Marius Huguet

Véronique Raimond

Emmanuelle Kaltenbach

Vincent Augusto

Lionel Perrier
email: lionel.perrier@lyon.unicancer.fr

How much does the hospital stay for infusion of anti-CD19 CAR-T cells cost to the French National Health Insurance? Coût du séjour hospitalier lié à l'injection de CAR-T anti-CD19 pour l'Assurance Maladie

Keywords: Cancer, CAR-T cell, Costs, Leukemia, Lymphoma, France Cancer, CAR-T Cell, Coûts, Leucémie, Lymphome, France

Chimeric antigen receptor T-cells (CAR-T cells) have the potential to be a major innovation as a new type of cancer treatment, but are associated with extremely high prices and a high level of uncertainty. This study aims to assess the cost of the hospital stay for the administration of anti-CD19 CAR-T cells in France. Data were collected from the French Medical Information Systems Program (PMSI) and all hospital stays associated with an administrated drug encoded 9439938 (tisagenlecleucel, Kymriah®) or 9440456 (axicabtagene ciloleucel, Yescarta®) between January 2019 and December 2020 were included. 485 hospital stays associated with an injection of anti-CD19 CAR-T cells were identified, of which 44 (9%), 139 (28.7%), and 302 (62.3%) were for tisagenlecleucel in acute lymphoblastic leukaemia (ALL), tisagenlecleucel in diffuse large B-cell lymphoma (DLBCL), and axicabtagene ciloleucel respectively. The lengths of the stays were 37.9, 23.8, and 25.9 days for tisagenlecleucel in ALL, tisagenlecleucel in DLBCL, and axicabtagene ciloleucel, respectively. The mean costs per hospital stay were €372,400 for a tisagenlecleucel in ALL, €342,903 for tisagenlecleucel in DLBCL, and €366,562 for axicabtagene ciloleucel. CAR T-cells represented more than 80% of these costs. N = 13 hospitals performed CAR-T cell injections, with two hospitals accounting for more than 50% of the total number of injections. This study provides original data in a context of limited information regarding the costs of hospitalization for patients undergoing CAR-T cell treatments. In addition to the financial burden, distance may also be an important barrier for accessing CAR T-cell treatment.

Introduction

Extensive in-depth research has led to the development of chimeric antigen receptor T cells (CAR-T cells), which are engineered human T cells with modified T-cell receptors for use in immunotherapy [START_REF] Anderson | A review of chimeric antigen receptor T-cells in lymphoma[END_REF][START_REF] Andrea | Engineering next-generation car-t cells for better toxicity management[END_REF][START_REF] Dunbar | Gene therapy comes of age[END_REF][START_REF] Mohty | CAR T-cell therapy for the management of refractory/relapsed high-grade B-cell lymphoma: a practical overview[END_REF]. They have the potential to be a major therapeutic development, especially for the treatment of blood cancers [START_REF] Beyar-Katz | Advances in chimeric antigen receptor T cells[END_REF][START_REF] Chicaybam | Overhauling car t cells to improve efficacy, safety and cost[END_REF]. However, management of the associated toxicities is essential to reduce the morbidity and mortality [START_REF] Shpall | Chimeric antigen receptor[END_REF]. Indeed, cytokine release syndrome can occur in up to 100% of cases with some CD19-targeted CAR-T cells, whereas neurotoxicities have been reported to occur in up to 61 and 67 percent of patients with lymphoma and leukemia, respectively [START_REF] Siegler | Neurotoxicity and Cytokine Release Syndrome After Chimeric Antigen Receptor T Cell Therapy: Insights Into Mechanisms and Novel Therapies[END_REF]. Although the toxicities remain very substantial, tisagenlecleucel (Kymriah®, Novartis) and axicabtagene ciloleucel (Yescarta®, Gilead) are the first CAR-T cells to obtain marketing authorization in the US in 2017, and one year later for European countries. In France, the early access program "temporary use authorization" has even made it possible to make tisagenlecleucel and axicabtagene ciloleucel available to patients prior to the European Medicines Agency's marketing authorization [START_REF] Jorgensen | Outcomes-based reimbursement for gene therapies in practice: the experience of recently launched CAR-T cell therapies in major European countries[END_REF][START_REF] Rémuzat | Market access pathways for cell therapies in France[END_REF]. The Transparency Committee from the French authority for health (HAS) rated (i) tisagenlecleucel as having a substantial medical benefit (SMR) and a moderate added medical benefit (ASMR III) in refractory B-cell acute lymphoblastic leukemia (ALL) that has relapsed after transplantation, or after the second or later relapses in young adult patients up to the age of 25 years; and a substantial medical benefit and a minor added medical benefit (ASMR IV) in third-line or later treatment of refractory or recurrent diffuse large B-cell lymphoma (DLBCL); (ii) axicabtagene ciloleucel as having a substantial medical benefit and a moderate added medical benefit (ASMR III) for diffuse large B-cell lymphoma and relapsed or refractory primary mediastinal large B-cell lymphoma in third-line or more [START_REF]Kymriah® ( Tisagenlecleucel ) Lymphome diffus à grandes cellules B -Avis de la Commission de la Transparence[END_REF][START_REF]Haute Autorité de Santé. Kymriah® ( Tisagenlecleucel ) Leucémie aigue lymphoblastique -Avis de la Commission de la Transparence[END_REF][START_REF]YESCARTA ® (Axicabtagene ciloleucel)-Avis de la Commission de la Transparence[END_REF]. Several published economic evaluations have been conducted in order to determine the costs and the efficiency of these innovations [START_REF] Sarkar | Cost-Effectiveness of Chimeric Antigen Receptor T-Cell Therapy in Pediatric Relapsed/Refractory B-cell Acute Lymphoblastic Leukemia[END_REF][START_REF] Thielen | Cost-Effectiveness of Anri-CD19 chimeric antigen receptor T-Cell therapy in pediatric relapsed/refractory B-cell acute lymphoblastic leukemia. A societal view[END_REF][START_REF] Schmitt | Comments on "Cost of decentralized CAR T cell production in an academic non-profit setting[END_REF][START_REF] Ran | Reply to: Comments on "Cost of decentralized CAR T cell production in an academic non-profit setting[END_REF][START_REF] Yadav | CAR T cell therapy: newer approaches to counter resistance and cost[END_REF][START_REF] Flowers | What can cost-effectiveness analysis tell us about chimeric antigen receptor T-cell therapy for relapsed acute lymphoblastic leukemia?[END_REF][START_REF] Lin | Cost effectiveness of chimeric antigen receptor T-cell therapy in multiply relapsed or refractory adult large B-cell lymphoma[END_REF][START_REF] Lyman | Economic Evaluation of Chimeric Antigen Receptor T-Cell Therapy by Site of Care Among Patients With Relapsed or Refractory Large B-Cell Lymphoma[END_REF][START_REF] Harrison | Chimeric antigen receptor-T cell therapy manufacturing: modelling the effect of offshore production on aggregate cost of goods[END_REF][START_REF] Ran | Cost of decentralized CAR T-cell production in an academic nonprofit setting[END_REF][START_REF] Hernandez | Accounting for All Costs in the Total Cost of Chimeric Antigen Receptor T-Cell Immunotherapy-Reply[END_REF][START_REF] Roth | Cost-effectiveness of axicabtagene ciloleucel for adult patients with relapsed or refractory large B-cell lymphoma in the United States[END_REF]. They mostly report that these treatments are cost-effective, even though the French Economic and Public Health Committee (CEESP, French Authority for Health), as well as the National Institute for Health and Care Excellence (NICE) in the United Kingdom, have expressed several reservations, especially a high degree of uncertainty due to the short period of follow-up [START_REF] Jorgensen | Outcomes-based reimbursement for gene therapies in practice: the experience of recently launched CAR-T cell therapies in major European countries[END_REF][START_REF]AVIS D'EFFICIENCE : Kymriah® ( Tisagenlecleucel ) Leucémie aigue lymphoblastique[END_REF][START_REF]AVIS D'EFFICIENCE : Kymriah® ( Tisagenlecleucel ) Lymphome diffus à grandes cellules B[END_REF][START_REF]AVIS D'EFFICIENCE : YESCARTA® (axicabtagene ciloleucel)[END_REF]. Thus, there is a clear need for additional evidence based on observational data regarding the costs and consequences of CAR-T cell treatments. Additionally, these products are expensive, even though the estimated research and development costs have been shared between public and private payers [START_REF] Prasad | Tisagenlecleucel -The first approved CAR-T-cell therapy: Implications for payers and policy makers[END_REF]. Moreover, as mentioned by J.

Jørgensen, there is limited European data on the cost of hospitalization for patients treated with CAR-T cell therapies [START_REF] Jorgensen | Outcomes-based reimbursement for gene therapies in practice: the experience of recently launched CAR-T cell therapies in major European countries[END_REF]. In this context, the aim of this study was to assess the costs of the hospital stay for infusion of anti-CD19 CAR-T cells and to explore the geographic distribution of patients and hospitals in France. Our contribution to the literature stems in part from the use of a nation-wide administrative dataset, which allows us to describe the costs associated with the administration of anti-CD19 CAR-T cells for the French National Health Insurance, and the geographical breakdown of patients and hospitals using real-world data.

Method

In this study, we identified three populations of interest (i.e., patients treated with tisagenlecleucel for ALL, tisagenlecleucel for DLBCL, or axicabtagene ciloleucel), by using hospital discharge data from the French Medical Information Systems Program (PMSI), managed by the government agency Agence Technique de l'Information sur l'Hospitalisation (ATIH).

