Urbach-Energy-Dictated Spatial Propagation of Electrons in Thermodynamically Tuned Amorphous Zirconia Thin Films

Thermodynamically tuned zirconia thin films are fabricated for diverse Urbach energies in a homogeneous condensed system. In the analysis, the electrical breakdown of zirconia thin films is ascribed to the tunneling-driven electron propagation involving virtual photons. An externally applied electric field is considered to expand the Urbach-energy-characterized energy distribution of sub-bandgap states into their spatial distribution. In this expansion, the virtual-photon energies activate the tunneling-driven electron propagation through localized observer states. The integral of the virtual-photon energies over the entire tunneling path is equal to the initial energy barrier.