Isaac Fatokun

Arun Raveendran Nair

Thamer Mecharnia

Maxime Lefrançois

Victor Charpenay

Fabien Badeig

Antoine Zimmermann

Modular Knowledge integration for Smart Building Digital Twins

Keywords: BIM, IFC, Digital Twin, Linked Data, Knowledge Graphs, Modular Design, KNX

It is accepted in the Linked Data for Architecture and Construction (LDAC) community that generating knowledge graphs (KGs) from the BIM model of a building enables higher level use cases such as integration with geographic information systems, operational system integration, semantic digital twins (DTs), or automatic compliance checking. However, existing approaches generate a large, monolithic knowledge graph that is difficult to integrate with other knowledge such as Thing Descriptions (TDs) of Internet of Things (IoT) devices, or information about office occupants and room occupancy schedules. In this work, we describe a set of three modular knowledge graphs that enable knowledge integration for the semantic DT of our building at Mines Saint-Étienne, leveraging the principles of Linked Building Data: (1) KG LBD is automatically generated from the Revit model of our building, (2) KG FOAF is semi-automatically generated from the employee directory of Mines Saint-Étienne, and (3) KG TD is automatically generated from the ETS5 project file describing the KNX network in our building using the W3C TD ontology, and points to real-time and historical data. Our approach offers an alternative with respect to the state of the art such that: (1) relevant bits of the building's KG can be accessed using a simple REST-like interface, where each small KG contains links to other entities that themselves are identified by an IRI and have a small KG accessible; (2) Knowledge potentially served by different servers can be integrated in the same solution;

(3) simple access control can be implemented for some parts of the global KG.

Introduction

The digitization in the AECOO (Architecture, Engineering, Construction, Owner, and Operation) industry grounds on the development of Building Information Modeling (BIM) and the Internet of Things (IoT). Linking the building's digital model with data about smart devices and intelligent applications is fast becoming indispensable [START_REF] Siountri | Developing smart buildings using blockchain, internet of things, and building information modeling[END_REF]. As a result, BIM professionals have had to embrace various methods, one of which is the use of Digital Twins (DTs) [START_REF] Batty | Digital twins[END_REF]. Although there is a misconception that digitized 3D models are DTs, the concept of a DT transcends the basic idea of a computer-aided 3D model [START_REF] Fuller | Digital twin: Enabling technologies, challenges and open research[END_REF]. For a model to be considered a DT, there must be full integration of data between the physical object and the virtual model in both directions [START_REF] Fuller | Digital twin: Enabling technologies, challenges and open research[END_REF]. Thus, in the case of Building DTs, a change in the building could reflect in its DT and vice versa, all in real-time.

In practice, however, modeling changes that occur over time in building design is complex as one must define what elements are the same (with some changes) or completely new [START_REF] Rasmussen | Managing interrelated project information in AEC knowledge graphs[END_REF]. In addition, with DTs, one must be able to inject data specific to a device (such as a heater) or property (such as a room temperature) from IoT devices and other sources into the BIM model. The problem with this is that although BIM models are very useful, they were originally designed to provide data only about the building in the design and construction phase, not necessarily in the operation phase [START_REF] Wills | Integration of Real-Time data in BIM enables FM processes[END_REF]. As such, there is no standard approach to use them in dynamic situations as needed in a DT. Moreover, BIM data is largely fragmented depending on the source of the data [START_REF] Bakar | A Proposal to Harmonize BIM and IoT Data Silos using Blockchain Application[END_REF], thus to add data, it must be in a manner that allows this data to be associated with the right domain and to be managed independently of the overall system if needed. As a result, the use of Semantic Web technologies to aid this integration is becoming popular. With the use of Knowledge Graphs (KGs), BIM models can become more useful by integrating BIM data in KGs, or linking BIM data to KGs thus providing better contextual information [START_REF] Liu | Ontology-based semantic approach for construction-oriented quantity take-off from bim models in the light-frame building industry[END_REF].

Even so, integrating BIM data and IoT data poses a new set of challenges due to the monolithic nature of most KGs. For one, the existing reasoning engines are unable to effectively process large-scale KGs because they load and compute them as a whole, as demonstrated by the authors of [START_REF] Wang | A modular reasoning approach to knowledge graph[END_REF]. Modular design, or modularity in design, refers to a design paradigm where components work through a combination of distinct building blocks or modules to achieve an overall objective or function [START_REF] Stone | Towards a theory of modular design[END_REF]. For the knowledge engineering domain, d'Aquin [START_REF] D'aquin | Ontology modularization for knowledge selection: Experiments and evaluations[END_REF] describes modularity as a way of designing graphs to support maintenance and re-usability by the combination of self-contained, independent, and reusable knowledge components.

This necessitates the need for ways to use subsets of KGs or more simply the use of modular design in knowledge engineering [START_REF] Terkaj | A method to generate a modular ifcOWL ontology[END_REF]. To this end, this work presents a framework to integrate BIM with data from external sources such as IoT devices, and manually curated knowledge in a modular manner. Backed by Linked Data (LD) principles, this work is motivated by a vision of a building of the future where all information is encoded such that information can be gotten from the IFC model of the building, sensors, and actuators stationed at various parts of the building, and other sources, such that every single element in the building is interconnected to enable faster data exchange and visual monitoring of user comfort parameters as well as room occupancy in real-time.

In this paper we propose and discuss an approach that is based on a large set of small, linked KGs. Our primary research problem centers on how to integrate BIM models in the IFC format with data from external sources such as IoT device configurations and live IoT data, and manually curated KGs, in a modular manner, improving overall system performance in DTs. We focus on the following research question:

Could modular graphs facilitate knowledge integration in the semantic DT of a Smart Building?

We demonstrate the benefits of our approach on the semantic DT of our smart building at Mines Saint-Étienne. The rest of this work is structured as follows. Section 2 recalls some background on the linked data principles, modular design, the Building Topology Ontology (BOT), and the WoT Thing Descriptions (TDs). Section 3 presents some related work, then Section 4 describes the Espace Fauriel building of Mines Saint-Étienne. Section 5 presents our proposed approach, preliminary results, and a demonstration use case. Section 6 discusses the benefits of our approach, and Section 7 concludes the paper.

Background

The modern idea of linked data is based on the linked data principles presented by Tim Berners-Lee in a design issue note: 11. Use URIs as names for things, 2. use HTTP URIs so that people can look up those names, 3. When someone looks up a URI, provide useful information, using the standards (RDF, SPARQL), 4. Include links to other URIs, so that they can discover more things. The W3C Linked Building Data community group (LBC-CG) brings together experts in the area of BIM and Web of Data technologies, who are working to address the challenge of managing the huge amount of data that is generated across the building life cycle. They propose to adapt the linked data principles for building-related data as follows:

1. Using URIs as names for building-related things such as: rooms, walls, products, elements, enable different parties to provide complementary descriptions of the same uniquely identified entities in different knowledge graphs. 2. Using HTTP URIs for these things enables the authority responsible for these URIs to provide reference information about this entity when one looks it up on the Web. For example, products in a catalogue, building appliances, or even the building itself. 3. Providing information using common standards (RDF, SPARQL) and common KG models enable semantic interoperability between data sources. 4. Include links to other URIs can help to discover more things, such as a link to the catalogue an appliance has been chosen from, or a link to the Web of Things Servient that enables it to interact with this appliance. This group's flagship result is the Building Topology Ontology (BOT) [START_REF] Rasmussen | BOT: the Building Topology Ontology of the W3C Linked Building Data Group[END_REF], an ontology that provides a high-level semantic description of the topology of buildings including storeys, spaces, and the building elements they contain.

The W3C Web of Things (WoT) Working Group seeks to counter the fragmentation of the IoT through standard complementing building blocks (e.g., metadata and APIs) that enable easy integration across IoT platforms and application domains. 2 TDs [START_REF] Käbisch | Web of Things (WoT) Thing Description, W3C Recommendation 9[END_REF] is the main building block of the W3C's WoT architecture introduced to solve the interoperability problem in different IoT devices. The TD of an IoT device contains four main components: 1. some metadata about the device itself, 2. descriptions of interaction capabilities for the device including Properties, Actions, and Events, 3. web forms to enact these interaction capabilities, and 4. relationships to other devices.

Related Work

In this section, we present a brief review of works related to the conversion of IFC models to KGs and integration with IoT data.

IFC to KGs

Although there aren't many ontologies that adequately cover the scope of IFC, ifcOWL [START_REF] Beetz | Ifcowl: A case of transforming express schemas into ontologies[END_REF][START_REF] Pauwels | EXPRESS to OWL for construction industry: Towards a recommendable and usable ifcOWL ontology[END_REF] is a game changer. Introduced in 2009 by Beetz et. al., ifcOWL is a direct mapping of IFC express schema into OWL thus, it has the same status as IFC's EXPRESS and XSD schemas. A downside however is that the graphs produced by the ifcOWL mapping are complex in terms of structure and size [START_REF] Pauwels | EXPRESS to OWL for construction industry: Towards a recommendable and usable ifcOWL ontology[END_REF]. [START_REF] Terkaj | A method to generate a modular ifcOWL ontology[END_REF] provided a first attempt to modularize an ifcOWL KG. Alternative approaches such as SimpleBIM lighten ifcOWL graphs by pruning everything related to the geometry [START_REF] Pauwels | Simplebim: From full ifcowl graphs to simplified building graphs[END_REF].

The IFC-to-LBD converter [START_REF] Bonduel | The ifc to linked building data converter-current status[END_REF][START_REF] Oraskari | Ifctolbd[END_REF] generates a lighter KG from an IFC file using the ontologies from the LBD-CG group. After conversion, important information about the building such as topology, elements classification e.g Wall, Space, etc, and their properties are saved in one to three large graphs. When compared to the output of the ifcOWL-based IFC-to-RDF converter [START_REF] Pauwels | [END_REF], the graph structure becomes more concise (minimum 83% fewer triples) and substantially simpler to query.

