  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.
