Long-range Coulomb interaction in arrays of self-assembled quantum dots

An array of $3\times {10}^7$ Ge self-assembled quantum dots is embedded into the active channel of a Si metal-oxide-field-effect transistor. Conductance oscillations with a gate voltage resulting from a successive loading of holes into the dots are observed. Based on measurements of the temperature dependence of the conductance maxima, the charge-transfer mechanism in the channel is identified as being due to variable-range hopping between the dots, with the typical hopping energy determined by interdot Coulomb interaction. The characteristic spatial dimension of the hole wave functions as well as the charging energies of the dots are determined from the conductance data. The effect of the proximity of a bulk conductor on hopping transport is studied. We find that putting a metal plane close to the dot layer causes a crossover from Efros-Shklovskii variable-range hopping conductance to two-dimensional Mott behavior as the temperature is reduced. At the crossover temperature the hopping activation energy is observed to fall off. The metal plane is shown not to affect the conductance of samples which show Mott hopping. In the Efros-Shklovskii hopping regime, the conductance prefactor was found to be $\simeq e^2/h,$ and the conductance to scale with the temperature. In the fully screened limit, the universal behavior of the prefactor is destroyed, and it begins to depend on the localization length. The experimental results are explained by a screening of long-range Coulomb potentials, and provide evidence for strong electron-electron interaction between dots in the absence of screening.