Directed inelastic hopping of electrons through metal-insulator-metal tunnel junctions

We have used the metal/amorphous silicon/metal tunnel junction as a model system to explore the role of localized states in electron transport through thin insulating layers. We measured the tunneling conductance as a function of temperature T, bias voltage V, and barrier thickness d. The data show marked deviations from the classical WKB tunneling theory in the limit of low T and V with d intermediate between the decay length in the barrier and the Mott variable range hopping length. The data are instead consistent with directed inelastic hopping along statistically rare but highly conductive ‘‘chains’’ of localized states. The most effective chains for a given set of conditions (T,V,d) contain a definite number of localized states, N>1, configured in a nearly optimal way in space and energy. The conductance of the lowest-order hopping channel (all chains with N=2) exhibits the characteristic voltage and temperature dependences ${\mathit{G}}_2^{\mathrm{hop}}$(V)∝${\mathit{V}}^{4/3}$, and ${\mathit{G}}_2^{\mathrm{hop}}$(T)∝${\mathit{T}}^{4/3}$, respectively, as predicted by theory. Higher-order channels (N>2) also conform to the theoretical predictions remarkably well. The physical nature of these highly conductive channels and their implications for conduction through thick tunnel barriers and thin dielectrics is discussed.