The PMSI is an exhaustive nationwide database that records information about each hospital stay in France [START_REF] Boudemaghe | Data resource profile: The French national uniform hospital discharge data set database (PMSI)[END_REF]. Each observation in the PMSI corresponds to a hospital stay, which is composed of one or more Medical Unit Summaries. Indeed, a Medical Unit Summary is produced at the end of each patient's stay in a medical unit providing medical, surgical, obstetrical, and dental care. These summaries contain administrative and medical information, coded according to standardized nomenclatures and classifications to allow automated processing. Thus, we also recorded the number of medical unit summaries for the hospital stay, as well as the number of medical procedures performed during the hospital stay. To identify our populations of interest, we first included all of the hospital stays associated with an administrated drug (Unite Commune de Dispensation UCD) encoded 9439938 (tisagenlecleucel) or 9440456 (axicabtagene ciloleucel) between the 1 st of January 2019 and the 18 th of December 2020. In France, in 2019, each stay for which a patient is treated by injection of CAR-T cells is coded according to the applicable methodological guidelines and classified according to the grouping function, which in practice most frequently corresponds to diagnosis-related groups (DRGs) 17M08 "Acute leukemia, under 18 years of age", 17M09 "Acute leukemia, over 17 years of age", or 17M15 "Lymphomas and other lymphoid malignancies" according to the pathology coded as the main diagnosis. Each stay is hence valued according to its level of severity [START_REF]Agence Technique de l'Information sur l'Hospitalisation. Campagne tarifaire et budgétaire 2019 Nouveautés « financement[END_REF][START_REF]Agence Technique de l'Information sur l'Hospitalisation. Campagne tarifaire et budgétaire 2020 Nouveautés « financement[END_REF]. The hospital stays associated with tisagenlecleucel were then subdivided into ALL and DLBCL groups based on the corresponding medical indication.

For each hospital stay, we extracted the FINESS code (a unique identifier for hospitals in France) for hospitals where CAR-T cell injections were performed, the exact location of the hospitals, the residential location of the patients (at the municipality level), the duration of the patients' hospital stays, the patients' age, the International Classification of Disease tenth revision (ICD-10 code), the Diagnosis Related Group (DRG), and information regarding the costs.

The costs were restricted to the perspective of the French National Health Insurance and valued from the national tariffs. The costs that were funded in addition to the DRG-based payment (e.g., medicines placed on the list of innovative high-cost medicines, use of intensive care units) were added. Only hospital stays related to anti-CD19 CAR-T cells infusion, which are likely the most expensive in terms of patient management, were taken into account in this study. Hence, the inpatient and outpatient costs for pretreatment, rehospitalizations, patient-out-of-pocket costs, informal carer payments, and end-of-life costs were not included. Transportation costs were also not taken into account. Costs were not discounted due to the short time horizon.

We also computed the straight-line distances in kilometers between the patients' residential municipalities and the exact locations of their hospitals. Information about the type of hospital (public, private for-profit, private not-for-profit) was included from the French Hospital Survey (Statistique annuelle des établissements -SAE) managed by the Directorate for Research Studies Evaluation and Statistics (DREES).

Descriptive statistics were performed. The continuous data are presented as mean values with the standard deviation (SD) and the categorical data as frequencies and percentages. Statistical Analysis Software (SAS Institute Inc. Cary, North Carolina, USA) was used for all of the analyses. One-way sensitivity analyses were conducted by varying cost parameters by plus or minus 20% (except for the costs associated with DRG where the lower vs. higher national tariffs were retained) and illustrated graphically in a Tornado diagram. 95% confidence intervals (CI) for the mean total costs were also computed.

This study was conducted in compliance with the reference methods (MRs) for data processing in health research (MR-005 access to the PMSI).

Results

We identified 485 hospital stays associated with an injection of either tisagenlecleucel or axicabtagene ciloleucel between 2019 and 2020. We observed a maximum of one injection per patient for tisagenlecleucel and for axicabtagene ciloleucel. These injections of CAR-T cells were performed in 13 hospitals in mainland France. Of these, 11 (84.6%) were university teaching hospitals and 2 (5.4%) were not-for-profit cancer centers. Figure 1 shows that the distribution of CAR-T cell injections among the 13 providers was rather centralized, with both hospital number 12 and number 13 accounting for more than 50% of the total market share.

[INSERT FIGURE 1]

As reported in Table 1, out of all of the injections of tisagenlecleucel and axicabtagene ciloleucel, 44 (9%) were tisagenlecleucel for ALL, 139 (28.7%) were tisagenlecleucel for DLBCL, and 302 (62.3%) axicabtagene ciloleucel. Even though all of the patients in the tisagenlecleucel ALL group had an ICD-10 code for acute lymphoblastic leukemia, we observed a degree of variation in the ICD-10 codes for the tisagenlecleucel DLBCL and the axicabtagene ciloleucel groups. Indeed, out of the 302 injections of axicabtagene ciloleucel, comprised follicular lymphoma, peripheral T-cell lymphoma, mediastinal large B-cell lymphoma, non-Hodgkin lymphoma, septic shock, and antineoplastic chemotherapy or immunotherapy. Similarly, out of the 139 injections of tisagenlecleucel for DLBCL, 130 (94%) were for diffuse DLBCL, while the diagnoses for the remaining nine injections (6%) included follicular lymphoma, lymphoblastic lymphoma, non-follicular lymphoma, pneumonia due to pseudomonas, and antineoplastic chemotherapy or immunotherapy.

[INSERT TABLE 1]

Table 2 displays the patient characteristics and information about the hospital stays for the CAR-T cell injections. On average, the patients were 14.8 years of age for the tisagenlecleucel ALL group, 60.8 years of age for the tisagenlecleucel DLBCL group, and 59.1 years of age for the axicabtagene ciloleucel group. It should be noted that tisagenlecleucel for ALL is indicated for patients up to 25 years of age. The length of stay for the infusion of anti-CD19 CAR-T cells was broadly similar for the lymphoma patients (i.e., on average 23.8 nights for tisagenlecleucel and 25.9 nights for axicabtagene ciloleucel), and substantially higher for the tisagenlecleucel ALL patients, with on average of 37.9 nights spent in the hospital. A higher standard deviation, as well as a wider distribution, are shown in Figure 2, indicating a greater variation in the length of the stay for the tisagenlecleucel ALL patients compared with the tisagenlecleucel DLBCL patients and those treated with axicabtagene ciloleucel, with a maximum of 148 nights spent in the hospital for the leukemia patients. Regarding the composition of the hospital stays for the CAR-T cell injections, the average number of medical procedures during the hospital stay was 19.34 for the tisagenlecleucel ALL patients, 8.34 for the tisagenlecleucel DLBCL patients, and 12.81 for the patients treated with axicabtagene ciloleucel. Similarly, the number of medical unit summaries for the hospital stay, which relates to the variety of medical units involved, was on average 2.02 for the tisagenlecleucel ALL patients, 1.47 for the tisagenlecleucel DLBCL patients, and 1.39 for the patients treated with axicabtagene ciloleucel. As only 13 hospitals performed CAR-T cell injections in the period considered in mainland France, the travel distances from the patients' residential locations to the hospitals is an important factor to be taken into account. The average distances were indeed relatively long, with 200.6 kilometers for the tisagenlecleucel ALL patients, 112.2 kilometers for the tisagenlecleucel DLBCL patients, and 98.6 kilometers for the patients treated with axicabtagene ciloleucel.

[INSERT TABLE 2] [INSERT FIGURE 2]

Table 3 provides a description of the costs associated with the hospital stay for the CAR-T cell injections. On average, the cost per hospital stay for the infusion of anti-CD19 CAR-T cells was €372,400 (95% CI: [360,045; 384,754]) for the tisagenlecleucel ALL patients, €342,903 (95% CI: [339,188; 346,617]) for the tisagenlecleucel DLBCL patients, and €366,562 (95% CI: [364,457; 368,667]) for the patients treated with axicabtagene ciloleucel. These costs include the cost of the CAR-T cell products (€303,916.9 for tisagenlecleucel and €333,867 for axicabtagene ciloleucel), the cost associated with the stay itself, i.e. DRG (€27,423.96 for tisagenlecleucel ALL treatment, €14,090.9 for tisagenlecleucel DLBCL treatment, and €15,971.1 for axicabtagene ciloleucel), as well as extra charges including intensive care (€41,059.4 in case of tisagenlecleucel for ALL, €24,895.9 in case of tisagenlecleucel for DLBCL, and €16,724.2 in case of axicabtagene ciloleucel). Considering only the intensive care surcharge, it reached on average €13,934 for the tisagenlecleucel ALL patients, €8,716 for the tisagenlecleucel DLBCL patients, and €8,406 for the axicabtagene ciloleucel patients. Finally, CAR-T cell products represented 81.61%, 88.63%, and 91.08% of the total stay for tisagenlecleucel with ALL, tisagenlecleucel with DLBCL, and axicabtagene ciloleucel, respectively; the share of the cost associated with the DRG was 7.36%, 4.1%, and 4.36% for tisagenlecleucel with ALL, tisagenlecleucel with DLBCL, and axicabtagene ciloleucel, respectively; the intensive care units 3.74% %, 2.54%, and 2.29% for tisagenlecleucel with ALL, tisagenlecleucel with DLBCL, and axicabtagene ciloleucel, respectively; the other supplements 7.28%, 4.72%, and 2.26% for tisagenlecleucel with ALL, tisagenlecleucel with DLBCL, and axicabtagene ciloleucel, respectively.

The vast majority of hospital stays for tisagenlecleucel with ALL were associated with a DRG for acute leukemia (DRGs 17M08 and 17M09), and to a DRG for lymphomas and other lymphoid malignancies (DRG 17M15) for tisagenlecleucel with DLBCL and axicabtagene ciloleucel. Nevertheless, we also observed a high degree of variation in the cost of the hospital stay for the infusion of anti-CD19 CAR-T cells according to the associated DRG. For example, the total cost exceeded €400,000 for the DRGs for hematopoietic stem cell allografts and autografts (DRG 27Z02, 27Z03, and 27Z04Z). The costs were naturally higher for the DRGs with higher severity levels.

