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

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 $10\phantom{\rule{0.2em}{0ex}}\text{ns}$ and autocorrelation times down to $5\phantom{\rule{0.2em}{0ex}}\text{ns}$ 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 the random bit streams generated by our SMTJ is evaluated with a statistical test suite (NIST STS, sp 800-22) and shows true randomness after three exclusive or (xor) operations of four random SMTJ bit streams. 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, most often Joule heating is neglected. However, with a resistance-area (RA) product of $15\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{m}}^{2}$ and current densities of the order of $1\phantom{\rule{0.2em}{0ex}}{\text{MA/cm}}^{2}$, 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, the device design can be optimized based on our findings.