Nicolas Castagné
email: nicolas.castagne@grenoble-inp.fr

Annie Luciani
email: annie.luciani@acroe-ica.org

THE PHYSICS NETWORKS SCRIPTING LANGUAGE TO DESIGN MASSES-INTERACTIONS PHYSICAL MODELS FOR ARTS

Masses-interactions modeling, also called physics Newtonian networks modeling, was pioneered in the late 70's with the CORDIS-ANIMA formalism. It is a modular physics-based approach, used in sound design, musical instruments design and musical composition, and also in computer graphics animation, virtual reality, gesture interaction, and more generally for digital creativity.

Within the research that progressively position physicsbased modeling as a core mean to improve creativity with the computer, the paper introduces the Physics Network Scripting Language. PNSL is aimed at accompanying the modeling processes of any user, including artists, with masses-interactions modeling. It serves in particular, but not only, sound and musical purposes.

The paper describes the PNSL language: context, goals and general choices; labeling system tailored to support modeling complexity by managing freely large module sets; main features and syntax choices; and implementation and exemplary usage contexts.

INTRODUCTION

Current research in the field of physics-based modeling for sound and music question various axes, including:

1. Research toward innovative modeling tools, able to serve the practice of physics-based modeling within creative processes -that is: enabling the user, e.g. a musician, to design his/her own physical models.

2. Research on core physics-based computational techniques and algorithms, such as works aimed at improving the precision of digital solving of partial differential equations, e.g. in non-linear problems such as [START_REF] Bilbao | A family of conservative numerical schemes for the dynamical von Karman plate equations[END_REF], or in collision such as [START_REF] Chatziioannou | An Energy Conserving Finite Difference Scheme for Simulation of Collisions[END_REF], etc.

3. Research toward new models. This includes high fidelity modeling of existing acoustical instruments and structures, but also adaptable generative models aimed at sound/musical quality, but without necessarily referring to a real instrument. Today's research focus in particular on non-linear phenomena, such as non-linear resonators, on multisensory models (sound + visuals + gesture), etc.

4. Research on musical use and musical relevance of physical modeling, especially regarding incorporation of modeling at the core of creative processes.

This paper is a contribution to the 1 st of the aboveproposed axis, hence may serve developments along the 3 rd and 4 th axis.

There is today an increasing use of predesigned physics-based algorithms within digital musical instruments, which probably relates to the sound quality enabled by simulation. Beyond, work along the 4 th research axis above progressively demonstrates that the design of physical models by musicians themselves has musical relevance -see for example [START_REF] Cadoz | The Physical Model as Metaphor for Musical Creation. pico..TERA, a Piece Entirely Generated by a Physical Model[END_REF] and [START_REF] Kojs | Cyberinstruments via Physical Modeling Synthesis: Compositional Applications[END_REF]. However, and though such promising research results, the practice of physical modeling itself is still rare among musicians. For example, it is still far less incorporated in daily creative practices than signal-based patching. As a hypothesis for this fact, one could remind that designing a physical model can be particularly difficult. We assume that another reason lies in limits of available modeling/creative tools, besides past successful achievements. For example, we assume that the physical modeling activity hardly well incorporates into today's usual signal-based musical tools. Given the hope to progressively turn physical modeling into a daily creative practice, there is still a need for innovative modeling and creative technologies: adequate modeling tools, modeling languages, modeling GUIs principles, etc. This is today a challenge for the research in software design in our fields.

As a contribution to this context, this article introduces the Physics Network Scripting Language, PNSL.

Regarding the core modeling/simulation approach, PNSL roots on the masses-interactions networks physicsbased approach, as defined in the CORDIS-ANIMA formalism. It was pioneered in the late 70's by Claude Cadoz during his PhD thesis, then first published in the 80's, e.g. in [START_REF] Cadoz | Responsive Input Devices and Sound Synthesis by Simulation of Instrumental Mechanisms: The Cordis System[END_REF]. Within this modular formalism, a model consists in a network of masses bilaterally interconnected with physical interactions. Similarly to Kirchhoff's networks developed in electrical engineering, the approach fits within lumped modeling systems. Similarly to [START_REF] Karjalainen | BlockCompiler: Efficient Simulation of Acoustic and Audio Systems[END_REF], it is a type of block-based representations connected by bilateral links. In this context, CORDIS-ANIMA networks are particularly adapted to target any dimensionality (scalar, 1D, 2D, 3D), for uses in Computer Music, Physics, Computer Animation and Haptics. Given these various properties and uses, CORDIS-ANIMA networks have been called in [START_REF] Luciani | Art kinesthésique et art plastique : contribution à l'émergence d'un art visuel dynamique[END_REF] "Physics Newtonian Networks", or shortly "Physics Networks". [START_REF] Castagné | 10 criteria for evaluating physical modelling schemes for music creation[END_REF] discusses the approach with others in the field.

The approach has so far supported the design of tens to hundreds of thousands physical models. It has been employed in about one hundred artworks -counting only those with contribution from ACROE. Regarding only models aimed at sound and music, examples include [START_REF] Tache | Organizing mass-interaction physical models: the CORDIS-ANIMA instrumentarium[END_REF]: linear and non-linear vibrating sound structures (strings, acoustic tubes, membranes, plates, bars, gongs, etc.), sound boards and resonators of many sorts, instantaneous and continuous excitation means (striking, plucking, bowing, blowing, scrubbing, etc.), modifications of the vibrating structure (damping, pinching, pulling, deforming, fracturing…), sound propagation models (room effects, models aimed at sound spatialization in multichannel audio, etc.), models of sound transformations and processing, etc. Beyond sound synthesis and instrumental models, works target also generation of musical events, and musical composition. As to them, the approach supported the invention of quite new compositional processes, centered on the physical modeling activity itself, such as Cadoz' "compose (with) physical modeling", first discussed in [START_REF] Cadoz | The Physical Model as Metaphor for Musical Creation. pico..TERA, a Piece Entirely Generated by a Physical Model[END_REF]. Finally, besides musical purposes, the approach developed also in Computer Animation and Virtual Reality [START_REF] Evrard | MIMESIS: Interactive Interface for Mass-Interaction Modeling[END_REF], gesture interaction including force-feedback [START_REF] Cadoz | Responsive Input Devices and Sound Synthesis by Simulation of Instrumental Mechanisms: The Cordis System[END_REF], and more generally as a mean to generate dynamic phenomena aimed at the human sensori-motor skills and at creativity with the computer.

On the side of creative tools that support CORDIS-ANIMA masses-interactions modeling, the GENESIS series [START_REF] Castagné | G3: GENESIS Software Environment Update[END_REF] is a series of modelling/simulation GUIs aimed at instrument and sound design, and at musical composition by means of physical modeling. Other related technologies include for example synth-a-modeler [START_REF] Berdahl | An introduction to the synth-a-modeler compiler: Modular and opensource sound synthesis using physical models[END_REF], Cymatic [START_REF] Howard | Cymatic: A Tactile Controlled Physical Modelling Instrument[END_REF], the PMPD extension for PureData [START_REF] Henry | pmpd : Physical modelling for Pure Data[END_REF]. Also, the masses-interactions approach progressively spreads within other audio/musical software, such as Max/SP, PureData, Processing and others. However, along with these existing technologies, there still is a need for a generic modelling language for creativity with the approach.

The paper presents a domain-specific language [START_REF] Van Deursen | Domainspecific languages: an annotated bibliography[END_REF], called the Physics Network Scripting Language (PNSL), that has been designed by considering the properties of masses-interactions modeling and tailored to support the modeling processes of the user, including artists, toward any model falling into the scope of masses-interactions models, especially in creative contexts.

Rather than a detailed description of the language, that could not take place in a paper, we first review our objectives with PNSL and then we introduce its main structure, characteristics and implementation. This includes a discussion of the labeling system, tailored to support managing each single module, as well as very large module sets, when building complex networks.

PNSL -GOALS AND SPECTRUM

We aimed at supporting with PNSL the design of any model falling into the spectrum of masses-interactions modeling, as formalized in CORDIS-ANIMA [START_REF] Cadoz | Responsive Input Devices and Sound Synthesis by Simulation of Instrumental Mechanisms: The Cordis System[END_REF].

PNSL, a language to practice CORDIS-ANIMA

A CORDIS-ANIMA model consists in a network composed of interconnected elementary physics-based modules taken from two categories: material points (called <MAT>), and interactions between two material points (called <LIA>, for the French LIAison). <MAT> modules support inertial behaviors, and <LIA> express physical influence between <MAT>. Connection between <MAT> and <LIA> is always bidirectional: they exchange with each other's a bidirectional data flow of dual variables, forces and positions. Hence, a <MAT> receives forces (intensive variables) from the connected <LIA>, and outputs to them its position (extensive variable), whereas a <LIA> outputs two opposite forces computed from the positions received from its two connected <MAT>.

The exchanged variables, forces and positions, may be 1D, 2D or 3D, depending on the dimensionality of the targeted phenomena.

The <MAT> and <LIA> categories further derive in a series of basic "module types". Each module type models an elementary physical behavioral law, through an optimized algorithm, with specific physical parameters. A <MAT> can be, for example, a simple mass, a fixed point, a viscous mass, etc. And a <LIA> can be many types of interactions, either linear or non-linear: potential such as attraction, elastic, cohesive, plastic with hysteresis, or dissipative such as viscosity or dry friction, etc. With such variety of <LIA>, it is possible to model percussions and collisions, including prolonged contacts, cohesions, repulsions, bowing or plucking interactions, irreversible breaking, etc. Non-linear capabilities, when needed, are included within the <LIA> modules themselves, under the form of non-linear profiles functions or finite state automata -see e.g. [START_REF] Cadoz | Responsive Input Devices and Sound Synthesis by Simulation of Instrumental Mechanisms: The Cordis System[END_REF][START_REF] Evrard | MIMESIS: Interactive Interface for Mass-Interaction Modeling[END_REF][START_REF] Castagné | G3: GENESIS Software Environment Update[END_REF].

