We demonstrate that the rectifying field effect transistor, biased to the subthreshold regime, in a large signal regime exhibits a super-linear response to the incident terahertz (THz) power. This phenomenon can be exploited in a variety of experiments which exploit a nonlinear response, such as nonlinear autocorrelation measurements, for direct assessment of intrinsic response time using a pump-probe configuration or for indirect calibration of the oscillating voltage amplitude, which is delivered to the device. For these purposes, we employ a broadband bow-tie antenna coupled Si CMOS field-effect-transistor-based THz detector (TeraFET) in a nonlinear autocorrelation experiment performed with picoseconds-scale pulsed THz radiation. We have found that, in a wide range of gate bias (above the threshold voltage mV), the detected signal follows linearly to the emitted THz power. For gate bias below the threshold voltage (at 350 mV and below), the detected signal increases in a super-linear manner. A combination of these response regimes allows for performing nonlinear autocorrelation measurements with a single device and avoiding cryogenic cooling.