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

Abstract

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.

Energy resolution and related charge carrier mobility in LaBr3:Ce scintillators

“…2,6,21,29,35,36 It is attributed to radiationless electron-hole pair recombination in the regions of a high concentration n(x) of charge carriers along the ionization track as shown in Fig. 1.…”

“…An important factor determining the rate at which carriers leave this volume is the carrier diffusion coefficient. 2,6,23 Another very important parameter is concentration of luminescence or trapping centers inside the high ionization density volume. At high concentration of Ce 3þ in LaBr 3 essential part of the charge carriers can be promptly removed from the diffusionquenching process.…”

“…2,6,[21][22][23][24][25] This process together with an ionization density that changes along an electron track and with primary electron energy causes the deterioration of the energy resolution. To avoid the recombination losses, charge carriers should be effectively transferred from the primary track to luminescence centers.…”

“…An important factor determining the rate at which carriers leave this volume is the carrier diffusion coefficient. 2,6,23 A high diffusion coefficient contributes to a more rapid transport of electrons, holes and excitons to regions further from the track where the radiationless recombination rate does not depend on ionization density.…”

“…In inorganic scintillators, that is the topic of this work, the created free charge carriers need to escape the volume of high ionization density to be trapped by a luminescence center and recombine under emission of photons. 6 Scintillation crystals are widely used as spectroscopic detectors of ionizing radiation in nuclear science, space exploration, medical imaging, homeland security, etc. The important parameters for X-or c-ray spectrometry are the total light output by the scintillator expressed in photons emitted per MeV of absorbed ionizing energy, decay time of the scintillation light flash, energy resolution for the detection of the ionizing particle and the detection efficiency.…”