Abstract
A Monte Carlo model of electron thermalization in inorganic scintillators, which was developed and applied to CsI in a previous publication [Wang et al., J. Appl. Phys. 110, 064903 (2011)], is extended to another material of the alkali halide class, NaI, and to two materials from the alkaline-earth halide class, CaF_{2} and BaF_{2}. This model includes electron scattering with both longitudinal optical (LO) and acoustic phonons as well as the effects of internal electric fields. For the four pure materials, a significant fraction of the electrons recombine with self-trapped holes and the thermalization distance distributions of the electrons that do not recombine peak between approximately 25 and 50 nm and extend up to a few hundreds of nanometers. The thermalization time distributions of CaF_{2}, BaF_{2}, NaI, and CsI extend to approximately 0.5, 1, 2, and 7 ps, respectively. The simulations show that the LO phononenergy is a key factor that affects the electron thermalization process. Indeed, the higher the LO phononenergy is, the shorter the thermalization time and distance are. The thermalization time and distance distributions show no dependence on the incident γ-ray energy. The four materials also show different extents of electron-hole pair recombination due mostly to differences in their electron mean free paths (MFPs), LO phononenergies, initial densities of electron-hole pairs, and static dielectric constants. The effect of thalliumdoping is also investigated for CsI and NaI as these materials are often doped with activators. Comparison between CsI and NaI shows that both the larger size of Cs^{+} relative to Na^{+}, i.e., the greater atomic density of NaI, and the longer electron mean free path in NaI compared to CsI contribute to an increased probability for electron trapping at Tl sites in NaI versus CsI.
The authors would like to acknowledge Professor A. Akkerman for insightful discussions. This research was supported by the National Nuclear Security Administration, Office of Nuclear Nonproliferation Research and Engineering (NA-22), of the U.S. Department of Energy (DOE).
I. INTRODUCTION
II. COMPUTATIONAL METHODS
A. Thermalization process
B. Origin of the model parameters
III. RESULTS AND DISCUSSION
A. Pure materials: CsI, NaI, CaF_{2}, and BaF_{2}
B. Dopedmaterials: CsI(Tl) and NaI (Tl)
IV. CONCLUSIONS
Key Topics
- Phonons
- 39.0
- Doping
- 15.0
- Phonon electron interactions
- 12.0
- Electron scattering
- 11.0
- Plasmons
- 10.0
C30B31/00
G01T
H01J47/00
Figures
Kinetic energy distributions of the electrons at the end of the electron cascade for an incident γ-ray energy of 2 keV.
Kinetic energy distributions of the electrons at the end of the electron cascade for an incident γ-ray energy of 2 keV.
Electron-phonon scattering rates as a function of electron energy.
Electron-phonon scattering rates as a function of electron energy.
(a) Fraction of recombined electron-hole pairs as a function of incident γ-ray energy. (b) Distributions of the fractions of recombined electrons (FREs). (c) Initial electron-hole pair distribution functions. (b) and (c) are for an incident γ-ray energy of 2 keV. (d) Electron mean free paths as a function of electron energy.
(a) Fraction of recombined electron-hole pairs as a function of incident γ-ray energy. (b) Distributions of the fractions of recombined electrons (FREs). (c) Initial electron-hole pair distribution functions. (b) and (c) are for an incident γ-ray energy of 2 keV. (d) Electron mean free paths as a function of electron energy.
Thermalization distance distributions for the (a) recombined and (b) stopped electrons for a 2-keV incident γ-ray. The inset in (b) shows the ratio of LO phonon creation and LO phonon annihilation scattering rates.
Thermalization distance distributions for the (a) recombined and (b) stopped electrons for a 2-keV incident γ-ray. The inset in (b) shows the ratio of LO phonon creation and LO phonon annihilation scattering rates.
Thermalization time distributions for the (a) recombined and (b) stopped electrons for a 2-keV incident γ-ray. The inset in (b) shows an enlarged view of the time distribution of CsI.
Thermalization time distributions for the (a) recombined and (b) stopped electrons for a 2-keV incident γ-ray. The inset in (b) shows an enlarged view of the time distribution of CsI.
Fraction of Tl-trapped electrons and recombined electron-hole pairs as a function of Tl concentration for an incident γ-ray energy of 2 keV.
Fraction of Tl-trapped electrons and recombined electron-hole pairs as a function of Tl concentration for an incident γ-ray energy of 2 keV.
Fraction of Tl-trapped, stopped and recombined electrons as a function of incident γ-ray energy for a Tl concentration of 0.1 mol. %.
Fraction of Tl-trapped, stopped and recombined electrons as a function of incident γ-ray energy for a Tl concentration of 0.1 mol. %.
(a) Maximum thermalization time and (b) thermalization distance peak of the stopped electrons as a function of Tl concentration for an incident γ-ray energy of 2 keV. Inset shows the thermalization distance and time distributions for three Tl concentrations in CsI.
(a) Maximum thermalization time and (b) thermalization distance peak of the stopped electrons as a function of Tl concentration for an incident γ-ray energy of 2 keV. Inset shows the thermalization distance and time distributions for three Tl concentrations in CsI.
Tables
Primary and secondary model parameters.
Primary and secondary model parameters.
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