In many respects, France's solar photovoltaic policy jump-started the development of what could be called "individual" photovoltaic projects: one project, one roof, one owner. Given this policy framing, projects that pursue an alternative approach to solar development (more-thanindividual investment strategies) have to channel their assembling in different ways. This paper investigates community-based solar experiments -the "centrales villageoises" in south-eastern France's Rhône-Alpes region. This approach is innovative as it consists in assembling multiple panels on multiple roofs with mixed (public and private) owners. The analysis follows these emerging collective solar projects as a matter of binding together a large set of heterogeneous materialities, such as panels, roofs, buildings, electricity grid network and landscapes, and providing them with a shared status. We argue that the solar resource is defined along with these emerging socio-technical systems. Thus, its appreciation as a "common good" (or lack of such) relies on methods, tools and capacities that allow protagonists to have flexibility in forming material entanglements endowed with a collective dimensionsharing roofs, investments, risks and gains. Finally, the analysis shows that a fair solar energy project is one that not only fairly redistributes the benefits but also, in the long run, preserves the possibility of having collective discussions on diverse dimensions, especially the integration of social and landscape-related issues (landscape of justice) within the solar energy's development agenda.

Introduction

Despite the numerous arguments in favour of increasing and accelerating the energy transition (depletion of fossil fuels, rise in carbon emissions), the ongoing development of renewable energies still faces many hurdles and what has been called carbon locks-in [START_REF] Unruh | Understanding Carbon Lock-in[END_REF][START_REF] Unruh | Escaping Carbon Lock-In[END_REF]. Some academic researchers approach the emergence of local energy initiatives as a potential means to overcome these hurdles [START_REF] Dóci | Exploring the Transition Potential of Renewable Energy Communities[END_REF][START_REF] Walker | What Are the Barriers and Incentives for Community-Owned Means of Energy Production and Use?[END_REF][START_REF] Walker | Trust and Community: Exploring the Meanings, Contexts and Dynamics of Community Renewable Energy[END_REF]) and create posi-tive renewable energy development terms [START_REF] Catney | Big Society, Little Justice? Community Renewable Energy and the Politics of Localism[END_REF]). Among these positive terms, one key question deals with the capacity of local energy initiatives to improve the distribution of renewable energy profits by putting them within reach of a wider range of actors [START_REF] Aitken | Wind Power and Community Benefits: Challenges and Opportunities[END_REF][START_REF] Allan | The Importance of Revenue Sharing for the Local Economic Impacts of a Renewable Energy Project: A Social Accounting Matrix Approach[END_REF][START_REF] Cowell | Acceptance, Acceptability and Environmental Justice: The Role of Community Benefits in Wind Energy Development[END_REF]. This paper argues that the construction of local renewable energy initiatives not only acts as a way to redistribute the renewable energy incomes but mainly questions the construction of the energy resource itself and its collective appreciation as a "common" [START_REF] Ostrom | Governing the Commons: The Evolution of Institutions for Collective Action[END_REF]. Following processes of community-based solar developments, the paper specifically analyses how solar energy is "commonised" and configured (or not) as a collective resource. The interwoven analyses of the emergence of a local energy initiative and the characterisation of a (solar) resource offer a worthwhile insight into energy justice issues. Beyond the unique scope of distributional justice, these processes are examined in the light of issues of gaining access to and constructing the resources. Indeed, the goal of the collective solar initiatives is not only to maximise their projects' economic outcomes but also to construct and maintain greater collective qualities of the resource. Thus, they struggle to produce both a new energy landscape and a landscape of justice [START_REF] Mitchell | Cultural Landscapes: Just Landscape or Landscape of Justice?[END_REF].

This paper seeks to tackle these issues while focusing on a critical case study: the French context of photovoltaic development. French solar policy (feed-in tariff, grid management, costs and procedures of grid connection) has mainly triggered the development of what could be called "individual" photovoltaic projects: one project, one roof, one owner. This French policy has led to the rapid growth of a new solar energy landscape comprising myriad small individual units of solar energy production. This widespread phenomenon drives us to learn from alternative and more concerted approaches to the solar resource.

In this context, our conception of what a resource is goes beyond how the notion tends to be understood. A resource not only refers to the result of a socio-technical process of production but also encompasses all the materialities summoned during the production process. Thus, the solar resource is neither only the solar rays nor the usable electricity generated after these solar rays have come into contact with a photovoltaic panel. The term solar energy resource also encompasses the electric grid (electric lines, substations), the roofs that might host the photovoltaic panels, the photovoltaic panels and the elements of the landscape within which the solar energy projects are developed.

This paper starts with a focus on the context of French photovoltaic policy and the way in which it frames and constrains the development of local solar energy initiatives ( §1); it then proceeds with the analytical proposition to tackleby using assemblage thinking theorythe processes of both solar resource and collective solar project construction, as well as the energy issues these processes raise ( §2). The analytical proposition is tested with an analysis of two specific collective solar energy pro-jects within the French context ( §3). Finally, several of the discussion's elements are drawn from this analysis regarding the issues raised by our approach of the solar energy resource ( §4).

2. An examination of the qualitative outcomes of French photovoltaic policy Since the early 2000s, the French government has adapted its energy policy more and more to its international commitments.1 As a result, in the wake of the European agenda on renewable energy production, French solar photovoltaic policy is primarily structured around quantitative contribution goals with regard to the national electric mix. This policy sets up favourable technical and economic conditions to trigger massive photovoltaic developments without considering qualitative and multidimensional issues on the local scale. This policy's unique dimension primarily targeted the development of photovoltaic systems on roofs rather than on the ground. Beyond this quantitative framework, France's photovoltaic policy appears to trigger specific forms of photovoltaic developmentmostly large industrial operations or small-sized private operations on residential roofs. These photovoltaic developments emerged from three main strands of action: a feed-in-tariff scheme, grid connection and grid reinforcement policies and, finally, tax credits. Since its first implementation in 2002, the feed-in-tariff scheme has been regulated by the French government but has constantly overflowed as a result of numerous unforeseen developments on the market [START_REF] Cointe | The Emergence of Photovoltaics in France in the Light of Feed-in Tariffs: Exploring the Markets and Politics of a Modular Technology[END_REF][START_REF] Cointe | From a Promise to a Problem: The Political Economy of Solar Photovoltaics in France[END_REF]. The regulation of the scheme related to both the value of the feed-in tariff and the conditions for its attribution. With the creation of many different tariff categories in accordance with roof and integration criteria (surfaces of panels, building uses, integration modalities of the panels), the scheme quickly became more complicated. Then, the purchase agreement that set the feed-in tariff between the EDF (Electricité de France) and the electricity producers depends on every operation being connected to the electric grid. By decree, the French government determines the share of responsibility for grid connection (from 0% to 100% at the expense of the electricity producer) and the possible costs for reinforcing the grid. Before the passage of the NOME (New Organisation for Electricity Market) Law at the end of 2010, the costs had been shared equally between the photovoltaic-electricity producer and the EDF, whose public service mission is renewable energy development; ever since, however, the producer has had to foot the bill. This decision might not be of any consequence to large producers but certainly affects smaller producers, especially those who need to cover the cost of the grid-reinforcement operations. Finally, France's solar photovoltaic development is supported by various tax credits meant for households to acquire panels and photovoltaicrelated benefits for small operations, which means that collective projects cannot benefit from these credits.

In this context, each roof has a unique economic profitability potential. This profitability potential might vary drastically from one roof to the next within the same neighbourhood, even if they benefit from the same exposure to sunlight and present similar solar orientations, lowslope roofs and no solar masks. Therefore, this framework makes the emergence of collective solar projects more com-plicated. A project developer seeking to capitalise on the emergence of collective photovoltaic operations faces many difficulties in gathering roofs and bringing together roof owners. As a result, the French photovoltaic policy primarily triggers a private and individual form of photovoltaic development.

