«William Geoffrey West A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Nuclear Engineering ...»
the same temperature T, and luminescence would result, as there would have been an optical transfer of charge from deep traps not thermally annealed to shallow traps accessed during the TL examination. In this case, without knowing about the PTTL process in the material, the experimenter may have assumed that the material had received a dose of ionizing radiation between the first and second TL readouts. In this way, PTTL can be confounding. On the other hand, PTTL can be a useful tool for investigating the optical absorption and transition processes that occur in OSL materials during illumination. In addition, if properly known and characterized, the PTTL behavior of a material can be harnessed for use as a dosimetry method since, like OSL, the PTTL signal intensity is proportional to both the original dose of radiation and the intensity of the optical excitation. However, it is generally preferable to simply use TL or OSL techniques for dosimetry purposes.
Summary of Optical Absorption Transitions It is helpful in understanding, and discriminating amongst, the various possible optical processes above, to employ a visual metaphor. As such, an energy-level diagram showing the various possible optical absorption transitions is presented as Figure 1.2.
This figure shows the seven different possible light-induced electron transitions in a semiconductor: ionization, exciton formation, defect ionization, intra-center excitation, and trap ionization.
6 1 2 3 4 5 7
Figure 1.2: Energy-level diagram showing the possible optical absorption transitions in a semiconductor.
The possible transitions are: (1) ionization; (2) exciton formation; (3, 4) defect ionization; (5) intra-center excitation; and (6, 7) trap ionization.
Ionization of electrons directly out of the valence band, designated as transition type 1 in Figure 1.2, is typically not possible at optical wavelengths for insulators such as Al2O3, which has a band gap of ~6.6 eV(36), as well as semiconductors with very wide band gaps. However, it can be important for semiconductors such as ZnSe(1), which has a band gap of 2.7 eV(37).
Exciton formation, labeled transition type 2 in Figure 1.2, results in a localized charge which can then lead to OSL and/or TL, but this type of transition generally only occurs at vacuum ultraviolet wavelengths and is therefore not usually important in dosimetry applications(1).
Defect ionizations, shown as transition types 3 and 4 in Figure 1.2, are where an incident photon is energetic enough to cause ionization at a defect site within the material, but not necessarily energetic enough to cause ionization in the bulk crystal
irradiation phase of the OSL method, using somewhat less energy. Subsequent to this type of transition, trapping of the electron may occur, leading to the possibility of later OSL and/or TL. As with transition type 2, these transitions would typically require photon energies corresponding to ultraviolet stimulation wavelengths and would not be desired transitions for dosimetry applications.
Intra-center transitions or excitations, designated as transition type 5 in Figure 1.2, involve the excitation of an electron in a defect from a ground state to an excited state.
This type of transition is the genesis of PL, which is produced by the subsequent radiative relaxation of the excited electron back to its ground state. As discussed previously, since this transition type does not involve the transport of charge from one defect site to another, or elevate electrons into the conduction band, this is not an OSL phenomenon. If the defect itself was caused by the irradiation of the material, however, this would be called radiophotoluminescence (RPL) instead of PL. While RPL could be used to determine the radiation dose to a material, unlike the OSL method, where defects are not induced by the irradiation but merely populated, there would be no way to ‘reset’ the material back to its original unirradiated condition using optical methods. One additional consideration for transition type 5 is that if the temperature is sufficiently high and the excited defect state is sufficiently close in energy to the bulk material conduction band energy, then thermal ionization of the excited state electron can occur, leading to subsequent TL. This phenomenon has been exploited in certain geologic dating applications where reuse of the sample is unnecessary(38-39).
constitute OSL. These transitions are made possible by the initial trapping of electrons and holes at defect sites during irradiation, followed by the release of those trapped charges by absorption of light energy. The subsequent recombination of the electrons and holes results in OSL emission. It is worth mentioning that these types of transitions are also the mechanism behind phototransfer mechanisms such as PTTL, as well as optical bleaching of TL and/or OSL signals – that is, when light exposure ‘clears’ or optically anneals a sample.
Mathematical Description The intensity of the OSL signal at any given time is related to the rate at which the charge carriers are excited from defect traps and experience recombination. The rate at which charge carriers are excited from the traps is a function of the concentration of trapped charges in the material. In the simplest case of first-order behavior, this rate is linearly proportional to the trapped charge concentration. If one plots the intensity of the luminescence as a function of time, as is customary for OSL readouts, a characteristic luminescence-versus-time curve results. In the simplest case of a material with a single trap with first-order kinetics, this curve follows a simple exponential decay function. The integral of the luminescence-versus-time curve is related to the trapped charge concentration, which is, in turn, proportional to the absorbed radiation dose. This methodology is the basis for the use of OSL measurement for radiation dosimetry. In addition to the induced luminescence signal being proportional to the initial dose of
optical stimulation. How these parameters affect the luminescence signal is discussed below.
For OSL to occur, it is first necessary for an optical absorption to occur that stimulates charge carriers out of a trap, or optically ionizes them. The probability of optical ionization, p, of any given trap is simply the product of the incident light intensity and the probability that the trap will ionize by stimulation with a photon of this light.
