Abstract:
We model “soft” error rates for writing (WSER) and for reading (RSER) for perpendicular spintorque
memory devices by solving the Fokker-Planck equation for the probability distribution of
the angle that the free layer magnetization makes with the normal to the plane of the film. We
obtain: (1) an exact, closed form, analytical expression for the zero-temperature switching time
as a function of initial angle; (2) an approximate analytical expression for the exponential decay
of the WSER as a function of the time the current is applied; (3) comparison of the approximate
analytical expression for the WSER to numerical solutions of the Fokker-Planck equation; (4) an
approximate analytical expression for the linear increase in RSER with current applied for
reading; (5) comparison of the approximate analytical formula for the RSER to the numerical
solution of the Fokker-Planck equation; and (6) confirmation of the accuracy of the FokkerPlanck
solutions by comparison with results of direct simulation using the single-macrospin
Landau-Lifshitz-Gilbert (LLG) equations with a random fluctuating field in the short-time
regime for which the latter is practical.
