Temperature-stimulated transition from a macroscopic to a mesoscopic behavior of the hopping conductivity in a quantum-dot ensemble

A temperature-induced transition to the macroscopic behavior of the hopping conductivity is observed in Ge/Si quantum-dot heterostructures upon the investigation of light-induced mesoscopic fluctuations of the electric current in these heterostructures. It is shown that the temperature dependence of the relative amplitude of the fluctuations A is described by a power law $A\sim T^{-0.93}$, which corresponds to the temperature dependence of the correlation length of the percolation cluster $L_c\sim T^{-1.24}$ This result is in good agreement with the theoretical dependence $L_c(T)$. By considering the correspondence between the size of the structure and the transition temperature, the correlation length has been estimated as $\sim 130$ nm at $4.2$ K.