The number of elementary module types is small -noticeably smaller for example than the core library of modules in most signal-based patching systems. Each algorithm is rather simple, though physically meaningful. Hence, complex behaviors emerge from the building of large models made of many elementary modules interconnected into a network, through a constructive modeling process.

PNSL supports all module types defined in CORDIS-ANIMA, no matter of the employed simulations frequencies, and dimensionalities.

PNSL, a modeling language for varied uses

PNSL is centered on the modeling activity with CORD-IS-ANIMA. It was aimed at supporting the user progressive process toward a model, rather than as a tool to provide a static description of a given model. It seeks providing the necessary but sufficient means to cope with the building of any masses-interactions network with all its properties, from the simplest to the most complex, no matter the foreseen usage.

The physical phenomena simulated by a physics network can be heard through a loudspeaker (provided it generates centered oscillations in the appropriate frequency ranges), but can equivalently be visualized on screen, or e.g. used to generate the feedback of a force feedback device. Hence, PNSL was made neutral in regards to the aim pursued with modeling. It qualifies for the design of both mechanical and acoustical models, in either Computer Music, Computer Graphics, Virtual Reality, Haptics or multisensory real time synchronous simulation.

In regards to its potential musical uses, PNSL was also designed to be as neutral as possible. Hence, though it can serve in particular musical creation, it does not embed musical vocabulary nor musical notation of any sort. Similarly, though physical modeling especially enables modeling the instrumental universe, the language itself does not provide predesigned instrumental blocks, such as e.g. membranes or air tubes. It is conversely a mean to build, and to play around as wished, such instrumental, sound, or musical elements. In this way, it is a tool that hopefully lets musicians freely explore and write the stilllargely blank page of musical creation by means of physical modeling.

This being said, and though this article focuses on PNSL basics, a library of scripts is progressively built and shared among users, with various routines that correspond to specific sound and musical model parts or goals.

Other General Goals with PNSL

Targeting the end user. PNSL users can be for example artists, composers, animation designers, etc. who may not be used to Physics nor to programming. Consequently, we sought a low entrance cost of the language, and its learning curve was an important factor. However, some users are skilled programmers, and the language hopefully allows them to benefit from their higher programming skills.

Adaptability. The features of the language can be adapted to the context of the target application at hand. In particular, the available module types, and, following, the categories of physics networks the user can define, can be varied from a target application to another. Also, in a given application, it is also possible to restrict the set of available features to those needed in the current modeling phase. For example: let the user access only the features related to the topology of the network, or only those related to physical parameters editing, or those related to initial state of the modules, etc.

Efficiency. Search for generality required possibility to manage large networks, possibly with hundreds of thousands <MAT> and <LIA> modules.

Expression power. Typical models' sizes and structures impact also the needed expression power. In particular, an analysis of past existing models and their design process showed that the modeling user needs handling large overlapping sets of modules at a glance, but also requires being able at any time to select and target any single module anywhere in the network. This required designing features able to target modules either individually or globally. It was achieved through the labeling system, which is presented in section 4. It also implied that any PNSL command should be able to process numerous attributes in various modules, with a single call and hopefully a concise syntax.

PNSL -GENERAL DESIGN CHOICES

This section situates our design choices regarding PNSL in the field of Domain Specific Languages [START_REF] Van Deursen | Domainspecific languages: an annotated bibliography[END_REF].

PNSL: a Scripting Language

There is no agreement in the literature of Domain Specific Languages regarding whether or not it should be an executable language [START_REF] Wile | Supporting the DSL Spectrum[END_REF]. Though, PNSL aims at accompanying the modeling user throughout his/her modeling activity toward the final model, including exploration and trial and error loops. We hence stated that PNSL should not be descriptive or declarative languages only able to describing the state of a given model. Conversely, PNSL is a full-featured programming language, and enables performing any modification of the model, or browsing any of its properties, at any time. We further chose to set up a script language, as opposed to compiled languages, so as to increase the ease of use (e.g. easily launch a single command) and embedding possibilities.

System Front End pattern

PNSL follows the System Front End pattern of Domain Specific Languages, as defined in [START_REF] Spinellis | Notable design patterns for domainspecific languages[END_REF]: the end-user language itself is offered as a programmable front end, called PNSL_front, that allows accessing an underlying core data structure and application programming interface, called PN_Core.

Though, the choice of the System Front End pattern was not carried out to ease the management of a preexisting system, nor to reduce the development effort of PNSL, as considered in [START_REF] Spinellis | Notable design patterns for domainspecific languages[END_REF]: both PN_Core and PNSL_Front were developed altogether. We rather adopted this pattern as a mean to enable cohabitation of multiple front-ends on top of the core data structure of the model being designed. Indeed, in our case, the System Front End pattern made it possible to articulate the language itself (PNSL_front) with WIMP and direct manipulation featured in interactive graphical user interfaces. Hence, the new releases of GENESIS [START_REF] Castagné | G3: GENESIS Software Environment Update[END_REF] and MIMESIS [START_REF] Evrard | MIMESIS: Interactive Interface for Mass-Interaction Modeling[END_REF] now offer graphic/textual cooperation, and become multimodal modeling frameworks -in the sense of representational or interaction modality, as defined in HCI.

Language Extension and Specialization patterns

PNSL employs the Language Extension pattern [START_REF] Spinellis | Notable design patterns for domainspecific languages[END_REF] or Embedding Pattern [START_REF] Mernik | When and how to develop domain-specific languages[END_REF], or Extension Approach [START_REF] Wile | Supporting the DSL Spectrum[END_REF] -and the Language Specialization pattern [START_REF] Spinellis | Notable design patterns for domainspecific languages[END_REF] in order to benefit from and adapt the syntax, semantics and libraries of an existing full-featured language.

We chose in our case the Tool Command Language Tcl [START_REF] Ousterhout | Tcl and the Tk toolkit[END_REF], by considering the simplicity of Tcl's grammar; its procedural, non-object oriented style; its promotion of variadic commands; its generalized use of strings, which is quite adequate to the PNSL's labeling system presented in the next paragraph (though using strings as the fundamental data representation also has drawbacks); and the fact that mathematical computation is rarely an important need in the context of masses-interactions CORDIS-ANIMA modeling processes, so that it is worth using Tcl's expr command. Though, to further accommodate users, other front ends may be deployed for PNSL in the future within another language, with a reasonable development effort thanks to the use of the Front End pattern.

LABELING SYSTEM

A masses-interactions CORDIS-ANIMA model may exhibit a large number of modules, possibly millions. Acquired experience shows that real-cases models gather both finely structured network parts (where modules are interconnected one-by-one into a specific topology), and regular network parts (with some regularities in the network's topology). Similarly, a model often has parts with homogeneous attributes (physical parameter, initial states…), but also parts with non-homogeneous attributes, where for example each single module is given carefully chosen parameter values.

Given the above, the modeling process often requires handling various sets of modules together, and importantly these sets often overlap with each other's. But conversely the modeling process also requires being able to target any specific module separately, in particular, but not only, when it comes to assemble the modules pointto-point, or to deal with initial state of the modules.

Hence, the means provided to the user to reference both any individual modules and numerous overlapping sets of modules were paid specific attention. Additionally, these means had to be manageable both through the language, and through the GUI. The Labeling System was specifically designed by considering these aims.

A review of known concepts to cope with complexity in modular frameworks

In modular modeling frameworks, and in particular in creative contexts, when facing the need to let the user structure large datasets, most systems build on the principles of encapsulation: "capsules" or "macro modules" are created by the user by gathering various sub-partsor, recursively, inner capsules -into a super structure. For example, encapsulation is a popular mean to cope with complexity in the context of signal-based modular patching environments such as PureData and MaxMSP, but also Simulink and others in other application fields. Similarly, in 3D shapes modeling, encapsulation is usually tied to the notion of object: various "objects", that may be rather complex, such as a sphere, a house, a character, etc., are placed into the scene. Tied to the notion of objects, 3D modeling also often promotes a hierarchical structure for the scene, through the notion of scene graph: an object can be made of sub-objects, in a recursive manner (e.g. a house made of walls, made of bricks, etc.). Noticeably, encapsulation also powers a number approaches to physics-based modeling, such as for example the BlockCompiler system [START_REF] Karjalainen | BlockCompiler: Efficient Simulation of Acoustic and Audio Systems[END_REF].

Indeed, encapsulation can be seen as a virtue of Informatics. It enables drawing boundaries around the "capsules", hiding their inner complexity, and minimizing the "surface" or "outside" of these capsules. It enables cop-ing with complexity by promoting a bottom-up hierarchical approach to complex modeling activities. And, importantly, it promotes reusability. However, encapsulation is not appropriate to massesinteractions networks modeling. Indeed, complex physics networks do not match a strict tree-like structural organization. This relates first to the fact that, by principle, masses-interactions networks are coupled structures, where any part of a model is interacting with (and not acting upon) the other parts. It also relates to the idea that, with PNSL, we wanted the user to gain access to the elementary level at each and any corner of modeling process, so that e.g. musicians could experiment with "composing the inner of the sound" (as J-C. Risset founded), rather than managing only macro categories of vibrating objects. Indeed, past experiments showed that featuring the principles of encapsulation in PNSL would require the user to access individually, quite often, the inner modules of a capsule, for example to change series of parameters, or to modify a <LIA> connection inside the capsule or with another module in another capsule, etc. Symmetrically, it would require letting each "capsule" exhibit most, possibly all, its inner properties on its "surface", including its inner topology (e.g.: letting all the <MAT> of a capsule accessible to outside connections) and the its modules' physical parameters. This contradicts the core interests of encapsulation.

