# Delayed avalanches in Multi-Pixel Photon Counters

## TL;DR

This study investigates the causes of after-pulsing in Multi-Pixel Photon Counters, revealing that earlier models experienced delayed avalanches due to photon absorption and hole diffusion, which was mitigated in post-2013 devices.

## Contribution

The paper identifies the primary source of after-pulsing as photon absorption and hole diffusion in pre-2013 devices and demonstrates that improvements made in 2013 significantly reduced this effect.

## Key findings

- Pre-2013 devices show delayed avalanches up to several hundred nanoseconds.
- Post-2013 devices exhibit about 25 times lower after-pulsing.
- Photon absorption in silicon bulk causes delayed avalanches in older devices.

## Abstract

Hamamatsu Photonics introduced a new generation of their Multi-Pixel Photon Counters in 2013 with significantly reduced after-pulsing rate. In this paper, we investigate the causes of after-pulsing by testing pre-2013 and post-2013 devices using laser light ranging from 405 to 820nm. Doing so we investigate the possibility that afterpulsing is also due to optical photons produced in the avalanche rather than to impurities trapping charged carriers produced in the avalanches and releasing them at a later time. For pre-2013 devices, we observe avalanches delayed by ns to several 100~ns at 637, 777nm and 820 nm demonstrating that holes created in the zero field region of the silicon bulk can diffuse back to the high field region triggering delayed avalanches. On the other hand post-2013 exhibit no delayed avalanches beyond 100~ns at 777nm. We also confirm that post-2013 devices exhibit about 25 times lower after-pulsing. Taken together, our measurements show that the absorption of photons from the avalanche in the bulk of the silicon and the subsequent hole diffusion back to the junction was a significant source of after-pulse for the pre-2013 devices. Hamamatsu appears to have fixed this problem in 2013 following the preliminary release of our results. We also show that even at short wavelength the timing distribution exhibit tails in the sub-nanosecond range that may impair the MPPC timing performances.