Theoretical Analysis of the Time Transient of the THz Self-Mixing Rectification Voltage in a Semiconductor Barrier

THz detection in a silicon structure can be an effective instrument not only for image detection, and material and gas sensing, but also for communications. Next-generation 6G communications assume the possibility of achieving a large-band transmission, using free space propagation with THz carriers. This possibility relies on the availability of an effective, low-cost detector technology. THz detection by self-mixing can provide an effective amplitude demodulation of the incoming carrier, with antennas directly fabricated on the chip. In this case, the speed of the detectors represents a crucial point in the definition of the bandwidth whereby several GHz are indeed required by the communication systems. The self-mixing process is intrinsically very fast, since it depends on the non-linear interaction of the radiation with the majority carriers inside the semiconductor structure. In this paper, we evaluate analytically the time dependence of the onset of the rectified voltage. A potential propagation along the detector channel follows the self-mixing rectification, accompanied by the charging of the parasitic capacitances of the structure. A numerical simulator can easily evaluate the delay due to this propagation along the structure, but the transient of the true origin of the signal, i.e., the establishment of the self-mixing voltage, at the current time, can be only inferred by analytical approach. In this work, we use the model developed for the THz rectification in the depletion region of an MOS capacitance to develop a transient model of the formation of the characteristic self-mixing charge dipole, and of the generation of the rectified potential. Subsequently, we show by TCAD simulations the propagation of the effect on the semiconductor structure, which surrounds the rectifying barrier, and evaluate the overall time response of a detector.