Probability distribution of write failure in a memory cell array consisting of magnetic tunnel junction elements with distributed write error rates

Write failure (WF) is a major reliability issue for applications of magnetoresistive random access memory (MRAM), and much effort has been devoted to reducing the write error rate (WER), which is the probability of write failures of a memory cell. Recently, it was shown that the WER of MRAM obeys a skewed probability distribution even though the variation in material parameters obeys a normal distribution. However, little is known about the effect of WER distribution on WF in a memory cell array. Here, we study WF in a memory cell array consisting of magnetic tunnel junction elements with distributed WERs based on numerical simulations. We simulated Bernoulli trials of writing, assuming that the WER obeys a beta distribution. The results show that for typical writing patterns, WF in a memory cell array obeys a binomial distribution, with the mean of the WER as the probability of success. The statistical properties of WF in a memory cell array are not affected by the variance and skewness of the WER. The results provide a basic understanding of the statistical properties of WF in a memory cell array and will be useful for the development of computing systems that exploit erroneous memories.