# Time Response of Silica-Based Scintillators and Other Challenges for Innovative Medical Dosimetry

Franck Mady, Marjorie Grandvillain, Marie Vidal, Joël Hérault, Mourad Benabdesselam

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Franck Mady, Marjorie Grandvillain, Marie Vidal, Joël Hérault, Mourad Benabdesselam. Time Response of Silica-Based Scintillators and Other Challenges for Innovative Medical Dosimetry. 14th International Conference on SiO2, Dielectrics and Related Devices, SiO2 2023, Jun 2023, Palermo, Italy. hal-04584958

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# Time Response of Silica-Based Scintillators and Other Challenges for Innovative Medical Dosimetry

Franck Mady, Marjorie Grandvillain, Marie Vidal, Joël Hérault, Mourad Benabdesselam

► To cite this version:

Franck Mady, Marjorie Grandvillain, Marie Vidal, Joël Hérault, Mourad Benabdesselam. Time Response of Silica-Based Scintillators and Other Challenges for Innovative Medical Dosimetry. 14th International Conference on SiO2, Dielectrics and Related Devices, SiO2 2023, Jun 2023, Palermo, Italy. hal-04584958

HAL Id: hal-04584958

https://hal.science/hal-04584958v1

Submitted on 23 May 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

Public Domain
# Time Response of Silica-Based Scintillators and Other Challenges for Innovative Medical Dosimetry

Franck Mady¹, Marjorie Grandvillain¹,², Marie Vidal², Joël Hérault² and Mourad Benabdesselam¹

¹Université Côte d'Azur, Fédération Claude Lalanne, Institut de Physique de Nice (INPHYNI), CNRS UMR 7010
17 rue Julien Lauprêtre, 06200, Nice, France, [franck.mady@univ-cotedazur.fr](mailto:franck.mady@univ-cotedazur.fr)

²Centre Antoine Lacassagne, Fédération Claude Lalanne, 227 avenue de la Lanterne, 06200 Nice, France

**Keywords:** Silica glasses, radioluminescence, dosimetry

## INTRODUCTION

Real-time dosimeters used in radiotherapy (RT) have become ill-adapted to highly conformational and stereotactic irradiation fields or to ‘pencil-beam scanning’ irradiations in the case of high-energy protontherapy (HEP). Their large sensitive volume (a few mm) does not allow accurate resolution of high dose gradients inherent in these techniques. They are moreover based on radio-electric conversion which is neither suited to MRI-guided RT nor to the high dose rates used in pulsed-RT techniques (HEP or the forthcoming “flash-RT”). Radioluminescence (RL) dosimetry is, by contrast, insensitive to magnetic constraints and perfectly suited to high-dose rate operation. Our FIDELIO project (ANR-20-CE19-0024 [1]) aims at developing specific silica-based fiber RL dosimeters that meet, in addition, the need for both miniaturization (sensitive volume down to a few tens of microns) and near “tissue-equivalence” contrary to other inorganic scintillators. Literature on the assessment of various silica-based scintillators has mainly promoted the linearity of their equilibrium RL level against dose rate, over 2-6 decades [2,3]. A linearity range extended up to almost 12 decades was even recently demonstrated [4]. But linearity is not the problem in developing new RL sensors. The design of silica-based fiber dosimeters for pulsed-RT applications faces 3 much more critical issues which have not been properly tackled so far: the rather large rise and fall times of their RL, the repeatability/stability of their response and the so-called “scintillation quenching” (SQ), a misunderstood effect detrimental to high-LET proton dosimetry. This paper will discuss on the physical origin of these problems (through modeling) and on potential opportunities for their reduction or circumvention.