As shown by recent studies, only a few collective photovoltaic projects have been developed in France2 [START_REF] Devisse | Quelle Intégration Territoriale Des Énergies Renouvelables Participatives? ADEME[END_REF], although their number has been rising steadily [START_REF] Nadaï | French Policy Localism: Surfing on 'Positive Energie Territories' (Tepos)[END_REF][START_REF] Yalçın-Riollet | Energy Autonomy in Le Mené: A French Case of Grassroots Innovation[END_REF]. This evolution is supported by the work of NGOs comparing different legal frameworks [START_REF] Poize | Etude du cadre législatif et réglementaire applicable au financement participatif des énergies renouvelables[END_REF][START_REF] Poize | Projets citoyens pour la production d'énergie renouvelable, comparaison France-Allemagne[END_REF] and offering a collective financing scheme (e.g. Energie Partagée) to guide collective photovoltaic initiatives along a more suitable path. Within this increasing number of collective operations, there is a wide range of projects regarding the type of development [START_REF] Devisse | Quelle Intégration Territoriale Des Énergies Renouvelables Participatives? ADEME[END_REF]. This paper does not tackle the causes of these collective solar developments but examines their potential contributions to an energy transition in the making. Based on two case studies, the paper focuses on emerging solar cooperatives and questions their strategies to "commonise" the solar energy resource. The examination of these case studies provides some elements to answer our main questions: (1) How are these solar energy cooperative projects developed, and what are the difficulties they face? (2) What makes these collective operations more innovative than individual investments in solar energy? Do they constitute new ways of resource grabbing, or do they implement new forms of re-distributing benefits [START_REF] Jenkins | Energy Justice: A Conceptual Review[END_REF])? (3) And finally, do these collective projects encourage a commonisation of the solar resource, and do they offer new perspectives on energy justice [START_REF] Dardot | Commun: essai sur la révolution au XXIe siècle[END_REF][START_REF] Moss | Whose Energy Transition Is It, Anyway? Organisation and Ownership of the Energiewende in Villages, Cities and Regions[END_REF][START_REF] Nayak | Commonisation and Decommonisation: Understanding the Processes of Change in the Chilika Lagoon, India[END_REF]?

Solar energy collectives as dynamic assemblages

Materiality is recognised for playing a central role in the construction and valorisation of energy resources [START_REF] Bridge | Resource Geographies I: Making Carbon Economies Old and New[END_REF][START_REF] Kaup | Negotiating Through Nature: The Resistant Materiality and Materiality of Resistance in Bolivia's Natural Gas Sector[END_REF][START_REF] Mitchell | Carbon Democracy: Political Power in the Age of Oil[END_REF]. The focus on the role of materiality brings attention to relational dynamics in the process of resource commodification. In this context, we study how these relational dynamics bring specific values to the solar energy resource. The qualities of a resourcethe types of values and uses it is related withdo not emerge from physics (e.g. the sun's rays) but from a relational process of construction that engages a multiplicity of materialities (e.g. photovoltaic panels, buildings, roofs, electric grid, landscape ...) and power relations in a place.

The present case studies deal with local attempts to harness the sun's energy and produce electricity. As a starting point, one could emphasise the material specificity of the sun as an energy resource. Unlike coal or oil, the sun is a diffuse energy resource. It needs to be concentrated (from solar radiation to the panels to the grid) in order to produce kilowatt-hours. From a large solar plant to individual small-sized operations, this operation may take various forms, but in all cases a broad range of materialities are needed to produce energy from the sun. In this paper, "resource" refers to all the entities engaged in this process of producing electricity: sun, buildings, landscapes, territories etc. Turning the sun into kilowatt-hours raises the practical issue of turning a territory into a unit of power production.

As a starting point, this paper proposes specifying the way in which the sun and its related materialities enter the process of concentration. In our case studies, what makes the concentration of solar energy very distinctive is the process of pooling roofs distributed across a wide area to create a power generation unit. Thus, the solar energy resource's qualities would emerge from the way roofs are locally pooled and envisioned as a shared materiality to produce electricity. The operation of pooling and sharing a common materiality is challenged by the diversity of statuses and qualities the roofs are attached to (ownership, property value, familial or professional values, architecture, urbanism, landscape, connection to the electric grid, feedin-tariff category). In addition, in the French context, community-based solar projects face high levels of uncertainty and have to adapt to critical technical and economic conditions. Thus, the gathering of roofs to collect energy from the sun often follows non-linear processes and sometimes ends up failing as a collective approach, which leads to separate private individual projects making a comeback. Figuring out these processes requires a specific investigation of assemblage thinking and ANT in order to gain a better understand-ing of the dynamic growth of assemblages.

In the field of human geography, the analysis of materiality and relational dynamics has largely been fuelled by the mostly convergent, although distinct, ANT and assemblage thinking theories (Müller and Schurr 2016, 217). This paper engages specifically with assemblage thinking as a meth-odological point of view to tackle the uncertainty of an energy transition "in the making" [START_REF] Baker | Assemblage Thinking as Methodology: Commitments and Practices for Critical Policy Research[END_REF][START_REF] Labussière | Energy Transition: A Sociotechnical Inquiry[END_REF]. However, it also partially engages with ANT in order to capture, by using more empirically grounded concepts (Müller and Schurr 2016, 220), the multifaceted relations between human and non-human actors during the non-linear emergence of solar energy collectives.

Assemblage thinking has been developed in philosophy [START_REF] Deleuze | A Thousand Plateaus: Capitalism and Schizophrenia[END_REF]: "an assemblage is a multiplicity made up of heterogeneous terms and which establishes relations between them; the only unity of the assemblage is the one of a co-functioning, it is a symbiosis" (Deleuze and Parnet 1996, 69). Our inquiry into assemblage thinking deals with a specific line of questioning: Does an assemblage have the capacity to manage both its growth and its decline? How does it maintain its identity through non-linear evolutions? And does the attention paid to a resource's materialities provide the analysis with a better understanding of an assemblage's adaptive capacity? Deleuze and Guattari distinguish between two different kinds of multiplicities underpinning assemblages: "one qualitative and fusional, continuous, the other numerical and homogeneous, discrete" (1987,484). The "qualitative and fusional" kind is identified as being made up of relations and structured by dimensionsa unity that changes in nature when it is divided. The "numerical and homogeneous" kind of multiplicity comprises metrics, is structured by directions, is a totality that pre-exists its parts and has an unchanging nature when divided. This view offers the first elements to characterise the dynamic of assemblages: Assemblages made up of relations change their intensity when recomposing their materiality. For example, one can divide movement into the gallop, trot and walk, but in such a way that what is divided changes in nature at each moment of the division, without any one of these moments entering into the composition of the other (Deleuze and Guattari,483).

Assemblages composed of added elements do not undergo material transformations when they change. Nevertheless, this approach remains limited when explaining how an assemblage passes from one state to another, that is, from a gallop to a trot and the other way round. The same goes for the consequences of these transformations (growths, decreases) regarding the identity of the assemblage.

Following Deleuze and Guattari, DeLanda (2006) defines the assemblage underlying the clear connection between its materiality and its expressivity (e.g. body language in a face-toface conversa-tion). These approaches introduce materiality as a resource that allows an assemblage to modulate its capacity for both internal and external coordination. DeLanda focuses on what he calls the "coding/decoding" processes: Many assemblages are not highly coded or territorialised but learn from experience in a more flexible way. Assemblages can adapt to contingency and non-linear evolutions and still maintain their identity to some degree. This paper's proposal is to characterise: (a) the practical operations used to manage the growth of an assemblage dynamically and (b) the challenges raised by the articulation of heterogeneous (relational, metric) socio-technical assemblages. To advance in this direction, the paper offers two paired notions: to aggregate and to detach as a way to manage the growth and decrease of an assemblage based on relations and dimensions, and to granulate and to subtract as a way to manage assemblages based on metrics and directions. These two pairs of notions describe two heterogeneous ways of gathering the materiality.

The notion of aggregation highlights how project managers patiently construct roof aggregates, how they pool roofs with their individual heterogeneous qualities and how multiple attachments are made to co-exist. The notion of aggregates, as discussed in philosophy [START_REF] Deleuze | A Thousand Plateaus: Capitalism and Schizophrenia[END_REF], suggests a specific relational approach to the ties between individuals and collectives. Contrary to the notion of granulation, which tends to describe an assemblage of entities that compose a new entity in which initial entities stop having an individual existence (e.g. fragments of several different rocks are crushed to make gravel), the notion of an aggregate describes the creation of a new entity in which the initially separate entities still exist as such. The aggregation and granulation operations adhere to different existing philosophical trends. The aggregation operation leads to an understanding of the construction of collective forms with ontological privilege given to relations [START_REF] Debaise | Un empirisme spéculatif: lecture de "Procès et réalité[END_REF][START_REF] Simondon | L'individu et sa genèse physico-biologique[END_REF][START_REF] Simondon | L'individu et sa genèse physico-biologique[END_REF] when the granulation operation tends to provide the ontological privilege to constituted and pre-existing individuals. Exploring collectives as aggregates allows us to overcome the limits of both the holistic and the atomistic approaches. Aggregation is theorised as an operation of the juxtaposition of elements that retain their heterogeneity and not as a modality to create a homogeneous entity. Thus, aggregating is a different operation than adding, assembling, uniting and joining: Aggregating allows the creation of a collective dimension while maintaining capacities to return to a previous stage of existence. It is envisioned as a relational process of making a wholea massout of a heterogeneous materiality. An aggregation may be shaped very differently according to its materiality and its rhythm of growth.

