  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.