## RL KINETICS

The rise (and fall) times of the RL response towards (and from) the RL equilibrium level are critical parameters that can greatly limit the dosimeter sensitivity in pulsed operation (repetition of short high-dose rate pulses). RL is produced upon recombination of free carriers at recombination centers (RCs). In most rare-earth doped silica glasses (except Ce-doped ones), RCs consist of trapped electrons recombined by free holes. A legitimate model then considers a single RC type (electrons trapped by trivalent rare-earth ions) and a set of continuously distributed trapped-hole states that compete with RCs by capturing/releasing holes. Then, rate equations describing electron-hole pair generation (rate $g_0$, proportional to the dose rate), trapping, detrapping and recombination can be readily written and solved numerically to simulate RL. A formal treatment is however important to get explicit solutions in a few limit cases, understand simulation results and demonstrate general properties. We will for instance show that the RL intensity obtained in the absence of trapping of holes (only recombination with trapped electrons) is $I_{no\_trap}$ in equation (1). This case sets the smallest rise time $\tau_{min} = (g_0\sigma_r v_{vb})^{-1/2}$, where $\sigma_r$ is the recombination cross-section and $v_{vb}$ the thermal velocity in the valence band. $I_{no\_trap}$ is $0.58 \times g_0$ at $t = \tau_{min}$, reaching $0.99 \times g_0$ at $3 \tau_{min}$. $\tau_{min}$ varies from a few to a few tens of ms at 1 Gy s⁻¹. Then, the RL intensity would initially exhibit a quadratic dependence on both dose rate $g_0$ and time $t$: $I_{no\_trap} = \sigma_r v_{vb} g_0^2 t^2$, $t \ll \tau_{min}$. In the opposite limit case, where free holes can trap but not detrap, the long-term RL growth will be demonstrated to be $I_{no\_trap}$ when traps remain far from saturation (usual cases); see (1) where *N* is the total density of hole traps and $\sigma_c$ the hole capture cross-section. This case leads to the longest rise time $\tau_{max} = N\sigma_c/(2g_0\sigma_r)$ and to a linear initial rise: $I_{no\_trap} = \sigma_r g_0^2 t/(N\sigma_c)$, for
# Time Response of Silica-Based Scintillators and Other Challenges for Innovative Medical Dosimetry

Franck Mady¹, Marjorie Grandvillain¹,², Marie Vidal², Joël Hérault² and Mourad Benabdesselam¹

¹Université Côte d'Azur, Fédération Claude Lalanne, Institut de Physique de Nice (INPHYNI), CNRS UMR 7010
17 rue Julien Lauprêtre, 06200, Nice, France, [franck.mady@univ-cotedazur.fr](mailto:franck.mady@univ-cotedazur.fr)

²Centre Antoine Lacassagne, Fédération Claude Lalanne, 227 avenue de la Lanterne, 06200 Nice, France

**Keywords:** Silica glasses, radioluminescence, dosimetry

## INTRODUCTION

Real-time dosimeters used in radiotherapy (RT) have become ill-adapted to highly conformational and stereotactic irradiation fields or to ‘pencil-beam scanning’ irradiations in the case of high-energy protontherapy (HEP). Their large sensitive volume (a few mm) does not allow accurate resolution of high dose gradients inherent in these techniques. They are moreover based on radio-electric conversion which is neither suited to MRI-guided RT nor to the high dose rates used in pulsed-RT techniques (HEP or the forthcoming “flash-RT”). Radioluminescence (RL) dosimetry is, by contrast, insensitive to magnetic constraints and perfectly suited to high-dose rate operation. Our FIDELIO project (ANR-20-CE19-0024 [1]) aims at developing specific silica-based fiber RL dosimeters that meet, in addition, the need for both miniaturization (sensitive volume down to a few tens of microns) and near “tissue-equivalence” contrary to other inorganic scintillators. Literature on the assessment of various silica-based scintillators has mainly promoted the linearity of their equilibrium RL level against dose rate, over 2-6 decades [2,3]. A linearity range extended up to almost 12 decades was even recently demonstrated [4]. But linearity is not the problem in developing new RL sensors. The design of silica-based fiber dosimeters for pulsed-RT applications faces 3 much more critical issues which have not been properly tackled so far: the rather large rise and fall times of their RL, the repeatability/stability of their response and the so-called “scintillation quenching” (SQ), a misunderstood effect detrimental to high-LET proton dosimetry. This paper will discuss on the physical origin of these problems (through modeling) and on potential opportunities for their reduction or circumvention.

