Dr Inès Gabarret
email: ines.gabarret@edcparis.edu

Dr Annabelle Jaouen
email: a.jaouen@supco-montpellier.fr

Dr Walid A Nakara
email: wnakara@gmail.com

Dr Benjamin Vedel
email: benjamin.vedel@iae.univ-lille1.fr

Why are small public incubators "lagging behind"? Learning from disability in the selection practices of a French incubator 1

Keywords: Small public incubator (SPI), Selection practices, Entrepreneurial support, Resources, Entrepreneur, Paradox, Strategic positioning

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INTRODUCTION

Interest in entrepreneurship and business creation has grown substantially in recent years. One explanation for this phenomenon is the proliferation of public policies that support business creation, provide for new and more flexible legal status, strengthen technology transfer, protect intellectual ideas and, more specifically, establish business incubators. The incubation process is indeed at the heart of many recent studies seeking to better define the role of business support and capture the broad the diversity of the actors [START_REF] Messeghem | L'accompagnement entrepreneurial, une industrie en quête de levier de performance ?[END_REF].

Incubators are politically embedded structures that guide the development of new businesses [START_REF] Hackett | A systematic review of business incubation research[END_REF]. Moreover, they provide access to multiple resources (managerial, relational, financial, legal, rental, etc.) and, as new projects often lack resources and skills, this assistance helps to improve survival rates. [START_REF] Aernoudt | Incubators: tool for entrepreneurship?[END_REF] and [START_REF] Bollingtoft | The bottom-up business incubator: leverage to networking and cooperation practices in a self-generated, entrepreneurial-enabled environment[END_REF] point out that the word 'incubator' is a generic term that covers several realities. The names and labels given to these structures, such as technological incubator, pre-incubator, regional incubator, and so on, generally reflect the strategy that has been selected. In France, there is a distinction between 'incubator' and 'pepinière' that separates the structures dealing with projects before and after administrative creation. However, this distinction is not always very clear and depends on the sponsor's objectives.

The literature recognises several generations of incubators [START_REF] Bruneel | The evolution of business incubators: comparing demand and supply of business incubation services across different incubator generations[END_REF]. The first generation, which appeared in the early 80s, provided non-value-added resources (such as office space, secretarial services, and office equipment). The second generation, which appeared in the early 90s, had a qualitative range of services (consulting and training) and also provided funds for tenant companies. The third generation appeared in the early 2000s and focuses on technology projects [START_REF] Bollingtoft | The bottom-up business incubator: leverage to networking and cooperation practices in a self-generated, entrepreneurial-enabled environment[END_REF] and the provision of resources through networks [START_REF] Bruneel | The evolution of business incubators: comparing demand and supply of business incubation services across different incubator generations[END_REF][START_REF] Tello | Nascent entrepreneurs access and use of network resources in a technology incubator[END_REF]. The work of [START_REF] Bruneel | The evolution of business incubators: comparing demand and supply of business incubation services across different incubator generations[END_REF] shows the differences between incubator modes of operation through the generations. In the firstgeneration incubators, projects were hosted for long periods of time (over five years), in contrast to the latest generation where projects are hosted for shorter periods. Another difference concerns learning: [START_REF] Van Geenhuizen | University-linked incubators as a model of the "Modern" Triple Helix?[END_REF] suggest that learning curves are shorter in the latest-generation incubators (they learn from their elders).

From a strategic point of view, incubators can implement several types of actions [START_REF] Carayannis | Architecting GloCal (Global-Local), Real-virtual Incubator Networks (G-RVINs) as catalysts and accelerators of entrepreneurship in transitioning and developing economies: lessons learned and best practices from current development and business incubation practices[END_REF]Schwartz and Hornich, 2010). An incubator's strategic choices will influence its operations (admission criteria, business support, exit criteria) and determine its value [START_REF] Aernoudt | Incubators: tool for entrepreneurship?[END_REF][START_REF] Allen | Structure, policy, services, and performance in the business incubator industry[END_REF][START_REF] Brooks | Economic development through entrepreneurship: incubators and the incubation process[END_REF][START_REF] Grimaldi | Business incubators and new venture creation: an assessment of incubating models[END_REF][START_REF] Vanderstraeten | Service-based differentiation strategies for business incubators: exploring external and internal alignment[END_REF].

Small public incubators (SPIs) are small structures with few incubatees; they generally depend on small cities and often face difficulties due to a lack of resources and inadequate competitiveness in comparison with well-equipped, more dynamic incubators that may sometimes be geographically close by. The selection of projects is the keystone in the development of these small structures. Indeed, the choice of hosted companies and entrepreneurs is one of the principal factors in the survival and sustainability of SPIs.

The developmental stage of an incubator also has a direct influence on the services and resources it can offer [START_REF] Lalkaka | Business incubation and enterprise support system in restructuring countries[END_REF]. Incubators that are just starting out may suffer from the 'liability of newness' [START_REF] Stinchombe | Social Structure and Organization[END_REF]. New incubators, like other small organizations, may have limited resources [START_REF] Clarysse | Spinning out new ventures: a typology of incubation strategies from European research institutions[END_REF] and face a complex political environment [START_REF] Alsos | Stakeholders theory approach to technology incubators[END_REF][START_REF] Hackett | A systematic review of business incubation research[END_REF]. In this situation, the team, the availability of resources and the relationship with sponsors are of great importance [START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF]. The literature indicates that small incubators are not capable of the same economies of scale as large structures, but they can propose personalised services [START_REF] Aerts | Critical role and screening practices of European business incubators[END_REF].

What is the most appropriate strategy for an SPI with large competitors? To investigate this central issue [START_REF] Vanderstraeten | Service-based differentiation strategies for business incubators: exploring external and internal alignment[END_REF], we conducted an extensive exploratory study of an SPI. Our objective was to better understand the difficulties faced by the structure given its lack of resources and the competition from large incubators. This research aimed to analyse its selection and support, as well as its evolution and formalisation, including a change in the management team.

We developed a qualitative approach based on a single case study (French SPI).

Representatives from all the incubated projects were interviewed, as well as all the managers, and we performed a thematic analysis of the discourses. The in-depth study of the selection practices and the project portfolio revealed a paradox regarding the incubator's strategic positioning objectives and the availability of resources. We conclude by discussing the strategic positioning of SPIs regarding in-house resources and the selection process.

LITERATURE REVIEW

Strategic adaptation of incubators

Incubators can specialise in a particular geographical area (regional or national) and in one or more sectors (specialised or diversified), or they can decide to focus on a particular segment, such as technology transfer, or a particular population of entrepreneurs [START_REF] Aernoudt | Incubators: tool for entrepreneurship?[END_REF][START_REF] Colombo | How effective are technology incubators? Evidence from Italy[END_REF][START_REF] Schwartz | Specialisation versus diversification: perceived benefits of different business incubation models[END_REF]. Each incubator will set up admission and exit policies in line with their objectives [START_REF] Allen | Structure, policy, services, and performance in the business incubator industry[END_REF]. For instance, for-profit incubators searching for financial autonomy will look for companies able to pay rent after a short period of incubation [START_REF] Grimaldi | Business incubators and new venture creation: an assessment of incubating models[END_REF], while incubators with innovation-oriented strategies will require strong relationships with universities and laboratories and will need to be located in urban areas to have better access to consultants, intellectuals, etc.

Incubator managers can adapt the strategies as needed. [START_REF] Lumpkin | Screening practices of new business incubators: the evaluation of critical success factors[END_REF] and [START_REF] Mian | The University Business Incubator: a strategy for developing new research/technology based firms[END_REF] show that selection criteria vary depending on how crucial it is to have the incubator filled and how much importance is given to this need. [START_REF] Alsos | Stakeholders theory approach to technology incubators[END_REF] indicate that to meet the expectations of various stakeholders, the incubator manager can implement several strategies. He can reinterpret goals and choose those corresponding to the stakeholder most critical for the incubator's survival. The incubator's capacity for value creation stems from its talent for coherently combining the available resources and competences with the objectives given by its sponsors.

The need to solve two problems justifies the adaptation of strategies. The first problem is internal to the incubator: the gap between public policy or sponsor objectives and the incubator's actual skills, competences and available resources [START_REF] Von Zedtwitz | Are service profiles incubator-specific? Results from empirical investigation in Italy[END_REF]. This problem arises when an incubator is created by imitation, as when a model is transferred from another culture [START_REF] Abetti | Government-supported incubators in the Helsinki region, Finland: Infrastructure, results, and best practices[END_REF], or when the defined objectives exceed the inhouse expertise [START_REF] Clarysse | Spinning out new ventures: a typology of incubation strategies from European research institutions[END_REF].

An incubator needs time to develop its resources. This can be a major limitation to the effectiveness of the structure at the beginning [START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF]. Another limitation may be the lack of experience of some of the business managers [START_REF] Versino | The incubation of knowledge-intensive firms in Argentina: a review on the sectors' 10 th Anniversary[END_REF].

The second problem, which is external to the incubator, arises from the complexity of the environment and the clarity with which the incubator manager perceives the sponsor's objectives. The adaptation of strategy is more likely when the environment is politicised or when the incubator must meet the expectations of various stakeholders at the same time [START_REF] Alsos | Stakeholders theory approach to technology incubators[END_REF].

