  We investigate the impact of edge roughness on the electrical transport
properties of magnetic tunnel junctions using non-equilibrium Greens function
formalism. We have modeled edge roughness as a stochastic variation in the
cross-sectional profile of magnetic tunnel junction characterized by the
stretched exponential decay of the correlation function. The stochastic
variation in the shape and size changes the transverse energy mode profile and
gives rise to the variations in the resistance and switching voltage of the
magnetic tunnel junction. We find that the variations are larger as the
magnetic tunnel junction size is scaled down due to the quantum confinement
effect. A model is proposed for the efficient calculation of edge roughness
effects by approximating the cross-sectional geometry to a circle with the same
cross-sectional area. Further improvement can be obtained by approximating the
cross-sectional area to an ellipse with an aspect ratio determined by the first
transverse eigenvalue corresponding to the 2D cross section. These results
would be useful for reliable design of the spin transfer torque-magnetic random
access memory (STT-MRAM) with ultra-small magnetic tunnel junctions.