## RL KINETICS

The rise (and fall) times of the RL response towards (and from) the RL equilibrium level are critical parameters that can greatly limit the dosimeter sensitivity in pulsed operation (repetition of short high-dose rate pulses). RL is produced upon recombination of free carriers at recombination centers (RCs). In most rare-earth doped silica glasses (except Ce-doped ones), RCs consist of trapped electrons recombined by free holes. A legitimate model then considers a single RC type (electrons trapped by trivalent rare-earth ions) and a set of continuously distributed trapped-hole states that compete with RCs by capturing/releasing holes. Then, rate equations describing electron-hole pair generation (rate $g_0$, proportional to the dose rate), trapping, detrapping and recombination can be readily written and solved numerically to simulate RL. A formal treatment is however important to get explicit solutions in a few limit cases, understand simulation results and demonstrate general properties. We will for instance show that the RL intensity obtained in the absence of trapping of holes (only recombination with trapped electrons) is $I_{no\_trap}$ in equation (1). This case sets the smallest rise time $\tau_{min} = (g_0\sigma_r v_{vb})^{-1/2}$, where $\sigma_r$ is the recombination cross-section and $v_{vb}$ the thermal velocity in the valence band. $I_{no\_trap}$ is $0.58 \times g_0$ at $t = \tau_{min}$, reaching $0.99 \times g_0$ at $3 \tau_{min}$. $\tau_{min}$ varies from a few to a few tens of ms at 1 Gy s⁻¹. Then, the RL intensity would initially exhibit a quadratic dependence on both dose rate $g_0$ and time $t$: $I_{no\_trap} = \sigma_r v_{vb} g_0^2 t^2$, $t \ll \tau_{min}$. In the opposite limit case, where free holes can trap but not detrap, the long-term RL growth will be demonstrated to be $I_{no\_trap}$ when traps remain far from saturation (usual cases); see (1) where *N* is the total density of hole traps and $\sigma_c$ the hole capture cross-section. This case leads to the longest rise time $\tau_{max} = N\sigma_c/(2g_0\sigma_r)$ and to a linear initial rise: $I_{no\_trap} = \sigma_r g_0^2 t/(N\sigma_c)$, for
$$I_{\text{no\_trap}}(t) = g_0 \times \tanh^2(\sqrt{g_0 \sigma_r v_{\text{vb}}}) \quad \text{and} \quad I_{\text{no\_detrap}}(t) = g_0 \times \frac{\sqrt{1 + \frac{g_0 \sigma_r}{N \sigma_c} t - 1}}{\sqrt{1 + \frac{g_0 \sigma_r}{N \sigma_c} t}} \quad (1)$$

$t \ll \tau_{\text{max}}$ (note again the quadratic dependence on the dose rate). $I_{\text{no\_detrap}}$ is just $0.29 \times g_0$ at $t = \tau_{\text{max}}$; reaching $0.99 \times g_0$ requires $t = 9999 \times \tau_{\text{max}}!$ With typical ranges of parameter values in silica, $\tau_{\text{max}}$ should vary between 1ms and 10 s at 1 Gy s⁻¹, well implying a very slow increase up to equilibrium.