While the notions to aggregate and to granulate refer to two different ways of managing the growth of an assemblage, to detach and to subtract refer to two different operations of reducing assemblages. The relational perspective introduced by the idea of aggregation is continued by that of detachment. Detaching may be the complementary operation to adjust an assemblage without exhausting it by playing on relations through which things are defined and positioned. These are two modalities of arranging multiplicities that make it possible to analyse the dynamics of collective configuration and reconfiguration without assuming a priori what the collective might or should be, as [START_REF] Deleuze | A Thousand Plateaus: Capitalism and Schizophrenia[END_REF] suggest. To subtract is a more mathematical operation. In order to make the materiality divisible, subtraction tends to reduce it to its physicality (e.g. the sun as a flow of radiation reducible to its intensity). Thus, the operation of subtracting implies an operation of abstraction, which erases any chance of returning to previous levels of heterogeneity.

Such a theoretical framework leads us to embrace the solar energy cooperative collectives as "relational becomings", that is, their qualities are always uncertain and under construction. Depending on the construction of the collective of roofs, the solar resource also appears to be a "relational becoming", with its qualities emerging from the evolution of the "attachments" between the solar rays, the roofs and various materialities called up during the resource construction process: for example, the electric grid, the landscape and symbolic elements of a place's architecture. The concept of "attachment", as discussed within ANT theory (Gomart and Hennion 1999;[START_REF] Latour | Factures/Fractures. De La Notion de Réseau À Celle D'attachement[END_REF], is seized upon as a way to understand the multifaceted relations through which such assemblages are engaged in a process of becoming that is always open to negotiation (Table 1). This paper goes on to argue that the creation of solar energy collectives raises challenging matters for energy justice. It has been underlined that local experiments of sustainable approaches to solar energy offer stimulating insights into distributional energy justice issues [START_REF] Jenkins | Energy Justice: A Conceptual Review[END_REF]). However, distributional justice relates not only to sharing the benefits allowed by a national high solar feed-in tariff: This paper contends that other dimensions gradually become matters of justice, especially the emerging landscapes of solar energy. Drawing from Mitchell's idea that landscapes are forms of power relations' materialisation, the paper questions whether the emerging landscapes of solar energy are "landscapes of justice or just landscapes" [START_REF] Mitchell | Cultural Landscapes: Just Landscape or Landscape of Justice?[END_REF]. This question directly refers to the battle for solar energy in the field andas is the case with the community-based solar model analysed in this paperhow people on the local level are engaged in a struggle against private solar developers to generate alternative ways of making energy and energy landscapes. To discuss this point, we specifically refer to the works of [START_REF] Olwig | Landscape Nature and the Body Politic: From Britain's Renaissance to America's New World[END_REF] and [START_REF] Olwig | Justice, Power and the Political Landscape: From American Space to the European Landscape Convention[END_REF] on landscape as a dwelling place that is made and transformed through daily practices and discussed and regulated through local assemblies. From this perspective, a land is progressively turned into a landscape while testing collective frameworks that govern local practices on the land. Do these new landscape result from a solar rush led by private interests and a quest for individual private economic profits? Or, on the contrary, do they result from collective and collaborative processes in which more-than-economic collective qualities are constructed? This paper's analytical scope positions the answer to these questions within the debates and day-to-day actions of the com-munity-based solar energy processes of emergence.

Aggregation/detachment and granulation/subtraction are taken as complementary notions to be challenged through the assumption that a cooperative solar entity would result from the collective's capacity to pool materiality and form roof aggregates. This assumption leads us to con-sider the forms of aggregation that actors imagine and the tools and processes they use to seize materiality.

Between 2012 and 2016, we examined these operations behind the construction of solar cooperatives. During the first phase of inquiry, we carried out more than 20 semi-structured interviews with project managers and decision makers (regional technicians and elected officials, local technicians and elected officials, natural park technicians, members and presidents of the solar cooperatives and experts who had worked on the projects, such as architects and landscape and electric-grid experts). We also observed participants at regional and local meetings. In the second phase of the inquiry, we analysed the interviewees' archives with two specific points of focus: the timeline of the projects and the tools and instruments (maps, tables, decision methodologies, participation methodologies) that were designed and used during the projects. Finally, in the third phase of the inquiry, we conducted a few additional semi-structured interviews to gather specific information about what we considered to be key moments and instruments.

Table 1 -Following the dynamic growths of (relational, metric) assemblages.

Politics of the sun: pooling roofs to valorise an energy resource

Our assumptions were challenged by the findings obtained through two case studiestwo community-based solar energy projects emerging from the same programme, named the "centrales villageoises". This programme is supported through European (European Regional Development Fund) and regional (French administrative region Rhône-Alpes) financial investments and coordinated by the RAEE (Rhône-Alpes Energy and Environment), a regional NGO in charge of energy and environment-related issues. It is an experiment on the constitution of solar energy cooperatives. One expected outcome was the creation of generic tools to help the development of more community-based solar energy projects, as well as the production of an alternative model of photovoltaic development. Such tools aim to cover four distinct challenges: (1) gathering inhabitants and elected officials and getting them involved in the governance and funding of a local cooperative; (2) creating legal tools (company statutes, leases for roofs) that would be adequate for a collective and cooperative operation; (3) con-structing technical and economic tools to select the roofs on the basis of their collective profitability and (4) improving the landscape and architectural integration of solar panels.

Established in 2010, the programme brought together eight pilot operations, all located within natural regional parks. The set of landscape and architectural issues that the RAEE addresses are a testament to its ambition to test energy alternatives on a national level. The RAEE has worked closely with its technical staffs to gather local inhabitants, companies and public authorities around collective solar projects. Starting in the early 1980s, the RAEE developed this partnership to test working methods and foster community-based energy alternatives. These emerging solar cooperative projects allowed the organisation to launch a new wave of experiments, especially to train inhabitants and public authorities to learn how to initiate and manage such community-based projects. This programme led to the emergence of more than 50 community-based solar energy projects (bearing the name "centrales villageoises" or inspired by it) between 2012 and 2017. However, such community-based projects remain marginal within the French solar energy policy arena, and many lessons from their development still have not received much attention.3

The two specific case studies examined in this paper are the pilot operations that started electricity production first. The analysis focuses on how the processes of pooling roofs influenced the valorisation of an energy resource and how the actors ended up dealing with a large array of local and national during this process. Our analytical focus is on the collaborative approaches and the (environ-mental, technical and economical) instruments that project managers mobilised during the process, what these approaches and instruments led them to do, their political effects and the progressive construction of distinct solar energy potentials (Figure 1).

The Pilat case study: a relational appraisal of sun-related materialities

The first case study was conducted in the northern part of the Pilat Regional Natural Park (hereafter "the Natural Park") (#1), to the south of Lyon and the east of Saint-Etienne. The initial area of the "centrale villageoise" project is limited to one inter-municipal entity (11 municipalities, 129 km2 in area, with 17,000 inhabitants). Except for the city of Condrieu, which is located in the Rhône Valley and affected by the presence of factories and the influence of Lyon, this is mostly a hilly, rural area. The median income of households in 2013 was €21,000,4 which is near the national average. Most of the area's mayors and elected officials on the municipal level are very influential as they participate in both the inter-municipal and the Natural Park's decisions. In this way, the three institutions tend to agree on all decisions regarding the community-based solar project.5

Project developers wanted to generate a solar operation concentrated in space, connecting the roofs of houses and buildings that are located close to each other. During an exploratory phase, they set up a participatory method to define a pilot site from the initial area. The issue was to agree collectively on relevant criteria that would allow the participants to compare potential pilot sites with each other rather than let local political competition manage the selection. This called for discussing solar qualities with respect to local issues. At that time, a team of technicians from the Natural Park steered the project. After a round of public meetings in the area, four municipalities were selected on the basis of their inhabitants' motivations to join the collective solar project. For these municipalities, the technicians did fieldwork to evaluate roof solar intensities and their landscape co-visibilities. They also interviewed inhabitants to find out more about their desire to be part of a collective solar project. These and other observations (roof surfaces, roof's feed-in-tariff category) were aggregated into a database managed by a geographical information system. The technicians developed a set of maps for every municipality. These maps were made to comprise multiple over-lapping layers that draw on all the datasets the technicians had already gathered, including solar intensities, feed-in-tariff categories, owners' motivations and landscape integration (see Figure 2). They allowed the technicians to identify the first aggregates of roofs. Through these maps, roofs became surfaces on which solar intensity, roof owners' motivations and co-visibilities were made perceptible and comparable. This made it possible to add or remove criteria when discussing the potential pilot sites collectively and to determine pools in which the roofs were individually complying with every register of qualities and collectively endowed with a visual coherence. This exploratory step led to the selection of the village of Les Haies as the pilot site for the programme.

