Variable Range Hopping Conduction in Semiconductor Nanocrystal Solids

The temperature and electrical field dependent conductivity of $n$-type CdSe nanocrystal thin films is investigated. In the low electrical field regime, the conductivity follows $\sigma \sim \exp [-(T^{*}/T{)}^{1/2}]$ in the temperature range $10<T<120\mathrm{K}$. At high electrical field, the conductivity is strongly field dependent. At 4 K, the conductance increases by 8 orders of magnitude over one decade of bias. At a very high field, conductivity is temperature independent with $\sigma \sim \exp [-(E^{*}/E{)}^{1/2}]$. The complete behavior is very well described by variable range hopping with a Coulomb gap.