Title: Nanosecond True Random Number Generation with Superparamagnetic Tunnel Junctions -- Identification of Joule Heating and Spin-Transfer-Torque effects

Abstract: This work investigates nanosecond superparamagnetic switching in 50 nm diameter in-plane magnetized magnetic tunnel junctions (MTJs). Due to the small in-plane uniaxial anisotropy, dwell times below 10 ns and auto-correlation times down to 5 ns are measured for circular superparamagnetic tunnel junctions (SMTJs). SMTJs exhibit probabilistic switching of the magnetic free layer, which can be used for the generation of true random numbers. The quality of random bitstreams, generated by our SMTJ, is evaluated with a statistical test suite (NIST STS, sp 800-22) and shows true randomness after three XOR operations of four random SMTJ bitstreams. A low footprint CMOS circuit is proposed for fast and energy-efficient random number generation. We demonstrate that the probability of a 1 or 0 can be tuned by spin-transfer-torque (STT), while the average bit generation rate is mainly affected by the current density via Joule heating. Although both effects are always present in MTJs, Joule heating most often is neglected. However, with a resistance area (RA) product of 15 $\Omega \mu$m$^2$ and current densities of the order of 1 MA/cm$^2$, an increasing temperature at the tunneling site results in a significant increase in the switching rate. As Joule heating and STT scale differently with current density, device design can be optimized based on our findings.