Selection as leverage for strategic adaptation

Project selection is one of the main levers that the incubator can use to deal with these two constraints (resources and goals). The incubator can determine its project portfolio to rationalise the use of resources. For example, the incubator might decide to specialise in a particular industry, which means that the hosted projects will share similar needs (Schwartz and Hornich, 2008). In contrast, the grouping of several competing companies within the incubator may restrict exchange and learning between companies [START_REF] Chan | Assessing technology incubator programs in the science park: the good, the bad and the ugly[END_REF][START_REF] Mcadam | Building futures or stealing secrets? Entrepreneurial cooperation and conflict within business incubators[END_REF]. [START_REF] Bergek | Incubator best practice: a framework[END_REF] distinguish the selection process along two dimensions: the selection criteria (selection of an idea or an entrepreneur) and the intensity with which these criteria will be applied (strict or flexible). The latter dimension refers to whether the incubator will be highly selective by favouring few projects with a high potential for success (strict selection) or more willing to select a large number of projects (flexible selection). This choice will influence the characteristics of the projects that will be hosted, the assistance they will receive and the added value for the incubator [START_REF] Brooks | Economic development through entrepreneurship: incubators and the incubation process[END_REF].

Strict selection requires the establishment of many levels of control to ensure the recruitment of projects that are in line with the incubator's development strategy (the search for ideal projects). This kind of selective recruitment allows the incubator to host, for instance, technological companies [START_REF] Van Geenhuizen | University-linked incubators as a model of the "Modern" Triple Helix?[END_REF], which are likely to create more value, although they also consume more resources [START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF]. With a policy of flexible selection, the incubator agrees to recruit a wide range of companies and trusts the market to distinguish the most promising projects, both during incubation and once the company has left the incubator. Flexible selection builds a portfolio of diversified companies. However, as they are not acting specifically in technological sectors, the value added per project will be lower than that achieved by strict selection.

Several authors have discussed the ideal composition of a project portfolio. For example, [START_REF] Alsos | Stakeholders theory approach to technology incubators[END_REF] distinguish two types of projects: ideal and actual (i.e. non-ideal). Ideal incubatees are firms that the incubators target and primarily wish to have as tenants; examples include projects that are technology-based, with innovative or research-based ideas, and high growth potential. These projects will benefit from the best services of the incubator. Because of their rarity, ideal entrepreneurs have negotiating power at the recruitment stage as they are scarce resources. An incubator with a modest reputation will have less bargaining power [START_REF] Aaboen | Explaining incubators using firm analogy[END_REF]. Other factors, such as problems filling the incubator, may increase the bargaining power of the ideal project and change the incubator's selection criteria [START_REF] Lumpkin | Screening practices of new business incubators: the evaluation of critical success factors[END_REF][START_REF] Mian | The University Business Incubator: a strategy for developing new research/technology based firms[END_REF]. However, selecting only ideal projects is not a sufficient condition to properly operate an incubator. To create an attractive pole (critical mass), incubators also require non-ideal (or 'actual') projects [START_REF] Alsos | Stakeholders theory approach to technology incubators[END_REF]. Networking within the incubator is a benefit that incubators provide, and without other firms this is impossible. Consequently, many incubatees do not fit the required ideal image: no motivation or potential to grow or low technology specification. For [START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF], a good portfolio should include several types of projects as they assume that a mix of projects will improve incubator functioning. [START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF] propose a classification of hosted projects based on the degree of maturity and their potential for growth (Table 1 below). Source: [START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF] Superstar firms are attractive because they are more developed than others. They require less assistance from the incubator and at the same time they improve the incubator's reputation and provide role models for other hosted companies. Up-and-coming companies need more assistance from the incubator and more time to develop. They may at some later date move on to the superstar category. Long-shot companies need a supportive environment and much more time. They do not require proactive assistance from the incubator. Anchor tenants are interesting because they can pay rent and provide service to others tenants, and they do not require assistance from the incubator [START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF].

The literature shows that selection is the keystone for incubator functioning. This research explores the selection practices in a SPI, the portfolio composition and its consequences in terms of resources, support and strategic positioning regarding the competition.

METHODOLOGY

This research was designed to be comprehensive and exploratory. We developed a qualitative approach based on the case study method. The choice of a single case study is justified by its purpose: to reveal a phenomenon, not exceptional, but not yet available to the scientific community [START_REF] Yin | Case Study Research: Design and Methods[END_REF]. Cases are defined as a contextualised and contemporary phenomenon in a real life context where the boundaries between phenomenon and context are not clear [START_REF] Yin | Case Study Research: Design and Methods[END_REF]. The relevance of the single case study was demonstrated by the French anthropologist Marcel Mauss (1966, p.391) for whom 'when a relationship has been demonstrated in one case, even if this case is unique, but it has been methodologically and thoroughly studied, the reality is as certain as when, in order to demonstrate it, we illustrate it with numerous but disparate facts'. Indeed, a case study provides a qualitative reading of the studied phenomenon and allows for abductive theorisation embedded in empirical data [START_REF] Eisenhardt | Theory building from cases: opportunities and challenges[END_REF]. These authors note that the single case study method is insufficiently known in academic research, whereas it can contribute greatly to new theory construction.

According to [START_REF] Siggelkow | Persuasion with case studies[END_REF], the case study method usually describes a new phenomenon that merits investigation. This approach is relevant for our research because the problematic of SPI strategy has been underexplored in the academic literature to date. Interviews are thus considered as a good research tool [START_REF] Fontana | Interviewing: the art of science[END_REF]. Nevertheless, this method provides limited external validity, which reduces statistical generalisation. Thietart (2007) notes that this method also limits the reliability of the data produced. Yin (2012) speaks about analytical (or theoretical) generalisation, by which he means 'using a study's theoretical framework to establish a logic that might be applicable to other situations' (Yin, 2012, p.18). [START_REF] Dumez | Méthodologie de la Recherche Qualitative[END_REF] indicates that one of the main theoretical results of a comprehensive study is the identification of social mechanisms (constituting a link between the observed phenomenon and the possible causes). Our choice is justified by our intention to understand the selection practices and the stakeholders' perceptions of SPIs.

Case study

This work was conducted in a small public incubator in the south of France. For this study, we named it 'IncubLR'. This local incubator was established in 2003 in a geographical area between two major cities, each having its own incubator (larger structures). IncubLR is a public non-profit structure, funded by the city in which it is domiciled with no participation of private investors or venture capitalists. The city is the only sponsor. The incubator director is quite free to choose the strategic directions for the incubator, although the sponsor's objectives are to develop local companies that create value and innovation and to keep them in the territory. IncubLR proposes several services in the same building: pre-incubator, business incubator, Chamber of Commerce, financing platforms, accountants, etc. The incubator also offers rental offices at very competitive prices. Twenty-five offices and eleven workshops are available to entrepreneurs.

IncubLR is a small incubator with limited resources that has developed in two stages. The The current selection practices are composed of an initial interview with an incubator manager, followed by a second one two weeks later (with a dossier showing the advancement of the project). The entrepreneur then presents his/her project to a committee composed of the four managers, one or two 'older' incubatees, and sometimes an external partner. This committee will decide whether the entrepreneur can join the incubator for a 'test-phase' of four months. During this period, the entrepreneur benefits from the technical support of the incubator, as well as advice and other exchanges with the other incubated entrepreneurs. A presentation at the end of the four months determines whether the project will be incubated. If yes, a convention is signed by both parties and regulates the incubation period: two years before creation, and three years after. The incubatees are required to stay at least five years on the territory at the end of the convention.

When the new director arrived in the incubator, several projects that had been incubated since the beginning of IncubLR were still in the building; there were few exchanges with these incubatees and limited monitoring. The new director (A1) is currently trying to create a clear strategic position, but he faces two problems. The first problem is that the internal (human and financial) resources of the incubator are limited. Given that the managers' technical competences cannot cover all the domains of the incubated projects, IncubLR tries to develop networks and synergies among the incubated entrepreneurs. Consequently, the 'older' entrepreneurs, with their greater experience and acquired competences, are expected to provide 'peer support' (or mentoring) to the newer tenants. The second problem is the strong competition from the two bigger incubators in the neighbouring cities. The main competitor has a 6M€ budget, the second has 1.4M€, whereas IncubLR has only 200K€. The best projects therefore tend to try first to be accepted by one of these competitors and come to IncubLR only after having been refused by them. We investigate these issues in our study.

Data collection

We conducted 20 semi-directive face-to-face open-ended interviews with all the incubator actors (16 entrepreneurs and four incubator managers) with the objective of gathering discursive data reflecting the conscious or unconscious mental universe of the entrepreneurs and the managers [START_REF] Miles | Qualitative Data Analysis: An Expanded Sourcebook[END_REF]. Secondary data were also collected from websites, firm brochures and catalogues.

We elaborated an interview guide for both types of actor, using a "mirroring" technique to cross-validate the discourses [START_REF] Klein | A set of principles for conducting and evaluating interpretive field studies in information systems[END_REF]: when possible, each question was asked to both the entrepreneur (e.g. what kind of selection process did you follow?) and the incubator manager (e.g. what kind of selection process did you use for this project?). We divided the pre-structured interview guide into seven themes for entrepreneurs and eight for incubator managers:

-Entrepreneurs: personal history, entrepreneurial motivation, professional career, selection process to enter the incubator, type of support received, overall satisfaction, perception of the evolution of the incubator.

-Incubator managers: professional career, competences, seniority within the incubator, type of projects hosted, selection practices and methods, provided support, perception of the evolution of the incubator, exit policies for 'old' projects.

The interviews were tape-recorded to ensure that the collected data were exhaustive and reliable. The interviews were transcribed within 24 to 72 hours.

Table 2 presents all the incubated projects of IncubLR. Each entrepreneur was interviewed.