[INSERT TABLE 3] Figure 3 shows Tornado diagrams that illustrated the impact of ±20% variation in the values of cost parameters (except for the costs associated with DRG where the lower vs. higher national tariffs were retained) on the cost of the hospital stay for the infusion of anti-CD19 CAR-T cells. The vertical lines represent the mean cost per patient when all parameters assume their base values. The most sensitive parameters were the costs of CAR-T cell products. Decreasing these costs by 20% decrease the cost from €372,400 to €311,616 for the tisagenlecleucel ALL patients, from €342,903 to €282,120 for the tisagenlecleucel DLBCL patients, and from €366,562 to €299,789 for the patients treated with axicabtagene ciloleucel.

[INSERT FIGURE 3]

In order to provide evidence regarding patient access to CAR-T cell injection, the two maps in Figure 4 illustrate the geographical repartition of the hospitals, the patient density, and the distance to a hospital per department in mainland France. It can be seen that the 13 hospitals performing CAR T-cell injections are relatively well spread over the French territory, except for the center of France and Corsica. Nevertheless, we observed a high degree of spatial variation in the patient-hospital distance, ranging from 0 -50 kilometers on average in some departments to more than 200 kilometers in other departments. Central western France, as well as Corsica, were particularly affected by long travel distances. In terms of patient access to CAR-T cell injections, there was also a broad trend of a higher density of patients receiving CAR-T cell injections in departments where there is a hospital with a record of performing CAR-T cell injections.

[INSERT FIGURE 4]

Discussion

The use of CAR-T cells has the potential of becoming a major innovation in the treatments of leukemia and lymphomas that needs to be confirmed with longer-term data [START_REF] Beyar-Katz | Advances in chimeric antigen receptor T cells[END_REF][START_REF] Chicaybam | Overhauling car t cells to improve efficacy, safety and cost[END_REF]. Indeed, the costs and the consequences of these innovations remain uncertain due to a lack of evidence based on real-world data [START_REF] Sarkar | Cost-Effectiveness of Chimeric Antigen Receptor T-Cell Therapy in Pediatric Relapsed/Refractory B-cell Acute Lymphoblastic Leukemia[END_REF][START_REF] Thielen | Cost-Effectiveness of Anri-CD19 chimeric antigen receptor T-Cell therapy in pediatric relapsed/refractory B-cell acute lymphoblastic leukemia. A societal view[END_REF][START_REF] Yadav | CAR T cell therapy: newer approaches to counter resistance and cost[END_REF][START_REF] Flowers | What can cost-effectiveness analysis tell us about chimeric antigen receptor T-cell therapy for relapsed acute lymphoblastic leukemia?[END_REF][START_REF] Lin | Cost effectiveness of chimeric antigen receptor T-cell therapy in multiply relapsed or refractory adult large B-cell lymphoma[END_REF].

In this study, we assessed the costs of the hospital stays for the infusion of anti-CD19 CAR-T cells for the French National Health Insurance using nation-wide administrative data from 2019 -2020. From January 2019 to December 2020, 485 patients received a single CAR-T cell injection of either tisagenlecleucel or axicabtagene ciloleucel in France. Most of the injections of CAR-T cells were related to lymphoma treatments, while only 10% were related to leukemia (Table 1). The costs of the hospital stay for the infusion of anti-CD19 CAR-T cells, including the cost of the CAR-T cell product, were €372,400 on average for tisagenlecleucel ALL treatment, €342,903 for tisagenlecleucel DLBCL treatment, and €366,562 for axicabtagene ciloleucel (Table 3). In concordance with the literature, the leading component of these costs was the acquisition of the anti-CD19 CAR T-cell drug, at a cost of €303,916.9 for tisagenlecleucel and €333,867 for axicabtagene ciloleucel. G.H. Lyman, for example, reported a cost expressed in 2018 US dollars from lymphodepletion to 30 days after CAR-T cell infusion in patients with relapsed or refractory DLBCL of $454,611 in academic hospitals. The CAR-T cell drug cost was $373,000 (82.05%) and the hospitalizations and office visit costs $53,360 (11.74%) [START_REF] Lyman | Economic Evaluation of Chimeric Antigen Receptor T-Cell Therapy by Site of Care Among Patients With Relapsed or Refractory Large B-Cell Lymphoma[END_REF]. In the economic analysis in pediatric patients with relapsed/refractory ALL performed by Thielen et al., the cost of the CAR-T cell product (€320,000) represented 78.13% of the total costs from a healthcare perspective (i.e., €409,563). The costs of the treatment, which included the drug and the procedure costs, and the costs for the inpatient and the outpatient visits reached €338,122 [START_REF] Thielen | Cost-effectiveness of Anti-CD19 chimeric antigen receptor T-Cell therapy in pediatric relapsed/refractory B-cell acute lymphoblastic leukemia. A societal view[END_REF]. This cost, as well the cost input related to the administration of anti-CD19 CAR-T cells (i.e., €15,932), appears to be lower than the cost determined in our study. However, comparisons should be made very cautiously, as health systems vary and costs do not necessarily include the same items. In any case, real-life studies are needed to generate new results and to refine the assumptions of future models in a context of limited data regarding the costs of the hospitalizations of patients undergoing CAR-T cell treatments.

As initial coverage decisions were based on preliminary data, our study shows that beyond the reevaluation of the clinical benefits, the costs and the cost-effectiveness analyses submitted to the CEESP also need an update. Indeed, the total cost estimated by the manufacturers over 10 and 20 years for tisagenlecleucel and axicabtagene ciloleucel, respectively, and our results, based only on the hospital stay for the administration of anti-CD19 CAR-T cells, appear to be similar despite measuring costs at different time horizons [START_REF]AVIS D'EFFICIENCE : Kymriah® ( Tisagenlecleucel ) Leucémie aigue lymphoblastique[END_REF][START_REF]AVIS D'EFFICIENCE : Kymriah® ( Tisagenlecleucel ) Lymphome diffus à grandes cellules B[END_REF][START_REF]AVIS D'EFFICIENCE : YESCARTA® (axicabtagene ciloleucel)[END_REF][START_REF] Raimond | Challenges raised by the economic evaluation of CAR-T-cell therapies. The review by the French National Authority for Health[END_REF].

In regard to the geographical approach, our findings indicate an average distance between the patients' residential municipalities and the hospital locations of 200.6 kilometers for tisagenlecleucel ALL treatment, 112.2 kilometers for tisagenlecleucel DLBCL treatment, and 98.6 kilometers for treatments involving axicabtagene ciloleucel (Table 2). These relatively long distances can be explained by the fact that only 13 hospitals performed CAR-T cell injections in mainland France in 2019-2020. Moreover, the distribution of CAR-T cell injections among the 13 providers was rather centralized, with two of the providers accounting for more than 50% of the total market share (Figure 1). The longer travel distance for tisagenlecleucel ALL patients could be explained by the fact that among the 13 hospitals, only 7 hospitals (54%) performed injections of tisagenlecleucel for ALL, while all 13 of the hospitals performed injections of either tisagenlecleucel for DLBCL or axicabtagene ciloleucel or both. Thus, leukemia patients had fewer options to choose from when seeking a hospital for a CAR-T cell injection, which might in turn increase travel distances.

We also observed a high degree of spatial variation in the distance between the patients' residential municipalities and the hospital locations, ranging from 0 -50 kilometers on average in some departments to more than 200 kilometers in other departments, which could be due to a lack of hospitals in central western France, as well as in Corsica (Figure 3). In terms of patient access to CAR-T cell injections, it also appears that patients living in departments where there is an established hospital were more likely to be treated compared to patients living farther away from a provider, which is even more important considering the low number of hospitals providing CAR-T cell treatment in mainland France (Figure 3). But population densities are also higher in the large cities where university hospitals and not-for-profit cancer centers are located. Further research, including incidence data, is, therefore, necessary. Distances may be an important barrier to access to CAR-T cell therapy. In the US, for example, fewer than one-hundred hospitals are certified to infuse Axicabtagene ciloleucel, while 46.6% of the population lives within thirty minutes of one of the 200 transplant centers. The longer travel distance for pediatric and young adult patients are also concordant with the literature [START_REF] Delamater | Geographic access to hematopoietic cell transplantation services in the United States[END_REF][START_REF] Kansagra | Expanding Access to Chimeric Antigen Receptor T-Cell Therapies: Challenges and Opportunities[END_REF].

The stakes for CAR-T cell therapy are major: (i) the scientific stakes related to the prospect that research that has broadly involved several generations of researchers, physicians, and many other personnel and that has required massive public and private investments can deliver very significant benefits for patients [START_REF] Dunbar | Gene therapy comes of age[END_REF]; (ii) clinical issues because even though there have been clear successes with anti-CD19 CAR-T cell therapy, the CAR-T cells' persistence or antigen escape may be limited and there is still ample room for improvement of the safety and efficacy of the use of CAR-T cells to treat blood cancers [START_REF] Chicaybam | Overhauling car t cells to improve efficacy, safety and cost[END_REF][START_REF] Siegler | Neurotoxicity and Cytokine Release Syndrome After Chimeric Antigen Receptor T Cell Therapy: Insights Into Mechanisms and Novel Therapies[END_REF][START_REF] Grain | CAR-T cells in acute lymphoblastic leukemias: What's new?[END_REF]. Moreover, some facilities perform very few injections. It is not clear how many should be performed to ensure quality of care. Is there a cumulative effect? There needs to be a balance between proximity and the activity threshold. Indeed, there have been hundreds of studies investigating the volume-outcome relationship in healthcare, and they indeed tend to indicate that higher-volume hospitals tend to provide higher-quality care, especially for complex procedures such as surgeries in cancer care [START_REF] Cowan | Is It Time to Centralize Ovarian Cancer Care in the United States?[END_REF][START_REF] Friebel | Centralisation of acute stroke services in London: Impact evaluation using two treatment groups[END_REF]; (iii) the economic stakes due to the extremely high prices of tisagenlecleucel and axicabtagene ciloleucel. The costs could be even higher when used in combination with other cancer therapeutics such as immunotherapies [START_REF] Yadav | CAR T cell therapy: newer approaches to counter resistance and cost[END_REF]. These very high costs raise the question of the sustainability of the health care systems to cope with expenses of this nature and the capacity of patients to cope with the remaining out-of-pocket costs. Fortunately, there appear to be options to improve and even ensure access to all patients requiring such treatments: the implementation of different production methods. T. Ran assessed the "on-site" CAR-T cell production costs in a non-profit setting in Germany including leukapheresis, cell production, cryopreservation, and additional contamination control to being close to €60,000 at the maximum capacity of the machine. The cost could have even decreased to €45,000 if three machines would be installed as a result of the economies of scale [START_REF] Schmitt | Comments on "Cost of decentralized CAR T cell production in an academic non-profit setting[END_REF][START_REF] Ran | Reply to: Comments on "Cost of decentralized CAR T cell production in an academic non-profit setting[END_REF][START_REF] Ran | Cost of decentralized CAR T-cell production in an academic nonprofit setting[END_REF]; the development of innovative pricing mechanisms [START_REF] Barlow | Are Payers Ready, Willing, and Able to Provide Access to New Durable Gene Therapies?[END_REF]; and the generation of on-the-shelf universal T cells [START_REF] Chicaybam | Overhauling car t cells to improve efficacy, safety and cost[END_REF].

