Reduction of electron tunneling current due to lateral variation of the wave function

Electron tunneling in solids is usually envisioned in terms of a simple barrier model based on free electrons tunneling through a region of homogeneous potential. We point out that this model neglects the variation of the wave function in the plane of the interface and show that oscillations of the wave function parallel to the interface increase its rate of decay perpendicular to the interface. This simple observation has important implications for spin-dependent tunneling and may explain why $``s$ electrons'' seem to tunnel much more readily than $``d$ electrons.''