Reappraisal of Variable-Range Hopping in Quantum-Dot Solids

Abstract

The temperature dependence of the electrical conductivity of assemblies of ZnO nanocrystals, studied with an electrochemically gated transistor is very accurately described by the relation ln σ ) ln σ 0 -(T 0 /T) x with x ) 2/3 over the entire temperature range from 7 to 200 K, independent of charge concentration and dielectric environment. These results cannot be explained by existing models but are supported by results on Au nanocrystals where an identical temperature dependence was observed (Zabet-Khosousi et al., Phys. Rev. Lett. 2006, 96 (15), 156403). We propose an adaptation of the Efros-Shklovskii variable-range hopping model by introducing an expression for nonresonant tunneling based on local energy fluctuations, which yields exactly the temperature dependence that is observed experimentally.

Substitutional doping in nanocrystal superlattices

“…3c and Extended Data Fig. 10), similar to the conductivity observed for Au nanocrystal solids linked with alkane dithiols that have more than five carbons 24,25 . The observation of this behaviour in sub-percolation doped superlattices is expected, because conductivity is constrained by hopping beyond nearest neighbours.…”

Controlled Chemical Doping of Semiconductor Nanocrystals Using Redox Buffers

“…In contrast to chemical methods, thermodynamic control of doping has been achieved using electrochemical methods, which shift the Fermi level of the nanocrystal solid through reversible charge transfer from the electrode. [12][13][14][15][16] Fine control over the applied potential (± 1 mV) allows the doping level to be set with precision. Despite this advantage, electrochemical doping methods are not suited to large area solution processing of nanocrystal solids and require specialized equipment.…”

Electrical Transport Mechanisms in Ensembles of Silicon Nanocystallites

“…For completeness, we also note the fact that there are models that consider a related mechanism but yield the Arrhenius-like dependence as given by Eq. (4.4) (with c ¼ 2/3 [43]). For our purpose, it is important to note that the above two types of mechanisms apply to very narrow potential barriers such as we encountered for high densities of Si NCs in our samples.…”

“…Starting with the s(T) results that were obtained from 3D ensembles [9,56,[79][80][81][82][83][84], it appears that, considering the uncertainties in the expression of the experimental data in terms of an exact c (Eq. (4.4)-like) dependence [43], the first attempt to suggest a rather welldefined transport mechanism in 3D systems based on s(T) data was that of Fujii et al [79], who measured the temperature dependence of the conductivity s(T) of a cosputtered Si-SiO 2 film between 20 and 300 K. Their results yielded a c ¼ 1/4 behavior that was interpreted to be due to VRH. However, in this case the samples were not annealed and the Si content was not specified, so that it is not clear whether it is the Si NCs network or the amorphous Si (a-Si) tissue in the sample that is responsible for the observations.…”

“…For example, a similar study of Banjeree [81] on the ensembles of Ge NCs embedded in a SiO 2 matrix was claimed to yield a c ¼ 1/4 value. However, a more careful analysis of his data reveals more difficulties [43] in deriving the reliable c-values from the limited T range available than yielding the actual c-values. In fact, one can fit his data almost equally well to a linear log s / log T or a c ¼ 1/4 behavior.…”