Ho³⁺ codoping of GGAG:Ce: a detailed analysis of acceleration of scintillation response and scintillation efficiency loss

Abstract

In this study, we investigate the effects of Ho³⁺ codoping on the luminescence and scintillation properties of GGAG:Ce, with a particular focus on timing properties and scintillator efficiency. The research reveals that Ho³⁺ codoping and subsequent resonant energy transfer from Ce³⁺ to Ho³⁺ can significantly reduce the 5d₁ excited state decay time of Ce³⁺ and shorten scintillation pulses of GGAG:Ce registered by using photomultipliers, although this reduces scintillator efficiency as well. The study presents a detailed analysis of the loss of scintillator efficiency due to Ho³⁺ codoping, identifying the most significant loss pathways and estimating their impact. The findings suggest that Ho³⁺ codoping is an effective method for accelerating the scintillation response of GGAG:Ce. Furthermore, the study presents a high level of consistency of the Ce³⁺ kinetics with the Inokuti–Hirayama model and with results obtained in the previous studies on similar systems, demonstrating the predictability of the effect of RE³⁺ codoping on scintillator properties.

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Introduction

Codoping with trivalent rare-earth ions (RE³⁺) was proven to be an effective method for shortening of the activator decay time and scintillation response in Ce³⁺/Pr³⁺ activated garnet scintillators. This has been demonstrated in our previous studies on Er³⁺ and Ho³⁺ codoping of YAG:Ce (Ce³⁺ doped yttrium aluminum garnet),^1,2 Ho³⁺ codoping of LuAG:Pr (Pr³⁺ doped lutetium aluminum garnet)³ and other RE³⁺ codoping of garnets.^4,5

The acceleration of the activator decay is enabled by resonant energy transfer (RET). This effect involves transition of one of the centers (donor) to a lower energy state and simultaneous promotion of another distant center (acceptor) to a higher energy state. The mechanism of RET is depicted in Fig. 1.

Fig. 1 Schematic of RET mechanism directed from donor (D, asterisk indicates excited state) to acceptor center (A). Radiative transitions – donor excitation and acceptor emission – drawn with solid line, relaxation to lower energy drawn with dotted line, resonant ET drawn with dashed line.

Unlike reabsorption, where energy emitted in the form of a photon by one center and absorbed by another, the RET does not include the formation of a photon. It is driven by multipole electro–magnetic interaction. RET is enabled between luminescence centers in resonance, i.e. centers whose emission and absorption spectra overlap. Rate of RET is proportional to the overlap of the emission spectra of the donor f_D,em and absorption spectra of the acceptor f_A,abs and is inversely proportional to the power of the distance between ions R

where s is set to 6, 8 or 10 for dipole–dipole, dipole–quadrupole and quadrupole–quadrupole interaction of the ions, respectively. For our application, it is favorable to restrict RET between ions only to one direction. This can be ensured by selecting center with large Stokes shift as the donor center and/or center with fast relaxation of the excited state to energetically lower states as acceptor. Then RET contributes to the total decay rate k_tot of the donor center as follows

k_tot = k_inh + k_rET (2)

where k_inh is inherent decay rate of the donor and k_rET is decay rate due to RET towards acceptor, and thus, increase its decay rate, shorten its decay time, and eventually accelerates the scintillation response of the material they are hosted in.

The downside of the RE³⁺ codoping is reduction of the donor emission and subsequently scintillator efficiency. Same as shortening of the donor decay time, reduction of the activator emission is caused by RET, hence inevitable. In this sense, the Ho³⁺ acceptor can be considered a killer center for Ce³⁺ 5d → 4f emission. Then, using the model for number of UV/visible photons N_ph generated per energy of incident radiation E derived in^6–8

where E_g stands for the material band gap, S and Q are quantum coefficients related to efficiency of the transport and luminescence stages and β is a phenomenological parameter found to be between 2 and 3 for most materials. See Fig. 1 in ref. 9 for schematic explanation of the role of S, Q quantum coefficients in the scintillation mechanism. Ho³⁺ content will affects the coefficient Q that reflects the contribution of killer centers.⁹ The coefficient Q is inversely proportional to Ho³⁺ content, i.e. the greater the content of the acceptor centers the lesser the Q coefficient, and eventually the lesser the number of photons emitted by Ce³⁺ center and scintillator efficiency.

Ho³⁺ ions have been found to be particularly effective acceptor codopants for Ce³⁺ and Pr³⁺ activated garnets as they enable acceleration of the Ce³⁺/Pr³⁺ decay time due to RET without introducing any additional signal to the detection spectrum or introducing slow components of light, see ref. 1 and 3.