IoT + BIM

Since IoT devices are fundamental in the Operation phase of a Smart Building lifecycle, there have been a number of studies centered around the integration of IoT data with BIM information. Tang et. al. [START_REF] Tang | A review of Building Information Modeling and the Internet of Things devices integration: Present Status and Future Trends[END_REF] reviewed several methods of integrating building contextual data and time-series data generated in the IoT layer. Their work showed that an efficient approach would be to represent the building contextual data and sensor information as an RDF graph and also serialize timeseries data from IoT devices into another RDF graph. The final step of this approach is to then link both graphs using unique identifications. The architecture of this method is shown in Figure 1. Based on the knowledge from [START_REF] Tang | A review of Building Information Modeling and the Internet of Things devices integration: Present Status and Future Trends[END_REF], the same researchers went on to develop a hybrid approach to facilitate information exchange between BIM-based building data, timeseries data generated from the IoT devices (in a relational database), and Building Automation System (BAS) metadata using Semantic Web Technology [START_REF] Tang | A Framework for BIM, BAS, and IoT Data Exchange Using Semantic Web Technologies[END_REF]. As mentioned earlier, this work made use of the conversion mechanism identified in [START_REF] Tang | A review of Building Information Modeling and the Internet of Things devices integration: Present Status and Future Trends[END_REF]. How-ever, to avoid the massive data and high computational power required to convert IoT time series data to RDF representation, the researchers used online URLs to access IoT data directly from the relational database (thus the hybrid approach). In 2020, Markus et. al. [START_REF] Kuller | Conceptual design of a Digital Twin based on Semantic Web Technologies in the Smart Home context[END_REF] proposed another framework to implement a novel DT for smart homes and buildings based on WoT TDs. This framework contains three components: 1. a converter (which converted device data to WoT format), 2. a triple-store to store the generated knowledge graphs, 3. and a web service to publish the data via REST API for the DT. The Architecture of the proposed framework is shown in Figure 2. Donkers et. al. [START_REF] Donkers | Creating occupant-centered digital twins using the Occupant Feedback Ontology implemented in a smartwatch app[END_REF] presented a method for occupant-based feedback gathering and integration with building information. Their DT integrates BIM data, sensor data, and occupant feedback using the Occupant Feedback Ontology implemented in a smartwatch app. The system was evaluated and validated using the case study of an apartment building. Although their approach proved effective in collecting occupant feedback as intended, it made use of a monolithic KG.

Similarly, to improve indoor condition monitoring, Desogus et. al. [START_REF] Desogus | BIM and IoT sensors integration: A framework for consumption and indoor conditions data monitoring of existing buildings[END_REF] presented a data platform for the visualization of building indoor conditions (e.g., temperature, luminance, etc.) and energy consumption parameters. It was tested using a case study in Italy. Their approach integrate the Revit software with the Dynamo visual programming platform and a specific API.

Cimmino et. al. [START_REF] Cimmino | eWoT: A semantic interoperability approach for heterogeneous IoT ecosystems based on the Web of Things[END_REF] introduced eWoT, an approach that enables transparent interaction with an IoT ecosystem made up of Web-accessible heterogeneous IoT devices through SPARQL queries. To profile the various IoT devices, the technique uses TDs. However, TDs could not handle the expressivity necessary to handle the variety of IoT devices. Thus, they also presented an extension of TDs called WoT-Mappings. The TDs and WoT-Mappings were then stored in a single store to be used by the eWoT system to perform both context-based and content-based device discovery every time a SPARQL query is sent. Again, it is clear that every time data was needed for a particular device, the system had to query the entire triple store.

In order to support real-time data integration and dynamic decision-making in Asset Management (AM) applications, Moretti et. al. [START_REF] Moretti | An openBIM Approach to IoT Integration with Incomplete As-Built Data[END_REF] presented an openBIM methodology that makes use of the IfcSharedFacilitiesElements schema to process and integrate geometric and semantic information of existing and newly created IFC objects. The approach incorporates data from the BIM environment, IoT platform, and Building Management Systems to support the asset management team's workflows and operations during the asset's use phase. For improved interoperability and cross-platform use, the technique was built utilizing open-source software and IFC. The case study showed how the suggested strategy could support an asset anomaly detection application and boost digital AM automation. The Espace Fauriel (EF) building of Mines Saint-Étienne, built around 1920 by mail-order selling company Manufrance and re-empowered in 1994 for the Mines Saint-Étienne higher education institute, is an eight storeys building of 6720 m2 used for research and teaching. It includes lecture halls, classrooms, offices, meeting rooms, and a space filled with industrial robots and workshops called the IT'M Factory. 3The 3D model of the EF building is made available under the CC-by 4.0 license as Revit (137 MB), IFCv4 (186 MB), and Xeokit (12 MB). 4The Building Management System consists of an historical EIB bus (European Installation Bus, which became KNX ISO-IEC 14543-3) installation for controlling HVAC and alarm systems, and several IoT devices deployed to monitor comfort parameters such as humidity, temperature, luminosity, CO2, windows opening status. In addition, smart meters are deployed to measure the electric consumption at the level of storeys, and at the level of a few individual equipments. Sensor data is published in real time to an MQTT broker, and a subset of the historical data is made publicly available under the CC-by 4.0 license. 5

The Espace Fauriel Building of Mines Saint-Étienne

Interlinked Modular KGs for a Building's DT

Our approach aims to interlink three different KGs: (1) KG LBD is automatically generated from the Revit model of the building, and describes its topology and static properties using the BOT ontology; (2) KG FOAF is semi-automatically generated from Mines Saint-Étienne's employee directory, and uses identifiers from KG LBD to link employees to their office and the desk they work on; (3) KG TD is automatically generated from the ETS5 project file, and describes the configuration of KNX sensors and actuators using the TD ontology. KG FOAF uses identifiers from KG LBD , KG LBD uses identifiers from KG TD , and KG TD describes means to access the real-time and historical IoT data. Figure 4 illustrates the general methodology of our approach, which we detail in the rest of this section. The knowldege graphs are served as static files by an Apache 2 server, and have the following entrypoints: https://ci.mines-stetienne.fr/emse/ for the LBD graph, https://ci.mines-stetienne.fr/knx/ for the KNX configuration graph, https: //ci.mines-stetienne.fr/mqtt/ for the historical IoT data as CSV files.

KG LBD -A Modular LBD KG

To prepare the linking of KG LBD to KG TD , a 'KNX Device' family is created in Revit, and elements are positioned in different spaces and are given a KNX address parameter as shown on Figure 5. The Revit model is first exported to IFC, then converted to RDF using the IFC-to-LBD tool. 6This results in a large 256k triples graph that is unsatisfactory for our use cases, which justifies the following sequence of post-processing steps, implemented as python scripts. The sources of our post-processing scripts and instructions to re-generate KG LBD are openly available.7 1_repareCharacters.py. Wrongly encoded Unicode characters are restored. For example: "\n" was encoded as "\\X\\0D\\X\\0A", "é" was encoded as "\\X\\00E9\\X\\0A". 2_pruneObjects.py. We only need a few type of elements for our use case. This step keeps triples with RDF terms whose IRI contain one of: "site", "building", "storey", "space", "wall", "window", "ifcowl_ifcfurniture", "electricappliance". It prunes triples with RDF terms whose IRI contain one of "airterminal", "beam", "cablecarrierfitting", "cablecarriersegment", "column", "covering", "curtainwall", "ductfitting", "ductsegment", "flowterminal", "ifcowl_ifcopeningelement", "lightfixture", "member", "plate", "railing", "ramp", "roof", "slab", "stair", "stairflight". The total number of triples after this step is 129 k. 3_transformObjects.py. This step re-generates a KG by executing a set of SPARQL construct queries that select a subset of the triples and replace properties. For example the following properties had the same literal objects: props:familyAndType_simple, props:family_simple, props:objectTypeIfcObject_attribute_simple, props:typeId_simple, props:type_simple.

Only one is kept and we use property rdfs:label instead. Output contains 28,5 k triples. 4_renameObjects.py. IRIs were all under the same inst: namespace, their local name is made of a type name and a UUID. This step establishes a more natural IRI structure that reflects the organisation of the building. For example <{building}>, <{building}/{storey}>, <{building}/{storey}/{space}>, <{building}/{storey}/{space}/{knx_device_in_space}>. 5_readSchedules.py. This step generates triples from the Revit schedules and the output of Dynamo scripts, which are exported as CSV files. Its goal is to recover important knowledge that was lost somewhere in the Revit-to-IFC-to-LBD pipeline: (i) in which space furnitures and devices are located, (ii) which spaces windows and doors are adjacent to, (iii) adjacency between spaces, (iv) quantity values for properties were floored to the nearest integer, with no unit. The total number of triples after this step is 50 k. extracts a small number of triples that describe each resource, and serializes these small RDF graphs in Turtle files named after the resources' IRIs. KG LBD contains a total of 4.414 RDF graphs, with 19,64 triples per graph on average. The total number of triples contained in those graphs is 86.686 while the number of triples in the non-modularized graph is 52.979. Two triples per graph are just metadata, this means that 24.879 triples are duplicates and are useful to help clients navigate in the knowledge graph. The set of static RDF documents are served by an Apache 2 server with the URL of the bot:Site as an entrypoint: https://ci.mines-stetienne.fr/emse#. Listing 1 shows an excerpt of the graph that describes Office 416. Table 1 lists the number of instance (and graphs) for each main class, and gives an example one can access. @base <https://ci.mines-stetienne.fr/> . @prefix bot: <https://w3id.org/bot#> . @prefix cdt: <https://w3id.org/cdt/> . @prefix coswot: <https://w3id.org/coswot/> . @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> . @prefix skos: <http://www.w3.org/2004/02/skos/core#> .

KG FOAF -Employees and their offices

Knowledge graph KG FOAF is the result of crawling the Mines Saint-Étienne employee directory, generate a small RDF graph for each employee that works in the EF Building, and identify them with obfuscated IRIs for privacy reasons. As an additional manual step, each employee is linked to the desk it works at, using IRIs from KG LBD . At the exception of a few, access to all RDF graphs in KG LBD requires authentication. Listing 2: KG FOAF sample: RDF document available at https://ci.mines-stetienne.fr/foaf/ b54952c3-e4a6-423d-b724-ed9392f6f2a1. Note 1: the coswot vocabulary is under development. Note 2: base and namespace declarations are shared by listings.

