Crossover From Quantum Mechanical Tunneling to the Superlinear Power Law in Silicon Microcrystal, Doped by Boron and Nickel

In the work, research was carried out on filamentous silicon crystals doped with boron admixture to concentrations corresponding to the metal–insulator transition (MIT) in silicon, as well as with an admixture of the transition metal nickel. Investigations were conducted at cryogenic temperatures in the interval 4.2–70 K using alternating current in the frequency range from 10 Hz to 250 kHz. Different conduction mechanisms have been established according to Jonscher's power law as σ(ω) ≈ Aωⁿ. In the low-frequency range up to 20 kHz a quantum–mechanical tunneling mechanism is observed for the  conduction for temperatures 4.2–30 K with a frequency-dependent coefficient  n that is proportional ω^0.8, which with increasing frequency to 250 kHz  increases to values n ≈ ω^1.8. In this case, the low-temperature conductivity increases linearly according to the superlinear power law (SLPL).