Andrey Sadovykh
email: a.sadovykh@innopolis.ru

Dragos Truscan
email: dragos.truscan@abo.fi

Pierluigi Pierini
email: pierluigi.pierini@intecs.it

Gunnar Widforss
email: gunnar.widforss@mdh.se

Adnan Ashraf
email: adnan.ashraf@abo.fi

Hugo Bruneliere
email: hugo.bruneliere@imt-atlantique.fr

Pavel Smrz
email: smrz@fit.vutbr.cz

Alessandra Bagnato
email: alessandra.bagnato@softeam.fr

Wasif Afzal
email: wasif.afzal@mdh.se

Alexandra Espinosa
email: alexandra.espinosa@mdh.se

On the Use of Hackathons to Enhance Collaboration in Large Collaborative Projects -A Preliminary Case Study of the MegaM@Rt2 EU Project

Keywords: Hackathon, Collaboration, Project

In this paper, we present the MegaM@Rt2 ECSEL project and discuss in details our approach for fostering collaboration in this project. We choose to use an internal hackathon approach that focuses on technical collaboration between case study owners and tool/method providers. The novelty of the approach is that we organize the technical workshop at our regular project progress meetings as a challenge-based contest involving all partners in the project. Case study partners submit their challenges related to the project goals and their use cases in advance. These challenges are concise enough to be experimented within approximately 4 hours. Teams are then formed to address those challenges. The teams include tool/method providers, case study owners and researchers/developers from other consortium members. On the hackathon day, partners work together to come with results addressing the challenges that are both interesting to encourage collaboration and convincing to continue further deeper investigations. Obtained results demonstrate that the hackathon approach stimulated knowledge exchanges among project partners and triggered new collaborations, notably between tool providers and use case owners.

I. INTRODUCTION

MegaM@Rt 2 is a three-years project, funded by European Components and Systems for European Leadership Joint Undertaking (ECSEL JU) under the H2020 European program, that started in April 2017 [START_REF] Espinosa | The MegaM@Rt 2 ECSEL project: MegaModelling at Runtime Scalable model-based framework for continuous development and runtime validation of complex systems[END_REF], [START_REF]MegaM@Rt 2 Project Website[END_REF].

One of the main issues arose during the first plenary meeting, held in Rome, was the limited concrete and effective technical results in terms of cooperation between partners and experiments as well as the lack of progress related to the application of the available tools to the use cases. Therefore, we approached the following plenaries with a more balanced distribution of managerial and technical staff across meeting days, devoting a hackathon-like day as a strategy to foster collaboration between case study owners and tool/method providers on challenging technical issues.

We considered that the plenary meetings are the recommended venue for such events since at least one member of each project organization is typically present and available for face-to-face meetings. The latter are considered by different practitioners more efficient compared to virtual meetings [START_REF] Morgan | 5 Fatal Flaws with Virtual Meetings[END_REF].

The novelty of our approach is that we organize an internal technical workshop as a challenge contest. Case study partners submit in advance their challenges related to the project goals. These challenges should be concise to be experimented within 4 hours. The teams are then formed around those challenges. On the hackathon day, partners have 4 working hours to come with a result that should be both interesting and convincing.

In the following sections, we provide a high-level overview of the MegaM@Rt 2 project, challenges to manage technical collaboration in such a huge project, our approach for internal hackathons and preliminary results. We believe that the presented approach can be successfully applied to many other collaborative projects.

II. OVERVIEW OF THE MEGAM@RT2 PROJECT

The main goal of the MegaM@Rt 2 project is to create an integrated framework incorporating methods and tools for continuous system engineering and runtime validation and verification (V&V). The underlying objective is to develop and apply scalable model-based methods and tools, in order to provide improved productivity, quality and predictability of large and complex industrial systems.

One of the main challenges is to cover the needs coming from diverse and heterogeneous industrial domains, going from transportation and telecommunications to logistics. Among the partners providing case studies in the project, we can cite Thales, Volvo Construction Equipment, Bombardier Transportation or Nokia. These organizations have different product management and engineering practices, as well as regulations, commercial and legal constraints.

This results in a large and complex catalogue of requirements to be realized by the architecture building blocks at different levels of abstraction. Thus, the development of the MegaM@Rt 2 framework is based on a feature-intensive architecture and on a related implementation roadmap. The MegaM@Rt 2 framework plans to integrate 28 tools implementing the above-mentioned methods and satisfying requirements coming from 9 industrial case studies.

III. ISSUES OF HUGE COLLABORATIVE PROJECTS

Some instruments for collaborative projects gather very large and complex projects, sometimes involving more than 100 person years and sometime over 100 partners (beneficiaries). The average number of participants per project in Horizon 2020 in general is 4.69, in the second pillar alone the average is 5.91, in ICT it is 7.4, but in ECSEL it is 34.22 [START_REF]H2020 participation -full details[END_REF]. At the web page of ECSEL JU are 40 projects listed ranging from 9 to 109 participants [4].

There is an assumption that the larger a project is, the more complementary the resources of different partners can be, and the larger the impact as well, but large consortia may not be that efficient. Thus, large projects are not good per se.

To some degree, a project thrives with more partners of different kinds. Different views, backgrounds, competencies, networks, focuses etc., make the collaboration better and enrich the work because of complementary and mutual learning.

However, there are some evidences that over a certain size, the larger a project is, the lower the effect of complementary becomes. This is because of larger uncertainties, higher transaction costs and a cognitive distance among partners [4] [START_REF] Nooteboom | Inter-firm Alliances: Analysis and Design[END_REF]. Cognitive distance poses both a problem and an opportunity for collaboration, in that a large distance provides the potential for novelty and creativity (i.e. to learn something new) but at the same time makes understanding more difficult between the parties involved [4]. The dimension of the projects poses several challenges for its management. Hence, it is not likely that all the staff from two partners ever meet in the project, as it was concluded for another similar project [START_REF] Spanos | Conditionally-mediated effects of scale in collaborative R&D[END_REF] [7] [START_REF] Nooteboom | Inter-firm Alliances: Analysis and Design[END_REF].

Thus, in large, collaborative multi-partner projects there is a distance between the partners, that has to be addressed and bridged. The concept of distance involve different aspects:

• the kinds of partner organizations that span from academia to small, medium and large enterprise; • the kinds of project members expertise and seniority, varying between industrial employees or academic pro-fessors, younger researchers and developers, managers, administrators, entrepreneurs etc.; • the difference in national cluster either in terms of number of organizations and, most importantly, in funding and budget restrictions due to different national rules in economic support; • last, the cultural heritage that affects the personal approach to the job activities and relationships. We experienced a need to bridge this distance, since during the kick-off and the first plenary meeting, held in Rome, we received substantial feedback from the staff complaining that the content was too administrative or managerial. Instead of just using the plenary meetings to planning and reporting, we thought we should take advantage of our differences and plan the meeting in a manner that challenges also the technical competence represented by the most of the partners.

A. Challenges

In the following, we enumerate several challenges that can be found in European projects such as MegaM@Rt 2 .

Dimension and partner organization. In the case of MegaM@Rt 2 , we have 27 beneficiaries, distributed among academia (7 universities and 3 research centers), Small and Medium Enterprises (8 SMEs) and Large Enterprises (9 LEs) from 6 countries (Finland, Sweden, Czech Republic, Italy, Spain and France), slightly below the average ECSEL project. Anyhow, we have well over 120 participants/members directly involved in the project.

National clusters. The differences are partially related by the different composition of researches, SMEs and LEs. But the most significant issue is related to the different funding rates. The European Commission (EC) covers 25% to 35% of the total budget. National support vary significantly based on country and type of organization. National funding rate for LEs is null in France, as small as 10% in Italy, increasing up to 25% in Finland. SMEs span from 15% to 35%. Academia and research centers may receive up to 60% of total budget. These facts may impact the planning and the level of participants expertise engaged by each organization in the project.

Cultural heritage. Studies about differences in social relationships and habits represent a huge discipline. Hofstede Insights apply a structural approach and model to understand and exploit cultural knowledge for business. A comparison chart [START_REF]Hofstede Insights -Compare Countries[END_REF] classifies the differences between European countries into six categories (see for instance "Fig. 1"):

• Power Distance: The extent to which the less powerful members of society accept that power is distributed unequally; • Individualism: (Individualist versus Collectivist) Collectivism: people belong to in-groups (families, organizations, etc.) who look after them in exchange for loyalty. Individualism: people only look after themselves and their immediate family; • Masculinity: The dominant values in society are achievement and success versus caring for others and quality of life;

• Uncertainty/avoidance: The extent to which people feel threatened by uncertainty and ambiguity and try to avoid such situations. • Long term orientation: The extent to which people show a pragmatic or future-oriented perspective rather than a normative or short-term point of view • Indulgence: The extent to which people try to control their desires and impulses. Expertise and seniority. Last but not least, we can classify the participants from the same organization as business managers and technical persons. The former participate mainly in coordination activities, while the latter are the ones who develop and deliver the actual results, so they have to be involved to interact with counterparts from other organizations.

B. Common drawbacks of traditional plenary meetings

The authors have participated in more than 30 collaborative research projects. Collectively we can identify several common issues with traditional approaches for project regular plenary meetings. We received many complaints that the plenary meetings are very administrative. Usually, a plenary is divided in slots for presentation by various partners (e.g. Work Package leaders) about the current state of the project and future plans. Many times, the discussions are kept at minimum. Many participants feel disengaged and consider plenary meetings as a waste of time. As consequence, many partners apply cost savings and send managers only without involving the technical staff, while, in fact the technical persons is actually producing the deliverables and would stronger benefit from tighter links with colleagues in other organizations working on the same deliverables. Thus, the output of plenary meetings becomes questionable.