KG TD -KNX Configuration Linked to the BIM Model

Devices in a KNX network are identified with a two bytes address, which defines some topology for the network. The first four bits is the Area, the next four bits is the Line, and the remaining eight bits is the Bus Device. For example the selected KNX Device on Figure 5 in Office 416 has address 1/2/184. Devices have some configurable properties and communication objects that may be readable and/or writable. Communication objects of devices are linked by socalled group addresses, which are also encoded on two bytes, and are used in read/write KNX messages. Group addresses may be displayed with a 3-level structure 5 bits/3 bits/8 bits, and are how messages are passed from communication objects of sensors to communication objects of actuators. For example group address 2/0/117 links Object O-12 of Device 1/2/185: the output command of a Hager TX320 room thermostat deployed in Office 423, with Object O-140 of Device 1/2/171: one the controllable relays of a Hager TYA608C 8x16A Output module (which controls the heater in Office 423). The first step to generate KG TD is to export the ETS5 configuration project to a 1 MB .knxproj file, which is an archive that contains multiple XML files, including a 7 K lines XML project file, a 450 lines XML hardware description file, and 42 hardware XML definition files. We then automatically extract from these files relevant bits of information about the KNX network: the KNX topology, devices properties and communication objects, and the list of group addresses.

Devices are modeled as instances of td:Thing, and each property and communication object is modeled as a td:PropertyAffordance. Each property affordance is further described as a js:DataSchema using the JSON Schema in RDF vocabulary. 8 Group addresses are also modeled as td:PropertyAffordance and are where td:Forms are defined: Each form describes how a certain operation can be made to interact with the property. These forms are shared by different property affordances using a property coswot:sharesFormsWith we introduced.

coswot:sharesFormsWith a owl:SymmetricProperty, owl:TransitiveProperty . td:hasForm owl:propertyChainAxiom ( coswot:sharesFormsWith td:hasForm ) .

Listing 3: Axioms on coswot:sharesFormsWith.

There are three kinds of forms currently defined in KG TD : 1. KNX forms use a proposed knxip:// URL scheme for KNX/IP addresses, where the host and port are those of the KNX/IP gateway service, and the path defines the group address to read or write. They also use a proposed coswot:KNXMethodName property we introduced to define if the address needs to be read or written to. 2. MQTT forms use the MQTT vocabulary for RDF (mqv), which is under development. 9 3. HTTP forms to access the historical data as CSV files. As these files have a different schema (an array of objects with value and timestamp properties), we choose to define separate property affordances for them. The sources of our post-processing scripts and instructions to re-generate KG LBD are openly available. 10 Listing 4 shows how the current and historical temperature values of Office 416 are described. @base <https://ci.mines-stetienne.fr/knx/emse/fayol/> . @prefix schema: <https://schema.org/> . @prefix td: <https://www.w3.org/2019/wot/td#> . @prefix hctl: <https://www.w3.org/2019/wot/hypermedia#> . @prefix mqv: <https://www.w3.org/2019/wot/mqtt#> . @prefix htv: <http://www.w3.org/2011/http#> . @prefix js: <https://www.w3.org/2019/wot/json-schema#> . <1/2/184> a coswot:Device, td:Thing ; rdfs:label "Sonde Reg. 4ET/416 salle" ; skos:hiddenLabel "1/2/184" ; schema:description "TX320 Thermostat" ; schema:model "TL320B V1. 1 lists the number of instance (and graphs) for each main class, and gives an example one can access. The MQTT broker (Mosquitto) and the KNX/IP gateway are only available when connected to the building's network. The CSV logs are openly available under the CC-by 4.0 license. 11 These logs include the history of the outside temperature, offices temperatures, room thermostat setpoint commands, and room thermostat acknowledgement messages. Note that there exists a proposal for a KNX ontology http://schema.knx.org/2020/ontology/, however in this work we wanted to abstract from KNX and therefore rather used the W3C TD ontology.

Demonstration Use Case: Comfort parameter monitoring

To illustrate the combined use of the three KGs, this section describe a scenario comfort parameter monitoring. Preliminary demonstrations of the Territoire Databat scenario are available online 12 .

An employee of Mines Saint-Étienne, Marie-Line, works in room 416 of the EF building. She logs in the Territoire Databat platform, and the camera point of view directly jumps to the center of her desk. She can then navigate in the 3D model using the arrow keys, step in front of the box that represents the KNX Device next to her office door, click on it, and visualize the current and historical state of the room thermostat. As she is registered as the user of this office, she can select a different setpoint, or request a change in the temperature setpoint.

In practice, this scenario only requires the Territoire Databat server to enable authentication, and after a successful login send to Marie-Line's browser the URL of the graph G FOAF1 that describes her in KG FOAF . The client may then download and parse G FOAF1 . It can then dereference the object of the coswot:worksAtDesk property, and obtain graph G LBD1 with the IfcGUID of the furniture, and a link to the office it is an element of. The client can use the IfcGUID to determine the XYZ coordinates of the center of the desk. When Marie-Line clicks on the KNX Device on the wall, the client can dereference its URL, a) check it is located in Marie-Line's office, and b) fetch the graph G TD1 in KG TD that describes the device. From G TD1 , it can find more graphs and ultimately obtain the forms it can use to visualize the history of the temperature in the room and the thermostat setpoints.

Discussion

Although other studies had worked on BIM modeling using semantic web approaches, we propose to use modular knowledge graphs which we believe has several benefits compared to using monolithic graph architectures. Modular graphs allow merging independently developed KGs into a single one that is easier-to-understand, better to reason with, and also reusable as demonstrated in [START_REF] Grau | A Logical Framework for Modularity of Ontologies[END_REF]. In addition, when integrated with real-life systems, modular graphs improve performance by loading only the needed segments, eliminating problems with querying and reasoning in large stores.

Thus, in contrast to the other works that used monolithic [START_REF] Pauwels | EXPRESS to OWL for construction industry: Towards a recommendable and usable ifcOWL ontology[END_REF] or semi-modular [START_REF] Terkaj | A method to generate a modular ifcOWL ontology[END_REF] approaches, our work proposes a proactive approach to BIM and IoT integration by breaking down otherwise complex KGs into a set of small graphs. Instead of using complex queries, our approach allows users to interact with the system by browsing through the graphs via URLs as recommended by the Linked Data principles, making it more user-friendly. In the context of DTs, our approach allows us to distinctly select and update knowledge components without impacting the overall system. As such, problems related to querying and reasoning on the graphs as we would encounter with large stores are eliminated as we only work with subsets of the graph as needed.

Serving static documents with an Apache 2 server is more scalable than exposing SPARQL endpoints, and this is also better aligned with the vision of a hypermedia-driven Web and the Web of Linked Data. True, more processing is required on the client side to fetch and parse multiple smaller RDF documents, and query the subset of the graph that has been fetched at any given point in time. On the other hand, the application gains responsivity as little data is needed when the application starts.

Our motivation may be positioned with respect to the Linked Data Fragments spectrum [START_REF] Verborgh | Triple pattern fragments: a low-cost knowledge graph interface for the web[END_REF], where on one far end the server bares all the query processing work, and on the other far end the client downloads the whole graph as a dump and queries it. 13 Arguably, our approach applies to KGs what tilemaps apply to 2D or 3D game development: the global KG is made out of small, regular-shaped graphs that we could call LBD Knowledge Tiles, which results in performance and memory usage gains.

Conclusion and Future Work

We have presented a methodology to integrate different knowledge graphs so as to contribute to the building's semantic Digital Twin vision. Our approach has been implemented on the Espace Fauriel building of Mines Saint-Étienne, and results in the creation of a set of resources that may be useful for other researchers in the community. As for future work, we aim to improve the knowledge graphs with more knowledge useful for doing thermal simulations of rooms, serve live and historic IoT data as RDF using the SOSA/SSN ontology, serve live data with MQTT over websocket, further develop the 3D visualization platform shallowly demonstrated in Section 5.4, and experiment with autonomous agents in this virtual environment.

Figure 1 :

 1 Figure 1: Integration of time-series data and building contextual data (Source: [20])

Figure 2 :

 2 Figure 2: Workflow of DT using WoT TDs (Source: [22])

Figure 3 :

 3 Figure 3: Espace Fauriel Building of Mines Saint-Étienne

Figure 4 :

 4 Figure 4: Overview of the methodology to integrate modular knowledge graphs for the EF Building's Digital Twin. (Sources of the Knowledge Graph images: DALL•E 2)

Figure 5 :

 5 Figure 5: KNX Device objects prepare the linking from the KG LBD to the KG TD knowledge graphs.

Table 1

 1 Number of graphs in KG LBD and example individuals. This step explicits some SOSA/SSN Properties for spaces and elements, which are useful for some of our use cases. For example each space is associated a temperature, CO2, and humidity property. Each door and window is associated an open/close status. The total number of triples after this step is 53 k. 7_storeTurtleFiles.py. Finally, this step iterates over the resources in the KG, automatically

	Element	#	Example
	bot:Site	1	https://ci.mines-stetienne.fr/emse#
	bot:Building	1	https://ci.mines-stetienne.fr/emse/fayol#
	bot:Storey	9	https://ci.mines-stetienne.fr/emse/fayol/4ET#
	bot:Space	215	https://ci.mines-stetienne.fr/emse/fayol/4ET/416#
	bot:Door	323	emse/fayol/4ET/door/1VMOlJ3knDeODu7af36Nwh#
	:Device	137	emse/fayol/4ET/416/device/1bDMdL0k55X8oOMH5VKzRL#
	:Furniture	1386 emse/fayol/4ET/416/BureauD'Angle/1VMOlJ3knDeODu7af36LS_#
	:Wall	1729	emse/fayol/4ET/wall/1Qfe3f5n95yfrQ8nllTW3_#
	:Window	313	emse/fayol/4ET/window/1VMOlJ3knDeODu7af36GPu#
	6 _addProperties.py.

  Listing 1: KG LBD sample: excerpt of the RDF document available at https://ci.mines-stetienne.fr/emse/fayol/4ET/416. Note 1: the coswot vocabulary is under development. Note 2: base and namespace declarations are shared by listings.

