P Souček

L Cassayre

R Malmbeck

E Mendes

R Jardin

J.-P Glatz

Electrorefining of U-Pu-Zr-alloy fuel onto solid aluminium cathodes in molten LiCl-KCl

Pyrochemical separation / Electrorefining / Actinides / Alloy formation / LiCl-KCl eutectic

Introduction

Partitioning and transmutation technologies are investigated worldwide in order to minimize the long term radiotoxicity of the highly radioactive spent nuclear fuel produced at present during operation of the conventional nuclear reactors. The development of efficient partitioning techniques is also a key point for future reactor systems, where the application of an integrated advanced nuclear fuel cycle is considered [START_REF]Accelerator Driven Systems (ADS) and Fast Reactors (FR) in Advanced Nuclear Fuel Cycles -A Comparative Study[END_REF][START_REF]A Technology Roadmap for Generation IV Nuclear Energy Sys[END_REF][START_REF] Magill | Impact limits of partitioning and transmutation scenarios on radiotoxicity of actinides in radioactive waste[END_REF]. Pyrochemical reprocessing is an option for the management of all actinides (An) in advanced fuels or minor actinides (MA = Am, Cm) in transmutation targets which might not be suitable for reprocessing using aqueousbased processes.

Electrorefining and molten salt/liquid metal reductive extraction are the most developed pyrochemical separation techniques. In the electrorefining process developed in Argonne National Laboratory, uranium in metallic alloy fuel is recovered onto inert solid steel cathodes [START_REF] Laidler | Development of pyroprocessing technology[END_REF] and the process has been further developed to recover also Pu and MA in liquid Cd cathodes [START_REF] Uozumi | Electrochemical behaviors of uranium and plutonium at simultaneous recoveries into liquid cadmium cathodes[END_REF][START_REF] Kato | Separation behaviors of actinides from rare-earths in molten salt electrorefining using saturated liquid cadmium cathode[END_REF]. The use of reactive electrodes is very advantageous for the recovery of actinides, *Author for correspondence (E-mail: rikard.malmbeck@ec.europa.eu).

as the actinide metals are stabilized by the formation of alloys with the cathode material. According to the known activity coefficients of Pu, U and Ce in different reactive metals, aluminium has been identified as the electrode material enabling the highest separation factors of actinides from lanthanides (Ln) [START_REF] Conocar | Promising pyrochemical actinide/lanthanide separation processes using aluminium[END_REF]. This has led to the development of a process based on the separation of actinides by reductive extraction into molten Al pool [START_REF] Conocar | Extraction behavior of actinides and lanthanides in a molten fluoride/liquid aluminum system[END_REF].

In ITU, an electrorefining process in molten chloride salt using solid aluminium cathodes is being developed [START_REF] Serp | Electroseparation of Actinides on Solid Aluminium in LiCl-KCl Eutectic[END_REF]. In this process, actinides are recovered from a metallic An-Zr alloy fuel in the form of An-Al alloys. A very high selectivity of the process for recovery of An from Ln has been already shown as well as the capability of solid aluminium electrodes to form stable An-Al alloys using Al rods, foils [START_REF] Serp | Electroseparation of Actinides on Solid Aluminium in LiCl-KCl Eutectic[END_REF] and a foam [START_REF] Serp | Electroseparation of actinides from lanthanides on solid aluminum electrode in LiCl-KCl eutectic melts[END_REF] as the cathodes. In addition, a large-surface aluminium electrode has been used to study the maximum amount of actinides that can be collected on a single electrode by a constant current electrolysis [START_REF] Cassayre | Investigation of electrorefining of metallic alloy fuel onto solid Al cathodes[END_REF].

In this paper, this issue has been further investigated by U and Pu electrodeposition applying potentiostatic and galvanostatic electrolytic techniques and using Al plate cathodes of different dimensions with the objective to reach as high An loading as possible. The experiment was carried out with U-Pu-Zr alloy (71-19-10 wt. %) anodes and a relatively high concentration of actinides in the bath (up to 10 wt. %). Gadolinium chloride was also introduced in the bath at a concentration of 1.6 wt. % to verify the selectivity of the process compared to lanthanides. The electrodes deposits were characterised by γ -spectroscopy, SEM-EDX analysis and XRD.

Experimental

All experiments and storage and handling of chemicals were carried out in a glovebox under purified Ar atmosphere (< 5 ppm of water and oxygen). The detailed description of the technique is described in reference [START_REF] Masset | Thermochemical properties of lanthanides (Ln = La,Nd) and actinides (An = U,Np,Pu,Am) in the molten LiCl-KCl eutectic[END_REF]. Cyclic voltammetry (CV) measurements were carried out using a threeelectrode setup and a PAR 273 potentiostat with EG&G M270 electrochemical software. The working electrode was prepared using a metallic wire (d = 1 mm) and inserted approximately 5 mm into the bath, while a Mo wire bent into the shape of a spiral served as the auxiliary electrode. The reference electrode used was an Ag/LiCl-KCl-AgCl (1 wt. %) prepared in a Pyrex glass tube and potential values mentioned in this work refer to this reference potential.

During the electrorefining experiments, an aluminium plate was used as a cathode and a tantalum basket containing the U-Pu-Zr alloy (ITU stock material, 71-19-10 wt. % respectively) was connected as an anode. All cathodes were made either from 0.5 mm or 2.0 mm thick aluminium plate and the dimensions of the immersed part varied from 5 × 20 to 40 × 20 mm 2 . The active part of the cathode surface area was determined after each experiment by measuring the immersion depth of the electrode. Both anodic and cathodic potentials were simultaneously monitored during the electrolysis using the above-described Ag/AgCl reference electrode. A specially-prepared combination of two multimeters with a laboratory power supply served both for control of the process and for data acquisition. The scheme of the experimental set-up used during electrorefining experiments and a picture of the anodic basket, cathode and crucible are shown in Fig. 1.

A bath consisting of U 3+ , Pu 3+ and Gd 3+ ions dissolved in the LiCl-KCl eutectic mixture (Aldrich 99.99%) was prepared by oxidation of a piece of the U-Pu-Zr metallic alloy dipped into the melt in a tantalum basket. The preparative oxidation was performed by addition of BiCl 3 according to reaction (1).

An 0 U-Pu-Zr + Bi 3+ salt-phase An 3+ salt-phase + Bi 0 (An = U, Pu) .

(

) 1
The reduced Bi metal was collected in a Bi pool at the bottom of the Al 2 O 3 crucible. GdCl 3 (Aldrich 99.99%) was used as received from the producer without any additional treatment. The initial concentrations in the bath were analysed to be 1.84 wt. % U, 2.08 wt. % Pu and 1.30 wt. % Gd. By further oxidation, the actinides content was increased during the experiment up to 6.03 wt. % U and 4.48 wt. % Pu, i.e. in total more than 10 wt. % actinides in the salt. The oxidation reaction was followed by CV measured on an inert tungsten electrode. The chemical composition of the salt was monitored by ICP-MS analysis of regularly-taken salt samples dissolved in 1 M nitric acid. After the electrorefining, the adhered salt on the electrodes was removed by vacuum distillation and/or by washing in ethanol. SEM/EDX and XRD was used for some surface analysis and the deposit composition was investigated by γ spectrometry [START_REF] Abousahl | Development of quantitative analytical methods for the control of actinides in pyrochemical partitioning process[END_REF].

Results and discussion

Cyclic voltammetry

Cyclic voltammetry measurements on an inert W working electrode were used to monitor the quality of the bath during the complete experiment. A voltammogram of the bath containing dissolved U (3.17 wt. %), Pu (1.18 wt. %), Gd (1.66 wt. %) and Zr (0.32 wt. %, oxidised during the course of the experiment) is shown in Fig. 2. The first cathodic wave I c is attributed to the soluble-soluble transition associated with U 4+ /U 3+ transition at -0.25 V [START_REF] Masset | Electrochemistry of uranium in molten LiCl-KCl[END_REF]. The following peaks II c -V c represent the reduction of Zr [START_REF] Smolenski | A potentiometric study of the interaction of Zr(IV) and O(II) ions in the LiCl-KCl eutectic molten salt[END_REF], U [START_REF] Masset | Electrochemistry of uranium in molten LiCl-KCl[END_REF], Pu [START_REF] Serp | Electrochemical behaviour of plutonium ion in LiCl-KCl eutectic melts[END_REF] and Gd [START_REF] Caravaca | Electrochemical behaviour of gadolinium ion in molten LiCl-KCl eutectic[END_REF] ions to metals in reaction M 3+ + 3e -→ M, respectively.

On a reactive aluminium electrode, the deposition potentials of both actinides and lanthanides are shifted to more positive values due to the formation of alloys with the electrode material. The values of the deposition potentials on Al have been published for U [START_REF] Cassayre | Investigation of electrorefining of metallic alloy fuel onto solid Al cathodes[END_REF], Pu [START_REF] Serp | Electroseparation of actinides from lanthanides on solid aluminum electrode in LiCl-KCl eutectic melts[END_REF] and Gd [START_REF] Bermejo | The electrochemistry of gadolinium in the LiCl-KCl on W and Al electrodes[END_REF][START_REF] Caravaca | Formation of Gd-Al Alloys Films by Molten Salt Electrochemical Process[END_REF] (see Table 1). Due to the different concentrations of AgCl in the Fig. 2. Cyclic voltammogram of the bath containing dissolved U (3.17 wt. %), Pu (1.18 wt. %), Gd (1.66 wt. %) and Zr (0.32 wt. %) measured on W electrode, 100 mV s -1 , 460 • C. Cyclic voltammogram of the bath containing dissolved U (3.17 wt. %), Pu (1.18 wt. %), Gd (1.66 wt. %) and Zr (0.32 wt. %) measured on W electrode, 100 mV s -1 , 460 • C. a: Exact concentration used for the measurement with solid Al electrode is not specified in the reference.

used reference electrodes, the potentials were recalculated to the scale of Ag/AgCl (1 wt. %) reference electrode. The difference in the deposition potentials between Pu and Gd onto Al is 230 mV, which is enough to provide a selective deposition of actinides.