We decided to re-think the plenary organization focusing the multiple objectives of the meeting: the administrative ones, to address the housekeeping issues related to the project status and its evolution, but the technical ones as well to trace the guidelines and focus the objectives of the new developments. To comply with this last point, we have directed towards a revision of the hackathon concept in order to effectively apply it to our needs.

IV. HACKATHON RELATED WORK

In recent years, hackathons have emerged as a popular way of attracting people with technical backgrounds to work together in teams and quickly produce working solutions. Nandi and Mandernach [START_REF] Nandi | Hackathons as an Informal Learning Platform[END_REF] investigated informal learning aspects of hackathons and reported that hackathons provide a structure for increased informal learning, promote peer learning and boost motivation of the participants to learn new skills.

Anslow et al. [START_REF] Anslow | An Experience Report of Data Hackathons for Data Science Education[END_REF] proposed to augment computer science curriculum with datathons (hackathons focusing on data analytics) and presented their results from four datathons involving computer science students and volunteer data scientists. In these datathons, the teams explored different datasets and helped the participating organizations find better uses of their data. Decker et al. [START_REF] Decker | Understanding and improving the culture of hackathons: Think global hack local[END_REF] argued that hackathon culture is usually intimidating. They proposed an alternative non-competitive, community-based format for hackathons called Think Global Hack Local (TGHL), which is aimed at making hackathons more inclusive and fun for all participants. They also reported results from two successful TGHL events involving non-profit organizations and computer science students.

Hackathons are not limited only to education and learning environments. They are also useful for rapidly exploring new business ideas and producing software prototypes [START_REF] Komssi | What are Hackathons for?[END_REF]. However to generate revenue and create real business value, promising prototypes must be developed further and transformed into finalized products.

Raatikainen et al. [START_REF] Raatikainen | Industrial Experiences of Organizing a Hackathon to Assess a Device-centric Cloud Ecosystem[END_REF] presented their experience from a hackathon organized to assess and validate the requirements and design of a device-centric cloud ecosystem. They reported that hackathon is a useful approach for this kind of task as it allows an efficient assessment of software artifacts and provides directions for further development and improvement of such systems. The hackathon resulted in a set of new requirements and three prototypes. Raatikainen et al. [START_REF] Raatikainen | Industrial Experiences of Organizing a Hackathon to Assess a Device-centric Cloud Ecosystem[END_REF] also highlighted some social benefits of hackathons including collaboration, inspiration, and motivation.

Komssi et al. [START_REF] Komssi | What are Hackathons for?[END_REF] reported results from five hackathon events, each having a different purpose. The most relevant of these hackathons was aimed at a collaboration among companies and research organizations. The hackathon resulted in six working prototypes and continued collaboration between two companies to further develop the ideas and prototypes.

Rosell et al. [START_REF] Rosell | Unleashing innovation through internal hackathons[END_REF] introduced the concept of internal hackathons, which are organized particularly for the internal employees of an organization. They also described some benefits of internal hackathons and reported their experience from a successful internal hackathon which was organized to find new creative ways of using a new communication protocol. The internal hackathon extended the usual hackathons in two ways. First, a special attention was given to the preparation of the participants. Secondly, the hackathon was open to employees in both technical and non-technical positions. Out of 120 participants, 48% came from non-development departments while 13% had a purely non-technical background. The hackathon teams produced a wide range of solutions and identified six areas of innovation and improvement for the communication protocol.

Frey and Luks [START_REF] Frey | The innovation-driven hackathon[END_REF] presented innovation-driven hackathons as a mean for overcoming organizational obstacles and challenges which hinder and slow down innovation within medium and large sized companies. They suggested to invite best people with different skills and backgrounds from both within and outside the organization to participate in compact 1-3 days events. They also proposed that the main event should have time-boxed iterations comprising four phases: problem definition, solution alternatives, prototypes, pitch and feedback. The final pitch should be given in front of a jury, which may select one or more concepts or prototypes for further development in the context of the project.

V. THE HACKATHON APPROACH IN MEGAM@RT2

The main goal of the approach presented in this paper is to boost the project development by increasing the efficiency of the plenary meetings:

• involving at plenary meetings not only management personnel responsible for project coordination, but also actual doers (i.e. technical people) in order to foster collaboration and cross-fertilization among partners; • creating positive synergies between use case and technology providers; • helping use case providers to bootstrap the baseline experiments by providing use case providers dedicated technology demonstrators on a clearly limited subset of their specific industrial challenge (based on realistic concrete material, e.g. models, code, etc.); • using the demonstrators to track project progress with respect to project deliverables, illustrating results as well as spotting the innovation at early stages; • ensuring that all the case studies have several partners involved. In order to address the above goals, we devised an internal hackathon event that we applied at two plenary meetings and which is planned to be also organized in future plenaries. Based on the above arguments, we decided to design a custom internal hackathon that will enhance the collaboration and exchange of ideas between different project partners. Our approach to internal hackathons is described in the following.

A. Specifics of our internal hackathon.

In the MegaM@Rt 2 project we apply a customized version of the hackathon, involving 5 prerequisites:

• Technical staff must be involved;

• For each challenge proposed by a use case owner, there should be at least one technology provider subscribed; • Defined time boxes for the work;

• Competition, entertainment and small prizes;

• Inclusive environment where everybody feels concerned. Our hackathon process comprises of three main phases: before, during, and after, each with own set of activities, as follows.

Before phase is characterized by a call for hackathon: case study providers are required to prepare hackathon challenges (i.e. a well-defined and limited experiment related to use cases that can be explored in a half day work) and announce them to the rest of the participants. Tool and technology providers subscribe to these hackathon challenges proposing methods and tools that can solve the challenge. This approach allows all the involved participants to identify punctual challenges and prepare in advance for them, by providing the corresponding documentation, artifacts and tools, and by choosing the corresponding technical personnel to participate in the event.

During the hackathon session, each hackathon challenge is presented by the case study providers as a technical pitch in the morning of the event. On one hand, this allows the entire audience to be aware of the details of the challenge. On the other hand, it gives the possibility for additional participants (i.e. not already subscribed) to join the hackathon challenge. Then working groups are formed for each challenge to work in parallel in 2 sessions of 4 hours each.

After the hackathon sessions, each challenge provider gives in plenum a short overview of the main outcomes of the work and plans for future collaboration. In addition, all plenary participants are asked to evaluate the results of each challenge using an anonymous online voting system.

B. Evaluation metrics

Four aspects are evaluated: Technical innovation -how novel is the presented result, is it a breakthrough or an evolution?; Exploitation potential -can this demo be a step to generate revenues, foster market access to tool providers and help case study providers to improve their own developments?; Technological readiness -(for demonstration purposes) -does the team work look as a finished demonstration that we can reuse?; and Entertainment (fun) -does the team present the results in a way that is both instructive and easy to digest? An example is given in "Fig. 2".

The best demos/presentations voted by the audience are selected as showcases for different project dissemination activities. managerial sections and the general feeling on hackathon experience. For instance, when we asked the plenary participants to specify the three best parts of the plenary the hackathon received the most votes, as shown in "Fig. 3".

Furthermore, the participants provided positive feedback when asked to comment on the hackathon experience as illustrated in "Fig. 4".

Last but not least, the vast majority of the participants considered the progress generated by the internal hackathon as significant. They were planning to work further on the ideas developed during the hackathon after the plenary meeting in order to foster inner project collaboration and boost the project overall progress.

Finally, they voted to continue with such an approach at the following plenary meetings.

VI. CONCLUSIONS AND LESSON LEARNED

In this paper, we presented an internal hackathon approach that we defined and applied in the context of the MegaM@Rt 2 project in order to boost project collaboration and development. After the first project's plenary meeting held in Rome that highlighted the lack of effective technical results, the internal hackathon initiative has been applied in the two following plenary meetings in Helsinki and Paris. Based on the positive feedback from the project participants, we plan to apply it again in future ones.

The best hackathon results of each plenary meeting have been selected for dissemination activities. In addition, they were presented in the first official review meeting of the project, where both the approach and the results received the appreciation of the project reviewers.

The long-term effects are still under observation and need to be quantified in a more formal way, but some significant benefits are already tangible and concrete. So far, we have observed the following immediate effects:

• General improvement of the project working atmosphere; • Significant improvement on partner interactions either among use cases and tools providers and between tool providers, that also identified new opportunities to integrate with each others tools (sometime complementary) or new features to improve their offers.

However, we will continue to improve and evaluate our internal hackathon approach in the next plenary meetings while keeping in mind the following risks:

• Hackathons produce prototypes used as proof-ofconcepts, that should not be considered as final products; • Hackathons are focused on well-delimited challenges.

The longer-term focus can be missed without proper follow-up and monitoring of the related activities; • Hackathons cannot be used as a day-to-day practice, since the daily effort is very intense and the team may easily burn out.

The main mitigation for the above risks is to repeatedly make the project partners aware of them both at the plenary meetings and throughout the project. In addition, we are considering to adjust the hackathon sessions over several days of the plenaries, and interleaving them with the project coordination sessions to make the two technical and administrative aspects more cohesive.

Fig. 1 .

 1 Fig.1. Hofstede country charts comparison example[START_REF]Hofstede Insights -Compare Countries[END_REF]

Fig. 2 .

 2 Fig. 2. Example of challenge evaluationAdditional questions helped to understand the acceptance and the adequacy of the plenary tuning among technical and

Fig. 3 .

 3 Fig. 3. Best part of the plenary meeting based on participants' votes

Fig. 4 .