Eight hosted companies can be considered as having a significant degree of maturity and form Group 1: E1, E2, E3, E4, E5, E6, E7 and E8. By degree of maturity, we mean that the incubator considers that they do not need any more support, are able to leave the structure, and generate sufficient value to be sustainable. Eight other companies present a low degree of maturity and comprise Group 2: E9, E10, E11, E12, E13, E14, E15 and E16. These companies still need support. First, the gross database was analysed through thematic coding. For each category (entrepreneurs and managers), this analysis consisted of determining the units of meaning (words, sentences or phrases related to one of the seven pre-determined themes) and counting the respective occurrences (to measure the weight of each in the discourse). The occurrences were noted in matrices that included personal observations and certain particularly striking or illustrative remarks by the interviewees. Second, we grouped the occurrences into subthemes via subcodes. The aim was to compare the discourses concerning each theme and to identify the constants and differences. The data were analysed by the authors separately. Then, the analysis and categories were discussed jointly. This contributes to the reliability and validity of the data and findings [START_REF] Grant | Small business and entrepreneurial research meta-theories, paradigms and prejudices[END_REF]. The next section provides a detailed summary of our results.

RESULTS

The in-depth study of this SPI generated several results. First, certain problems were linked to the first developmental stage of IncubLR and the change in the management team. These elements generated a highly heterogeneous project portfolio, which is analysed in the second section. We also identified dysfunctions, such as the lack of synergy among the incubatees.

Last, we found that the strategic positioning of IncubLR (specialisation) created a paradox regarding the available resources.

The consequences of flexible selection and a 'full-house' strategy

Several problems were identified. Some of them were the consequence of the first development stage of IncubLR. During the starting phase (2003 to 2008) with the first team (which has been completely renewed since), the strategy had been to 'fill' the incubator. The incubator was young and unattractive compared with the bigger competitors, so the selection process was intuitive, short, flexible, not selective and based solely on the profile of the new entrepreneurs: 'Entrance into IncubLR was fast. I had only one interview with the director' (E4). E11 also explains: 'I arrived at a time when there were no new projects, so my project was interesting to them. They gave me the opportunity to stay and think about my idea'.

No formal contract was proposed to the entrepreneurs, especially concerning the exit conditions, for which no clear rule was established. One of the current managers explains:

'For almost 5 years, all projects first went to [the big incubators]. Here, there were not many projects, so we needed to "fill up". This was really the expression used by the former director' (A3). The structure was informal and the relationships between the entrepreneurs and incubator managers were highly personalised.

Consequently, the new director faced several difficulties when he arrived at IncubLR. First, the 'full-house' strategy had created a highly heterogeneous project portfolio, with little complementarity among the projects. Second, the absence of clear exit conditions had generated problems. The 'oldest' incubatees had negotiated not to leave or explained that they still needed the incubator to survive. Thus, space was unavailable for new tenants. Third, the former management team had developed very close relationships with the incubatees, and the arrival of the new team created a feeling of resistance to change. Communication became difficult between the managers and these entrepreneurs. The team had little information, for example, on the financial health of some of the incubatees because of the lack of feedback or regular meetings. The newest managers (A3 and A4) did not know the oldest incubatees.

Worse, the newest tenants who would have liked to have offices or workshops had no access to them because they were occupied by the oldest projects. This created tensions and conflicts among the incubatees recruited by the first and the second teams. 'You have divisions between the entrepreneurs, and when you are with "one group", you're not necessarily well perceived by the "other group".

[…] And this incubator has lived through a lot of very strong divisions' (E9).

The new manager and his team arrived five years after creation and inherited a situation in which they need to find legitimacy. This is even more complicated because the new team has different skills from the first one. They tend to focus on the recruitment of projects that best suit their skills. This creates misunderstanding and dissatisfaction for some of the older hosted projects. As a result of these changes in the life of the incubator, the incubator today is composed of a variety of projects. We will now analyse the composition of the portfolio and the interactions between the tenants, using Rice and Matthews' typology (1995).

Diagnosis of the project portfolio

According to [START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF], a good portfolio should include a mix of projects to improve incubator functioning. Using their typology, the portfolio of IncubLR is as follows in Table 5.

Table 5. Portfolio of Incubated Projects

(#1) recruitment by the 1 st team; (#2) recruitment by the 2 nd team.

The analysis of our mature sample (companies E1 to E8) shows the presence of two mature types: superstars and anchor tenants. Superstar businesses are successful projects that no longer need the incubator. Their function is to improve IncubLR's reputation and visibility, and they also have an exemplary role for other hosted projects. Two of them can be considered as 'ideal' according to [START_REF] Alsos | Stakeholders theory approach to technology incubators[END_REF]. Their activity is at the heart of the target project sought by the sponsor (i.e. cosmetics). They are not seeking resources and are in a position to help the other hosted projects. Their viability and stability are beneficial for the incubator, not only in terms of legitimacy, but also because of their capacity to coach their peers, which is recognised as a real success factor for young companies [START_REF] Jaouen | Accompagnement par les pairs, confiance partagée et résilience : Illustration au travers du cas Voiles d'Oc[END_REF].

Because they are already successful, projects in this category (E2, E5, E6, and E8) do not have much real interaction with incubator staff. E2 explains: 'With the managers, we bump into each other from time to time […] there's no real monitoring in the strict sense of the term'.

Level of maturity of the firm High Low

Growth potential of the firm

High

Superstars E2 (#1) E5 (#1) E6 (#1) E8 (#1) Up-and-comers E10 (#2) E11 (#2) E14 (#2) E15 (#2) Low Anchor Tenants E1 (#2) E3 (#1) E4 (#1) E7 (#1) Long Shots E9 (#1) E12(#1) E13 (#1) E16 (#1)
Anchor tenants should help the incubator to achieve financial autonomy (by paying higher rent) and provide other projects with access to various services. As they are already developed, they do not require assistance from the incubator. In our sample, a group of developed companies fell into this category (E1, E3, E4, E7). However, they do not pay higher rent and do not provide services to other hosted companies. On the contrary, their presence is motivated strictly by the low rent of the incubator. 'They accepted me in specific circumstances but I did not need them; I really needed an office and to overcome the crisis' (E1).

The less developed projects can also be divided into two categories. The first category consists of promising projects (Up-and-comers). They have been accepted by the second incubator team (E10, E11, E14, E15) with more formalised contracts. The Up-and-comers were the last to be recruited and their projects were carefully selected by the new SPI staff.

Their potential for development is unknown and their need for assistance is high. They have no pressure to leave the incubator and their legitimacy within the incubator is strong.

The second category in this group of less mature projects (Long shots) appears to be high risk (E9, E12, E13, E16). They are characterised by a longer incubation time (over five years) and they have to leave the incubator. Three out of four are not ideal projects because they are not in the cosmetic sector. Although they continue requesting assistance, these companies are rather opposed to the new team, as they were recruited by the first team. For this group of projects, leaving the incubator represents failure and closure. 'There are people that have been there for six, seven years, languishing' (E2).

Our first observation is that there is a limited presence of the target population in the IncubLR portfolio (i.e. cosmetics). Second, half of the incubated projects in our sample do not fulfil their roles (Anchor tenants and Long shots). Anchor tenants should help the managers by providing peer support (mentoring) and paying higher rents, but they don't. Long shots are even more problematic because their very survival is dependent on their presence in the incubator: despite high pressure from the new incubator manager, most of them refuse to leave, arguing the fact that they are ill-prepared to survive outside the structure. Their main argument is the lack of an exit clause in their contracts, and some of them have been incubated for more than five years. The bond between the IncubLR managers and these tenants seems to be irreparably broken. Others, like the Superstars, are sufficiently developed and no longer need the incubator, but they will remain in the incubator until the construction of a new industrial site in the neighbourhood is completed. Indeed, the incubator sponsor is building this new site in line with the objective of keeping companies in the local area (for at least five years).

The project portfolio of an incubator is both a reflection of the strategy that has been implemented and the constraints it faces: competitors, available resources and competences.

Paradox between resources and strategic choices

The project portfolio contains two Superstar projects in cosmetics: E6 and E8. The IncubLR director seems to be oriented towards a strategy of specialisation in this industry, which would help the incubator to differentiate from its competitors. Nevertheless, several constraints limit this strategy: the high proportion of incubatees with no complementarity with cosmetics, few available offices, limited financial resources and few adapted competences.

Indeed, implementing a strategy targeting the cosmetic industry is intimately related to the incubator's competitive position. This SPI is facing increasing competition from large incubators, which benefit from substantial and very competitive financing and tend to capture the best projects. Thus, several entrepreneurs have come to the small local incubator only after being rejected by the bigger ones. IncubLR is thus considered as a second choice. 'I had two interviews with X (big incubator), and I was not invited to continue the selection process.

It was not a problem with the project; I think it was because they were already hosting a similar company' (E5); 'I went to Y (big incubator), I had a first contact, then I came here because it (big incubator) was not interested' (E13); 'When we went to see X (big incubator), they were not interested because our project was not high tech, nobody was interested' (E7);

'I went to Y (big incubator), there was no office available at that time, so I came here' (E2).

IncubLR needs a clear position with regard to its competitors (high selectivity) but it lacks the resources and skills for in-depth monitoring of technical projects and cannot meet the demands for financial and legal assistance. Normally, specialisation requires specific technical resources such as new adapted spaces, a network of specialised contacts, and expertise in monitoring such companies [START_REF] Vanderstraeten | Service-based differentiation strategies for business incubators: exploring external and internal alignment[END_REF]. However, the new team is only able to provide generic support (marketing and web) and is oriented towards 'laissez-faire' support [START_REF] Bergek | Incubator best practice: a framework[END_REF], as we can see in several discourses: 'Having regular meetings with an incubator manager to give an update the business plan, the project, the progress on the project, clients, this is something that doesn't really happen today' (E2); 'We don't have regular support, we have support on demand' (E9); 'In general, support is only when you ask for it" (E5); 'In general, it's the entrepreneurs who seek assistance. When we have no news, we send them an e-mail' (A2).