Electrorefining of U-Pu-Zr alloy

Galvanostatic and potentiostatic electrolysis were used to examine the maximum possible loading of the solid Al electrodes. In the galvanostatic mode, the maximum current was reached after applying a stepwise current increase while maintaining both cathodic and anodic potentials within the selected limits. The cathodic cut-off potential was set to a value of -1.25 V which ensures conditions for a selective grouped separation of An from Ln [START_REF] Serp | Electroseparation of actinides from lanthanides on solid aluminum electrode in LiCl-KCl eutectic melts[END_REF][START_REF] Cassayre | Investigation of electrorefining of metallic alloy fuel onto solid Al cathodes[END_REF]. A potential of -1.00 V was used as the anode cut-off potential to avoid oxidation of Zr from the U-Pu-Zr alloy [START_REF] Iizuka | Modelling of anodic dissolution of UPuZr ternary alloy in the molten LiCl-KCl electrolyte[END_REF]. For all runs under potentiostatic conditions, a cathode potential of -1.25 V was applied. The electrolysis was terminated when the current became too low or if the expected loading of the cathode was achieved. In total 5 runs were carried out (see Table 2). The expected electrode reactions were anodic oxidation of actinides from the alloy and their reduction on the cathode forming An-Al alloys according to the following reaction schemes:

Anodic side: M x 0 Zr y → M 3+ + 3e -+ M x-1 0 Zr y (2) Cathodic side: M 3+ + 3e -+ zAl → M 0 Al z (M = U, Pu) .
(3)

In addition to the two galvanostatic and two potentiostatic runs, one experiment was performed without applying an anodic cut-off potential to evaluate the influence of oxidation and co-deposition of Zr on the quality of the deposit (run 2). Because of a poor adhesion of the deposit, only qualitative evaluation is available for this run (see Sect. 3.4).

Galvanostatic electrolysis

Galvanostatic experiments were carried out using large area Al electrodes made from plates either 0.5 or 2.0 mm thick. The thinner plates were used to examine the capacity of an Al electrode to retain actinides (runs 1 and 3). For these two experiments, an excess of U-Pu-Zr alloy was introduced as anodic material to avoid Zr co-dissolution during the electrolyses. The anodic potential varied between -1.30 and -1.00 V, which corresponds to a congruent oxidation of the actinides from the U-Pu-Zr alloy.

Selective reduction of uranium and plutonium forming a U-Pu-Al surface alloy occurred at the cathode and the potential showed a decreasing trend, starting from -1.05 V and in the end reaching the minimum value of -1.25 V. With the build up of the An-Al surface alloy layer, the cathodic reaction is more and more limited by diffusion of the reduced elements forming the surface alloy layer, i.e. U, Pu and Al. The record of potentials and current for the galvanostatic electrolysis in run 3 is presented in Fig. 3.

The thicker plate was used for the measurement without anodic limitation and a stoichiometric amount of the alloy was added to the anodic basket (run 2). During the electrolysis co-oxidation of zirconium together with the actinides occurred at the anode, which was evidenced by a positive shift in anodic potential from -1.30 V to -0.70 V. Moreover, Zr ions released from the anode were also reduced onto the aluminium cathode together with the actinides, as the deposition potential of Zr is more positive than that of the actinides.

Potentiostatic electrolysis

Two potentiostatic electrolyses were carried out with small area electrodes made from plates of 0.5 and 2.0 mm thickness (runs 4 and 5). The aim was to examine the Al electrode capacity to alloy actinides and consequently an excess of U-Pu-Zr alloy was used as anodic material. The cathodic potential was kept constant at -1.25 V in both runs to ensure a selective deposition of actinides.

The record of anodic potential development and current for a typical potentiostatic electrolysis (run 5) is shown in Fig. 4. In this case, the current gradually decreased from -20 mA to almost 0 as a result of the increasing thickness of the U-Pu-Al alloy. Due to the decrease of the current, the anodic potential symmetrically dropped from -1.0 V up to -1.3 V.

Evaluation of the Al electrodes capacity to load actinides

After the electrodeposition, the electrodes were left for some time just above the bath at 450 • C in order to let the adhered salt drop down. The estimated mass of adhered salt was in the order of 0.2 g. In two cases (run 1 and 3), a vacuum distillation was used for removal of the salt that remained on the electrode surface. The efficiency of the distillation (performed at 500 • C) turned out to be quite low and at most only 50% of the salt was removed. A quantitative Pu assay was performed by gamma spectrometry in a far-field counting geometry (sample-todetector distance = 19 cm) relative to a Pu reference sample of similar Pu isotopic composition and known Pu element content. The relative accuracy of this kind of Pu assay is estimated to be 5%. Separate gamma measurements with close sample-to-detector distances were performed for the determination of the Pu/U ratio using gamma rays from 239 Pu and 235 U, combined with the known isotopic composition of Pu and U for the calculation of the Pu/U weight ratio. The relative uncertainty of the measured Pu/U weight ratio ranges between 1.7 and 2.5%. The results are summarised in Table 3 (quoted uncertainties at ±1-sigma). The evaluation of the loading of the electrodes with actinides is given in Table 4. The weight percent ratio of An in the Al cathode was calculated according to Eq. ( 4):

An wt. % in Al = m An m An + m Al . ( 4
)
The mass of actinides m An resulting from gamma spectroscopy measurements was used for the calculation and the relevant aluminium mass was derived from the measured immersed depths of each electrode. The theoretical mass of the deposit was calculated assuming 100% faradic yield, thus the charge passed during the experiment was converted to a mass of actinides (according to the U/Pu ratio obtained from the gamma measurement) collected on the cathode.

If AnAl 3 alloy is assumed as the main constituent of the formed deposit, the maximum possible loading is 2.94 g of An in 1 g of Al, which corresponds to 74.7 wt. % An in Al. The highest An content in Al was achieved for potentiostatic electrolysis, with 2.33 g of An loaded into 1 g of Al (70.0 wt. % An in Al). This is 94 % of the maximum Al capacity. The average value was 2.25 g of An, i.e. 69.3 wt. % An in Al. In galvanostatic electrolyses, the average loading achieved was somewhat lower, 1.58 g of An in 1 g of Al (61.2 wt. % An in Al). Nevertheless, it still confirms a high capacity of Al to take up actinides

The diffusion of An and Al through the An-Al alloy surface deposit seems likely to be the most important factor for this process. As the diffusion rate increases with temperature, then actinide-richer and possibly thicker alloy layers could be expected at higher temperatures. More detailed studies will be necessary to correctly evaluate the dependency of the maximum actinide loading of aluminium cathodes during electrorefining on the applied temperature and the thickness of the cathodes.

Characterization of the alloys

Electrodes from run 1 and 2 were further characterized by SEM-EDX analysis and XRD. The aim was to evaluate the thickness, the structure and the composition of the formed An-Al alloys (run 1) and to assess the influence of Zr co-deposition on the quality of the deposit (run 2). From each electrode a piece was cut, embedded in epoxy resin and surface-polished for SEM analyses. From the remaining cathode some deposit was scraped off, well ground and embedded in epoxy resin and slightly polished for precise X-ray powder diffraction analysis.

Galvanostatic electrolysis applying both potential limits

The electrode from run 1 was selected to be characterized by SEM-EDX analysis. SEM micrographs and results of EDX analysis are shown in Figs. 5 and6. A uniformly thick and porous surface deposit is well visible on the micrograph shown in Fig. 5a. At some places, almost all aluminium has reacted, as shown in Fig. 5b, which corresponds well to the above-calculated An/Al weight ratio of 1.5. The maximum thickness of the deposit with no Al metal remaining was measured as 1.2 mm (see arrows in Fig. 5b), compared to 0.5 mm initially.

An analysis of the deposit was performed using EDX at 21 spots selected at various heights of the electrode with different thicknesses of deposit. Composition profiles from the middle towards the surface of the electrode were compiled for U, Pu, Al, Cl and Gd. As expected, Gd was not detected in the deposit. Cl was found in the porous parts, which indicates the presence of salt inclusions. The molar ratio Al/(U + Pu) is plotted in Fig. 6 as function of the distance from the centre of the electrode. The average Al/(U + Pu) ratio was determined to be 3.01. Thus the deposit is most probably composed of a (U,Pu)Al 3 alloy. The values for the U/Pu molar ratio were scattered, with a U/Pu ratio comprised between 4 and 10. The average value was U/Pu = 7.0, which is somewhat lower than the ratio determined by gamma spectroscopy (10.1).

The XRD pattern of the deposit was indexed on the basis of a cubic (a = 4.2652(1) Å) unit cell corresponding to (U,Pu)Al 3 alloy. This result is in a very good agree- ment with the EDX determination of the Al/(U + Pu) molar ratio (average value 3.01). Although the cell parameters for UAl 3 and PuAl 3 are very similar (4.266 Å and 4.264 Å, respectively [START_REF] Tougait | Stoichiometry of UAl 4[END_REF][START_REF] Runnalls | Polymorphic transformations in PuAl 3[END_REF]), the measured spectrum indicates the formation of a (U,Pu)Al 3 solid solution, as no splitting of diffraction peaks was observed. The XRD pattern is shown in Fig. 7.