	<emse/fayol/4ET/416/device/1bDMdL0k55X8oOMH5VKzRL#> a bot:Element, coswot:Device .
	...
	<emse/fayol/4ET#> a bot:Storey ; bot:hasSpace <emse/fayol/4ET/416#> .
	<emse/fayol/4ET/416#> a bot:Space ;
	rdfs:label "416" ;
	rdfs:comment "Office" ;
	skos:hiddenLabel "2IRRGeGVD4mwnjuD6Rcm6i" ;
	bot:adjacentElement <emse/fayol/4ET/door/1VMOlJ3knDeODu7af36Nwh#>, ... ;
	bot:adjacentZone <emse/fayol/4ET/418#>, <emse/fayol/4ET/waiting-area#>, ... ;
	bot:containsElement <emse/fayol/4ET/416/device/1bDMdL0k55X8oOMH5VKzRL#> , ... ;
	coswot:canWalkTo <emse/fayol/4ET/418#>, <emse/fayol/4ET/waiting-area#>, ... ;
	coswot:hasAreaStableValue "20 m2"^^cdt:ucum ;
	coswot:hasTemperatureProperty <emse/fayol/4ET/416#temperature> ;
	...

  Table 2 lists the number of instances in KG FOAF . Listing 2 is an example of an openly accessible RDF graph in KG FOAF .

Table 2

 2 Number of graphs in KG LBD and example individuals.

	Element	#	Example
	foaf:Person 80 personal data, requires authentication
	@base <https://ci.mines-stetienne.fr/> .
	@prefix foaf: <http://xmlns.com/foaf/0.1/>.
	@prefix org: <http://www.w3.org/ns/org#>.
	<foaf/b54952c3-e4a6-423d-b724-ed9392f6f2a1> a foaf:Document ;
	foaf:primaryTopic _:person .

_:person a foaf:Person ; foaf:name "Xxx Xxx" ; foaf:img <data:image/png;base64, /.....> ; foaf:phone <tel:+xxxxxxxxxxx> ; foaf:mbox <mailto:xxxxxxxxxxxxxxxx@emse.fr> ; org:memberOf <https://www.imt.fr/>, <https://mines-stetienne.fr/>, <foaf/fayol> ; coswot:worksAtDesk <emse/fayol/4ET/416/BureauD'Angle/1VMOlJ3knDeODu7af36LS_#> .

  The generated RDF graph contains a total of 40.721 triples, which are then distributed in 1.043 graphs with an average of 53,3 triples per graph, totalling 55.556 triples (36% redundancy). Static RDF documents in KG LBD are served by an Apache 2 server, with entrypoint https: //ci.mines-stetienne.fr/knx. Listings 5 shows an excerpt of how the KNX device 1/2/184 is linked to from KG LBD .Listing 5: Graph emse/fayol/4ET/416/device/1bDMdL0k55X8oOMH5VKzRL# links the KNX Device in Office 416 to TD Thing knx/emse/fayol/1/2/184.

	skos:hiddenLabel "1bDMdL0k55X8oOMH5VKzRL" ;
	coswot:KNXAddress "1/2/184" ;
	coswot:category "Communication Devices" .
	2" ;
	td:hasPropertyAffordance <1/2/184#O-10>, <1/2/184#O-10-history>, ...
	...
	<1/2/184#O-10> a js:NumberSchema, td:PropertyAffordance ; Table
	rdfs:label "Indication d'état" ;
	coswot:objectSize "2 Bytes" ;
	coswot:sharesFormsWith <ga/3/0/27> ;
	td:description "Température ambiante" ;
	td:title "O-10" .
	<ga/3/0/27> a coswot:KNXGroupAddress, td:PropertyAffordance ;
	rdfs:label "T°amb secrétariat N4" ;
	skos:hiddenLabel "3/0/27" ;
	coswot:sharesFormsWith <1/2/184#O-10> ;
	td:hasForm hctl:forContentType "text/plain" ;
	hctl:hasOperationType td:observeProperty ;
	hctl:hasTarget <mqtt://193.49.165.40:1883> ;
	mqv:controlPacket "subscribe" ;
	mqv:filter "emse/fayol/4ET/416/temperature/current" ],
	[ coswot:KNXMethodName "read" ;
	hctl:hasOperationType td:readProperty ;
	hctl:hasTarget <knxip://195.83.140.67:3761/1/8/27> ] .
	<ga/3/0/27#history> a js:ArraySchema, td:PropertyAffordance ;
	coswot:sharesFormsWith <1/2/184#O-10-history> ;
	js:items [ a js:ObjectSchema ;
	js:properties [ a js:NumberSchema ; js:propertyName "value" ],
	[ a js:StringSchema ; js:propertyName "timestamp" ] ] ;
	td:hasForm [ htv:methodName "GET" ;
	hctl:forContentType "text/csv" ;
	hctl:hasOperationType td:readProperty ;
	hctl:hasTarget <https://ci.mines-stetienne.fr/mqtt/emse/fayol/4ET/416/temperature/
	current/log.csv> ] .
	Listing 4: Current and historical temperature affordances for Office 416. Note 1: the coswot
	vocabulary is under development. Note 2: base and namespace declarations are shared
	by listings.
	<emse/fayol/4ET/416#> bot:containsElement <emse/fayol/4ET/416/device/1bDMdL0k55X8oOMH5VKzRL#> .
	<emse/fayol/4ET/416/device/1bDMdL0k55X8oOMH5VKzRL#> a bot:Element,
	coswot:Device ;
	rdfs:label "KNX Device:Thing" ;
	owl:sameAs <knx/emse/fayol/1/2/184> ;

Table 3

 3 Number of graphs in KG TD and example individuals.

	Element	#	Example
	td:Thing	4539	https://ci.mines-stetienne.fr/knx/emse/fayol/1/2/159
	td:PropertyAffordance 215 https://ci.mines-stetienne.fr/knx/emse/fayol/3/0/20#history

https://www.w3.org/DesignIssues/LinkedData.html

Source: https://www.w3.org/groups/wg/wot

IT'M Factory: Virtual visit https://itm-factory.fr/index.php/objectif_et_visite_360/

3D model of the EMSE EF building https://ci.mines-stetienne.fr/EMSE_EF/

Raw data for smart meters and heating devices https://ci.mines-stetienne.fr/mqtt/

Settings for the conversion are described in https://github.com/maximelefrancois86/databat-kgc-revit/tree/main/rvt

https://github.com/maximelefrancois86/databat-kgc-revit

JSON Schema in RDF vocabulary https://www.w3.org/2019/wot/json-schema

MQTT vocabulary for RDF -https://www.w3.org/TR/wot-binding-templates/

https://github.com/maximelefrancois86/databat-kgc-knxproj

Raw data for smart meters and heating devices https://ci.mines-stetienne.fr/mqtt/

Demo: https://ci.mines-stetienne.fr/ldac2023/demo/demo1.mp4 -https://ci.mines-stetienne.fr/ldac2023/demo/ demo2.mp4

Linked Data Fragments -https://linkeddatafragments.org/

Acknowledgments

This work was partially funded through the following projects: HyperAgents (grant ANR-19-CE23-0030-01), CoSWoT (grant ANR-19-CE23-0012-04), ACCORD (Horizon Europe R&I programme grant agreement no. 101056973).


Romain Vollondat
email: romain.vollondat@etu.unistra.fr

Daniel Stoeffler

Daniele Preziosi

Stéphane Roques

Abdelilah Slaoui

Thomas Fix

Tunability of silicon clathrate film properties by controlled guest-occupation of their cages

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. Introduction

Clathrates 1 are crystallographic guest-host structures in which the framework is made of a chemical species forming polyhedral cages that can enclose guest of other species. Silicon Clathrates are a subset of this family and as their name implies their framework is made of Silicon atoms which are covalently linked with each other by sp 3 bondings. The cavities formed by this framework are large enough to host alkali metals further stabilizing the structure. Silicon Clathrates are themselves divided from binary 2 to quaternary 3 structures as various species of guest atoms can occupy simultaneously the structure. Thus, Silicon Clathrates encompass a wide range of materials with properties varying with the nature of the guest species alluring in various field from thermoelectricity 4,5 , superconductivity 6 to photovoltaics 7 , batteries 8 and hydrogen storage 9 . Among all those materials, the first inorganic Clathrates synthesized were the binary silicon clathrates of Type I (SiCL-I) Na8Si46 and Type II (SiCL-II) 10 NaxSi136. Both crystal structures are depicted on Figure S1 of the Supplemental Material for easier visualization. The SiCL-I structure crystalizes in a simple cubic system of the 𝑃𝑚3 ̅ 𝑛 (#223) space group. One unit cell of this structure is made of 8 cages of two kinds: two are relatively small cages denoted Si20 exhibiting twelve pentagonal faces, while the remaining six are slightly larger Si24 cages made of twelve pentagonal and two hexagonal faces. Each of these cages are filled by exactly one Na atoms corresponding to the Na8Si46 formula. The Type II structure is crystalizing in a face centered cubic lattice of the 𝐹𝑑3 ̅ 𝑚 (#227) space group. This structure is made of twenty-four cages, of which sixteen are similar to type I, i.e. small Si20, while the remaining are "large" Si28 cages exhibiting twelve pentagonal faces and four hexagonal faces. In contrast to most type of Silicon Clathrates, the Type II structures is characterized by not only its unique ability to be partially filled with guest atoms but also to be able to let guest species in 11 and out 12,13 of structures under certain conditions. This flexibility allows wide range of structures, almost fully empty, as previously demonstrated for the type II germanium clathrates 14 , or fully filled, characterized by the usual formula Na0<x<24Si136. In the latter case, dimerization of Na in the large cages has been demonstrated under high-pressure high-temperature conditions leading at even higher occupation levels 15 .

