Carrier mobility extracted from low-field electrical measurements is widely used to interpret transport in field-effect transistors; however, its physical meaning becomes ambiguous as devices approach the quasi-ballistic regime. The Y-function method, although numerically robust, implicitly assumes drift-diffusion transport and attributes deviations in measured characteristics solely to gate-field-dependent mobility degradation. Here, we show that this assumption leads to a systematic breakdown of mobility interpretation in short-channel devices, even when polynomial Y-function analysis remains numerically stable. Temperature-dependent analysis of linear-regime transfer characteristics demonstrates that conventional Y-function-based extraction yields unphysical mobility attenuation parameters as transport departs from the diffusive limit. These anomalies do not arise from fitting instability or enhanced scattering, but from neglecting finite channel-length and injection-limited effects inherent to quasi-ballistic transport. By reinterpreting Y-function-extracted mobility within the Landauer transport formalism, we introduce a Landauerconsistent framework that explicitly separates scattering-limited mobility from ballistic constraints imposed by finite channel length. This minimal correction restores physically meaningful mobility parameters and enables self-consistent reproduction of both drain current and transconductance across the diffusive-to-quasi-ballistic transition, establishing a physically grounded approach for mobility analysis beyond the conventional applicability of the Y-function method.