Using these promising aggregates produced with the help of GIS tools, the Natural Park's land-scape architect began exploring the landscape and architecture-related issues of the project in Les Haies. She returned to fieldwork to see, in situ, the roofs (incline, orientation, presence of chimneys, antennas and windows) at various scales (building, village, landscape). This marked a major change to the way the aggregate was considered. Beyond a two-dimensional approach, other principles of aggregating the roofs emerged from this close attention paid to the relationships between the roofs and the buildings, the village and the structuring lines of the landscape. A new solar point of view was produced through this relational work. With sketches and drawings, the landscape architect brought to light two solar energy landscape scenarios (see Figure 3). The first scenario was to organise the potentially myriad photovoltaic panels along one line, well exposed to direct sunlight, consistent with an inherited alignment of houses along a street and underlining the smooth incline of a hill on the other side of the village. The second prioritised two coherent gatherings of buildings: one in the old part of the village, so as to include a public building in the project, and another in a recently developed neighbourhood. These scenarios made it possible to refine solar potentials, deal more precisely with the materiality of things and provide them with a new internal coherence.

In order to estimate the overall cost of these scenarios, project managers asked the grid operator for a cost estimate to connect the projects and asked an engineering office for an estimate to install the panels (#2). At this point, the project was organised around roof aggregatesconcentrated in space and individually and collectively expressing various qualities regarding landscape, architecture, owners' motivations, feed-in tariffs and solar exposure. This aggregate's first encounter with the logics of the electric grid and its normativities appeared to be very disruptive. According to his calculation tool, the grid manager looked at the project not as a whole but as the sum of roofs to be divided into individual units. This allowed him to quantify the electricity produced by each panel, identify the panels sharing the same substation and answer the question as to whether a given substation would support these new connections. As a result, the roofs were reduced to surfaces and amounts of electricity. Heterogeneity was no longer considered. Instead of a relational aggregate, the roofs were "granulated", i.e. individualised and reduced to standardised electric qualities. The cooperative solar project fell back into the hands of the inhabitants as a hierarchy of costs to connect each of the panels (from a few hundred to more than 10,000 euros). According to the capacities of the existing grid segments, some operations on several roofs would require grid reinforcement. Such differences in the individual costs of connecting the roofs made the project managers' task of creating a collective project on multiple roofs impossible. At the same time, project managers received cost estimates for the installation of the solar panels. This second quotation detailed the installation costs and the estimated profitability of each individual roof.

Instead of an inclusive appraisal of roofs according to architecture and landscape dimensions, these two quotations introduced a new hierarchy that ranked the roofs according to their costs, benefits and individual profitability. In other words, the cooperative approach, which attempted to share the sun by commonising heterogeneous materialities, was turned into a competition between standardised units. At this point, project leadersmost of whom are retired inhabitants of different villages in the Natural Park and have experience with activist actions but not with energy-related projects tried to finalise the roof selection to set up the final funding plan and start installing the panels (#3). During this selection process, roofs were considered according to their individual costs (connection, works) and their profitability. However, project leaders decided to make the final roof selection a matter of cost (what brings roofs together in the project, calculated as euros invested/Wp installed) rather than selecting roofs according to their profitability (difference between the roofs, calculated as euros invested/euros earned) (see Figure 4). This choice allowed some roof options with important qualities for the collective (architecture and landscape integration, selection of symbolic roofs) to continue to exist when they would not have had this possibility in a collective responding to a profit-maximising logic. The challenge was to reduce the size of the assemblage without losing the initial ambition of their alternative solar development. The project managers decided to create two new scenarios of roof aggregation. Both included the roofs with the important collective qualities but with different options of panel integration and selection of additional roofs. Thus, roof selection instruments had more to do with "making a collective" than "making a profit". The final package of roofs was selected according to previous proposals drawn up in earlier stages of the process. This consisted in reducing the scope of the project by detaching roofs from their heterogeneous assemblage without excluding their owners from the project. The final roof package did not present the spatial coherence expected, as the roofs were not all concentrated in the same area. Nevertheless, some of the initial roof selection's landscape and architecturerelated goals were ultimately fulfilled (panel integration, aesthetic coherence of the roof surfaces) (Table 2).

(#1) Project managers tended to aggregate roofs and give them both an internal and an external coherence. Each roof had multiple individual qualities regarding solar intensity, owners' motivations and feed-in-tariff categories. As a group, the selected roofs had an aesthetic coherence from different perspectives: street, neighbourhood and village. The heterogeneous roof qualities emerged through-out the collective construction process.

(#2) The roof aggregate and its qualities did not resist confrontation with the local electricgrid scheme. The previous relational construction was deconstructed. Roofs only tended to be selected according to their homogeneous electric qualities. The spatial and aesthetic continuity among selected roofs was not kept.

(#3) Project managers decided to return to a previous stage of organisation by reducing the number of roofs within the collective operation but maintained many roofs that were selected in the first place. Electric qualities were not the only selection factor but one factor among many others that had previously been identified. Thus, project managers maintained the collective land-scape and architectural ambitions and did not succumb to economic pressures. The final selection maintained heterogeneous qualities among the roofs, as well as a collective coherence.

The Bauges case study: appraisal of sun-related materialities fails to produce a relational perspective

The second case study was carried out in the Massif des Bauges Regional Natural Park, next to the city of Chambéry (#0). The initial area of the "centrale villageoise" project was once again limited to one inter-municipal entity (six municipalities, 101 km2 in area, with 4,000 inhabitants and the same median household income of €21,000 as in the first case study6). Within this area of midsize mountains, mayors and other local elected officials are also involved in the inter-municipal entities' and the Natural Park's decisions and, as in the previous case study, the three institutions work hand in hand with each other.7

The first discussions about a community-based solar project took place among local elected officials serving together on a board. In this rural mountain area, several kilometres separate one village from the next, and these villages are not visible from each other. The elected officials wanted the pilot project to be concentrated in space in order to be as visible as possible. The operation was conceived as a symbol of the area's sustainable development. This point increased the rivalry between the mayors as all of them wished it to be located in their own municipality. Their first decision was to exclude two municipalities because of their remote geographical locations. That decision was based on existing maps showing the areas where road traffic was low and their locations poorly visible.

The solar project really started with the work of a landscape architect hired by the project man-agers to initiate a local dynamic by organising public landscape workshops. It aimed to discuss the issues relating to the development of a photovoltaic project in the area (opportunity to refurbish roofs, visual impacts from one mountainside to the other) with inhabitants. After each meeting, volunteers were equipped with a set of simple tools to explore which roofs in the area were potentially relevant and could be used in the integration of the collective operation. This allowed them to measure the roofs' incline and collect all the basic but necessary information about their solar qualities (estimate of surface, incline, orientation, presence or absence of solar masks, presence of chimneys or windows). On the basis of the roofs that the participants proposed, the landscape architect organised collective field visits to see the roofs in situ and identify the architectural challenges they might pose, as well as their co-visibilities. In the end, however, the approach failed to deliver the first package of roofs because not enough inhabitants attended the meetings to offer proposals.

Although this qualitative appraisal of roofs focused on their relationships with their buildings and surroundings, the project managers decided to run the process of site selection by bringing the four municipal areas' supporters together for a face-to-face debate (#1). A public meeting gathered the inhabitants and the elected officials motivated by the operation, as well as the technicians (from the regional natural park and the RAEE regional association) who managed the project. It aimed to set up criteria to be graded and ranked for the four municipalities, namely visibility, involvement of inhabitants, roof surfaces and orientations. However, if the intention was to avoid making a choice that might produce conflict, the meeting missed its target. The grading system failed to create differences, and the two best candidates ended up with the same ranking (see Figure 5). Furthermore, the solar criteria (solar intensity and roof orientations) as they were set out within the grading system created no differences between the candidates. The only grading differences related to site visibilities and the surfaces of roofs. The arbitrary selection of one pilot site over another was not understood and created conflict, which resulted in all the officials and inhabitants of the municipalities that were not selected quitting the programme. The outcome appeared to be paradoxical in the way the selected pilot site obtained a good grade even though the materialities of the solar project had not really been explored. Conditions for both the roofs and the electric grid were not really known at the time, and there had been no direct contact with the roof owners.

Figure 5 -Pilot-site selection table. Source: Rhônalpénergie-Environnement.

After this meeting, the selected municipality's elected officials started approaching the roof owners to find out more about their motivation to join a collective solar operation. The results of this door-to-door inquiry were entered into a table. This table, which is very descriptive, mentioned every single roof in the area and their respective features (surface, orientation, solar masks and estimated electricity production capacities). In addition, project managers ordered a technical study to estimate the cost of installing panels on every roof for which the owners gave authorisation. However, by registering the owner's motivations in this table, the project managers failed to instil a collective ambition in the project despite their desire to do so. In fact, roof packages a collective and spatialised dimension were used again. Roofs were selected because of their individual costs. The selected roofs were placed in several remote municipalities without any collective aesthetic coherence. However, project managers succeeded in including innovative options for panel integration on some roofs, even if it meant additional costs for the collective. Roofs included in the collective operation presented homogeneous economic qualities, as well as some specific landscape and architecture qualities (Table 3).

