Electronic states of Si nanostructures in a strong electric field: Bandgap ionization and Stark ladders

The electronic states of Si slabs contained within SiO₂ barriers and placed in strong electric fields have been calculated using tight-binding theory. The SiO₂ barriers resolve the problem of dangling bonds and surface termination in a simple and unobtrusive manner, and also relate to actual nanostructures. Two critical fields are identified from the calculations. The electronic density of states (DOS) change very slowly until the first critical field F_c1 begins to be reached. This first critical field at 7 MV cm^-1 corresponds to the onset of the silicon-bandgap ionization, in excellent agreement with the vacuum emission experiments. The second critical field F_c2 is revealed by the clear fragmentation of the density of states into Wannier-Stark ladders. Our theoretical methods apply directly to Si/SiO₂ and other superlattice structures as well. The field-dependent DOS results presented here are relevant to theories of electroluminescent devices, high-field hot-electron transport as well as to opto-electronic switching devices.