(iv) the ethics stakes, with key issues raised by the national ethics counselor for life sciences and health sciences: why are the prices of these innovative therapies so high? The necessity to rapidly bolster a regulatory system that allows joint preservation of public and industrial interests. The search for a "fair price" is part of a negotiation between private and public parties, whose interests are partly divergent (profit vs. public health) [START_REF]Comité consultatif national d'éthique pour les sciences de la vie et de la santé[END_REF]. In France, an annual reassessment of clinical benefits includes adverse events based on long-term follow-up data from pivotal trials, and the collection of real-world data has been scheduled for the anti-CD19 CAR-T cell products tisagenlecleucel and axicabtagene ciloleucel.

This study has some limitations, in particular the fact that only the hospital stay related to the infusion of anti-CD19 CAR-T cells was taken into account. Hence, several cost items were not included, e.g., inpatient and outpatient hospitalizations/office visits pre-and post-infusion, patient-out-of-pocket costs, informal carer payments, the fixed-price supplement of €15,000 applies only to the tisagenlecleucel and axicabtagene ciloleucel specialties within the indications of the market access and within the limit of the target population of 400 patients, or the possible financial costs related to the delay between the date of payment by the hospitals for the treatment and the date of reimbursement by the health insurance. We also computed straight-line distance in kilometers between the patients' residential municipalities and the exact locations of the hospitals, which minimizes the actual distances travelled.

Furthermore, although the PMSI is a tool of particular interest, the risk of coding errors in hospital discharge data cannot be ignored [START_REF] Champeaux | Epidemiology of meningiomas. A nationwide study of surgically treated tumours on French medico-administrative data[END_REF][START_REF] Scotte | The Cost of Thromboembolic Events in Hospitalized Patients with Breast or Prostate Cancer in France[END_REF][START_REF] Asfari | Chocs anaphylactiques d'origine médicamenteuse : sousnotification et PMSI[END_REF]. Indeed, variations were observed in the ICD-10 codes for the tisagenlecleucel DLBCL and the axicabtagene ciloleucel groups. Several worldwide studies have investigated the accuracy of routinely collected hospital episode data in order to determine to what extent overall rates of accuracy coding errors impact the quality of results. These studies measured the coding accuracy by comparison of routine discharge statistics for an episode of hospital care with the original medical record.

The overall levels of accuracy were generally found to be quite high [START_REF] Gouverneur | Concordance entre les codes de diagnostic du PMSI et les données de dossiers médicaux pour identifier le cancer colorectal métastatique et les comorbidités associées chez des patients âgés[END_REF][START_REF] Campbell | Systematic review of discharge coding accuracy[END_REF][START_REF] O'malley | Measuring diagnoses: ICD code accuracy[END_REF]. Nevertheless, as shown by our study, it is important to follow the coding rules (the ATIH provides a yearly methodological coding guide), to use the correct ICD 10 codes, and to develop coding improvements using, for example, data mining techniques [START_REF] Djennaoui | Improvement of the quality of medical databases: Data-mining-based prediction of diagnostic codes from previous patient codes[END_REF].

Figure 1 - 1 Figure 2 - 1 Figure 3 Figure 4 -

 112134 Figure 1 -Number of anti-CD19 CAR-T cell injections per hospital

Table 1 : Prescription of anti-CD19 CAR-T cells by diagnosis code (ICD-10)

 1

				Frequency of patients
	ICD-10 Code	Label	tisagenlecleucel	tisagenlecleucel	axicabtagene	Total
			ALL	DLBCL	ciloleucel
	C829	Follicular lymphoma, unspecified	0	4	2	6
	C833	Diffuse large B-cell lymphoma	0	130	290	420
	C835	Lymphoblastic (diffuse) lymphoma	0	1	0	1
	C839	Non-follicular (diffuse) lymphoma, unspecified	0	1	0	1
	C844	Peripheral T-cell lymphoma, not classified	0	0	1	1
	C852	Mediastinal (thymic) large B-cell lymphoma	0	0	5	5
	C857	Other type of Non-Hodgkin lymphoma	0	0	1	1
	C859	Non-Hodgkin lymphoma, unspecified	0	0	1	1
	C910	Acute lymphoblastic leukemia [ALL]	44	0	0	44
	J151	Pneumonia due to Pseudomonas	0	1	0	1
	R572	Septic shock	0	0	1	1
	Z511	Appointment for antineoplastic chemotherapy and	0	2	1	3
		immunotherapy
	Total		44	139	302	485
	Note: International Classification of Diseases (ICD-10)

Table 2 : Patients and hospital stay characteristics for infusion of anti-CD19 CAR-T cells tisagenlecleucel

 2 Distance patient -hospital 200.6 231.1 [2.9; 960.2] 112.2 120.4 [0.1; 683.5] 98.6 105.6 [2.3; 778.3] Note: Number of (#); Standard deviation (Std); Minimum (Min); Maximum (Max); Frequency (n). The patient-hospital distance is in kilometers, the patients' age in years, and the length of stay in nights.

	ALL	tisagenlecleucel DLBCL	axicabtagene ciloleucel
	(n=44)	(n=139)	(n=302)
	Mean Std [Min; Max] Mean Std [Min; Max] Mean Std [Min; Max]

Table 3 : Costs of the hospital stay associated with anti-CD19 CAR T-cell injections based on the national tariffs

 3

				tisagenlecleucel ALL		tisagenlecleucel DLBCL	axicabtagene ciloleucel
	DRG	DRG cost (€, V2020)	n	(Value RR 2020 = 303,916.9) Extra. IC Total	n	(Value RR 2020 = 303,916.9) Extra. IC Total	n	(Value RR 2020 = 333,867) Extra. IC Total
				Mean (Std)	Mean (Std)		Mean (Std)	Mean (Std)	Mean (Std)	Mean (Std)
	04M074	7,887.81	0			1	21,186.8 (.)	367,663.4 (.)	0
	17C084	21,855.71	0			0			2	18,548.9	398,336.2 (1,970.7)
									(7,320.6)
	17M064	8,197.67	0			2	11,890 (1,528.6) 324,785.1	1	10,197.3 (.)	349,110.5 (.)
								(1,236.5)
	17M083	18,119.42	5	13,644.8	349,072.3	0			0
				(3,491.5)	(8,985.1)
	17M084	34,849.92	15	16,615.1	384,109.4	0			0
				(6,202.9)	(29,330)
	17M093	12,002.84	5	9,041.9 (1,518.1)	339,390.4	0			0
					(13,603.1)
	17M094	24,687.03	11 10,012.1 (4,398)	368,617.4	1	19,024.1 (.)	353,064.7 (.)	0
					(21,165.8)
	17M151	1,578.14	0			0			1	808.2 (.)	336,636.4 (.)
	17M152	4,492.29	0			1	0 (.)	316,038.9 (.)	0
	17M153	8,254.22	0			28	6,880.1 (4,212.2)	336,596.8
								(27,496.8)

Acknowledgments

This work was supported by the SIRIC LYriCAN (INCa-DGOS-INSERM_12563) and the Institut Convergences Plascan (ANR-17-CON-002). The authors wish to thank the Agence Technique de l'Information sur l'Hospitalisation (ATIH) for the access to the PMSI database. The authors are grateful to Sophie Domingues-Montanari who helped with the final editing of the manuscript. The authors also thank the reviewers for their valuable comments.

Conflict of Interest

The authors declare that they have no competing interests.

Cet article fait partie du numéro supplément Nouvelles stratégies en immunothérapie : CAR-T et cellules bispécifiques réalisé avec le soutien institutionnel de Celgene


Sophie Eve
email: sophie.eve@ensicaen.fr

Alexis Ribet

Jean-Gabriel Mattei

Clara Grygiel

Eric Hug

Isabelle Monnet

STRUCTURAL AND MECHANICAL MODIFICATIONS OF GaN THIN FILMS BY SWIFT HEAVY ION IRRADIATION

Keywords: GaN, irradiation, swift heavy ions, lattice disorder, residual stresses, TEM observations, mechanical behavior

The structural modifications and the evolution of mechanical behavior of gallium nitride (GaN) thin films irradiated by 92 MeV 129 Xe 23+ at different fluences have been investigated. The modifications induced by irradiation in GaN have been studied using a combination of high resolution X-ray diffraction and Transmission Electron Microscopy observations coupled to nanoindentation. The crystalline lattice of the GaN is modified by irradiation, with an extension of the lattice along the cdirection parallel to the ion path, leading to the development of residual stresses. Correlated to the crystallographic disorder, modification of the deformation mechanisms of the material is observed: damaged areas (highly disordered zones near the surface and black dots deeper in the bulk) hinder the dislocation motion, such as after irradiation, dislocation slip occurs only along the basal plane, and no more prismatic or pyramidal slip is observed. This results in increasing the dislocation loop density, with a subsequent increase in hardness of the GaN film. At higher fluence, the overlapping of the

Introduction

Because its attractive merits such as high break down voltage, high carrier saturation mobility, wide direct band gap, strong interatomic bonds, and high thermal conductivity, gallium nitride GaN is one of the most promising materials for light emission or detection. Thereby, GaN is currently widely used for the fabrication of opto-electronical components such as Light Emitting Diodes (LEDs), laser diodes, UV sensors or power devices [START_REF] Morkoc | High-Luminosity Blue and Blue-Green Gallium Nitride Light-Emitting Diodes[END_REF][START_REF] Fasol | Room-Temperature Blue Gallium Nitride Laser Diode[END_REF]. Moreover, GaN is considered for applications in severe radiative environments, as in spatial or nuclear industry, where the components might be exposed to high energy ionic radiations [START_REF] Lien | Harsh photovoltaics using InGaN/GaN multiple quantum well schemes[END_REF][START_REF] Lv | Study of proton irradiation effects on AlGaN/GaN hich electron mobility transitors[END_REF], with energies up to the MeV.

