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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, stimulation intensity is a function of time, and can be expressed as

(1.66)

where Φ₀ and β_Φ are a constant of stimulation and a proportional constant of the stimulation intensity if we assume a linear time dependence. If Φ(t) is constant, it represents a continuous wave OSL (CW‐OSL), and the OSL intensity becomes

(1.67)

where t(E₀) is 1/p(E₀). If Φ(t) is not constant, the situation is a linear modulation OSL (LM‐OSL), and the OSL intensity is

(1.68)

where we assume Φ₀ = 0. Generally, we measure OSL in typical PL machines where the environment is free from any other light, and Φ₀ = 0 is a valid assumption. In this case, the OSL intensity becomes

(1.69)

Based on these analytical equations, OSL intensity shows exponential decay under stimulation, and this is an important property to distinguish PL and RPL from OSL. If readers would like to study OSL in more detail, it will be better to read specialized books on OSL (for example, [3]).

Sections 1.4.2 and 1.4.3 describe common confirmed formulations of TSL and OSL, but up to now, a widely accepted formulation of RPL has not been obtained. RPL is treated as PL after carrier trapping phenomena, and general treatment of PL can be applied.