Origin of the breakdown of Wentzel-Kramers-Brillouin-based tunneling models

Abstract

The tunneling conductance of three varieties of $\mathrm{Co}\mathrm{Fe}\mathrm{B}∕\mathrm{Mg}\mathrm{O}∕\mathrm{Co}\mathrm{Fe}\mathrm{B}$ magnetic tunnel junctions depends quadratically on the applied voltage to anomalously high biases. Within the framework traditional of WKB models, this implies unphysical tunnel barrier parameters: heights near $20\mathrm{eV}$, or widths corresponding to fewer than two MgO lattice constants. We demonstrate that the failure of such models to yield physically reasonable parameters originates from an experimentally unavoidable distribution of barrier thicknesses, possibly acting synergistically with the band structure of the barrier material. This implies that existing WKB models may lead to physically incorrect barrier parameters for contemporary tunnel junctions, magnetic or otherwise.