Galvanostatic electrolysis without upper anodic cut off potential

In contrast to the electrode from run 1, the deposit formed during co-deposition of zirconium is not dense and it contains a lot of incorporated salt, which could not be removed by washing. SEM micrographs of the electrode and a detail of the interfaces Al-salt-deposit are shown in Fig. 8. The initial deposit appears to be dense and adherent, but later this gives way to a very porous deposit that is filled with salt (see Fig. 8b). The outer layer is the attached salt. Thus the codeposition of Zr together with actinides rapidly hampers the formation of a dense An-Al alloy and results in a significant deterioration of the quality of the deposit.

EDX analyses indicated high heterogeneity of the deposit composition and presence of many salt-filled pores. The average Al/(Pu + U) ratio was determined to be 3.8 using the analyses of the deposit parts composed of an alloy. This indicates the formation of a mixture of AnAl 3 and AnAl 4 alloy. In some analyses, high Zr concentrations up to 40 wt. % were measured. The large spread in results makes a correct qualitative evaluation of total Zr content in the deposit impossible. The major phases detected by XRD analysis of the deposit are composed of (U,Pu)Al 3 alloy and KCl. Other determined compounds are ZrAl 3 , (U,Pu)Al 4 and LiCl.

Development of concentration profile during the experiments

Concentrations of U, Pu, Zr and Gd were regularly monitored by ICP-MS analysis of the salt samples during the complete experiment. The resulting concentration profile as a function of the total passed charge is plotted in Fig. 9.

The effectiveness in the application of cut-off potentials was verified, as the concentration of gadolinium remained at its initial level and zirconium concentration was below the detection limit during the major part of the runs. An exception was detected for the run 2, where Zr was intentionally electrochemically oxidized from the U-Pu-Zr alloy together with the actinides. After this run, all dissolved zirconium was chemically reduced by the UPuZr alloy, in the anode basket, back to a concentration value below the detection limit.

The uranium concentration showed a decreasing trend during all the runs. This is explained by the congruent An dissolution of the U 0.71 Pu 0.19 Zr 0.10 alloy on the anodic side and the predominant deposition of U compared to Pu at the cathode (U/Pu mass ratio in the deposit is ∼ 10). In addition a chemical reaction, i.e. reductive extraction of U 3+ by Al from the electrode can also occur which would also lead to a decrease of the U 3+ concentration [START_REF] Cassayre | Uranium underpotential deposition onto solid aluminium in molten LiCl-KCl eutectic[END_REF]. On the other hand, the plutonium concentration gradually increased during the experiment. The concentration increase of both actinides at 4000 C was caused by intentional chemical oxidation of the alloy by addition of BiCl 3 according to reaction (1) in order to increase the concentration of the actinides in the bath.

Conclusion

The use of solid aluminium electrodes for the reprocessing of spent nuclear fuel by electrorefining in molten chlorides seems to be very advantageous. Reduced actinides form solid and dense alloys with aluminium and a very high capacity of aluminium to retain actinides has been proven in the above experiments on electrorefining of U-Pu-Zr alloy in LiCl-KCl eutectic at 450 • C. Galvanostatic and potentiostatic electrolytic techniques were applied during the experiment and almost 6000 C has been passed during the 5 evaluated runs, which were carried out under conditions suitable for a grouped separation of actinides from lanthanides. Uniform and thick deposits mainly composed of An-Al 3 alloy were obtained with a high current efficiency.

On the other hand, the presence of zirconium ions in the bath and the related zirconium co-deposition had very negative effects yielding porous and non-compact deposit. Although it is thermodynamically possible to avoid Zr dissolution from U-Pu-Zr alloy by applying an anodic cut-off potential, the complete recovery of actinides during elec-trorefining of An-Zr alloy fuels can not be achieved without co-dissolution of some Zr [START_REF] Ahluwalia | Removal of zirconium in electrometallurgical treatment of experimental breeder reactor II spent fuel[END_REF]. Further studies on this issue will be necessary to optimize the process.

Fig. 1 .

 1 Fig. 1. Picture of anodic basket, cathode and crucible before start of the experiment (a) and scheme of experimental set-up (b).

Fig. 3 .

 3 Fig.3. Evolution of cathodic and anodic potentials during the galvanostatic electrolysis using both cut-off potentials (Run 3).

Fig. 4 .

 4 Fig. 4. Evolution of anodic potential and current during the potentiostatic electrolysis (run 5) at E = -1.25 V vs. Ag/AgCl.

Fig. 5 .

 5 Fig. 5. SEM micrographs of the crosssections of electrode from run 1.

Fig. 6 .

 6 Fig. 6. SEM-EDX determination of the Al/(U + Pu) molar ratio vs. the distance from the electrode surface (run 1).

Fig. 7 .

 7 Fig. 7. XRD pattern of the deposit from run 1 (Symbols = observed points, solid line above = calculated profile, solid line below = difference between observed and calculated profiles, ticks below the peaks = 2θ hkl Bragg positions: (1) UAl 3 ).

Fig. 8 .

 8 Fig. 8. SEM micrographs of the electrode from run 2.

Fig. 9 .

 9 Fig. 9. Concentration profile of U, Pu, Zr and Gd in the bath during the electrorefining. The run carried out between runs 2 and 3 was not evaluated due to technical problems.

Table 1 .

 1 Measured deposition potentials of U, Pu and Gd on solid Al in molten LiCl-KCl.

	Reduced Temperature	Concentration	Dep. potential Ref.
	ions	[K]	in the salt [wt. %] [E vs. Ag/AgCl]
	U 3+	733	1.50	-1.05	[11]
	Pu 3+	733	1.25	-1.18	[10]
	Gd 3+	723	1.58-2.64 a	-1.44	[18]
	Gd 3+	733	1.58	-1.41	[19]

Table 2 .

 2 Runs carried out during U-Pu-Zr electrorefining experiment.

	Run	Technique		Cathode		Treatment	Analysis
			Mass	Thickness	Surface	Vacuum	γ -	S E M -	X R D
			[g]	[mm]	[cm 2 ]	distillation	spectroscopy	EDX
	1	G E+ L	0.61	0.5	9.3	yes	yes	yes	yes
	2	GE	2.43	2.0	10.2	no	no	yes	yes
	3	G E+ L	0.54	0.5	8.3	yes	yes	no	no
	4	PE	0.27	2.0	1.5	no	yes	no	no
	5	PE	0.23	0.5	3.6	no	yes	no	no

GE (+L) = Galvanostatic electrolysis (applying limiting cut-off potentials); PE = potentiostatic electrolysis.

Table 3 .

 3 Gamma spectroscopy analysis of U and Pu content in the electrodes' deposits.

	Run	Pu content	U/Pu	U content	Sum (Pu + U)
		(mg)	Weight ratio	(mg)	(mg)
	1	8 4 .0 ± 4.2	10.09 ± 0.17	849 ± 44	933
	3	4 7 .1 ± 2.4	18.07 ± 0.30	852 ± 45	899
	4	5 1 .0 ± 2.6	11.35 ± 0.19	579 ± 30	630
	5	6 7 .7 ± 3.4	6.37 ± 0.16	431 ± 24

Table 4 .

 4 Evaluation of results achieved during U-Pu-Zr electrorefining experiments.

	Run	Charge	Mass	Deposit weight [mg]	Current	An	Weight
		[C]	Al [g] Theoretical	Analysed efficiency [%]	wt. %	ratio Al/An
	1	1423	0.61	1171	933	79.7	59.9	1 : 1.49
	3	1527	0.54	1256	899	71.6	62.5	1 : 1.67
	4	773	0.27	632	630	99.7	70.0	1 : 2.33
	5	766	0.23	637	499	78.3	68.5	1 : 2.17

Acknowledgment. The authors wish to thank H. Ottmar and B. Lynch for γ -spectroscopy measurements, T. Wiss for SEM analysis, C. Scheppler, S. Birck and S. v. Winckel for ICP-MS analysis as well as M. Ougier and A. Rodrigues for experimental support. This work was carried out with the European Commission financial support in the 6th framework program, under the contract FI6W-CT-2003-408854, "EUROPART".


Ferdinand Lédée
email: ferdinand.ledee@cea.fr

Javier Mayén-Guillen

Stéphanie Lombard

Julien Zacarro

Jean-Marie Verilhac

Eric Gros-Daillon
email: eric.grosdaillon@cea.fr

Evidence for a build-in remnant field in symmetrically contacted MAPbBr 3 X-ray detectors

Keywords: X-ray detectors, halide perovskites, sensitivity, simulation, Hecht equation 1

Millimeter-thick methylammonium lead tribromide (MAPbBr3) single crystal X-ray detectors have recently raised attention due their high X-ray attenuation efficiency and good charge transport properties. However, an intriguing feature of the photocurrent response of MAPbBr3 detectors has been largely overlooked in the literature. After biaising, transient sensitivity is measured under X-rays at short-circuit (Bias = 0V), thus revealing a large remnant electric field that build-up under bias. Here, we exploit the X-ray sensitivity of MAPbBr3 detectors at zero-bias in order to probe the internal builtin field, as well as to investigate the charge transport properties of the perovskite material. Our model derived from the Hecht equation is able to fully rationalize the response of the detectors both at shortcircuit and under moderate applied bias. Moreover, we provide a method for the estimation of the internal electric field, and for the sum of the electrons and holes mobility-lifetime products 𝜇 𝑒 𝜏 𝑒 + 𝜇 ℎ 𝜏 ℎ . This general method could extend to any perovskite-based X-ray detector exhibiting transient sensitivity at zero-bias.

