Harnessing Stochasticity in 2D Materials: Phonon-Assisted Defect Charge Dynamics in WS₂ by the First-Principles

Stochasticity plays an important role in cryptography, stochastic and neural-like computing, facilitating low-cost, error-tolerant solutions to complex problems such as integer factorization, invertible logic and optimization. Specifically, we investigate phonon-assisted defect charge dynamics in 2D materials, e.g. a sulfur vacancy in WS₂ monolayer (V_S-WS₂), using first principles calculations. We find that a true random bit generation scheme based on V_S-WS₂ optimally balances bitrate, energy efficiency, and tunability of bit probability. The entropy source based on VS-WS2 enables unbiased random bit generation at bitrates of 27 Mbps, which can be further optimized up to terabits per second by minimizing the energy barrier for defect-to-band electron transition through 3% tensile strain of the host-material. Furthermore, the direct dynamic process of defect charge transition is simulated by combining Landau-Zener formula with Langevin equation, which generates high-quality random bits tested by NIST statistical test suite. We explore the conditions needed to achieve true random bits, unveiling new possibilities in 2D material-based entropy sources. The essential insights into phonon-assisted defect charge dynamics combines with practical designs for high-performance, energy-efficient stochastic devices.