Beyond encapsulation, the labeling system is our proposal to cover the need of dedicated features to cope with complexity while modeling with masses-interactions Physics Networks.

Labels and Containers

In PNSL, a label is a string that refers to a module. We say that a label targets a module.

Upon creation, a label is said to be declared; upon deletion, it is forgotten. Declaring and forgetting labels never creates nor deletes modules themselves. It only deals with modules' labels.

Each module is given by the system a unique permanent label upon instantiation, in the form @<integer> (e.g. @147).

Then, the user can define for each module as many user labels as needed, that is: as many labels as there are contexts in which he/she wants to name, select, connect, parameterize, or more generally handle the module. User-defined labels can feature any number of slash (/) separators. Hence, /string67/extermities/lia1 could be a label. Based on such separators, user labels are stored as a tree structure. A walk through the tree from the root "/" down to a leaf corresponds to a label, and refers to a module.

The sub-tree below an internal node, or symmetrically the labels sharing a part of their path from the label's tree root, can be seen as a context in which the user needed to name, or more generally consider, the targeted modules altogether. Each substring between two slashes separators in a label is hence called a contextual name.

We define internal nodes of the label tree as name containers, or containers. A container contains contextual names -and can if needed contain multiple contextual names targeting the same module. So as modules, containers may be targeted by numerous labels if needed. Containers enable managing (selecting, handling, para-metrizing…) all the modules it contains in one shot or, more formally, all the modules that have at least one label starting with one of the container's labels.

Finally, contextual names are indexed within containers. The user labels tree is hence a rooted and ordered tree.

Label Picker Expressions

Label picker expressions (LPE) enable "picking" (or "selecting") multiple labels, and consequently the modules they target, based on their syntactic proximity. Solving a LPE consists in retrieving the list of labels it picks. Most the Tcl commands that form PNSL_Front accept LPEs as arguments. This allows dealing with multiple labels (or multiple modules) in one shot.

Table 1 provides a few LPE and their effects in picking labels, to give a taste of the LPE system. In this table, Part A presents basic examples. Part B illustrates LPE's regular expression syntax. Part C exemplifies "filtering operators", that restrict the picked label. Part D provides examples of "substitution operators", that replace the picked labels with another label for the same module or container, and "ordering operators", that enable managing the order of the picked labels.

Comparison of the labeling system

The labeling system enables referencing both individual modules and overlapping sets of modules within complex networks. The user can declare as many labels for a module or a container as there are contexts, or editing tasks, in which the module or the container is to be involved. Symmetrically, a module may be named in as many containers as needed. With the labeling system, the modules, and the network, are left unstructured: only the modules' labels are hierarchically organized. As for it, the label picker expression mechanism enables picking many labels with a dedicated syntax.

The labeling system can be compared to UNIX/Linuxstyle file systems: files and their unique inodes, directory hierarchy, and hard links enabling multiple paths for a given inode. Symmetrically, the label picker expression mechanism shares similitude with the regular expressions featured in UNIX shells -these were indeed a source of inspiration in our design. However, hard links in file systems are not very common at the end-user level, whereas, in PNSL, a user usually rapidly defines multiple labels for each module. Other differences are the indexing of names in containers, the handling of integers in labels and in label picker expressions, and the prefixed operators featured in LPEs. Noticeably, the goals pursued with label picker expressions, could also be compared with the principles of Semantic File Systems.

The system shares also similitude with the address patterns featured by the Open Sound Control OSC protocol. A first difference is that OSC does not distinguish methods from their unique name in the OSC's address space. Also, the number of entities both systems were designed to deal with differs: usually up to some hundreds in OSC, to hundreds of thousands, possibly millions, in PNSL. Besides the necessity of optimization, this addresses the processing of numbers inside the labels' contextual names.

The XPath query language for XML documents, and also possibly jQuery in the JS/XML world, are other technologies of interest in our context: XPath enables selecting nodes in a hierarchical XML document, where an LPE select labels in the label tree. A difference lies in the fact that XPath manages the object of interest itself (the XML document), whereas LPEs manage labels as means to target modules in the designed network. Also, XPath (and also JQuery) provide more selection possibilities. In particular, XPath selection patterns may not only act over the XML tree, but also on any attribute of any XML node. Conversely, in LPEs, the prefixed operators are so far limited to the type of the targeted modules. This indeed leaves room for possible future improvements, for example toward filtering labels based on modules' parameters or connections.

A @23

Picks a single module, through its permanent label. /oscilator1/stiff_lia Picks a single label.

B @*

Picks all the modules' permanent labels in the model (or, simply "all the modules").

/strings/>> picks all the labels starting with /strings, down to the leaves in the label tree.

/membrane/> Picks all the labels in the container /membrane, without descending further the tree.

/audio_outputs/mass+ picks all the labels that start with /audio_outputs/mass, followed by an integer. @12..87 picks all the modules' permanent labels between @12 to @87 /strings1/#5..8

Picks the labels for the 5 th to 8 th based on the contextual names' indexing /rhythm_gen/RG1/mass11.. In /rhythm_gen/RG, pick modules named with mass followed by an integer >= 11.

C

LIA:@* Picks all the <LIA> (i.e. all the interaction modules) in the model.

3D:@SELECTION/*

Picks all the module with a 3D dimensionality that are currently selected in the GUI.

uniq:REF:/melody/>> Picks the labels starting with /melody/ that target linear visco-elastic modules (REF), and also ensures unicity of targeted modules (only one label is kept for each module).

D @:/part25/>>
Picks the permanent labels of the modules having a label starting with /part25/ #:/gesture1/* # orders the picked labels according to the indexes of the terminal contextual names, instead of using lexicographic ordering. Table 1. Label picker expressions. Single label (A); regular expressions (B); substitution (C) and filtering (D) operators.

PNSL'S FRONT END

PNSL's front end allows a user to start with PNSL without the need of programming skill. As an example, a simple model could be designed in PNSL without the need of Tcl built in features. Tcl is however available whenever the user needs to go beyond PNSL's basics to start a deeper programming of his modeling process.

Tcl packages

PNSL_Front splits into 14 packages. Each package groups the commands necessary to handle a phase of the modeling process, or other services: create/delete modules; handle the topology of the masses-interactions network at hand; manage labels and the labels' tree; pick labels by using LPEs; manage physical parameters; handle initial state of the MAT modules; setup audio outputs or the visual mapping of the model during simulation; etc. Thanks to the 14 packages, a host application can restrict which features the user can access in a given interpreter. So doing, the host application may respect and guide the various phases of the user's modeling process. For example, at a given time, an interpreter may handle only the topology of the network, only physical parameters, only initial state, etc.

Common choices for PNSL_Front's commands

Implementing a domain-specific language on top of Tcl usually consists in extending Tcl with new Tcl commands. PNSL is implemented through 67 such commands. They are usually split in pairs of getters to access properties of the model at hand, and setters to modify them. Most PNSL commands share a comparable syntax, and most accept one or several LPE (hence: "any number of modules") as arguments. When appropriate, to optimize: commands acting on modules rather than on the label tree, directly compute the LPEs into a list of modules, instead of retrieving full labels; and commands may silently add filtering operators adapted to its semantic.

Example

To provide a taste of the language, Figure 1 presents a simple PNSL script, translated to English in this paper from the French-based PNSL script. This exemplary script builds and parameterizes a simple GENESIS "linear string", with a few inhomogeneous parameters, very basically excited with an initial velocity.

In this example, line 1 controls the number of masses for the string. Line 2 creates a container in which to build the labels for the new string's modules. Note that the + will be substituted by the first integer that has never been used so far after the chosen radix /string. Hence, the created container could be automatically named /string23 if, prior to execution, the label /string22 had already been defined at some point in the model. Lines 3 to 6 create the needed modules: masses (MAS_U), visco-elastic interactions (chosen linear in this example: REF_U), fixed points (SOL_U), and audio output (SOX_U). The acronyms employed for the module types are those defined by the CORDIS-ANIMA formal-ism. With the same commands, we decide to declare some initial labels for each created modules. The needed name containers are silently created by the system. The use of @ (for "use permanent labels") at the end of some of the declared labels denotes that we here do not want explicit contextual names for the modules in the container. For example, a label for the first created mass could be /string23/mas/@675, provided @675 is its permanent label automatically given by PNSL. Figure 1. A simple PNSL script Lines 7 to 10 declare other labels for some of the modules, enabling to later refer to these modules specifically. For instance, line 7 creates and fills the name container /string23/mat/ that gathers all the <MAT> (masses + fixed points) of the string. Line 11 to 15 set up <LIA> -<MAT> physical connections for all the modules of the string. Connections are established here by using the basic connect_lia command, but a straightforward feature provided in the PNSL library of scripts could also build such a simple string topology. Line 16 to 25 set up the modules' properties: position on the GENESIS GUI's 2D topological bench (see [START_REF] Castagné | G3: GENESIS Software Environment Update[END_REF]), then physical parameters and initial state. For instance, line 21 affects "default parameters" to all the modules throughout the string. Then, lines 22-23 introduce some inhomogeneity, by modifying a few parameters in a few modules. Symmetrically, line 24 puts the model at rest, and line 25 introduces some energy by changing the initial speed of one of the masses.