The exposure of semi-conductive materials to ion radiations could result in important modifications of their electrical, optical and mechanical properties, so that the behavior of these compounds under irradiation, within a wide range of energy and projectile mass, is a real issue [START_REF] Kumar | Investigations on the 100 MeV Au 7+ ion irradiation of GaN[END_REF][START_REF] Son | GaN-based High Temperature and Radiation-Hard Electronics for Harsh Environments[END_REF][START_REF] Gou | Effects of irradiation of 290 MeV U-ions in GaN epi-layers[END_REF][START_REF] Hu | Raman investigation of lattice defects and stress induced in InP and GaN films by swift heavy ion irradiation[END_REF].

Indeed, in the case of irradiation in the low energy ion range, the ions lose their energy by elastic collisions with the target nucleus (nuclear energy loss), where atoms could be directly displaced from their lattice sites. In the case of irradiation in the high energy range, the main process of energy deposition is by inelastic interactions with the target electrons (through electronic energy loss), where the projectiles transfer their energy to the electrons of the target. This leads to excitation and ionization processes, and relaxation mechanisms of the lattice through electron-phonon interactions inducing the formation of latent track around the ion path.

With Swift Heavy ions (SHI), the energy deposition is dominated by electronic stopping power.

In many materials, predominantly in insulators but also in a few selected semiconductors and metals, continuous or discontinuous tracks could be observed along the ion paths, creating columnar structural modifications. The formation of these latent tracks is only observed above a threshold in electronic stopping power. These tracks could consist of amorphous cylinders embedded in the crystalline matrix. There also exist many other ion-induced structural modifications including amorphous tracks in an amorphous matrix [START_REF] Toulemonde | Transient thermal process after a high energy heavy-ion irradiation of amorphous metals and semiconductors[END_REF][START_REF] Klaumünzer | Ion tracks in quartz and vitreous silica[END_REF], tracks consisting of a different crystalline phase than the initial nonirradiated crystal [START_REF] Schuster | Response behavior of ZrO2 under swift heavy ion irradiation with and without external pressure[END_REF][START_REF] Benyagoub | Phase transformation induced in pure zirconia by high energy heavy ion irradiation[END_REF], and tracks of a more complex core-shell structure as discussed below. The formation of these tracks is by now often explained in literature by a thermal effect, called thermal spike [START_REF] Seitz | Displacement of atoms during irradiation[END_REF], for which the description in complex oxides ceramics is among the more advanced [START_REF] Lang | Advances in understanding of swift heavy-ion tracks in complex ceramics[END_REF].

Majority of researches on GaN thin films have been focused on its optoelectronics characteristics, but an increasing interest developed in the last decades to study its mechanical properties. It has been shown that the lattice mismatch-induced stress between GaN thin films and the available substrates, significantly affecting the threshold power density in simulated emission of GaN optoelectronic devices [START_REF] Weyher | Study of individual grown-in and indentation-induced dislocations in GaN by defect-selective etching and transmission electron microscopy[END_REF][START_REF] Bradby | Indentation-induced damage in GaN epilayers[END_REF][START_REF] Kucheyev | Nanoindentation of epitaxial GaN films[END_REF][START_REF] Jian | Berkovich indentation-induced deformation behaviors of GaN thin films observed using cathodoluminescence and cross-sectional transmission electron microscopy[END_REF]. Suresh et al. [START_REF] Suresh | Structural, optical, and electrical characteristics of 70 Mev Si5+ ion irradiation-induced nanoclusters of gallium nitride[END_REF] show that the irradiation of the GaN with energetic particles can produce N vacancy and Ga interstitials, and can result in changes in electrical properties like resistivity, mobility and density of carriers. Furthermore, the irradiation can induce migration of the atoms, leading to internal strain / stress levels into the material [START_REF] Kumar | Electrical and optical isolation of GaN by high energy ion irradiation[END_REF][START_REF] Look | Defect Donor and Acceptor in GaN[END_REF][START_REF] Devaraju | Electronic stopping dependence of ion beam induced modifications in GaN[END_REF][START_REF] Devraju | Ion beam-mixing effects in nearly lattice-matched AlInN/GaN heterostructures by swift heavy ion irradiation[END_REF][START_REF] Zhang | Damage to epitaxial GaN layer on Al2O3 by 290-MeV 238 U 32+ ions irradiation[END_REF]. Previous observations by Transmission Electron Microscopy (TEM) of SHI irradiated GaN films have shown the development of damage [START_REF] Sall | Track formation in III-N semiconductors irradiated by swift heavy ions and fullerene and re-evaluation of the inelastic thermal spike model[END_REF][START_REF] Mattei | Fullerene irradiation leads to track formation enclosing nitrogen bubbles in GaN material[END_REF]. This damage mainly consists in discontinuous latent tracks of a few nanometers in diameter, and appear in GaN along the ions path, for an electronic stopping power threshold of 17 keV/nm. The occurrence of such tracks in GaN after irradiation has been already related by several authors [START_REF] Mattei | Fullerene irradiation leads to track formation enclosing nitrogen bubbles in GaN material[END_REF][START_REF] Strite | and InN: A review[END_REF][START_REF] Satish | AFM and optical study of damage created by swift heavy ion irradiation in GaN epitaxial layers[END_REF][START_REF] Karlušić | Response of GaN to energetic ion irradiation: conditions for ion track formation[END_REF][START_REF] Pearton | GaN: Processing, defects, and devices[END_REF][START_REF] Shen | Cosmic ray induced explosive chemical desorption in dense clouds[END_REF][START_REF] Sequeira | Unravelling the secrets of the resistance of GaN to strongly ionising radiation[END_REF]. However, regarding GaN, authors agree on the fact that the damage does not lead to a complete amorphisation of the track: whatever the fluence, the material presents a high disorder of its lattice, but remains crystallized [START_REF] Sequeira | Unravelling the secrets of the resistance of GaN to strongly ionising radiation[END_REF][START_REF] Kucheyev | Ion Implantation into GaN[END_REF][START_REF] Kucheyev | Lattice damage produced in GaN by swift heavy ions[END_REF][START_REF] Gloux | Transmission electron microscopy investigation of the structural damage formed in GaN by medium range energy rare earth ion implantation[END_REF][START_REF] Baranwal | Rapid thermal and swift heavy ion induced annealing of Co ion implanted GaN films[END_REF]. An increase in the fluence of the ions results in a recrystallization of overlapping tracks [START_REF] Sequeira | Unravelling the secrets of the resistance of GaN to strongly ionising radiation[END_REF] and an increase of the defects concentration and of the size of the damaged zone, from the film surface through its thickness, with a saturation at high fluence (dechanneling of 80% observed in Rutherford Backscattering Spectroscopy in a channeling direction, RBS-c [START_REF] Kucheyev | Lattice damage produced in GaN by swift heavy ions[END_REF]). At high fluence, a highly disorder zone (HDZ) appears at the near surface [START_REF] Sall | Track formation in III-N semiconductors irradiated by swift heavy ions and fullerene and re-evaluation of the inelastic thermal spike model[END_REF][START_REF] Gloux | Transmission electron microscopy investigation of the structural damage formed in GaN by medium range energy rare earth ion implantation[END_REF].

The practical use of GaN in radiative environments requires knowledge of its damage behavior and the effect on its resistance, because, during use, the material may be subjected to mechanical loads arising from for example shock loading in mobile systems. Actually, insuring the long-term stability of the irradiated GaN requires identifying the defects created by irradiation and their effects on the material properties. In this study, we have investigated and correlated the structural and mechanical evolution of GaN thin films irradiated using SHI. Irradiation leads to a distortion of the GaN crystalline lattice, characterized by XRD, and the development of residual stresses in the film.

Nanoindentation has been used to investigate the mechanical properties of pristine and irradiated GaN thin films. TEM observations underneath the indents underline an evolution in the deformation mechanisms, linked to the crystalline disorder and damage development caused by SHI. Using this deposition technique, the reactive species are transported in a gaseous form to the substrate and simultaneously pyrolysed, so that growing temperatures range between 900° and 1200° C, after the deposition of a low temperature GaN buffer layer. GaN films were then doped by Si (n-type), at a carrier concentration of about 2.10 18 /cm 3 . The initial dislocations density, correlated to the difference in the lattice parameter between the sapphire substrate and GaN, was about 10 9 /cm². These samples were then irradiated at GANIL accelerator (Caen, France), on the IRRSUD line, with 92 MeV 129 Xe 23+ ions. Ion irradiation is carried out under normal incidence, at room temperature, and with a flux lower than 5.10 9 ions/cm 2 .s, to avoid macroscopic sample heating. The electronic stopping power of the ions decreases along the ion path until the projected range, which is localized in the current setup deep, into the substrate. In order to study the influence of the ion fluence on the modifications induced to the material, and to identify the damage mechanisms, two fluences were considered: 2.10 13 and 2.10 14 ions/cm². Non-irradiated GaN samples were also characterized as reference material.

