Charge and energy transport in films of touching nanocrystals

This talk deals with films of nanocrystals (NC), which touch each other by small facets with radius ρ. First I calculate the matrix element for electron tunneling from one NC to another and show that it is proportional to ρ3. I use this matrix element to calculate two transport properties of NC films: conductivity and exciton diffusion length. In the first case I focus on the critical concentration of electrons for the insulator-metal transition (IMT) in the film. The famous Mott's criterion answers this question only in bulk materials. The same critical concentration as in a bulk material is not sufficient for the IMT in NC films because of the weak coupling between NCs. For IMT in NC films, one needs much larger concentration at which the typical electron wave packet becomes smaller than the facet radius ρ and can pass through the facet. The predicted critical concentration is proportional to 1/ρ3 and is in good agreement with experimental data obtained by Kortshagen's group for silicon NC films. In the second part of the talk, I consider the exciton diffusion length in NC films. In photovoltaic devices based on NC films, absorption of a light quantum creates of an exciton (electron-hole pair) in a NC. The diffusion length of an exciton is important parameter determining the volume from which photons are harvested. It is known that an exciton can hop between nearest-neighbor NC via the Forster mechanism. For touching NC, I propose another mechanism where the electron and hole tunnel through the small contact facet in tandem. The tandem tunneling occurs through the intermediate state in which the electron and hole are in different NCs. I show that for majority of materials the tandem tunneling exciton transfer rate is comparable with the Forster rate, while for silicon the tandem tunneling dominates