Introduction

Metal halide perovskites are the current key players in the field of radiation detection, challenging the performance of classical semiconductors in several applications while maintaining competitive manufacturing costs. In particular, methylammonium lead tribromide (MAPbBr3) in single crystal form is one of the most intensively studied emerging material for the direct detection of X-rays. [START_REF] Wei | Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals[END_REF]- [START_REF] Zhang | Mechanical polishing with chemical passivation of perovskite single crystals for high-performance X-ray detectors[END_REF] Despite the high quality of these as-grown single crystals, [START_REF] Saidaminov | High-quality bulk hybrid perovskite single crystals within minutes by inverse temperature crystallization[END_REF]- [START_REF] Yao | Room-temperature liquid diffused separation induced crystallization for highquality perovskite single crystals[END_REF] several features of this semiconducting material remain unexplained. Notably, in some cases the photocurrent response of MAPbBr3 seems to deviate from the Hecht model. [START_REF] Wei | Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals[END_REF], [START_REF] Wang | PIN Diodes Array Made of Perovskite Single Crystal for X-Ray Imaging[END_REF], [START_REF] Xu | High-Performance Surface Barrier X-ray Detector Based on Methylammonium Lead Tribromide Single Crystals[END_REF], [START_REF] Geng | High-Quality Single Crystal Perovskite for Highly Sensitive X-Ray Detector[END_REF] Hecht model is the most widely used model to describe the photoresponse of semiconductor-based X-rays detectors such as CdTe, CdZnTe, GaAs; and shall be applied as well to halide perovskites. [START_REF] Hecht | Zum Mechanismus des lichtelektrischen Primärstromes in isolierenden Kristallen[END_REF]- [START_REF] Bertolini | Semiconductor Detectors[END_REF] In particular for MAPbBr3, it is often applied in the form displayed in Eq. ( 2) to fit the experimental sensitivity-voltage (S-V) dataplots in order to extract the mobility-lifetime product 𝜇𝜏 of the electronic charge carriers. [START_REF] Wei | Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals[END_REF], [START_REF] Wei | Monolithic integration of hybrid perovskite single crystals with heterogenous substrate for highly sensitive X-ray imaging[END_REF], [START_REF] Song | Facile Strategy for Facet Competition Management to Improve the Performance of Perovskite Single-Crystal X-ray Detectors[END_REF], [START_REF] Tan | Characterization of solution grown 3D polycrystalline methylammonium lead tribromide for x-ray detection[END_REF] Yet, previous work from our group revealed that the X-ray photoresponse of Cr/MAPbBr3/Cr devices is not in accordance with the Hecht model. [START_REF] Guillén | MAPb(Br1-xClx)3 Hybrid Perovskite Materials for Direct X-ray Detection[END_REF] Moreover, in the recent work of Alvarez et al, it is shown that sizeable X-ray photocurrent can be measured in Cr/MAPbBr3/Cr devices in short-circuit conditions. Unlike photovoltaic-inspired devices that provide stable photocurrent output under irradiation, [START_REF] Gou | Self-Powered X-Ray Detector Based on All-Inorganic Perovskite Thick Film with High Sensitivity Under Low Dose Rate[END_REF], [START_REF] Sakhatskyi | Stable perovskite single-crystal X-ray imaging detectors with single-photon sensitivity[END_REF] the X-ray photocurrent measured in Cr/MAPbBr3/Cr photoconductors at zero-bias decays over time and follows the relaxation dynamics of the dark current. [START_REF] Alvarez | Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection[END_REF] We propose that this is the outcome of a residual electric field created upon biasing that relaxes when the bias is removed. This residual field would originate from the build-up of a space-charge when the Cr/MAPbBr3/Cr device is biased, and would result in a diminished net applied electric field under operation. The internal electric field would be responsible for the anomalies listed above, in particular the discrepancy between the experimental sensitivity-voltage (S-V) data and the Eq. ( 2). This paper aims to provide a detailed picture of the X-ray photoresponse of Cr/MAPbBr3/Cr single crystal devices under short-circuit conditions. Starting from the assumption that the residual electric field prevalent at zero-bias is also present under an externally applied bias, we developed a model derived from the Hecht model that is able to assess with great precision the internal electric field that opposes the externally applied bias under operation. In addition, we use our model to bring an alternative pathway to establish relevant intervals for the 𝜇𝜏 products in MAPbBr3-based detectors. We believe that this work sheds new light on the X-ray photoresponse of MAPbBr3 detectors; and will gives new insights into the residual charges that are formed in millimeter-thick lead halide perovskite devices under bias, as well as their aftermath on the detection performances.

Discussion on the internal electric field

In a semiconductor-based planar detector, the photocurrent measured under X-ray results from the induction of current by the photogenerated charges on the contact electrodes, also referred as the Ramo-Shockley theorem. [START_REF] Ramo | Currents Induced by Electron Motion[END_REF] The integration of the photocurrent over the X-ray pulse duration brings one of the methods that allow to estimate the sensitivity, hereby expressed in µC mGy -1 cm -2 . Without any trapping, the sensitivity reaches a maximum value and depends only on the amount of photogenerated charges in the semiconductor :

𝑆 0 = ∫ 𝑠 0 (𝑥)𝑑𝑥 (1)
With 𝑠 0 the charge generated in an elemental volume dx of the semiconductor (see Methods section).

With trapping and for a planar detector with two facing electrodes, the analytical integration of the Ramo theorem over the charge carrier lifetime τ gives the sensitivity-voltage (S-V) relationship which reads:

𝑆(𝑉) = 𝑆 0 𝜇𝜏𝑉 𝐿 2 [1 -𝑒𝑥𝑝 (- 𝐿 2 𝜇𝜏𝑉 )] (2)
With 𝑆 0 the maximum sensitivity, 𝜇 the charge carrier mobility, 𝑉 the applied bias and 𝐿 the distance between the electrodes. This relation is only valid when the following conditions are met altogether i) the energy is absorbed close to the irradiated electrode ; ii) only one type of charge carrier drifts in the device; iii) the electric field is uniform. [START_REF] Hecht | Zum Mechanismus des lichtelektrischen Primärstromes in isolierenden Kristallen[END_REF] When the photocurrent contribution from the second charge carrier type cannot be neglected, e.g. when the absorption length is not negligible with respect to 𝐿, the relation becomes a function of the depth. It translates into the two-carriers Hecht equation which reads:

𝜂(𝑥, 𝑉) = 𝜇 𝑒 𝜏 𝑒 𝑉 𝐿 2 [1 -𝑒 - 𝑥𝐿 𝜇 𝑒 𝜏 𝑒 𝑉 ] + 𝜇 ℎ 𝜏 ℎ 𝑉 𝐿 2 [1 -𝑒 - 𝐿(𝐿-𝑥) 𝜇 ℎ 𝜏 ℎ 𝑉 ] ( 3
)
Where 𝜂 is the charge induction efficiency (CIE), x is the position of creation of the charge carriers (0<x<L), and the subscripts e and h denote for electrons and holes, respectively. The S-V relationship now reads :

𝑆(𝑉) = ∫ 𝑠 0 (𝑥)𝜂(𝑥, 𝑉)𝑑𝑥 ( 4
)
With 𝑠 0 the charge generated in an elemental volume dx of the semiconductor (see Methods section). Further details on the fabrication of the detector, on the Hecht model and calculation of 𝑆 0 are provided in the Methods section.