Material and methods

Samples

Using SRIM code [START_REF] Ziegler | The Stopping and Range of Ions in Matter -SRIM[END_REF], the ion energy losses are calculated for 92 MeV 129 Xe 23+ in GaN with a material density of 6.15 g.cm -3 and displacement energies of 25 eV and 28 eV for Ga and N atoms respectively. At this energy, the electronic regime is predominant on the ion beam path in the nitride.

At the surface, the value of the electronic stopping power Se is 23 keV/nm, above the electronic stopping power threshold Se,th for track formation (Se,th ≈ 17 keV/nm), corresponding to a depth of about 2 µm [START_REF] Moisy | Optical bandgap and stress variations induced by the formation of latent tracks in GaN under swift heavy ion irradiation[END_REF]. The values of Sn remain very small on the path compared to Se values: the ENSP ratio (Electronic over Nuclear Stopping Power Se/Sn) has been determined around 111 at the entrance of the ions in the material, while is about 30 at the end of the GaN layer (after a path of 3.5 µm).

Moreover, the mean value of the number of displacements per atom (dpa) created by ballistic collisions over the 3.5 µm of the GaN film has been estimated to 0.05 for a fluence of 2.10 14 ions/cm². Such values evidence the importance of the Se compared to the Sn all along the ion path in the GaN thin film.

In order to characterize the modifications of the structure of GaN thin films due to the irradiation by SHI, we made use of the same methodology previously developed to define the damage profiles of Al2O3 after irradiation by SHI [START_REF] Ribet | Damage depth profile in α-Al2O3 induced by swift heavy ions[END_REF]. Namely, high resolution XRD analyses were performed using with a four-circle Bruker D8 Discover diffractometer using CuKα radiation (λ = 1.5406 Å). A Göbel mirror was used to obtain a parallel beam. Table 1 presents the different characteristics of each studied reflection. 2θ corresponds to the diffraction angle between the incident beam and the detector, ω the incident angle between the X-ray source and the sample surface. 2θ = ω setting is used for symmetric geometry whereas 2θ ≠ ω is used for asymmetric geometry. Moreover, χ is the inclination angle (0-90°) between the crystallographic plane and the sample surface, and the probed depth is calculated from the material density, the wavelength of the anode, and a value equal to 90% of I/I0 intensity ratio. Several reflections were recorded with different optics and geometries allowing observing the whole damaged area, from the surface down to the end of the GaN layer and even more in the substrate. Triple-axis geometry, using a 2-bounce Ge-220 monochromator, an analyzer crystal and a scintillation detector, enables to obtain high resolution symmetric patterns (0004 reflection), symmetric skew patterns (101 1, 112 2 and 213 3 reflections, χ ≠ 0 and χ < 90°), asymmetric patterns (101 4 (-) and 112 4 (-) reflections with (-) meaning "grazing" incident beam, χ= 0°) and 2D maps. 2D maps were obtained by taking a series of 2θ-ω patterns (± 0.5° around the reference position) at successive ω values (± 0.5° around the reference position). To probe sample near surface, where the Se value is the highest, in-plane geometry (χ= 90°) was used. By means of equatorial slits (0.1°) and a LYNXEYE detector in 0D, (101 0) reflection was recorded with an incident grazing angle of 0.35°, probing sample up to 430 nm. Several software were used to analyze the XRD measurements: Bruker Eva was used of the analysis of the raw patterns, Bruker Leptos for the simulation of the raw 2θ-ω patterns or 2D map representations in direct space, and DxTools [START_REF] Boulle | DXTools: processing large data files recorded with the Bruker D8 diffractometer[END_REF] The damage created in the GaN films by irradiation ions has been investigated by TEM. For that purpose, samples were prepared using Focused Ion Beam (FIB) station with Ga ions at 30 keV. The voltage is decreased in several steps down to 2 keV for final step in order to avoid damage due to FIB.

TEM lamellas were then examined in a JEOL 2010 FEG TEM operating at 200kV with a point-topoint resolution of 0.23 nm and a lattice resolution of 0.10 nm.

The mechanical behavior of pristine and irradiated GaN thin films has been studied using nanoindentation. This technique is indicated since the tested material volume is scalable with respect to the modified layer thickness, allowing to extract the mechanical characteristics of the film (hardness and elastic modulus), as well as investigating the deformation mechanisms. Tests were conducted using a MTS NanoXP system (MTS Systems Corporation, USA), with a contact module loading head equipped with a three-sided pyramidal Berkovich diamond indenter with a nominal tip radius of curvature of 20 nm. Tests were performed in displacement control by employing the continuous stiffness measurement (CSM) technique, which allows the continuous evaluation of the hardness and the elastic modulus during the indentation loading period. A penetration depth of 200 nm was used, to indent the GaN film at less than 10% of its thickness, and avoid the influence of the sapphire substrate on the measurements. At least 9 indentations were performed for each test, at room temperature. The loading curves were analyzed and the indentation hardness and the elastic modulus were extracted from indentation data, according to the classical Oliver and Pharr method [START_REF] Oliver | An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments[END_REF].

Results and discussion

Evolution of the GaN lattice parameters induced by irradiation

Fig. 1 shows 2D maps in the direct space, recorded for four reflections at different ion fluences up to 2×10 14 ions/cm². Such maps allow getting a general view of structural modifications induced in irradiated GaN. The dotted lines on the maps help to observe the contribution of the non-irradiated layer of the samples, called reference peaks. On virgin sample and for all reflections, well-defined and intense reflections are observed, assessing for the high crystalline quality of the virgin GaN film.

Streaks formation is also noticed, and is explained by the used optics (monochromator and analyzer).

With the increase of the fluence, a large broadening of the (0004) reflection is observed on 2θ axis, meaning that strain is induced by irradiation. Regarding the three other reflections, weaker variations are observed, with a broadening on 2θ axis, correlated to a slight decrease in intensity.

Along ω axis, few modifications with ω angle are depicted for all reflections, as function of the fluence, meaning that very few mosaicity, i.e. spread of crystal plane orientations, is present in the material under irradiation. Moreover slight diffuse signal or scattering appears at higher angles for the highest fluence of 2×10 14 ions/cm², which indicates disorder and compressive area formation. reflections with a low resolution [START_REF] Gou | Effects of irradiation of 290 MeV U-ions in GaN epi-layers[END_REF][START_REF] Sall | Track formation in III-N semiconductors irradiated by swift heavy ions and fullerene and re-evaluation of the inelastic thermal spike model[END_REF][START_REF] Harutyunyan | High resolution x ray diffraction strain stress analysis of GaN_sapphire heterostructures[END_REF][START_REF] Kisielowsk | Strain related phenomena in GaN thin films[END_REF][START_REF] Zhang | Structural and optical study of irradiation effect in GaN epilayers induced by 308 MeV Xe ions[END_REF]. The position of these different diffraction peaks allows calculating the deformation of the crystalline lattice, according to the relation:

εc = (cp -c0)/c0 (1)
where c0 and cp are the value of the c parameter related to the reference peak and the maximum peak (peak occurring with increasing the fluence), respectively. This deformation gradient, appearing for a fluence of 2.10 13 ions/cm², resulting in a shift of maximum peak corresponding to the maximum tensile strain (at the lowest angle on the pattern) to lower angle or higher strain as the fluence increases. This gap between the reference peak and the peak of maximum strain increases up to a full strain value of about 0.3% +/-0.05% for 2.10 14 ions/cm², corresponding to a lattice expansion in the direction of the c-parameter, parallel to the ion beam.

The analysis of the 2θ diffraction patterns associated to the symmetric (101 1), (112 2) and (213 3) reflections, allows to calculate the evolution of the average strain for a-and c-parameters deeper in the film, beyond the extreme surface, using the equations ( 2) and (1), respectively:

εa = (ai-a0)/a0 (2)
The values are given in the Table 2 as a function of the ion fluence, and reveal a slight strain gradient along these directions, higher in c-direction than in a-direction.

Fluence (ions/cm²) εa (%) εc (%) 0 0 0 2.10 13 -0.034 0.092 2.10 14 -0.115 0.311 Other crystallographic directions have been investigated by recording 2D maps of (101 4) and

(112 4) asymmetric reflections for different irradiation fluences. As asymmetric geometry associated to a grazing incidence entrance of the X-ray beam is used for these measurements, the material is probed up to 15.1 µm in thickness for the (101 4) reflection, i.e. more than the GaN film thickness. Fig. 3 shows 2D maps of the two asymmetric reflections for the virgin sample and the samples irradiated with a fluence of 2×10 14 ions/cm². Qz is directly linked to c-parameter and Qx axis to a-parameter through the formula for the (101 4) reflection:

Qz=8π/c (3) Qx=4π/(a√3) (4)
Fine and intense reflection can be observed on the virgin sample with streaks coming from optics.

At high fluence 2.10 14 ions/cm², the occurrence of diffuse zones of smaller intensity around the intense broader reference peak evidences the formation of crystalline disorder, keeping the crystalline coherence of the initial structure.

In order to measure the irradiation effect in the perpendicular direction to the ion beam, the (101 0) in-plane reflection is also measured as function of the irradiation fluence. This geometry brings also sensitivity to the only topmost irradiated surface layer where only electronic stopping power is deposited. The evolution of patterns on 2θ axis is not represented as very few modifications of the peak are observed. However, the analysis of these patterns allows to calculate the lattice a-parameter extracted from the (101 0) position, and the deformation along the a-axis. Very slight fluctuation around the virgin value is observed even up to high fluence, and then, we could conclude that no evolution of the in-plane lattice parameter (up to 430 nm) is observed, corresponding to the perpendicular direction to the ion beam.

