A Quasi-Analytical Model for Energy-Delay-Reliability Tradeoff Studies During Write Operations in a Perpendicular STT-RAM Cell

Kamaram Munira, William H. Butler, and Avik W. Ghosh, IEEE Transactions on Electron Devices , 59 (8) :2221-2226 (2012).
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# Abstract

One of the biggest challenges that the current spin-transfer-torque-based random access memory (STT-RAM) industry faces is maintaining high thermal stability while trying to switch within a given voltage pulse and energy cost. In this paper, we present a physics-based analytical model that uses a modified Simmons tunneling expression to capture the spin-dependent tunneling in a magnetic tunnel junction (MTJ). Coupled with an analytical derivation of the critical switching current based on the Landau–Lifshitz–Gilbert equation and the write error rate derived from a solution to the Fokker–Planck equation, this model provides us a quick estimate of the energy-delay-reliability tradeoffs in perpendicular STT-RAM devices due to thermal fluctuations. In other words, the model provides a simple way to calculate the energy consumed during write operation that ensures a certain error rate and delay time while being numerically far less intensive than a full-fledged stochastic calculation. We calculate the worst case energy consumption during antiparallel (AP)-to-parallel (P) and P-to-AP switchings and quantify how increasing the anisotropy field $$H_{K}$$ and lowering the saturation magnetization $$M_{S}$$ can significantly reduce the energy consumption. A case study on how manufacturing variations of the MTJ cell can affect the energy consumption and delay is also reported.