 4 Fig. 4. Participants comments on the first hackathon

•

  Continuation of the hackathon work on new research lines, and new applications of project tools to use cases; • Easier development progress status tracking of use cases and tools, comprehension of practical demonstration;

ACKNOWLEDGMENT

This work has received funding from the Electronic Component Systems for European Leadership Joint Undertaking under grant agreement No 737494. This Joint Undertaking receives support from the European Unions Horizon 2020 research and innovation programme and Sweden, France, Spain, Italy, Finland, the Czech Republic.


Bruno Chaudret
email: chaudret@insa-toulouse.fr

Montserrat Gomez
email: gomez@chimie.ups-tlse.fr

Montserrat Go ´mez •

Karine Philippot
email: karine.philippto@lcc-toulouse.fr

Montserrat Go ´mez

Metal Nanocatalysts in Solution: Characterization and Reactivity

published or not. The documents may come

Homogeneous catalysis has emerged as a very important field thanks to the high selectivities reached nowadays by these catalysts and to the molecular understanding of the reactions involved. Heterogeneous catalysis continues to be of very high industrial importance and will be a major actor in the energy transition. Present trends in this field concern the precise monitoring of molecular surface reactivity.

Colloidal catalysis, which remained marginal for a long time, has gained more and more interest. Thus it concerns reactions typical of molecular chemistry such as carboncarbon or carbon-heteroatom coupling. One major goal in this field is to reach enantioselectivity comparable to the molecular systems. However this remains a challenge although some novel approaches become available, such as the ones described in this issue. Colloidal catalysis also allows access to reactions that standard molecular chemistry cannot achieve such as arene hydrogenation or Fischer-Tropsch synthesis and addresses the important field of energy (Fischer-Tropsch synthesis again and hydrogen generation). Colloidal catalysis is also part of the tendency of chemistry to ''go green'', nanoparticles may be soluble in water or in ionic liquids which offer the advantage of resembling supported catalysis while allowing facile heat diffusion.

The synthesis of nanoparticles has progressed tremendously for the past 20 years and now it is possible to prepare controlled species, mono or bimetallic, either with or without stabilizers at the metallic surface (such as ligands, salts, polymers, hydrides, CO, and so on), which eventually may be deposited on a support to give rise to well-defined heterogeneous catalysts. These species may expose a defined surface, a controlled chemical order or a number of ordered surface ligands and have given rise to the concept of ''Nanocatalysis.'' Spectroscopic investigations are carried out in order to lead to a molecular description of the surface reactivity, in particular through the development of more and more precise NMR methods while the chemical understanding of surface reactivity today benefits from the impressive progresses in DFT modeling which can now use ab initio methods.

This issue of Topics in Catalysis profits from the diverse approaches described here above to offer a snapshot of the present tendencies in this important field.


Mathieu Aucejo
email: mathieu.aucejo@lecnam.net

Olivier De Smet

Jean-François Deü

On the interest of a space-time regularization for reconstructing sparse excitation sources

In time domain, force reconstruction problems are commonly solved from Tikhonov and LASSO regularizations. Practically, these approaches can lead to inaccurate reconstructions, if the sources to identify don't share the same space-time characteristics or the corresponding force vector doesn't exhibit the desired structure. To alleviate this potential drawback, we have recently introduced a multiplicative space-time regularization that allows exploiting one's prior knowledge of the spatial distribution of the sources as well as their time history. In this contribution, the proposed regularization strategy is compared to the multiplicative Tikhonov and LASSO regularizations through an experimental application to point out the practical interest of exploiting simultaneously both spatial and temporal prior information in terms of quality and robustness of the reconstructed excitation sources.

Introduction

Force reconstruction problems in time domain still remain an active topic in the structural dynamics community. To solve this problem, several approaches have been developed, such as Kalman filtering [1] or adaptive filtering [START_REF] Sturm | Proc. ISMA[END_REF]. However, the most widespread strategy is certainly the regularization, and more particularly, the Tikhonov and LASSO regularizations. From a theoretical standpoint, Tikhonov regularization should be used when the force signal exhibits a certain continuity [START_REF] Bennani | [END_REF]4] and the spatial distribution of the sources is rather smooth [START_REF] Boyd | Convex optimization[END_REF]. On the contrary, LASSO regularization should be used when the excitation signal is rather impulsive [START_REF] Ginsberg | Proc. ISMA[END_REF][START_REF] Qiao | [END_REF] and the spatial distribution of the sources is sparse [8]. It results that classical strategies developed in the literature are theoretically not always well adapted to tackle both the localization and time reconstruction problems at the same time, except for configurations where the force vector to identify has the desired structure or the spatial distribution of sources and the nature of the excitation signals share the same space-time characteristics, such as the sparsity [9]. To the best of our knowledge, only a few methods have been developed to address this specific issue and they generally consist in solving the space-time reconstruction problem in a separated manner [10].

In this contribution, we propose to highlight the practical interest of exploiting simultaneously both the spatial and temporal features of excitation sources to solve the inverse problem efficiently thanks to the multiplicative space-time regularization, recently introduced by the authors [11]. To this end, the proposed regularization strategy is compared to the multiplicative Tikhonov and LASSO regularizations through an experimental application. In particular, it is shown that properly exploiting one's prior knowledge of the sources to identify allows improving the quality and the robustness of the regularized solutions.

Multiplicative space-time regularization

Regularization consists in including in the formulation of the inverse problem some prior information on the excitation field to identify in order to constrain the space of solutions. In the present contribution, it is proposed to seek the unknown global excitation field F as the solution of the following minimization problem:

F = argmin F\{0} F(Y -HF) • R(F), (1)
where

• F(Y -HF) is the data-fidelity term which controls the a priori on the noise corrupting the data. Here, it is assumed that the reconstruction model is linear and defined such that:

Y = HF; (2)
• R(F) is the regularization term that encodes prior information on the excitation field F, i.e. what is known about the excitation field before making any measurement.

It should be noted here that the previous minimization problem is referred to as multiplicative regularization. This choice has been made, because this approach is generally computationally more efficient than its additive counterpart (a.k.a. Tikhonov-like regularization) given that it is free from the preliminary definition of any optimal regularization parameter [14]. That being said, it is clear from Eq. ( 1) that the quality of the reconstructed excitation field is not only conditioned to the adequacy of the data-fidelity and regularization terms with the actual noise and the actual space-time source characteristics, but also to the quality of the reconstruction model describing the dynamic behavior of the considered structure. That is why, all the ingredients of the method are described separately for the sake of clarity.

Derivation of the reconstruction model

The reconstruction model given by Eq. ( 2) can be classically established either from the discretization of the Duhamel's integral or from the discretization of the state-space representation of the mechanical system. In the present paper, the reconstruction model is built from a discretized state-space representation, because it can easily deal with kinematic data of various types (displacement, velocity, acceleration, strain).

The state-space representation is composed of a state equation and an output equation. In this contribution, we propose a state-space model based on the generalized-α integration scheme [15], because this method is unconditionally stable and second-order accurate and minimizes the numerical damping at low frequencies for a given high-frequency damping level.

To derive the state equation from the generalized-α method, let us consider a regular partition of the time domain such that t 0 < • • • < t k < • • • < t f (t 0 and t f : initial and final instants) and let h = t k+1 -t k denote the time step size. For a mechanical system described by its mass, stiffness and damping matrices (M, K, C), one has to start from the following equations [16]:

M .. d k+1-αm + C . d k+1-α f + K d k+1-α f = S f f k+1-α f , (3a)
.

d k+1 = . d k + (1 -γ) h .. d k + γ h .. d k+1 , (3b)
d k+1 = d k + h . d k + 1 2 -β h 2 .. d k + β h 2 .. d k+1 , (3c)
where γ and β are the parameters of the Newmark method, α m and α f are two averaging parameters associated to the inertia and internal/external forces, while

d k = d(t k ) and f k = f(t k )
are, respectively, the displacement and excitation vectors at time t k , S f being the selection matrix of the excitation degrees of freedom. In the previous equation, the quantity d k+1-α must be read as:

d k+1-α = (1 -α) d k+1 + α d k . (4)
For linear systems, it is a common practice to use a modally reduced order model to limit the computational costs. In this regard, when the displacement vector is expanded on its modal basis, the previous equation of motion becomes:

..

q k+1-αm + Z n . q k+1-α f + Ω 2 n q k+1-α f = Φ T n S f f k+1-α f , (5a)
.

q k+1 = . q k + (1 -γ) h .. q k + γ h .. q k+1 , (5b)
q k+1 = q k + h . q k + 1 2 -β h 2 .. q k + β h 2 .. q k+1 , (5c)
where q k is the generalized displacement, Φ n is the matrix of the mass-normalized mode shapes,

Ω n = diag(ω 1 , . . . , ω n ) and Z n = diag(2ξ 1 ω 1 , . . . , 2ξ n ω n ),
where ω n and ξ n are respectively the modal angular frequency and the modal damping ratio of the mode n.

After some manipulations, detailed in Ref. [11], and considering that the state vector x k is defined such that

x k = [q T k . q T k .. q T k ] T ,
we obtain the following state equation:

x k+1 = A x k + B + f k+1 + B -f k , (6)
where A is the system matrix, while B -and B + are the input matrices applied to the force vector at time k and k + 1.

Regarding the output equation, it can be expressed as:

y k = S d d k + S v . d k + S a .. d k = S d Φ n q k + S v Φ n . q k + S a Φ n .. q k = O x k , (7)
where y k is the output vector, S d , S v and S a are, respectively, the selection matrices of the displacement, velocity and acceleration data measured on the structure and O = [S d , S v , S a ]Φ n is the output matrix.

