Thermalization of electron-hole pairs in LaBr3, CeBr3 and CLLB: Monte Carlo simulation

A Monte Carlo model is used to investigate electron-hole (e-h) generation created by incident gamma-ray radiation in ${\mathrm{LaB}}_{3}, {\mathrm{CeBr}}_{3}$, and ${\mathrm{Cs}}_{2}{\mathrm{LiLaBr}}_{6}$ (CLLB) scintillators. Our approach follows the detailed energy loss mechanisms and describes the microscopic structure of ionization tracks in order to address differences in the scintillation properties of these three materials. The mean energy required to create an e-h pair, $W$, theoretical light yield, and the spatial distribution of e-h pairs are determined. We found that $W$ approaches constant and similar values at high incident energies for ${\mathrm{LaB}}_{3}$ and CLLB, suggesting that these materials should have similar light yields. However, the experimental light yield of CLLB is almost half that of ${\mathrm{LaBr}}_{3}$. Unlike for ${\mathrm{LaBr}}_{3}, W$ of ${\mathrm{CeBr}}_{3}$ increases with increasing energy excitation and shows a nonlinear behavior in e-h creation, potentially explaining slightly lower light yield and worse energy resolution of ${\mathrm{CeBr}}_{3}$. Furthermore, we observed that the spatial distributions of electron-hole pairs in ${\mathrm{LaBr}}_{3}$ and ${\mathrm{CeBr}}_{3}$ are very similar, while the number of high-density e-h domains in CLLB is greater in comparison. This discrepancy could explain the lower light yield of CLLB. The thermalization model of e-h pairs showed that the longitudinal optical phonon energy has a profound effect on the thermalization time and distance of e-h pairs, leading to a much higher density of excitation in ${\mathrm{LaBr}}_{3}$ but a more diffuse one in CLLB. This effect leads to steeper gradients in ${\mathrm{LaBr}}_{3}$, resulting in varying density effects and worse proportionality, while CLLB suffers from more uniform but more pronounced quenching. The fraction of nonradiatively recombined electrons in ${\mathrm{LaBr}}_{3}$ and CLLB was estimated to be 30% and 45%, respectively. These results correlate well with experimental observations of the scintillation properties of these materials. The approach can be used to predict the expected properties of new materials and support further development of existing materials.