AC Conductance in Dense Array of the Ge$_{0.7}$Si$_{0.3}$ Quantum Dots in Si

Abstract

Complex AC-conductance, $σ^{AC}$, in the systems with dense Ge$_{0.7}$Si$_{0.3}$ quantum dot (QD) arrays in Si has been determined from simultaneous measurements of attenuation, $ΔΓ=Γ(H)-Γ(0)$, and velocity, $ΔV /V=(V(H)-V(0)) / V(0)$, of surface acoustic waves (SAW) with frequencies $f$ = 30-300 MHz as functions of transverse magnetic field $H \leq$ 18 T in the temperature range $T$ = 1-20 K. It has been shown that in the sample with dopant (B) concentration 8.2$ \times 10^{11}$ cm$^{-2}$ at temperatures $T \leq$4 K the AC conductivity is dominated by hopping between states localized in different QDs. The observed power-law temperature dependence, $σ_1(H=0)\propto T^{2.4}$, and weak frequency dependence, $σ_1(H=0)\propto ω^0$, of the AC conductivity are consistent with predictions of the two-site model for AC hopping conductivity for the case of $ωτ_0 \gg $1, where $ω=2πf$ is the SAW angular frequency and $τ_0$ is the typical population relaxation time. At $T >$ 7 K the AC conductivity is due to thermal activation of the carriers (holes) to the mobility edge. In intermediate temperature region 4$ < T<$ 7 K, where AC conductivity is due to a combination of hops between QDs and diffusion on the mobility edge, one succeeded to separate both contributions. Temperature dependence of hopping contribution to the conductivity above $T^*\sim$ 4.5 K saturates, evidencing crossover to the regime where $ωτ_0 < $1. From crossover condition, $ωτ_0(T^*)$ = 1, the typical value, $τ_0$, of the relaxation time has been determined.