the spectral sensitivity of Si‐PD. For practical uses, Ce3+ is co‐doped to suppress the afterglow level. Recently, Eu3+‐doped (Lu,Gd)2O3 [39] has attracted much attention for X‐ray CT. The emission intensity is higher than other materials, and the emission wavelength is in red where Si‐PD has a high sensitivity. In addition to these materials, we have investigated doping with other rare‐earth ions in order to develop near‐infrared emitting scintillators. For this purpose, Nd3+, Ho3+, Er3+ Tm3+, and Yb3+ have been selected as the emission center.
Emission due to 5d‐4f transitions of trivalent and divalent rare‐earth ions are very important in recent scintillation detectors because they show intense and fast emissions by the spin‐ and parity‐allowed transitions. The most common emission center is Ce3+, and examples of commercial scintillators are Ce‐doped Lu2SiO5 (LSO) [40], (Lu,Y)2SiO5 (LYSO) [41], Gd3(Al,Ga)5O12 (GAGG) [42], Y3Al5O12 (YAG) [43], YAlO3 (YAP) [44], LaBr3 [45], and Cs2LiYCl6 [46]. Except for garnet materials, including GAGG, most scintillators have emission wavelengths of 300–400 nm with 30–60 ns decay times, and these properties are suitable for conventional PMT readouts. In addition to Ce3+, Pr3+ can also show luminescence due to the 5d‐4f transition in some host materials. The appearance of the 5d‐4f transition depends on the relative positions between the lowest 5d and 1S0 levels. Common Pr‐doped scintillators are Pr‐doped LuAG [47], Lu2Si2O7 (LPS) [48], and YAP [49], which show light yields of 10 000–20 000 ph/MeV with a 20 ns decay time. Compared with Ce‐doped scintillators, the emission of Pr‐doped materials appears in the shorter wavelength range, typically at 250–350 nm. Some other trivalent rare‐earth ions show 5d‐4f transitions only in hosts with a wide‐band gap energy, and the emission wavelength is in VUV. A common example is Nd‐doped LaF3, which has an emission wavelength at 175 nm with a few‐ns decay time [50] due to the 5d‐4f transition of Nd3+. Divalent Eu also shows a very high scintillation light yield with a typically ~1 μs decay time, which is acceptable for the photon counting type detectors. Typical examples are Eu2+‐doped SrI2 [51], CaF2 [52], LiI [53], and LiCaAlF6 [54]. Recently, luminescence due to the 5d‐4f transitions of Sm2+ ions was also reported [55], and further investigations are in progress. Sm2+ shows emission in the near‐infrared range, and has attracted much attention for use in Si‐PD type photodetectors. Figure 1.5 shows typical scintillation spectra of such scintillators with various emission wavelengths superposed with typical quantum efficiency curves of common photodetectors. It should be noted that the emission wavelength by 5d‐4f transitions strongly depends on the crystal field, which is specific to each host lattice; the presented data are only examples.
Figure 1.5 Emission spectra of scintillators under X‐ray irradiation and typical quantum efficiencies of Si‐PD and PMT.
1.3.3 Scintillation Light Yield and Energy Resolution
In addition to the emission wavelength, light yield is the most important property for scintillators because it directly determines the signal to noise ratio (S/N) in all types of scintillation detectors. The scintillation light yield generally uses the unit of ph/MeV, which means a number of emitted scintillation photons with 1 MeV absorption of ionizing radiation. Typically, we measure it by X‐ and γ‐ray irradiation. It must be noted that the light yields of one scintillator are different by species of irradiated ionizing radiation. If we irradiate 5.5 MeV α‐ray from 241Am and 662 keV γ‐ray from 137Cs to one sample, the observed light yields are different. The relative ratio of light yields under α‐ray and γ(β)‐ray irradiation is known as the α/γ‐ (α/β‐) ratio. Although we do not have a universal theory for this ratio, empirically, the ratio of halide scintillators is close to 1, while that of oxide scintillators is ~0.2. In some fields of radiation physics and chemistry, the difference of energy conversion efficiency of different ionizing radiation species is recognized as the linear energy transfer (LET) effect.
Here, we will introduce the common explanation on the scintillation light yield. The semi‐empirical approach was made in 1980 by Robbins [56] based on semiconductor physics. In the semiconductor radiation detector, empirical relation of ξ (average energy consumed per electron–hole pair) and Eg (band‐gap energy) are connected by a parameter β as
(1.2)
In this approach, to consider ξ, the energy of electron–hole pairs, falls below the threshold energy for impact ionization:
where Ei, Eop, and Ef represent the threshold energy for impact ionization, energy emitted as optical phonons, and average residual energy of electron–hole pairs, respectively. Throughout this discussion, the unit of ξ (energy) is eV. Here, we consider the branching ratio of optical phonon emission with the probability of r and the impact ionization with (1‐r) under the initial absorbed energy of E0. If the energy after some processes, such as impact ionization and phonon emission, remains at >Ei, the impact ionization (excitation process) continues. In the ideal case, the limiting efficiency (Y) of the production of electron–hole pairs is
and by using this relation, the average energy per electron–hole pair is re‐written as
where Lf = Ef/Ei and K means the ratio of rate of optical phonons rate of energy loss by ionization, expressed as
(1.6)
In this equation, ℏωLO means the energy of the longitudinal optical phonon. If we assume this energy and the optical phonon energy is constant, K can be expressed as
(1.7)
Here, we assume special conditions of: (i) Ionization rate is constant for carrier energy; and (ii) Ei = 1.5Eg, and according to the avalanche multiplication data of Si, then K can be approximated to
In
