Theory of Thermoluminescence
by Dr. Reuven Chen
Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.
The basic theory of thermoluminesence (TL) is based on the occurrence of imperfections, impurities, and defects, found within an insulating material. These lattice sites may capture electrons and holes during the excitation of the sample and later, during the heating, these charge carriers can recombine and produce the emission of light in the form of a TL glow curve. The process leading to recombination includes, in many cases, the transition of charge carriers through the conduction or valence band, but localized transitions may also take place. In most cases, the theory consists of solving the relevant sets of coupled differential equations,either by using some simplifying assumptions or by solving numerically the equations for certain sets of trapping parameters.
1 Introduction
The effect of thermoluminescence (TL) is the emission of light from solids, usually crystalline insulators, following excitation, usually by some irradiation. Energy is absorbed in the sample during the excitation, and released during the heating, yielding a glow curve, namely, a graph of emitted-light intensity versus temperature. The glow curve usually includes one or more glow peaks that may be either separate or overlapping. The emitted light may include different spectral components which indicate different transitions taking place during the heating. Practically always, the glow curve can be detected only following a first heating, and a subsequent heating does not produce any light emission until another irradiation takes place. The main application of TL, along with the closely related effect of optically stimulated luminescence (OSL) is in dosimetry. The dependence of the measured luminescence on the preceding excitation dose should be taken into consideration; linear dose dependence is desirable, but other dependencies often occur. Different dose-dependence behaviours are observed when using different sources of radiation. [math]\alpha\lt/math), \ltmath\gt \beta [/math], and [math]\gamma[/math] irradiations as well as X-rays, UV light, high-energy particles and neutron beams may be used to induce TL in different crystals. Another application of TL, derived from the property of dose dependence is the dating of archaeological and geological samples. An important subject in the study of TL has to do with the evaluation of the trapping parameters, mainly the activation energy and the frequency factor of the involved traps. Also the stability of the TL signal at ambient temperature has been studied extensively. Normal thermal fading as well as anomalous fading have been observed in different materials and a number of theoretical explanations have been provided. TL has been studied in hundreds of different materials in the quest for an optimal material for TL dosimetry.
2 Basic theory
The main requirement for producing a glow peak is the occurrence of two imperfections in the lattice. During excitation, one is capable of trapping an electron and the other traps a hole. A schematic energy level diagram is shown in Fig. 1. The basic theory of TL was first introduced by Randall and Wilkins (1945). These authors assumed that during excitation by irradiation, electrons are trapped in an electron trap of concentration N (cm[math]^{-3}[/math]), and holes are trapped in hole centres, M (cm[math]^{-3}[/math]). During heating, electrons are raised thermally into the conduction band and, according to this basic theory, they recombine almost immediately with a hole in a centre to produce photons. The basic differential equation for this process was given by Randall and Wilkins as a first-order equation
[math]I(T)=-\frac{\mathrm{dn} }{\mathrm{d} t}=sn\, exp\left ( -E/kT \right )\tag{1}[/math]
where n (cm[math]^{-3}[/math]) is the instantaneous concentration of trapped electrons, E (eV) the activation energy for releasing trapped electrons, s ([math]^{s-1}[/math]) the frequency factor, k (eV/K) Boltzmann's constant, T (K) the temperature, t (s) is the time and I the emitted intensity. As is, the units of I(T) are cm-3s-1, however, a dimensional constant should be added which has been set arbitrarily to unity. With this constant, I(T) will be in units of photons per second or energy per second. In order to solve this equation, one should use a heating function that relates temperature and time. In many cases, a linear function is used, [math]T=T_{0}+\beta t[/math] where [math]\beta[/math](K/s) is the constant heating rate and T0 the initial temperature.The solution of Eq. (1) is