Multiple RE³⁺ ions other than Ho³⁺ could be used as acceptor in pair with Ce³⁺ donor in GGAG, i.e. would reduce the decay time of the 5d state of Ce³⁺ due to RET. According to ref. 10 and 11, they are Pr³⁺, Nd³⁺, Pm³⁺, Sm³⁺, Eu³⁺, Tb³⁺, Dy³⁺, Er³⁺ and Tm³⁺. However, as shown in our previous studies for Er³⁺,^1,2 Dy³⁺,³ and Nd³⁺ (ref. 4) and studies of other authors for Sm³⁺,¹² Eu³⁺ and Tb³⁺,¹³ and Tm³⁺ (ref. 14) unlike Ho³⁺ all of them have parity-forbidden 4f → 4f emission positioned in the range of Ce³⁺ emission which would introduce slow components into detectable emission when using common photomultipliers or even Si-based semiconductor photodetectors. This is counterproductive to the effect of shortening of the scintillation response and would unavoidably lead to impaired timing properties of the scintillator. The situation is specific for Pr³⁺. This ion is typically used as an activator of garnet scintillators for its fast 5d → 4f emission positioned in UV range but emits also between 480 and 650 nm due to 4f → 4f transitions.¹⁵ However in case of Pr³⁺ codoping of GGAG:Ce, its 5d → 4f emission transition would transfer energy into the Gd sublattice which diminishes fast scintillation response,¹⁶ while, the 4f → 4f transitions would remain active and introduce slow light to detectable signal same as the RE³⁺ ions above. Pm³⁺ is not considered due to low practical use of this element due to absence of stable isotope.

This study builds on upon these previous findings by examining Ho³⁺ codoping of GGAG:Ce,Mg (gadolinium aluminum gallium garnet doped with Ce³⁺ and Mg²⁺). GGAG:Ce is a representative of multicomponent garnets compounds of general chemical formula of the host (Gd,Lu,Y)₃(Al,Ga)₅O₁₂. They have been reported firstly in the ceramic form^17,18 and their enormously high scintillation light yield up to 50 000 phot per MeV and excellent energy resolution of 4.8%@662 keV immediately interested researchers in scintillator field. These materials can be prepared also in single crystal form, most frequently reported by Czochralski technique where even 4 inch diameter large crystals have been achieved.¹⁹ Another preparation techniques, e.g. floating zone has also been reported.²⁰ High entropy alloys in multicomponent garnet family were also studied which was fueled by an interest to find unusual stable compositions with unique properties²¹ and combinatorial research strategy was applied as well.²² Effects of composition and growth parameters on phase formation in multicomponent aluminum garnet crystals was systematically studied.²³ Luminescence investigation focused on the interplay between the Ce³⁺ luminescence center and the host due to decreasing ionization barrier of the Ce³⁺ 5d₁ excited state,^24,25 traps states acting in scintillation mechanism were studied by thermoluminescence techniques.²⁶ In the study of scintillation characteristics special attention was paid to stabilization of Ce⁴⁺ by stable divalent dopants as Mg²⁺ or Ca²⁺ which creates new fast radiative recombination pathway at Cerium centers and accelerates noticeably the scintillation response.^27–30 Other codopants were studied for this purpose as well.³¹ Dependence of the bandgap value on the host composition was also studied^32,33 and garnet compounds luminescence and scintillation characteristics were reviewed in ref. 34. The application potential of multicomponent garnets for fast timing application in medical imaging and high energy physics was evaluated in ref. 35 and 36.

In this paper, to better understand the mechanisms behind the acceleration of scintillation response due to RE³⁺ codoping, its benefits and drawbacks, we examine not only direct effects of Ho³⁺ codoping on scintillation characteristics of GGAG:Ce,Mg like decay time and light yield (LY), but also investigate the effect of Ho³⁺ codoping on specific stages of scintillation mechanism in detail. Further, findings obtained in this, and previous studies are compared and discussed and build up the picture of the RE³⁺ codoping for modification of scintillation properties as a method in general.