The occupation of the cages of these structures is known to have striking impact on their structural and optoelectronic properties 16 . In particular, the SICL-II show different behaviors depending upon the cage occupation level. For guest-free or low occupation cases, this material is behaving like a semiconductor with a direct bandgap around 1.9 eV 17 that is beneficial when compared to the indirect 1.1 eV bandgap of "usual" diamond silicon and thus attractive for photovoltaic applications. On the other side, for occupations higher than x = 8, the material turns into a metal similar to its SiCL-I Na8Si46 counterpart. To obtain materials usable for optoelectronic applications, the thermal decomposition pathway 18 used previously for powder or monocrystalline samples has been derived to obtain films of Silicon Clathrates 19,20 . Although better control over the quality and thickness of Silicon Clathrates layer using various processes is still being largely investigated [21][22][23] , a pathway to obtain a control over the cages occupation, in order to grant a tunability of the films' properties is still of importance. Here, we report for the first time the impact of the thermal decomposition parameters on the occupation of the Si-CL films, and we will discuss how our approach to evacuate or intercalate Na atoms in the cages of the structures have a large impact on the properties of the Silicon Clathrates films.

II. Experimental section

The two step-process of thermal decomposition used for the synthesis of the Silicon Clathrates films is identical to the one reported in the previous study of the group and in the literature 19,24 . A Na slice is obtained from a Na ingot (99.8% purity, Alfa Aesar, CAS #7440-23-5) and immediately transferred in a hermetic cyclohexane (99+% purity, Alfa Aesar, CAS #110-82-7) filled container to limit the oxidation of the Na. The two chemicals are managed under safety precautions. A Silicon wafer (c-Si (001)) is sliced into rectangular shape of 54 x 37 mm with a thickness of 525 ± 25 µm and washed with a 10 % vol HF solution. The wafers are mainly p-type with resistivity of 1-5 Ω•cm but intrinsic wafers with resistivity over 10 kΩ•cm when electrical measurements of the films are required. Quickly after, the Na slice is placed into an Inconel boat (54 x 18 x 13.3 mm 3 , ANALAB, ref. AR9001) which is then promptly covered with the sliced silicon wafer. This system is then placed in a stainless-steel tube kept under a 1.5 bar flush of Argon along with a tantalum wire to absorb any trace of oxygen. The tube is placed in a tubular furnace and heated at temperature of either 630°C or 600°C, to obtain SiCL-I or SiCL-II respectively, using a ramp of 5°C/min and a dwell time between 13 h and 19 h. Once done, the tube is let to reach room temperature naturally and flushed with Argon anew. The Silicon wafer with the synthesized Na4Si4 zintl phase is exited out of the stainless-steel tube and quickly put in quartz tube to be heated in a dynamic vacuum of maximum 4.5x10 -5 Pa to prevent prolonged any exposure to ambient humidity with the Na4Si4. When the desired vacuum is reached, the quartz tube is enclosed in a furnace and heated at 400°C with a ramp of 10°C/min for a duration between 1 to 25 h and let to cool down naturally. The obtained sample is washed with ethanol then deionized water to remove any excess Na which is identifiable by the bubbling coming from the surface of the film. The film is then blow-dried and ready for further characterizations or post-treatments.

The process to reduce the amount of Na in the SiCL-II films has been inspired by the one reported by Ammar et al. 13 . Instead of using a sealed glass tube heated in an electrical furnace, we recycled the heating and pumping units of a BET instrument to reach a primary vacuum in a test tube previously filled with samples and iodine (99+%, AnalaR NORMAPUR, CAS #7553-56-2) in excess. Once the targeted vacuum is reached, the test tube is sealed, and the pumping system is turned off. Then the test tube is slowly heated to a temperature of 300°C for a 10 h duration and naturally let to cool down. Purple iodine vapor inside and crystallization of iodine on the inner wall of the test tube is witnessed. The experimental setup is shown in Figure S2. The sample is gathered and cleaned with acetonitrile then deionized water and blow-dried.

Samples submitted to this treatment show no detection of Iodine under EDS. X-ray diffraction (XRD) is performed with a Bruker D8 DISCOVER with a Cu Kα1 wavelength of 0.154059 nm. Lattice parameters, atomic positions and displacements along with the Na occupation of the synthesized materials were estimated using Jana2006 25 software by performing LeBail and Rietveld refinement on the XRD data taking as reference previously reported structures for SiCL-I 15 and SiCL-II 26 . Energy Dispersive X-ray Spectroscopy (EDS) measurement were performed on the samples using a JEOL JSM-IT200 scanning electron microscope equipped with a DrySD SSD detector with a resolution of 130 eV or less. The conductivity measurements were performed using Hall effect technique using a ECOPIA HMS-5000 system in the Van der Pauw configuration. Contact with the surface of the samples was performed directly on each corner using gold plated spring needles of a diameter of around 100 µm. Electric conductivity, in the planar orientation, as well as the nature, the mobility and the density of the carriers were determined. Raman spectroscopy and Photoluminescence (PL) are measured at 293 K using a JOBIN YVON LabRam Aramis apparatus with a 532 nm laser. For each sample, measurements were performed using a 532 nm laser at 1.1 mW using a 2400 g.mm -1 grating with a 50 µm slit on five different locations of the film with a total exposition time of 4.5 min per spot. The intensity of the laser is kept at 1.1 mW to prevent the degradation of the SiCL into Si at 11 mW 24 .

Transport measurements were performed by using a Physical Properties Measurement System DynaCool system of Quantum Desing in a four-point configuration with Ag-stripe electrodes.

III. Band structure calculations

Band structure calculations were performed using the Vienna Ab initio Simulation Package (VASP5.4) 27,28 allowing to determine accurately the electronic structure of the considered system. It uses so-called Augmented Plane Waves and is based on the Projector Augmented Wave (PAW) 29 method using pseudopotentials to determine the wave function outside the augmentation region. For such large cells, all calculations are performed with the GGA functional 30 , a cut-off energy of 600 eV and a k-points sampling of 8x8x8 or 6x6x6 depending on the symmetry of the Brillouin Zone. After full relaxation of the lattice parameters and the internal structural position for all atoms, the total density of states TDOS and the band structure E(k) were obtained. For a given NaxSi136 system, a symmetry analysis allowed to identify the equivalent cells and to investigate only one cell per group. For example, for x = 4 the 70 possible cells reduce to 4 groups having 2, 12, 24 and 32 equivalent elements. The TDOS is obtained by a weighted average over individual TDOS with a unique Fermi level set as the energy origin.

IV. Results and discussion

The attention of this study is put on the Na guest atoms enclosed in the synthesized Silicon Clathrates of SiCL-I and SiCL-II films. Let alone the precursor formation step which mainly impacts the type of Silicon Clathrates structures in presence 24 , the first experimental stage with a major impact of the occupation of Na in the structure is the annealing under vacuum step. While the rate of heating has been demonstrated to affect the quality of the film obtained, its duration is the main factor influencing the occupation of the cages. For SiCL-I films, even for extended annealing under vacuum, there are no variations of the X-ray diffractogram peaks profile, visible in Figure 1a, implying that there is no Na removal from the silicon cages of the structure. This inability for the Na8Si46 phase to exhibit cages without guest atoms sustaining them through the thermal decomposition process is an indicator of the low stability of the Si46 framework which has only been yet attained in small quantities using Hoffman redox reaction 31 . Considering SiCL-II Silicon Clathrate films this time, when comparing X-ray diffractogram of the samples obtained for various annealing under vacuum duration, large discrepancies are identifiable by the global profile of peaks intensities.

As the synthesized films are polycrystalline and that no epitaxial growth has been observed for Type-II SiCL c-Si (001) wafer, these variations of the relative intensities of the peaks are an indicator of the number of Na guest atoms occupying the cages of the structure. To give a better visualization of this assessment, calculated diffraction pattern using the software VESTA 32 at a wavelength of 1.54059 Å for the NaxSi136 structure where the guest occupation has been changed from guest-free (x = 0) to fully occupied (x = 24) by gradual steps are available in Figure S3. For these diffraction patterns, the preferential filling of the large Si28 cages over the smaller Si20 ones is In order to reach an effective filling of the sixteen small Si20 cages, we adapted a method used to intercalate Na atoms in SiCL-II powders 11 for the films studied here.

To do so, a similar process than the one performed for the first annealing of the thermal decomposition is used, with the difference that the silicon wafer is replaced by a sapphire wafer on which the SiCL-II films cut into square of around 1.5 x 1.5 cm² are stick using silver paste. Then the usual method is executed except that the temperature is lowered to temperature between 320 and 380°C to prevent the degradation of the Silicon clathrates, the mass of the Na slice is of 0.4 g and the reaction time is extended to 50 h. The reaction was performed at three different temperatures. The lowest is 320°C for which no Na addition is witness by XRD nor EDS even though bubbling was observed when washing the samples. The temperature was then boost up to 350°C which allow to rise the Na occupation from x = 4.3 to 6.8 indicating a filling of the remaining empty Si28 cages. In order to establish if this result is the real equilibrium of the reaction at 350°C or only due to its slow kinetic, the same sample was resubmitted to the same treatment. This repetition led to the successful filling of the large cages with also some Na atoms taking place in the small cages. A third cycle was performed in order to assess if the temperature was sufficient to fill the small cages but proved

inefficient. An annealing at 380°C was then performed and led this time to the filling of almost all the cages of the structure resulting in formula Na23.1Si136. All the refined parameters of these samples are available in Table SII. EDS analysis made on the two samples, reported in Figure S4, are in agreement with the refined values of occupation of the samples submitted to Na addition. The lattice parameters refined indicate this time a significant expansion of the structure, which remained almost the same for x between 2.3 to 10 at around 14.63 Å to reach 14.71 Å for x = 23.1. This is consistent with the evolution of the lattice parameter along with the occupation established by Beekman et al. 33 . The sudden increase of the Na content of the structure as the temperature is increased successively from 350°C to 380°C underlines that the energy barrier required in order to allow the cages filling seems lower for the Si28 polyhedron, which are filled at lower temperature, compared the Si20 ones. This is supposedly due to the increasing presence of point defect 12 with the temperature, facilitating the migration of the Na guest throughout the various faces of the cages.

