Phosphors for Radiation Detectors. Группа авторов

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СКАЧАТЬ href="#ulink_242ee382-cec8-587a-b8a1-736b660d2d01">Equation (1.8) is a glow curve deconvolution function (GCD) of first‐order kinetics. In the case of second‐order kinetics (b = 2), Equation (1.39) becomes

(1.49)

      When I(T) shows the maximum, we can obtain equations such as

      (1.50)

(1.51)

      and

(1.52)

If we combine Equation (1.51) with Equation (1.49), the TSL intensity can be expressed as

(1.53)

      When the TSL intensity shows the maximum I_m, Equation (1.49) can be rewritten as

(1.54)

When we combine Equation (1.52) with Equation (1.54), the maximum intensity can be expressed as

      (1.55)

      and relationship of

(1.56)

is deduced. Finally, if we combine Equation (1.56) with Equation (1.53), we obtain the equation on the second‐order kinetics of

      (1.57)

      In addition to these standard analysis, analogical consideration of TSL efficiency with scintillation is considered as

      (1.58)

      where η_trap, S′, and η_esc are the trap efficiency of carriers at trapping centers, carrier transfer efficiency to luminescence centers, and a probability that emitted photons are not absorbed in TSL material [81]. Other parameters have the same meaning with scintillation. Some analogical relation is proposed to TSL and OSL [82], and they essentially have the same physical meaning that scintillation and storage luminescence should be treated as one theory.

      1.4.3 Analytical Description of OSL

      Here, we introduce a basic analytical treatment of OSL, and explanations on practical applications and common materials are described in Chapter 8. The concentration of the metastable state occupied with an electron or hole (N_OSL(t)) can be expressed as

      (1.59)

      where γ₁, γ₂, … γ_m mean the stability of the metastable state, that is they govern the probability per unit time in which the system will return to equilibrium, and n(γ₁, γ₂, …γ_m, t) is a weighting function, or distribution, expressing the concentration of occupied states possessing the parameters γ₁, γ₂, … γ_m, t. Then, OSL intensity I_OSL(t) is written as

      (1.60)

      If we assume that P(t) is the probability per unit time of the decay of the metastable states N_OSL(t),

      (1.61)

In this formula, l = 1 means a first‐order function. If each state n(γ₁, γ₂, …γ_m, t) has its own probability function p(γ₁, γ₂, … γ_m) under the condition of l = 1, then

      (1.62)

      where we assume that no interaction between states occur. This formula has no time dependence of t, and if we would like to treat the probability time dependently, p(γ₁, γ₂, … γ_m, t) should be used. The form of p depends on the stimulation methods such as TSL or OSL. For optical stimulation (OSL), we have

      (1.63)

      where E₀, Φ, and σ(E₀) are the threshold of optical stimulation energy, optical stimulation intensity, and photoionization cross‐section, respectively. If m = 1, γ₁ equals to E₀. In previous works [83, 84], photoionization cross‐section is expressed as

      (1.64)

      where hν is the energy of the incident photon of wavelength λ, m* is the charge carrier effective mass, and m₀ is the rest of mass, respectively. There are several expressions of the photoionization cross‐section, and the more simple form [85] is

      (1.65)

      Photoionization is basically the same as the photoelectric (photoelectric absorption) effect, described in scintillation, but the energy assumed here is around visible photons (several eV).

      Generally, СКАЧАТЬ