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We report progress in developing a sensitive detector for terahertz radiation, based on a semiconductor quantum dot (QD) capacitively coupled to a metallic single electron transistor (SET). A charge polarization of the QD induced by the absorption of individual photons is detected by the voltage-biased SET. We investigate the sensitivity of the detector to broadband radiation, over a range of QD barrier heights, and find that there is a measurable photo-signal over wide range of gate voltages defining the QD. This is an improvement on previous designs of terahertz detector based on the QD/SET principle, and makes the new detector a candidate for use in an imaging device.