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In this paper, we report our studies on field effect transistor (FET) THz detectors operating in the non-resonant mode based on the Dyakonov-Shur plasma wave detection theory, where the quantum capacitance dominates. The influence of quantum capacitance in detector response is theoretically developed and numerically simulated at low and high frequencies. Fundamental constraints in the upper frequency limit are also analyzed for FET THz detectors based on various materials, showing advantages of GaN for 8 - 20 THz applications. Experiments at microwave and THz frequencies have been carried out for GaN based devices showing agreement with the theory.