Sample characterization

Scanning Electron Microscopy (SEM) of undoped ZnO shows micro-nanostructures (Fig 1.a) with hexagonal crystalline shape and the preference of this material to grow in a well-formed rod structure. The surface morphology is formed by overlapping ZnO micro-nanorods. The diameter and length average values were about 0.1-0.4 and 1 µm, respectively. A random inspection over the substrate area showed that it was uniformly covered by this kind of microstructure. It is possible to observe uniformity in diameters and lengths of the hexagonal crystals.

Fig. 1 Scanning Electron Microscopy micrographs of the surface morphology for; a) undoped ZnO, and b) Terbium-doped ZnO. The diameter (d) and length (l) average values are indicated. 

These characteristics possibly result from typical growing processes of these films properly influenced by local chemical and/or thermodynamic environment. The nature of substrate also influences on film growth; this coating formation is a consequence of reactive nature of aluminum substrate, which is not the case for other substrates. Incorporation of Tb ions into ZnO host lattice produces some changes in the surface morphology of Tb-doped ZnO films (Fig. 1b). In this case, it is possible to observe hexagonal rods with larger diameters mainly and lengths. An additional kind of microstructures was observed: some particles consisting of rods emerging radially from a single point. Similar results have been obtained in other studies on ZnO: Tb³⁺ (Sreeja et al., 2017).

Raman analysis of unirradiated ZnO samples exhibited bands peaked at 439, 519, and 716 cm^-1 (Fig 2.a). These bands are ascribed to the zinc oxide, and the one located at 439 cm^-1 is related to würtzite hexagonal phase characteristic of ZnO. Also this band was observed by Nehru (^{Nehru et al., 2012}) and Yousefi (Yousefi et al., 2020) located at 439 cm^-1 and 437 cm^-1, respectively. In the case of the Tb-doped ZnO (Fig 2.b), the spectrum was complex and the values were slightly shifted (438, 518, 716 cm^-1) which may be perturbed by presence of Tb ions inside zinc oxide films. The peak at 716 cm^-1 is generated by combinations of phononic and optical modes that describe longitudinal acoustic and transverse processes of the optical lattice. In irradiated samples, Figs. 2c and 2d, Raman spectra were obtained such as a broad band centered about 1900 cm^-1 for ZnO, and it was shifted to 2000 cm^-1 for Tb-doped ZnO and less intensity was observed due to Tb ion impurity into host lattice. Photoluminescence (PL) spectra of ZnO and ZnO:Tb samples were made using an excitation line (λ_exc) of 350 nm. The PL spectra for the ZnO and ZnO:Tb samples were very different. In the undoped sample (Fig. 3a) typical peaks of band-to-band transitions or near band edge (NBE) emissions (385 nm) were observed in the unirradiated sample.

Fig. 2 a) and b) Raman spectra of the unirradiated samples, c) and d) corresponding to ZnO and ZnO:Tb gamma-irradiated samples, respectively. 

Fig. 3 Photoluminescence spectra of the samples, a) ZnO, and b) ZnO:Tb³⁺. Unirradiated and gamma-irradiated samples. 

Visible emissions in ZnO originated from oxygen vacancies to the valence band were exhibited such as bands centered approximately: 405, 426, and 450 nm. These bands were raised in their intensity when ZnO films were irradiated. The shoulder at 450 nm may be a phonon replica of the main peak located at 426 nm. (Fig. 3b) (for unirradiated sample) exhibits a spectrum with visible ZnO emissions and typical emissions of Tb³⁺ ions superimposed. The unirradiated ZnO:Tb exhibited emissions at 490, 544, 582, and 620 nm due to the ⁵D₄-⁷F_j=_6,5,4,3 transitions of the Tb³⁺ ion in the ZnO phosphor. These values are in agreement with those emissions observed by radioluminescence (RL) on terbium-doped zinc oxide crystals by implanted Tb ions forming nanoparticles (^{Cetin et al., 2009}). In the case of the irradiated samples (terbium-doped zinc oxide), inhibition of Tb emissions was detected, and appears a broad band (from 400 to 650 nm) centered at 502 nm. In several reports, this band is related to intrinsic defects, such as zinc and oxygen vacancies and interstitial oxygen (^{Isik et al., 2016}; ^{Cetin et al., 2009}; Parta et al., 2013).