Realistic cases involve hole trapping and detrapping in addition to hole recombination at RCs. Only those unstable ‘shallow traps’ can modify the kinetics of $I_{\text{no\_detrap}}$ (the notion of ‘shallow traps’, which is time-dependent, will be thoroughly discussed in the final paper), but the limit of very intense detrapping necessarily corresponds to the ‘no-trapping case’. Therefore, simulated RL curves are necessarily comprised between the two limit curves set by $I_{\text{no\_trap}}$ and $I_{\text{no\_detrap}}$. We can then apply a kind of sandwich theorem to draw important conclusions: (i) all RL curves tend towards $g_0$ (recombination events per unit time and volume) at equilibrium, (ii) RL is proportional to dose rate $g_0$ at any time, not only at equilibrium, thus offering opportunity to exploit the transient RL for dosimetry instead of expecting for equilibrium, (iii) RL curves should initially rise in $t^\alpha$, with $\alpha$ between 1 and 2 (the closer $\alpha$ to 2, the more intense the detrapping), (iv) this initial rise is always proportional to the square of the dose rate. Conclusion (iii) implies that hole release from shallow traps strongly reduces the RL rise time. But we will also show that it lengthens the fall time (slower phosphorescence decay). An example is illustrated in figure 1, where the hole density of trapping states (DOTS) for silica was extracted from thermoluminescence experiments [5].

<figure><img src="image_1.png" /><figcaption>**Figure 1** – RL simulated for a 10 s irradiation at 10 Gy s⁻¹. Red and black plots: $I_{\text{no\_trap}}$ and $I_{\text{no\_detrap}}$ of equation (1), respectively. Green plot: RL curve simulated for displayed parameter values and hole DOTS for silica shown in the top right figure. Bottom right figure: zoom on phosphorescence decay, greatly slowed by detrapping.</figcaption></figure>

## KINETIC INSTABILITY

The above conclusions imply that any pre-existing shallow trap filling will significantly impact the rise and fall times of the current RL response, without affecting its equilibrium level. This induces an instability in the RL kinetics, i.e. changes according to the “history” of the dosimeter (past given doses, irradiation times and time elapsed from last irradiation). These predictions are well observed experimentally, for instance for gadolinium-doped silica [6]. If pulses are much shorter than the RL rise time, as in HEP (down to 8 µs pulses), the RL will not reach its plateau within a pulse and the dosimetry will only rely on partial growths and decays which should be as stable as possible to prevent from tedious and frequent re-calibration. This explains the need for a careful modeling of the trap structure to understand related transients and develop stabilization strategies. The effect of a pre-dose and various delays on rise and fall times is illustrated by simulation in figure 2.
$$I_{\text{no\_trap}}(t) = g_0 \times \tanh^2(\sqrt{g_0 \sigma_r v_{\text{vb}} t}) \quad \text{and} \quad I_{\text{no\_detrap}}(t) = g_0 \times \frac{\sqrt{1 + \frac{g_0 \sigma_r}{N \sigma_c} t - 1}}{\sqrt{1 + \frac{g_0 \sigma_r}{N \sigma_c} t}} \quad (1)$$

$t \ll \tau_{\text{max}}$ (note again the quadratic dependence on the dose rate). $I_{\text{no\_detrap}}$ is just $0.29 \times g_0$ at $t = \tau_{\text{max}}$; reaching $0.99 \times g_0$ requires $t = 9999 \times \tau_{\text{max}}!$ With typical ranges of parameter values in silica, $\tau_{\text{max}}$ should vary between 1ms and 10 s at 1 Gy s⁻¹, well implying a very slow increase up to equilibrium.

