Simulation of the Charge Collection in a Nonuniform Electric Field for MAPbI3 Semiconductor Nuclear Detector With Schottky Contact

The Hecht equation is often used to calculate the mobility–lifetime product ( ${\mu } {\tau }$ ) of semiconductors by assuming a uniform electric field based on the Shockley–Ramo theory. However, the Schottky contacts are usually found at high resistivity semiconductor/metal interface, leading to a nonuniform electric field inside the bulk semiconductor. We used a slice model instead of the Hecht equation to calculate the charge collection efficiency (CCE) and found that the CCE in a nonuniform field can deviate significantly from that given by the Hecht equation in a uniform field, with the difference relying heavily on the space charge distribution and the ${\mu } {\tau }$ value. For semiconductors with a high ionized acceptor impurity concentration of $5\,\, \times 10^{9}$ cm⁻³, such as MAPbI₃, the electron ${\mu } {\tau }$ value may be seriously underestimated when adopting the Hecht equation assuming a uniform field. The invalid application of the Hecht equation for a Schottky interface may be one of the possible reasons for the underestimation of electron ${\mu } {\tau }$ value for p-type perovskite materials with relatively low resistivity.