X-ray diffraction (XRD) measurements were carried out to investigate the crystalline structure of the ZnO and Tb-doped ZnO samples (Figs. 4a and 4b), both patterns were identical. The diffractogram for ZnO:Tb (1 at.%) (Fig. 4b) corresponds to the ZnO hexagonal wurtzite phase (JCPDS 36-1451) (^{Moura et al., 2010}). It is possible to observe well-defined diffraction peaks and the highest intensity is obtained for 2θ < 35°, for (100) line, which could be associated with the preferred orientation along the c axis, as reported by Kumar (^{Kumar et al., 2013}). Peaks for Tb compounds were not observed. This is indicative that the presence of the Tb ions in the ZnO host lattice does not disturb the crystalline structure. In this case, the doping concentration was about 1 at. %, probably the XRD technique may not be sensitive to these terbium quantities in this phosphor.

Fig. 4 XRD patterns of a) undoped ZnO, b)Tb-doped ZnO samples. 

Atomic effective number (Z_eff)

The Z_eff was obtained due to the important characteristic of zinc oxide phosphor to expected for thermoluminescent (TL) response at different energies, in this case, exposed to gamma radiation. Considering that the material response depends on the atomic number Z of the constituents,

Where: a₁, a₂ … an are the fractional contents of electrons belonging to elements Z₁, Z₂…Z_n respectively, n_i is the number of electrons belonging to each element Z_i and N_A is the Avogadro number. The value of x is 2.94 (Furetta, 2010). For undoped ZnO and Tb-doped ZnO preparations were obtained Ze_ff = 27.74 and Ze_ff = 56.47 values, respectively. Since the effective atomic numbers of the samples are about 4 and 8 times greater than that of human tissue (Ze_ff = 7.4) respectively, an accurate calibration should be done for its use in personal and high field radiation applications.

Thermoluminescence (TL) and computerized glow curve deconvolution (CGCD)

The glow curves Fig. 5a and 5b, exhibit a wide structure; in such case, a computerized glow curve deconvolution (CGCD) is useful to obtain kinetic parameters such as activation energy (E) and frequency factor (s); R_m and α parameters of the traps are involved in TL model too. The algorithm of deconvolution program is based on Mixed Order Kinetic model (^{Kitis et al., 2000}; ^{Chen et al., 1981}; ^{McKeever et al., 1985}) given by the following expression:

Fig. 5 a) and b) Glow curves as a function of doses: 0.25-20 kGy obtained with 2 K/s heating rate, c) and d) Deconvolution of the glow curves, assuming the mixed order kinetics model, the experimental glow curves (open circles) at the dose of 12 kGy and 170 Gy/min gamma dose rate, for undoped ZnO and Tb-doped ZnO, respectively. 

Where: k is Boltzmann constant, I_m and T_m are the maximum luminescence intensity and temperature in peak deconvoluted, respectively, and other quantities are: ∆=2kT/E, ∆m=2kTm/E, and Rm=AnAm where A_m is recombination probability and A_n is trapping probability, α=n0n0+c is factor that directly determines the value of kinetic order in model of mixed-order kinetics and as a consequence α influences the shape of glow curve, c is a constant, and n₀ (cm⁻³) is electron trap concentration. In Rm factor the explicit expression for A _m is:

The equation (9.b) is a definition of α, as an implicit function of two parameters α and ∆m . The explicit form α cannot be obtained analytically but relationship of term Am and parameter α was examined in a very broad region of parameters, α = 0.1-0.95, E = 0.6-2.2 eV, and s = 10⁷-10²² s^-1. For this range of values, dependence of Am on ∆m can be neglected. So, R_m is obtained:

And finally, frequency factor s is defined by:

The curve fitting procedure was performed using the Figure of Merit (FOM). A FOM equal to or less than 5 % means an acceptable fit (^{Balian et al., 1977}). In Fig. 5c glow curve of sample A shows one wide resolved peak, at 450 K, as shown in Fig. 5d, glow curve of sample B is quite similar to previous one: first peak appears at 475 K. The TL glow curves for both preparations were similar.