Realistic cases involve hole trapping and detrapping in addition to hole recombination at RCs. Only those unstable ‘shallow traps’ can modify the kinetics of $I_{\text{no\_detrap}}$ (the notion of ‘shallow traps’, which is time-dependent, will be thoroughly discussed in the final paper), but the limit of very intense detrapping necessarily corresponds to the ‘no-trapping case’. Therefore, simulated RL curves are necessarily comprised between the two limit curves set by $I_{\text{no\_trap}}$ and $I_{\text{no\_detrap}}$. We can then apply a kind of sandwich theorem to draw important conclusions: (i) all RL curves tend towards $g_0$ (recombination events per unit time and volume) at equilibrium, (ii) RL is proportional to dose rate $g_0$ at any time, not only at equilibrium, thus offering opportunity to exploit the transient RL for dosimetry instead of expecting for equilibrium, (iii) RL curves should initially rise in $t^\alpha$, with $\alpha$ between 1 and 2 (the closer $\alpha$ to 2, the more intense the detrapping), (iv) this initial rise is always proportional to the square of the dose rate. Conclusion (iii) implies that hole release from shallow traps strongly reduces the RL rise time. But we will also show that it lengthens the fall time (slower phosphorescence decay). An example is illustrated in figure 1, where the hole density of trapping states (DOTS) for silica was extracted from thermoluminescence experiments [5].

<figure><img src="image_1.png" /><figcaption>**Figure 1** – RL simulated for a 10 s irradiation at 10 Gy s⁻¹. Red and black plots: $I_{\text{no\_trap}}$ and $I_{\text{no\_detrap}}$ of equation (1), respectively. Green plot: RL curve simulated for displayed parameter values and hole DOTS for silica shown in the top right figure. Bottom right figure: zoom on phosphorescence decay, greatly slowed by detrapping.</figcaption></figure>

## KINETIC INSTABILITY

The above conclusions imply that any pre-existing shallow trap filling will significantly impact the rise and fall times of the current RL response, without affecting its equilibrium level. This induces an instability in the RL kinetics, i.e. changes according to the “history” of the dosimeter (past given doses, irradiation times and time elapsed from last irradiation). These predictions are well observed experimentally, for instance for gadolinium-doped silica [6]. If pulses are much shorter than the RL rise time, as in HEP (down to 8 µs pulses), the RL will not reach its plateau within a pulse and the dosimetry will only rely on partial growths and decays which should be as stable as possible to prevent from tedious and frequent re-calibration. This explains the need for a careful modeling of the trap structure to understand related transients and develop stabilization strategies. The effect of a pre-dose and various delays on rise and fall times is illustrated by simulation in figure 2.
<figure><img src="image_2.png" /><figcaption>**Figure 2** – RL simulated at 0.15 Gy s⁻¹ for various pre-doses (in legend, given at 2.6 Gy s⁻¹) and various delays between pre-dose and RL simulation. Simulation parameters will be detailed in the final paper.</figcaption></figure>

## CONCLUSIONS

Our work is intended to understand the origin of the main flaws of RL silica-based fiber dosimeters that may prevent them from reaching the response rapidity, sensitivity and stability required by pulsed operation and medical use. We demonstrated important properties of the RL response for most of rare-earth doped silica glasses based on a model that is well suited to these materials (the case of Ce-doped silica will be treated after introducing specific amendments). Even if not examined in this short abstract, the problem of scintillation quenching (specific to proton irradiations) will be introduced in the final paper. Discussions on possible improvement routes inspired by our basic studies, as those illustrated here, will also be included.

## REFERENCES

[1] https://anr.fr/Projet-ANR-20-CE19-0024

[2] M. Benabdesselam, F. Mady, M. Cieslikiewicz-Bouet, W. Blanc, H. El Hamzaoui, A. Cassez, G. Bouwmans, M. Bouazaoui, B. Capoen, “Ge-doped optical fibers for passive and active radiation detection modes”, *IEEE Sensors J.*, to be published.

[3] M. Benabdesselam, J. Bahout, F. Mady, W. Blanc, H. El Hamzaoui, A. Cassez, R. Habert, G. Bouwmans, M. Bouazaoui, B. Capoen, “TL properties of RE-doped and co-doped sol-gel silica rods. Application to passive (OSL) and real-time (RL) dosimetry”, *IEEE Sensors J.*, 21(24), 27465-27472, 2021. DOI: 10.1109/JSEN.2021.3124602

[4] J. Vidalot, C. Campanella, J. Dachicourt, C. Marcandella, O. Duhamel, A. Morana, D. Poujols, G. Assaillit, M. Gaillardin, A. Boukenter, Y. Ouerdane, S. Girard, P. Paillet, “Monitoring of ultra-high dose rate pulsed X-ray facilities with radioluminescent nitrogen-doped optical fiber”, *Sensors*, 22, 3192, 2022. DOI: 10.3390/s22093192.