Experimental methods

Electron probe microanalysis (EPMA) analysis was performed using JEOL JXA-733 microprobe. Crystal structure was examined by powder X-ray diffraction pattern analysis (XRD) measured at powdered small piece of the samples using the Bragg–Brentano focusing configuration on the powder diffractometer Empyrean of PANalytical (λCu, Kα = 1.54184 Å) that was equipped with a fixed divergent slit and PIXcel3D detector. 120 minutes long measurements were made from 4 to 100° 2θ with 0.013° step size and 300 s per step. Absorption spectra were measured with a Shimadzu 3101 PC spectrometer. A Horiba Jobin Yvon 5000M spectrofluorimeter equipped with a TBx-04 photon counting detector was used for the steady-state spectral measurements and measurement of the photoluminescence decay. Excitation was performed with a Seifert tungsten X-ray tube (40 kV, 15 mA) and an Heraus deuterium lamp for radioluminescence and photoluminescence spectroscopy, respectively. All the spectra were corrected for the spectral distortions of the setup. The photoluminescence decay kinetics of the Ce³⁺ center were measured by a time-correlated single photon counting method³⁷ with a Horiba NanoLED nanosecond excitation source. The scintillation decay curves were obtained with use of ¹³⁷Cs γ-ray excitation, Tektronix TDS3052C digital phosphor oscilloscope, and a fast photomultiplier Hamamatsu R7207-01 working in current regime. Amplitude spectra for LY measurement^38,39 were obtained with a shaping time of 1 μs, ¹³⁷Cs γ-ray excitation, and a hybrid photomultiplier Photonis PP0475B. All before mentioned measurements were performed at room temperature. Thermally stimulated luminescence (TSL) was measured in range 77–700 K with heating rate 0.1 K s⁻¹. Temperature of the sample was regulated with Janis N2 VPF-800 cryostat. Initially, sample was irradiated with X-ray (40 kV, 15 mA) for 10 minutes at 77 K. Then, spectrally unresolved TSL glow curves were recorded using IBH Scotland TBx-04 photomultiplier in the photon counting mode and 1 s sampling rate. Photoluminescence and scintillation decay kinetics were analyzed using iterative least-square re-convolution method⁴⁰ and Python packages LMfit⁴¹ and SciPy.⁴²

Results and discussion

Preparation and composition analysis of the samples

A set of six GGAG crystals was prepared by the Czochralski method⁴³ from melts with starting compositions Gd_2.9844−xCe_0.015Mg_0.0006Ho_xGa_2.7Al_2.3O₁₂, with x = 0.00, 0.015, 0.030, 0.045, 0.090 and 0.150. Platelets of the thickness of 1 mm were prepared from the tip parts of the crystal's, see Fig. 2. As the Mg²⁺ codoping has no effect on the Ce³⁺–Ho³⁺ energy transfer process, the materials will be referred only as GGAG:Ce, or Ho³⁺ codoped GGAG:Ce in the texts below, even though they contain the Mg²⁺ dopant as well.

Fig. 2 Photography of GGAG:Ce crystals codoped with various concentrations of Ho³⁺. The reddish tint is due to Ho³⁺ codoping of the crystals.

Actual concentrations of the Ce³⁺ and Ho³⁺ dopants were determined using the EPMA and absorption spectroscopy. At first, the concentration of Ce³⁺ and Ho³⁺ was measured using EPMA for sample x = 0.045 providing 0.18 and 1.97 at% (expressed as a percentage of Gd atoms replaced by the dopant), respectively. Concentration of the dopants in the remaining samples was determined using the integrals of absorption peaks,⁴⁴ namely the 4f → 5d₁ transition for Ce³⁺ (390–510 nm), ⁵I₈ → ⁵S₂ + ⁵F₄ (520–561 nm) and ⁵I₈ → ⁵F₅ (626–674 nm) transitions for Ho³⁺. Concentrations of Ce³⁺ dopant were found at the value of 0.18 ± 0.02 at% for all the samples. For Ho³⁺ the values of 0.00, 0.13, 0.59, 1.97, 3.56 and 6.21 at% were found. Concentrations of Mg²⁺ were too low to be measured by EPMA, i.e. lower than 0.01 at%.

XRD analysis confirmed single garnet phase in all the samples (see example in Fig. S2†) with the exception of the highest Ho concentration one, i.e. GGAG:Ce with 6.21 at% of Ho³⁺, see Fig. S1 in ESI.† In this sample, the secondary phase of the same garnet structure with a little bigger lattice constant was found. Its content (estimated from XRD analysis) is less then 5wt%. EPMA analysis of the secondary phases islands, see Fig. S3,† showed it is most probably due to reduced content of Ho³⁺ in the secondary phase.

Given the volume of the secondary phase in GGAG:Ce with 6.21 at% of Ho³⁺ its effect on the studied energy transfer phenomena is considered negligible. Further details on XRD and EPMA analysis are provided in ESI.†

Acceleration of Ce³⁺ decay time and scintillation properties due to Ho³⁺ codoping