In almost all glow curve deconvolutions of samples (A and B), R_m values were greater than or equal to unity, therefore trapping process is predominant, as shown in Table 1. Finally, the assumption of mixed order kinetics (MOK) comparing with other models, as general order kinetics (GOK), is more useful because MOK has a physical basis (^{Sadek et al., 2014}). The greatest R_m values were for sample B (Tb-doped ZnO), hence Tb ions promote capture of charge carrier.

When the zinc oxide samples were prepared by the co-precipitation method (Parta et al., 2013) they were composed by nanorods which showed broad glow curves peaked at 530 K (255 °C) for Tb-doped ZnO and 465 K (190 °C) for undoped sample. The activation energy (E) and frequency factors (s) obtained by Chen´s method were 0.98 eV and 2.77x10⁸ s^-1, respectively, for ZnO:Tb. Both peaks, 530 K and 465 K, follow the first-order kinetics and other satellite peaks at lower side temperature of glow curves obey second-order kinetics. Pal and co-workers (Pal et al., 2006) reported the TL of undoped ZnO spherical particles as nanophosphor obtained using glycol mediated chemical synthesis. Two glow peaks at 420 K (second-order) and 490 K (first-order) deconvolved by a computer fitting program, with activation energy about 0.8 eV and 1.2 eV, and frequency factor at 7x10⁸ and 1x10¹² s^-1, respectively, were obtained. It seems that TL glow curves are influenced by preparation methods and also by heating rate. However in this last case, if it is considered separately, each of four TL peaks (Table 1) in which the whole glow curves of samples A and B are deconvolved shows a slight shift to higher temperatures as dose increases. But the overlap of peaks 1, 2, and 3 give rise to experimentally recorded high-temperature peak, the maximum of which does not shift as dose was increased. The results indicate a variation of activation energy E as a function of heating rate; this has been attributed to temperature lag and decrease of TL intensity as well as to activation energy and can be referred to as a thermal quenching effect(^{Gökce et al., 2009}). However, if variation of E is due to temperature lag one should expect same variation for all peaks. Therefore, an analysis of temperature lag in TL glow-curve measurement is necessary and its implementation is described in next section.

Temperature lag in TL glow curve measurement analysis

Due to variation in kinetic parameters and effects on structure of glow curves, a compute of theoretical model proposed by Kitis (^{Kitis et al., 1998}) will be carried out to correct for temperature lag in TL glow curve. The relationship among α-values and kinetics order (b) showed that overall scattering of values obtained for b corresponding to any value found of α was within approximately ±10% (^{Sunta et al., 2002}). The α-values for peaks 1, 2, and 3 of samples A, B were found to be 0.4-0.6 evidencing that b ranged between 1.2 and 1.4 values. Then use of model given by equation (10) to correct lag in TL glow-curve is adequate(^{Kitis et al., 1998}), and T_j temperature is necessary to evaluate:

Where c=Ti Tj kE , k is Boltzmann constant, and taking the case that Ti  and Tj  are peak maximum temperatures Tm , obtained for two different rates of heating βi<βj, and Ti<Tj. The glow peak due to heating rate βi is shifted towards higher temperatures, where: ∆T=Tg-Tm, Tg=T0+ t, Tm=T0+βeff t and last term β_eff is obtained:

As activation energies of undoped ZnO deconvoluted glow peaks are too close; 0.65 eV, 0.67 eV, and 0.64 eV (Table 1), only that of first peak deconvolved was computed to validate equation (10).

The results of the analysis for this approximation are shown in Table 2. The theoretically evaluated glow peak maximum temperatures are listed in column 2 for E = 0.65 eV. Analogously, equation (10) was applied only to the first and third deconvoluted glow peaks of the Tb-doped ZnO sample (Table 3).