This is described by the following equation(1):
where Φ is the optical stimulation intensity and σ(E) is the photoionization crosssection for interaction of the trap with an incident photon. E is the energy of the individual photons of incident light. Since the photoionization cross-section for a trap is a function of the photon energy of the incident light, the probability of trap ionization depends on the photon energy. It is important to note here that p does not predict in full the OSL light output of a material. If the material is opaque to its own emitted OSL light, or does not possess radiative recombination processes, the output OSL signal will be reduced or eliminated. In any case, if a material produces OSL, p will be proportional to the OSL output and is therefore an important parameter to understand.
The photoionization cross-section σ, as a function of incident photon energy E, can be either calculated theoretically or determined empirically. Several models exist to calculate the shape of this function and these models make different underlying
Though a thorough review of the different models is beyond the scope of this introduction, it should be said that no one model created to date fully describes the photoionization behavior of every trap in every material. It is also important to note that all models predict the following behavior: that trap ionization does not occur below a threshold optical activation energy, Eo, and that as the photon energy increases beyond this threshold, the photoionization cross-section increases quickly. Where the models differ is in exactly how fast this cross-section increases with energy, and also whether continued increases in photon energy result in a sustained high cross-section, or whether the cross-section begins to decrease again and to what extent. One model frequently used for dosimetric materials, due to its high level of predictive value for wide-band-gap insulators commonly used as dosimetry materials, is described by the following
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where h is Planck’s constant, υ is the frequency of the incident photon and Eo is the threshold optical ionization energy of the trap.
In this model, the photoionization cross-section reaches its maximum when the photon energy is twice the trap threshold energy and then declines very slowly at higher photon energies. A graph showing this function is presented as Figure 1.3.
Figure 1.3: Photo-ionization cross-section versus incident photon energy as predicted by the Lucovsky theoretical model.
In this graph, the threshold optical ionization energy Eo has been set to 2 eV.
In addition to predictive models, the shape of the photoionization cross-section curve can also be determined experimentally. In one method, the photoconductivity of a sample is measured during illumination, as the wavelength of the incident light source is increased, typically using a scanning monochromator. In another method, the OSL output intensity is measured as wavelength is increased. In either case, since both the photoconductivity and the OSL signal of a material are directly proportional to the photoionization cross-section, these techniques yield the latter.
It is interesting to note that since the photoionization cross section for a given trap has a minimum activation energy, and since the probability of OSL signal resulting from the trap rises quickly with the photon energy above that threshold, this suggests a method for reading, or emptying, traps in a material individually. If the excitation light is scanned from long wavelength to short wavelength, it is possible to produce an OSL
from a shallow trap without producing any signal from, or affecting, a deeper trap even if that deeper trap is similar in energy level. This characteristic results in a benefit to OSL over TL in being able to clearly discriminate closely-spaced traps in a material by use of careful wavelength selection. It is this particular technique that is employed in Chapter 5 of this dissertation to examine the fading behavior of different traps in several OSL materials.
The Relation between OSL and TL Mechanics It is useful when comparing a material’s TL and OSL behavior to understand the relation between the thermal activation energy of a trap, Et, and the trap’s optical activation energy, Eo. The optical ionization energy is not equal to the thermal activation energy since some of an excitation photon’s energy is converted in phonon energy, or lattice vibrations. As such, the optical ionization energy is somewhat greater than the
thermal activation energy, according to the following equation(32):
where S is the Huang-Rhys factor and ωp is the phonon vibration frequency of the material. These parameters are material properties generally determined experimentally using a variety of crystallographic material testing techniques, such as x-ray diffraction and scattering.
The thermal activation energy, Et, is the amount of energy required to excite an electron from one energy level, as shown on a classical energy level diagram, to a higher level. This value, if not already known for a specific trap, can be estimated using TL techniques. By noting the temperature in the TL glow curve at which the maximum TL signal is emitted, one can estimate this thermal activation energy. The relation linking
these two values(32), is as follows:
where Et is the average thermal activation energy (or trap depth) of the peak in units of eV. k is Boltzmann’s constant, 8.62 × 10-5 eV K-1. Tm is the temperature of the peak at its maximum in units of K. This relation yields only an approximate value since the heating rate, the attempt-to-escape frequency factors, and the thermal conductivity of the material, affect the exact value of Tm in the material. However, without knowledge of attempt-to-escape frequency factors, which may be determined using thermally
for linking the TL output of a material to known defect states in that material.
By understanding the relationship between Et, Eo and Tm, it becomes possible to use both the TL and OSL techniques to partially validate the results of the other, and also to form a more complete picture of a material’s energy level structure and mechanisms.
Readout Methods Three different readout methods are common in the OSL literature: continuouswave OSL (CW-OSL), linearly modulated OSL (LM-OSL) and pulsed OSL (POSL).
The methods differ by the manner in which the excitation light source is modulated (or not modulated) to optically excite the sample. In CW-OSL, the excitation light source is turned on for a single readout period and its intensity is held constant throughout the readout. The OSL output signal is collected concurrently with the sample excitation so that a system of filters, monochromators, and/or other frequency-selecting apparatus are needed to ensure that the excitation light is prevented from stimulating the OSL reader detection system to an extent that the OSL signal cannot be resolved. In LM-OSL, the excitation light source is ramped up from zero intensity to maximum intensity in a linear fashion. Like with CW-OSL, the OSL signal is collected during the sample excitation, so apparatus must be employed to prevent detection of the incident excitation light signal.