A quasi-analytical model for energy-delay-reliability tradeoff studies during write operations in perpendicular STT-RAM cell

摘要

One of the biggest challenges the current STT-RAM industry faces ismaintaining a high thermal stability while trying to switch within a givenvoltage pulse and energy cost. In this paper, we present a physics basedanalytical model that uses a modified Simmons' tunneling expression to capturethe spin dependent tunneling in a magnetic tunnel junction(MTJ). Coupled withan analytical derivation of the critical switching current based on theLandau-Lifshitz-Gilbert equation, and the write error rate derived from asolution to the Fokker-Planck equation, this model provides us a quick estimateof the energydelay- reliability tradeoffs in perpendicular STTRAMs due tothermal fluctuations. In other words, the model provides a simple way tocalculate the energy consumed during a write operation that ensures a certainerror rate and delay time, while being numerically far less intensive than afull-fledged stochastic calculation. We calculate the worst case energyconsumption during anti-parallel (AP) to parallel (P) and P to AP switchingsand quantify how increasing the anisotropy field HK and lowering the saturationmagnetization MS, can significantly reduce the energy consumption. A case studyon how manufacturing variations of the MTJ cell can affect the energyconsumption and delay is also reported.