Variable-range-hopping conductivity of Mott and Efros–Shklovskii in the films formed by silicon nanoparticles, doped by the phosphorus and boron

The electrical characteristics of thin films formed from Si nanoparticles ($nc$-Si) with various degrees of doping are studied. To exclude the influence of ionic conductivity, the current parameters of the films were recorded in an ultrahigh vacuum (P $\sim$ 3–5·10$^{-9}$ Torr) with preliminary high-temperature (950$^\circ$C) annealing. An analysis of the temperature dependences of the conductivity showed that in $nc$-Si films formed from heavily doped nanoparticles (the concentration of free electrons $n_{\mathrm{e}}$ is greater than 10$^{19}$ cm$^{-3}$), the transport is determined by variable-length hopping (VRH). In these samples, the Mott conductivity prevails at temperatures above 300$^\circ$C and at lower temperatures, the Efros–Shklovskii type variable range hopping conduction is dominate. In films with a medium level of doping of nanoparticles ($n_{\mathrm{e}}<$ 10$^{19}$ cm$^{-3}$), transport is realized by the Mott, Efros–Shklovskii and thermally activated conductivities. At the same time, thermally activated conductivity is dominated at temperatures above 560$^\circ$C. In $nc$-Si films formed from undoped nanoparticles, the transport parameters are determined by thermally activated conductivity and Mott's conductivity. Conductivity of Efros–Shklovskii is not observed in such films. From the analysis of the parameters corresponding to the Mott and Efros–Shklovsky conductivities, the localization lengths of wave functions, the density of states at the Fermi level (G(E$_{\mathrm{F}}$)), and average hopping lengths are found. The average hopping lengths in $nc$-Si films from nanoparticles pre-etched in HF are in the range 56–86 nm, which indicates that hopping in such films occurs via intermediate nanoparticles.