Quantum capacitance-induced transconductance anomalies in cryogenic quasi-ballistic transistors

Understanding the transconductance (g_m) at cryogenic temperature remains a major challenge in the physics-based modeling of nanoscale field-effect transistors. Although short-channel drain current (I_D)-gate voltage characteristics can often be described accurately within transport-based formalisms, the corresponding g_m commonly exhibits pronounced low-temperature anomalies that remain unexplained. Here, we investigate a 65 nm Si n-channel transistor measured from 250 K down to 12 K and show that a Landauer-consistent model provides an accurate quasi-ballistic transport baseline for the I_D across the full temperature range, but fails to reproduce the shoulder-like g_m feature that emerges at deep cryogenic temperature. We show that this residual discrepancy originates not from transport nonidealities but from quantum capacitance (C_q)-induced electrostatic renormalization of gate-induced charge modulation. By decomposing the g_m into transport and charge-response contributions, and introducing a gate-control factor governed primarily by the C_q, we derive a compact framework in which the corrected g_m consists of renormalized baseline and differential electrostatic terms. A two-crossover parameterization of C_q in the effective gate-overdrive domain enables simultaneous and self-consistent reproduction of both the I_D and g_m, including the cryogenic shoulder. These results identify anomalous cryogenic g_m as a C_q-induced signature of rapidly varying gate-to-charge coupling in quasi-ballistic transistors.