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Analytical expressions for the local light yield as a function of the local deposited energy (-dE/dx) and total scintillation yield integrated over the track of an electron of initial energy E are derived from radiative and/or nonradiative rates of first through third order in density of electronic excitations. The model is formulated in terms of rate constants, some of which can be determined independently from time-resolved spectroscopy and others estimated from measured light yield efficiency as a constraint assumed to apply in each kinetic order. The rates and parameters are used in the theory to calculate scintillation yield versus primary electron energy for comparison to published experimental results on four scintillators. Influence of the track radius on the yield is also discussed. Results are found to be qualitatively consistent with the observed scintillation light yield. The theory can be applied to any scintillator if the rates of the radiative and non-radiative processes are known.2

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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 10 20 eh/cm 3 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 CsI 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 socalled intrinsic nonproportionality of electron response limits 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 (3 equations) and one dopant (4 more equations per dopant). Applying it first to the experimentally well-characterized system of CsI and CsI:Tl 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 CsI at temperatures of 295 K and 100 K, as well as thallium dopant in CsI:Tl 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.

Electron-hole pairs created by the passage of a high-energy electron in a scintillator radiation detector find themselves in a very high radial concentration gradient of the primary electron track. Since nonlinear quenching that is generally regarded to be at the root of nonproportional response depends on the fourth or sixth power of the track radius in a cylindrical track model, radial diffusion of charge carriers and excitons on the ∼10 picosecond duration typical of nonlinear quenching can compete with and thereby modify that quenching. We use a numerical model of transport and nonlinear quenching to examine trends affecting local light yield versus excitation density as a function of charge carrier and exciton diffusion coefficients. Four trends are found: (1) nonlinear quenching associated with the universal “roll-off” of local light yield versus dE/dx is a function of the lesser of mobilities μe and μh or of DEXC as appropriate, spanning a broad range of scintillators and semiconductor detectors; (2) when μe ≈ μh, excitons dominate free carriers in transport, the corresponding reduction of scattering by charged defects and optical phonons increases diffusion out of the track in competition with nonlinear quenching, and a rise in proportionality is expected; (3) when μh ≪ μe as in halide scintillators with hole self-trapping, the branching between free carriers and excitons varies strongly along the track, leading to a “hump” in local light yield versus dE/dx; (4) anisotropic mobility can promote charge separation along orthogonal axes and leads to a characteristic shift of the “hump” in halide local light yield. Trends 1 and 2 have been combined in a quantitative model of nonlinear local light yield which is predictive of empirical nonproportionality for a wide range of oxide and semiconductor radiation detector materials where band mass or mobility data are the determinative material parameters.

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