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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 E_g (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:

(1.3)

where E_i, E_op, and E_f 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 >E_i, the impact ionization (excitation process) continues. In the ideal case, the limiting efficiency (Y) of the production of electron–hole pairs is

(1.4)

and by using this relation, the average energy per electron–hole pair is re‐written as

(1.5)

where L_f = E_f/E_i and K means the ratio of rate of optical phonons rate of energy loss by ionization, expressed as

(1.6)

In this equation, ℏω_LO 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) E_i = 1.5E_g, and according to the avalanche multiplication data of Si, then K can be approximated to

(1.8)

In order to proceed with the calculation, we assume a polaron model where a polaron accompanies α/2 phonons, then α can be expressed as

(1.9)

where K_∞ and K₀ are static and high‐frequency dielectric constants, respectively. Under this condition, the optical phonon generation rate is proportional to

(1.10)

Thus, K can be expressed as

(1.11)

By using these equations, we can estimate the scintillation emission efficiency semi‐empirically. Following this first approach, the model was modified for actual use in daily experiments. In 1994 [57], the scintillation light output L per unit energy was expressed as

(1.12)

where n_e‐h is the number of electron–hole pairs under γ‐ray with energy of E_γ irradiation, n_max is the number of electron hole pairs which would be generated if there were no losses to optical phonons, S stands for transfer efficiency from the host to luminescence centers, Q is luminescence quantum efficiency at localized luminescence centers, and η is total scintillation efficiency.

Here, we will proceed with further consideration that this assumption is E_i = 1.5E_g. In the Robbins approach [56], the average energy used to produce one electron–hole pair under assumption of no optical phonon loss is ξ_min = 2.3E_g, and in this case, n_max = 10⁶ E_γ/2.3E_g where we use the energy unit of eV. Because n_e‐h = 10⁶ E_γ/2.3ξ and n_max = 10⁶ E_γ/ξ_min, we can deduce that β_s = ξ_min/ξ. In Equation (1.5), if we assume K = 0, we have ξ_min = 1.5E_g(1 + 2L_f), and if we use the relation of ξ_min = 2.3E_g, L_f = 0.27. If we assume L_f does not depend on K, we can use L_f = 0.27 in Equation (1.5), and the average energy consumed per electron–hole pair can be expressed as ξ = E_g(2.3 + 1.5 K). Under this condition, the parameter β is approximated to

(1.13)

The number of electron–hole pairs is

(1.14)

Thus we can obtain

(1.15)

Equation (1.15) is a convenient form because it contains a parameter of optical phonon loss, and the evaluation of the model under various temperatures was made in 2010 [58].

Generally, experimental evaluations of effects of optical phonon (thermal) loss is difficult. For experimental research a very convenient model assuming β_s = 2.5 is proposed, based on the data of various scintillators [59], and most research uses this formula which is described as

(1.16)

In this formula, we can determine L, E_g, and Q experimentally, and we can deduce S by using these values. L can be evaluated by the pulse height spectrum, E_g by optical absorption or reflection spectrum, and Q by PL quantum yield measurement. Although we cannot predict the scintillation light yield by these formulae, we can understand why halide and sulfide materials show higher light yields than oxide materials by E_g. In most cases, Q of commercial scintillators is close to 100%. As described in Chapter 11, in the case of the integration‐type detector, a factor representing the absorption of ionizing radiation is multiplied to Equation (1.16).

Typical ways to determine L is to compare with the pulse height of a single photoelectron (~single photon) of photodetector with high quantum efficiency, and we can know the number of photoelectrons from the scintillator. In this manner, we can directly measure L after dividing the number of photoelectrons by the quantum efficiency of the photodetector at the emission wavelength of the scintillator. The other common way is to compare the pulse height of ⁵⁵Fe 5.9 keV X‐ray measured directly by Si‐based photodetectors. The photoabsorption peak due to 5.9 keV X‐ray corresponds to ~1640 electron–hole pairs, and we can evaluate the number of photoelectrons generated by scintillation photons if we use the same experimental conditions. Another way is to compare relative pulse height with scintillators with known scintillation light yield. In these evaluation techniques, finally, we must divide the observed number of photoelectrons by the quantum efficiency of photodetectors at emission wavelength, and it contains a certain amount of error because the quantum efficiency of photodetectors has a wavelength dependence. Typically, the error for the estimation is 5–10% for experts of these kind of experiments. In some research, the scintillation light yield is calculated by the area intensity of the radioluminescence spectrum, and this is generally incorrect because radioluminescence intensity is not a quantitative but a qualitative value. The main reason is that we cannot correct the absorption probability of ionizing radiations in scintillators. For example, we have two samples with the same light yield, but one is light and the other is heavy. If we irradiated X‐rays to these samples, the latter would show higher radioluminescence intensity. The other reason is the effect of TSL at room temperature, and we also cannot correct any effects from TSL. If we are to measure scintillation light yield quantitatively, pulse height measurements must be conducted. At present, we cannot measure the pulse height of scintillators with very slow decay (> 0.1 ms), and further technical development is required to measure pulse height.

