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 Vth=445 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.