Single-Grain Hopping Transport and Hall Effect in Type-II Silicon Clathrate Thin Films

Type-II silicon clathrate (Si₁₃₆:Naₓ) is a silicon-compatible platform of interest for spin-based quantum technologies, combining a near-direct ≈2 eV gap with localized donor states that may support long T₁/T₂. To decouple intrinsic clathrate transport from amorphous-Si pathways at grain boundaries, we microfabricate devices that electrically isolate individual plate-like grains (2–100 µm) and enable 2- and 4-probe magnetotransport from 3–300 K. Our process—ultrasonic cleaning, planarizing photoresist (KMPR), reactive-ion etching, maskless photolithography, and magnetron sputtering—yields reproducible low-temperature contacts suitable for single-grain measurements. In isolated grains we observe thermally activated resistivity with ε₁ ≈ 65 meV and a low-T hopping-like regime characterized by ε₃ ≈ 0.3 meV. Hall data show n(T) increasing by ~10²–10³ between 10–100 K, while μ(T) tracks the freeze-out and phonon-limited trends typical of lightly doped semiconductors. Below ~10 K, ln ρ vs T^-1/4 is consistent with variable-range hopping, supporting a disorder-mediated channel that is suppressed when amorphous pathways are excluded. A low-temperature maximum in ρ(T) coincides with the free-carrier maximum seen in prior EPR measurements, linking transport to spin-active donors. These results establish a CMOS-compatible route to intrinsic clathrate transport and quantify donor activation and hopping regimes relevant for integrating clathrates into silicon-based QIS architectures.