[5] F. Mady, A. Guttilla, M. Benabdesselam, W. Blanc, S. Girard, Y. Ouerdane, A. Boukenter, H. Desjonquères, C. Monsanglant-Louvet, “Optical fibers under irradiation: quantitative assessment of the energy distribution of radiation-induced trapped states”, Proc. SPIE 11357, Fiber Lasers and Glass Photonics: Materials through Applications II, 113571B, 2020, DOI: 10.1117/12.2557834

[6] M. Grandvillain, M. Benabdesselam, F. Mady, “Study of silica optical fibers for realtime dosimetry of pulsed radiotherapy”, this conference.
<figure><img src="image_2.png" /><figcaption>**Figure 2** – RL simulated at 0.15 Gy s⁻¹ for various pre-doses (in legend, given at 2.6 Gy s⁻¹) and various delays between pre-dose and RL simulation. Simulation parameters will be detailed in the final paper.</figcaption></figure>

## CONCLUSIONS

Our work is intended to understand the origin of the main flaws of RL silica-based fiber dosimeters that may prevent them from reaching the response rapidity, sensitivity and stability required by pulsed operation and medical use. We demonstrated important properties of the RL response for most of rare-earth doped silica glasses based on a model that is well suited to these materials (the case of Ce-doped silica will be treated after introducing specific amendments). Even if not examined in this short abstract, the problem of scintillation quenching (specific to proton irradiations) will be introduced in the final paper. Discussions on possible improvement routes inspired by our basic studies, as those illustrated here, will also be included.

## REFERENCES

[1] https://anr.fr/Projet-ANR-20-CE19-0024

[2] M. Benabdesselam, F. Mady, M. Cieslikiewicz-Bouet, W. Blanc, H. El Hamzaoui, A. Cassez, G. Bouwmans, M. Bouazaoui, B. Capoen, “Ge-doped optical fibers for passive and active radiation detection modes”, *IEEE Sensors J.*, to be published.

[3] M. Benabdesselam, J. Bahout, F. Mady, W. Blanc, H. El Hamzaoui, A. Cassez, R. Habert, G. Bouwmans, M. Bouazaoui, B. Capoen, “TL properties of RE-doped and co-doped sol-gel silica rods. Application to passive (OSL) and real-time (RL) dosimetry”, *IEEE Sensors J.*, 21(24), 27465-27472, 2021. DOI: 10.1109/JSEN.2021.3124602

[4] J. Vidalot, C. Campanella, J. Dachicourt, C. Marcandella, O. Duhamel, A. Morana, D. Poujols, G. Assaillit, M. Gaillardin, A. Boukenter, Y. Ouerdane, S. Girard, P. Paillet, “Monitoring of ultra-high dose rate pulsed X-ray facilities with radioluminescent nitrogen-doped optical fiber”, *Sensors*, 22, 3192, 2022. DOI: 10.3390/s22093192.

[5] F. Mady, A. Guttilla, M. Benabdesselam, W. Blanc, S. Girard, Y. Ouerdane, A. Boukenter, H. Desjonquères, C. Monsanglant-Louvet, “Optical fibers under irradiation: quantitative assessment of the energy distribution of radiation-induced trapped states”, Proc. SPIE 11357, Fiber Lasers and Glass Photonics: Materials through Applications II, 113571B, 2020, DOI: 10.1117/12.2557834

[6] M. Grandvillain, M. Benabdesselam, F. Mady, “Study of silica optical fibers for realtime dosimetry of pulsed radiotherapy”, this conference.