Microstructural evolutions of GaN induced by irradiation

Fig. 4 presents a TEM micrograph of the sample irradiated with a fluence of 2.10 14 ion/cm². A Highly Disordered Zone (HDZ) is observed at the extreme surface of the sample, formed by the accumulation of numerous crystallographic defects and resulting in a very different contrast on the TEM image (darker than more in depth in bright field on Fig. 4). The thickness of this zone has been evaluated to be of 110 ± 6 nm for this fluence. This zone presents several contrasts of diffraction, meaning that the material remains mainly crystallized, despite the high disorder in its crystalline lattice [START_REF] Sequeira | Unravelling the secrets of the resistance of GaN to strongly ionising radiation[END_REF][START_REF] Kucheyev | Ion Implantation into GaN[END_REF][START_REF] Kucheyev | Lattice damage produced in GaN by swift heavy ions[END_REF][START_REF] Gloux | Transmission electron microscopy investigation of the structural damage formed in GaN by medium range energy rare earth ion implantation[END_REF]. Beyond this layer, important variations of diffraction contrasts (small areas of black contrasts named black dots) are observed, corresponding to a damaged zone. This contrast decreases as the depth increases, such as almost no black dots are observed near the GaN/sapphire interface. Such an evolution was also observed with 106 MeV 238 U (almost the same electronic stopping power than 92

MeV 129 Xe) [START_REF] Sall | Track formation in III-N semiconductors irradiated by swift heavy ions and fullerene and re-evaluation of the inelastic thermal spike model[END_REF].

The damage evolution through the GaN film thickness can be evidenced thanks to the variation of the electron beam intensity detected as a function of the considered depth. The transmitted intensity is related to the diffraction contrasts of the different zones of the sample, linked to the presence of black dots. As presented in the insert in Fig. 4, a peak of intensity is detected at the sample surface, corresponding to the platinum layer deposited during the sample preparation. At the end of the depth, a sharp increase in the transmitted intensity is observed, corresponding to the transition from the damaged GaN film to the Al2O3 substrate at the interface. Just before this sharp increase, the transmitted intensity is higher than in the zone between the HDZ and this zone. This is due to the fact that at this depth there are much less black dots. Thanks to these observations, the depth of the damaged zone of the GaN film can be estimated to about 2.8 µm (see insert in Fig. 4). We can note the presence of contrast in the sapphire, linked to the presence of disorder since the ion electronic stopping power is above the threshold of damage creation. Just under the interface, there is an amorphous layer of Al2O3 (few tens of nanometer) followed by a defected but still crystalline material. This is in agreement with the known evolution of sapphire under SHI [START_REF] Ribet | Damage depth profile in α-Al2O3 induced by swift heavy ions[END_REF].

Observations of samples irradiated with lower ion fluences reveal an important damage, with a high density of "black dots", decreasing as a function of the depth, and almost no black dots after 2 µm in depth. The HDZ is hardly visible at this fluence (2.10 13 ions/cm²), at most few nm.

Estimation of the stresses induced in the GaN film by irradiation

Residual stresses developed in the material can be computed based on the values of deformation calculated previously from XRD data and the elastic parameters of the GaN. The development of residual stresses in thin films could be linked to either mismatch in lattice parameters between the substrate and the film (growth stress), phase transformations or plastic deformation of the materials, as well as a consequence of materials irradiation. In the last case, the hydrostatic component of the stress is an isotropic tensile stress, related to the swelling of the material due to the formation of point defects, defects accumulation or ions tracks development. The biaxial component is a compressive stress linked to the in-plane influence of the non-irradiated material on the damaged layers. The increasing quantity of defects can thus induce expansion or contraction of the unit cell in the crystal lattice, and three-dimensional stress may appear in samples if the defects are uniformly distributed in the crystal lattice [START_REF] Hu | Raman investigation of lattice defects and stress induced in InP and GaN films by swift heavy ion irradiation[END_REF][START_REF] Harutyunyan | High resolution x ray diffraction strain stress analysis of GaN_sapphire heterostructures[END_REF].

According to the basic linear and isotropic elastic theory, out-of-plane (along the c-direction) and in-plane (along the a-direction) strain components for the hexagonal structure of (0001)-GaN layer, εa and εc, are the superposition of biaxial and hydrostatic strains [START_REF] Kisielowsk | Strain related phenomena in GaN thin films[END_REF], according to the relations:

εc = + εh ( 5
)
and: εa = + εh [START_REF] Son | GaN-based High Temperature and Radiation-Hard Electronics for Harsh Environments[END_REF] with:

εh = ν + (7)
and the Poisson coefficient:

ν = / / ( 8
)
where εh is the hydrostatic strain, and are the biaxial strains in the c-and a-directions, respectively, and Cij are the elastic constants of GaN.

Biaxial stress in the basal plane is defined such as the stress component in the crystallographic bdirection equals the component in the a-direction, whereas the biaxial stress component in the cdirection equals zero. For the hydrostatic stress σh, the stress in the a-, b-and c-directions are equal.

Accordingly, hydrostatic and in-plane biaxial stresses in the GaN layer can then be determined from the relationships:

σh = (9)
and:

σb =Mf [START_REF] Klaumünzer | Ion tracks in quartz and vitreous silica[END_REF] with:

Mf = C11+C12 -2 C13²/C33 (11)
Mf is the biaxial elastic modulus for a material with a hexagonal structure strained along the [0001] crystallographic direction. Using C11 = 390 GPa, C12 = 145 GPa, C13 = 104.5 GPa, C33 = 401.5 GPa, according to [START_REF] Harutyunyan | High resolution x ray diffraction strain stress analysis of GaN_sapphire heterostructures[END_REF][START_REF] Zhang | Structural and optical study of irradiation effect in GaN epilayers induced by 308 MeV Xe ions[END_REF][START_REF] Varadarajan | Structural, optical and electrical properties of high energy irradiated Cl-VPE grown gallium nitride[END_REF][START_REF] Kumar | Effect of 100mev Ni9+ ion irradiation on MOCVD grown n-GaN[END_REF][START_REF] Moram | X-ray diffraction of III nitrides[END_REF][START_REF] Pereira | Strain and composition distributions in wurtzite In-GaN/GaN layers extracted from x-ray reciprocal space mapping[END_REF], the value of ν = 0.207 for the Poisson coefficient, and Mf = 480.6 GPa for the biaxial elastic modulus, are obtained from Eq. ( 8) and [START_REF] Schuster | Response behavior of ZrO2 under swift heavy ion irradiation with and without external pressure[END_REF], respectively.

The hydrostatic stress in the GaN film is then computed from ( 9), using the value of Poisson coefficient calculated from ( 8), a value of E = 286.5 GPa for the Young's modulus [START_REF] Harutyunyan | High resolution x ray diffraction strain stress analysis of GaN_sapphire heterostructures[END_REF][START_REF] Moram | X-ray diffraction of III nitrides[END_REF][START_REF] Pereira | Strain and composition distributions in wurtzite In-GaN/GaN layers extracted from x-ray reciprocal space mapping[END_REF], and the value of the hydrostatic strain obtained from [START_REF] Gou | Effects of irradiation of 290 MeV U-ions in GaN epi-layers[END_REF]. The biaxial stress can be calculated from [START_REF] Klaumünzer | Ion tracks in quartz and vitreous silica[END_REF], substituting the values of biaxial strain in the a-direction and biaxial elastic modulus.

In order to compute the variation of the stresses with the irradiation fluence, the first hypothesis has been taken that the values of the elastic constants Cij and of the Young's modulus E are constant under irradiation, whatever the fluence, what we know to not be correct but it is a start point to approach absolute values.

and (213 3) reflections. Both the hydrostatic and the biaxial stress increase up to a fluence of 2.10 14 ions/cm², linked to the increasing damage of the GaN film created by irradiation.

The relationship between the biaxial stress in the film and the electronic stopping power Se of the ions is well established: biaxial stresses increase with the Se of ions, as already observed by Moisy et al. [START_REF] Moisy | Optical bandgap and stress variations induced by the formation of latent tracks in GaN under swift heavy ion irradiation[END_REF], who concluded that when the projectiles exhibit an electronic stopping power Se lower than the ion track formation threshold Se,th of 17 keV/nm, the measured stress values stay relatively low, whereas the formation of ion tracks implies large biaxial stress in the GaN layer, of about 1.5 GPa here. Such an increase in the residual stresses has been also observed by Zhang et al. [START_REF] Zhang | Structural and optical study of irradiation effect in GaN epilayers induced by 308 MeV Xe ions[END_REF] in a 3 µmthick GaN film under irradiation by Xe 308 MeV ions.

Mechanical characterization of the GaN films by nanoindentation

The evolution of the mechanical properties of the material induced by the microstructural modifications, the damage and the development of residual stresses in the GaN film due to irradiation, has been investigated using the nanoindentation technique.

Fig. 6 shows the average CSM load-hold-unload curve as a function of depth obtained by nanoindentation of non-irradiated and irradiated GaN, for a maximum indentation depth of 200 nm, i.e. less than 10% of the film thickness, in order to avoid any eventual influence of sapphire substrate on GaN properties. An elasto-plastic behavior of the pristine and irradiated GaN films is observed, correlated to an important residual deformation after unloading, of about 70%. As compared to the pristine GaN, the load requested for the indenter penetration into the material is higher for the sample irradiated with the fluence of 2.10 13 ions/cm², and decreases for the fluence of 2.10 14 ions/cm². Fig. 7 presents the evolution of the elastic modulus and the hardness of the materials as a function of the fluence, evaluated using Oliver and Pharr method [START_REF] Oliver | An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments[END_REF]. It is noticed that the pristine GaN and the sample irradiated at 2.10 13 ions/cm² exhibit a rather stable value of modulus and hardness along the penetration depth. On the contrary, the sample irradiated with the highest fluence of 2.10 14 ions/cm² shows a different behavior, with an increase of the mechanical parameters as a function of the penetration, which is closed to the behavior of an amorphous material.