On lines 26 to 29, we print a few information about the created string and its modules' labels. On line 27, the ESL @:uniq:$root/>> selects the permanent labels of all the created modules (@ selector), and ensures each of them appears only once (uniq selector). Then, the loop prints all the labels of each module.

Finally, line 30 ensures selection of the created modules in the modeler's GUI once the script terminates. Noticeably, in the above script, keywords such as for, to, in are optional. Also, it would have been possible to omit certain aspects (e.g.: omit physical parameters setup), and let the user design them later in the GUI once the script has been executed. Finally, note that the PNSL library of scripts provides routines that generate fullfeatured strings, membranes, plates, etc. -which could be employed in real-case situations to generate such a simple model, instead of this exemplary script.

IMPLEMENTATION

PNSL is accessible to the user as a stand-alone scripting language, which uses CORDIS-ANIMA simulation engine to simulate the designed models. Besides, thanks to the use of the Front End Pattern, the language is now also incorporated into the interactive modeling software frameworks. This includes the GENESIS environment for sound design and musical composition [START_REF] Castagné | G3: GENESIS Software Environment Update[END_REF] and the MIMESIS environment for movement and animated image synthesis [START_REF] Evrard | MIMESIS: Interactive Interface for Mass-Interaction Modeling[END_REF]. In these environments, both the GUI and PNSL now fully rely on PN_Core for their core data structures and features. These creative tools are disseminated through 3 mechanisms: through research and creative cooperative projects, commercially, and through pedagogy/teaching/workshops.

The language itself, PN_Front, is first used internally, as a file format, to save and share models in a humanreadable way, and also to manage the undo/redo mechanism in the GUIs.

Second, on the user side, PN_Core features are available both in the language and in the graphical interface. Three embedding mechanisms are available to the user in the GUIs: (1) PNSL is accessible within a command-line interpreter, to fire any PNSL command on demand; (2) It is offered in a script editor, to program, then execute, any modifications of the designed model; (3) It can be used to program new user-defined modeling actions, hence to extend the GUI with new commands specialized for the user's needs. Hence, whenever adequate, the user can employ the language to implement any modeling tasks, as a vis a vis of the graphical direct-manipulation and WIMP features of the GUI -see Figure 2. The network of modules (including its topology, its parameter and its initial states, etc.), and all the labels, are transparently accessible and can be edited through any of the two interaction mechanisms, language and GUI. Hence, these environments now fall into the scope of multimodal interfaces (as defined in Human-Computer Interaction, when a given interface gathers multiple "representational" or "interaction" modalities), by enabling cooperation of the graphics-based and the textual-based humancomputer interaction modalities within Physics Networks modeling.

CONCLUSIONS

This article introduced the Physics Network Scripting Language, PNSL, a domain specific language that extends today's modeling possibilities by allowing a user to design by programming any physics-based model within the physics-network, or masses-interactions, paradigm. elementary modules. Its label tree is rather complex, with close to 1000 overlapping name containers, and a tree-height of 6. On the right corner, the widget displays and enables managing the label tree from the GUI front end. Note that, as explained above, modules are sometimes unnamed in name containers (e.g. @67), and sometimes named with an explicit user-defined name.

At a time when, in the field of physics-based simulation, often only preconceived models or large predesigned building blocks are available to artists, PNSL aims at empowering the user (e.g. an artist, a musical composer, an animation designer, a researcher…) with the modeling of his/her own physics-based models. PNSL builds on the CORDIS-ANIMA formalization of Physics Networks. Thus, the language may apply to various modeling process rooted on masses interconnected by physical interaction -including mass-spring meshes, and others. PNSL supports modeling no matter the network's topology (regular and irregular), its complexity (from a few to hundreds of thousand modules), its parameters, the dimensionalities of its modules, and the application domain pursued, including Computer Music, Computer Graphics and Virtual Reality, Physics teaching, research, etc.

Since the first release of PNSL, the usage of PNSL developed into various directions.

First, a number of existing models have been re-written using PNSL: large unstructured models (e.g. of nonlinear gongs, smoke models…), finely structured models (puppets, vehicles…), models of many sound structures, musical instruments models and past music pieces.

Second, users of GENESIS and MIMESIS have started experiencing with PNSL, for artistic works falling either into the field of musical creation and visual creation, and for research purposes. The feedbacks we obtained show that users that are neither scientists nor programmers are able to start learning and using PNSL, and in particular are able to apprehend the labeling system; and conversely that PNSL enables more complex scripting of modeling tasks. For example, users scripted the generation of large regular model's parts with specifically crafted topology, the computing of the physical parameters of a model to match various desired effects ("inverse problem"), the management of the spatial organization of a model, the selection of modules in the GUI according to searched properties, etc. Users also reported that the language enabled opening new branches in their creative effort. This concerns for example the design of large networks' parts with specific topology and their articulation with other parts in the model, thin managing of physical parameters' profiles by mathematical laws, and programming of systematic modeling/simulation experimental loops -all of these being difficult to implement with a direct manipulation GUI.

Hence, we hope PNSL is a contribution to the technology serving the trend that envisages physics-based modeling, and not only physics-based simulation, as a core mean to extend creativity with the computer.

Figure 2 :

 2 Figure 2: a representation of the musical piece Helios by Claude Cadoz, 2015, in the current version of GENESIS equipped with PNSL. Helios' model is made of 116 933elementary modules. Its label tree is rather complex, with close to 1000 overlapping name containers, and a tree-height of 6. On the right corner, the widget displays and enables managing the label tree from the GUI front end. Note that, as explained above, modules are sometimes unnamed in name containers (e.g. @67), and sometimes named with an explicit user-defined name.

C:\Users\nicolas\Desktop\test05.tcl jeudi 30 avril 2020 14:37

Acknowledgments

This work has been supported by the French Ministry of Culture, and the collaborative project DYNAMe funded by the French Agence Nationale de la Recherche. We thank the PNSL beta testers, especially Fabien Henry, Ali Allaoui, Clément Werner, Jérôme Villeneuve and Francisco Huguet; Peter Torvik for the help on the English terminology for PNSL features; and the Tcl community for its assistance.

SMC torino2020

Proceedings of the 17th Sound and Music Computing Conference


Anne Teresa De Keersmaeker For Rosas

Alban Déléris

Anne Teresa de Keersmaeker is considered as one of the most important choreographers on the contemporary dance scene. Her new performance surely confirms this idea and presents an original conception of the human body language. By adapting Shakespeare's pastoral play As You Like It, Anna Teresa de Keersmaeker gives us an hybrid show, between theatre and dance, a faithful reconstruction of the Elizabethan play and iconoclast reading of a 'classic'.

The beginning of the show is indeed very striking. A dozen of dancers enter on stage, walking very slowly to the sound of the song by Brian Eno which gives the play a part of its title: 'Golden Hours'. The dancers, each interpreting a character of the play, make circles on the stage, while the soundtrack is repeated four times. The song of the 1978 album Another Green World constitutes a musical leitmotiv of the play. Eno's music, a mingling of pop and repetitive soundtrack, dialogues in several ways with Orlando and Rosalind's love story. One of the characters is a guitarist, playing several songs from Eno's album. The intricacy between the music and the play, far from producing an anachronism, creates a very gentle mixture and recalls the popular roots of Shakespeare's play.

Brian Eno's songs also provide also the musical background of the performance, but the structure used is the same than as in Shakespeare's play, with all five acts of As You Like It and the epilogue during which Rosalind addresses the spectators.

The choreographer's project could be summed up in a few words: translating the dramatic and spoken language into physical language. The dance imagined by Keersmaeker is both physical and expressive, and its language is made of movements, gestures, jumps and sudden accelerations. Body talk replaces Shakespeare's text, even though the spectators can follow it. Passages are projected on the wall at the back of the stage, making the comprehension of the 'tale' easier.

The projected extracts can be read as textual fragments as well as reminiscences or memories of the play. But the text is not totally absent from the performance itself, since the dancers whisper it several times during the show, to themselves or to each other. The knowledge of the play is thus a prerequisite for an embodied expression that is substituted to the spoken language.

The dance designed by Keersmaeker is minimalist and explores the foundations of choreographic art by showing its essential components. With her company Rosas, created in 1983, and since her early performances, such as Fase in 1982, the Belgian choreographer still experiments new formulas based on a few basic principles, which are like mantras: walking, breathing and, in the case of Golden Hours (As You Like It), the contradictory relations between silence and speech, between speech and dance. Before Brian Eno's pop music, she worked with Steve Reich's minimalist compositions, Joan Baez's rock music and even with John Coltrane's jazz. The performance staged during the Montpellier Danse Festival can be considered as the continuation of those experimentations, focusing on the articulation between the spoken language (or the absence of speech) and the danced language.

Thus, the choreographer's choices are remarkable by their obvious boldness: most of the play is silent, except for the sound of the dancers' movements and breathing. Moreover, an important aspect of the performance is the fact that Keersmaeker follows the main structure of the play and takes up its conduct and its details. The fidelity toward the spirit of

the Elizabethan play can be traced in the androgyny of the interpreters, and especially in that of Aron Blom, who plays the character of Rosalind. The dancer, who studied at PARTS (Performing Arts Research and Training Studios), the school founded by Keersmaeker, stands out for his delicacy and his long curled hair, which produce a confusion of genders specific to the play. This ambiguity culminates when Rosalind dresses up like a man to fight Orlando. Similarly, the character of Jaques is played by a young woman, who embodies the slapstick madness of Shakespearean clowns and fools.