A common approach in the research applied to perovskite X-ray detectors consists of using equation ( 2) or (4) to fit the experimental sensitivity-voltage data in order to extract a value for the mobilitylifetime product 𝜇𝜏. In most of the works, the maximum sensitivity 𝑆 0 (or the maximum induced current 𝐼 0 ) is not estimated, and thus is set as a free parameter in the Hecht fits. We propose that this produces a lot of misinterpretation of the S-V data. As an illustration, Fig. 1 displays experimental S-V curve for a MAPbBr3 single crystal planar detector fitted both with and without a calibrated and fixed 𝑆 0 value. The 𝜇𝜏 product for electrons extracted from the fit differs by almost an order of magnitude depending on the method. Furthermore, in Figure 1b, the Hecht model is not in good accordance with the experimental S-V. The experimental sensitivity measured at higher biases is lower than the value predicted with the Hecht model, and seems to plateau to a much lower value than 𝑆 0 (typically 𝑆 𝑚𝑎𝑥 = 0.25 𝑆 0 ). Here the 𝑆 0 value has been estimated using Klein's rule (W = 14/5*Eg + 0.5) [START_REF] Klein | Bandgap Dependence and Related Features of Radiation Ionization Energies in Semiconductors[END_REF], however choosing a W value equal to that experimentally determined for CsPbBr3 by He et al. does not change the result of the fit (see Fig. S1 for further details). [START_REF] He | High spectral resolution of gamma-rays at room temperature by perovskite CsPbBr3 single crystals[END_REF] Furthermore, the Many equation also fails to fit our experimental S-V data (Fig. S4). This behavior has already been observed by our group for all our MAPbBr3-based devices, as well as for various perovskite compositions. [START_REF] Guillén | MAPb(Br1-xClx)3 Hybrid Perovskite Materials for Direct X-ray Detection[END_REF] The plateau of the sensitivity to a lower 𝑆 value in MAPbBr3-based devices is overlooked in the literature because the maximum sensitivity 𝑆 0 (or 𝐼 0 ) is mostly set as a free parameters as in Fig. 1a. [START_REF] Wei | Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals[END_REF] Note that in that case, the 𝑆 0 value is not linked to any macroscopic quantity. Besides, S-V graphs are often plotted in semilog scale, which misleads the reader into thinking that the fit is better than it actually is (see Fig. S2 for an illustration). [START_REF] Wei | Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals[END_REF], [START_REF] Wei | Monolithic integration of hybrid perovskite single crystals with heterogenous substrate for highly sensitive X-ray imaging[END_REF], [START_REF] Song | Facile Strategy for Facet Competition Management to Improve the Performance of Perovskite Single-Crystal X-ray Detectors[END_REF] Remarkably, we carried out a S-V measurement adding a depolarization time (bias =0V) inbetween each bias step. Despite the relatively long (5-10 min) depolarization time and the relatively short (≈ 5s) bias pulse duration, the low 𝑆 𝑚𝑎𝑥 plateau is still present and the Hecht equation fails to fit the results (see Fig. S3 for further details). We attribute the plateau at lower 𝑆 0 value to a non-uniform electric field across the detector at higher applied bias. Several phenomena may distort the electric field, including charge trapping in the bulk of the semiconducting material [START_REF] Zanichelli | Charge collection in semi-insulator radiation detectors in the presence of a linear decreasing electric field[END_REF], surface polarization, [START_REF] Principato | Polarization phenomena in Al/p-CdTe/Pt X-ray detectors[END_REF] depletion region due to Schottky contacts [START_REF] Meng | Simulation of the Charge Collection in a Nonuniform Electric Field for MAPbI3 Semiconductor Nuclear Detector With Schottky Contact[END_REF] or ion accumulation at the vicinity of the contact electrodes. [START_REF] Jia | Ion-Accumulation-Induced Charge Tunneling for High Gain Factor in P-I-N-Structured Perovskite CH 3 NH 3 PbI 3 X-Ray Detector[END_REF] All of these potential mechanisms may lead to mis-estimation of the values of 𝜇𝜏 products in MAPbBr3-based detectors using Eq. 2. To date, the hypothesis of ion accumulation seems to be the prevailing one in the literature on perovskite detectors. [START_REF] Jia | Ion-Accumulation-Induced Charge Tunneling for High Gain Factor in P-I-N-Structured Perovskite CH 3 NH 3 PbI 3 X-Ray Detector[END_REF], [START_REF] Baussens | An insight into the charge carriers transport properties and electric field distribution of CH 3 NH 3 PbBr 3 thick single crystals[END_REF] Considering the numerous works on the migration of ionic species in MAPbBr3, [START_REF] Luo | Direct Observation of Halide Migration and its Effect on the Photoluminescence of Methylammonium Lead Bromide Perovskite Single Crystals[END_REF]- [START_REF] García-Batlle | Coupling between Ion Drift and Kinetics of Electronic Current Transients in MAPbBr3 Single Crystals[END_REF] it seems to be the most possible explanation to the best of our knowledge. Another intriguing feature of our MAPbBr3-based devices arises from the so-called bias memory effect in short-circuit conditions. As notified in previous works, after biasing, MAPbBr3 and other halide perovskites devices exhibit transient dark current relaxation with inverted sign at 0V. [START_REF] Alvarez | Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection[END_REF], [START_REF] García-Batlle | Mobile Ion-Driven Modulation of Electronic Conductivity Explains Long-Timescale Electrical Response in Lead Iodide Perovskite Thick Pellets[END_REF] In addition the dark current transient is accompanied with non-negligible sensitivity under X-rays during the relaxation window at 0V, as shown in Fig. 2(c). Notably, the sensitivity at 0V decays over time with slow dynamics akin to the dark current transient (Fig. S5). Fig. 2(d-e-f) provides a depiction of the bias memory effect. Several works suggest that upon biasing, the displacement of mobile ions toward the contact electrodes builds up a space-charge that distorts the electric field (Fig. 2d and2e). [START_REF] Baussens | An insight into the charge carriers transport properties and electric field distribution of CH 3 NH 3 PbBr 3 thick single crystals[END_REF], [START_REF] Almora | Long-Term Field Screening by Mobile Ions in Thick Metal Halide Perovskites: Understanding Saturation Currents[END_REF] Consequently the net electric field in the bulk region of the device is reduced with respect to the uniform case (dotted blue line in Fig. 2e). [19][27] In the present work, we approximate the electric field in the bulk to

V-Vi L -wi
where Vi is the potential drop associated to the space-charge formation, wi the total space-charge width. When the bias is subsequently released, the space-charge built-up by the accumulations of ions prevails and creates a residual electric field that we approximate to Vi L -wi in the bulk region (Fig. 2f). Note that during both biasing and recovery steps, we deem the electric field to be flat in the bulk region of the detector and non-uniform in the space-charge regions, in accordance with previous works. [START_REF] Alvarez | Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection[END_REF], [START_REF] Jia | Ion-Accumulation-Induced Charge Tunneling for High Gain Factor in P-I-N-Structured Perovskite CH 3 NH 3 PbI 3 X-Ray Detector[END_REF] After bias removal, the residual field during the recovery step gradually fades out as the mobile ions return to equilibrium. It should be noted again that the present work does not assume an origin for the internal electric field, which can originate from any space charge build-up in the perovskite material. Nonetheless, the migration of mobile ions provides a comprehensive picture to describe these results, as depicted in the schematics of Fig. 2d. In this picture, the dark current recovery measured at 0V would originate from an interplay between ionic and electronic currents [START_REF] Alvarez | Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection[END_REF]; and the photogenerated charge carriers may drift along the residual electric field at 0V during a characteristic recovery time, thus generating decaying photocurrent over time (Fig. 2c). Fig. 3 gives additional insights about the residual electric field for a Cr/MAPbBr3/Cr single crystal device.

For the moderate biasing time range (400-2000 seconds) and applied bias (10V) used in this experiment, the sensitivity at 10V decreases slightly over time (Fig. 3a). We attribute this to the spacecharge build-up that gradually reduces the net electric field in the bulk region of the device, with a consequent reduction of the sensitivity. [START_REF] Baussens | An insight into the charge carriers transport properties and electric field distribution of CH 3 NH 3 PbBr 3 thick single crystals[END_REF] When the bias is released, sensitivity is measured at 0V owing to the residual electric field. Notably, the sensitivity measured at 0V immediately after removing the bias is the same regardless of the biasing duration in the [400-1800s] bias duration range investigated in this work (Fig. 3a). It suggests that, for this 2-mm thick MAPbBr3 device, the spacecharge build-up is rather fast (≤400 seconds) and remains constant. Thus, the sensitivity of the device at 0V is initially the same for biasing duration ≥400s. In addition, the residual electric field varies with the applied bias. As seen in Fig 3b, the sensitivity at 0V measured immediately after removing the bias scales with the previous bias value accordingly, indicating that the space-charge build-up is a function of the applied electric field; that could indicate the drifting of mobile ionic species. [START_REF] García-Batlle | Moving Ions Vary Electronic Conductivity in Lead Bromide Perovskite Single Crystals through Dynamic Doping[END_REF], [START_REF] García-Batlle | Coupling between Ion Drift and Kinetics of Electronic Current Transients in MAPbBr3 Single Crystals[END_REF] However, we noted only a 30% increase in the residual sensitivity at 0V with bias increasing from 10V to 150V, which would suggest that most of the mobile ions have already reach the electrode for biases ≥10V and biasing duration ≥400 seconds. Markedly, this experiment could partially explain why the experimental S-V is not well fitted with the Hecht equation in Fig. 1b. Along with the rising space-charge that produces distortion of the electric field at high bias, the net electric field in the bulk is progressively reduced by the internal field build-up as the applied bias is increased. As a consequence, the net electric field in the device can be underestimated, as it will be discussed below. Finally, the dynamics of the transient sensitivity at 0V may provide further information on the mobility and the concentration of mobile ionic species in the material. This will be discussed in a future work. In the present work, we will focus on the sensitivity at 0V measured immediately after removing the bias, and develop a model that accords accurately the above-mentioned results.

Model

In the following, we propose to model the sensitivity of a 2-mm thick MAPbBr3 planar device considering the following assumptions : (i) the electric field is mainly uniform throughout the device;

(ii) an internal electric field is created upon biasing, and is equivalent to the residual electric field at 0V immediately after removing the bias ; (iii) the internal electric field opposes the externally applied electric field (see Fig. 3a). Regarding (i), the simulations carried out by Alvarez et al. show that the accumulation of mobile ions forms a depletion region at the very vicinity of the electrodes, with a depletion width only up to a few micrometers when the device is previously biased at 10V. [START_REF] Alvarez | Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection[END_REF] Besides, the electric field as function of the depth is mostly flat in the bulk, [START_REF] Alvarez | Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection[END_REF], [START_REF] Jia | Ion-Accumulation-Induced Charge Tunneling for High Gain Factor in P-I-N-Structured Perovskite CH 3 NH 3 PbI 3 X-Ray Detector[END_REF] and for a 2-mm thick device wi<<L, thus the internal field in the bulk region is approximated by Vi L (Fig. 4). We can consider a uniform electric field in the sensitivity model provided that the penetration depth of the X-rays is much greater than the depletion width. In the present case, the hard RQA5 X-rays with a high mean energy of 53 keV generate charges throughout the volume of the 2-mm thick MAPbBr3 device, as evidenced in Fig. 4c (dotted line). In addition, we limit our model to rather moderate applied bias (10V), for which the electric field distortion is limited. Finally, the assumptions (ii) and (iii) are justified by the dark current and sensitivity-time measurements displayed in Fig. 2 and Fig. 3.

