Hybrid Photon Detector: Monte Carlo Simulation of Secondary Electrons and Initial Distribution for Gain Avalanche Process*

Photon detectors featuring single-photon sensitivity play a crucial role in various scientific domains, including high energy physics, astronomy, and quantum optics. Fast response time, high quantum efficiency, and minimal dark counts are the characteristics that render them ideal candidates for detecting individual photons with exceptional signal-to-noise ratios, at frequencies in the range of hundreds of MHz. Recently, the Instrumentation Division at Brookhaven National Laboratory looked to improve a previous design of a compact Hybrid Photon Detector (HPD) by achieving a lower cost per unit of large area fast position-sensitive photon detectors while preserving single photon sensitivity, low noise, high spatial resolution, and picosecond-scale time resolution. Overcoming these challenges is needed to develop a sensor that can enable the next generation of experiments, which will require detectors with tens of square meters of active area. A Monte Carlo simulation for the production secondary electrons by impact ionization of primary electron beam generated at the photocathode will be used to obtain better quantitative understanding of the final gain measured after the avalanche process, taking place inside the low gain avalanche diode (LGAD). The present paper will show the current version of a Monte Carlo simulation developed using the Octave programming language. The simulation calculates mass stopping power during the normal routine and the inelastic mean free path inside the "fn_IMFP" function. Electrons trajectory and deflection angles are calculated implicitly from the simulation geometry and previous equations using the "fn_ranrir2" function. The program produced a gain of ~600 for every electron and a final signal of ~12 mA. The simulated trajectories and max distances concur with the available Monte Carlo simulation package CASINO (monte Carlo Simulation of electron trajectory in sOlids). Differences in the path of electrons can be explained with differences in choice of mathematical calculations.