(#0) In the project's first phase, project managers attempted to create roof aggregates in which the roofs present multiple heterogeneous qualities: architecture, landscape integration, orientation, slope, feed-in-tariff categories. However, the participative approach failed because of a lack of local participation.

(#1) As a result, the project managers decided to compile lists of roofs with qualities in tables in order to select suitable roofs without paying attention to their spatial collective coherence. The roof collective was reduced to a list of individual roofs with their individual qualities: what is different rather than what they have in common. Consequently, the selection of the roofs that aimed to lead to the construction of the collective tended to create a roof granulate with shared homogeneous qualities.

(#2) This roof collective was drastically reduced due to grid-connection costs. Gridconnection costs were added in the roof summary tables and became one of the most decisive selection factors. However, the reduction in the number of roofs did not retain the collective as intended but instead led to its collapse.

(#3) In the end, the project managers decided to restart the process of collective photovoltaic operation construction by using the same instruments. Thus, the new group of roofs was selected according to homogeneous qualities they shared and did not emerge from a relational approach (regarding architecture and landscape integration coherence). The final roof selection is made of roofs with homogeneous economic and grid-related qualities. 5. Politics of the sun: local strategies of (re-)assembling materiality to manage discontinuity Community-based solar projects are just getting off the ground in France. Although a few successful operations have been studied [START_REF] Cointe | The Emergence of Photovoltaics in France in the Light of Feed-in Tariffs: Exploring the Markets and Politics of a Modular Technology[END_REF][START_REF] Cointe | From a Promise to a Problem: The Political Economy of Solar Photovoltaics in France[END_REF], most of them struggle because of a national solar policy that is based on high feed-in tariffs and the lack of regulatory framework at the local level. With respect to the French context, the two case studies considered in this paper are very original. They are embedded in a regional process whose aim is to foster alternative paths to develop solar energy with the help of groups of inhabitants and public authorities at the local level.

At the beginning of the paper, we posed three main questions related to the difficulties faced by the collective solar initiatives during their structuring, the innovative dimension of such cooperative developments compared with individualist investments in solar energy, and their capacity to encourage a commonisation of the solar resource, as well as new perspectives of energy justice. The analysis followed how different materialities (roofs, houses, grid electricity network and landscapes) have been brought together into specific assemblages to configure the access to the solar energy resource locally. A key outcome is that these emerging sociotechnical systems are very unstable and subject to non-linear evolutions (increase, decrease) to which they have to adapt, with varying degrees of success. We draw four points of discussion from this analysis.

The first point of discussion relates to materiality and space, an aspect not often studied in the literature about managing shared resources [START_REF] Ostrom | Governing the Commons: The Evolution of Institutions for Collective Action[END_REF]). Solar energy is a diffuse energy resource. On the Earth, it is spatially available from almost everywhere. Nevertheless, a ray of sunlight has to be concentrated in order to generate kilowatt-hours. This point focuses attention on the local material conditions as it may offer suitable configurations to channel a diffuse energy resource. Which spatialities would concentrate the sunlight? The development scheme initially envisioned by the regional Rhône-Alpes Energy Environment NGO was to colonise building's roofs in order to create solar plants at the scale of villages. This led to different approaches to materiality and space. The Pilat case looked at roofs in relation to buildings and their surroundings, which offered a view of roofs in terms of scales and relations (architecture, landscape). The aggregation of roofs was an operation that went beyond adding roof surfaces. It was a matter of creating a solar territory. By contrast, the Bauges case largely ignored the sun-related materialities. It reduced the roof to a sun intensity/surface ratio, and the territory to a matter of usual governance between rival municipalities. In the case of a diffuse energy resource such as solar energy, the "deposit" is not easily defined. In our case studies, it is collectively explored through various attempts to requalify diverse materialities (roof, building, area) to give them a shared (solar) existence in the project. Such an exploration of the buildings, the architecture and the landscape as sun-related materialities promotes a revision of the notion of "resource" beyond its usual categories. At first sight, the sun does not matter. It belongs to everybody and is not affected by individual use. The notions proposed in this paper (aggregation, granulation) focus on the emerging socio-technical assemblages progressively built up to turn the sun into an energy resource, as well as the spatial systems they generate. This leads to the second point, namely the local strategies for assembling sun-related materialities. The initial question related to how an assemblage manages to grow and adapt to non-linear evolutions. Assemblage thinking usually insists on assembling things through either continuity (by relations/attention to heterogeneity) or discontinuity (by standardisation/homogeneity). In practice, the solar assemblages in this study cross over these categories. Thus, a new question may be: How do emerging assemblages strategically deal with discontinuity? In our fieldwork, discontinuity relates to various aspects: private interests (individual profitability), usual governance (compartmentalised space) and electric heritage (individual connectivity). Different strategies were used to this end, and here is a lesson from our study: The Pilat case study benefitted from an early relational appraisal of the landscape and architectural issues with respect to solar developments. This first solar assemblage did not resist the normativity of the grid expertise and its electric zoning but was strong enough to allow the project leaders to re-arrange its internal organisation in order to preserve its first qualitative ambition because other dimensions had not been subtracted. The ability to shift from one state of organisation to another was facilitated by the attention that had been paid to relations in the earlier steps of the process. This made it possible to detach roofs from the aggregate without pushing out their owners. These owners were still part of and interested in preserving a new balance between public and private roofs, panel exposure and architectural quality. Following the approach of Deleuze and Guattari, this assemblage may be re-organised at a lower intensity without losing the density of its attachmentsand, thus, its collective spirit. In other words, this solar assemblage has maintained a relational potential for coherent growth in the future. By contrast, the Bauges case failed to create a concerned collective around the solar-related materialities and their issues. The solar project was discussed early on through tables that did not show an assemblage but myriad solar units to be added up. The grid expertise emphasised this trend and contributed to reducing individual roofs to a matter of electric production and profitability ("granulation"). This paved the way for competition and exclusive solar adventures and eventually led to an unmanageable process of subtracting the less profitable roofs. In other words, the first case managed discontinuity by detaching roofs without subtracting roof owners (so as to keep the cooperative dimension of the project alive) and kept the relational potential to collectively process and play with the electric grid; the second case failed to separate the two aspects of solar energy because a roof was accidentally also considered as an individual's roof and a surface to produce electricity.

The relations between private/individual materialities (roofs) and public/large infrastructures (electric grid) lead us to our third point, which concerns the politics of the sun in the making. [START_REF] Ostrom | Governing the Commons: The Evolution of Institutions for Collective Action[END_REF] stresses the idea that the management of the commons constitutes a third way between having a publicly centralised authority regulating them and having economic agents regulate through the market. Our case study differs from the ones in this literature because the solar resource is inter-twined neither with management practices in the long run nor with highly institutionalised ones. The paper focuses on the setting up of collective frameworks to share the sun as an energy resource. Following sun-related materialities, from an individual building to a public electric grid, the paper makes visible the process of commonisation as a trial to be completed in the midst of both private and public issues. A continuum has to be invented that would allow the sun to pass from one side to another. As seen before, it is a matter of managing different types of discontinuities (individual profitability, as well as non-negotiable public infrastructure). From this point of view, the process of commonisation is not beyond private and public strategies but structures them around new materialities and issues. The notions that were envisioned (aggregation, granulation) to follow the gathering of roofs by local groups might receive further theoretical meaning if passages between different ways of seizing materialities were analysed (Table 4). This approach offers a new understanding of the difficult development of France's solar policy. The development of small photovoltaic units was particularly invasive, especially when the tariffs were high and the regulatory framework was lacking, as was the case in France. Consequently, the individuals involved in solar projects used to be criticised for their opportunistic engagement mainly driven by high profitability. The current case studies stress the fact that these community-based solar pro-jects are not reducible to groups of private individuals. Some of them invent and test regulatory frameworks that are open to architecture and landscape-related issues. In a way, they experiment locally with what the state fails to work on at the national level: a sustainable approach to solar development, in the form of local gains, landscaping and a controlled rhythm of growth. These experiments call for resources underestimated by both the policymakers and the inhabitants in these groups. One resource this paper points to is the ability of a group to manage the increase and the decrease in an emerging assemblage to face economic and technical constraints. To pass from a higher level of organisation to a lower one (1 to 2) requires the capacity to revise key attachments (profitability, connectivity) without losing the project's collective dimension.