The effect of Ho³⁺ codoping of GGAG:Ce was examined using multiple spectroscopic methods. Results of the experiments and discussion of the findings are described in the following paragraphs. First, overlap of the Ce³⁺ emission and Ho³⁺ absorption spectra, that is a prerequisite for RET, were studied using photoluminescence steady-state spectroscopy and absorption spectroscopy. Absorption and photoluminescence spectra (excited by 440 nm) of GGAG:Ce and Ho³⁺ codoped GGAG:Ce crystals are shown in Fig. 3. The non-codoped GGAG:Ce crystal shows typical absorption bands of Ce³⁺ allowed 4f → 5d₁ and 4f → 5d₂ transitions at 440 and 340 nm, a wide absorption band below 340 nm induced by charge transfer (CT) absorption band of Ce⁴⁺, that is induced by Mg²⁺ codoping in Ce³⁺ activated garnets⁴⁵ and absorption lines of parity forbidden 4f → 4f transition of Gd³⁺ at around 275 and 310 nm.⁴⁶ The same absorption patterns are observed in Ho³⁺ codoped crystals as well. In addition to that, multiple sets of narrow absorption lines of parity forbidden 4f → 4f transitions from Ho³⁺ ground state ⁵I₈ to ⁵G₆ and ⁵F₁ around 449 nm, ⁵F₃ and ⁵F₂ and ³K₈ around 486 nm, ⁵S₂ and ⁵F₄ around 538 nm and ⁵F₅ around 636 nm excited states can be observed. Multiple Ho³⁺ sets of absorption lines are located below 440 nm as well. For more detailed information on UV/VIS spectrum refer to ref. 47, which reports optical transitions of Ho³⁺ in structurally similar YAG. Photoluminescence spectra of both non-codoped and Ho³⁺ codoped GGAG:Ce are dominated by wide Ce³⁺ 5d → 4f emission band ranging between 450 and 720 nm. In line with,⁴⁷ that states the emission of Ho³⁺ in garnet matrix is positioned in the IR spectrum, no Ho³⁺-related emission is observed in the UV/VIS region. Ce³⁺ emission bands in Ho³⁺ codoped GGAG:Ce crystals are deformed due to re-absorption of emitted light by overlapping Ho³⁺ absorption lines. The same spectral overlap fulfills the prerequisite for RET.

Fig. 3 Photoluminescence (excitation to 440 nm) and absorption spectra of non-codoped GGAG:Ce and Ho³⁺ codoped GGAG:Ce shows the spectral overlap.

The time-resolved PL spectroscopy of Ho³⁺ codoped GGAG:Ce crystals was used to investigate changes of the Ce³⁺ decay kinetics due to Ho³⁺ codoping and related RET, see Fig. 4. Time-resolved PL spectra of Ce³⁺ decays with excitation to 455 nm and emission 530 nm were recorded and reveals substantial acceleration of Ce³⁺ decay in Ho³⁺ codoped and the fact the acceleration is proportional to Ho³⁺ content. The acquired decay curves were fitted to Inokuti–Hirayama (IH) model for donor luminescence kinetics. Assuming homogenous distribution of the donor and acceptors centers through the crystal, decay kinetics of the donor center I(t) will obey the following

where I₀ is magnitude of the decay curve, τ_D is the inherent decay time of the donor center, s is the parameter related to order of the multipole interaction equal to 6, 8 or 10 for dipole–dipole, dipole–quadrupole or quadrupole–quadrupole interaction, respectively and α is coefficient related to rate of the ET defined as , where Γ(x) is the gamma function, c is the concentration of the acceptor center and c₀ is critical concentration of the acceptor, i.e. the concentration of acceptor that yields rate of RET equal to the rate of the inherent decay rate of the donor, i.e. k_rET = k_inh. The best match was achieved for s = 6, which refers to dipole–dipole interaction between Ce³⁺ and Ho³⁺. In line with presumptions of Inokutu–Hirayama model, parameter α is proportional to Ho³⁺ content, see the inset of Fig. 4. Linearity of the relation between parameter α and Ho³⁺ content was used to determine the critical concentration of Ho³⁺ in GGAG:Ce to 4.6 at%. The calculated 1/e decay time of Ce³⁺ center was shortened from 56 ns for the non-codoped GGAG:Ce to 8 ns for the GGAG:Ce codoped with 6.2 at% of Ho³⁺. Refer to Table 1 for all calculated 1/e decay times.

Fig. 4 Photoluminescence decay kinetics of Ce³⁺ (excitation 455 nm, emission 530 nm) in non-codoped GGAG:Ce and Ho³⁺ codoped GGAG:Ce. The red lines show the IH model fit of the data.

Table 1 Summary of photoluminescence and scintillation properties of Ho³⁺ codoped GGAG:Ce in relation to Ho³⁺ content. PL an SC τ_1/e stands for 1/e decay time of Ce³⁺ and scintillation decay, respectively, Rel. PL and SC τ_1/e for relative change of decay times, Rel. LY for relative LY and the last columns lists relative overall efficiency. All relative values are compared to that of the non-codoped GGAG:Ce

Ho^3+ conc. [at%]	PL τ1/e [ns]	Rel. PL τ1/e [%]	SC τ1/e [ns]	Rel. SC τ1/e [%]	Rel. LY [%]	Rel. eff. [%]
0.00	56.1	100	90.3	100	100	100
0.13	51.9	92	105.5	117	98	111
0.59	41.8	74	82.3	91	75	89
1.97	25.2	45	53.1	59	46	59
3.56	14.7	26	36.4	40	28	40
6.21	7.9	14	25.2	28	15	22