But maybe the real subject of the show performed in Montpellier is Time. As the Chorus in the other Shakespeare's pastoral play, The Winter's Tale, Time is presented in its different aspects. A time of the action, a time for silence, a time for absence, for repetition and variation: Keersmaeker does not hesitate to expand the length of the performance and keeps following the narrative thread of As You Like It (and it was not surprising to see a lot of spectators leaving the Agora theater in Montpellier that summer night). But the moral of both Shakespeare's play and Keersmaeker's performance is definitively positive and joyful. Spring, the season of the love story between Rosalind and Orlando, metaphorizes the treatment of the play suggested by the choreographer.

This astonishing reading of Shakespeare's play is thus reinforced by the technical virtuosity of the choreography: the silent or whispered ballet renews the pastoral genre and reveals its popular roots. It reminds us that dramatic art, and most of all Shakespeare's plays, is not simply with a question of words, it's also all about gestures, movements, music and silence. Golden Hours (As You Like It) demonstrates also the possibility of staging Shakespeare without words, as a dumb and meaningful show.

Alban Déléris completed a PhD about the relationships between the English and French theatres between the mid-sixteenth century and the early 1640s, and the poetics of formal and generic hybridizations in the plays of this period. IRCL, University Paul Valéry -Montpellier 3 Email: alban.deleris@yahoo.fr


B Benmohammed
email: b.benmohammed@gmail.com

Cutting forces measurements during discontinuous machining process

Keywords: compensation of inertial forces, cutting forces measurements machining, discontinuous turning process

He presents the various cases where the measurement of cutting forces in fast transitory mode is necessary. He exposes also a method of compensation of inertial effects which denatures the signals provided by the most used piezoelectric dynamometers. The possibilities of this method, based on the accelerations measurements of the upper part of the dynamometer, are exposed for the case of a discontinuous turning process. It is shown that the undesirable effects related to the resonance frequencies of the dynamometer and to its base movements are mainly eliminated.

Introduction

Measuring cutting forces generated during cutting or abrasion processes is one of the best ways to characterise these operations. The analysis of cutting forces is necessary to understand the cutting phenomenon, to control static and dynamic behaviour of a whole piece-tool machine system and is a natural way of monitoring and diagnosis for cutting operations.

Many authors such as [START_REF] Chung | A modal of high performance dynamometer[END_REF] have studied the possible measurement inaccuracies, when using piezoelectric dynamometers in the machining processes.

The main measurement inaccuracies result from the fact that dynamometers behave approximately as a weakly damped second order system. It presents a resonance frequency depending on the sensors type and their layout.

Resonance is all the more perceptible as damping is weak (about 500 N.s.m -1 ). During cutting operations, the fluctuating frequencies of cutting forces approach or exceed the resonance frequency, making a difference between the dynamometer signals and the exerted forces.

Three cases of dynamometer disturbances could be described:

During discontinuous cutting operations; even if the frequency of force signals repetition is weak. The presence of transitions with abrupt variations produces a wide range of frequencies and could generate unacceptable distortions. This is the case for milling, discontinuous turning and broaching operations. The following example (Figure 1) shows a typical response signal in the case of discontinuous turning process. It seems obvious that when the rotating speed increase, the repetition frequency increases and could reach the dynamometer resonance frequency.

During the appearance of a vibration phenomenon such as chatter, the frequency could range from some hundred Hertz to some kilo Hertz. Nevertheless, this analysis is very important because it emphasises a damping phenomenon, which has to be taken into account for a good simulation of vibration phenomena. We could meet such conditions in the case of an external vibration source such as in ultrasonic abrasive machining.

During the superposition of a random force to the continuous force. Generally, we meet this case during the study of influence of the local material micro hardness variations on the cutting force evolution. It is very important to take into account the dynamometer distortions. Distortions attenuation could be considered in several ways. The first one consists in making use (or creating) a dynamometer having a satisfying bandwidth [START_REF] Gautschi | Cutting forces in machining and their routine measurement with multi-component piezoelectric force transducers[END_REF]. We could then set up preliminary calibrating operations [START_REF] Kegg | Cutting dynamics in machine tool chatter[END_REF][START_REF] Komanduri | Dynamic calibration of dynamometers[END_REF]. These operations are difficult and took a long time to be implemented. They are only valid for a given measuring system configuration. Most efficient methods are divided into two classes:

1 Those of the first class aim at attenuating inertial errors and damping forces. For this, it is necessary to carry out simultaneous measurements of different accelerations. They allow firstly the evaluation of inertial effects and secondly the evaluation of speed and consequently damping forces. This inertial effects compensation has been particularly studied for one dimensional system by [START_REF] Tanaka | Accelerometer applications to tool dynamometers with approved dynamic response[END_REF] and by [START_REF] Tlusty | Measurement of the milling force over the wide approved dynamic response[END_REF]. The general case was envisaged by [START_REF] Gygax | Experimental full cut milling dynamics[END_REF].

2 The second class of distortions attenuation methods is based on a special adaptive filters use and it was done by [START_REF] Spiewak | Adaptive compensation of in-process sensors[END_REF] and [START_REF] Chung | A modal of high performance dynamometer[END_REF].

Possibilities of the first class method used in laboratory for the fine analysis of cutting forces are presented in this research work.

Modelling of dynamometer signals

The dynamometer employed in our investigation is 9257B 'Kistler' model (Figure 2, [START_REF] Benmohammed | Identification des lois d'effort de coupe de tournage en régime dynamique[END_REF]. It is made up from a system of four 'three-directional measure elements', which are inserted between the dynamometer base and superior plate 'platform'. On the dynamometer higher plate is fixed the work piece or the cutting tool.

The dynamometer base and superior plates are considered as rigid elements, and every measure element is assimilated in each of the three directions to a spring associated to a viscous damper.

The platform (the dynamometer superior plate) is considered as a rigid body, which has six degrees of freedom, three translations and three rotations. Considered as a dynamic system, the platform exhibits six resonance frequencies associated with its vibration modes. The considered dynamometer installed on a machine tool is a part of a larger multi degrees of freedom system, as explained in (Figure 3). the masses distribution of the cutting tool and the dynamometer's higher plate are symmetrical to the dynamometer YZ plane of symmetry (Figure 3) all the dynamometer characteristics (the sensor's: stiffness, damping coefficients and sensitivities) are symmetrical to the dynamometer YZ plane of symmetry external force is applied in the contact point of the cutting tool on the work piece it has been assumed that the dynamometer base plate is immobile (it is supposed as a rigid body).

He presents, in the beginning of his research work, the acceleration compensation principal.

The principle of the acceleration compensation is exposed for the case of one dimensional configuration. The sensor is composed of a sensitive element pre-stressed between the base and the higher plates (Figure 4). Under these conditions, he has [START_REF] Benmohammed | Identification des lois d'effort de coupe de tournage en régime dynamique[END_REF] obtained a plane movement characterised by the two translations (y, z), of the gravity centre of the dynamometer platform; and also its rotation ( ) around the X axis.

The dynamic equation giving the dynamometer superior (or higher) plate movement is:

ec i M.q F (t) F (t) (1) tt t e y z x ci cyi czi cxi xx m0 0 q[ yz ] , F F F M , F F F M a n d M 0 m 0.

00I

Usually, each of the F cyi and F czi force components is decomposed into two values: one corresponding to the elastic deformation of sensing elements and the other is due to their damping characteristics.

He has used the following relationship: cyi kyi ayi czi kzi azi FFF a n d FFF .

By calling z i and z bi the sensitive (i) displacements in the Z direction, which are respectively linked to the dynamometer superior and base plates, he has found the following relationship:

czi zi i bi zi i bi F k .z z c .z z (2)
The same relationship is valid for the Y direction: He supposes that the emitted signal from sensor (i) in Z direction is proportional to the term zi i bi k. ( z z) . Under these conditions, the dynamometer base movement is taken into consideration and he could then write the equation (1) as follows: em e s ia i M . q F ( t )F ( t )F ( t ) (4) Equation ( 4) makes possible the calculation of the applied force F e (t) component from the three other terms. The term mesi F( t ) is given by the dynamometer, providing that he separately process the signals emitted by the different sensors. The term M.q is obtained from accelerations measurements. The valuation of the damping term ai F( t ) is more difficult.

He could then evaluate the dynamometer platform speeds from the accelerations measurements, but it would be necessary to known the dynamometer base plate movements.

This modelling is not valid unless the dynamometer platform has a rigid body and also a special attention to the cutting tool fixation, on the dynamometer platform, should be paid.

Applicability of the developed model to turning process

The layout of the cutting tool on the dynamometer higher-plate is described in Figure 6 [START_REF] Benmohammed | Identification des lois d'effort de coupe de tournage en régime dynamique[END_REF]Lapujoulade, 1996a, 1996b). In his current study, only Z component of cutting force has been evaluated. Otherwise it would have been necessary to add an accelerometer in the Y direction. He supposes that symmetry hypothesis around the dynamometer YZ plane are satisfied. Especially, the turning cutting tool does not generate a force in the X direction. He could then evaluate the sensors speeds after the accelerations integration. The damping coefficient (C) is determined by observing the signal oscillations decrease after a shock, and the damping forces corresponding to the sensors C 12 and C 34 are evaluated from these data.

The mass of the dynamometer platform and the cutting tool, and the position of their gravity centre (G) are difficult to evaluate. It is necessary to operate by identification in the area where there is no machining, otherwise where the external force is null, (Figure 6).

