Modeling the Effects of Temperature and Electric Field on the Dark Count Rate of Photomultiplier Tubes

Abstract

Although photomultiplier tubes (PMTs) are sufficiently sensitive for applications based on counting single photons, the thermionic emission of electrons from the photocathode is one of the dominant background sources. In this study, we modeled the dark count rate of a given PMT as a function of the temperature and external electric field based on the Richardson-Dushman equation and incorporated the Schottky effect. To validate the model, measurements were performed using an eight-centimeter Hamamatsu R14374 PMT equipped with a bialkali photocathode. The dark count rate was measured over a range of temperatures from 10 to 40 degree Celsius. An external electric field was applied to the outside surface of the optical window with the photocathode by varying the potential difference between the photocathode and the surrounding medium from 0 to 1100 V. The result confirmed that the influence of the external potential difference remained relatively small within a difference of 200 V, with the increase in the dark count rate remaining below 50 % across all measured temperatures. This behavior was incorporated into the proposed model by including an error function to predict the dark count rate under operating conditions with varying temperatures and external electric fields.