Phosphors for Radiation Detectors. Группа авторов

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 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,