Then he obtained the following relationship: The objective is to ascertain values of coefficients (m, B 12 and B 34 ) so that the relationship ( 6) is the best possible. To resolve this problem he has used the optimisation technique and he has chosen the least square method. Then these coefficients are used to evaluate the external cutting force. Figure 7 shows the F z cutting force component under its rough form given by the dynamometer and also after the inertial effects compensation. The profile of the observed force signal is very close to the correct supposed form defined by calculation. He compares two signal forces, the first given directly by the dynamometer and the second obtained by calculation from relation (4): em e s i a i F(t) M . q F (t) F (t) (7)

The rising front in the cutting force signal is respected. It remains oscillations of weak amplitude and of a frequency superior to that of previous perturbations.

Their source is due to the cutting process or to the dynamometer functioning, which is more complex in reality than the developed model. Especially, there are flexion vibrations of the dynamometer platform. On the other hand, the oscillations of lower frequency occur and they are corresponding to the cutting tool vibrations.

The quality of the cutting force signal after compensation of inertial effects is to be compared to that given by a simple low-passes filtering of the initial cutting force signal (Figure 8). Besides the lag on the force signal, which could be eliminated by appropriate techniques, the filtered signal presents perturbations that are not a residue of the eliminating frequency, but the result of the stiff front filtering.

Conclusion

The compensation of inertial forces [START_REF] Benmohammed | Identification des lois d'effort de coupe de tournage en régime dynamique[END_REF] is vital for the study of cutting forces in discontinuous machining and particularly in the case of a discontinuous turning process. It is also a necessity for the study of cutting process in vibrations presence.

Within the framework of laboratory instrumentation, the compensation of inertial forces by acceleration measurements is possible. It is relatively simple to implement, each time that we could simplify the dynamometer modelling by creating a symmetry distribution of mass and force, as compared to the dynamometer median planes XZ or YZ.

Force signals obtained in discontinuous turning process allow a very fine analysis of the cutting force in the presence of abrupt variations.

This modelling is not valid unless the dynamometer platform has a rigid body. Also a special attention to the cutting tool fixation on the dynamometer platform should be paid.

Figure 1

 1 Figure 1 Discontinuous turning process (see online version for colours)

Figure 2 Figure 3

 23 Figure 2 Mechanical design of the considered dynamometer: a '9257B model'

Figure 4

 4 Figure 4The piezoelectric sensor as a pre-stressing system

Figure 5

 5 Figure 5 Mathematical modelling of the sensitive element

  ) and (y y ) are the displacements of sensor (i) in Z and Y directions. ) and (y y ) are the speeds of the sensor (i) displacements in Z and Y directions.

Figure 6

 6 Figure 6 Discontinuous turning process

Figure 7

 7 Figure 7 Discontinuous turning process (see online version for colours)

Figure 8

 8 Figure 8 Cutting force signals obtained by simple low-passes filtering (4,000 Hz and 6,000 Hz) and the force signal after inertial effects compensation (see online version for colours)

  gravity centre in Z direction Cutting tool gravity centre rotation around X axis F e Vector of external forces and moment applied to the dynamometer F ci Vector of forces acting on the dynamometer platform F ki Vector of elastic force components F ai Vector of damping force components K yi , K zi The sensor (i) stiffness respectively in Y and Z directions C yi , C zi The sensor (i) damping coefficients respectively in Y and Z directions I Index denoting the location of piezoelectric sensors (C 1 , C 2 , C 3 , C 4 ) inside dynamometer M Mass of the cutting tool -dynamometer higher plate M Elements of the matrix M of mass q Generalised coordinates vector. I xx Moment of inertia of the cutting tool on the dynamometer platform in X direction

  Under these conditions, the emitted signals by C 1 and C 2 sensors are summoned as they are emitted by a unique sensor C 12 , and similarly for the sensors C 3 and C 4 ; they are summoned to a unique sensor C 34 .

	12 34 12 acc .b z. 34 12 34 acc .b bb
	He could also write:
	12 z B .acc 12	34 B .acc , 34
	with
	12 B	12 b b	34 bb 34 34 12 b 12 a n d B. 34 b
	By taking into consideration only the Z direction force component, equation (4) could
	be rewritten as follows:
	12 Fz m.z Fz Fz	34	12 Fa	Fa	34	(5)
	With the sign conventions linked to the dynamometer, he could express the Fz 12 and Fz 34
	components as a function of the measured values Fmz 12 and Fmz 34 delivered by the
	sensors:
	12 Fz	12 Fmz and Fz	34	34 Fmz .

The acceleration of the gravity centre of the dynamometer platform in Z direction is calculated from the measured accelerations acc 12 and acc 34 , as follows:


domain: phys spi

text:
W Khelifi

C Coinon

M Berthe

D Troadec

G Patriarche

X Wallart

B Grandidier

L Desplanque

Improving the intrinsic conductance of selective area grown in-plane InAs nanowires with a GaSb shell

The nanoscale intrinsic electrical properties of in-plane InAs nanowires grown by selective area epitaxy are investigated using a process-free method involving a multi-probe scanning tunneling microscope. The resistance of oxide-free InAs nanowires grown on an InP(111)B substrate and the resistance of InAs/GaSb core-shell nanowires grown on an InP(001) substrate are measured using a collinear four-point probe arrangement in ultrahigh vacuum. They are compared with the resistance of two-dimensional electron gas reference samples measured using the same method and with the Van der Pauw geometry for validation. A significant improvement of the conductance is achieved when the InAs nanowires are fully embedded in GaSb, exhibiting an intrinsic sheet conductance close to the one of the quantum well counterpart.

I. INTRODUCTION

With its low electron effective mass and its strong spin orbit interaction, InAs exhibits exceptional electron transport properties that are particularly appealing for the fabrication of quantum devices involving Majorana bound states in hybrid semiconductor/superconductor one dimensional (1D) nanostructures [1][2][3]. One of the main technological challenges in this quest lies in the required material and interface quality to preserve the quantum coherence of electrons over a micrometre scale distance after standard semiconductor processing techniques.

Up to date, the best configuration to optimize the electron mean free path is generally obtained with a semiconducting layer sandwiched between larger band gap barriers that confine the charges into the channel and limit their interaction with surface or mismatch interface states, forming a twodimensional electron gas (2DEG). For InAs channels, Al(Ga)Sb barriers offer a large conduction band offset enabling the formation of 2DEG with a Hall mobility as large as 1.85x10 6 cm 2 .V -1 .s -1 at 1.3K on lattice matched GaSb substrate [4]. The hybridization gap that can be engineered in composite InAs/GaSb channel may also result in topologically protected edge states that could significantly improve the robustness of charge transport against disorder [5,6]. However, processing 1D nanostructures from 2D quantum well results irremediably in a degradation of the transport properties caused by the sidewall surface states after etching. Bottom-up approaches involving the Vapor Liquid Solid (VLS) growth of vertical InAs nanowires (NWs) and their subsequent transfer on a host substrate for processing have emerged to avoid nanoscale semiconductor etching [7][8][9][10]. Controlling the position of the nucleation and organizing the growth of vertical NWs into arrays have been enabled by combining the design of nanoholes in a dielectric mask on the substrate with the selective area epitaxy (SAE) of NWs [11][12][13][14]. Later, this technique have evolved toward template assisted epitaxy [15] and in-plane SAE in order to achieve more complex architectures and a scalable nano-device process [16].

When grown in this latter configuration, the good control of the NW conductivity requires the use of semi-insulating substrates. However, the large lattice mismatch of InAs with standard III-V semi-insulating substrates such as GaAs or InP prevents the formation of high quality InAs NWs with competitive electron mobility. A compromise consists in growing a thick metamorphic buffer layer to limit the impact of surface roughness and threading defects on transport properties when the growth occurs at full wafer scale [17,18]. This drawback can also be limited by nanoscale selective area epitaxy on (111) oriented substrates [19,20] or by using a thin nanoscale template to reduce the mismatch prior to InAs deposition on GaAs(001) substrates [21][22][23].

In this paper, we investigate the intrinsic conductance of InAs NWs grown by SAE. To minimize the number of processing steps to contact the NWs, the electrical conductance is measured with four-probe Scanning Tunneling Microscopy (4P-STM), which allows the arbitrary arrangement of non-invasive probe electrodes onto a single NW [24]. Two sets of NWs are considered and benchmarked with InAs-based 2DEG grown on GaAs(001) substrates. The first type of NWs corresponds to InAs NWs directly grown on InP(111)B, as such a substrate favors the growth of nearly defect-free InAs NWs [25]. In this case, the removal of a thin amorphous arsenic protecting layer prior to the transport measurements in Ultra-High Vacuum (UHV) ensures the formation of ohmic contacts on oxide-free facets. The second type of NWs deals with InAs/GaSb core-shell NWs grown on InP(001). For both types of NWs, the knowledge of the geometry of 100 nm and 200 nm-wide InAs channels based on electron microscopies allows to determine their sheet resistances. These experiments reveal the benefit of embedding the InAs NWs in GaSb, which shows a sheet resistance close to the analog 2D heterostructure. The different samples used in this experiment are grown by Molecular Beam Epitaxy (MBE) in a RIBER Compact 21 system equipped with valved cracker cells for As and Sb evaporation. A RF plasma cell is also set-up on the system to produce an atomic hydrogen flux used for substrate deoxidization and selectivity improvement during SAE of GaSb [23]. The different III element fluxes are calibrated by recording the Reflection High Energy Electron Diffraction (RHEED) specular intensity oscillations during the homoepitaxy of InAs or GaAs for indium and gallium respectively or during the growth of AlAs on GaAs for aluminium. As and Sb fluxes are calibrated using V-element limited RHEED specular intensity oscillations during the homoepitaxy of GaAs and GaSb respectively.

