Difference between revisions of "Thermoluminescence"

Revision as of 18:41, 18 May 2017

by Dr. Adrie J. J. Bos

Luminescence Materials Research Group, Delft University of Technology, Faculty of Applied Sciences, Mekelweg 15, NL 2629 JB Delft, The Netherlands

Thermoluminesence (TL) also called Thermally Stimulated Luminescence (TSL) is the emission of light from an insulator or semiconductor when it is heated following a previous absorption of energy from an external source (McKeever 1988).[1]

Characteristic of a material that shows TL is that the material is capable of storing some energy, that is released in the form of light when the material is heated. It should be realized that the heating is just the trigger not the cause of the luminescence. The emission of TL is made possible by previous absorption of energy usually from ionisation radiation. Once a material is heated it will show no TL again simply by cooling the material and reheating. In order to show TL again the material has to be re-exposed to radiation. The time between exposure and readout, i.e. the heating of the material can vary from seconds to thousands of years. Thermoluminescence should be distinguished from black body radiation, the light spontaneously emitted from a substance when it is heated to incandescence. In this case no prior absorption of energy from an external source is necessary. Instead of heat, radiation in the visible or infra-red region can also be used the produce luminescence. In that case the phenomenon is called Optically Stimulated Luminescence (OSL)(Yukihara and McKeever 2011).[2]

Explanation with a Simple Model

An explanation of the phenomenon is based on the energy band model of solids where each atom is subject to a periodic array of potential wells. Allowed energies for the electrons lie in allowed zones (valence band, conduction band). These bands constitute a ‘forbidden zone’ or ‘band gap’.However, whenever structural defects occur in a crystalline solid, or if there are impurities within the lattice, it becomes possible for electrons to possess energies which lie in the band gap. These so-called localized energy states play a crucial role in the TL mechanism. They act as trapping centres for the charge carriers which are freed during the exposure to radiation. In a simple TL model at least two levels are assumed (see Fig. 1). The highest level, indicated by Tr, is situated above the equilibrium Fermi level ([math]E_{f}[/math]) and thus empty in the equilibrium state, i.e. before the exposure to radiation and the creation of free electrons and holes. It is therefore a potential electron trap. The other level, indicated by R, is full at equilibrium and is a potential hole trap and can function as recombination centre. The absorption of radiant energy with energygreater than the band gap results in ionisation of valence electrons, producing energetic electrons and holes which will, after thermalization, produce free electrons in the conduction band and free holes in the valence band.A certain percentage of the freed charge carriers will be trapped: the electrons at Trand the holes at R(transitions b).There is a certain probability that the charge carriers escape from their traps due to thermal stimulation. The probability per unit time of release of an electron from the trap is assumed to be described by the Arrhenius equation:

[math]p=s\exp\left (-\frac{E}{kT} \right ) \tag{1} [/math]

where p is the probability per unit time. The pre-exponential factor s is called the frequency factor or attempt-to-escape factor. In the simple model s is considered as a constant (not temperature dependent) with a value in the order of the lattice vibration frequency, namely [math]10^{12} – 10^{14}s^{-1}[/math]. E is called the trap depth or activation energy, the energy needed to release an electron from the trap into the conduction band (see Fig. 1). The other symbols have their usual meaning; k = Boltzmann’s constant = [math]8.61710\times 10^{-5}\frac{eV}{K}[/math], and T the absolute temperature. The quantities E and s are called the trap parameters. Their values determine whether the electron will escape at a certain temperature T. In the simple model it is assumed that there is no quenching and no retrapping i.e. all electrons released into the conduction band gives rise to recombination under the emission of light. Let us denote n ([math]m^{-3}[/math]) as the concentration of trapped electrons and m ([math]m^{-3}[/math]) the concentration of holes trapped at R. Then the TL intensity, [math]I(t)[/math], in photons per unit volume and per unit time ([math]m^{-3}s^{-1}[/math]) at any time t during heating is proportional to the rate of recombination of holes and electrons at R and that is under the mentioned assumptions equal to the rate of thermal excitation of electrons from [math]T_{r}[/math] into the conduction band:

[math]I(t)=-\frac{dm}{dt}=-\frac{dn}{dt}=ns\exp \left ( -\frac{E}{kT} \right ) \tag{2}[/math]

This differential equation describes the charge transport in the lattice as a first-order process. Usually TL is observed as the temperature T is raised as a linear function of time t according to: [math]T(t)=T_{0}+\beta t\tag{3}[/math] with [math]\beta (Ks^{-1})[/math] a constant heating rate and [math]T_{0}[/math] the temperature at time [math]t=0[/math]. Solving Equation (2) with this temperature profile leads to the well-known Randall-Wilkins equation:

[math]I(T)=-\frac{1}{\beta }\frac{dn}{dt}=n_{0}\frac{s}{\beta }\exp \left ( \frac{-E}{kT} \right )\exp\left [ -\frac{s}{\beta } \int_{T_{0}}^{T}\exp \left ( -\frac{E}{kT^{'}}dT^{'} \right )\right ] \tag{3} [/math] with [math]n-{0}[/math] the total number of trapped electrons at [math]t=0[/math]and [math]T'[/math] a dummy variable. This equation describes the shape of a peak. Such a shape can be understood as follows. As the temperature increases the intensity initially increases because of the detrapping of the trapped charge carriers and consequent recombination which initiates luminescence, than the intensity reach a maximum and finally decreases as the number of charges carriers becomes depleted. The shape and the position of the peak maximum are governed by the trap parameters (material constants) and the heating rate (readout parameter).