Dimensional Scaling Effect in Percolative Oxide Semiconductor Transistors

Percolation transport dominates the charge conduction in amorphous and polycrystalline semiconductors. This study identifies a dimensional scaling effect unique to transistors using percolative semiconductors as channel materials, where the materials' percolation threshold (p_c) exhibits a strong correlation with the transistor threshold voltage (V_T). We demonstrate that both parameters are fundamentally governed by the semiconductor channel geometry. By reducing channel thickness, width, or length, p_c is modulated because the availability of conductive pathways is constrained by the channel dimensions, directly driving the observed V_T shifts. A quantitative link between p_c and V_T is established through the percolation potential landscape visualized by scanning tunneling microscopy. The result reveals that the energy landscape is determined by the Fermi level, a characteristic of percolative channels, where device turn-on occurs as the Fermi level exceeds the potential barriers to form conductive pathways. This mechanism is confirmed by temperature-dependent transport measurements, where the extracted activation energies exhibit a strong geometric dependence consistent with the p_c and V_T shifts. This scaling effect appears consistently in both n-type In₂O₃ and p-type SnO transistors, showing its universality across percolative semiconductors regardless of the carrier type. These findings demonstrate that transport in amorphous semiconductor devices is defined by percolation-governed transport rather than conventional electrostatics or quantum confinement, and establish geometry as a key design parameter for future amorphous electronics.