In the typology of [START_REF] Bergek | Incubator best practice: a framework[END_REF], 'laissez-faire' support is the opposite of the strong intervention needed in the case of specialisation. This strategic adaptation can be explained by the new team's lack of experience and the low pressure from sponsors: "A1 is marketing, A3 is web and A4 is supposed to coach the cosmetic industry and on sustainable development. My specialty, I don't really have one, I take care of the website and organize events' (A2); 'Even the incubator managers are sometimes a little disconnected from what the creation of a company really is' (E1).

Today, the incubator is facing a paradox: the director wants to select targeted, innovative projects, without being 'equipped' to provide services that are 'good enough' to meet the expectations or needs of these specialised projects.

DISCUSSION

This research contributes to the knowledge on SPIs by identifying several key issues for these organisations: support, relevant project selection and making strategic decisions in line with incubator capacities (internal skills, available resources, etc.). Moreover, the change in the director and the management team provided us with an opportunity to look closely at how these changes affected the selection practices and strategic positioning.

Support issues of SPIs

Our results show several internal issues that SPIs are likely to confront. SPIs have limited resources and often lack the necessary skills to cover all the incubatee needs. In response to these problems, IncubLR tried to encourage the development of networking and 'peer support' among the incubatees. Nascent entrepreneurs view the incubators as a nexus of resource networks [START_REF] Tello | Nascent entrepreneurs access and use of network resources in a technology incubator[END_REF]. But our results suggest that trying to involve the most mature tenants was insufficient, as overall IncubLR had no real internal network and little cooperation among the tenants, despite the director's decision to develop internal and external networking. The lack of synergy among the entrepreneurs is accentuated by the heterogeneity of the selected projects.

Moreover, the lack of regular meetings between the oldest incubatees and the managers indicates minimal support, possibly due to two factors: (a) the very close relationship between these 'older' incubatees and the previous management team, which created a feeling of rejection of the new team, and (b) the incompatibility between the managers' skills and the tenants' expectations. The new management team has different skills focused mainly on marketing innovation and web marketing, and this choice to recruit young employees with general skills (and no specific skills in finance, accounting or cosmetics, for example) seems to limit the capacity of the incubator and its fields of support. The managers declare that their support is based mainly on networking, coaching and sometimes 'laissez-faire'.

In addition, our research highlights that some tenants think that they do not receive adequate support, as well, which suggests that the incubator staff are under-informed about the expectations and satisfaction of their incubatees. Undeniably, tenant feedback on the offer of support is inadequate or overlooked. Yet such feedback seems vitally important for incubators [START_REF] Allen | Small business incubators: A positive environment for entrepreneurship[END_REF][START_REF] Bakkali | Pour un outil de mesure et de pilotage de la performance des incubateurs[END_REF][START_REF] Cooper | The role of incubator organizations in the founding of growth-oriented firms[END_REF][START_REF] O'cass | Examining the firm's value creation process: a managerial perspective of the firm's value offering strategy and performance[END_REF] as a good understanding of entrepreneurial support needs would help to customise the support offer and build closer relationships between the SPI managers and the entrepreneurs. Closer relationships would in turn be likely to promote greater incubatee involvement in the daily life of the incubator and might prompt 'older' entrepreneurs to share their knowledge, experience and competencies with the newer tenants [START_REF] Jaouen | Accompagnement par les pairs, confiance partagée et résilience : Illustration au travers du cas Voiles d'Oc[END_REF].

In conclusion, the management team needs to create personalised and adapted support, which requires a better combination of individual, collective and inter-organisational resources [START_REF] Clarysse | Spinning out new ventures: a typology of incubation strategies from European research institutions[END_REF][START_REF] Li | A dynamic taxonomy for managing knowledge assets[END_REF][START_REF] Newbert | Value, rareness, competitive advantage, and performance: a conceptual-level empirical investigation of the resource-based view of the firm[END_REF][START_REF] Newbert | Looking beyond resources: exploring the importance of entrepreneurship to firm-level competitive advantage in technologically intensive industries[END_REF][START_REF] Srivastava | The resource-based view and marketing: the role of market-based assets in gaining competitive advantage[END_REF]. [START_REF] Bruneel | The evolution of business incubators: comparing demand and supply of business incubation services across different incubator generations[END_REF] also underlines the risk of an incoherent strategy. Offer a not adapted support, without clear turnover rules (linked to entry and exit policies) could be problematic. The management team need to put into place a means to assess tenant satisfaction on a regular basis [START_REF] Abduh | Building futures or stealing secrets? Entrepreneurial cooperation and conflict within business incubators[END_REF], as well as the advantages and disadvantages of the offer of support [START_REF] Mcadam | Building futures or stealing secrets? Entrepreneurial cooperation and conflict within business incubators[END_REF]. In this sense, authors like [START_REF] Bruneel | The evolution of business incubators: comparing demand and supply of business incubation services across different incubator generations[END_REF] suggest that the tenants should evaluate the incubator's value proposition and strategy [START_REF] Vanderstraeten | Service-based differentiation strategies for business incubators: exploring external and internal alignment[END_REF].

Strategic positioning of SPIs

Another interesting finding concerns the importance of strategic positioning in SPIs: in our results, we identify a paradox in decision-making that impacts the strategic positioning of IncubLR. On the one hand, the director wants to implement a strategy of specialisation, with a focus on cosmetics. This decision is motivated by the success of two cosmetic companies formerly hosted by the incubator. On the other hand, some of the organisational decisions do not fit this strategy.

The first ill-adapted organisational decision concerns the selection process. The director oscillates between recruiting 'available' projects and specialised projects in the targeted industry (cosmetics). We know that SPIs are sometimes forced to recruit 'actual' incubatees [START_REF] Alsos | Stakeholders theory approach to technology incubators[END_REF] in order to reach critical mass. Consequently, IncubLR plays a 'social role' by recruiting the 'excluded entrepreneurs', or those who have been rejected by other incubators. But, by filling the incubator with actual projects without a formalised strategy for rooting out the oldest projects [START_REF] Adegbite | Business incubators small enterprise development: the Nigerian experience[END_REF], no new space is available for new, ideal projects.

The second organisational decision that seems paradoxical concerns the limited and inadequate resources with regard to the support requirements in the cosmetic industry. Thus, we observe an incompatibility between the available resources (human and financial) and the requirements dictated by the strategic choice. This echoes the findings of Von Zedtwitz and [START_REF] Von Zedtwitz | Are service profiles incubator-specific? Results from empirical investigation in Italy[END_REF]. The authors found that cognitive gaps could exist between sponsors that evaluate the incubator and managers who implement the actions. For example, little knowledge about incubator's environment or incubatees' needs creates misunderstandings that could lead to strategic adaptation [START_REF] Alsos | Stakeholders theory approach to technology incubators[END_REF] or tenant's dissatisfaction [START_REF] Von Zedtwitz | Are service profiles incubator-specific? Results from empirical investigation in Italy[END_REF]. Incubators are black boxes that are difficult to understand [START_REF] Hackett | Inside the black box of business incubation: Study B-scale assessment, model refinement, and incubation outcomes[END_REF]. [START_REF] Vanderstraeten | Service-based differentiation strategies for business incubators: exploring external and internal alignment[END_REF] highlight the lack of connection between strategy and internal aspects of these organizations. Incubators in the position of IncubLR thus need to readjust and recombine resources and competencies by developing new skills. For example, IncubLR could invest in training [START_REF] Campbell | Change agents in the new economy: business incubators and economic development[END_REF][START_REF] Mian | Assessing and managing the University Technology Business Incubator: an integrative framework[END_REF][START_REF] Rice | Growing New Ventures, Creating New Jobs: Principles & Practices of Successful Business Incubation[END_REF] (or change employees) to acquire new competencies and expertise in the cosmetic industry. These internal limitations also restrain the competitiveness and legitimacy of the incubator.

How to develop new resources for SPIs?

Reputation

Another implication of this research is to underline the importance of reputation of SPIs.

Several studies (see, for example, [START_REF] Fischer | The good, the bad, and the unfamiliar: the challenges of reputation formation facing new firms[END_REF][START_REF] Schwartz | Specialisation versus diversification: perceived benefits of different business incubation models[END_REF] have shown that new organisations lack reputation. With increasing competition from big incubators, IncubLR's top management is aware of the need to differentiate by specialising in order to enhance its legitimacy and its reputation among competitors [START_REF] Rao | The social construction of reputation: certification contests, legitimation, and the survival of organizations in the American automobile industry[END_REF].

In fact, this SPI has not been able to attract the best projects because it lacks a sufficiently good reputation. Yet recent research has shown that companies that are hosted by 'specialised business incubators' have a better image in the eyes of potential partners and investors [START_REF] Schwartz | Specialisation versus diversification: perceived benefits of different business incubation models[END_REF]. The choice of the tenants is thus logical: they prefer to be hosted by prestigious regional and/or national incubators that provide better support, easier access to financing and more powerful networks (internal and external).

A specialisation in the cosmetic industry would attract not only regional projects but also national and even international projects. IncubLR could thus become a reference in this industry and highly visible to stakeholders. However, the director of this SPI needs to be careful because such repositioning requires a deep knowledge of the internal and external environment [START_REF] Brax | Developing integrated solution offerings for remote diagnostics[END_REF][START_REF] Li | A dynamic taxonomy for managing knowledge assets[END_REF].

