Quantum freeze-out effect in a size-limited intrinsic transport

The size-limited resistivity of intrinsic thin films is calculated theoretically in the size-quantum limit (SQL), where the film thickness d is comparable to the de Broglie wavelength λD of the electrons (λD≥d). The variation of the intrinsic carrier concentration with the film thickness is taken into account. We find that in the SQL, the ratio of the thin film resistivity to the bulk resistivity increases exponentially with decreasing film thickness. This arises because of the increase in the effective band gap of an intrinsic thin film with film thickness as a result of size quantization.