Thickness Fluctuations Produce Apparent Long-Range Tunneling in Large-Area Junctions: The Case of Polyelectrolyte Multilayers

Abstract

The electron-tunneling (ET) current through a barrier of thickness h is generally analyzed with the Simmons model, j ∼ exp­(−βh), where β is the tunneling decay coefficient. We show that fluctuations in barrier thickness produce apparent β values systematically smaller than the real ones, which may lead to incorrectly postulating long-range electron tunneling. We reached this conclusion by performing the first tunneling studies through polyelectrolyte-multilayer films of different average thicknesses using impedance spectroscopy and EGaIn/Ga2O3 top contacts. We explained these measurements with a model that considers ET through a film with a Gaussian distribution of thicknesses, as observed by atomic force microscopy. It is shown that even relatively small thickness fluctuations can introduce a systematic error in the determination of β and that when the average film thickness and its standard deviation become commensurable, it is impossible to determine β.