Theoretical expressions for minimizing write current and write power consumption in magnetoresistive random access memories (MRAMs) are presented. The expressions are derived based on a generalized asteroid curve which approximately represents the minimum switching magnetic fields of magnetic tunnel junction (MTJ) memory cells recently developed for smaller write currents and better cell selectivity. The generalized asteroid curve has a shape parameter to fit the curve to the switching characteristics of MTJ cells. The derived expressions contain the shape parameter as well as other cell and array structural parameters, and thus give theoretical limits of the write current and power from physical points of view including MTJ shape.
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