Due to high penetration depth of the X-rays used in the present study, using the two-carriers Hecht equation ( 3) is compulsory. Considering the assumptions listed above, the model reads as follow. The sensitivity under bias measured a fraction of time before removing the bias writes:

𝑆(𝑉 -𝑉𝑖) = ∫ 𝑠 0 (𝑥)𝜂 𝑏𝑖𝑎𝑠 (𝑥, 𝑉 -𝑉𝑖)𝑑𝑥 ( 5)

𝜂 𝑏𝑖𝑎𝑠 (𝑥, 𝑉 -𝑉𝑖) = 𝜇 𝑒 𝜏 𝑒 (𝑉 -𝑉𝑖) 𝐿 2 [1 -𝑒 - 𝐿(𝐿-𝑥) 𝜇 𝑒 𝜏 𝑒 (𝑉-𝑉𝑖) ] + 𝜇 ℎ 𝜏 ℎ 𝑉 𝐿 2 [1 -𝑒 - 𝑥𝐿 𝜇 ℎ 𝜏 ℎ (𝑉-𝑉𝑖) ] (6)
The sensitivity at 0V measured immediately after removing the bias writes :

𝑆(𝑉𝑖) = ∫ 𝑠 0 (𝑥)𝜂 𝑠ℎ𝑜𝑟𝑡 (𝑥, 𝑉𝑖)𝑑𝑥 (7) 𝜂 𝑠ℎ𝑜𝑟𝑡 (𝑥, 𝑉𝑖) = 𝜇 𝑒 𝜏 𝑒 𝑉𝑖 𝐿 2 [1 -𝑒 - 𝑥𝐿 𝜇 𝑒 𝜏 𝑒 𝑉 ] + 𝜇 ℎ 𝜏 ℎ 𝑉𝑖 𝐿 2 [1 -𝑒 - 𝐿(𝐿-𝑥) 𝜇 ℎ 𝜏 ℎ 𝑉𝑖 ] ( 8
)
Where V is the externally applied bias, 𝑉𝑖 is the potential associated to the internal electric field = 𝑉𝑖 𝐿 , 𝜂 𝑏𝑖𝑎𝑠 is the CIE before removing the bias and 𝜂 𝑠ℎ𝑜𝑟𝑡 is the CIE after removing the bias and x is the position of interaction of the X-ray in the MAPbBr3 device. Note that the equations ( 6) and ( 8) correspond to the case where a positive bias is applied to the irradiated electrode. For a 2-mm thick MAPbBr3 device and borderline hard ~50 keV X-rays, the response in biasing conditions is slightly dominated by hole transport (Fig. 4a), and the response in short-circuit conditions is slightly dominated by electron transport (Fig. 4b). Fig. 4c displays the results of the model calculation for the following input parameters : 𝜇 𝑒 𝜏 𝑒 = 1.10 -4 cm 2 V -1 ; 𝜇 ℎ 𝜏 ℎ = 2.10 -4 cm 2 V -1 ; L = 0.2 cm ; V = 10V ; Vi = 1V. It can be seen that the total induced charge under X-rays -or in other word, the sensitivity S -is close to the experimental value shown in Fig. 3a (S ≈ 0.2 µC mGy -1 cm -2 at 10V and S ≈ 0.02 µC mGy -1 cm -2 at 0V). Notably, it implies that the internal electrical field at 10V could be as high as 5 V/cm ; which corresponds to 10 percent of the externally applied electric field (50 V/cm). It indicates that there could be a 10% uncertainty on the value of the applied bias that could partially explain the discrepancy between the S-V plot and the Hecht model, as depicted in Fig. 1b.

Results and discussion

In this part, it will be demonstrated how the model allows to estimate precisely the internal electric field in a Cr/MAPbBr3/Cr planar device, as well as reasonable ranges for the 𝜇 𝑒 𝜏 𝑒 and 𝜇 ℎ 𝜏 ℎ products.

The set of equation (5-8) has 3 unknown parameters : 𝜇 𝑒 𝜏 𝑒 ; 𝜇 ℎ 𝜏 ℎ and 𝑉𝑖. Only two experimental measurement of sensitivity are used as inputs for the model : S at 10V before removing the bias, and S at 0V immediately after removing the bias. Hence it may provide only a set of solution (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ,𝑉𝑖). Nonetheless, we will see that the set of possible solution is limited and allow to establish a credible range for the above cited parameters.

The model was applied to the measurements displayed in Fig. 3a for a MAPbBr3 single crystal planar device with 2-mm thickness, 5 x 5 mm² chromium electrodes and RQA5 X-rays. The picture of the device is shown in Fig. 2a. Further details on the fabrication of the device and the experimental setup are supplied in the Methods section. The experimental measurement of sensitivity gives : S(10-Vi) = 0.17 µC mGy -1 cm -2 and S(Vi) = 0.021 µC mGy -1 cm -2 . We calculated all the possible (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ,𝑉𝑖) for which S(10-Vi) and S(Vi) are both equal to the above cited values at the same time. The Fig. 5a. displays the results of the calculation in the (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ) space. For all Vi, S(10-Vi) and S(Vi) form two straight lines that only cross for a limited number of Vi values ranging from 0.9 V to 1.2 V. The intersection of the two S(10-Vi) and S(Vi) lines implies that it exists a set of (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ,𝑉𝑖) that allows to fully describe the experimental sensitivity measured under X-ray, or in other word, it provides a solution of the equation system. Hence, all the possible solutions (intersections) for this experiment are displayed in or is equal to 5.1 V/cm with 15% uncertainty. Regarding the possible values for (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ), the range of solutions is much broader. 𝜇 𝑒 𝜏 𝑒 spans from 5 x 10 -6 cm 2 V -1 to 3 x 10 -4 cm 2 V -1 and 𝜇 ℎ 𝜏 ℎ spans from 1 x 10 -7 cm 2 V -1 to 2.5 x 10 -4 cm 2 V -1 . The uncertainty on the individual 𝜇 𝑒 𝜏 𝑒 and 𝜇 ℎ 𝜏 ℎ values is therefore very high with this model. Nonetheless, more notable is the fact that this experiment computes quite precisely a value for the sum 𝜇 𝑒 𝜏 𝑒 + 𝜇 ℎ 𝜏 ℎ , as displayed by the linear fit in Fig. 5b. All of these solutions are aligned, and the sum 𝜇 𝑒 𝜏 𝑒 + 𝜇 ℎ 𝜏 ℎ has a near constant value of ~2.5 x 10 -4 cm 2 V -1 . Here, the range of solutions is a straight line because we are dealing with small electric fields, which means that the mean free path of the charge carriers is small compared to the thickness of the device. In that peculiar case, the exponential term in the Hecht equation becomes negligible, and the CIE becomes

≃ 𝜇 𝑒 𝜏 𝑒 𝑉 𝐿 2 + 𝜇 ℎ 𝜏 ℎ 𝑉 𝐿 2 = (𝜇 𝑒 𝜏 𝑒 +𝜇 ℎ 𝜏 ℎ )𝑉 𝐿 2
. Substituting this into equation 7 gives 2.6 x 10 -4 cm 2 V -1 for Vi =1V, which is consistent with the above results. The information on the sum 𝜇 𝑒 𝜏 𝑒 + 𝜇 ℎ 𝜏 ℎ provides new insights into the charge transport properties of the material. Using other complementary measurements, it is then possible to fully rationalize the transport of the material. For instance, the rather symmetric S-V plot displayed in Fig. 1. indicate that the respective 𝜇 𝑒 𝜏 𝑒 and 𝜇 ℎ 𝜏 ℎ values probably have the same order of magnitude. Otherwise, the S-V data would be very asymmetrical for the X-ray exposure conditions and device thickness used in this work. (see supplementary Fig. S6). This is consistent with photocurrent measurements made under the AM-241 source, which indicate that the 𝜇 𝑒 𝜏 𝑒 and 𝜇 ℎ 𝜏 ℎ could be separated only by a factor of 2. [START_REF] Bennett | Charge transport comparison of FA, MA and Cs lead halide perovskite single crystals for radiation detection[END_REF], [START_REF] Liu | Charge Transport Behavior in Solution-Grown Methylammonium Lead Tribromide Perovskite Single Crystal Using α Particles[END_REF] Fig. 5. Calculations of the (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ,𝑉𝑖) solutions for S(10-Vi) = 0.17 µC mGy -1 cm -2 (solid lines) and S(Vi) = 0.021 µC mGy -1 cm -2 (dash lines). To assess the robustness of the method, we simulated the response of MAPbBr3 devices for hypothetical (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ,𝑉𝑖) and thickness values. Several of these simulations are displayed in Fig. 6. Remarkably, we noticed that it does not seem to exist a case where the two S(10-Vi) and S(Vi) lines doesn't cross in one point in the (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ) space for a single Vi value. As seen in Fig. 6a and 6b, the lines are almost parallel when the (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ) values are moderate (≤ 1 x 10 -4 cm 2 V -1 ). When the charge transport is better (≈ 1 x 10 -3 cm 2 V -1 ) as in Fig 6c, the model still provides a single solution for a single Vi value. In the latter case however, the S(V-Vi) line is no longer parallel to the S(Vi) line. It implies that the error on Vi is much higher than in the moderate charge transport case since the position of the S(Vi) line varies sizably with the Vi value (Fig. 6a-b). It can be understood by considering that high sensitivity increases the total number of possible solutions for the model. If the transport is high, the sensitivity is high accordingly, and the model struggles to resolve accurately a value for Vi. If such a case were to be met, a quick fix would consist of reducing the applied bias V in order to reduce the charge carrier mean free path. As seen in Fig. 6d, it results in a reduction of the curvature of the S(V-Vi), and an increased precision on the estimation of Vi. In addition, having straight S(V-Vi) and S(Vi) lines is associated to a low mean free path for the charge carriers, which allows to establish accurately a value of the sum 𝜇 𝑒 𝜏 𝑒 + 𝜇 ℎ 𝜏 ℎ (see Fig. 5b). Lowering the bias during the biasing step to reduce the mean free path is thus interesting to increase the precision for both the internal potential Vi, and the sum of the mobility lifetime products 𝜇 𝑒 𝜏 𝑒 + 𝜇 ℎ 𝜏 ℎ .

