Coupled rate and transport equations modeling proportionality of light yield in high-energy electron tracks: Csl at 295 K and 100 K; Csl:TI at 295 K

A high-energy electron in condensed matter deposits energy by creation of electron-hole pairs whose density generally increases as the electron slows, reaching the order of 1020 eh/cm3 near the end of its track. The subsequent interactions of the electrons and holes include nonlinear rate terms and transport as first hot and then thermalized carriers in the nanometer-scale radial dimension of the track. Charge separation and strong radial electric fields occur in a material such as Csl with contrasting diffusion rates of self-trapped holes and hot electrons. Eventual radiative recombination has a nonlinear relation to the primary electron energy because of these interactions. This so-called intrinsic nonproportionality of electron response limits the achievable energy resolution of a given scintillation radiation detector material. We use a system of coupled transport and rate equations to describe a pure host (three equations) and one dopant (four more equations per dopant). Applying it first to the experimentally well-characterized system of Csl and Csl:TI in this work, we use results of picosecond absorption spectroscopy, interband Z-scan measurements of nonlinear rate constants, and other experiments and calculations to determine most of the more than 20 rate and transport coefficients required for modeling. The model is solved in a track environment approximated as cylindrical and is compared to the proportionality curve and total light yield of undoped Csl at temperatures of 295 and 100 K, as well as thallium dopant in Csl:TI at 295 K. With this degree of validation, the space and time distributions of carriers and excitons, both untrapped and trapped, are examined within the model to gain an understanding of the main competitions controlling the nonproportionality of response.