Ultra-fast, GaAs-based multi-quantum well photodetectors operating in the 9.5-11.5um range are demonstrated, with a 3dB-cutoff bandwidth of 100GHz at room temperature. The multi quantum-well active region is sandwiched between a bottom metallic ground-plane and a top two-dimensional array of patch antennas connected in parallel. We study arrays of different dimensions and measure their frequency response in the range 0-220GHz. Beyond 100GHz we find a roll-off dominated by the 2.5ps-long, intrinsic capture time of the photo-excited electrons. To demonstrate the potential of these detectors for fast sensing applications, we show that they can be used to measure electronically and in real-time the time-dependent emission frequency of a quantum cascade laser operated in pulsed mode over a frequency range >60 GHz. By exploiting broadband electronics, and thanks to its high signal-to-noise ratio, this technique allows the acquisition, in a single-shot, of frequency-calibrated, high resolution heterodyne mid-infrared spectra spanning up to 100GHz and beyond.