Timepix3: single-pixel multi-hit energy-measurement behavior

The event-driven hybrid-pixel detector readout chip, Timepix3, has the ability to simultaneously measure the time of an event on the nanosecond timescale and the energy deposited in the sensor. However, the behaviour of the system when two events are recorded in quick succession of each other on the same pixel was not studied in detail previously. We present experimental measurements, circuit simulations, and an empirical model for the impact of a preceding event on this energy measurements, which can result in a loss as high as 70~\%. Accounting for this effect enables more precise compensation, particularly for phenomena like timewalk. This results in significant improvements in time resolution -- in the best case, multiple tens of nanoseconds -- when two events happen in rapid succession.