All things considered, the state-space representation of the dynamical system deriving from the generalized-α method is given by:

x k+1 = A x k + B + f k+1 + B -f k y k = O x k . ( 8
)
At this stage, a last step is required to derive the reconstruction model as defined in Eq. ( 2). For this purpose, it is first necessary to express the state vector at time t k from the state and input vectors at times t j ≤ t k . In doing so, it can be shown that the state vector x k writes:

x k = A k x 0 + A k-1 B -f 0 + k-1 j=1 A k-j-1 B f j + B + f k , for t k > t 0 , (9)
where B = A B + + B -and x 0 et f 0 are the known initial state and input vectors.

From the previous relation, it results that the output vector y k , for t 0 < t k ≤ t n (n: number of time samples), is given by the relation:

y k = OA k x 0 + OA k-1 B -f 0 + k-1 j=1 OA k-j-1 B f j + OB + f k . ( 10
)
In the end, the proposed reconstruction model simply writes:

Y = H F, (11)
where

Y =        y 1 y 2 y 3 . . . y n        -        OA OA 2 OA 3 . . . OA n        x 0 -        OB - OAB - OA 2 B - . . . OA n-1 B -        f 0 , H =       OB + 0 • • • 0 OB OB + . . . . . . . . . . . . . . . 0 OA n-2 B OA n-3 B • • • OB +       , F =        f 1 f 2 f 3 . . . f n        .
Here, it is important to note that the initial state and input vectors are chosen so that x 0 = 0 and f 0 = 0. In other words, this means that it is compulsory to start the recordings of the output data before exciting the structure.

General formulation of the reconstruction problem

To obtain consistent reconstructions, it has be seen that a proper choice of the data-fidelity and regularization terms is crucial, since the more the prior information on the noise and the sources is meaningful, the more the confidence in the reconstruction is high [12]. Consequently, developing a particular regularization strategy is equivalent to propose particular data-fidelity and regularization terms. In the present case, this means that the data-fidelity has to reflect one's prior knowledge on the noise corrupting the data, while the regularization term must reflect one's prior knowledge on the spatial and temporal characteristics of the forces to reconstruct.

Regarding the data-fidelity term, a common assumption consists in considering that the measured data are corrupted by an additive Gaussian white noise, leading to a data-fidelity term of the form:

F(Y -HF) = Y -HF 2 2 . ( 13
)
The choice of the regularization term requires more reflection, since it must encode available information about the space-time characteristics of the excitation field to identify. To this end, it is relevant to define a regularization term based on a mixed p,q -norm. Practically, the regularization term is defined such that:

R(F) = F q p,q . (14)
To better understand the influence of the space-time regularization term in the formulation of the inverse problem, one can represent the unknown force vector F as a matrix, where the rows correspond to the time signal at a particular location and the columns to the excitation field at a specific instant. In doing so, it comes:

F = [f 1 . . . f j . . . f n ] =        f 11 • • • f 1j • • • f 1n . . . . . . . . . f i1 • • • f ij • • • f in . . . . . . . . . f m1 • • • f mj • • • f mn        , ( 15
)
where m is the number of reconstruction points of the excitation field.

On the other hand, if one reminds that the mixed p,q -norm is defined by:

F p,q =    m i=1   n j=1 |f ij | p   q p    1 q , ∀ (p, q) ∈ R * + , (16)
it becomes clear that the proposed regularization term introduces an explicit coupling between the coefficients of F and allows promoting some structures observed in real signals [13]. To illustrate this particular property of the mixed norms, let us consider the case for which (p, q) = (2, 1). In this situation, the matrix F is supposed to be sparse along the columns (space) and full along the rows (time). In other words, one promotes the spatial sparsity of the excitation field and the continuity of the time signals.

From the foregoing, the general formulation of the proposed space-frequency multiplicative regularization is given by:

F = argmin F\{0} Y -HF 2 2 • F q p,q . (17)
From a numerical standpoint, the previous formulation is solved from an adapted Iteratively Reweighted Least Squares algorithm described in Ref. [11]. Interesting readers can refer to the latter reference for more details.

Hammer impact reconstruction

In this section, the experimental reconstruction of a hammer impact is studied. This application intends to investigate the practical interest of applying the proposed approach for solving force reconstruction problems. The main objective of this real-world application is to demonstrate the advantages of the proposed strategy in terms of identification quality and robustness in operating conditions, compared to regularization strategies based on standard regularization terms.

Description of the structure under test

The structure under test is a thin aluminum plate of 60 cm in length, 40 cm in width and 6 mm in thickness, clamped along its length in a wooden support. The effective width of the plate resulting from the mounting conditions is 39.1 cm. To perform all the subsequent measurements the system is suspended to a rigid structure through a set of elastic bungee cords [see Fig. 1].

Reconstruction model

In the present application, the reconstruction model is built from a modal reduction and by considering that only acceleration data are available. Practically, this means that only the modal parameters of the structure and the selection matrix of the acceleration data S a have to be known to establish the reconstruction model given by Eq. (11).

To obtain the modal parameters of the structure, an experimental modal analysis (EMA) has been conducted from a roving hammer test performed on a grid of 17× 17 points using three reference accelerometers and an impact hammer equipped with a steel tip to properly excite all the modes below 6500 Hz. The goal of the EMA is to extract the modes of the real structure in order to limit the influence of modeling errors when establishing the reconstruction model. The locations and the associated identification numbers of the references accelerometers with respect to the measurement grid are presented in Fig. 2. All in all, the first 83 flexible modes and 2 suspension modes (at 1 Hz and 2.5 Hz) have been extracted.

Measurement of acceleration data and excitation signal

The output data resulting from a hammer impact have been collected using four accelerometers mounted on the structure. The input and output measurement devices have been located at nodes of the grid defined for the EMA to ensure the consistency of the reconstruction process. The locations and the identification numbers (ID) of the measured input and output data are defined in Fig. 3. In particular, it can be seen that no accelerometer is located at the excitation point (ID: 236).

In the present experiment, the hammer is equipped with a soft rubber tip, so as to fix the cutoff frequency of the excitation around 500 Hz. In this way, the convergence of the reconstruction model in terms of modal series is ensured. Regarding the signal processing parameters, the sampling frequency has been set to 16384 Hz for 32768 lines, meaning that the data have been recorded every 61 µs during 2 s.

Application

F = argmin F\{0} Y -HF 2 2 • F q q , ( 18
)
where q = 2 for mTIK and q = 1 for mLASSO.

In the following, the reconstructions are performed considering that the acceleration data are measured at nodes 19, 66, 153, 228 of the grid used for the EMA and the excitation sources are identified at nodes 19, 66, 228, 236 [see Fig. 3].

A first comparison is performed by reconstructing the applied forces on a sequence of 24 ms. To apply ST regularization, it is necessary to fix the value of the norm parameters p and q. Because the reconstruction of the hammer impact is performed on a rather short duration, it is reasonable to promote the continuity of the reconstructed excitation signals and the sparsity of the source distribution on the structure. As a result, the norm parameters defining the spacetime regularization term are set to (p, q) = (2, 0.5).

When applying mTIK (q = 2), mLASSO (q = 1) and ST regularizations on the selected sequence, we observe that all the three regularization approaches give very similar reconstructed excitation fields, which are in very good agreement with the target excitation field [see Fig. 4]. This surprising result can be partly explained from the analysis of Fig. 3 showing that the reconstruction points are rather distant from each other. This probably makes the reconstruction easier over this relatively long sequence compared to the impact duration. Over a shorter duration, however, the results significantly differ. Indeed, when the reconstructions are performed on a sequence of 5.4 ms, obtained reconstructions show that, in this particular situation, only ST regularization allows obtaining a consistent space-time reconstruction of the target excitation field [see Fig. 5]. Consequently, this experimental application clearly indicates that properly exploiting simultaneously the space-time characteristics of excitation sources is beneficial in terms of quality and robustness of reconstructed solutions.

Conclusion

The practical interest of taking advantage of one's prior knowledge of the space-time characteristics of the sources to identify has been demonstrated in this contribution through a real-world application. More specifically, it has been clearly established that developing a regularization strategy based on the definition of a space-time regularization term allows improving the quality and robustness of reconstructed excitation sources.

Figure 1 :

 1 Figure 1: Structure under test

Figure 2 :Figure 3 :

 23 Figure 2: Locations of the reference accelerometers with respect to the grid used for EMA -(•) Roving hammer excitation points and ( ) Measurement points (reference accelerometers)

Figure 4 :

 4 Figure 4: Reconstruction of the excitation field corresponding to a hammer impact over 24 ms -(a) Waterfall representation -mTIK regularization, (b) Waterfall representation -mLASSO regularization, (c) Waterfall representation -ST regularization for (p, q) = (2, 0.5) and (d) Identified time signal at excitation point -(-) Reference signal and (--) Tikhonov regularization, (-• -) LASSO regularization and (• • • ) ST regularization

Figure 5 :

 5 Figure 5: Reconstruction of the excitation field corresponding to a hammer impact over 5.4 ms -(a) Waterfall representation -Tikhonov regularization, (b) Waterfall representation -LASSO regularization, (c) Waterfall representation -ST regularization for (p, q) = (2, 0.5) and (d) Identified time signal at excitation point -(-) Reference signal and (--) Tikhonov regularization, (-• -) LASSO regularization and (• • • ) ST regularization


Alexandre Le Roch
email: alexandre.le-roch@isae-supaero.fr

Student Member, IEEE Cédric Yirmontois

Member, IEEE Philippe Paillet

Member, IEEE Jean-Marc Belloir

Member, IEEE Serena Rizzolo Oe

Student Member, IEEE, Clémentine Durnez oe Federico Pace

Member, IEEE Pierre Magnan

Member, IEEE Vincent Goiffon Oe

S Rizzolo

C Dumez

V Goiffon

J.-M Belloir

Radiation-Induced Leakage Current and Electric Field Enhancement in CMOS Image Sensor Sense Node Floating Diffusions