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In the next paragraph, a comparison of the Ho³⁺-codoping of GGAG:Ce and YAG:Ce grown by edge-defined growth method, that was investigated in our previous study,¹ will be discussed. As the both matrices (GGAG and YAG) are structurally very similar and the same donor–acceptor pair was used in the studies analogical effects of the Ho³⁺-codoping are expected. In both cases, RET is enabled by overlap of the wide Ce³⁺ 5d → 4f emission band and Ho³⁺ absorption lines related to parity-forbidden 4f → 4f transitions and a good match of Ce³⁺ PL kinetics with IH model was achieved. The Ce³⁺–Ho³⁺ interaction is of dipole–dipole type, in both systems. The critical concentration of Ho³⁺ in GGAG:Ce was found just slightly higher when compared to 4.4 at% found for Ho³⁺ in YAG:Ce. The difference in critical concentration can be accounted by either of two following explanations or their combination. First, the lattice parameters increase when Y and Al are substituted by Gd and Ga, respectively – lattice parameter increase from 12 to 12.21 and 12.55 Å for Y₃Al₅O₁₂, Gd₃Al₅O₁₂ and Gd₃Ga₅O₁₂, respectively.⁴⁸ Hence, higher content of Ho³⁺ acceptor is required to achieve the mean distance between donor–acceptor pairs to be critical distance in GGAG:Ce. Second, the actual and nominal values of Ho³⁺ content in Ho³⁺ codoped YAG:Ce crystals may vary, as the nominal values refer to content of Ho³⁺ in melt.

Consistency of results observed in structurally similar, but not identical GGAG and YAG matrices, grown by different methods and a good match of the measured PL decay curves with the IH model in both cases make the Ho³⁺-codoping well predictable method for tuning of Ce³⁺ luminescence kinetics. It is necessary to say, the application of the studied method is not restricted to RE³⁺ codoping of Ce³⁺ and Pr³⁺ activated garnets, but can be universally applied to any family of matrices and combination of donor–acceptor pairs. The only condition is the resonance between the donor and acceptor transitions.

The effect of Ho³⁺-codoping of GGAG:Ce on its scintillation kinetics was studied using time-resolved spectroscopy of scintillation pulses. The scintillation decay curves for non-codoped GGAG:Ce and Ho³⁺ codoped GGAG:Ce crystals are presented in Fig. 5. The effect of shortening Ce³⁺ decay time due to Ho³⁺ codoping is evident in the scintillation response as well. The 1/e decay time dropped from 90 ns for non-codoped GGAG:Ce to 25 ns for the GGAG:Ce with 6.2 at% of Ho³⁺ codopant. Refer to Table 1 for 1/e scintillation decay times of all examined crystals.

Fig. 5 Scintillation decay kinetics of non-codoped GGAG:Ce and Ho³⁺ codoped GGAG:Ce excited by ¹³⁷Cs γ-radiation.

RL spectra confirm the expected trend of overall efficiency decrease in Ho³⁺ codoped GGAG:Ce crystals, see the Fig. 6, the concentration dependence of RL spectra integrals in the inset of this figure and Table 1 for listed values of relative overall efficiency (compared to that non-codoped GGAG:Ce). In general, the overall efficiency decreases with Ho³⁺ concentration. For the GGAG:Ce with the highest content of Ho³⁺ codopant the RL spectrum integral drops to 22% of the non-codoped GGAG:Ce. The only deviation from the decreasing trend can be seen for the crystal codoped with 0.13 at% of Ho³⁺ which shows a bit superior RL intensity than the non-codoped GGAG:Ce.

Fig. 6 Radioluminescence (40 kV, 15 mA X-rays) spectra of non-codoped GGAG:Ce and Ho³⁺ codoped GGAG:Ce. Radioluminescence spectra integrals plotted against Ho³⁺ codopant concentration in the inset.

The same crystal deviates from the decreasing trend of scintillation 1/e scintillation decay time with value greater by 17% than that of the non-codoped crystal. No such pattern is observed in the trend of 1/e photoluminescence decay time or LY measurement, i.e. measurements that are mostly determined by the fast components of the scintillation pulses. Due to these facts, the deviation of RL and 1/e scintillation decay time is attributed to higher contribution of the slow components, probably due to increased content of traps and defects in the crystal.

In line with our observations from previous studies on Ho³⁺ codoped YAG:Ce¹ and LuAG:Pr,³ no or just negligible Ho³⁺-related emission in the UV-VIS region is observed in RL spectra of Ho³⁺ codoped GGAG:Ce. According to ref. 47, the emission of Ho³⁺ centers in YAG host is located in IR region. The same behavior is anticipated for Ho³⁺ in GGAG. As described above, this makes Ho³⁺ the ideal codopant as it does not introduce any slow components into the detectable light when usual photomultipliers are used as photodetectors. Another advantage of using Ho³⁺ codoping, or RE³⁺ codoping in general, for acceleration of scintillation response using RET in garnet hosts is the expected homogeneous distribution of codopant along the crystal due to very favorable segregation coefficient close to 1.⁴⁹ This ensures rather homogeneous scintillation characteristics in all the volume of the crystal grown. Another, recently published⁵⁰ acceleration mechanism in heavily doped GAGG:Ce,Mg crystals which is based on luminescence quenching in the Ce–Mg pairs, is much more problematic in this respect.