Tables 2 and 3 show that approximation of equation (10) gives acceptable results for a quite large range of used heating rates (1-40 K/s) thus validating it for their use. Glow peak shifts for lower heating rates (2-5 K/s) are about 15 K, which is easily measured. Furthermore, the constant c₁ is very sensitive to T_m, which should be calculated within an accuracy better than 1 K. This is not difficult for low heating rates. The measurements at low rates of heating are the reference, so they need special attention to avoid temperature lags as a high-temperature gradient in sample (^{Kitis et al., 1998}; ^{Bos et al., 1992}).

As heating rate grows, it produces two pronounced effects on glow curves of zinc oxide: a TL emission increase and a considerable broadening of peak located at 420 K occur as shown in Figs. 6a and 6b. Temperature lag at higher readout heating rates also influences determination of E values by glow curve fitting. As shown in Figs. 6c and 6d, integrated TL intensities maximum and minimum occurred for 5 and 40 K s⁻¹ for both samples, respectively. However, a more detailed explanation for variation of integrated TL intensity and peak intensity with heating rate may be achieved by considering influence of more than one effect involved in TL of zinc oxide. Considering peak 2 (Figs. 6e and 6f) for ZnO and ZnO:Tb, respectively, a variation of activation energy for different heating rate and a strong decay of E value at 40 K/s for ZnO:Tb were observed. It seems that Tb impurity in zinc oxide modifies TL mechanism and then behavior of activation energy. The Tb³⁺-vacancy and clusters can be participating during heating rate, and also defect interaction with different time reactions for low and a high heating rate may occur increasing integrated area of glow curves (^{Piters et al., 1993}; Subedi et al., 2010; Cuz-Zaragoza et al., 2011). It should be taken into account that temperature lags involved also a complex TL mechanism because recombination of several types of defects occurred during heating stimulation; the T_m, total area of glow curves, and activation energy (E) values can be affected by dopant cluster and thermal quenching. Almost two stages were observed for Tb-doped ZnO (Fig. 6f); E increased from 2-10 K/s, and a variation from 15 K/s and decay at 40 K/s. This last decay may occur due to large reaction time at that high heating rate. If the variation of activation energy (E) is due to the temperature lag same evolution should be expected for all peaks of zinc oxide.

Fig. 6 a) and b) Glow curve as a function of the heating rate from 5 to 40 K/s, c) and d) integrated TL for peaks 1 and 2, and e) and f) activation energy (E) values as a function 2-40 K/s heating rate. 

Annealing effect on the TL signals and signal reproducibility

The effect of thermal treatment as annealing is to stabilize trap levels so that in subsequent uses both intrinsic background and TL response should be reproducible. The zinc oxide samples were annealed in a tube furnace at 350 K for 60 min and then cooled down up to room temperature, after that all the samples were irradiated with 12 kGy of gamma photons from a ⁶⁰Co source irradiator.

The annealing effect on zinc oxide samples shows a complex structure of their glow curves (Fig. 7) which peaked around 450 K. The TL intensity of ZnO: Tb was observed to be less than that of undoped ZnO. The TL signals of both samples grown by a factor of 2 after annealing. It implicates that a major quantity of defects as vacancies was generated in samples with previous annealing treatment. The TL signal of ZnO samples increases as annealing temperature enhanced, and does not alter the value of peak temperature and is the optimized temperature for heating samples (^{Raunak et al., 2015}).

Fig. 7 Glow curves of undoped ZnO and Tb-doped ZnO phosphors with a dose of 12 kGy. 

The reproducibility of TL signals as a function of readout cycles should be characterized for a phosphor with a dosimetric purpose. Furetta (Furetta, 2010) gives a procedure to check reproducibility of TL signal as a function of successive irradiation-readout cycles. The coefficient of variation (CV) for TL dosimeter is given by:

