold Switching Devices for Probabilistic Computing

We present probabilistic bits (p-bits) implemented using a simple and fabrication-friendly Ti/SiOx/Ti stack for probabilistic computing. Sputter-deposited thin SiOx films (<10 nm) exhibit threshold switching (TS) behavior under dc characterization, producing continuous output voltage ( ${V} _{\text {out}}$ ) oscillations in response to a given input voltage ( ${V} _{\text {in}}$ ) pulse. When a chemically reactive Ti scavenging layer is introduced, nonuniform TS properties are observed, resulting in switching voltage (or resistance) variability and unexpected oscillation failures. Consequently, ${V} _{\mathbf {out}}$ oscillations begin to be detected in the form of random spikes, emulating the probability of representing data as “1” (P1). Notably, we demonstrate that when the SiOx layer is sandwiched between Ti scavengers at both interfaces, the value of ${P} _{{1}}$ can be controlled between 0 and 1 in an inversely proportional relationship to ${V} _{\mathbf {in}}$ . This sigmoid ${P} _{{1}}$ curve derived from Ti/SiOx/Ti p-bits plays a crucial role in executing simulated annealing (SA) algorithms. This capability is validated through MATLAB simulations, where the approach is applied to solve vehicle routing problems (VRPs) by identifying optimal solutions.