Coopetition

In addition, some of the incubatees expressed doubts about being incubated with projects in the same industry. This reluctance is due to fears about competition and the risk of losing their technologies, customers, etc., but it also reveals the lack of confidence and communication among the tenants. Yet, trust is the key to establishing a strong internal network and cooperation and it can reduce opportunistic behaviour [START_REF] Tötterman | Start-ups: business incubation and social capital[END_REF][START_REF] Uzzi | Social structure and competition in interfirm networks: the paradox of embeddedness[END_REF]. [START_REF] Tötterman | Start-ups: business incubation and social capital[END_REF] indicate that cooperation between tenants is linked to a trustworthy environment and this is mainly obtained by the incubator manager's choice to incubate tenants in the same place (same building, same roof). Many studies (e.g. [START_REF] Gnyawali | Co-opetition and technological innovation in small and medium-sized enterprises: a multilevel conceptual model[END_REF][START_REF] Lado | Competition, cooperation, and the search for economic rents: a syncretic model[END_REF][START_REF] Loebbecke | SMEs, co-opetition and knowledge sharing: the role of information systems[END_REF][START_REF] Vanderstraeten | Service-based differentiation strategies for business incubators: exploring external and internal alignment[END_REF] highlight the benefits of coopetition between organisations. [START_REF] Gnyawali | Co-opetition and technological innovation in small and medium-sized enterprises: a multilevel conceptual model[END_REF] show that small businesses engaged in coopetition improve their level of technological innovation. Similarly, [START_REF] Schwartz | Specialization as strategy for business incubators: an assessment of the Central German Multimedia Center[END_REF] show the beneficial effect of technology transfer between companies in the same sector and incubated nearby. The idea of building a centre dedicated to cosmetics may therefore be a promising strategy for this SPI.

The director and managers should act as 'facilitators' in the interactions between companies [START_REF] Salvetat | The tertius roles in a coopetitive context: the case of the European aeronautical and aerospace engineering sector[END_REF] to overcome the SPI's lack of resources.

CONCLUSION

This research analyses the selection practices in a SPI, the portfolio composition and its consequences in terms of resources, support and strategic positioning regarding the competition. Our results show that the incubator faced a paradox that affected its operations and strategic positioning. From an internal point of view, the selection practices and the available resources do not fit the strategic choices. The results also indicated that the SPI lacks the networks and influential partners to further boost its development. This makes it less attractive in terms of the funding and investment that the hosted entrepreneurs require. SPIs are characterised by a lack of reputation even at the regional level. This might explain why they are not composed of only small but promising companies and why they have difficulties in attracting ideal projects.

Our findings also raise a key question about the purpose of SPIs. Is it to promote a specific industry in order to create a competitiveness cluster in the region? This would increase the incubator's attractiveness as long as it can count on a related infrastructure and develop a recruitment strategy of specialised managers. The policy adopted for project selection can also be a strong lever for the strategic fit.

This research has two main limitations. The first concerns the generalisation of our results to other small public incubators. Our case displayed several specificities (e.g., change in the management team, geographical proximity of big incubators, young age of managers), and future research to replicate this study would do well to multiply the number of cases. A quantitative study on a larger scale would also enhance the robustness of the findings.

Moreover, we chose the French context to explore our research question. Cross-national study to compare the strategies of small business incubators in different contexts would determine whether our findings are applicable to other countries.

  first stage(2003)(2004)(2005)(2006)(2007)(2008) was characterised by a very small team (one director and one manager), the need to fill the incubator (implying very low selection), and personal relations between entrepreneurs and managers in a very informal organisation. The second stage(2008- 2012) was characterised by a renewal of the support team and formalisation of the selection practices in 2011.

Table 1 . Matrix of Growth Potential/Level of Maturity Level of maturity of the firm High Low Growth potential of the firm

 1

	High	Superstars	Up-and-comers
	Low	Anchor Tenants	Long Shots

Table 2 . Characteristics of the Incubated Projects

 2

	Group Com	Sector	Entrepreneur	Beginning	Company
	pany		age	incubation	creation
	E1 Development of video games and serious gaming	41	2005	2007
	simulation, 3D representation, artificial intelligence...
	E2 Software for automatic layout of catalogues, product	53	2006	2005
	information management and crossmedia
	E3 Development of management software for SMEs	59	2005	2006
	(management control, reporting, budget estimates, margin
	analysis and cost)
	E4 Building solutions for web 3.0 security	46	2006	2007
	E5 Temperature traceability for tracking vehicles and parcels	40	2010	2008
	E6 Creator of the concept of 'oléoactifs', a new generation of	52	2009	2010
	bioactive complex oil for cosmetic use
	E7 Travel agency for photo travel	33	2005	2006
	E8 Patents for multiple emulsions for natural cosmetics	35	2005	2007
	E9 Artistic label designers, artistic decoration of living spaces,	36	2006	2006
	especially for children
	E10 Sale of anesthetic gases for veterinary use	39	2011	2011
	E11 Solutions for organic waste management	45	2010	2009
	E12 Improvement of image resolution, processing of infrared	44	2005	2004
	images
	E13 Agricultural sensor		35	2006	2008
	E14 Web platform for associations	25	2012	Not yet
	E15 Platform for pharmacies, sale of OTC products via the	23	2012	2012
	Internet
	E16 Creation and sales of organic cosmetics	45	2007	2008

Table 3

 3 presents the support team of IncubLR, which consists of four managers. Most of them joined the team only recently. A1, the director, was previously a commercial manager in several structures and then created his own company in marketing consulting. He joined IncubLR in 2008. He manages the oldest projects (i.e. those selected by the previous team) and intervenes according to need in all the projects that have marketing issues.A2 worked for ten years in a 'Boutique de gestion' (i.e. French support structure for necessity entrepreneurs or small and low-innovative activities) and joined IncubLR in 2010. A legal assistant with competences in both law and accountancy, she is in charge of cosmetic and 'green tech' projects, without specific training in these fields.

			Table 3. Incubator Managers
	Person Function	In the	Age	Specific competences
			incubator since
	A1	Director	2008	44	Management, Strategy, Marketing
	A2	Manager	2010	39	Law, Accounting, General support
	A3	Manager	2011	25	General support, Administrative tasks
	A4	Manager	2012	28	Web marketing, Social media, Web development

A3 recently received a Master degree in 'Entrepreneurship Support' and was recruited by A1 in 2011, after two six-month internships. She is in charge of the initial contacts with the entrepreneurs, the administrative part of their projects, and she offers generalist support.

A4 was previously an incubated entrepreneur in IncubLR. His web project was created with an associate, but a problem of divergent vision led him to withdraw from the project. At that time, A1 (the IncubLR director) needed a manager with good competences in web development and web marketing, and A4 was recruited in 2012. A4 has the profile of a (previous) entrepreneur but has no specific training in commercial, financial or legal support.

This research received financial support from the French National Research Agency through the program "Investments for the Future" under reference number ANR-10-LabX-11-01.

Data analysis

We performed a content analysis [START_REF] Bardin | L'Analyse de contenu[END_REF] centred on the thematic analysis of speech [START_REF] Evrard | Market[END_REF]. This approach, which interprets discourses to find meaning in order to discern what is important for the interviewee, seems particularly appropriate in this context.

We developed a multinomial encoding method [START_REF] Dumez | Méthodologie de la Recherche Qualitative[END_REF], and an extract of the data encoding process is given in Table 4.

Table 4. Extract of the Multinomial Encoding Process

Code

Code definition Sub-codes


Sudhanya Chatterjee

Olivier Commowick

Onur Afacan

Simon K Warfield

Christian Barillot

Identification of Gadolinium contrast enhanced regions in MS lesions using brain tissue microstructure information obtained from diffusion and T2 relaxometry MRI

Keywords: diffusion MRI, T2 relaxometry, microstructure, brain, multiple sclerosis

Identification of Gadolinium contrast enhanced regions

in MS lesions using brain tissue microstructure information obtained from diffusion and T2 relaxometry MRI

