The transconductance $g_m=d{I}_D/d{V}_G$ of a field-effect transistor (FET) is conventionally read as a proxy for carrier density. We show that it is instead a spectroscopic probe of the carrier distribution: because $g_m$ weights the spectral current $j(E)$ by the gate-voltage derivative $\partial f(E)/\partial V_G$ and integrates over energy, it is sensitive to the shape of $f(E)$, not merely its integrated weight $n$. We develop an energy-resolved transport framework for two-dimensional (2D) FETs and, within a gate-independent spectral-kernel approximation, derive the decomposition $g_m=g_m^{(n)}+g_m^{(\alpha )}$ into the conventional density-modulation term $g_m^{(n)}$ and a distribution-shape-driven term $g_m^{(\alpha )}$. The latter, obtained as the residual after subtracting the smooth density-modulation background from the measured $g_m$, exhibits a characteristic anomalous peak at a gate voltage $V_G^{\text{pk}}$. This peak has no counterpart in equilibrium transport and cannot be explained by carrier density modulation alone. With the spectral kernel calibrated, the peak position and height—extracted from standard dc/lock-in $g_m$ sweeps—constrain the hot-carrier energy $E_0$, spectral width $\sigma$, and generation threshold $n_c$, realizing a steady-state, all-electrical spectroscopy of the carrier distribution. An optional time-resolved extension further recovers the carrier relaxation time $\tau$ from the transient response following a pump excitation, establishing the 2D FET as a distribution-function spectrometer that requires no optical readout.

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• Carrier dynamics
• Transport phenomena
• 2-dimensional systems
• Field-effect transistors
• Semiconductors
• Electrical transport techniques
• Spectroscopy