The fourth and final point of discussion relates to energy and environmental justice. At first glance, cooperative solar projects seem to initiate an inclusive approach of photovoltaic development. Through collective operations, everyone seems to be able to take part in photovoltaic projects, even if some people don't have a suitable roof for solar development or substantial capital. Thus, such collective adventures allow new actors to initiate or join energy transition actions and to access their economic outcomes. The collective management of such new local incomes might then foster the development of further energy transition-related actions at the local level (e.g. buildings' thermal refurbishing, other renewable energy projects), as planned by the public authorities we studied. However, this paper aims to go beyond merely how economic outcomes are distributed. Solar energy cooperatives might contribute in multiple ways to the construction of what Agyeman and colleagues call "just sustainabilities" (2003) by tackling issues of both sustainable development and energy/environment justice. More specifically, this paper underlines that the landscape lens appears to be an additional focus to discuss the issues of energy justice in the deployment of the energy transition. Our study has shown that the solar community's attempts to develop projects that are not fuelled only by economic factors include qualities that the feed-in-tariff scheme does not consider valuable. Their goal is to contribute not only to the emergence of new solar energy landscapes but also to the emergence of landscapes of justice [START_REF] Mitchell | Cultural Landscapes: Just Landscape or Landscape of Justice?[END_REF] resulting from a more-than-economic collective and concerted process. This reasoning is based on the way the collectives look at the materiality beyond a productive asset. In the case of Pilat, roofs were relationally considered as architectural and landscape components and not reduced to surfaces and potential objects of economic profitability. It became easier for the local group to modulate its collective organisation and face uncertainty. Thus, the fair solar energy project is not the one that only fairly distributes the benefits among the stakeholders but the one that can maintain enlarged collective qualities. In this case, an in-land "law" of justice means taking care of both the people engaged in a collective project and their attachments to a changing landscape by aggregating/detaching roofs without splitting up the group and its ambitions for a qualitative landscape. In this way, by trying to regulate the feed-in-tariff scheme, these collective solar initiatives try to play a role that neither the state nor the market plays. Their action does not apply to a modification of the scheme itself, but they try to work with the profitability that this scheme creates and add new qualities to what it might produce.

The creation of new energy commons leads to fragile processes underpinned by non-linear evolutions. These processes are susceptible to drifting in different directions, from commonisation to privatisation, even if the initial perspective centres on the development of alternative renewable energy ways. While many emerging collective assemblages decrease and sometimes split up, these processes will not systematically lead to a process of decommonisation. For this reason, only a few cases show the ability of a group to manage its internal and external relations strategically in order to increase resource accessibility.

Table 4 -Moving between materialities and their normativities: How to make the sun circulate from the roof to the grid.

Figure 1 -

 1 Figure 1 -Location of the two solar case studies (Pilat, Bauges). Source: IGN Licence ouverte 2012, Authors.

Figure 2 -

 2 Figure 2 -Maps of the city of Les Haies (solar intensity, visual impact, roof owners' motivations). Source: Pilat Regional Natural Park.

Figure 4 -

 4 Figure 4 -Roof selection scenarios in a table listing roofs according to the investment/production ratio. Source: Rhônalpénergie-Environnement.

Notes 1 .

 1 See the papers from[START_REF] Meritet | French Perspectives in the Emerging European Union Energy Policy[END_REF] and[START_REF] Andriosopoulos | French Energy Policy: A Gradual Transition[END_REF] for more on this point. 2. The same remark applies to other renewable energies such as wind power or micro hydroelectric plants. 3. The recent Ecological Transition for Green Growth Law (2015) initiated momentum towards loosening the conditions for participative funding (by citizens and local communities) of renewable energy production projects. However, this law did not lead to a significant change in renewable energy policies with regard to the community-based dimension of the projects. 4. According to the Institut National de la Statistique et des Etudes Economiques (INSEE) in 2013. 5. As a result, our description of the local political context is very limited; instead, we focus on the tools and methodologies used by the developers. 6. According to the Institut National de la Statistique et des Etudes Economiques (INSEE) in 2013. 7. As a result, our description of the local political context is very limited; instead, we focus on the tools and methodologies used by the developers as in the previous case study.

Table 2 -

 2 Summary of case study no 1.

Table 3 -

 3 Summary of case study no 2.

Acknowledgements

Thanks to assistance from the PACTE Laboratory, the paper also benefitted from English proofreading services.

Disclosure statement

No potential conflict of interest was reported by the authors. Funding This research was carried out with financial support from the French Research Agency -Agence Nationale de la Recherche (grant number ANR, programme sociétés innovantes, convention 2011-SOIN-003-01, project COLLENER) and the French Environment and Energy Efficiency Agency (grant number ADEME, 1110C0079, project CLIMENCORED).

Authors' copy (2018) -Antoine Fontaine and Olivier Labussière Figure 3 -Scenarios of integration of the solar panels. Source: Pilat Regional Natural Park. by using this table, there was an assumption that a community solar project could be built by adding individual solar units. The lack of attention paid to the roofs' materiality and spatial relations tended to "granulate" the solar potential, that is, to standardise its appraisal and eventually hamper the emergence of its collective existence.

At this point, the project managersa mix of engineers, young entrepreneurs and retired inhabitants with experience in the development of energy-related projects but not with activist actionsused the table to agree on the first package of roofs and to ask for a quotation to evaluate the cost of the grid connection (#2). As in the previous case study, the grid expertise provided the local leaders with a hierarchy of the roofs according to their grid connection costs and zoning by substation. Two of the three areas required reinforcement operations. The group of inhabitants could not cover the costs for these areas. In other words, the photovoltaic project was only achievable if there was an electric substation with enough capacity nearby. Because no siting effort had previously been undertaken, the zoning that the grid manager proposed became the only reason for adding the roof. Thus, the process consisted in subtracting roofs from the initial inventory. The solar and architectural qualities that had barely been identified no longer existed amid this new roofs' surfaces selection process. This reduced the operation of finding the right number of roofs for the electrical grid's capacity. In the light of homogeneous economic and electric qualities, the package of roofs no longer included heterogeneous qualities and did not appear to reflect the programme's initial ambitions.

In order to finalise the roof choice, project managers created a new table to rank every roof according to its individual profitability (euros invested/euros earned). The final roof package was put together based on the overall profitability, calculated as the sum of every roof's individual profit-ability. Through this table, profitability bypassed all other qualities (architecture, landscape, spatial coherence). However, this single economic dimension did not fully ensure the success of the collective operation. At the time, the French government introduced a new category in the feed-in-tariff scheme. Private residential roofs had a greater tariff than public roofs. The reason behind this differentiation was that it seemed easier to obtain roof owners' consent for public roofs because they did not have as many attachments (ownership, property value, familial values, inheritance value) as private residential roofs do. However, the extra profitability that feed-in tariffs provided to private roof reinforced their importance in the project at the expense of public roofs. Along the way, a few private owners discovering how profitable their roof was became reluctant to commit any further to a collective project that was less profitable. At this point, the project managers' calculation tools worked against the construction of the collective. These roof owners eventually refused to include their roofs in the collective project because they felt that they were individually paying for the overall collective costs. As a result, the group split up without any possibility of returning to the previous stage of collective organisation. The collective solar potential was reduced to individual units and private gains.

In the final step of the development process, regional project managers tried to revive the operation (#3). They wanted the operation to be led no longer by local elected officials but only by roof owners and local activists in the field of environment protection and renewable energy. Regional project managers decided to look for these motivations in a larger area by getting rid of the perimeter's previous restrictions (six municipalities). In addition, the French government removed the feed-in-tariff distinction between public and private roofs. Hence, the roof survey was re-oriented. The importance of private residential roofs in the first part of the project prompted the new local project managers to look mainly for public roofs in order to simplify the development. However, the instruments that had previously been used and failed to give


Nicolas Chauvin

Amaury Mavel

Gilles Patriarche

Bruno Masenelli

Michel Gendry

Denis Machon

Pressure dependent photoluminescence study of wurtzite InP nanowires

Keywords: InP nanowires, wurtzite material, high-pressure, optical properties, deformation potentials

The elastic properties of InP nanowires are investigated by photoluminescence measurements under hydrostatic pressure at room temperature and experimentally deduced values of the linear pressure coefficients are obtained. The pressure-induced energy shift of the A and B transitions yields a linear pressure coefficient of α = 88.2 ± 0.5 meV/GPa and α = 89.3 ± 0.5 meV/GPa with a small sublinear term of β = β = -2.7 ± 0.2 meV/GPa . Effective hydrostatic deformation potentials of -6.12±0.04 eV and -6.2±0.04 eV are derived from the results for the A and B transitions, respectively. A decrease of the integrated intensity is observed above 0.5 GPa and is interpreted as a carrier transfer from the first to the second conduction band of the wurtzite InP.