Introduction

Multiple sclerosis (MS) patients have multiple focal lesions in the brain. In the early stages, the MS lesions undergo active blood brain barrier (BBB) breakdown [START_REF] Guttmann | The evolution of multiple sclerosis lesions on serial mr[END_REF][START_REF] Lassmann | Heterogeneity of multiple sclerosis pathogenesis: Implications for diagnosis and therapy[END_REF]. Lesions in this stage are referred to as enhancing lesions and the clinical significance of its identification is well established. Gadolinium based contrast agents (GBCA) are popularly used by radiologists to identify enhancing MS lesions. A T1-weighted MRI acquired post GBCA injection is a part of the recommended MRI protocols for diagnosis and follow-up examinations of MS patients [START_REF] Brownlee | Diagnosis of multiple sclerosis: progress and challenges[END_REF]. However, the use of GBCAs has been a recent topic of debate, primarily due to reports of Gd deposition in the brain [START_REF] Kanda | High signal intensity in the dentate nucleus and globus pallidus on unenhanced t1-weighted mr images: relationship with increasing cumulative dose of a gadolinium-based contrast material[END_REF][START_REF] Olchowy | The presence of the gadolinium-based contrast agent depositions in the brain and symptoms of gadolinium neurotoxicity-a systematic review[END_REF]. Suggestions insisting on greater debate before GBCA administration has gained traction due to observed MRI signal changes in the brain tissues due to repeated GBCA administrations and other possible health issues [START_REF] Gulani | Gadolinium deposition in the brain: summary of evidence and recommendations[END_REF]. A MS lesions in its enhancing stage has different pathological traits as compared to late or non-enhancing MS lesions [START_REF] Lassmann | Heterogeneity of multiple sclerosis pathogenesis: Implications for diagnosis and therapy[END_REF]. Regions of lesion undergoing active BBB breakdown has a higher water content owing to the undergoing tissue damages such as functional impairment of the morphologically intact endothelial cells [START_REF] Guttmann | The evolution of multiple sclerosis lesions on serial mr[END_REF]. Hence by the virtue of the brain tissue microstructure characteristics of MS lesions, we may identify enhancing regions in the lesion (if any). Although MRI effectively provides in-vivo images of the brain, it is constrained by the limited imaging resolution it can provide. This limitation is primarily attributed to hardware limits and the need for adhering to reasonable scan times for clinical implementations. However, advanced MRI methods, such as diffusion MRI (dMRI) and T2 relaxometry help us obtain estimates on condition of brain tissue microstructure. The multi-compartment models (MCM) [START_REF] Panagiotaki | Compartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison[END_REF] in dMRI provide information on the organization of the nerve fibers in the brain. MS lesions disrupt the normal organization of fibers in the brain. The extent of this damage may be assessed from the tissue microstrucutre estimates derived from dMRI MCMs. Myelin is also a critical biomarker in neurodegenerative diseases such as MS [START_REF] Lassmann | Heterogeneity of multiple sclerosis pathogenesis: Implications for diagnosis and therapy[END_REF][START_REF] Laule | Magnetic resonance imaging of myelin[END_REF][START_REF] Mackay | Magnetic resonance of myelin water: An in vivo marker for myelin[END_REF]. Demyelination marks the onset of MS [START_REF] Lassmann | Heterogeneity of multiple sclerosis pathogenesis: Implications for diagnosis and therapy[END_REF]. Myelin has a very short T2 relaxation time (<50ms) due to its tightly wrapped structure [START_REF] Lancaster | Three-pool model of white matter[END_REF]. Due to higher TEs in dMRI, the myelin information is not present in the dMRI signals. However, myelin information can be obtained by estimating the myelin water fraction (MWF) from T2 relaxometry MRI signal [START_REF] Laule | Magnetic resonance imaging of myelin[END_REF][START_REF] Mackay | Magnetic resonance of myelin water: An in vivo marker for myelin[END_REF]. The inflammation in MS lesions can be assessed from T2 relaxometry and dMRI signal. Hence, by combining the tissue microstructure information from these two MRI methods, we can obtain considerable information on brain tissue health. In this work we combine the microstructure information obtained from T2 relaxometry and dMRI to identify Gd enhanced regions in MS lesions.We performed experiments to evaluate whether combining the tissue microstructures is advantageous as compared to using them alone. The observations from this experiment is carried forward to the next stage where we perform enhancing lesion region predictions in a MS patient.

Material and methods

Multi-compartment T2 relaxometry model (MCT2)

Three T2 relaxometry compartments are considered in a voxel based on their T2 relaxations times and are referred to as short-, medium-and high-T2. The short-T2 compartment conveys information on brain tissues with T2 relaxation times shorter than 50ms. These tissues primarily include myelin and highly myelinated axons [START_REF] Lancaster | Three-pool model of white matter[END_REF]. The high-T2 compartment represents the tissues with T2 values greater than 1000ms, comprising primarily of free fluids (CSF in healthy volunteer) and water accumulated in tissues due to pathology (edema regions in MS lesions). The medium-T2 compartment is a mixed pool and conveys information on intracellular matter (such as unmyelinated axons and glia), intra and extracellular fluids [START_REF] Lancaster | Three-pool model of white matter[END_REF]. The T2 space is modeled as a weighted mixture of the three compartments, where each compartment is represented by a continuous probability density function (PDF). The signal of a voxel at the i-th echo in the MCT2 is modeled as:

s (t i ) = 3 j=1 α j ∞ 0 f j (T 2 ; p j ) EP G (T 2 , T E, i, B 1 ) dT 2 (1)
In Eq. ( 1), f j (T 2 ; p) is the chosen PDF to represent the j-th compartment with parameters p j = {p j1 , p j2 , . . .}. We used the 2D multislice Carr-Purcell-Meiboom-Gill (CPMG) sequence to acquire T2 relaxometry data. CPMG sequences suffer from the effect of the stimulated echoes due to imperfect refocusing. It is important to address this effect as this leads to errors in T2 estimation [START_REF] Crawley | Errors in t2 estimation using multislice multiple-echo imaging[END_REF]. Here we tackle is the problem of stimulated echoes using the iterative technique of Extended Phase Graph (EPG) algorithm [START_REF] Prasloski | Applications of stimulated echo correction to multicomponent T2 analysis[END_REF]. Each compartment's weight is obtained as, w j = α j / i α i . Simultaneous estimation of the weights and parameters of the distributions of such multi-compartment models is nontrivial and not reliable in terms of robustness and accuracy [START_REF] Layton | Modelling and estimation of multicomponent t2 distributions[END_REF]. Hence we choose to fix the PDF parameters. In this work, the {f j (•)} 3 j=1 are chosen as Gaussian PDFs. Their mean and standard deviation are fixed based on the findings from the literature [START_REF] Laule | Magnetic resonance imaging of myelin[END_REF][START_REF] Mackay | Magnetic resonance of myelin water: An in vivo marker for myelin[END_REF][START_REF] Lancaster | Three-pool model of white matter[END_REF] and are set as µ = {20, 100, 2000} and σ = {5, 10, 80} (all values in milliseconds). Estimating the model thus resorts to finding the optimal {α j } 3 j=1 and B 1 for the following least squares problem:

α, B1 = arg min α,B1 m i=1   y i - 3 j=1 α j λ j (t i ; B 1 )   2 (2)
where Y ∈ R m is the observed signal; m is the number of echoes; α ∈ R + 3 . Although the optimization of α and B 1 are linear and non-linear in nature, these variables are linearly separable. α and B 1 are computed by non-negative least squares and BOBYQA optimization respectively. The weights of short-T2 (w s ), medium-T2 (w m ) and high-T2 (w h ) compartment for every voxel are used as a feature for each voxel.

Multi-compartment Diffusion model (MCDiff )

For diffusion MRI (dMRI), we considered the recently introduced MCM as they provide an intuitive way of describing the different fascicles, cells and free water contributions to each voxel. MCM are defined as a weighted sum of several compartments each describing a fascicle (i.e. a dense set of fibers sharing the same orientation) or isotropic matter (such as free water or water trapped in cell bodies). Similar to T2 relaxometry, each compartment in MCDiff is defined by a PDF. However in MCDiff, the PDFs describe water diffusion probability inside the compartments. A variety of compartment types may be defined [START_REF] Panagiotaki | Compartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison[END_REF] based on the assumed white matter microstructure and the acquired dMRI data (the more gradient directions and b-values, the more information may be extracted). Our proposed method is quite independent of this choice and can be applied generically to all parameters that may be extracted from MCM. In the specific study in Section 3, we have focused on the following model:

p(x) = f w p F W (x) + N =3 i=1 a i p i (x) (3)
where f w + i a i = 1 are the weights of the individual compartments, p F W is an isotropic Gaussian PDF specific to free water (i.e. with a variance of 3.0 × 10 -3 mm 2 .s -1 ), p i (x) denotes the i-th fascicle compartment PDF here defined as a stick model (i.e. a Gaussian PDF with equal secondary eigenvalues, fixed from an outside reference). We have specifically chosen this ball and stick model for our experiments as it can be estimated reliably on our clinical data (see Section 2.3). This estimation was performed using the method proposed by Stamm et al. [START_REF] Stamm | Comprehensive Maximum Likelihood Estimation of Diffusion Compartment Models Towards Reliable Mapping of Brain Microstructure[END_REF], which uses a variable projection on the linear elements of the cost function (the compartment weights) to perform a fast maximum likelihood estimation of the model parameters with Levenberg-Marquardt optimization. We then defined different parameters from this MCM which describe the white matter microstructure inside the voxel. First, each anisotropic compartment p i is defined as a constrained tensor. Hence we can extract the usual tensor scalar maps for each anisotropic compartment. However, to enable comparison between voxels, we need to average those compartment specific values over all anisotropic compartments. We have thus computed the weighted average of those values (using the weights a i ) to get the following scalar maps: fractional anisotropy (F A mc ), apparent diffusion coefficient (ADC mc ) and axial diffusivity (AD mc ).

In addition to those maps, the weight of isotropic free water (f w ) is a crucial one that could identify edema or other free water related phenomena and we therefore included it in the parameters as well.

Data

All acquisitions were made on a 3T MRI scanner. The T2 relaxometry data was obtained using a 2D multislice CPMG sequence with the following specifications: first echo time (TE) = 13.8ms; echo spacing = 13.8ms; 7 echoes; repetition time (TR) = 4530ms; 1.33 × 1.33 × 3mm 3 voxel resolution; acquisition time was just less than 7min. The dMRI acquisition was performed with 30 directions on a single shell of b-value at 1000s/mm 2 , with a 2 × 2 × 2mm 3 voxel resolution, on a 128 × 128 × 60 matrix with TE and TR of 94ms and 9.3s respectively. Transverse SE T1-w images (1 × 1 × 3mm 3 ) post Gd contrast agent infusion (0.1mmol/kg gadopentetate dimeglumine) were acquired to find Gd enhanced lesions. A T1-w image was also acquired for performing the distortion correction in diffusion images. A 3D MPRAGE image was acquired with inversion time, TR and TE of 900ms, 1900ms and 2.98ms respectively. The voxel resolution was 1×1×1mm 3 on a 256×256×160 matrix. Lesions were segmented on T2-w images by radiologist. Hence all images were registered to the T2 image (1 × 1 × 3mm 3 voxel resolution) linear registration using a block-matching algorithm [START_REF] Commowick | Block-matching strategies for rigid registration of multimodal medical images[END_REF][START_REF] Ourselin | Block matching: A general framework to improve robustness of rigid registration of medical images[END_REF].