Keywords: Charge storage, CMOS image sensor (CIS), dark current (DC), displacement damage dose

This paper investigates the leakage currents as well as the leakage current Random Telegraph Signais (RTSs) sources in sense node floating diffusions (FDs) and their conse quences on imaging performances specifi cally after exposure to high-energy particle radiation. Atonùc displacement damage and iorùzation effects are separately studied thanks to neutron and X-ray irradiations. Proton irradiations have been performed to simultaneously study displacement damage dose (DDD) and total iorùzing dose (TID) effects white being more representative of the space environment. The studied DDD ranges from 500 TeV •g-1 to 40 GeV • g-1 , and the TID ranges from 24 krad(Si02) to 72 krad(Si02)-High-magnitude electric fi eld effects, such as transfer-gate-induced leakage current, are investigated to further understand the phenomena involved in FDs white giving new insights into the Electric Field Enhancement of the charge gen eration mecharùsms. This paper shows that FDs are very sensitive to ionizing radiation because of the presence of depleted Si/Si02 interface with high-magnitude electric fields around the junction. On the other hand, displacement damage in the FDs is a major source of high amplitude leakage current RTSs and leakage current nonurùfornùty. Such radiation-induced degradations can prevent the use of CMOS image sensor with long FD retention time (e.g., global shutter operating mode or burst imagers) in radiation environments.

INTRODUCTION

C MOS image sensors (CISs), also called active pixel sensors (APSs), are solid-state imaging arrays where the transistors are integrated within the pixels. Arnong CISs, the four-transistor (4T) pinned photodiode (PPD) CIS, which cross section and top view are both shown in Fig. l, is com posed of pixels made of a buried photodiode (the PPD), a transfer gate (TG), a sense node (SN) floating diffusion (FD), and three other transistors, which are not represented, for reset and readout purposes [l]. Once the collected charges are transferred from the PPD to the FD throughout the TG by joining the two space-charged regions, they are stored for a certain amount of time, differing from the integration time, before being readout. For some specific applications using long-duration charge storage in FDs such as CISs operated in global shutter mode or burst mode, the role of the FDs becomes prominent [START_REF] Lauxtermann | Comparison of global shutter pixels for CMOS image sensors[END_REF], [START_REF] Meynants | Global shutter imagers for industrial applications[END_REF]. lndeed, contrary to the rolling shutter CISs, the long storage time in FDs required in global shutter image sensors makes them very sensitive to FD leakage current. Since global shutter and burst CISs are considered in various space and scientific applications in harsh radiation environments, it appears necessary to study radiation-induced FD leakage current in CISs.

Radiation-induced leakage currents in CISs photodiodes, also called dark current (DC), have been extensively studied both in the conventional photodiode and PPD technologies and reported therein [START_REF] Goiffon | Radiation effects on CMOS active pixel image sensors[END_REF]. Arnong these sources, two distinct phenomena can be differentiated: first, a continuous leakage current based on the Shockley-Read-Hall kinetic with a constant generation rate [START_REF] Sah | Carrier generation and recombination in P-N junctions and P-N junction characteristics[END_REF] and second, a leakage current fluctuation called Random Te legraph Signal (RTS) charac terized by a random and discrete fluctuations of the leakage current presenting several generation rates [START_REF] Hopkins | Random telegraph signals from proton-irradiated CCDs[END_REF]- [START_REF] Bogaerts | Random telegraph signals in a radiation-hardened CMOS active pixel sensor[END_REF]. The origin of these fluctuations remains unclear but possibly relies on metastable generation centers presenting several configurations leading to several generation rates [START_REF] Hopkins | Random telegraph signals from proton-irradiated CCDs[END_REF], [START_REF] Jay | Simulation of single particle displacement damage in silicon-Part II: Generation and long-time relaxation of damage structure[END_REF]. Due to its random fluctuations as well as its high leakage current variations, this parasitic process severely affects the performances of OSs. Even though numerous studies focus on leakage current sources in CISs photodiodes, a very few works are dedicated to the FD leakage current [START_REF] Tsai | Twinkling behavior in ultra-high-resolution CMOS global shutter pixels[END_REF], and none is dedicated to the radiation effects on the FD leakage current_

Il. EXPERIMENTAL DETAILS

This section aims to describe the sensors under test as well as the setup used to characterize the leakage current and the leakage current RTS before and after irradiation. The CIS under test is a 512 x 512 4T PPD custom imager manufactured in a commercially available 180-nm CIS technology. This sensor has been designed and built for scientific research pur poses allowing modifying most of the relevant potentials in the pixels. The structure of the pixels is similar to the illustration presented in Fig. 1. As this paper focuses on the FD structure, the CIS is operated as 3T CISs where the FD is assimilated to the photosensitive element. To do so, the TG is kept at its low bias level (OFF condition), and variable FD integration time is inserted between the signal and the reference samples. This FD integration time is directly linked to the retention time in the case of a global shutter configuration as well as in the case of any application where the signal is stored in-pixel on an FD. AU the measurements are performed in the dark at 22 °C. Leakage current RTS analysis uses a rising edge detection algorithm [Il], [START_REF] Durnez | In-depth analysis on radiation induced multilevel dark current random telegraph signal in silicon solid state image sensors[END_REF] with a 1-s sampling period on 15 000 images. The considered neutron and proton irradiations were performed at Université Catholique de Louvain in Louvain, Belgium. X-ray irradiation was performed using an Aracor 10 keV X-ray irradiator at CEA DAM in Bruyère le Chatel, France. Irradiation parameters are summarized in Ta ble I and were performed at room temperature with all the CIS pins grounded.

In this paper, the influence of the electric field on the FD leakage current is investigated using the TG low bias level (i.e., the TG OFF-voltage) from O to -1 V and the reset supply voltage from 1.8 to 3.3 V. The nominal bias conditions for Sections m and IV are O V for the TG and 3.3 V for the reset voltage. All the measurements have been performed after four weeks of annealing at room temperature. In order to compare the results obtained on the FD to the PPD technology addressed in many papers, this paper investigates both the PPD and the FD leakage current sources on the same sensor.

III. RADIATION EFFECTS ON THE LEAKAGE CURRENT

This section first addresses the radiation-induced mean leakage current increase over the sensor array. Results are compared with the universal damage factor (UDF) [START_REF] Srour | Universal damage factor for radiation-induced dark current in silicon devices[END_REF]. Tuen, the leakage current distribution is investigated giving more insights into the leakage current nonuniforrnity induced by radiation.

A. Mean Leakage Current

The mapping of PPD and FD leakage current over a small part of the sensor arrays is shown in Fig. 2. Before irradiation, while the mean leakage current in PPDs is only about 8 e--s-1 at 22 °C, the mean leakage current in FDs is about 1400 e-• s-1 at the same temperature. In the absence of radiation-induced degradation, the PPD depletion region does not reach any oxide. Hence, only silicon bulk defects could possibly bring a generation current contribution. Since the PPD exhibits a very low mean leakage current before irradiation, we can legitimately suppose that the PPD is almost free of bulk defect. This conclusion can be transposed to the FD, which shares the same silicon bulk. Hence, it can be inferred that the FD leakage current cornes from generation centers located at the SilSi02 interface, such as the TG oxide and the shallow trench isolation (STI) sidewalls, which are directly in contact with the FD depleted regions, as shown in Fig. 1. Such interface defects are known to be leakage current sources and are generally reduced by a process in the conventional photodiodes [l]. SN FDs usually do not benefit from such manufacturing process optirnization, and it does not appear surprising to measure such an intense leakage current before irradiation. Moreover, the FD mean leakage current is even more important after irradiation. Sirnilar displacement damage dose (DDD) induced by neutron and proton irra diations has been deposited in sensors and labeled as Al B

and El F, respectively, in Ta ble I. The mean leakage current after proton irradiation is one order of magnitude higher than the one after neutron irradiation as shown in Fig. 2 for DDD = 500 Te V• g-1 . This result points out the high sensitivity of the FDs leakage current to the total ionizing dose (TID). ln FDs, the leakage current is dorninated by SilSi02 interface defects before irradiation and by TID-induced inter face defects after ionizing energy exposition. The mean leakage current increase per unit volume mea sured all over the sensor array after irradiations are reported in Fig. 3 both for PPDs and FDs. Focusing on the PPDs results, we observe an increase of the mean leakage current for ail the irradiations. The considered PPD depleted volume is 23 µm 3 . The UDF model [START_REF] Srour | Universal damage factor for radiation-induced dark current in silicon devices[END_REF], which includes exclusively the displacement damage contribution, is in agreement with the experimental mean leakage current increase in PPD for both neutron and proton irradiations. These results confirm that the TID-induced leakage current in PPDs is negligible in front of the displacement damage contribution for 50-Me V protons on the considered TID range. Regarding the FDs mean leakage current increase after neutron irradiations, these results are also in good agreement with the UDF considering an FD depleted region of 6 µm 3 .

Since the UDF model is clearly applicable after neutron irradiations in the FD, it implies that the majority of defects, which have been created into the studied depleted volume, are not impacted by a significant Electric Field Enhancement (EFE). lndeed, it would have led to a mean leakage current increase higher than the UDF model prediction.

After proton irradiations, the FD mean leakage cur rent increase does not fit the UDF model prediction as shown in Fig. 3. This can be explained by the ionizing energy deposited by the protons leading to a multitude of Si/SiO2 interface defects as observed in conventional pho todiodes without surface pinning implant (i.e., the socalled 3T photodiodes) [START_REF] Goiffon | Radiation effects on CMOS active pixel image sensors[END_REF].