5.0x10 -6

1.0x10 -5 1.5x10 -5 2.0x10 -5 0.0 5.0x10 -6

1.0x10 -5

1.5x10 -5

2.0x10 -5 5.0x10 -5 1.0x10 -4 1.5x10 -4 2.0x10 -4 0.0 5.0x10 -5

1.0x10 -4

1.5x10 -4

2.0x10 -4 5.0x10 -4 1.0x10 -3 1.5x10 -3 2.0x10 -3 0.0 5.0x10 -4

1.0x10 -3

1.5x10 -3

2.0x10 -3 5.0x10 -4 1.0x10 -3 1.5x10 -3 2.0x10 -3 0.0

5.0x10 -4 1.0x10 -3 1.5x10 -3 2.0x10 -3 V = 10V Vi = 1V mt hole (cm 2 V -1
)

mt electron (cm 2 V -1 )
solutions S(V-Vi) solutions S(Vi)

m t e = 1.10 -5 cm 2 V -1 m t h = 1.10 -5 cm 2 V -1

mt hole (cm 2 V -1
)

mt electron (cm 2 V -1 )
solutions S(V-Vi) solutions S(Vi)

m t e = 1.10 -4 cm 2 V -1

m t h = 1.10 -4 cm 2 V -1 V = 10V Vi = 1V mt hole (cm 2 V -1
)

mt electron (cm 2 V -1 )
solutions S(V-Vi) solutions S(Vi)

m t e = 1.10 -3 cm 2 V -1

m t h = 1.10 -3 cm 2 V -1 V = 10V Vi = 1V mt hole (cm 2 V -1
)

mt electron (cm 2 V -1 )
solutions S(V-Vi) solutions S(Vi)

m t e = 1.10 -3 cm 2 V -1 6. Calculation of the S(V-Vi) and S(Vi) lines for different (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ,𝑉𝑖) input values. The thickness of the device is 2 mm. The intersection of the S(V-Vi) and S(Vi) lines provides the solution of the equation system.

m t h = 1.10 -3 cm 2 V -1 V = 3V Vi = 0.3V (a) (b) (d) (c) Fig.
Finally, we can use this model to estimate an order of magnitude for the space-charge density generated upon biasing. First, we considered the parallel plate capacitor approximation which reads Q = C × V and 𝑄 = 𝜀𝜀 0 𝑆 𝐿 with Q the charge, C the capacity, 𝜀 the relative permittivity of the perovskite, 𝜀 0 the vacuum permittivity, 𝑆 the electrode surface area and 𝐿 the device thickness. From the Fig. 5, we can assume a value for Vi ≈ 1V, corresponding to a charge of 50 nC. If we assume that this charge was extracted from the bulk of the crystals, e.g. via migration of charged ionic species, and that the totality of the charges reached the electrode, we can establish that the charge density in the bulk was initially 1 µC cm -3 . Now if we consider that this charge originate from moving ionic species, it would represent a density of 10 +13 ions cm -3 , which is in accordance with ionic concentrations previously measured in similar MAPbBr3 single crystal devices. [START_REF] Alvarez | Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection[END_REF], [START_REF] Duijnstee | Understanding Dark Current-Voltage Characteristics in Metal-Halide Perovskite Single Crystals[END_REF]

Conclusion

In this paper, we provide robust experimental evidences for the presence of an internal electric field in Cr/MAPbBr3/Cr X-ray detectors that builds up upon biasing. This internal electric field generates a significant but decaying response under X-rays at 0V; and diminish the net electric field in the device under bias. We propose that the discordance between the experimental S-V plots and the Hecht model is due to the internal electric field that alters the S-V relationship. Starting from a modified version of the Hecht equation, we developed a model for the sensitivity that involves an internal electric field with opposed sign to the externally applied electric field. We found that the model can accurately predict a value for the internal electric field, even without prior information about the charge transport properties of the material. Notably, the actual internal electric field in the bulk of our 2-mm MAPbBr3 device could be overestimated by about 10% at 50V/cm. In addition, we exploit our model as an alternative pathway for the evaluation of the 𝜇 𝑒 𝜏 𝑒 and 𝜇 ℎ 𝜏 ℎ products, and more precisely for the sum 𝜇 𝑒 𝜏 𝑒 + 𝜇 ℎ 𝜏 ℎ . We believe that our model rationalize some intriguing electrical properties of MAPbBr3 detectors under bias such as dark current relaxation and zero-bias sensitivity; and could be extended to other perovskite composition exhibiting dark current relaxation at zero-bias such as CH3NH3PbI3 and CsPbBr3. [START_REF] García-Batlle | Mobile Ion-Driven Modulation of Electronic Conductivity Explains Long-Timescale Electrical Response in Lead Iodide Perovskite Thick Pellets[END_REF], [START_REF] Zhang | Defect proliferation in CsPbBr3 crystal induced by ion migration[END_REF] Future work will bring further information on the remnant charge density in the MAPbBr3 material by exploiting the dynamics of sensitivity decay at zero-bias.

Methods Device Fabrication

Millimeter-sized methylammonium lead tribromide (MAPbBr3) single crystals were grown using the Modified Inverse Temperature Crystallization (MITC) method described in details in previous works. [START_REF] Amari | Optimization of the Growth Conditions for High Quality CH 3 NH 3 PbBr 3 Hybrid Perovskite Single Crystals[END_REF], [START_REF] Guillén | MAPb(Br1-xClx)3 Hybrid Perovskite Materials for Direct X-ray Detection[END_REF], [START_REF] Alvarez | Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection[END_REF] Briefly, the precursor solutions were prepared in an argon-filled glovebox by dissolving PbBr2 (ultra dry, 99.999 % metal basis) and MABr (≥99 %) in anhydrous N,N-Dimethylformamide with 1:1 molar ratio. The growth was carried out using a crystal seed, as described in [START_REF] Amari | Optimization of the Growth Conditions for High Quality CH 3 NH 3 PbBr 3 Hybrid Perovskite Single Crystals[END_REF]. Both the large facets of the crystals were mechanically polished with SiC disks and isopropanol, then with fabric disks and diamond paste in order to obtain a mirror grade quality. 100-nm Cr electrodes were subsequently thermally evaporated on both facets. We found that proper polishing and chromium electrodes enhance the electrical stability of the devices under bias, as also noted in previous works. [START_REF] Tan | Characterization of solution grown 3D polycrystalline methylammonium lead tribromide for x-ray detection[END_REF], [START_REF] Tan | Improved Radiation Sensing with Methylammonium Lead Tribromide Perovskite Semiconductors[END_REF]

X-ray characterization

Dark current and sensitivity measurements were conducted on the same setup using a Keithley 428 current amplifier and a Keithley 487 power supply. The samples were irradiated with short X-ray pulses (4 Hz repetition rate, 100 ms duration) using a medical-grade pulsed X-ray tube with tungsten anode and 70 kVp accelerating voltage. The incident X-rays were filtrated through a 0.8 mm beryllium window and 23.5 mm additionnal aluminium filters to yield a RQA5 spectrum, following the IEC 62220 International Standard. The incident dose was calibrated with a PTW Unidos dosimeter, yielding 24 ± 0.6 µGyair per pulse. The X-rays were collimated through a 12.6 mm² hole pierced in a ≈5mm-thick lead plate. Due to long-range diffusion of the X-ray generated charge carriers in the area not covered by the electrodes, the collimation is necessary to properly evaluate the absorption surface area of the incident X-rays, hence the sensitivity. Each sensitivity measurement consisted of 10 X-ray pulses that were averaged to reduce experimental error (see Fig. S7). Typical uncertainty on the sensitivity measurement was 3%.

Numerical simulation

The elemental charge deposited in the MAPbBr3 material 𝑠 0 and the maximum theoretical sensitivity 𝑆 0 were calculated using Eq. 9 and Eq. 10 that read: 𝑆 0 (𝑥) = 𝑒 × 𝐸 * (𝑥) 𝑊 ± [START_REF] Amari | Optimization of the Growth Conditions for High Quality CH 3 NH 3 PbBr 3 Hybrid Perovskite Single Crystals[END_REF] 𝐸 * (𝑥) = ∫ 𝑁(𝐸) × 𝐸 × 𝐴(𝑥, 𝐸) 𝑑𝐸 [START_REF] Yao | Room-temperature liquid diffused separation induced crystallization for highquality perovskite single crystals[END_REF] Where e is the elemental charge ; 𝐸 * is the energy deposited by the X-rays in the perovskite material (Fig. S8), 𝑊 ± is the electron-hole pair creation energy that was calculated using Klein's rule 𝑊 ± = 14 5 𝐸 𝑔 + 0.5 with 𝐸 𝑔 = 2.3 eV [START_REF] Guillén | MAPb(Br1-xClx)3 Hybrid Perovskite Materials for Direct X-ray Detection[END_REF], [START_REF] Klein | Bandgap Dependence and Related Features of Radiation Ionization Energies in Semiconductors[END_REF] ; 𝐷 is the dose per surface area ; 𝑁 is the number of incident photon emitted by the X-ray tube as function of photon energy 𝐸; 𝐴 is the absorbed fraction as function of the position of interaction of the X-rays in the MAPbBr3 device. The latter is computed as for Eq. 11 :

