A direct detector for terahertz radiation comprises a grating-gated field-effect transistor with one or more quantum wells that provide a two-dimensional electron gas in the channel region. The grating gate can be a split-grating gate having at least one finger that can be individually biased. Biasing an individual finger of the split-grating gate to near pinch-off greatly increases the detector's resonant response magnitude over prior QW FET detectors while maintaining frequency selectivity. The split-grating-gated QW FET shows a tunable resonant plasmon response to FIR radiation that makes possible an electrically sweepable spectrometer-on-a-chip with no moving mechanical optical parts. Further, the narrow spectral response and signal-to-noise are adequate for use of the split-grating-gated QW FET in a passive, multispectral terahertz imaging system. The detector can be operated in a photoconductive or a photovoltaic mode. Other embodiments include uniform front and back gates to independently vary the carrier densities in the channel region, a thinned substrate to increase bolometric responsivity, and a resistive shunt to connect the fingers of the grating gate in parallel and provide a uniform gate-channel voltage along the length of the channel to increase the responsivity and improve the spectral resolution.