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

TL;DR

This paper introduces a physics-based analytical model for evaluating energy, delay, and reliability tradeoffs during write operations in perpendicular STT-RAM, enabling quick estimations of performance metrics considering thermal fluctuations.

Contribution

It presents a novel, simplified analytical model combining tunneling, switching current, and error rate calculations for perpendicular STT-RAM, reducing computational complexity.

Findings

Increasing anisotropy field HK reduces energy consumption.

Lowering saturation magnetization MS decreases energy use.

Manufacturing variations impact energy and delay performance.

Abstract

One of the biggest challenges the current STT-RAM industry faces is maintaining a 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 energydelay- reliability tradeoffs in perpendicular STTRAMs due to thermal fluctuations. In other words, the model provides a simple way to calculate the energy consumed during a 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 anti-parallel (AP) to parallel (P) and P to AP switchings and quantify how increasing the anisotropy field HK and lowering the saturation magnetization MS, 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.