Analogously to RL spectroscopy, the amplitude spectroscopy of scintillation pulses confirms the expected decreasing trend of LY in the Ho³⁺ codoped GGAG:Ce crystals as well. A decrease of LY is proportional to Ho³⁺ concentration. For the highest content of Ho³⁺ LY drops to 15% when compared to that of the non-codoped GGAG:Ce crystal. The data for LY are summarized in Table 1.

The above findings show two effects of Ho³⁺ codoping on scintillation properties of on GGAG:Ce. The first is shortening of the scintillation pulses. In terms of 1/e scintillation decay time, the Ho³⁺ codoping can reduce this quantity by tens of percent in GGAG:Ce which improves timing properties of the scintillator, enabling e.g. increased detection rate. The second effect of Ho³⁺ codoping is the decrease of scintillator efficiency. In general, decrease of scintillator efficiency is unfavorable as it leads to impaired performance of the material, e.g. impaired energy resolution. In terms of LY, the rate of decrease is slightly higher than that of 1/e scintillation decay time in GGAG:Ce. One can think of RE³⁺-codoping as a method that enables trading scintillator efficiency for faster scintillation decay. Both measures are put into perspective in Fig. 7 which compares relative LY and scintillation 1/e decay time τ_1/e. The values are listed in Table 1.

Fig. 7 Scintillation 1/e decay time τ_1/e and LY of Ho³⁺ codoped GGAG:Ce plotted against Ho³⁺ codopant concentration in relative scale.

Energy loss pathways due to Ho³⁺ codoping and their quantification

As shown in the previous section, the Ho³⁺ codoping of GGAG:Ce induces simultaneously an acceleration of scintillation pulses and loss of scintillator efficiency. This is due to interference of Ho³⁺ codopant in multiple stages of the scintillation mechanism. The second part of this study is focused on examination of the origin of losses of scintillator efficiency caused by Ho³⁺ codoping. The main loss pathways are identified and their contribution in overall loss of scintillator efficiency is estimated. The estimations are further compared to the experimental LY data.

We identify following energy loss pathways within the scintillation mechanism of GGAG:Ce caused by Ho³⁺ codoping interferes:

(a) Degradation of the crystal quality due to high concentration of Ho³⁺ codoping. Introduction of new element, especially if introduced in high concentrations can make the crystal growth unstable, introduce new type of defects, and cause overall impairment of the crystal quality.

(b) Charge carriers capture on Ho³⁺ centers during the transport stage of scintillation process. Ho³⁺, same as Ce³⁺ and other RE³⁺ ions, creates recombination centers that capture the electrons and holes during the transport stage of the scintillation conversion mechanism. Once electrons and holes are trapped on Ho³⁺ center, they will slowly deexcite through the dense structure of Ho³⁺ excited states producing photons in IR region, outside detection range of used photosensitive elements of scintillation detectors. As a result, the amount of energy delivered to Ce³⁺ centers and used for generation of detectable scintillation photons is reduced by the part captured on Ho³⁺ codopant and the scintillator efficiency is impaired.

(c) Resonant energy transfer from Ce³⁺ to Ho³⁺. This effect enables shortening of the Ce³⁺ decay time. At the same time, it consumes part of the energy which would be emitted by Ce³⁺ in form of scintillation photons in absence of Ho³⁺ codopant but is resonantly transferred to the Ho³⁺ and consequently emitted in the IR region, i.e. technically lost, as described above.

(d) Reabsorption of Ce³⁺ emitted light by Ho³⁺. RET is enabled via overlap of Ce³⁺ emission and Ho³⁺ absorption peaks which inevitably enables not only non-radiative (resonant), but also radiative transfer of energy, i.e., part of the Ce³⁺ emitted photons is reabsorbed by Ho³⁺ codopant as shown in Fig. 3.