The following topics are limited to photon counting‐type detectors, since integration‐type detectors cannot measure the energy of ionizing radiation, except in some special cases. The scintillation light yield is one of the most important properties of scintillation detectors because it directly relates to the energy resolution. Generally, the energy resolution obeys Poisson statistics. If we represent the quantum efficiency of the photodetector as q, the number of electron–hole pairs after photodetector output n is a product of q and the number of scintillation photons. The energy resolution under the absorbed energy of E is expressed as

(1.17)

Therefore, we can obtain a better energy resolution in bright scintillators. In actual detectors, the energy resolution is different from the resolution derived from simple Poisson statistics, and the gap between actual dispersion of 𝑛 and dispersion of 𝑛 in Poisson distribution is called the Fano factor (F). By using the Fano factor, the limit of the energy resolution of actual detectors is expressed as

(1.18)

In semiconductor, gas, and scintillation detectors, F is ~0.1, 0.1–0.4, and 1, respectively. Therefore, semiconductor detectors such as Si, Ge, and CdTe are known to have a superior energy resolution compared to scintillation detectors, and the best energy resolution so far is ~2% at 662 keV [60, 61]. In practical detectors, energy resolution is not only affected by statistics but also by non‐uniformity of the scintillator. Especially in luminescence center doped scintillators, because we generally use bulky larger material to interact with ionizing radiations effectively, non‐uniform distribution of dopant ions cannot be avoided. The non‐uniform distribution causes differences of light output at each point on the scintillator, and in such a case, the photoabsorption peak or some other features caused by ionizing radiation become, for example, a superposition of multiple Gaussian. Eventually, the shape of the peak in the pulse height spectrum becomes broad, and the energy resolution becomes worse. Such a non‐uniformity is also observed in photodetectors, and the energy resolution observed in practical detectors depends on the non‐uniform response of scintillators and photodetectors.

In order to evaluate the energy resolution of scintillators fundamentally, sometimes intrinsic energy resolution [62] is evaluated. Before the twenty‐first century, the energy resolution was limited to 6–7% at 662 keV in common scintillators. After the invention of Ce‐doped LaCl₃ [63] and LaBr₃ [45], some new scintillators with high energy resolution (2–4% at 662 keV) appeared. If we say ΔE/E = 0.01 (1%), then n is 5590. If we use typical Si‐based photodetectors, quantum efficiency at visible wavelength is ~80%, and 5590/0.8 ~7000 photons are required to achieve ~1% energy resolution. However, actual scintillation detectors show a large discrepancy with this simple calculation, and in order to explain such a discrepancy, the intrinsic energy resolution was introduced [64]. Although there are several expressions about the intrinsic energy resolution, logically, the energy resolution can be divided into several terms, for example

(1.19)

where δ_sc, δ_cir, and δ_st represent the intrinsic energy resolution, resolution due to circuit noise, and resolution expected by Poisson statistics, respectively. In pulse height spectrum, we observe ΔE/E directly, and we can estimate δ_st by the number of scintillation photons and the quantum efficiency of the photodetector. The circuit noise δ_cir can be directly estimated by the injection of a test pulse into the electrical circuit. Thus, we can calculate δ_sc by the subtraction of δ_st and δ_cir from ΔE/E. Under most experimental conditions, estimation must consider a contribution not only by the scintillator but also by the photodetector, and the simplest measurement can be possible by Si‐PD because it has no internal gain. When we measured and calculate the intrinsic energy resolution, that at 662 keV of Tl‐doped NaI was 2.5% [64], Tl‐doped CsI was 5% [65], Ce‐doped LaBr₃ was 2.2% [66], Ce‐doped LuAG was 4.5% [66], and Ce‐doped LSO was 7.7% [66]. At present, the remaining problem is whether the intrinsic energy resolution we are observing is a fundamental limit or not, and whether the intrinsic energy resolution is the physical property of each material or not (detector property). The detailed explanations on energy resolution and intrinsic energy resolution are described in Chapter 12.

In an ideal scintillation detector, energy response (signal output intensity vs. incident radiation energy) should have a simple proportional relationship; however, the energy responses of actual detectors are not simple. The main reason is a non‐proportional energy response of scintillators. Figure 1.6 (top) shows a non‐proportional response plot, which shows a relationship between relative light output (pulse height) per unit energy and irradiated γ‐ray energy. Although Eu‐doped SrI₂, Ce‐doped CLYC, and Pr‐doped LuAG show a relatively flat response against γ‐ray energy, BaF₂, Ce‐doped GAGG, and Tl‐doped NaI exhibit a large fluctuation against γ‐ray energy. When we use the latter three types of scintillators as actual detectors, we must apply the gain correction function to measure the energy accurately. The main origin of the non‐proportional response is considered as related to the K‐edge of the main element of scintillator. This was first pointed out in Ce‐doped GSO [67]. Now, we understand that the flat response against γ‐ray energy is required to achieve high energy resolution. In practical scintillation detectors, we generally use a function between γ‐ray energy and pulse height, as shown in the bottom of Figure 1.6. In a simple case, we fit the relationship by a linear function with the least squares method, and the bottom panel in the bottom of Figure 1.6 shows the residual from linear fitting at each energy. After we prepare such a fitting function, we can convert pulse height channel to energy of ionizing radiation focused on each measurement. Although these two figures have the same physical meaning, people in basic science prefer a non‐proportionality plot, and those using the actual detector prefer a linearity plot.

Figure 1.6 (Top) Relationship between the scintillation decay time (ns) and emission wavelength (nm) and (bottom) relationship betweenγ‐ray energy and photoabsorption peak channel.