II. EXPERIMENTAL DETAILS

The first set of samples (A and B) consists of two InAs channel based heterostructures grown on GaAs(001) semiinsulating substrates as described in figure 1a and1b. In both structures, the large mismatch between InAs and GaAs is accommodated thanks to a buffer layer composed of a 4 monolayer (ML) AlSb nucleation layer and a 1 µm-thick GaSb layer [26]. In sample A, the 15 nm-thick InAs channel is sandwiched between Al0.8Ga0.2Sb barriers with a thickness of 50 nm for the bottom one and 5 nm for the top one. In sample B, the InAs channel is sandwiched between GaSb barriers with the same thickness. In both cases, a 5 nm-thick GaSb cap is deposited on top of the epitaxial structure to prevent the oxidation of AlGaSb for sample A and keep the same surface to channel distance for sample B. As shown in the simulation of the charge carrier density in the structure (figure S1, supplementary information), sample A should exhibit a type II band-line up between the InAs channel and the Al0.8Ga0.2Sb barrier whereas a broken gap band-line up between InAs and GaSb barriers should be obtained for sample B. This leads to the presence of an additional 2D hole gas concentrated in the GaSb bottom barrier at the interface with the overlying InAs channel whereas only a single 2DEG located in the InAs channel is obtained in the case of AlGaSb barriers.

The second set of samples (C and D) consists of selective area grown in-plane InAs NWs on semi-insulating InP substrates. Prior to the epitaxial growth, a 30 nm-thick SiO2 mask is prepared by means of plasma enhanced chemical vapour deposition, e-beam lithography, reactive ion etching and a final dilute HF treatment enabling the design of apertures as narrow as 50 nm in the SiO2 mask [27]. The geometry of most of the apertures corresponds to a segment with different in-plane orientations. A limited number of more complex geometries such as crosses is also considered. After the final HF treatment, the width corresponding to 100nm and 200nm nominal apertures are respectively about 130 and 230 nm. After outgassing the substrate for one hour at 200°C in a preparation chamber, the InP native oxide covering the bottom surface of the apertures is removed. This deoxidation process is performed by annealing the substrate under As4 flux and exposing it to atomic hydrogen for 30s while rising up the substrate temperature to 500°C. Sample C consists of a semiinsulating InP(111)B substrate, where InAs NWs are directly grown at 390°C inside the oxide-free apertures at a growth rate of 0.05ML.s -1 and a very large As4/In flux ratio of 110. The nominal thickness of the deposition is 30 nm. After growth, the SiO2 layer in between the NWs is chemically removed with an HF treatment. Then, the sample is re-introduced in the MBE system and the surface is deoxidized with an annealing up to 400°C under As4 and atomic hydrogen exposure. The substrate is then cooled down to 10°C and capped with amorphous arsenic for several minutes in order to prevent the surface from oxidation during the transfer to the 4P-STM. After the removal of the InP oxide as described above for sample C, a 100 nm-thick GaSb layer is first grown at a temperature of 470°C, with a growth rate of 0.1ML.s -1 , a Sb/Ga flux ratio of 2.5 and under atomic hydrogen exposure. These conditions have been demonstrated suitable for selective epitaxy as well as to optimize the GaSb nanostructure morphology on GaAs or InP (001) substrates [21,28]. InAs is then deposited on the GaSb nano-template with a nominal deposited thickness of 10 nm. A 10 nm-thick GaSb cap is finally deposited on the nanostructures.

The morphology of the nanostructures is analysed using Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM) and, for some NWs, Scanning Transmission Electron Microscopy (STEM) after preparation of thin cross-sections through the in-plane NWs using Focus Ion Beam (FIB) etching. The STEM studies are performed in a Titan Themis 200 (FEI) microscope equipped with a spherical aberration corrector on the probe and an Energy-Dispersive X-ray spectroscopy (EDX) system super X (0.7 srad solid angle of collection). The accelerating voltage is 200 kV. The (half) convergence angle of the probe is 17.6 mrad and the probe current 85 pA.

The transport properties of 2DEG in samples A and B are investigated at 300 K and 77 K by Hall measurements after the fabrication of Van der Pauw devices using optical lithography, chemical etching of the epitaxial layer down to the GaAs substrate and indium contact deposition. A picture of sample A after the Van der Pauw device fabrication can be seen in the right inset of figure 6. In parallel, the sheet resistance of the 2DEG in samples A and B is also deduced from the 4-probe measurements of the resistance with 4P-STM working in UHV (Nanoprobe, Omicron Nanotechnology). As the use of good electrical contacts is essential to inject and extract charge carriers, tungsten tips are prepared by an electrochemical etching in NaOH and thoroughly annealed in the UHV preparation chamber to remove the thin oxide layer covering the tips.

Prior to the 4P-STM transport measurements, all the samples are annealed at 120°C in UHV for a few hours. The InAs NWs grown on the InP(111)B substrate are further annealed at 320 °C to remove the As capping layer, while monitoring the As desorption with mass spectroscopy. For all the samples, the STM tips are always positioned with an in-line four-point geometry under the control of a SEM. The STM tips are first brought into electrical contact with the surface of the samples using the distance regulation of the STM control system. Then, a stable electric contact is obtained by further pushing down the STM tips in the feedback-off mode. Injection of the current I through the outer tips and measurement of the voltage drop V between the two inner tips give access to the four-point resistance. For the quantum well, the 4-point resistance is measured for different equidistant separations between the STM tips at temperatures of 300 K and 115 K. In the case of the NWs, the two outer tips are connected at the end of the NWs. An inner tip is connected close to one outer tip and kept fixed. The fourth tip is moved step by step from one side of the NW to the other one to acquire V(I) characteristics with different separations between the inner tips.

III. RESULTS AND DISCUSSION

Figure 2 displays the morphology of arrays of selective area grown in-plane InAs NWs with different widths and orientations that can be observed on sample C before mask removal and As cap layer deposition. It reveals a very good selectivity with respect to SiO2 and a uniform filling of the mask apertures with clean and well defined facets whose nature is determined by the aperture direction with respect to the (111)B-oriented substrate (figure S2). Whatever the aperture direction, the nanostructures are delimited by a top (111) surface. The atomic force microscope profile performed on an array of parallel NWs (figure S3) indicates that the top (111) surface is lying about 25 nm above the SiO2 surface which is consistent with a nominal NW thickness deposition of 30 nm and a SiO2 mask thickness of ~10 nm remaining after HF treatment prior to the growth. On the InP(001) substrate, the growth of a GaSb nanotemplate prior to the InAs film is necessary to ensure the continuity of a thin channel in the mask apertures. The SEM observations performed on sample D confirm the excellent selectivity and the very good continuity of the in-plane nanostructures in [𝟎𝟏 ̅ 𝟎] and [110] directions with well-defined facets (figure 3 and figure S4). The cross-sectional STEM analysis performed on a [110]-oriented NW and the associated EDX analysis reveals that the InAs channel adopts the shape of the underlying GaSb template with two lateral tilted wings grown on the (111) facets of the GaSb hexagonal prism (figure 3c-f). This is also true when the width changes from 100 nm to 200 nm (figure S5a). On the top (001) plane of the GaSb template, the InAs channel thickness is about 15 nm, slightly larger than the intended thickness. The same analysis also shows that the InAs channel is fully covered with GaSb even at the edge of the wings, preserving it from further oxidation. In the [𝟎𝟏 ̅ 𝟎] direction, the GaSb template looks more like a flattened cylinder for both widths of 100 nm and 200 nm (figure S5d andg). The growth of the InAs channel occurs predominantly on the top (001) GaSb facet, with two small separated channels observed on the sidewall of the GaSb template. Once again, the HAADF-STEM images show that the light grey-colored top InAs channel is embedded in GaSb and, hence, protected from further oxidation. The TEM bright field micrographs of figure S6 reveal that, despite the interface dislocation array formed at the GaSb/InP interface, some threading dislocations are still present inside the GaSb buffer. Their density appears to decrease with narrower apertures. For 100 nm wide ones, we note that the threading segments do not seem to reach the top InAs channel where neither threading dislocations nor stacking faults or twin defects are observed.

Both types of NWs are characterized with the 4P-STM setup for the main crystallographic orientations of the nanowires, i.e, the [010] and [110] orientations for NWs grown on InP (001) substrates and the [𝟎𝟏 ̅ 𝟏] and [𝟐 ̅ 𝟏𝟏] orientations for NWs grown on InP (111)B substrates. Whatever the chemical nature of the top facet in electrical contact with the STM tips, the variation of the potential measured with the inner probes as a function of the current injected and collected by the outer probes is linear. The slope of the V(I) curves yields the fourpoint resistance, R4P. As shown in figures 4 and 5 (also figures S7 and S8), R4P varies linearly with the separation of the inner tips, consistent with a diffusive transport regime. The resistance per unit length is about a few kΩ.m -1 , with a smaller resistance for the NWs embedded in GaSb. Such a range is comparable with the values of R4P measured for freestanding InAs NWs with a slightly larger diameter and grown based on the VLS mechanism [29]. It is also consistent with the resistance per unit length measured on InAs NWs grown on top of GaAs nanomembranes [21] and InAs NWs based on a template-assisted selective epitaxy when the diffusive transport regime is reached [15]. To assess the electrical quality of the NWs, four-point probe measurements of the resistance are also performed with samples A and B. As shown in figure 6, the R4P values are almost constant whatever the equidistant tip separation between 100 µm down to a few microns for both temperatures of 300 K and 115 K. Such a behavior is consistent with a 2D conductance [24]. As the four-point probe method shows some fluctuations, due to a small misalignment in the positioning of the STM tips, the transport properties of the 2D heterostructures are further studied with the Van der Pauw structures built in other areas of the same samples (right inset of Fig. 6). The Hall data of samples A and B are summarized in table 1. FIG. 6. Variation of the four-point probe resistance as a function of equidistant probes separations. The resistances deduced from the Van At 300 K, quasi-identical Hall resistances are achieved for both heterostructures, the higher mobility in sample A (33500 cm 2 .V -1 .s -1 ) being compensated by a lower sheet carrier density. At 77 K, the electron mobility increases to more than 300000 cm 2 .V -1 .s -1 for sample A with AlGaSb barriers whereas sample B exhibits half of this value. This difference is attributed to the lower conduction band offset between GaSb and InAs, which limits the electron confinement in the channel and expands a significant part of the electron wave function inside the larger electron effective mass GaSb barriers. Despite the type III configuration of the InAs/GaSb system and the thick GaSb buffer layer, it is interesting to notice that the transport is dominated by the electrons flowing in the InAs channel with a high mobility.

