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

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.