Classical and quantum percolation phenomena and controlling them in eutectic semiconductor-superconductor compositions

Experimental data on the conduction of heterogeneous systems have been traditionally interpreted in the context of the theory of percolation phenomena taking into account the relative threshold volume fraction ηC ≈ 0.16) of the high-conductivity phase. This work is concerned with the conduction of eutectic compositions semiconductor-normal metal at T > Tc (the classical limit) and semiconductor-superconductor at T < Tc (the quantum limit) obtained at various material growth rates; these materials contain metal particles as oriented whiskers in semiconducting matrices. The paper presents spatial and energy models of discrete, finite, and infinite clusters that well explain classical and quantum percolation conductivities. Depending on the growth rate of eutectic compositions, their classical and quantum conductivities can manifest themselves at arbitrary percolation thresholds ηp (0 < ηp ≤ ηc). It is shown that the density of whiskers, the distances between them, their diameters, and the critical supercurrent density per whisker can be controlled by varying the rate of composition growth.