As previously reported 13 , annealing under iodine vapour is a reaction which enables the evacuation of the Na atoms out of the SiCL-II cages by the favourable reaction of Iodine with Na to form sodium iodide (NaI). The operation method is adapted from the literature as described in the experimental section. Once washed, one sample was collected while another one was submitted to two more cycles. From a starting film with x = 4.2, the EDS analysis, available in Figure S5, indicates a drop to x = 1.1 and x = 0.1 respectively for one and three cycles of this iodine treatment. Compared to the minimal occupation reached by Kume et al 34 , the Na removal rate reported here seems less efficient which could be due to the lower temperature of annealing which is limited by the custom setup. Nonetheless, this process allows the obtention of Na occupation unattainable using only the annealing under vacuum method. For comparison purpose, Hall effect measurements were performed to determine the impact of the occupation on the electrical properties of our samples with thickness around 30 µm. The results

FIG. 3. Effect on the sodium occupation of the SiCL-II of the annealing under iodine atmosphere in red and of the sodium vapour annealing in green.

are listed in Table I for SiCL-I sample but also SiCL-II sample from almost guest free to x = 23. The SiCL-I film exhibits metallic behavior with 4.3 x 10 -2 Ω•cm and carrier mobility of 43 cm²/(V•s) as expected. For SiCL-II, there is a 4 order of magnitude variation of resistivity depending on the amount of Na located in the cages of the structure. The evolution of the electrical resistivity is rising as the Na atoms are evacuated from the Silicon Clathrates cages. This evolution seems to drastically quicken when coming close either to the guest free Si136 structure or to the completely filled Na24Si136. The SiCL-II films as-synthesized (x = 6 to 2) are direct band-gap n-type semiconductors as shown in our previous work 24 , which can be turned into the metallic phase Na24Si136 exhibiting a resistivity close to its SiCL-I counterpart or to the Si136, which would truthfully be an allotrope of Silicon. No major variation in terms of carrier mobility is observed as x is changing, there is a slight rise for samples with low occupation while it seems to be reduced when the small cages are starting to be filled and that the phase is becoming more and more metallic. The amplitude of the variation of the resistivity is similar to measurement single crystals 26 .

Na vapor 350°C for 50+50h

Na8Si136 -6.5 x 10 18 3.3 x 10 -1 6.1

Na vapor 380 for 50H

Na23Si136 -5.4 x 10 20 1.1 x 10 -2 4.1

However, their resistivities remain lower than the ones reported for powders samples hot-pressed into pellet 35 with close to two orders of magnitude factor and are higher than the value reported for single crystals by three orders of magnitude 26 . This difference is most likely due to the presence of numerous defaults and cracks in the Silicon Clathrates films 19,22,23 usually obtained by the thermal decomposition process which makes it even harder for charge carriers to move through the material. This gradual shift from a rather insulating phase to a metallic phase is due to the more and more intense hybridization between the Na atoms and the silicon framework conductivity as the Si20 cages are being filled.

Raman Spectroscopy is also used to inspect the above-mentioned samples and shown in Figure 4. Most of samples show good peak definition for all wavenumber investigated except for the SiCL-I sample and the SiCL-II for occupation above x = 8 as it can be seen from the lower signal to noise ratio compared to the other samples.

From the previous electrical measurements, it is obvious that this low signal harvesting for these samples is due to their metallic character lowering the effectiveness of the change in polarizability during molecular vibration on which rely Raman spectroscopy.

For all samples, no characteristic peaks of amorphous or crystalline silicon are observed. The SiCL-I exhibit predominantly a T2g vibration at 169 cm -1 with two other occupation values in Figure S6. For low occupation, the peaks are well defined and as

x is increased, all the peaks are subject to a low frequency shift. This shift is subtle and is observed for all the peaks. As x is superior to 8 and thus when the small cages are partially or almost completely filled, the Raman vibrations are of reduced intensities, and most of them are impossible to differentiate from each other's. Nonetheless, the peak energies are still subject to change. All identifiable peaks are keeping their movement toward lower frequencies this time, and as the small cages are being filled this shift is striking compared to lower occupation. The forementioned peaks and their corresponding wavenumber are listed in Table II. This red-shift phenomenon is often correlated with a crystallinity increase or when a material is subjected to tensile stress moving atoms away from each other. In our case, this shift is surely due to the expansion of the lattice parameters and thus of the chemical bonds' expansion, explaining the barely noticeable shift when the small cages are filled with lattice parameters revolving around 14.64 Å which become obvious when the structure is fully occupied and extend to 14.71 Å 33,38 . respectively with a possible contribution of less intense peak located at 1.8 eV originating from a surfacing disordered silicon materials as reported previously 22 . For Na23Si136, as the phase is metallic no peak is observed except the one related to surfacing impurities.

Transport measurements are performed on two different SiCL-II samples: highly occupied samples with x = 23 and the almost guest free Na0.1Si136. Figure 5 shows the temperature dependence of the measured sheet resistance which behavior is modulated from the metallic Na23Si136 to the semiconducting Na0.1Si136. This variation characterize also powder [START_REF] Cros | [END_REF] and single-crystal 12 samples. The increase of the resistivity with the decrease of the Na occupation originates from the more and more isolated state of the Na cluster further limiting the electron hoping at low temperature as revealed by Electron Spin Resonance measurements 42 .

DFT calculations of the densities of states for several SiCL-I and SiCL-II structures are reported in Figure 6. For the type I, both the experimentally obtained fully occupied structure and the guest-free Si46 densities of states were calculated. The guest-free SiCL-I exhibits a bandgap of 1.13 eV with a top-valence band originating from p states of the silicon while the bottom is due almost exclusively to the s states while the conduction band is originating both from p states and a non-negligible s states contribution. When the eight cages of the structure are filled with Na atoms, the valence band shows no significant change in its content while the conduction band is gathering both the previous Silicon contribution but also s states from the Na atoms. This Na contribution induces the extension of the conduction band by the hybridization between the silicon framework states and the states of the Na guests similarly observed in literature 43,44 . Thus, the Fermi level is now located in the conduction band, indicating a metallic behavior while the energy-gap between the two band is reduced to 0.53 eV.

The two Si136 and Si46 calculated structures exhibits quite similar density of states due

FIG. 1 .

 1 FIG. 1. XRD diffractogram fitted using Rietveld Refinement for a) SiCL-I and b) SiCL-IIwith various Na occupations.

FIG. 2 .

 2 FIG. 2. Sodium occupation of the SiCL-II structure depending on the duration of the duration of the thermal decomposition of the Zintl phase

Figure 1b exhibits diffractograms

  Figure 1b exhibits diffractograms of the almost guest-free, routinely synthesized and fully occupied structures next to each other while Figure 3 sums up the range of occupations accessible taking advantage of the various process. SiCL-I films were also submitted to these treatments without change in their composition without surprise.

  FIG. 4. Raman spectra for a) SiCL-I b) SiCL-II with low, classic and high sodium occupation.

FIG. 5 .

 5 FIG. 5. Sheet Resistance versus temperature measurements for the SiCL-II different cagesoccupations.

FIG. 6 .

 6 FIG. 6. Total Density of States calculated by DFT for a) Guest free and fully occupied SiCL-I b)Guest free and various occupation values of SiCL-II. The Fermi level corresponds to the vertical bar and is set to the energy origin for Na occupied SiCL.

TABLE I .

 I Electrical properties of the Silicon Clathrates as synthesized and submitted to various post-synthesis treatment.

	Type of SiCL	Treatment undergone	Formula	Carrier concentration (cm -3 )	Resistivity (Ω•cm)	Mobility (cm 2 /(V•s))
	SiCL-I	As-synthesized	Na8Si46	-1.5 x 10 19	4.3 x 10 -2	43
		3 Cycles of I2 annealing	Na~0.1Si136	-3.6 x 10 16	110	15
		1 Cycle of I2 annealing	Na1Si136	-9.2 x 10 16	40.7	21
		As-	Na4.2Si136	-2.1 x 10 17	4.2	7.1
	SiCL-II	synthesized	Na4.35Si136	-3.0 x 10 17	2.2	8.0
		Na vapor
		350°C for	Na6.9Si136	-9.2 x 10 17	6.3 x 10 -1	13.3
		50h

Table II :

 II Energies of the various Raman vibrations for the SiCL-II with low, classic, high sodium occupation compared to tabulated values.Figure S7 displays the photoluminescence spectra of various Silicon Clathrates filmsof various Na concentration. The broad peaks obtained are similar to previous results22,24,[START_REF] Krishna | Physics, Simulation, and Photonic Engineering of Photovoltaic Devices III[END_REF] , centered at 1.65 eV and 1.70 eV for Na0.1Si136 and Na4.35Si136

	Vibration	Si136 theory by Nolas et al.	Na0.1Si136	Na4.35Si136	Na23Si136
	mode	(cm -1 ) 39	(cm -1 )	(cm -1 )	(cm -1 )
	1T2g	121	122.7	121.6	-
	1Eg	130	135.9	134.9	131.6
	2T2g	176	184.3	183.5	-
	3T2g	267	276.7	275.7	257.0
	1A1g	316	323.9	323.8	314.5
	4T2g	325	330.7	330.2	-
	2Eg	360	365.8	365.4	367.2
	2A1g	397	398.2	398.4	-
	5T2g	406	408.4	407.8	406.7
	3A1g	458	461.1	460.6	442.5
	3Eg	463			456.0
			Not resolved from 3A1g
	6T2g	466			-
	7T2g	473	477.2	477.1	-
	8T2g	487	489.4	488.4	-

D. Xue and C. Myles, Materials, 2019, 12, 536.

Acknowledgments

We would like to thank Nicolas Zimmerman and Jeremy Bartringer for technical assistance, along with Marc Lenertz and the XRD platform of the IPCMS. This project has received financial support from the CNRS through the 80|Prime program. The authors would like to acknowledge the High Performance Computing Center of the University of Strasbourg for supporting this work by providing access to computing resources. Part of the computing resources were funded by the Equipex Equip@Meso project (Programme Investissements d'Avenir) and the CPER Alsacalcul/Big Data.

Data availability

The data that support the findings of this study are available within the article and its supplementary material and are available from the corresponding author upon reasonable request.

