Simulation of Electronic Transport in Silicon Nanocrystal Solids

Despite the emergence of quantum dot optoelectronics, so far very few attempts have been made to estimate theoretically the carrier mobility in nanocrystal solids. This paper presents a method to simulate hopping transport in 3D nanocrystal solids which is applied to silicon nanocrystals embedded in silicon oxide. Electronic states and charging energies are calculated separately for each nanocrystal. Electron transfer is calculated in the frame of Marcus theory with weak electronic couplings given by Bardeen’s formula. Additionally, the long-range nature of electrostatic interactions is explicitly taken into account. An accelerated kinetic Monte Carlo algorithm is employed to enable the simulation of an arbitrary degree of disorder. Electron mobility is found to be rather weakly impacted by size and positional disorder at room temperature, which is consistent with recent experimental results performed on PbSe nanocrystal solids. Electron mobility is also found to increase with decreasing nanocrystal size despite the increase of hops. Temperature dependent measurements, which have led to various interpretations in the literature, are indeed found to be tricky, as thermally activated mechanisms are numerous: inelastic hopping between nanocrystals, polaronic effects, or Coulombic repulsion, for instance. This suggests that simulation is a powerful tool to understand transport measurements and move toward the application of NC solids in optoelectronic devices.