A Course in Luminescence Measurements and Analyses for Radiation Dosimetry. Stephen W. S. McKeever

states are at different defects (different defect types) then they will remain localized and the system will no longer be in equilibrium. This is the metastable state.

      The situation is illustrated in Figure 1.2b. (Animated versions of Figures 1.2a and 1.2b are available on the web site under Exercises and Notes, Chapter 1.) The two localized energy states, one above the Fermi Level and one below, localize excited electrons from the conduction band and free holes from the valence band, respectively. When localized in this way, the system is in a metastable condition. Absorption of energy from an external stimulus can free electrons (say) from the trap causing a transition to the conduction band, and these may subsequently recombine with the trapped holes, returning the system to equilibrium.

      There may be multiple localized states available for electrons and holes. Consider an arbitrary distribution of available states Z(E). According to Fermi-Dirac statistics, the occupancy of any energy level E, at temperature T, is given by the distribution function f(E), where:

      

(1.1)

where EF is the Fermi Level and k is Boltzmann’s constant. At equilibrium (and at T = 0 K), f(E < EF) = 1 (all states full), and f(E > EF) = 0 (all states empty). The situation is illustrated in Figure 1.3a, for an arbitrary distribution Z(E).

      Figure 1.3 (a) Arbitrary distributions of available states Z(E), at equilibrium and T = 0 K, with the Fermi-Dirac occupancy function f(E). f(E) = 1 for E < EF, and f(E) = 0 for E > EF. (b) After irradiation some electrons occupy states above the Fermi level, and some states below this level are empty. Two quasi-fermi Levels can be defined, one for electrons EFe_, where EF < E < EFe and one for holes EFh, where EF > E > EFh, as shown. (c) During the return to equilibrium (i.e., during stimulation), the quasi-fermi Levels move toward EF as the occupancy of the localized states changes. (d) Eventually, the system returns to equilibrium.

      After irradiation (also at T = 0 K) the occupancy function f(E) changes, as illustrated by the red line in Figure 1.3b. In this view, two new energy levels can be defined, known as quasi-Fermi levels, one for electrons EFe and one for holes EFh. EFe is defined such that all localized states at energy level E are full when EF < E < EFe, and are empty when EF > E > EFh.

      During stimulation after irradiation, the states above EF empty while those below EF fill, and the two quasi-Fermi Levels move closer to the original Fermi Level, EF (Figure 1.3c). Eventually, when all localized states above EF are empty of electrons and all those below are full, EFe = EF = EFh and the system has returned to equilibrium (Figure 1.3d).

      The above picture describes the broad, conceptual notions describing the perturbation of a system from equilibrium due to irradiation, and the return of the system to equilibrium during either thermal stimulation or optical stimulation. If the final relaxation processes are radiative, TL and OSL result. In the chapters to follow, the equations describing the changes in occupancy of the various energy levels during excitation and stimulation will be examined. First, however, related processes including radiophotoluminescence, RPL, are introduced.

      1.2.3 Related Processes

      Thermoluminescence is one of a family of thermally stimulated phenomena that include:

       Thermoluminescence (TL);

       Thermally Stimulated Conductivity (or Current) (TSC);

       Thermally Stimulated Capacitance (TSCap);

       Deep Level Transient Spectroscopy (DLTS);

       Thermally Stimulated Exo-Electron Emissions (TSEE).

      Two additional and related phenomena should be added:

       Phosphorescence;

       Radioluminescence.

These have been described collectively in several text books (Bräunlich 1979; Chen and Kirsh 1981; Chen and McKeever 1997).

      Similarly, Optically Stimulated Luminescence is one of a family of phenomena, including:

       Optically Stimulated Luminescence (OSL);

       Photoconductivity (PC);

       Optically Stimulated Exo-Electron Emission (OSEE).

      As already noted, RPL does not involve ionization of the localized electrons from their trapping states and can be placed alongside other phenomena, including:

       Radiophotoluminescence (RPL);

       Electron Paramagnetic Resonance (EPR), also called Electron Spin Resonance (ESR);

       Photoluminescence (PL).

      All of the above phenomena, except PL, require the initial absorption of energy from an external radiation field before the signal (TL, OSL, RPL, EPR, DLTS, etc.) can be observed. The radiation energy must be sufficiently high to cause ionization within the material – i.e. the creation of free electrons and holes. Photoluminescence is an intrinsic property of the material; that is, it may be observed before irradiation and is not created by it. Ionization is not required. (Photoluminescence can be an interference signal in both RPL and OSL.)

The differences between the phenomena are illustrated schematically in Figure 1.4. Here is represented the energy band diagram previously discussed for an insulator or semiconductor. Ionization by the radiation creates free electrons and holes that may be subsequently trapped at electron and hole localized states. Stimulation (heat or light) induces recombination of the electrons and holes. (Note: We can describe these phenomena in terms of releasing trapped electrons to recombine with holes, or vice-versa. In this description, for ease of explanation, the discussion is limited to releasing electrons to recombine with holes.) Production of TL or OSL only occurs when a portion of the energy released during the electron-hole recombination is radiative. Thus, the TL and OSL signals include information about both the trap and the recombination center. Both are required for TL and OSL to be observed.

Figure 1.4 Schematic diagram illustrating the differences between several thermally and optically stimulated phenomena. Only TL and OSL contain information about both the trap and the recombination center.

      Phosphorescence is in fact an unstable form of TL in which the electrons are trapped in the localized energy levels for short periods of time. If the traps are characterized by a small energy barrier then trapped charge can be thermally stimulated even at room temperature, leading to recombination and therefore luminescence emission. Similarly, radioluminescence (RL) results when electrons excited to the conduction band recombine with holes localized in hole traps, without the step of becoming trapped themselves. Emission of RL occurs during the irradiation and decays quickly after the cessation of the radiation, on a time frame governed by the recombination lifetime of the free electrons in the conduction band. In practice, both RL and phosphorescence can be observed during irradiation and the timescale for the decay of the