Conductivity of 2-D Ag quantum dot arrays: Computational study of the role of size and packing disorder at low temperatures

The temperature dependence of the coherent DC conductivity of an Ag quantum dot (QD) monolayer has been computed allowing for size fluctuations of the QDs as well as for packing disorder. The computation uses a scattering formalism with an electron exchange coupling for adjacent QDs. The strength of this coupling can be tuned by compression of the array, and the same coupling is used as previously determined from second harmonic generation spectroscopy of such monolayers. To agree with the experimental results, the computations center attention on the regime of not fully compressed arrays, when the exchange coupling does not fully mask the role of disorder. At very low disorder and/or at higher compressions, the computations show a phase transition to a fully delocalized conducting regime. At very low temperatures, the computed conductivity increases with temperature as exp(- 2(E₀/kT)^1/2). The characteristic energy E₀ is found to be a measure of the effective coupling of next-nearest neighbors, suggesting that conduction occurs by variable range charge hopping or, in the language of electron transfer, by super-exchange. At higher temperatures, there is a crossover to an activated regime, exp(-(E_a/kT)), where the activation energy E_a is shown to be a measure of the mean excess energy of the moving charges. The transition temperature to activated conduction scales with the extent of disorder. The increase of conductivity with temperature is interpreted as reflecting a gap in the density of conducting states for energies just above the ground electronic state of the array.