A transport-based model of material trends in nonproportionality of scintillators

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.