B. Leakage Current Distribution

The PPD leakage current (i.e. DC) distributions before and after irradiations are shown in Fig. 4. Ail the irradiations lead to a commonly observed leakage current tail, which increases with the deposited DDD. The sirnilar distributions observed after neutron and proton irradiations, which have induced the same DDD, confirm that, on the whole PPD population, TID effects are negligible in front of DDD effects for 50-MeV protons on the considered TID (24 krad). The PPD leakage current distributions induced by DDD have been studied in numerous papers, and several empirical models have already been proposed [START_REF] Marshall | Proton-induced displacement damage distributions and extremes in silicon microvolumes charge injection device[END_REF]- [START_REF] Gilard | Statistical analysis of random telegraph signal maximum transition amplitudes in an irradiated CMOS image sensor[END_REF]. Simulation-based models have also been presented in the literature [START_REF] Inguimbert | Modeling the dark current non-uniformity of image sensors with GEANT4[END_REF]. In this paper, the analytical model developed in [START_REF] Belloir | Pixel pitch and particle energy influence on the dark current distribution of neutron irradiated CMOS image sensors[END_REF] is considered because it does not require any simulation and has been verified on several CIS technologies. The leakage current of one pixel after irradiation lctar kooo can be expressed as [START_REF] Fossum | A review of the pinned photodiode for CCD and CMOS image sensors[END_REF] where fctark is the leakage current before irradiation and Ll lctar kooo is the DDD-induced leakage current increase. Using the probability density fonction (pdf) to study the whole population of pixel over this array, the expression (1) becomes

fctar k000 ( x ) = fctark ( x ) * fMwtooo ( x ) (2)
where f Mwt ooo ( x ) is detailed in the Appendix. As expected, the leakage current increase distributions after irradiations are in good agreement with this DDD serniempirical mode!, demonstrating once again that bulle defects dorninate the PPD response in these irradiation conditions. The good agreement with the model also demonstrates clearly that EFE does not play a significant role on irradiated PPDs since EFE is not taken into account in the mode!. Fig. 5 shows the FDs leakage current distributions before and after irradiations. Before irradiation, the FDs leakage current distribution discloses a large leakage current tail in comparison with the one observed in PPDs visible in Fig. 4. Moreover, this distribution looks bent. This observation does not correspond to the leakage current distributions of the conventional 3T photodiodes dorninated by Si/SiO2 interface defects [START_REF] Goiffon | Ionization versus displacement damage effects in proton irradiated CMOS sensors manufactured in deep submicron process[END_REF]. These results could be explained by an EFE of the FDs leakage current of some pixels as discussed in [START_REF] Srour | Enhanced displacement damage effectiveness in irradiated silicon devices[END_REF] and [START_REF] Bogaerts | Enhanced dark current generation in proton-irradiated CMOS active pixel sensors[END_REF]. Hence, these observations suggest that FDs have intrinsic high-magnitude electric field regions, which could influence the FDs leakage current distribution.

After neutron irradiations, the rise of the FDs leakage current tail with the deposited DDD is observed. However, the semiempirical model used to predict the leakage current distribution after neutron irradiation does not fit the experimental results gathered on the FDs, as shown in Fig. 5. Indeed, it appears a leakage current distribution tail extension toward higher leakage current compensated by a reduction of the occurrence at lower leakage current values. It leads to a bend of the leakage current distribution tail, which is more and more obvious with increasing deposited DDD. This discrepancy from the model suggests that the DDD-induced defects behave differently in the FDs. The previously suggested presence of high electric field regions in the FDs before irradiation could also explain this observation by enhancing the carrier generation rates of the bulk defects induced by the DDD. This EFE is not visible on the average leakage current value (see Section III-A) because only a small population of pixels is dominated by this effect.

Contrary to what is seen on PPDs (see Fig. 4), the TID contribution induced either by proton or X-ray irradiations in the FD leakage current is visible in Fig. 5 as a clear Gaussian distribution centered on 2.8 × 10 4 e -• s -1 . The fact that the TID increases the FD leakage current of the whole pixel population is also clearly visible in Fig. 3 when comparing proton to neutron irradiations. Hence, it can be concluded that, after ionizing dose deposition, the FDs leakage current is mainly due to the creation of additional interface defects located either at the STI sidewalls or under the TG gate oxide.

Regarding the comparison between protons and X-rays, both irradiations share the same TID and reveal the same mean leakage current as well as the same Gaussian distribution as expected. Although after proton irradiation the mean leakage current is dominated by the interface state contribution, the distribution still reveals a leakage current tail, which corresponds to the DDD induced leakage current nonuniformity.

IV. RADIATION EFFECTS ON THE LEAKAGE CURRENT

RANDOM TELEGRAPH SIGNAL Fig. 6 shows the FD leakage current RTS evolution with time of five selected pixels of an unirradiated sensor. Fig. 6 shows that the FDs are already exhibiting the clear leakage current RTS behaviors before irradiation as reported in [START_REF] Tsai | Twinkling behavior in ultra-high-resolution CMOS global shutter pixels[END_REF]. Over the sensor array, 5% of the FDs disclose the RTS behavior versus 0.04% for the PPDs.

The leakage current RTS maximum transition amplitude distributions before and after irradiation are presented in Fig. 7 for the PPDs. The prediction model proposed in [START_REF] Goiffon | Radiation effects on CMOS active pixel image sensors[END_REF] and [START_REF] Goiffon | Multilevel RTS in proton irradiated CMOS image sensors manufactured in a deep submicron technology[END_REF] is in good agreement with the experimental data after DDD deposition by 22-MeV neutrons and 50-MeV protons. The typical mean RTS maximum transition amplitude is at A rts = 1200 e -• s -1 as expected at room temperature. For high DDD deposition, the prediction model underestimates the end of the RTS maximum transition amplitude distribution tail. This could be due to the presence of the second RTS center population with a higher amplitude than the main one, also observed in [START_REF] Robbins | An assessment of the bias dependence of displacement damage effects and annealing in silicon charge coupled devices[END_REF], which would only be visible when the studies RTS center population is large enough. The study of this deviation will be the subject of future work. The proton irradiation generates a clear peak at low RTS amplitude that corresponds to the TID contribution with a typical mean RTS maximum transition amplitude of A rts = 110 e -• s -1 at room temperature as reported in [START_REF] Virmontois | Total ionizing dose versus displacement damage dose induced dark current random telegraph signals in CMOS image sensors[END_REF]. The main conclusion here is that the main RTS center population in the PPD is well described by the existing predicting model for 22-MeV neutron and 50-MeV proton irradiations in the studied CMOS technology.

The leakage current RTS maximum transition amplitude distributions before and after irradiations are presented in Fig. 8 for the FDs. Unlike the PPDs which can be impacted by a low level of DDD as shown in Fig. 7, the relative increase in the RTS behavior at low DDD is less obvious in FDs, as shown in Fig. 8. Indeed, in the FD, the leakage current RTS is dominated by preirradiation interface defects as mentioned for the average leakage current. Once the sufficient DDD to obtain a clear signature of the DDD-induced RTS center is reached, an unusual RTS maximum transition amplitude distribution with a mean value of A rts = 10 000 e -•s -1 appears. This value is one order of magnitude higher than the classical value validated on many CMOS and CCD sensors ( A rts = 1200 e -•s -1 ) and reported in [START_REF] Goiffon | Ionization versus displacement damage effects in proton irradiated CMOS sensors manufactured in deep submicron process[END_REF]. This discrepancy could be due to a high-magnitude electric field effect, which would enhance the RTS defects generation rates. This hypothesis may seem to contradict the conclusion made in Section III-A, stating that the radiation-induced mean leakage current increase in the FDs is not enhanced by the electric field. However, the used RTS detection method detects the response of a single RTS center per pixel, the one that exhibits the largest maximum transition amplitude. Hence, technique isolates and highlights the most intense RTS fluctuations and hides the weakest ones, whereas the mean leakage current analysis averages the response of all the defects in a pixel, hiding the possible EFE. Therefore, it can be inferred that the high-magnitude electric field regions do not influence significantly the average leakage current increase in the FDs, but EFE plays a major role in the most extreme behaviors (i.e., the leakage current distribution tail and the leakage current RTS amplitudes).

After ionizing dose deposition either induced by X-rays or protons, the FD RTS maximum transition amplitude distributions do not follow the classical trend observed in the conventional photodiodes and PPDs. Indeed, the typical exponential distribution coming from the Si/SiO 2 interface defects usually induced by the TID with an RTS maximum transition amplitude of A rts = 110 e -• s -1 [START_REF] Virmontois | Dark current random telegraph signals in solid-state image sensors[END_REF] is not observed. Instead, the FDs reveal an unusual bent distribution, which could be explained here again by the presence of high-magnitude electric field regions, but this time at the Si/SiO 2 interface since they influence directly the TID-induced interface defect generation rates. The enhancement of TID-induced oxide RTS seems important enough to hide the DDD-induced RTS in the case of 50-MeV proton irradiations.

V. INDUCED ELECTRIC FIELD EFFECTS

ON THE FD LEAKAGE CURRENT After having suggested the existence of high-magnitude intrinsic electric field regions in the FD leading to an EFE of the defects generation rates, this section aims to highlight the role of this electric field by varying the biasing conditions.