Assume l_x, such as 0 ≤ l_x ≤ 1, is an estimated loss of scintillator efficiency induced due to one of the described energy loss pathways due to Ho³⁺ codoping, and f_x = 1 − l_X is multiplication factor representing scintillator efficiency after accounting the effect of the specific energy loss pathway. Then, if η₀ is the efficiency of the non-codoped crystal, the efficiency of the Ho³⁺ codoped crystal can be estimated as

η = f_degf_CCf_RETf_reabsη₀ (5)

where deg refers to overall degradation of crystal quality due to codoping, CC refers to charge capture by Ho³⁺, RET to resonant energy transfer from Ce³⁺ to Ho³⁺ and reabs to reabsorption of Ce³⁺ emitted light by Ho³⁺. In the next paragraphs loss of efficiency multiplication factors f_X will be estimated based on experimental data obtained on the non-codoped and Ho³⁺ codoped GGAG:Ce crystals. Finally, an estimate of relative scintillator efficiency can be calculated as

Experimentally obtained values of LY of the non-codoped and Ho³⁺ codoped GGAG:Ce crystals can be used as independent reference to validate estimates of the scintillation efficiency η/η₀.

To assess the effect of Ho³⁺ codoping of GGAG:Ce on overall crystal quality, mainly impairment due to introduction of new defects due to Ho³⁺ codoping, spectrally unresolved TSL measurement was performed. See Fig. 8 for the glow curve of the non-codoped GGAG:Ce and GGAG:Ce codoped with 3.6 at% of Ho³⁺. Both the glow curves are composed of TSL peaks with the maxima at the same temperatures, although their contribution differs in the non-codoped and Ho³⁺ codoped crystal. No additional TSL peaks referring to a new type of defects due to Ho³⁺ codoping are observed in Ho³⁺ codoped crystal. Therefore, loss of efficiency due to degradation of crystal quality and additional traps is considered negligible and the related multiplication factor f_deg is set 1 for all Ho³⁺ codoped crystals.

Fig. 8 Spectrally unresolved TSL glow curves of non-codoped and Ho³⁺ codoped GGAG:Ce measured after 10 minutes of irradiation with 40 kV/15 mA X-rays at 77 K and 0.1 K s⁻¹ heating rate.

The amount of energy resonantly transferred from Ce³⁺ donor to Ho³⁺ acceptor, i.e. the loss of efficiency due to RET, is proportional to a difference of integrals of the Ce³⁺ decay curves in the non-codoped and Ho³⁺ codoped crystal. The multiplication factor f_RET is then estimated as

using the results of the curve fitting to IH model. The resulting multiplication factors are listed in Table 2. The estimation shows, the crystal with the highest content of Ho³⁺ loses more than 80% of the efficiency when compared to the non-codoped one due to RET. Based on this result, it is clear, that RET is the main energy loss pathway caused by Ho³⁺ codoping.

Table 2 Summary table of factors of efficiency loss for non-codoped GGAG:Ce and Ho³⁺ codoped GGAG:Ce

Ho^3+ conc. [at%]	fdeg	fCC	fRET	freabs	η/η0	Rel. LY
0.00	1.00	1.00	1.00	1.00	1.00	1.00
0.13	1.00	1.00	0.94	0.99	0.93	0.98
0.59	1.00	1.00	0.77	0.98	0.76	0.75
1.97	1.00	1.00	0.51	0.97	0.50	0.46
3.56	1.00	1.00	0.32	0.97	0.31	0.28
6.21	1.00	1.00	0.19	0.79	0.15	0.15

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To estimate the loss of efficiency due to reabsorption of Ce³⁺ emitted light on Ho³⁺, the obtained photoluminescence spectra, shown in Fig. 3, were used. The loss is proportional to size of the reabsorption dips observed in the photoluminescence spectra of the Ho³⁺ codoped GGAG:Ce. The multiplication factor f_reabs is estimated as

where I_Ho-codoped(λ) and I_non-codoped(λ) are normalized photoluminescence spectra of the Ho³⁺ codoped and the non-codoped crystal. The spectra were normalized to the values at 580 nm, not to the maxima of the peak, as the maxima is disrupted by reabsorption dips, see Fig. 3. Resulting multiplication factors can be found in Table 2. As reabsorption is given also by length of optical path within the crystal, this estimate is restricted to crystals of the same dimensions as of those used in this study. The losses due to reabsorption of the Ce³⁺ light on Ho³⁺ reach 11% for the crystal with the highest content of Ho³⁺ when compared to the non-codoped crystal.

Summarizing the estimates of efficiency loss due to impaired crystal quality, RET, reabsorption on Ho³⁺ and the relative values of measured LY, we assume the loss of efficiency due to charge carrier capture by Ho³⁺ are very low or negligible.

In fact, if the multiplicative factor for charge losses due to charge carrier capture f_CC is assumed to be 1, we obtain a solid match between the resulting estimate of relative efficiency η/η₀ and independently measured relative LY values, see Fig. 9. In case, we assumed the loss of efficiency due to charge carrier capture non-zero, i.e. f_CC < 1, the resulting estimate of relative efficiency η/η₀ would only deviate from the experimental LY data. Hence the efficiency losses due to charge carrier capture are considered negligible and related multiplicative factor f_CC is estimated to 1 for all concentrations of Ho³⁺.

Fig. 9 Comparison of concentration dependence of estimated relative efficiency η/η₀ and measured relative LY.

