Probability Distribution of the Write-Error Rate of Voltage-Controlled Magnetoresistive Random-Access Memories

Abstract

In this study, we theoretically explore the probability distribution of the write-error rate (WER) of a voltage-controlled magnetoresistive random-access memory (VC MRAM). A probability density function (PDF) of the WER is analytically obtained using the change-of-variable technique with the assumption that the anisotropy constant of the VC MRAM follows the normal distribution. Furthermore, we assume that the WER of a single memory cell forms a parabola as a function of the anisotropy constant, resulting from numerical simulations by solving the Landau-Lifshitz-Gilbert equation based on the macrospin model. Theoretical analysis facilitates in identifying types of the PDF: a monotonic decreasing function with a peak at the smallest WER, and a function with local maximum.