Maicke Andrew, Arzate Jared, Liu Samuel, Kwon Jaesuk, Smith J Darby, Aimone James B, Misra Shashank, Schuman Catherine, Cardwell Suma G, Incorvia Jean Anne C
University of Texas at Austin, Austin, TX, United States of America.
Sandia National Laboratories, Albuquerque, NM, United States of America.
Nanotechnology. 2024 Apr 23;35(27). doi: 10.1088/1361-6528/ad3b01.
Perpendicular magnetic tunnel junction (pMTJ)-based true-random number generators (RNGs) can consume orders of magnitude less energy per bit than CMOS pseudo-RNGs. Here, we numerically investigate with a macrospin Landau-Lifshitz-Gilbert equation solver the use of pMTJs driven by spin-orbit torque to directly sample numbers from arbitrary probability distributions with the help of a tunable probability tree. The tree operates by dynamically biasing sequences of pMTJ relaxation events, called 'coinflips', via an additional applied spin-transfer-torque current. Specifically, using a single, ideal pMTJ device we successfully draw integer samples on the interval [0, 255] from an exponential distribution based on-value distribution analysis. In order to investigate device-to-device variations, the thermal stability of the pMTJs are varied based on manufactured device data. It is found that while repeatedly using a varied device inhibits ability to recover the probability distribution, the device variations average out when considering the entire set of devices as a 'bucket' to agnostically draw random numbers from. Further, it is noted that the device variations most significantly impact the highest level of the probability tree, with diminishing errors at lower levels. The devices are then used to draw both uniformly and exponentially distributed numbers for the Monte Carlo computation of a problem from particle transport, showing excellent data fit with the analytical solution. Finally, the devices are benchmarked against CMOS and memristor RNGs, showing faster bit generation and significantly lower energy use.
基于垂直磁性隧道结（pMTJ）的真随机数发生器（RNG）每比特消耗的能量比CMOS伪随机数发生器少几个数量级。在此，我们使用宏自旋朗道-里夫希茨-吉尔伯特方程求解器进行数值研究，探讨利用自旋轨道扭矩驱动的pMTJ，借助可调概率树直接从任意概率分布中采样数字。该树通过额外施加的自旋转移扭矩电流，动态地对pMTJ弛豫事件序列（称为“抛硬币”）进行偏置来运行。具体而言，使用单个理想的pMTJ器件，基于值分布分析，我们成功地从指数分布中在区间[0, 255]上抽取整数样本。为了研究器件之间的差异，根据制造的器件数据改变pMTJ的热稳定性。结果发现，虽然反复使用不同的器件会抑制恢复概率分布的能力，但当将整个器件集视为一个“桶”来无差别地抽取随机数时，器件差异会相互抵消。此外，需要注意的是，器件差异对概率树的最高层影响最为显著，在较低层的误差逐渐减小。然后，这些器件被用于为粒子输运问题的蒙特卡罗计算抽取均匀分布和指数分布的数字，结果显示与解析解的数据拟合良好。最后，将这些器件与CMOS和忆阻器RNG进行基准测试，结果表明其比特生成速度更快且能耗显著更低。