The estimations of losses of scintillator efficiency performed in the previous section helped to reveal more on the impact by Ho³⁺ codoping of GGAG:Ce on specific stages of scintillation mechanism.

The investigation shows by far the greatest part of the losses of scintillator efficiency are due to the RET from Ce³⁺ to Ho³⁺, the same process that is causing the acceleration of Ce³⁺ decay time. A smaller part of losses of scintillation efficiency is due to other means. In other words, most of the lost scintillator efficiency was used for the purpose of the method, i.e. acceleration of the activator decay time. This makes Ho³⁺ codoping of GGAG:Ce very effective method for modification of timing properties of scintillation response.

Minor losses of efficiency are caused by reabsorption of Ce³⁺ emitted light by Ho³⁺ centers. The losses might change for a different geometry of a crystal, however, even for large crystals the losses due to reabsorption should saturate at certain level as Ho³⁺ absorption lines are overlapping just a part of the broad emission band of Ce³⁺ and part of the Ce³⁺ emitted light would remain not absorbed. The losses due to reabsorption of Ce³⁺ emitted light on Ho³⁺ do not contribute to shortening of the Ce³⁺ decay time.

Interestingly, the results also suggest that Ho³⁺ does not interfere with charge carriers during the transport stage of scintillation conversion in GGAG:Ce, or, in other words, the Ho³⁺ ability to capture charge carriers is very low when compared to Ce³⁺, even if the concentration of Ho³⁺ is an order of magnitude higher. This could be attributed to Mg²⁺ codoping, that induces formation of Ce⁴⁺ centers that are more effective in capturing electrons when compared to Ce³⁺ capturing holes.

Conclusions

In this study the effect of Ho³⁺ codoping on GGAG:Ce luminescence and scintillation properties were investigated with the focus on timing properties and scintillator efficiency and the impact of the Ho³⁺ codoping on different stages of scintillation mechanism of GGAG:Ce. Our results show the Ho³⁺ codoping and the related resonant energy transfer from Ce³⁺ to Ho³⁺ can lead to significant reduction of the Ce³⁺ 5d₁ excited state decay time and shortening scintillation pulses of GGAG:Ce. At the same time scintillator efficiency is reduced as well. We found the 1/e scintillation decay time can be reduced by tens of percent, while light yield decreases by an equivalent amount when using Ho³⁺ codoping in GAGG:Ce.

Moreover, we showed that the Ho³⁺, unlike other RE³⁺as Dy³⁺, Er³⁺ or Nd³⁺, is favorable choice of codopant for the examined method due to absence of slow 4f → 4f emission in the UV/VIS region and thus absence of slow components in the detectable light when using usual photomultipliers.

We showed, the emission kinetics of the Ce³⁺ donor in Ho³⁺ codoped GGAG:Ce can be consistently described with the Inokuti–Hirayama model. Consistency with this model was observed also in our previous studies on various donor–acceptor pairs and matrices. Furthermore, we showed the method provides consistent results for both GGAG and YAG matrix and crystal growth method when doped by Ce³⁺–Ho³⁺ donor–acceptor pairs. Both the consistency with this model and consistency of the results for similar matrices show the effect of RE³⁺ codoping on scintillator properties is reliably predictable.

Further, losses of the scintillator efficiency due to Ho³⁺ codoping were analyzed in the detail. The most significant loss-of-efficiency pathways were identified, and their share on total loss of scintillator efficiency was estimated based on the experimental results. The major losses are attributed to the resonant energy transfer from Ce³⁺ donor to Ho³⁺ acceptor, i.e. the same mechanism that shortens Ce³⁺ decay time. Small part of the losses is due to Ho³⁺ reabsorption of Ce³⁺ emission and the losses due other pathways are negligible. Thus, we showed the Ho³⁺ codoping of GAGG:Ce is an effective method for acceleration of its scintillation response, as the largest part of scintillation efficiency losses are due to acceleration itself, not due to effects associated with Ho³⁺ codoping that do not accelerate the scintillation response.

The unprecedented advantage of the examined method is that it can be applied right away on many existing materials. Its use is not limited to garnet matrices or selection of the Ce³⁺–Ho³⁺ donor–acceptor pair, but can be applied to any family of matrices and combination of donor–acceptor pairs that meet the resonance criteria.

Data availability

Data are available upon request from the corresponding authors.

Author contributions

Juraj Páterek: conceptualization, formal analysis, investigation, methodology, visualization, writing – original draft; Pavel Boháček: crystal growth, resources, writing – review & editing; Bohumil Trunda: crystal growth, resources; Vladimír Babin, Richard Švejkar, Karel Jurek, Jan Rohlíček: investigation; Martin Nikl: funding acquisition, supervision, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The work was supported by the Czech Science Foundation under Grant No. 21-17731S.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ra02866j

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