A. Effects of the Transfer-Gate Bias on Leakage Currents

The structure of a typical 4T PPD pixel is shown in Fig. 1. The role of the TG is to transfer the collected charges from the PPD to the FD by creating a conductive the gate. To initiate the charge transfer, the TG is positively biased. However, during the integration time, the TG is negatively biased and isolates the photosensitive part, the PPD, from the FD SN. This last negative bias is commonly named V LoTG and can be typically set in a product to a value between 0.5 and -1 V in an application to favor, respectively, an antiblooming behavior or a low PPD leakage current. In this experiment, the TG bias is kept at its low-level V LoTG to study the FDs leakage current contribution and varies from 0 to -1 V.

Fig. 9 shows the FD mean leakage current versus the applied TG potential before and after irradiations. Before irradiation, the FD mean leakage current increases as the TG bias becomes more negative. The origin of this additional leakage current contribution in accumulation mode is similar to the one observed in MOSFET drains and 3T APS photodiodes in [START_REF] Pain | Excess noise and dark current mechanisms in CMOS imagers[END_REF], which is referred to as gate-induced leakage trap-assisted tunneling (GIL-TAT) in [START_REF] Yamashita | Analysis of dark current in 4-transistor CMOS imager pixel with negative transfer-gate bias operation[END_REF] or more commonly as gate-induced drain leakage current [START_REF] Martin | Electric field enhanced emission from non-Coulombic traps in semiconductors[END_REF], [START_REF] Noble | The effects of gate field on the leakage characteristics of heavily doped junctions[END_REF]. The location of this contribution is shown in Fig. 10 presenting the different leakage current sources in the FD structure. In the rolling shutter mode, the time delay between the reset sample and the signal sample is generally short enough (a few microseconds) to hide the effect of the FD GIL-TAT on the output signal. However, for longer FD charge storage durations, the FD l-"'!!,,,-.,-----rt-' 0 STI Interface Defects 0 TG Oxide Interface Defects 0 Bulk Defects GIL-TAT could be an important limitation parameter, and the high-negative TG bias should be avoided.

As shown in Fig. 9, neutron irradiations lead to a small increase of the FD mean leakage current. As the TG bias becomes more negative, the GIL-TAT is still observed but shifted upward because of the additional contribution of the neutron-induced leakage current. Radiation-induced bulle defects have no impact on the FDs mean leakage current in terms of GIL-TAT induced by the TG.

Contrary to the considered neutron irradiations in Fig. 9, the TID induced by the proton irradiation leads to a huge increase of the leakage current, which completely hides the GIL-TAT behavior on the average value. This result can be explained by the fact that the mean leakage current is mainly given by a large number of generated interface states that are not located in the GIL-TAT region 2 shown in Fig. 10.

The evolution of the FDs leakage current distribution before and after proton irradiation with the induced electric field is shown in Fig. 11. The previously observed GIL-TAT induced by the TG bias is visible before and after irradiation. Before irradiation, it results in a shift of the whole FDs leakage current distribution toward higher leakage currents. After the proton irradiation, it has been demonstrated in Section ill-B that the distribution can be decomposed in two parts: a Gaussian part due to the TID induced interface states and a high leakage current distribution tail generated by the DDD-induced bulle defects. The negative bias of the TG only leads to a slight change of the Gaussian part of the leakage current distribution with no effect on the DDD-induced tail mentioned in Fig. 5. It clearly shows that GIL-TAT after the proton irradiation only has an influence on some rare oxide defects, probably located under the gate oxide, but that bulle defects are not influenced by the TG bias.

B. Ejfects of the Reset Voltage on Leakage Currents

During the reset phase of an operating 4T PPD CIS shown in Fig. 1, the reset transistor is turned on, and the FD is positively biased at the commonly named VDDRsT potential. Once the FD capacity is charged, the reset transistor is turned off, and the charges coming from the leakage current sources are collected lowering the FD potential. As the generation rates of the FD leakage current sources can be impacted by the local electric field, FDs leakage current variation with the reset potential can be observed. In addition to the effect of the TG bias, Fig. 11 shows the evolution of the FD leakage current distribution with the reset voltage-induced electric field before and after proton irradiation. Before irradiation, the reset voltage modulates directly the whole tail of the leakage current distribution, suggesting that this tail of high leakage currents is due to the defects located in a high-magnitude field region created by the reset voltage. Since the presence of bulle defects before irradiation is very unlikely, these defects at the origin of the distribution tails are probably oxide defects. It is clear in Fig. 11 that the TG voltage has no influence on the end of the leakage current tail. Hence, the defects responsible for the leakage current tail are not likely to be located in region 2 in Fig. 10. The most probable location of the leakage current tail defects before irradiation is the STI sidewalls including the corners and the photodiode angles (source l in Fig. 10). Their generation rates are probably enhanced by a local high-magnitude electric field (most likely in the corner vicinity) induced by the reset voltage.

After the proton irradiation, the impact of the reset voltage on the leakage current distribution is also visible in Fig. 11. As the reset voltage decreases, the leakage current distribution shifts toward low leakage current. This result can be explained by a reduction of the FD depleted volume lowering the number of active defects. On the other hand, it can also be caused by the reduction of the GIL-TAT contribution, which magnitude is related to the potential difference between the TG and the FD implant. By lowering the reset voltage from 3.3 to 1.8 V, the GIL-TAT is also reduced. Furthermore, this trend is also observed in Fig. 11 after the proton irradiation with the variation of the TG bias but at a lesser extent. The above-mentioned increase of the leakage current distribution tail with the reset voltage before irradiation is also visible after the proton irradiation in Fig. 11. The increase of the reset voltage results in a slight extension of the Gaussian distribution attributed to the TID contribution. As shown for the preirradiation interface states, the reset voltage has an impact on the TID-induced interface defects and probably enhances their generation rates. Regarding the leakage current tail attributed to the DDD induced by the proton irradiation, FD leakage current RTS maximum transition amplitude distributions for several biasing conditions before and after neutron (DDD = 40 000 TeV • g -1 ) and proton [DDD = 500 TeV • g -1 and TID = 24 krad(SiO 2 )] irradiations. a reduction is observed with a decrease in the reset voltage, as shown in Fig. 11. Hence, these results suggest that the reset voltage has also an impact on the DDD-induced bulk defects generation rates.

To summarize, before irradiation, the reset voltage has an impact on the preirradiation defects located at the STI sidewalls including the corners and the photodiode angles. After irradiation, the reset voltage variation impacts both the TID-and DDD-induced defects.

C. Effects of the Transfer-Gate Bias on Leakage Current Random Telegraph Signals

As performed for the FD leakage current, this section focuses on the impacts of the induced electric field on the FDs leakage current RTS maximum transition amplitude. Fig. 12 shows the evolution of the FDs leakage current RTS maximum transition amplitude distribution with the induced electric field before irradiation (blue curves), after proton irradiation (green curves), and neutron irradiation (red curves). Before irradiation, the TG bias voltage does not influence the FDs leakage current RTS maximum transition amplitude distribution, showing that GIL-TAT does not play any role on the preirradiation RTS defects. The same results were observed after neutron irradiation. For the sake of clarity, the results are not reported in Fig. 12. As neutron irradiation does not lead to TID-induced defects, no high amplitude RTS contribution was observed with the TG bias variation.

After proton irradiation, biasing the TG more negatively leads to a clear EFE of the RTS maximum transition amplitudes, which extends the distribution toward higher RTS amplitudes. This high RTS amplitude contribution can be attributed to the TID-induced RTS defects located under the TG oxide, which are enhanced by the TG bias. This population can be linked to the one leading to the Gaussian deformation with the TG bias attributed to the TID-induced defect observed in Fig. 11. These results suggest that RTS defects located under the TG oxide do not play a major role in terms of leakage current RTS before irradiation but must be considered FD leakage current evolution with the TG bias after proton irradiation 500 TeV • g -1 and 24 krad(SiO 2 ).

after ionizing dose deposition as highlighted by the results shown in [START_REF] Chao | Random telegraph noises in CMOS image sensors caused by variable gate-induced sense node leakage due to X-ray irradiation[END_REF].

To illustrate these conclusions, the leakage current RTS evolution with time was followed while varying the bias applied on the TG. The results after the proton irradiation are presented in Fig. 13 for four selected pixels. The TG bias induces a classical GIL-TAT leakage current on pixel 1 by adding a continuous leakage current contribution, as shown in Fig. 11. For pixel 2, the GIL-TAT reveals a leakage current RTS behavior. Then, for pixels 3 and 4, the GIL-TAT clearly enhances the RTS amplitudes as already pointed out in Fig. 12.

D. Effects of the Reset Voltage on Leakage Current Random Telegraph Signals

In addition to the TG-induced effects, Fig. 12 shows the effects of the reset voltage on the RTS maximum transition amplitude distribution before and after proton and neutron irradiations. Before irradiation, the evolution of the RTS distribution with the reset voltage is clearly visible in Fig. 12. As the reset voltage decreases, the RTS distribution tail decreases and reveals an RTS maximum transition amplitude distribution slope at A rts = 110 e -• s -1 , which corresponds to the typical oxide DC-RTS signature in the absence of EFE.

After the proton irradiation, the increase of the reset voltage results in an extension of the RTS maximum transition amplitude distribution tail with no change in the main peak. As the RTS maximum transition amplitude distribution is dominated by interface states after ionizing energy deposition, it empathizes that the reset voltage plays a role on a small population of FDs presenting interface states with the leakage current RTS behavior.

Neutron irradiation sharing the same DDD than the studied proton irradiation leads to the same results as the one observed before irradiation because of the predominance of the preirradiation interface states in terms of leakage current RTS. After neutron-induced displacement at DDD = 40 000 TeV•g -1 , the reset voltage increase tends to increase the RTS maximum transition amplitude distribution tail. As the leakage current RTS is dominated by the induced DDD contribution at this dose, this result suggests that the reset voltage induced electric field plays a role on bulk RTS defects in the FD. Such reset voltage impact on the RTS behavior has not been observed in the 3T CIS photodiode [START_REF] Goiffon | Multilevel RTS in proton irradiated CMOS image sensors manufactured in a deep submicron technology[END_REF]. This difference can be explained by the higher electric field involved in FDs in comparison with the 3T CIS photodiodes.