INTRODUCTION

The integration of InP based nanowires (NWs) on silicon has attracted an intense interest to merge efficient optoelectronic devices with silicon (Si) based electronics. The monolithic growth of InP NWs on Si or InP substrates has already been investigated to design highly efficient solar cells, 1 lasers 2 or light emitted diodes. 3 InP NWs grown on Si substrates present usually a wurtzite (Wz) crystallographic phase. Contrary to III-Nitrides semiconductors, there is no Wz substrate for III-V semiconductors such as InP, InAs or GaAs. As a consequence, the investigation of the optical, structural, mechanical or electronic properties of these Wz materials requires working directly on the NW geometry. This situation has a direct implication on the knowledge of these Wz semiconductor band parameters. There is a lack of experimental values for parameters such as the elastic coefficients, deformation potentials, piezoelectric coefficients or effective masses and it is necessary to rely on theoretical values. 4,5 As far as the deformation potentials of Wz InP are concerned, only one theoretical paper has been published on this issue. 6 Three different sets of parameters have been proposed based on three different ab initio approaches. High-pressure studies of semiconductor materials can give access to the hydrostatic deformation potentials and to the linear pressure coefficients. 7 The interest for investigating III-V materials with a Wz crystallographic phase is reinforced by a specificity of the wurtzite band structure. Since the Wz structure has four atoms per cell while the zinc-blende (ZB) structure has only two atoms, there are twice more as many bands per k points in the Wz one. As a consequence, the Wz band structure contains two conduction bands: one associated with a direct emission and a second one with a pseudo-direct one. 8,9 In the case of GaAs and InP Wz materials, the energy spacing between these two bands is expected to be relatively small: in the order of 30 meV for GaAs 9 and between 0.2 to 0.4 eV for InP. 10,4 As shown by Signorello et al, 9 the small energy spacing in Wz GaAs NWs can be tuned using an uniaxial stress to control the optical and/or electrical properties of the material.

In this paper, the optical properties of Wz InP NWs have been investigated by high pressure photoluminescence at room temperature. These measurements allow us to extract the linear and quadratic pressure coefficients as well as the effective hydrostatic deformation potentials.

EXPERIMENTAL DETAILS

The Wz InP NW sample was grown on a Si(111) substrate by VLS-ssMBE using Au-In droplets as catalyst in-situ deposited at 500°C. Two growth steps were performed at different substrate temperatures to obtain the NWs. First, the NWs were grown during 10 minutes at 380°C with a indium beam equivalent pressure (BEP) corresponding to an InP 2D layer equivalent growth rate of 1 ML/s and with a PV/PIII BEP ratio equal to 20 in order to produce pure Wz InP NWs. 11,12 To increase the NW diameter, a second growth step of 20 minutes was performed at a lower temperature (340°C) to favor the NW radial growth. Scanning electron microscopy (SEM) studies revealed an averaged 1.7 µm length for these NWs (Figure 1). As far as the diameter is concerned a variation is observed as a function of the distance from the surface leading first to an inverse tapered geometry. An average diameter of 120 nm is observed at the NW foot while an average diameter of 190 nm is measured at 1.1-1.3µm from the surface. Then the NWs present a tapering for the last 400-600 nm. TEM studies have been performed on the NWs (see supplementary material). The NWs haves a perfect Wz crystallographic phase during the first 0.9-1 µm length. This length corresponds to the typical size of the InP NWs after the initial 10 min axial growth at 380°C. Then, some ZB insertions are observed in the upper part of the NWs. This part is related to the axial growth of the NWs during the 20 min growth at 340°C. 12 This second step is required to favor radial growth to increase the NW diameter: the NWs have usually a diameter in the 50-60 nm range after the first growth step.

After the second step, the NW diameter is at least 10 times bigger than the exciton Bohr radius of Wz InP which means that no quantum confinement is expected. 13 As far as the elastic coefficients are concerned, the Young modulus of these InP NWs should be similar to the bulk value. 14 From these theoretical and experimental results we assume that our InP NWs can be considered as bulk material.

The high pressure photoluminescence measurements were carried out using a diamond anvil cell with low-fluorescence diamonds having a culet size of 350 µm. The NWs were mechanically removed from the growth substrate and loaded into a hole drilled in a stainless steel gasket. To obtain a hydrostatic pressure, a standard 4:1 methanol-ethanol mixture was used as the pressure transmitting medium. The optical properties of the Wz InP NWs were investigated by photoluminescence (PL) measurements performed using a 50 mW 532 nm continuous wave (cw) diode-pumped solid-state laser as the excitation source and a nitrogen cooled silicon CCD detector coupled to a monochromator for the detection.

RESULTS AND DISCUSSIONS

b). At 13K, one peak related to the recombination of free excitons known as A-excitons in Wz

InP is observed at 1.491 eV. 15 At room temperature, the photoluminescence of InP NWs reveals a peak located at 1.423 eV (the A transition) and a shoulder around 1.458 eV (the B transition). The B transition is observed due to the thermal activation of the holes from the A to the B bands. 15 The

VB Г 9V Г 7V Г 7V Г 7C Г 8C Peak A Peak B (b)
energy splitting between these two bands has been theoretically and experimentally investigated by several groups and values in the 30-50 meV range have been reported. 15,16,17 The pressure dependence of the Wz transitions is investigated in the 0-3 GPa range (Figure 3). The position of the A transition could not be determined for pressure higher than 3 GPa because of a weak signal to noise ratio (SNR), due to a decrease of the A peak intensity with pressure.

Position of B peak is obtained by the analysis of the 2 nd derivative of the spectra. The following quadratic equation is used to fit the experimental data:

= E + αP + βP (1)
which gives linear pressure coefficients of α = 88.2 ± 0.5 meV/GPa and α = 89.3 ± 0.5 meV/GPa , for A and B transitions, respectively. The value of the quadratic pressure coefficient is the same for both bands: β = -2.7 ± 0.2 meV/GPa . The existence of a quadratic pressure coefficient can be explained by nonlinearities in the elastic bulk modulus. In the literature, experimental values in the order of 75 to 84 meV/GPa and in the -1.2 to -1.8 meV/GPa² range have been published for the InP band gap in the ZB crystallographic phase. 18,19 This means that the linear pressure coefficient of the Wz InP band gap (α ) is roughly 10% bigger than its value for ZB InP. This observation seems in agreement with theoretical studies on III-Nitride materials. Comparison of LDA-calculated band-gap pressure coefficients for nitrides in Wz and ZB phases have predicted larger values for the Wz phase. 20 The difference between the two crystal phases was in the order of few meV/GPa. This difference could be explained by the extra structural degrees of freedom available in the Wz structure: the variation of the band-gap due to the change in the c/a ratio (where c and a are the hexagonal lattice constants parallel and perpendicular to the [0001] axis), and the internal structural parameter u which represents the relative position of two hexagonal close-packed sublattices. 21 Theoretical values of α and α can be calculated from the knowledge of the elastic and potential deformation coefficients. As far as the elastic coefficients are concerned, we use the set calculated using the local density approximation (LDA) by C. Hajlaoui et al. 22 These coefficients can also be estimated from the ZB ones using a model based on a rotation of the crystal structure and a correction due to the internal strain state (see Table S1 of the supplementary information). 23,24 For a hydrostatic pressure P, the strain coefficients of a Wz material are: 25

= - + -2 ! !! " + # -2 ! $ %% = && = ' 2 = - !! -! !! " + # -2 ! $ "2#
Under the assumption of a strain-independent and isotropic spin-orbit interaction, the energies of the A, B and C transitions can be described as: 26,27 ( = ( + ") * -+ -+ ! # + ") *, -+ -+ -# '

. = . + ") * -+ -∆ 0 + ! # + ") *, -+ -∆ 0 + -# '

1 = 1 + ") * -+ -∆ 2 + ! # + ") *, -+ -∆ 2 + -# '
The coefficients ∆ ± are given by:

∆ ± = ± 31 + 8 5 ∆ 6 ∆ 7 2∆ 8 9 : 2 / ( 4
)
where ∆ is the crystal-field splitting and ∆ = ∆ ! = ∆ ;< 3 ⁄ with ∆ ;< the spin orbit coupling. Here, the experimental values reported in Ref 28, ∆ = 0.145 ?@ and ∆ = 0.025 ?@, are used to obtain the value ∆ 0 = 0.931. As far as the deformation potentials of Wz InP material are concerned, sets of parameters have been published in Ref 6 using three different ab initio calculation methods:

Heyd-Scuseria-Ernzerhof (HSE) density functional theory, generalized-gradient approximation in the Perdew-Burke-Ernzerhof (PBE) parametrization and single shot GW calculations (Table S2 of the supporting information). Another approach is to estimate the deformation potentials in Wz phase from the ZB ones using the quasi-cubic approximation. 29,30 The extracted theoretical values of the linear pressure coefficients can be found in table I A second analysis procedure can be used to extract the effective hydrostatic deformation potentials. The variation of the band gap can be related to the volume change using the relation: 7

= + B 51 - C D C 9 ( 5
)
where B is the effective hydrostatic deformation potential. The term effective is used to highlight the fact that the strain in a Wz structure is not perfectly isotropic under a hydrostatic pressure. The relative volume change caused by the applied pressure can be related to pressure by the Murnaghan equation of state:

$ = E 35 C D C 9 .E -1: (6)
with B the bulk modulus of Wz InP and B' its pressure derivative. The bulk modulus can be calculated using the relation

F = GC !! IC + C J -2C ! K "C + C + 2C !! -4C ! # ⁄
and a value of to 69 GPa is calculated. Effective hydrostatic deformation potentials of B L = -6.12 ± 0.04 eV and B N = -6.2 ± 0.04 eV are obtained for the A and B transitions, respectively.