Our data set consisted of 10 MS patient datasets demonstrating clinically isolated syndrome (CIS) condition. There were a total of 227 MS lesions in all patients, out of which 28 lesions had gadolinium enhancing regions. The voxels are divided into two groups: (a) (E+): voxels appearing on Gd enhanced T1 SE images and (b) (L-): lesion voxels which are hyperintense on T2-w images but do not appear on Gd enhanced T1-weighted images. The protocols were approved by the institutional review board, and all participants gave their written consent.

Identifying enhancing voxels in lesions

We performed enhancing voxel identification using the MCT2 and MCDiff estimates. In our database, we had 15012 and 3904 (L-) and (E+) voxels respectively. We adopted a random shuffle and repeat strategy to compensate for the imbalance in the class. 5000 (L-) and 3400 (E+) voxels are randomly selected from the dataset to train the classifier. The remaining (L-) and (E+) voxels are then used to evaluate the classifier performance. This method is repeated 100 times to avoid any bias in sampling the data set for model training. The accuracy statistics are recorded for every repetition. It shall be noted that the model from one repetition is not retained for the next. For a new repetition, the model is trained and validated on a different dataset. We then observe the validation error of the classifier over 100 repitions. We used support vector machine classifier (with radial basis function kernel) in this work [START_REF] Cortes | Support-vector networks[END_REF].

Experiment-1 The predictions are performed using three features sets: (a) MCT2 derived microstructure information: F R = {w s , w m , w h , } ∈ R 3 , (b) MDiff derived microstructure information: F D = {f w , F A mc , ADC mc , AD mc } ∈ R 4 and (c) a features set containing both MCT2 and MCDiff derived microstructure information F RD ∈ R 7 . The aim of this experiment is to observe whether combining the diffusion and T2 relaxometry derived microstructure increases the accuracy of prediction. The observations from this experiment will help us comment on complimentary nature of the feature sets (if any).

Experiment-2 In this experiment we illustrate the application of the proposed method on a MS patient. We maintain a MS patient dataset which was never used for training the data set in any of the repetitions. The classifier trained in every repetition is used to predict to which category the voxels in the validation image belong. We perform a majority voting on the 100 predictions to decide the final prediction for each voxel. Subsequently we compute the dice measure on the (E+) and (L-) masks to judge the performance of the classifier. The classifier implementation was performed using the scikit-learn package in Python v2.7.

Results

Experiment-1 We show in Fig. 1 comparison of the prediction performance of the classifier on validation sets over 100 repititions using features sets derived from:

(a) MCT2 model only (F R ), (b) MCDiff model only (F D ) and (c) combination of both (F RD ). The mean overall accuracy of prediction when using F RD , F R and F D are 85.57%, 84.24% and 81.73% respectively. From the overall accuracy plot shown in Fig. 1 we observe that combining the microstructure measures from MCT2 and MCDiff model yields better (E+) detection. The true positive rate (TPR) and true negative rate (TNR) plots in Fig. 1 show that MCT2 and MCDiff features are better than the other at detecting non-enhanced and enhanced voxels respectively in MS lesions. However, combining both features (F RD ) yields better prediction results. Hence we use F RD for performing predictions in experiment-2. Experiment-2 Results are shown in Fig. 2. This MS patient had 18 MS lesions out of which 3 of them had Gd enhancing regions. The dice score for (E+) and (L-) voxel prediction was 0.64 and 0.86 respectively.The top row in Fig. 2 shows a lesion which had only (L-) voxels and the proposed method successfully predicted that there were no (E+) voxels in the lesion. The second and third row of Fig. 2 shows performance of the method in presence of Gd enhanced voxels in the lesion. Our method identified the (E+) voxels in the lesion. However there were false positives around the Gd enhanced core of the lesions where non-enhancing voxels were identified as belonging to the enhancing region of the lesion.

Discussion

Our analysis shows that combining tissue microstructure information from multicompartment T2 relaxometry and diffusion MRI model helps at yielding better prediction accuracy as compared to each feature being used alone. The higher TPR of features derived from MCDiff might be attributed to the fact that during an active BBB breakdown, there is a greater presence of inter and extra cellular fluid matters and inflammation as compared to non-enhancing parts of the lesion. The high-T2 water fraction from MCT2 model is capable of identifying higher inflammation. However, the medium-T2 water fraction, as described section 2.1 is heterogeneous in terms of inter and extra-cellular fluids. However, MCDiff models are able to better explain such scenarios. The non-enhancing regions are demyelinated regions with inflammation which can be explained using MCT2 microstructure information.

Our study has certain limitations. The clinical data used in this work did not favour use of state of the art multi-compartment models. Single b-value data with 30 directions limited us to use a realtively simpler MCM model for MCDiff for reliable estimations. Higher number of echoes and shorter echo times for the T2 relaxometry data will facilitate MCT2 models. However, this study illustrates that even with clinical protocols, we have good detection of enhanced lesion regions using only MCT2 and MCDiff features.

Conclusion

We proposed a method to identify MS lesion voxels in which the brain tissues are undergoing active BBB breakdown using brain tissue microstructure information derived from advanced MRI techniques. The proposed method shows promise and motivation to work on improvement of the model from its current form. In the future work, we plan to have uncertainty measures on the predictions so that we can tackle the issue of false positive detection effectively. We also plan to test it on higher quality data to realize the true potential of the current framework.

Fig. 1 :

 1 Fig. 1: (Left to right): Overall accuracy, true positive rate and true negative rate of the predictions of the validation set over 100 iterations.

Fig. 2 :

 2 Fig. 2: The (E+) prediction results on a test image is shown here. Legend for the segmentation labels are shown below the illustrations.


Audrey Cayron

Christophe Viallon

Olga Bushueva

Ayad Ghannam

Thierry Parra

High-Performance Compact 3-D Solenoids for RF Applications

Keywords: Integrated Passive Devices, Above-IC, solenoid, high-Q inductor, three-dimensional inductor, 3-D inductor

come

I. INTRODUCTION

T HE integration of high-quality RF inductors remains a challenge, since the quite poor characteristics of these components are frequently limiting performance of integrated circuits (IC). Improvements can be achieved by implementing enhanced passive components on a specific chip beside the active die, by way of an integrated passive device (IPD) technology, or directly on the active die, from an above-IC integration. However, as IPD or above-IC current commercial technologies still propose only spiral inductors, the gain in performance is mainly based on the increased thickness of metal strips. The gain remains limited on Q-factor because of large inter-spire proximity effects, and the self-resonant frequency (SRF) is affected by the value of the substrate permittivity.

The solenoid topology can be an alternative to alleviate drawbacks of planar spiral structures. Because this threedimensional (3-D) device is using the vertical dimension, its footprint on the substrate is lower. Such a topology improves Q-factor and SRF when the core of the coil is thick enough and turn-to-turn spacing is minimum [START_REF] Joung | Chip-to-Board Micromachining for Interconnect Layer Passive Components[END_REF]- [START_REF] Yoon | Surface micromachined solenoid on-Si and on-glass inductors for RF applications[END_REF]. Several solutions have been proposed for the fabrication of solenoids: deposition of thick insulating layers along with electroplated metallization [START_REF] Young | Monolithic high-performance three-dimensional coil inductors for wireless communication applications[END_REF], micromachining technologies to form air-core solenoids on top of a substrate [START_REF] Joung | Chip-to-Board Micromachining for Interconnect Layer Passive Components[END_REF]- [START_REF] Yoon | Surface micromachined solenoid on-Si and on-glass inductors for RF applications[END_REF], [START_REF] Zine-El-Abidine | CMOS-Compatible Micromachined Toroid and Solenoid Inductors With High Q-Factors[END_REF], [START_REF] Lu | High aspect ratio air core solenoid inductors using an improved UV-LIGA process with contrast enhancement material[END_REF] or in a cavity etched into the substrate [START_REF] Gu | High-Q Solenoid Inductors With a CMOS-Compatible Concave-Suspending MEMS Process[END_REF]. Unfortunately, all these processes involve numerous and/or complex technological steps often constrained by equipment (masker resolution, UV source intensity and wavelength, etc.) and photoresist capabilities. As resulting core section and coil longitudinal compactness are usually too small, performance enhancement is not always in line with expectations.

The solution proposed in this paper addresses all the abovementioned issues by using a new technology for the manufacturing of 3-D metal structures. After the description of the main steps of the process flow, experimental performances are presented for various 3-D solenoid inductors integrated on a glass substrate. The above-IC integration of solenoids over a silicon substrate is investigated and then compared to more usual planar approaches.

II. FABRICATION PROCESS

The fabrication process flow (Fig. 1) relies on two copper plating steps of thickness ranging from the standard of 15 µm up to 40 µm for compliance with high-power applications. First, a seed layer is sputtered over the substrate (a). The bottom metal layer is electroplated into openings of a patterned photoresist (b). The photoresist and the seed layer are removed (c). A 100 µm-thick SU-8 core ( r = 2.85 and tanδ = 0.04) is shaped (d), a new seed layer is sputtered and a sacrificial mold is patterned (e). This step is crucial since the thickness and aspect ratio of this mold determines the minimum lateral conductors width and spacing. Then, both side and top parts of the solenoid coil are formed in a single 3-D copper electroplating step (f), as reported in [START_REF] Ghannam | 3-D Multilayer Copper Interconnects for High-Performance Monolithic Devices and Passives[END_REF]. Finally, thick photoresist mold is removed and the second seed layer is etched (g). As described, when using the 3-D copper electroplating process, vertical and upper metal sections are fabricated simultaneously, so the numerous and critical steps for via hole implementation are avoided. For this process, three masks are needed for device fabrication and only standard equipment is used. After optimization, critical dimension tolerance is within ±1.5 µm and SU-8 resin thickness variation is within ±3 µm. With a 100 µm-thick SU-8 layer, the minimum for metal width and spacing is 15 µm. When the low thermal budget, as well as the maximum temperature (bellow 150 • C) are taken into consideration, it can be highlighted that this process is compatible with above-IC integration [START_REF] Ghannam | 3-D Multilayer Copper Interconnects for High-Performance Monolithic Devices and Passives[END_REF].