Table 1. Hall data measured on the 2DEG of samples A (AlGaSb/InAs heterostructure) and B (InAs/GaSb heterostructure).

For comparison of the resistance between both techniques, the sheet resistance found with the Van der Pauw geometry is converted into a four-probe resistance [24],

𝑹 𝟒𝑷 = 𝒍𝒏𝟐 𝝅 𝑹 𝒔𝒉 (1) The results are plotted in figure 6. Although the separation between the macroscopic electrodes is larger than the STM tip separations, the data fall into the range of the measured resistances with 4P-STM at room and low temperatures, demonstrating the high quality of the heterostructures across the samples.

The resistances per unit of length measured for all the NWs are normalized by their width, which is deduced from the cross-sectional STEM analysis. For that purpose, the total width of the InAs channel for the [110]-oriented InAs/GaSb core-shell NWs takes into account the top (001) facet and the (111) side facets. Although the channel thickness seems reduced on the (111) facets, we assume a constant thickness of the InAs channel for the calculation of the sheet resistance. This approximation slightly over-estimates the sheet resistance values for [110]-NWs. Conversely, only the width of the top channel is considered for the [010]-oriented InAs/GaSb coreshell NWs. As the charge density is propably highly non uniform within the thickness of the InAs channel, we do not compare the resistivity of the different channels but the sheet resistance. This is particularly true for the 30 nm-thick InAs NWs without GaSb cap where the charge density results from the surface Fermi level pinning in the conduction band. Figure 7 summarizes the sheet resistances estimated on the different NWs for both NW widths of 100 nm and 200 nm and compares them with the sheet resistance found in the Van der Pauw structures obtained at room temperature. When the InAs NWs are directly grown on the (111)B-oriented InP substrate, whatever the orientation of the NWs is, the sheet resistance is about two times higher than the one for the InAs/GaSb coreshell NWs. This result is consistent with the observation of a doubling of the mobility when an InGaAs buffer layer is used in SAE NWs grown on GaAs (001) substrate to improve the interfacial quality of the InAs NWs [23]. It shows the key role of the pseudomorphic barriers that surround the InAs channel to reduce the deleterious effect of the surface states or mismatch interface states on the transport properties. For the [110]-oriented core-shell NWs, shrinking the width of the aperture seems to improve the sheet resistance. This is consistent with the reduction of the density of dislocations that originate from the mismatched GaSb/InP interface and thread up to the InAs channel as shown in figure S6.

Thanks to the presence of the GaSb buffer and capping layers, the conductance of the InAs channel is close to the one of the 2D InAs/GaSb heterostructure of samples A and B at 300 K. If one considers a sheet electron concentration in the InAs NWs of sample D similar to the one obtained from the Hall measurements in samples A and B (~2x10 12 cm -2 ), this implies an electron mobility as large as 16600 cm 2 .V -1 .s -1 at room temperature for the 100 nm-wide [110]-oriented NWs.

IV. CONCLUSION

The sheet conductance of in-plane InAs NWs grown on InP substrate and measured by 4P-STM is significantly improved when the InAs channel is embedded in a GaSb shell. The shell protects the electrons from surface state as well as mismatch accommodation scattering. While still larger than the conductance measured by Hall effect and confirmed by 4P-STM measurements on InAs/GaSb 2DEG, its value is close to the quantum well conductance at room temperature. Further investigations are now needed to evaluate the transport properties of InAs/GaSb in-plane NWs at cryogenic temperature. But the estimated mobility values at room Improving the intrinsic conductance of selective area grown in-plane InAs nanowires with a GaSb shell (Supplementary information)

FIG. 1 .

 1 FIG. 1. Schematic structure of the grown samples: (a) InAs/AlGaSb quantum well grown on GaAs (001), (b) InAs/GaSb quantum well grown on GaAs (001), (c) in-plane InAs NWs grown on InP(111)B and (d) InAs/GaSb core-shell nanostructures grown on InP(001).

FIG. 3 .

 3 FIG. 3. SEM micrographs of in-plane InAs/GaSb NWs grown by SAE on InP(001) (sample D). The 100 nm-wide NWs are oriented along (a) the [01 ̅ 0] and (b) [110] crystallographic directions. Insets: Magnified view of the NW end. (c) Cross-sectional high angle annular dark field (HAADF) STEM image of an InAs/GaSb NW oriented along the [110] crystallographic direction. Elemental mapping of the NW for (d) Sb, (e) In, (g) Ga and (f) As.For sample D, the mask is designed on a semi-insulating InP(001) substrate and consists of apertures with length of several micrometres and widths of 100 nm or 200 nm. The apertures are oriented along the [110] or [𝟎𝟏 ̅ 𝟎] directions. After the removal of the InP oxide as described above for sample C, a 100 nm-thick GaSb layer is first grown at a temperature of 470°C, with a growth rate of 0.1ML.s -1 , a Sb/Ga flux ratio of 2.5 and under atomic hydrogen exposure. These conditions have been demonstrated suitable for selective epitaxy as well as to optimize the GaSb nanostructure morphology on GaAs or InP (001) substrates[21,28]. InAs is then deposited on the GaSb nano-template with a nominal deposited thickness of 10 nm. A 10 nm-thick GaSb cap is finally deposited on the nanostructures.The morphology of the nanostructures is analysed using Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM) and, for some NWs, Scanning Transmission Electron Microscopy (STEM) after preparation of thin cross-sections through the in-plane NWs using Focus Ion Beam (FIB) etching. The STEM studies are performed in a Titan Themis 200 (FEI) microscope equipped with a spherical aberration corrector on the probe and an Energy-Dispersive X-ray spectroscopy (EDX) system super X (0.7 srad solid angle of collection). The accelerating voltage is 200 kV. The (half) convergence angle of the probe is 17.6 mrad and the probe current 85 pA.The transport properties of 2DEG in samples A and B are investigated at 300 K and 77 K by Hall measurements after the fabrication of Van der Pauw devices using optical lithography, chemical etching of the epitaxial layer down to the GaAs substrate and indium contact deposition. A picture of sample A after the Van der Pauw device fabrication can be seen in the right inset of figure6. In parallel, the sheet resistance of the 2DEG in samples A and B is also deduced from the 4-probe measurements of the resistance with 4P-STM working in UHV (Nanoprobe, Omicron Nanotechnology). As the use of good electrical contacts is essential to inject and extract charge carriers, tungsten tips are prepared by an electrochemical etching in NaOH and thoroughly annealed in the UHV preparation chamber to remove the thin oxide layer covering the tips.Prior to the 4P-STM transport measurements, all the samples are annealed at 120°C in UHV for a few hours. The InAs NWs

FIG. 4 .

 4 FIG. 4. Variation of the four-point probe resistance measured at different inner probe distances d on a bare [01 ̅ 1]-oriented InAs NW (purple diamond) and on a bare [2 ̅ 11]-oriented InAs NW (green stars), both with an aperture width of 100 nm. Purple and green lines are best linear fits of the data, from which the resistance per unit of length is extracted. Top inset. SEM image of the [2 ̅ 11]-oriented InAs NW grown on the InP(111)B substrate and in electrical contact with the four STM tips. The outer tips, which inject and collect the current are labelled Source I and Sink I, the inner tips, which measure the potential drop along the wire, are labelled V1 and V2. Bottom inset: V(I) curves measured at different tip separations and corresponding to the set of purple diamond data.

der

  Pauw devices are also indicated (cross) and horizontal lines intersecting these resistances are used as guidelines for comparison. Inset (left): SEM image of four collinear STM tips in electrical contact with Sample A at 300 K. The outer tips, which inject and collect the current are labelled Source I and Sink I, the inner tips, which measure the potential drop along the wire, are labelled V1 and V2. Right inset: photograph of a Van der Pauw sample.

FIG. 7 .

 7 FIG. 7. Sheet resistance estimated from four-probe resistance measurements on NWs of sample C and D and benchmarked with the sheet resistance of InAs/GaSb 2DEG (sample B).

W 1 1

 1 FIG.S1. Band diagram simulation of the 2DEG formed in sample A (left) and sample B (right) using Nextnano software[1]

ACKNOWLEDGEMENTS

This study was financially supported by the French National Research agency (INSPIRING project ANR-21-CE09-0026-01), the IEMN PCMP-PCP and CMNF platforms of the French Technological Network RENATECH, and the Région Hauts de France. 10 FIG. S7. Variation of the four-point probe resistance measured at different inner probe distances d on different 100 nm-wide (a) InAs/GaSb NWs of sample D and (b) InAs NWs of sample C. Lines are best linear fits of the point data. FIG. S8. Variation of the four-point probe resistance measured at different inner probe distances d on different 200 nm-wide (a) InAs/GaSb NWs of sample D and (b) InAs NWs of sample C. Lines are best linear fits of the point data.