Supplementary Material

See the supplementary material for additional information about the setup used for the iodine cycling, the values of the parameters obtained by Rietveld refinement of the various film along with EDS measurements backing their refined Na concentration. Supplementary Raman spectra for more occupation's values are available along with PL measurements and the band structures obtained by DFT.

Conflict of Interest

The authors have no conflicts to disclose.


Observables and Excluded Instrument

Our IV strategy uses sources of variations in wages that should be uncorrelated to the firms and to workers' observables to allow for causal inference. Our excluded instrument should in particular be uncorrelated to firms' and workers' observables.

In Table B1 -Panel A, we show that, altogether, workers' observables cannot explain the excluded instrument. In these estimations, we regress the observed instrument on the full set of workers' observables, and we obtain low f-statistics on these regressions: all f-stats are under the standard confidence levels, in particular as we have many observations. Then, Table B2 shows that there is no strong correlation between our baseline instrument and the set of workers' observables. In particular, we hardly estimate a significant and robust correlation independently of the fixed effects we use.

These two results suggest that our instrument is plausibly exogenous to workers: the instrument is quasi-randomly distributed across workers in our sample.

Table B1 -Panel B and Table B3 show there is no strong correlation between the excluded instrument and the firm controls either. Indeed, regressions of firm observables on the world import demand provide hardly significant coefficients. As for workers, the instrument is quasi-randomly distributed across firms in our sample. If one worries one might worry about bias from unobserved firm a ributes, Table B4 hereafter precisely accounts for this potential bias. Maybe firms are not completely randomly facing random foreign shocks: there may be some unobserved firm a ributes that lead some firms to be more exposed to shocks than others. We follow Borusyak and Hull (2020) to exclude this bias. For details, please refer to the discussion hereafter. exposure to these shocks. Intuitively, foreign shocks can hardly be correlated to firm and workers'

Worker FE ✓ ✓ ✓ ✓ ✓ ✓ Year FE ✓ ✓ ✓ ✓ ✓ ✓ Firm-Year Controls ✓ ✓ ✓ ✓ ✓ ✓ Worker Controls ✓ ✓ ✓ ✓ ✓ ✓ Occupation FE ✓ ✓ ✓
observables. Yet, a remaining concern is that firms are non-randomly exposed to those random export shocks. For instance, we could imagine that some firms have an export structure which is oriented toward specific foreign markets which may be correlated to the employment of specific workers (for instance, younger and more prone to live further away from their firm). In other words, the non-random exposure to the random shock may lead to a bias in our estimations. Our results should thus be insulated from this non-random exposure of firms to foreign demand shocks.

Borusyak & Hull (2020) develop a general econometric framework for shift-share se ings that allow for the possibility that shock exposure is non-random. They also provide a set of guidelines to implement this strategy in empirical applications. We follow these guidelines and use a "re-centering" process, i.e. we control for the random average exposure of firms, based on unobservables.

In formal terms, we have computed a set of 100 random counterfactual country-product-year level shocks, replicating the average distribution of the observed shocks ( . Armed with these 100 𝑀 𝑗𝑠𝑡 ) random shifts, we combined them with the observed firm-level weights, creating a set of 100 counterfactual instruments (i.e. firm-level trade shifts), then averaged by firm-year. We thus computed an average exposure of a firm to foreign shocks, out of random shocks. Following the idea in Borusyak & Hull (2020), this average instrument should capture the differential (and potential non-random) exposure of the firm to random shocks. 1We include this average firm-year instrument in the second-stage estimation. Results are presented in Table B4 and Table B5. Overall, controlling for the average, random exposure of firms and workers to foreign shocks, we obtain close estimates to our baseline results. Then, we also do not estimate a significant impact of the correction we implement here. Our instrument thus does a good job at capturing the demand shifts abroad, without being contaminated by non-random exposure of firms.

Plausibly exogenous instrument and resulting bounds

Another way to see the identification issues is to consider that the exclusion restriction is likely to hold in our exercise, but that we cannot exclude some minor violations of this condition. We thus implement a methodology proposed by Conley et al. (2012) to take into account this potential violation of exclusion restrictions. Intuitively, it consists in assessing to which extent the parameter of interest is actually biased if the exclusion restriction is close but not exactly satisfied. We provide the graphical representation emphasized in Conley et al. (2012).

In the short-run, Figure B1 shows that the estimated lies between 0.05 and 0.2, slightly depending α 1 on the size of the direct effect of world import demand on commuting distance (which should be exactly 0 if exclusion restrictions were perfectly met). Therefore, the IV results appear stable, despite potential minor violations of the exclusion restriction. In the long run, Figure B2 suggests that the estimated elasticities range between 0.1 and 0.3, i.e. twice as large as in the short run. Tables B6 andB7 present the estimation results and statistics to check the validity of our instruments.

These replicate the structure of Table 2 in terms of dependent variable and specification, but now include two IVs. Including a second IV allows us to test for overidentifying restrictions. We check the validity of our instruments using two different tests. Robust to heteroskedasticity and clustering, Hansen J statistics for overidentifying restrictions are unable to reject our set of instruments. The F-stat form of the Kleibergen-Paap statistic as a test for weak instruments is also reported. All statistics are well above the critical values, confirming that our choice of instruments is statistically appropriate, on top of intuitive reasons explained above.

Second-stage results are close to our baseline estimates. We always find a positive and significant relationship between yearly wage and commuting distance, of the same magnitude (around 0.15 in the short run, and 0.3 in the long run) as in the baseline estimates. Note that the precision of these estimates is higher, mainly because we included a second IV in the first stage.

Figure B1 -

 B1 Figure B1 -Resulting bounds for -Conley et al. (2012) -Short-run estimates α 1

Table A2 -

 A2 Domestic Sales -Long-run

	Dependent Var.: Log Commuting Distance
		(1)	(2)	(3)	(4)	(5)
	Log Yearly Net Wage	0.218***	0.263***	0.242***	0.285***	0.304***
		(0.023)	(0.039)	(0.027)	(0.043)	(0.065)
	Log Domestic Sales	-0.010***	-0.013***	-0.011***	0.014***	-0.014***
		(0.001)	(0.002)	(0.001)	(0.002)	(0.001)
	Worker FE	✓	✓	✓	✓	✓
	Year FE	✓	✓	✓	✓	✓
	Firm-Year Controls		✓		✓	✓
	Worker Controls			✓	✓	✓
	Occupation FE					✓
	Observations	280822	280822	280822	280822	280822

Notes: Second-stage IV estimations, in which World Import Demand (see text) is used as excluded instrument for yearly net wages. Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level. Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker and gender. Domestic Sales from the balance-sheet data.

Table A3 -

 A3 Previous Export Sales -Short-run

	Dependent Var.: Log Commuting Distance
		(1)	(2)	(3)	(4)	(5)
	Log Yearly Net Wage	0.193***	0.214***	0.202***	0.224***	0.225***
		(0.022)	(0.025)	(0.023)	(0.027)	(0.023)
	Log Exports t-1	0.001	0.001	0.002**	0.002***	0.002***
		(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
	Log Nb HS6 products t-1	-0.014***	-0.012***	-0.013***	-0.011***	-0.011***
		(0.002)	(0.002)	(0.001)	(0.001)	(0.001)
	Worker FE	✓	✓	✓	✓	✓
	Year FE	✓	✓	✓	✓	✓
	Firm-Year Controls		✓		✓	✓
	Worker Controls			✓	✓	✓
	Occupation FE					✓
	Observations	1310012	1310012	1310012	1310012	1310012

Notes: Second-stage IV estimations, in which World Import Demand (see text) is used as excluded instrument for yearly net wages. Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level. Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker and gender. Exports-related variables from the customs data.

Table A4 -

 A4 Previous Export Sales -Long-run

	Dependent Var.: Log Commuting Distance
		(1)	(2)	(3)	(4)	(5)
	Log Yearly Net Wage	0.253***	0.305***	0.264***	0.322***	0.349***
		(0.022)	(0.043)	(0.038)	(0.048)	(0.069)
	Log Exports t-1	0.006	0.003	-0.002	0.001	0.003*
		(0.001)	(0.001)	(0.001)	(0.004)	(0.002)
	Log Nb HS6 products t-1	-0.007***	-0.012**	-0.013***	-0.017***	-0.019***
		(0.007)	(0.005)	(0.005)	(0.004)	(0.003)
	Worker FE	✓	✓	✓	✓	✓
	Year FE	✓	✓	✓	✓	✓
	Firm-Year Controls		✓		✓	✓
	Worker Controls			✓	✓	✓
	Occupation FE					✓
	Observations	280822	280822	280822	280822	280822
	Notes: Second-stage IV estimations, in which World Import Demand (see text) is used as excluded
	instrument for yearly net wages. Robust standard errors in parentheses with ***, **, and *respectively
	denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level.
	Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per
	worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker
	and gender. Exports-related variables from the customs data.

Table B1 -

 B1 Instrument and Workers and Firms Observables

	Panel A: Workers' Observables
	Dependent Var.: Log WID (Current Weights)
		(1)		(2)		(3)	(4)	(5)
	Age	0.150					0.078	-0.040
		(0.231)					(0.225)	(0.207)
	Gender			0.092		0.121	0.244***
				(0.067)		(0.069)	(0.066)
	Skilled Dummy					0.281***	0.286***
						(0.098)	(0.089)
	F-stat	0.422		1.891	8.177	3.989	10.702
	Year FE	✓		✓		✓	✓	✓
	Occupation FE							✓
	Observations	1597288	1597288	1597288	1597288	1597288
	Panel B: Firms' Observables
	Dependent Var.: Log WID (Current Weights)
		(1)	(2)		(3)	(4)	(5)	(6)
	Assets	0.120**					0.544***	0.220**
		(0.058)					(0.132)	(0.101)
	Labor Prod.		0.568***			0.250	0.164*
			(0.183)			(0.163)	(0.097)
	Employment				0.058		-0.344***	-0.069
					(0.052)		(0.097)	(0.090)
	Total Sales					0.040	-0.110*	-0.043
						(0.044)	(0.062)	(0.045)
	F-stat	4.31	9.61		1.21	0.84	7.64	6.94
	Worker FE							✓
	Year FE	✓	✓		✓	✓	✓	✓
	Occupation FE						✓	✓
	Observations	1597288	1597288	1597288 1597288 1597288	1597288

Notes: Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level.