As for the influence of the TG biasing conditions, Fig. 14 shows the leakage current RTS evolution after the proton irradiation while varying the reset voltage on five selected pixels. As pixel 1, some of the FDs are not impacted at all by the reset voltage. On the contrary, pixel 2 has a leakage current, which generation rate is clearly enhanced with the reset voltage. Pixel 3 is an example of the pixel where the RTS behavior is revealed by the reset voltage. Finally, the pixels 4 and 5 exhibit the RTS amplitudes that are directly enhanced by the reset voltage induced electric field.

VI. CONCLUSION

Unlike for PPDs, the FD leakage current is dominated by the interface states contribution. Such defects are present before irradiation and are the limiting factor to reduce both the continuous leakage current and the leakage current RTS. Due to its high sensitivity to interface state density, the induced TID dominates the FDs leakage current contribution and is visible at low dose.

This paper also shows the behavior of the TID-and DDD-induced defects in the presence of high-magnitude electric field, which would explain the unusual leakage current and leakage current RTS distributions compared with the ones usually found in the optimized CIS photodiodes. Therefore, the results confirm that the EFE is not playing a significant role in the state-of-the-art CIS photodiodes. The field-assisted generation mechanisms identified in FDs are probably induced by the following three main characteristics shown in Fig. 10.

1) A high doping level of the n-implant into a p-well implant leading to a high-magnitude electric field within the p-n junction. Indeed, whereas the doping level of CIS photodiodes is optimized to avoid unwanted high-magnitude electric field, the FD structure is based on a transistor source/drain implant with a higher doping level at the junction (e.g., N D FD ≈ 10 17 cm -3 and N D 3T-PD/PDD ≈ 10 15 cm -3 ). 2) A large surface contact between the depleted region and the sidewalls of the STI. As shown in Fig. 15(a), depicting the cross section of a conventional 3T photodiodes, the doping profile of the n-implant is optimized to extend the depleted region at the bottom of the STIs avoiding the STI sidewalls and its corners. On the other hand, the PPD depleted region visible in Fig. 15(b) is totally isolated from the Si/SiO 2 interface. However, as shown in Fig. 10, the FD presents a large surface contact between its depleted volume and the STI sidewalls and thus all around the implant.

3) The proximity of the depleted region with the STI corners that present a high-magnitude electric field. Indeed, the FD depleted region can reach a few hundred of nanometers as shown in Fig. 10, leading to a contact with the corners of the STI generally presenting a high-magnitude electric field. High-magnitude electric field effects induced both by the TG and the reset voltage have been investigated. It confirms the existence of an EFE in the FDs. The TG induces a GIL-TAT current based on the interface defects located at the oxide of the TG. This identified field-assisted leakage current is more important after the absorption of ionizing energy and can also lead to a leakage current RTS in this region. Therefore, the FD GIL-TAT will be considered when operating CIS requiring long retention time in radiation environments. The reset voltage also plays a prominent role in the electric field of the FDs and impacts the defects generation rates within the depleted region of the FD. The influence of the electric field on the defects generation rates is also relevant for other technologies, such as single photon avalanche diodes, which intentionally use a high-magnitude electric field to reach the breakdown voltage of the junction. Leakage current RTS investigation in such structures will certainly bring new experimental insights into the mechanisms involved in the field-assisted charge generation.

To improve the radiation resistance of FDs while allowing long storage times for global shutter CISs or burst CISs, the conventional hardening techniques of PN junctions can be considered. FD closed gate as used in [START_REF] Hancock | Total dose testing of a CMOS charged particle spectrometer[END_REF] or charge storage in buried channels usually used for CCDs will be considered.

APPENDIX DETAILS OF THE SEMIEMPIRICAL MODEL USED FOR THE LEAKAGE CURRENT DISTRIBUTION

The pdf of the DDD-induced leakage current increase f I dark DDD , as introduced in [START_REF] Belloir | Pixel pitch and particle energy influence on the dark current distribution of neutron irradiated CMOS image sensors[END_REF], is based on an exponential pdf law to represent the leakage current increase contribution of a single nuclear interaction labeled f ν dark (x). This exponential law is expressed as

f ν dark (x) = 1 ν dark exp - x ν dark . ( 3
)
The term ν dark is the exponential mean of the pdf referring to the mean leakage current increase per nuclear interaction. It has been shown in [START_REF] Belloir | Pixel pitch and particle energy influence on the dark current distribution of neutron irradiated CMOS image sensors[END_REF] that ν dark = 4100 e -• s -1 . At high DDD, the pdf is convoluted to account for the superimposition of nuclear interaction in the pixels. The total leakage current increase distribution f I dark DDD (x) can be written as f I dark DDD (x) = P(0, μ) × δ(x) + P(1, μ) × f ν dark (x)

+ P(2, μ) × f ν dark (x) * f ν dark (x) . . . ( 4
)
where P is the Poisson probability and μ is the mean number of nuclear interaction per pixel. In (4), the first term P(0, μ) × δ(x) accounting for nonimpacted pixels have been added to the expression introduced in [START_REF] Belloir | Pixel pitch and particle energy influence on the dark current distribution of neutron irradiated CMOS image sensors[END_REF]. It permits to conserve the integrity of the consider pixel population over the array. Thanks to this adaptation, the convolution between the preirradiation leakage current distribution and the radiation-induced increase leakage current distribution presented in (1) is possible. In (4), μ can be expressed as

μ = V dep × γ dark × DDD (5)
where V dep is the considered depleted volume in μm 3 and DDD is the DDD in TeV • g -1 . The term γ dark is assumed independent of temperature and annealing and is expressed as

γ dark = K dark ν dark (6)
where K dark is the Srour factor defined in [START_REF] Srour | Universal damage factor for radiation-induced dark current in silicon devices[END_REF] and estimated at K dark = 0.098 e -• s -1 /Tev • g -1 /μm 3 after four weeks annealing at 22 • C [START_REF] Srour | Universal damage factor for radiation-induced dark current in silicon devices[END_REF].

Fig. 1 .

 1 Fig. 1. Cross section and top view of a 4T PPD pixel.

Fig. 2 .

 2 Fig. 2. Image depicting the leakage current in the PPDs before irradiation and in the FDs before and after irradiation.

7.82 X 10 11 -Fig. 3 .

 113 Fig. 3. Evolution of the mean lealcage current increase per unit volume with irradiations. The considered UDF value after one month annealing is R'cl ar k = 0.098 e-• s-• jTev • g-1 / µm 3 [13].

- 4 Fig. 4 .

 44 Fig. 4. Distributions of the PPDs lealcage current after 50-MeV protons and 22-MeV neutrons irradiations.

Fig. 5 .

 5 Fig. 5. Distributions of the FDs leakage current after 50-MeV protons and 22-MeV neutrons irradiations.

Fig. 6 .

 6 Fig. 6. Leakage current evolution with time of five FDs before irradiation. Four of them are exhibiting a leakage current RTS behavior.

Fig. 7 .

 7 Fig. 7. Distributions of the PPDs RTS maximum transition amplitude of the leakage current before and after 50-MeV protons and 22-MeV neutrons irradiations.

Fig. 8 .

 8 Fig. 8. Distributions of the FDs RTS maximum transition amplitude of the leakage current before and after 50-MeV protons and 22-MeV neutrons irradiations. The slope of the prediction model is at A rts = 1200 e -• s -1 .

Fig. 9 .

 9 Fig. 9. Evolution of the FD leakage current with TG OFF-voltage before and after 50-MeV protons and 22-MeV neutrons irradiations.

Fig. 1 O

 1 Fig. 1 O. Cross section of the FD structure sbowing the different leakage current sources.

! 4 Fig. 11 .

 411 Fig. 11. FD leakage current distributions for several biasing conditions before and after proton irradiation DDD = 500 Te V. g-1 and TID = 24 krad(SiO2).

Fig. 12 .

 12 Fig. 12.

Fig. 13 .

 13 Fig. 13.FD leakage current evolution with the TG bias after proton irradiation 500 TeV • g -1 and 24 krad(SiO 2 ).

Fig. 14 .

 14 Fig. 14. FD leakage current evolution with the reset voltage after proton irradiation 500 TeV • g -1 and 24 krad(SiO 2 ).

Fig. 15 .

 15 Fig. 15. Cross sections showing the different leakage current sources in the CIS photodiodes (to be compared with Fig. 10): 1 STI interface defects and 3 DDD-induced bulk defects. (a) Conventional 3T photodiode found in 3T CISs. (b) PPD found in 4T-PPD CISs.

TABLE I IRRADIATION PARAMETERS Sensor Ref A B C D E F G Particle Neutron Neutron Neutron Neutron Proton Proton X-Ray Energy (MeV) 22 22 22 22

	49.7	49.7

10 X 10-3 Fluence (cm-2 ) 1.3 X 10 11 3.9 X 10 11 1.0 X 10 12 1.0 X 10 13 1.3 X 10 11 3.8 X 10 11 - NIEL (keV.cm 2 .g-1 )

	3.99	3.99	3.99	3.99	3.97	3.97	-

DDD (TeV.g-1 ) 519 1560 4000 40000 500 1500 - 1 MeV Neutron Fluence (cm-2 ) 2.71 X 10 11 8.13 X 10 11 2.09 X 10 12 2.71 X 10 13 2.61 X 10 11