Analytical Photoresponses of Schottky-Contact MoS₂ Phototransistors

High-gain photodetectors based on 2D semiconductors have been extensively investigated in the past decades. However, the underlying mechanism remains in dispute without a proper analytical theory. On one side, the classical photogain theory is not applicable, as it was derived on two misplaced assumptions. On the other side, unexpected potential barriers usually present in 2D semi-conductors but their effect on the ultrahigh gain has been largely ignored. In this work, we first established a universal I-V equation for Schottky-contact MoS₂ phototransistors, modeled with two anti-symmetric Schottky diodes and a channel resistor in series. It has been proved to be valid under varying conditions of gate voltage, temperature, light illumination and bias voltage. Moreover, we established analytical equations for photocurrent and gain, which clearly shows that ultrahigh gain is created by light-induced modulation of potential barrier in exponential form. Finally, the theory was validated on 40 samples by verifying the I-V characteristics and minority carrier lifetime. Our results not only shed light on the working mechanism of 2D phototransistors, but also present important advance for device modeling and design in 2D integrated circuits.