Interchannel Coupling in Two-Channel THz Detectors]{Interchannel Coupling in Two-Channel AlGaN/GaN Plasmonic Terahertz Detectors

A second two-dimensional electron gas (2DEG) forms in AlGaN/GaN high-electron-mobility transistors (HEMTs) capped with AlN. The strong response of measured double-channel terahertz (THz) detectors has been attributed to the coupling between the channels, but a measured responsivity also contains the antenna coupling and the bias, so whether the coupling itself helps is not known. We isolate the coupling by modelling plasma-wave rectification in this detector and in uncapped and GaN-capped single-channel references. A semi-analytical theory, to our knowledge the first for rectification in asymmetric coupled channels, joins analytic coupled eigenmodes of the gated region to transmission-line access regions and splits the photovoltage exactly into modal terms. A full-device perturbation model adds Schr\"odinger--Poisson and two-dimensional electrostatics, a floating drain and hot electrons. A nonlinear time-domain solver verifies its implementation within 3.0% over 375 cases, the model reproduces the Dyakonov--Shur limit within 0.4%, and a Boltzmann (Mermin) estimate keeps kinetic corrections below 0.3% at zero bias. We find that in these AlN-capped devices the coupling does not help. For matched, conjugate or direct antenna coupling and a floating drain, the single-channel devices respond best (0.22--0.28\,V/W at 1\,THz, against 0.10\,V/W). A design map over upper-channel mobility and barrier thickness shows that a better upper channel makes the detector worse: it shunts the access regions and lowers the device impedance, while the rectification itself changes little. Toward threshold the small-signal noise-equivalent power falls to about 20--23\,pW/√ Hz in the hydrodynamic model. Both models apply to other stacks of capacitively coupled channels.