Table B2 -

 B2 Workers' Observables and Excluded Instrument -Short-run

	Dependent Variable:	Log Age	Gender Dummy	Skilled Dummy
		(1)	(2)	(3)	(4)	(5)	(6)
	Log WID (Current Weights)	-0.002	0.000	0.002	0.001	0.003	0.002*
		(0.001)	(0.000)	(0.003)	(0.001)	(0.003)	(0.001)

Table B3 -

 B3 Firm-level Observables and Excluded Instrument -Short-run

	Dependent Variable:	Log Assets	Log Labor Prod.	Log Employment
		(1)	(2)	(3)	(4)	(5)	(6)
	Log WID (Current Weights)	-0.004***	0.006***	0.0065	0.005	0.007*	-0.003*
		(0.002)	(0.004)	(0.003)	(0.004)	(0.004)	(0.002)
	Worker FE		✓		✓		✓
	Year FE	✓	✓	✓	✓	✓	✓
	Firm-Year Controls	✓	✓	✓	✓	✓	✓
	Worker Controls	✓	✓	✓	✓	✓	✓
	Occupation FE		✓		✓		✓
	Observations Observations	1597288 1597288 1597288 1597288	1597288 1597288 1597288 1597288 1597288 1597288 1597288 1597288

Notes: Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level. Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker and gender. The variable that is considered as the dependent variable is excluded from the controls.

Notes: Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level. Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker and gender. The variable that is considered as the dependent variable is excluded from the controls.

Table B5 -

 B5 Accounting for the non-random exposure of firms to foreign shocks. -Long-run

	Dependent Var.: Log Commuting Distance Dependent Var.: Log Commuting Distance
		(1) (1)	(2) (2)	(3) (3)	(4)	(4)	(5)	(5)
	Log Yearly Net Wage	0.324***	0.471***	0.377***	0.507***	0.614***
	Log Yearly Net Wage	0.142*** (0.022)	0.192*** (0.047)	0.154*** (0.032)	0.212*** (0.058)	0.198*** (0.094)
		(0.015)	(0.016)	(0.017)	(0.021)	(0.023)
	Log Expected Instrument Log Expected Instrument	0.001 -0.006*** (0.001)	-0.002** -0.008*** (0.001)	0.001 -0.007*** (0.001)	-0.002** -0.007*** -0.002** -0.007*** (0.001) (0.001)
		(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
	Worker FE Worker FE Year FE Year FE Firm-Year Controls Firm-Year Controls Worker Controls Worker Controls Occupation FE Occupation FE	✓ ✓ ✓ ✓	✓ ✓ ✓ ✓ ✓ ✓	✓ ✓ ✓ ✓ ✓ ✓	✓ ✓ ✓ ✓	✓ ✓ ✓ ✓	✓ ✓ ✓ ✓ ✓	✓ ✓ ✓ ✓ ✓
	Observations Observations	1792162 276502	1792162 276502	1792162 276502	1792162 276502	1792162 276502

Notes: Second-stage IV estimations, in which World Import Demand (see text) is used as excluded instrument for yearly net wages. Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level. Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker and gender. The expected Instrument variable is randomly created to capture the differential exposure of firms and workers to foreign demand shocks (see main text for details).

Notes: Second-stage IV estimations, in which World Import Demand (see text) is used as excluded instrument for yearly net wages. Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level. Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker and gender.

Table B6 -

 B6 Overidentifying restrictions -Full Sample, Short-run estimates : Second-stage IV estimations, in which World Import Demand with both contemporaneous and 10-year change in demand measures (see text) are used as excluded instruments for yearly net wages. Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level. Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker and gender.

	Dependent Var.: Log Commuting Distance
		(1)	(2)	(3)	(4)	(5)
	Log Yearly Net Wage	0.142***	0.166***	0.153***	0.180***	0.146***
		(0.013)	(0.016)	(0.017)	(0.020)	(0.022)
	Worker FE	✓	✓	✓	✓	✓
	Year FE	✓	✓	✓	✓	✓
	Firm-Year Controls		✓		✓	✓
	Worker Controls			✓	✓	✓
	Occupation FE					✓
	Observations	1671808	1671808	1671808	1671808	1671808
	Kleibergen-Paap rk Wald F statistic	678.965	521.997	465.522	354.029	281.461
	Hansen J statistic	0.312	5.295	0.238	1.188	3.816
	Hansen J statistic p-value	0.576	0.021	0.626	0.276	0.051

Notes

Table B7 -

 B7 Overidentifying restrictions -Movers Sample, Long-run estimates : Second-stage IV estimations, in which World Import Demand with both contemporaneous and 10-year change in demand measures (see text) are used as excluded instruments for yearly net wages. Robust standard errors in parentheses with ***, **, and *respectively denoting significance at the 1%, 5% and 10% levels. Standard errors are clustered at the sector-year level. Firm-Year controls include log Assets, Log Apparent Labor Productivity, defined as total value added per worker, and log Employment. Worker controls include a skilled/unskilled dummy, the age of the worker and gender.

	Dependent Var.: Log Commuting Distance
		(1)	(2)	(3)	(4)	(5)
	Log Yearly Net Wage	0.192***	0.259***	0.232***	0.311***	0.286***
		(0.024)	(0.036)	(0.029)	(0.041)	(0.060)
	Worker FE	✓	✓	✓	✓	✓
	Year FE	✓	✓	✓	✓	✓
	Firm-Year Controls		✓		✓	✓
	Worker Controls			✓	✓	✓
	Occupation FE					✓
	Observations	251934	251934	251934	251934	251934
	Kleibergen-Paap rk Wald F statistic	533.395	253.765	319.210	174.680	127.925
	Hansen J statistic	0.113	2.914	0.310	0.713	0.598
	Hansen J statistic p-value	0.737	0.088	0.577	0.398	0.439

Notes

Intuitively, suppose for instance that firm A is more exposed to foreign shocks than firm B, both belonging to the same sector or industry, only because firm A is more centrally located. Then, the centrality of firm A is likely to be captured in the average instrument. Non-random centrality should thus contaminate each instrument and thus the average instrument. Controlling for this average instrument thus acts as controlling for non-random centrality in this example.

Appendix B: Plausibly exogenous IV

The validity of our IV results relies on the validity of the excluded instrument we used. We now check the validity of the world import demand as an instrument and assess the sensitivity of the second-stage results. We proceed in 4 steps. This section displays further results regarding (i) an augmented specification of the event study estimation including interactions between initial controls and year fixed effects and (ii) the other measures of import demand (i) We first allow the specification to include the interaction between lagged controls and year fixed effects (as suggested by Goldsmith-Pinkham et al. 2020, see their section 5.2), with the benchmark WID. Results are plo ed in Figure C1.

(ii) Second, Figure C2 plots results of the impact of various measures of WID on commuting distance, using the various weighting schemes (see the discussion about weights in paper, subsection 6.2).


Is

Keywords:

energy solidarity a remedy for energy access difficulties of French households or a symptom of a troubled management of these difficulties ?

The energy concerns of the last few months, marked by the concomitant rise in global energy demand (following the post-Covid economic recovery), a geopolitical crisis in Europe and a slowdown in electricity production in France following the shutdown for maintenance of some of the country's nuclear reactors, has put the energy access difficulties of French households back in the media and political spotlight. Furthermore, the environmental issues (commitments to reduce GHG emissions, availability of energy resources, energy dependence. . . ) question the capacity of the State to act in the field of energy policy and the relevance of this level of action.

Yet the feeling that the State is the most appropriate interlocutor to limit the effects of rising energy prices (electricity, gas, fuel) has been reinforced by recent measures ("bouclier tarifaire", "indemnité inflation"). The public and collective management of the energy access difficulties of households relies on a variety of actions in the fields of the energy supply and the public service, the fight against poverty, housing renovation. These actions are tied up with an abundant terminology to designate situations (fuel poverty, energy exclusion, energy over-consumption, submissive energy sobriety), public or private devices (French "chèque-énergie", accompanied auto-rehabilitation, participative renovation site) and actors to deploy them ("ensemblier solidaire", "conseiller précarité-solidarité").

New forms of monetary and energy transfers have recently developed : "dons d'énergie" or "dons de chaleur",

which have yet to be characterized, and to some extent energy saving certificates, which operate on the same principle as CO2 certificates. These transfers involve various public, para-public and private actors : they are based on energy saving obligations (on the side of energy sellers) and become financing tools for associations that take charge of energy access difficulties of low-income households or some local public action actors. These transfers add to the already existing policies and tools, some of which could also share the title of "energy solidarity".

To what extend can these forms pf energy solidarity be linked to the principles of energy justice [START_REF] Jenkins | Energy justice : a conceptual review[END_REF][START_REF] Benjamin | Energy justice : conceptual insights and practical applications[END_REF] ? Considering with Éloi Laurent (2012), that fuel poverty is the symptom of several inequalities, what social and environmental inequalities do this diversity of energy solidarity target ? What does it tells us of the dynamic between the State, market actors, social and solidarity economy actors and civil society actors ? Is it a question of creating a form of collective action in order to compensate for an energy policy for which market logic produces excluded households that the State does not (or does not manage or does not wish to) take charge of ? Or is it a way for private actors to compensate for activities that produce these same excluded households ? Does energy solidarity disrupt the division of responsibility for access to energy between the State and 1 Adèle Sébert market actors, or is it simply a confirmation of this division ? Is it a new way to promote a fair but individualized energy transition relying on bilateral and compensatory economic relations ?

We propose to question the economic meaning of the notion of solidarity, understood as a link of "social interdependence" based on a "contractual principle of action" [START_REF] Blais | Être solidaire. De qui, pour quoi ?[END_REF], which would be applied to energy access, in order to establish a typology of forms of energy solidarity. We will work on a material collected during a PhD research from 2017 to 2022 and based on 41 semi-structured interviews with actors from fields of the energy supply and the public service, the fight against poverty, housing renovation. This typology would be a first try to answer the questions previously asked.