Where: σ and m are standard deviation and average value of 10 repeated readings of dosimeter, respectively. The half-width of confidence interval μ is given by μ=CVt2(n-1) where n is number of repeated cycles and t is value of student test. In present case n=10 and t=2.26 at a confidence level of 95 %. Then μ=0.53 CV and reproducibility test for dosimeters is acceptable if CV+μ≤7.5%. Which transforms, considering last equation in following acceptable level CV≤5%. So for data of successive irradiation-readout cycles, it was obtained: mA=39.52, σA=11.84,mB=57.87, σB=32.56, and consequently the variability coefficient of TL reproducibility signal for samples ZnO and ZnO:Tb was ranging among 29 and 57 %, respectively. At this point, it is an important remark about improving reproducibility of TL signals if it is considered to erase first glow peak deconvolved at 385 K, due to its high instability under fading showed by Park et. al. in undoped ZnO (^{Park et al., 2014}), while other peaks at a higher temperature (441 and 500 K) exhibited an acceptable TL reproducibility signal as reported by Pal and Manam for ZnO and ZnO:Tb (^{Pal et al., 2013}). Therefore, herein CV coefficient for undoped-ZnO and Tb-doped ZnO exhibit strong variations when whole glow curves were measured. Following, due to CV variation values, linearity analysis of dose-response was carried out for zinc oxide phosphor.

TL dose-response and linearity analysis

At 0.25 kGy gamma dose threshold was enough to generate main TL mechanism to detect TL signal, i.e., samples were sensible at that dose. The TL dose-response exhibited three stages (Fig. 8a): at relatively low doses (stage 1, 0.25-4 kGy) there was unclear linearity, at intermediate doses (stage 2, 6-12 kGy) both samples ZnO and ZnO:Tb showed an almost linear response, and at higher doses (stage 3,14-20 kGy) TL response showed a slowly steep increase.

Fig. 8 a) Integrated TL dose-response of ZnO and Tb-doped ZnO, b) Supralinearity index, c) Superlinearity index. 

The linearity at stage 2 range will be analyzed with more detail by supralinearity index f(D) and superlinearity index g(D), given by:

Where: M,(D), M,,(D) are the first and second derivative of MD, M₁, M₂ are TL contributions of each saturating exponential, and E01, E02 are the saturation doses of each contribution (Larson et al.,1976; Waligorsky et al.,1980; Waligorsky et al.,1993). These indexes characterize linearity of response, namely: f(D)>1, fD=1 or f(D)<1 indicate supralinearity, linearity, or sublinearity, respectively, while g(D)>1, gD=1 or g(D)<1 indicate superlinearity, linearity o sublinearity respectively. The supralinearity index f(D) (Fig. 8b) shows a switch from a supralinear behavior for doses below 5.5 kGy, to a sublinear one for greater doses. The superlinear index g[D] (Fig. 8c), shows a negative value for whole range. Despite these materials does not show clear linearity under these conditions, they should not be rejected as a radiation detector for high doses (i.e. kGy), and should be improved maybe modifying preparation method using a different annealing process and a codoping impurity in zinc oxide phosphor.

Fading of the TL signals

TL fading signal as a function of elapsed time can be useful in routine TL measurement and allows to characterize the TL signals decay of phosphor exposed to a radiation field. Zinc oxide samples were gamma-irradiated and they were stored in a dark environment. The TL signal was readout periodically for ZnO and ZnO:Tb samples, respectively, during 42 days (Fig. 9). Considering initial irradiation of samples followed by fading at room temperature and assuming first-order kinetics, for a storage time t_s>>t_i (irradiation time), following expression simulated this case is (^{Kitis et al., 2005}; ^{Gomez-Ros et al., 1996}): Φ = Φ₀exp(-pt) and then p = (-1/t)ln(Φ/Φ₀), where Φ can be considered integrated glow curve or peak area. So by taking into account at final 42 days of fading; p = 0.149 d^-1 or 14.9 % lost per day of TL signal for ZnO, and 15.9 % for ZnO:Tb. The constant p is less fast decay for undoped zinc oxide than that for Tb-doped ZnO.

Fig. 9 TL-Fading of ZnO and ZnO:Tb phosphor. 

In this case, Tb ions in ZnO contribute to stabilizing intrinsic defects in zinc oxide and well defined glow curves as can be seen in Fig. 7 too. It seems that fading observed in ZnO also depends on their preparation method and their thermal history.