𝐴(𝑥, 𝐸) = 𝑇(𝑥, 𝐸) -𝑇(𝑥 + 𝑑𝑥, 𝐸) = 𝑒 -𝜎(𝐸)𝜌𝑥 -𝑒 -𝜎(𝐸)𝜌(𝑥+𝑑𝑥) [START_REF] Hecht | Zum Mechanismus des lichtelektrischen Primärstromes in isolierenden Kristallen[END_REF] Where 𝑇 is the transmitted fraction; 𝜎 is the photon cross section; 𝜌 is the density (3.8 g cm -3 for MAPbBr3) [START_REF] Weber | CH3NH3PbX3, ein Pb(II)-System mit kubischer Perowskitstruktur / CH3NH3PbX3, a Pb(II)-System with Cubic Perovskite Structure[END_REF]. The photon cross section was obtained from NIST photon cross sections database considering only the photoelectric interaction, assuming that it is the predominant interaction mechanism in the 20-70 keV energy range for MAPbBr3. [START_REF]XCOM: Photon Cross Sections Database[END_REF] The number of incident photon𝑠 𝑁 was computed for a RQA5 spectrum using the SpekCalc software. [START_REF] Poludniowski | Calculation of x-ray spectra emerging from an x-ray tube. Part I. Electron penetration characteristics in x-ray targets[END_REF]- [START_REF] Poludniowski | SpekCalc : a program to calculate photon spectra from tungsten anode x-ray tubes[END_REF] It is given as function of incident X-ray dose in mGyair and per unit area (Fig. S9).

Fig. 1 .

 1 Fig. 1. Sensitivity-voltage plots of a MAPbBr3 device with corresponding two-carriers Hecht fits with (a) S0 set as a free parameter and (b) S0 set as the total charge generated in the device. See Methods for more details on the calculation of S0.

Fig. 2 .

 2 Fig. 2. (a) Microscope picture of a typical Cr/MAPbBr3/Cr single crystal device used in this study. (b) Schematic of the X-ray irradiation setup. (c) Dark current (black curve) and sensitivity-time (red curve) measurements during both biasing et recovery steps. (d-e-f) Proposed model for the electric field profile in the depth of the device during the experiment. The electric field is supposed linear in the bulk and is approximated by V-Vi L -wi during the biasing step (e), and Vi L -wi during the recovery step (f).

Fig. 3 .

 3 Fig. 3. (a) Sensitivity-time measurements for different biasing duration at +10V (b) Sensitivity measured immediately after removing the bias for different previously applied bias. The biasing duration is 400 seconds. Blue dotted line is an eye guideline.

Fig. 4 .

 4 Fig. 4. Schematics of the device during (a) the biasing condition and (b) the short-circuit condition. The internal and external electric fields are deemed uniform throughout the device (c) Results of the calculation. Blue and red lines are the CIE as function of distance at 10V and 0V respectively. Black dotted line is the photogenerated charge. The x-axis is the distance in the device from the irradiated electrode (x=0) to the back electrode (x=L=2mm). Calculated for RQA5 X-rays.

Fig. 5b .

 5b Fig. 5b. It allows us to establish that the internal electric field 𝐸𝑖 = 𝑉𝑖 𝐿 is in the range [4.4 -5.6] V/cm,

  Fig.5. Calculations of the (𝜇 𝑒 𝜏 𝑒 , 𝜇 ℎ 𝜏 ℎ ,𝑉𝑖) solutions for S(10-Vi) = 0.17 µC mGy -1 cm -2 (solid lines) and S(Vi) = 0.021 µC mGy -1 cm -2 (dash lines). (a) S(10-V) and S(Vi) lines as function of Vi. Each color corresponds to a different Vi input value. (b) Intersections of the S(10-V) and S(Vi) lines with Vi varying from 0.85 to 1.2V.

Acknowledgement

This work has received funding from the European Union's Horizon 2020 research and innovation program under the Photonics Public-Private Partnership (www.photonics21.org) with the project PEROXIS under grant agreement N° 871336.

Data Availability Statement

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Supplementary Material

The Supplementary Material is available free of charge at: Additionnal Hecht equation fitting plots, computations of the energy deposited by the X-rays and the number of incident photons, examples of X-ray-induced photocurrent pulses under bias and at shortcircuit.

Author Declaration section

Conflict of Interest Statement

The authors have no conflicts to disclose.

Author Contributions

F.L.: conceptualization, X-ray characterizations, computations, writing-original draft ; J.M-G. and S.L.: crystal growth, device fabrication ; J.Z. and J-M.V.: investigations, writing-review and editing , project administration ; E.G.-D.: conceptualization, methodology, writing-review and editing.


72 pt 1 in 25.4 mm 54 pt 0.75 in 19.1 mm 54 pt 0.75 in 19.1 mm 54 pt 0.75 in 19.1 mm

Clinical Relevance-This project is aimed to allow chronic patients to be treated in a personalized, painless and reliable manner. For instance, it would provide diabetics with a wearable device delivering a specific flow of insulin throughout the day.

I. INTRODUCTION

TDD is nowadays mostly used for topical applications such as local anesthesia. To provide a reliable wearable TDD device suitable for a broad range of drugs, the combination of MN and ITP was studied. MN are used as a painless way to perforate the outer layer of the epidermis, the stratum corneum (SC), creating a pathway for the drug to diffuse. This would not only allow heavy molecules to cross the skin barrier, but also increase reproducibility as SC irregularities like hairs or scars are avoided. ITP is used in addition to accelerate ionic diffusion by applying a small current, i.e. < 0.5mA/cm² [START_REF] Sylvestre | Iontophoresis of dexamethasone phosphate: Competition with chloride ions[END_REF], on screen-printed Ag/AgCl electrodes. The distance between anode and cathode can be adjusted for deeper migration which is an advantage for systemic applications.

II. METHODS

Injection-molded PLLA hollow microneedles were provided by Yamada Seiko, Japan.). They will be filled with a FITC-BSA solution (Merck, Germany). Compression tests were performed on skin models (50N, TAXT Plus Texturometer, UK) and penetration depths were measured by optical microscopy (Keyence VHX-7000, Japan).

Iontophoresis electrodes were screen-printed on Thermoplastic Polyurethane (TPU) with a set of silver, silver/silver chloride, carbon and dielectric inks (Creative Materials and Dupont, US). Silver and silver chloride particles distribution was observed and quantified by Scanning Electron Microscopy (SEM) coupled with Energy Dispersive X-ray (EDX) analysis (Zeiss Merlin, Germany), before, during and after drug delivery.

The diffusion of FITC-BSA will be compared as described in Figure 1. The amount of diffused FITC-BSA will be quantified by fluorimetry (Tecan Infinite M1000, Switzerland). However, a series of preliminary experiments were required beforehand such as the preparation of skin M. Rafie Jirdehi is with the University Grenoble Alpes, CEA LITEN/DTNM and LETI/DTBS, F-38000 Grenoble, France. Phone: +33438786450; e-mail: mehrsa.rafiejirdehi@cea.fr models or FITC calibration curves. As for iontophoresis, different electrodes lifetime and reproducibility were compared by chronopotentiometry (PalmSens, Netherlands) in an electrochemical cell filled with Phosphate Saline Buffer (PBS) 1X (diluted from PBS 10X, Merck, Germany).

III. RESULTS

MN arrays were tested on different mechanical skin models. It has been shown that gelatin/glycerol formulations give smaller penetration depths after MN removal, mimicking skin elastic response unlike clay for instance. These results help choosing an accurate skin model but also adjusting microneedles lengths for an effective yet painless drug delivery. As for ITP electrodes, the experimental setup was first simulated (COMSOL Multiphysics, Sweden) to validate the electrode design by visualising electric field lines or the current density distribution. Later on, chronopotentiometry measurements such as those shown in Figure 2 were performed to select the most long-lasting electrodes. SEM/EDX analyses infer that the reaction is limited by silver, whose available surface must be maximized in order to extend electrodes lifetime.

IV. DISCUSSION & CONCLUSION

Both ITP and MN are drug delivery technologies of medical interest and number of patents has been filed in this regard. A deeper understanding of the ITP electrochemical mechanism is necessary, as many commercialized devices have been withdrawn from the market [START_REF] Bakshi | Iontophoretic Skin Delivery Systems: Success and Failures[END_REF]. ITP and MN combination is a promising challenge for heavy molecules that are not yet considered suitable for TDD, which is why insulin will eventually be used in drug delivery experiments. Such device would be life-changing for children or chronic patients for whom treatments are constraining to take.

Novel technologies for transdermal delivery of active molecules

Rafie Jirdehi M., Jary D., Revaux A., CEA Grenoble, France

  Margin requirements for first page Paper size this page US Letter  Abstract-This PhD project is willing to develop a prototype of wearable device combining two transdermal drug delivery (TDD) technologies: iontophoresis (ITP) and microneedles (MN). ITP was used as an active delivery technique helping heavy molecules migrate faster and deeper through the effect of a small current. Injection molded poly-L-lactic acid (PLLA) hollow MN were placed on top of the positive electrode. Fluorescein isothiocyanate-labelled bovine serum albumin (FITC-BSA) was used as a drug model and followed by fluorimetry. For both ITP electrodes and MN, fabrication processes involved are suitable for industrial scale-up.

Figure 2 Figure 1 .

 21 Figure 2. Lifetime comparison of iontophoresis electrodes depending on the chosen ink or surface modification. The plateau aroung 1.7V corresponds to the electrolysis of water that takes places once the Ag/AgCl reaction is over