Mechanisms of low-temperature high-frequency conductivity in systems with a dense array of Ge_0.7Si_0.3 quantum dots in silicon

Abstract

High-frequency (HF) conductivity in systems with a dense (with a density of n = 3 × 10¹¹ cm⁻²) array of self-organized Ge_0.7Si_0.3 quantum dots in silicon with different boron concentrations n _B is determined by acoustic methods. The measurements of the absorption coefficient and the velocity of surface acoustic waves (SAWs) with frequencies of 30–300 MHz that interact with holes localized in quantum dots are carried out in magnetic fields of up to 18 T in the temperature interval from 1 to 20 K. Using one of the samples (n _B = 8.2 × 10¹¹ cm⁻²), it is shown that, at temperatures T ≤ 4 K, the HF conductivity is realized by the hopping of holes between the states localized in different quantum dots and can be explained within a two-site model in the case of

, where ω is the SAW frequency and τ₀ is the relaxation time of the populations of the sites (quantum dots). For T > 7 K, the HF conductivity has an activation character associated with the diffusion over the states at the mobility threshold. In the interval 4 K < T < 7 K, the HF conductivity is determined by a combination of the hopping and activation mechanisms. The contributions of these mechanisms are distinguished; it is found that the temperature dependence of the hopping HF conductivity approaches saturation at T* ≈ 4.5 K, which points to a τ₀ ≤ 1. A value of τ₀(T*) ≈ 5 × 10⁻⁹ s is determined from the condition ωτ₀(T*) ≈ 1.