Effect of Edge Roughness on Resistance and Switching Voltage of Magnetic Tunnel Junctions

We investigate the impact of edge roughness on the electrical transport properties of magnetic tunnel junctions using non-equilibrium Green’s 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 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 designing reliable spin transfer torque-magnetic random access memory (STT-MRAM) with ultra-small magnetic tunnel junctions.

I. Introduction

Magnetic tunnel junction (MTJ) comprises two ferromagnetic layers (free layer and pinned layer) separated by a tunneling barrier. Binary information can be stored in MTJs corresponding to parallel (P) and anti-parallel (AP) configurations of the magnetizations. The information can be read by measuring the resistance which is low for P and high for AP configurations respectively. Spin transfer torque (STT) produced by application of large positive and negative voltages to the free layer with respect to the fixed layer, stabilizes P and AP configurations respectively, and thus can be used for writing the memory. As ferromagnetic layers with perpendicular magnetic anisotropy (PMA) have lower threshold switching voltage () with enhanced thermal stability, they are preferred over in-plane magnetized layers [1]. Reliability analysis of STT-MRAM (Magnetic Random Access Memory) in terms of write error, tunnel oxide breakdown, temperature variations, etc. have been carried out before [2], [3], [4], [5], [6], [7].