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
When I(T) shows the maximum, we can obtain equations such as
(1.50)
and
If we combine Equation (1.51) with Equation (1.49), the TSL intensity can be expressed as
When the TSL intensity shows the maximum Im, Equation (1.49) can be rewritten as
When we combine Equation (1.52) with Equation (1.54), the maximum intensity can be expressed as
(1.55)
and relationship of
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 ηtrap, S′, and ηesc 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 (NOSL(t)) can be expressed as
(1.59)
where γ1, γ2, … γm 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, …γm, t) is a weighting function, or distribution, expressing the concentration of occupied states possessing the parameters γ1, γ2, … γm, t. Then, OSL intensity IOSL(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 NOSL(t),
(1.61)
In this formula, l = 1 means a first‐order function. If each state n(γ1, γ2, …γm, t) has its own probability function p(γ1, γ2, … γm) 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, … γm, 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,
