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This paper integrates quantum valley-deflection physics into a macroscopic Poisson-drift-diffusion model to analyze strain-induced valley sorting in MoS$_2$ field-effect transistors. The study reveals that the observed suppression of ON-state current in a contacted device is primarily determined by the source and drain metal-semiconductor interfaces, not the bulk channel. The findings highlight the critical role of tunneling-transparent, degenerately-doped contacts and introduce a valley-topological contact resistance ($R_{c,V}$) and an inverse-length scaling law for strain-engineered 2D heterostructures.
Strain-induced valley sorting in MoS$_2$ transistors is overwhelmingly a contact phenomenon, not a bulk one, with metal-semiconductor interfaces dictating device performance.
Strain engineering is a leading route to control valley-selective transport in monolayer transition metal dichalcogenides. Whether this quantum effect survives inside a fully contacted device remains an open question. Quantum transport models capture the underlying valley deflection but are limited to isolated nanoscale fragments, leaving it unclear if a full device registers strain-induced valley sorting in the bulk, at the contacts, or at all. Here, the quantum valley-deflection tensor of strained monolayer MoS$_2$ is embedded directly into a macroscopic Poisson-drift-diffusion model, extending this physics to a complete, contact-inclusive device. Applying this framework to a 300~nm monolayer MoS$_2$ transistor with a 3~nm HfO$_2$ gate dielectric at 77~K, under a localized 6.14~T pseudo-magnetic strain field, shows the resulting 63.6\% suppression of the ON-state current is not a bulk property. It is set almost entirely by the source and drain metal-semiconductor interfaces. The full suppression is reproduced when only the 15~nm contact regions are strained and nearly vanishes when the channel interior alone is strained, identifying the metal contact as the dominant site of strain-induced valley physics. Observing it requires tunneling-transparent, degenerately-doped contacts, since classical Ohmic barriers overwhelm the topological signal. A transmission-line analysis reduces this behavior to a single valley-topological contact resistance ($R_{c,V}$) and a predictive inverse-length scaling law. This framework applies to any strain-engineered 2D-material heterostructure and can be tested with standard multi-length contact structures. Ultimately, these results identify the metal-semiconductor interface as the decisive location for engineering and detecting valley-selective transport in real 2D-material devices.