Time-resolved Simulation of Optical Modulation from Ionization-induced Fast Charge Carriers

To greatly advance coincidence time resolution for positron emission tomography (PET), one possible mechanism is to utilize the transient free carrier effect resulting from 511 keV photon interactions in a crystal. It is challenging, however, to obtain precise timing information of carrier cascades, due to asynchronous decay of positrons. To address this problem, we propose to use relativistic electrons from ultrafast electron diffraction (UED) setup, which provides femtosecond (10
^-15
s) time resolution capabilities. We conducted simulation studies to understand the behavior of free carrier generation resulting from relativistic electrons, by expanding our previous work, which used 350 keV photo-electrons. Most UED facilities have higher electron energy than 511 keV, and we simulated 750 keV and 3 MeV for matching the actual experimental conditions. We report ionization electron cascade duration of 1.14 ps for 350 keV, 2.79 ps for 750 keV, and 12.1 ps for 3 MeV electrons in CdTe. We found that by decreasing the sample thickness, for example with 400 μm CdTe, the cascade time reduces to 2.1 ps, and absorbed the energy of 500 keV, approaching the regime relevant to PET. Time-resolved carrier cascade dynamics were simulated, which showed that the charge density decreased with higher energy (8.46 × 10
¹⁸
cm
^-3
for 350 keV, 2.48 10
¹⁸
cm
^-3
for 750 keV, and 1.02×10
¹⁸
cm
^-3
for 3 MeV), due to charge cloud spreading over longer cascade times. Finally, we obtained detectable optical modulation strengths in the first 350 μm in the charge carrier trajectory in CdTe, with maximum intensity change of 3.05% over a 120 μm by 160 μm area in z-projection. These results indicate the feasibility of using relativistic electron simulations to understand the temporal characteristics of ionization-induced electron cascade events generated by 511 keV photons.