III. RESULTS AND DISCUSSION

Four solenoid inductors have been designed and fabricated. Geometrical and measured electrical characteristics are summarized in Table I. Two of them are shown in Fig. 2. Devices L 1 and L 2 are both 3-turn and differ from conductor width w and spacing s. L 3 (6-turn) and L 4 (8-turn) are solenoids of large inductance values. They both share the same w and s as with L 2 . The parameters l s and w s mentioned in Table I refer to solenoid total length and width, respectively. Inductors are embedded in a 1-port setup. On-wafer characterization of such high-Q inductive device is somewhat challenging. Vector Network Analyzer (VNA) measurement uncertainties on gamma (Γ) strongly affect the accuracy of the extracted Q factors for values beyond 50 [START_REF] Kuhn | Measuring and Reporting High Quality Factors of Inductors Using Vector Network Analyzers[END_REF]. An accuracy of 0.002 is verified on Γ magnitudes, all over the 40 MHz-20 GHz frequency range. It translates into an uncertainty ∆Q of 7 for a Q value of 55 [START_REF] Kuhn | Measuring and Reporting High Quality Factors of Inductors Using Vector Network Analyzers[END_REF]. Parasitic interactions between the on-wafer setup and the inductor may have very visible effects when the Q-factor is high. These effects are minimized by tuning the internal dimensions and width of the metal ring surrounding the device under test (DUT) and connected to the ground tips of GSG probe [START_REF] Bushueva | On-Wafer Measurement Errors Due to Unwanted Radiations on High-Q Inductors[END_REF]. Finally, inductance and Q-factor are derived from the measured Γ without de-embedding access wires and pads in order to keep the best measurement accuracy and to avoid additional errors. As a consequence, Q and SRF value are underestimated, up to 18 % and 5 % respectively, while inductance values are slightly overestimated (+0.25 nH). However, the comparison with electromagnetic (EM) simulations carried out under the same conditions is more accurate [START_REF] Bushueva | On-Wafer Measurement Errors Due to Unwanted Radiations on High-Q Inductors[END_REF].

Post-layout simulated and experimental L and Q values of L 1 to L 4 are plotted versus frequency in Fig. 3. EM simulations are performed by a 3-D EM simulator (ANSYS HFSS). As it can be noticed, results from measurements are in very good agreement with simulated data. The comparison of L 1 with L 2 shows that inductance density widely benefits from the reduction of s and w. A larger number of turns (from L 2 to L 3 ) increases the inductance and improves the inductance density thanks to a better magnetic flux confinement. The maximum density of 63 nH/mm 2 is reached by the 8-turn inductor L 4 because the number of turns and an increased core cross-section. Q max is slightly decreased from L 1 to L 4 , mainly because of increasing capacitive contribution of SU-8 core. The simple expression (1) can accurately predict the inductance value of a solenoid knowing its geometrical data. Table I reports calculated values (L calc ) for L 1 to L 4 using (1) added by access wires contribution (≈ 0.25 nH).

L c = µ 0 n 2 A l s (1)
In (1), A is the solenoid core cross-section. With an integer number of turns n, l s and consequently L c are proportional to n. The same proportionality is obtained for the resistance. Hence, unlike planar spiral inductors, adding turns to a solenoid does not degrade its Q-factor, as it is verified experimentally by Fig. 3, as long as dielectric contribution remains negligible (frequencies under 2 GHz). EM simulations are used to evaluate the level of performance that can be expected from above-IC solenoids integrated using the proposed technology. The solenoids L 2 to L 4 are implemented above a 24 µm-thick layer of SU-8 resin, on top of a 10 Ω cm standard resistivity silicon substrate (Fig. 4(a)). As for CMOS and BiCMOS on-chip planar inductors, a patterned ground shield is integrated under the solenoid using the first metal layer (a 0.6 µm-thick Al layer) of the back-end of line (BEOL). With this shielding, substrate induced dielectric losses are minimized. The stacking of all insulating layers of the BEOL is modeled by a single material with an r of 4 and a thickness of 10 µm. Simulated data are presented in Fig. 4(b). As it can be expected, Q max and SRF values are slightly lowered when compared with onglass devices. Nevertheless, these values remain quite high, with Q max ranging from 37 to 45 and the SRF from 5.5 GHz to 14 GHz. Inductance values remain almost unchanged. In Fig. 5, the new tradeoff between compactness and performance that can be achieved using the here-proposed solenoids is highlighted by the comparison with conventional planar technologies. The three main characteristics, i.e. surface area, Q max and SRF, are reported versus inductor values in Fig. 5(a), (b) and (c), respectively. First, the comparison is made with on-chip silicon planar spiral inductors [START_REF] Pan | Performance trends of on-chip spiral inductors for RFICs[END_REF], [START_REF] Sia | Modeling and Layout Optimization Techniques for Silicon-Based Symmetrical Spiral Inductors[END_REF]. If these inductors occupy the smallest area (Fig. 5(a)), as required for minimizing substrate-induced losses, they still present the lowest Q max values (Fig. 5(b)), while SRF values remain close (Fig. 5(c)). Then, characteristics of some high-Q above-IC planar inductors [START_REF] Carchon | Wafer-level packaging technology for high-Q on-chip inductors and transmission lines[END_REF] are reported in Fig. 5, as well. The process, as described in [START_REF] Carchon | Wafer-level packaging technology for high-Q on-chip inductors and transmission lines[END_REF], is very close to best available IPD technologies: the inductor spiral is a 10 µm thick copper strip integrated on a 28 µm low r thick insulating layer of benzocyclobutene (BCB), with a 10 µm thick copper underpass implemented 12 µm underneath. This time, it can be observed that the area of these inductors is about twice the area of 3-D solenoids (Fig. 5(a)), while the maximum Q-factor Q max is twice for 3-D solenoids (Fig. 5(b)), and SRF remain quite close (Fig. 5(c)). These results again confirm the great interest of the proposed 3-D above-IC process. All other published solenoids are not reported in Fig. 5, either because their integration is not comparable, or because their performance is not in line with the expected level.

IV. CONCLUSION

A simple 3-D copper electroplating process involving two metallization steps has been successfully implemented for the fabrication of high performance highly integrated solenoid inductors. A maximum Q-factor Q max of 58 and a self-resonant frequency SRF of 19 GHz are experimentally demonstrated . Simulated characteristics of above-IC solenoids compared with onchip [START_REF] Pan | Performance trends of on-chip spiral inductors for RFICs[END_REF], [START_REF] Sia | Modeling and Layout Optimization Techniques for Silicon-Based Symmetrical Spiral Inductors[END_REF] and above-IC planar spiral inductors [START_REF] Carchon | Wafer-level packaging technology for high-Q on-chip inductors and transmission lines[END_REF].

for a 2.3 nH solenoid. The best inductance-to-area ratio of 63 nH/mm 2 is reached by an inductor of 9.5 nH whereas all other characteristics remain very good, with a Q max of 41 and a SRF of 8 GHz. When compared with planar inductors, these 3-D solenoids significantly improve the tradeoff between integration density and performance. Such a cost-effective 3-D technology then appears very promising for high-performance IPD or above-IC inductive device integration.

Fig. 1 . 3 -

 13 PhotoresistCopper

Fig. 2 .

 2 Fig. 2. Microphotographs of inductor L 1 (left) and SEM picture of L 4 (right).

Fig. 3 .

 3 Fig. 3. Measured ( ) and simulated ( ) Q an L values versus frequency of devices L 1 to L 4 .

Fig. 4 .

 4 Fig. 4. (a) layers added under above-IC solenoids, (b) simulated data of above-IC solenoids L 2 ( ), L 3 ( ) and L 4 ( ) versus frequency.

Fig. 5

 5 Fig.5. Simulated characteristics of above-IC solenoids compared with onchip[START_REF] Pan | Performance trends of on-chip spiral inductors for RFICs[END_REF],[START_REF] Sia | Modeling and Layout Optimization Techniques for Silicon-Based Symmetrical Spiral Inductors[END_REF] and above-IC planar spiral inductors[START_REF] Carchon | Wafer-level packaging technology for high-Q on-chip inductors and transmission lines[END_REF].

TABLE I SUMMARIZED

 I CHARACTERISTICS OF THE INDUCTORS

	Device	L 1	L 2	L 3	L 4
	Number of turns n	3.4	3.4	6.4	8.4
	w (µm) / s (µm)	30/30	20/20	20/20	20/20
	Area ws (µm) × ls (µm)	350 × 240	350 × 160	350 × 280	420 × 360
	Lmes @ 1 GHz /L calc	2.3/2.5 3.0/3.4 5.8/6.1 9.5/10.2
	Lmes/Area (nH/mm 2 )	28	54	59	63
	SRF (GHz)	19.1	16.8	11.4	8.1
	Qmax @ fmax (GHz)	58 @ 5.6	55 @ 5.5	47 @ 4.6	40 @ 3.0