Moreover the pressure derivatives of the bulk modulus can be deduced from the fit and values of F′ ( = 6.0 ± 0.4 and F′ . = 6.1 ± 0.4 are obtained. These values can be compared with the hydrostatic deformation potential of -6.6 eV 31 and the bulk modulus pressure derivative in the 4-4.6 range for bulk ZB InP. 32,33 Here again, the Wz phase behavior is quite different from the ZB one, forbidding any approximation of the Wz phase from the ZB one. Contrary to the linear pressure coefficient, the deformation potential is smaller for the Wz phase as compared to the ZB one. This can be explained by the fact that the bulk modulus and its derivative do not have the same values in the Wz and ZB phases.

Pressure (GPa)

Figure 4 shows the pressure dependence of the integrated intensity. The PL intensity decreased when the pressure was increased above 0.5 GPa. Such a decrease has already been reported for bulk ZB InP 19 and ZB GaAs 34 but for higher pressure (above 6 GPa for InP and 3

GPa for GaAs). In ZB material, this phenomenon is usually explained by the crossing of the Γ and X conduction band minima with increasing pressure and by the transfer of electrons from the Γ to the X valley. The carrier population in the Γ band decreases as ? 2∆P"Q# RS ⁄ where ∆ "$# is the energy spacing between the Γ and X minima. The electron transfer from a direct and radiative transition towards in indirect transition induces a strong reduction of the photoluminescence.

The situation is different for the band structure of a wurtzite material. Since the Wz structure has four atoms/cell while the ZB structure has only two atoms/cell, there are twice as many bands per k point in the Wz one. As a consequence the Wz band structure contains two conduction bands:

one band having a Γ7 symmetry and a second band with a Γ8 symmetry. The second band is related to the states found at the L-point in the ZB phase. 8,9,4 Electrons with the Γ7 symmetry can recombine with holes in the A or B bands which induces a strong PL emission due to a direct band gap. On the other hand, for electrons with the Γ8 symmetry the recombination with holes in the B band is forbidden and the recombination with holes in the A band is called a pseudo-direct transition.

The energy splitting between these two conduction bands is not well known for Wz InP material.

Theoretical values of 0.24 eV and 0.4 eV have been reported by Ref 10 and Ref 4 , respectively.

The experimental probing of the conduction band using highly n-doped Wz InP NWs revealed a value of 0.21 eV, 35 while a value of 0.23 eV was reported from photoluminescence excitation (PLE) measurements on undoped NWs. 36 We make the assumption that the decrease of the PL emission is related to the transfer of electrons from the Γ7 to the Γ8 band. The pressure dependence of the integrated intensity can be described by the equation:

T"$# = U D 0VW X∆Y"Z# [\ ⁄ (7)
where ∆ "$# is the energy spacing between the two conduction bands. A linear equation is used to describe this evolution:

∆ "$# = ∆ + ]$ (8)
To fit the experimental results, equation 7 is rewritten as T"$# = T G1 + ^?2_Q RS ⁄ K ⁄ where T , ^ and ] are the fitting parameters. The fitting of the experimental results gives a value ] ≈ -0.03 ?@/a$). As the second conduction band in Wz is related to the states found at the L-point in the ZB phase, a rough value of ] can be estimated from the pressure dependence of the Γ and L bands in ZB InP material. In the case of a hydrostatic deformation, the energy spacing between the Γ and L conduction bands is equal to:

b * -c * = ∆ * + 3") b * -) c * # b * -c * = ∆ * -3 ) b * -) c * + 2 $
with ∆ * the energy spacing without strain, ) b * and ) c * the hydrostatic pressure coefficients for the L and Γ valley and , elastic coefficients of the ZB InP. 31,20 As a consequence, ] should be in the order of:

] ≈ -3 ) b * -) c * + 2 ≈ -0.04 ?@/a$)

This slope is in the order of magnitude of the experimental value which confirms the hypothesis of an electron transfer from the first to second conduction band. We could also have imagined a redistribution of the holes between the A, B and C valence bands with pressure to explain the decrease of intensity. However, the variation of the energy spacing between the valence bands is in the order of few meV/GPa (Table I) that is one order of magnitude smaller than the experimental value of -30meV/GPa. Thus, hypothesis involving different valence bands can be discarded.

In conclusion, the impact of the pressure has been investigated on Wz InP NWs. The linear and

Figure 1 :

 1 Figure 1: SEM picture of the InP NWs on Si substrate.

Figure 2 :

 2 Figure 2: (a) PL emission from the InP NWs measured at 13K and 295K. (b) Schematic of the

Figure 2 .

 2 Figure 2.a shows the PL emission from the InP NWs recorded at 13K and at room

Figure 3 :

 3 Figure 3: (a) Pressure dependence of PL spectra of InP NWs. (b) Pressure dependence of the A

Figure 3 .

 3 Figure 3.b shows the shift of both A and B transitions as a function of the hydrostatic pressure.

Figure 4 :

 4 Figure 4: Pressure dependence of the PL integrated intensity.

  quadratic pressure coefficients have been measured for the A and B transitions. Values equal to α = 88.2 ± 0.5 meV/GPa, α = 89.3 ± 0.5 meV/GPa and β = β = -2.7 ± 0.2 meV/ GPa have been obtained. The linear coefficients are in agreement with ab initio calculations performed in Ref 6 in the HSE DFT framework. The effective hydrostatic deformation potentialshave also been extracted for the A and B transitions with values of -6.1 eV and -6.2 eV, respectively. Our results further confirm that approximating the Wz phase behavior from the ZB one is inappropriate. The reduction of the PL intensity upon pressure increase also reveals a reduction of the energy difference between the two conduction band minima at Γ point, leading to a pseudo-direct transition.ASSOCIATED CONTENTSupporting Information

Table I :

 I Experimental results of the present work compared to theoretical calculations of the linear pressure coefficients for the A , B and C bands.Our experimental results show that the set of parameters obtained by LDA and HSE methods provide a good approximation of the linear coefficients (cf. tableI). This study also shows the limits of the quasi cubic approximation for Wz InP. The linear pressure slope calculated from the elastic and deformation potential coefficients of the InP in the ZB phase give values roughly 14% smaller than the measured ones. Moreover A and B bands are assumed to have the same dependence with pressure. This is a consequence of the quasi cubic approximation which implies%% = && =and + ! = -2+ -which induces a α = α relation. This experimental studyshows that the quasi-cubic approximation, as described in Ref 29, does not provide accurate deformation potentials for the Wz phase and confirms that experimental or theoretical investigations are to be undertaken to have a clear picture of the situation.

		exp results	PBE	GW	HSE	From ZB InP
	α (meV/GPa) α (meV/GPa) α A (meV/GPa)	88.2 ± 0.5 89.3 ± 0.5	80.3 80.6 84.9	86.4 86.8 91	88.7 89.0 93.4	76 76 76

. The elastic coefficients calculated by LDA are used in the PBE, GW and HSE cases. A calculation is also performed using the elastic and deformation potential coefficients obtained from the ZB InP ones using

Ref 23 and Ref 29.

TEM investigations of InP NWs, experimental setup and the material parameters used in the analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

Funding Sources

This work has been supported by LABEX iMUST (ANR-10-LABX-0064) of Université de Lyon, within the program "Future Investments" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR) and under the ANR project TEMPOS (reference ANR-10-EQPX-50) obtained in the framework of the "Future Investments" program.

Notes

The authors declare no competing financial interest ACKNOWLEDGMENT This work has been supported by LABEX iMUST (ANR-10-LABX-0064) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR) and by the ANR project TEMPOS (reference ANR-10-EQPX-50) obtained in the framework of the " Future Investments " program. Authors thank P. Regreny, C. Botella, J.B. Goure for technical assistance on the Nanolyon technological platform.

AUTHOR INFORMATION

Corresponding Author

*E-mail: nicolas.chauvin@insa-lyon.fr.