The values of the modulus and the hardness of the pristine GaN film, measured in the stable domain, have been evaluated at 260 ± 6 GPa and 18 ± 1 GPa, respectively. These values are in good agreement with previous studies on epitaxial GaN films characterized by nanoindentation using a Berkovich tip, and slightly larger than parameters obtained by different indentor tips, mainly because of variations in the specific tip-surface contact configuration and stress distribution inherent to each measuring methods [START_REF] Kucheyev | Nanoindentation of epitaxial GaN films[END_REF][START_REF] Kucheyev | Ion Implantation into GaN[END_REF][START_REF] Tsai | Berkovich nanoindentation and deformation mechanisms in GaN thin films[END_REF][START_REF] Kavouras | Effects of ion implantation on the mechanical behavior of GaN films[END_REF].

Nanoindentation results show that the material irradiated using the fluence of 2.10 13 ions/cm² exhibits a value of hardness higher than the pristine material, of 24 ± 1 GPa, with a similar modulus.

Simulations show that the mean free path of 92 MeV 129 Xe 23+ in GaN is around 8 µm in these experimental conditions [START_REF] Toulemonde | Transient thermal process after a high energy heavy-ion irradiation of amorphous metals and semiconductors[END_REF]. That means that the SHI penetrate the total thickness of the GaN film, and implant into the sapphire substrate, so that the drastic change of the mechanical properties of the material cannot be caused by the presence of implanted Xe ions into the material. Then, it is argued that the microstructural modifications of the GaN induced by the irradiation can explain the evolution of the mechanical behavior of the GaN under irradiation. It has been shown that the penetration of the Xe ions in the material leads to damage in the crystalline lattice, with an increase of the defects concentration from the film surface through its thickness, and that this damage increases with the fluence, up to a maximum when the damage saturation is reached.

As previously discussed, TEM observations of sample irradiated with a fluence of 2.10 13 ions/cm² presents a high density of "black dots" in the region ear the sample surface, and a very thin HDZ of few nm. The high density of defects resulting from irradiation gives rise to an increase of the stresses in the material, as shown in the previous section. The relaxation of the stresses by plastic deformation induces the nucleation and the set of dislocations motion. An increase in strength of irradiated hexagonal closed packed structure materials has already been reported in the literature [START_REF] Onimus | In situ TEM observation of interactions between gliding dislocations and prismatic loops in Zr-ion irradiated zirconium alloys[END_REF], and attributed to the presence of a high density of small radiation-induced loops (here, "black dots"), that act as obstacles against dislocation glide. According to the damage observed in GaN sample irradiated with a fluence of 2.10 13 ions/cm², such a mechanism might take place and results in a subsequent hardening of the material after irradiation.

In order to support this analysis, TEM lamella underneath the indented spot have been cut into pristine and irradiated GaN with a fluence of 2.10 13 ions/cm². TEM images of these cross sections are presented in Fig. 8.

As suggested by Bradly et al. [START_REF] Bradby | Indentation-induced damage in GaN epilayers[END_REF] and by Jian [START_REF] Jian | Berkovich indentation-induced deformation behaviors of GaN thin films observed using cathodoluminescence and cross-sectional transmission electron microscopy[END_REF], Fig. 8a clearly displays that, within the pristine film, the deformation mechanisms are primarily driven by dislocation slip activity. Several types of gliding planes for dislocations are clearly evidenced. First, there are dislocations gliding in {0001} basal planes, parallel to the interface of GaN film-sapphire substrate. In addition, dislocations gliding in prismatic planes (i.e. perpendicular to the basal planes) are also visible. Finally, some dislocations are gliding in pyramidal planes in the plastically deformed area (slip bands oriented at ~60° to GaN surface).

Fig. 8b displays a TEM image underneath the indented spot after indentation of GaN thin film irradiated with a fluence of 2.10 13 ions/cm². It clearly shows a reduction in the number of available slip planes, as only slip bands aligning parallel to the interface of GaN film-sapphire substrate along the {0001} basal planes could be observed, but no more the slip bands oriented at ~60° to GaN surface previously observed under the indenter print in non-irradiated GaN film, or dislocation gliding in prismatic planes. As a consequence, since the main deformation mechanism in GaN film is dislocation slip mechanism, the irradiated GaN thin films become less susceptible to plastic deformation. This effect is observed in Fig. 6, which shows an extent of the elastic recovery of the sample irradiated with a fluence of 2.10 13 ions/cm², i.e. the reduction of the residual deformation observed on the loading curves. Such phenomenon of freezing of slip planes has already been reported in implanted GaN thin films [START_REF] Bradby | Indentation-induced damage in GaN epilayers[END_REF][START_REF] Kavouras | Effects of ion implantation on the mechanical behavior of GaN films[END_REF]. Both the destruction of long range crystalline order, and the residual stresses within the GaN film, hinders dislocation slip.

Finally, we noticed in Fig. 7 that the GaN irradiated with the highest fluence of 2.10 14 ions/cm² shows a mechanical behavior close to the one of an amorphous material, with an increase of the mechanical parameters as a function of the penetration. Moreover, the values of the modulus and the hardness, measured at a penetration of 200nm, are much smaller than the ones measured for pristine GaN, being estimated to 209 ± 3 GPa and 14.4 ± 0.2 GPa, respectively. The surface of the highlyirradiated GaN layer, presenting an extended HDZ at the extreme surface and an in-deep disorder could induce this smaller value of the modulus. Moreover, the densification resulting from compression and shear strain developed under the indenter tip, leads to easier plastic deformation, thus rendering the irradiated layer softer, exhibiting a smaller hardness value.

Conclusion

In this work, GaN/Al2O3 samples have been irradiated with 92 MeV 129 Xe 23+ at several fluences.

Main results obtained in this research can be summarized by the following points:

• According to XRD measurements, irradiation of GaN results in an average structure closed to the initial one with an extension of the lattice along the c-direction, parallel to the ions path, and almost no variations along the a-direction, perpendicular to ion beam. This deformation of the crystalline lattice causes the development of residual stresses within the GaN film.

• TEM observations have highlighted the existence of a HDZ near the free surface of the film, which grows with increasing the fluence, and the formation of black dots below. These results highlight that higher strain level develops near the surface and decrease as a function of depth.

• Nanoindentation was used to evaluate the impact of the irradiation on the mechanical behavior. The high crystalline disorder caused by irradiation, even larger as the ions fluence increases, and the development of residual stress within the film, significantly hinder the dislocations slip mechanism, reducing the GaN ability to deform plastically, and increasing the surface hardness for the sample irradiated with a fluence of 2.10 13 ions/cm².

• The overlapping of the latent tracks for the fluence of 2.10 14 ions/cm² results in a decrease of the strength of GaN, correlated to an amorphous-like mechanical behavior, probably linked to a growth of the ZFE at the extreme surface at high fluence.

Such modifications of the GaN crystallographic structure and mechanical behavior by irradiation with SHI have to be tackled for considering the practical use of GaN thin films based optics in radiative environments. Patterns are arbitrarily vertically shifted for a better visibility.

  consist in monocrystalline thin films of [0001] epitaxial GaN of 3.5 µm thick, deposited on a [0001] sapphire substrate by MOCVD (Metal Organic Chemical Vapor Deposition).

Fig. 2

 2 Fig.2 shows high-resolution pattern of the (0004) reflection for several fluences. Τhose plots evidence a high intensity reference peak (around 72.9°), corresponding to the reflection of unstrained (reference) zones in the sample. Moreover, with increasing the fluence, different new contributions of relatively high intensity are occurring at lower 2θ angles, linked to the deformation of GaN due to irradiation. Such behavior was already reported by several authors for the (0002) and (0004)

Fig. 5

 5 Fig.5 displays the evolution of the hydrostatic and the biaxial stresses developing in GaN, as a function of the fluence, computed from the XRD high resolution patterns of the (0004), (101 1), (112 2)

Fig. 1 :Fig. 2 :

 12 Fig.1: 2D maps for four reflections of GaN irradiated at different fluences. 2θ axis is from left to right, ω axis from bottom to top, maps correspond to a variation of ± 0.5° around the reference value for 2θ and ω. The same scale is used on all the maps.

Fig. 3 :

 3 Fig.3: Reciprocal space maps of the (101 4) reflection (a and b) and the (12 14) reflection (c and d), as function of the ions fluence (92MeV 129 Xe 23+ ).

Fig. 4 :Fig. 5 :

 45 Fig.4: (a) Cross-section TEM micrograph of GaN after irradiation with 92 MeV Xe at 2.10 14 ions/cm² (with diffraction vector 011 0). The white arrow shows the penetration direction of the ions in the material. HDZ defines the Highly Disordered Zone; (b) the evolution profile of the electron beam intensity detected as a function of the depth, according to the dashed box on the micrograph. The damaged thickness determined from the profile is reported on the TEM picture.

Fig. 6 :Fig. 7 :

 67 Fig.6: Loading curves by nanoindentation of GaN non-irradiated and irradiated with 92 MeV 129 Xe 23+ at 2.10 13 ions/cm² and 2.10 14 ions/cm².

Fig. 8 :

 8 Fig.8: TEM image underneath indented spots (with a close-up view in the heavily deformed region of GaN thin film) of (a) a non-irradiated GaN film, (b) a GaN film irradiated at a fluence of 2.10 13 ions/cm².

Table 1 :

 1

	for 2D map representations in

Characteristics of measured reflections: Bragg angle 2θ, inclination angle χ and the corresponding probed depth.

Table 2 :

 2 Strain of a-and c-parameter of the GaN lattice as a function of 92MeV 129 Xe 23+ fluence, calculated using the four symmetric (0004), (101 1), (112 2) and (2133) reflections.

Acknowledgements

The experiments were performed at the Grand Accélérateur National d'Ions Lourds (GANIL), Caen, France, and the authors thank the CIMAP, the CIRIL and GANIL staff for their helps. This work was partially supported by the ANR funding "Investissements d'avenir" ANR-11-EQPX-0020 and ANR10-LABX-09-01 LabEx EMC3, the FEDER and by the Region Basse-Normandie.