Terahertz (THz) detection has been extensively studied in the application fields of wireless communication, non-destructive imaging and spectrum inspection, etc., in the decades. Here, we report that a self-mixing terahertz detector based on hemispherical silicon lens and antenna-coupled InGaAs/AlGaAs high electron mobility transistor (HEMT) enables wide spectrum detection, and improves detection performances. In this device configuration, the optimal log-periodic antenna is used to enhance light field in the channel, the double-gate could further adjust the carrier concentration, and the hemispheric silicon lens can concentrate the terahertz radiation in the center of the hemisphere to effectively improve the terahertz wave collection efficiency, which could improve the sensitivity of the detector. The broadband Terahertz responsivity and noise equivalent power (NEP) of the detector are characterized at the range from 0.07 to 0.82 THz at room temperature. A peak responsivity of 2 kV/W and a minimum optical noise equivalent power of 59 pW/Hz1/2 at 0.8 THz without any external field, are reached from two-terminal configuration at 0.8 THz. The minimum optical NEP of the device can be reduced to 30 pW/Hz1/2 by applying a gate voltage, realizing scanning imaging demonstration.