Mott and Efros–Shklovskii Variable-Range Hopping Conduction in Films Formed by Silicon Nanoparticles Doped with Phosphorus and Boron

The electrical characteristics of thin films formed from Si nanoparticles ( nc -Si) with various degrees of doping are studied. To eliminate the influence of ionic conduction, the current parameters of the films are recorded in ultrahigh vacuum ( P ~ 3–5 × 10 – 9 Torr) with preliminary high-temperature (950°C) annealing. An analysis of the temperature dependences of the conductivity of nc -Si films show that in films that are formed from heavily doped nanoparticles (the concentration of free electrons n e exceeds 10 19 cm –3 ), the conductivity is determined by variable-range hopping (VRH). In these samples, Mott conduction prevails at temperatures higher than 300 K, while Efros–Shklovskii VRH dominates at lower temperatures. In films with a medium doping level of nanoparticles ( n e < 10 19 cm –3 ), transport in the films is determined by the joint effect of the Mott, Efros–Shklovskii, and thermally activated conductivities. At the same time, thermally activated conduction prevails at temperatures above 560 ° C. In nc -Si films of undoped nanoparticles, the transport parameters are determined by thermally activated conduction and Mott conduction. No Efros–Shklovskii VRH is observed in such films. From analysis of the parameters that correspond to the Mott and Efros–Shklovskii conductions, the localization lengths of the wave functions, the densities of states at the Fermi level ( G ( E F )), and the average hopping lengths are found. The average hopping lengths in nc -Si films consisting of nanoparticles, which were pre-etched in HF, are in the range of 56–86 nm, which indicates that hopping in such films occurs via intermediate nanoparticles.