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

Abstract

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.

CsBa2I5:Eu2+,Sm2+—The First High‐Energy Resolution Black Scintillator for γ‐Ray Spectroscopy

“…The self‐trapping process has been studied extensively in alkali halides and is very typical for halide materials. A recent study showed that most holes are self‐trapped before they reach the activator dopant in the scintillator. After the charge carriers have been trapped at Eu 2+ , energy is transferred nonradiative to Sm 2+ , which is then followed by the dipole‐allowed 5d‐4f emission at 755 nm.…”

Role of hot electron transport in scintillators: A theoretical study

“…The built‐in electric field due to the separation of electrons and holes is included in our modeling. The initial distribution is assumed to be a 3 nm Gaussian cylinder of independent electron/hole pairs with three on‐axis densities, 2 × 10 20 cm –3 , 2 × 10 19 cm –3 , 2 × 10 18 cm –3 , in general representing different sections of a whole excitation track in scintillators . The near‐track end on‐axis density is determined as ∼2 × 10 20 cm –3 from previous z ‐scan experiments describing the amount of nonlinear quenching quantitatively .…”

“…The near‐track end on‐axis density is determined as ∼2 × 10 20 cm –3 from previous z ‐scan experiments describing the amount of nonlinear quenching quantitatively . On the other hand, Monte‐Carlo based simulations with GEANT4 package suggested the on‐axis density at the beginning of the excitation track to be ∼2 × 10 18 cm –3 . A third local excitation density 2 × 10 19 cm –3 was also included to describe the intermediate part of the excitation track.…”

A continuum theory of scintillation in inorganic scintillating crystals

“…By the means of (62) and (66), then from (41) 1,4 we arrive at a fairly general reaction and diffusion-drift equation for the excitation carrier densities evolution: div (D(θ)∇n + M(θ)N(n)q ⊗ ∇ϕ) − K(n , θ)n =ṅ , in R t (68) D(θ)[∇n]m = 0 , on ∂R t which recovers and generalizes equation (22) from [13] (vid. also [15], [17], [18], [40]).…”