S Baghernezhad-Tabasi

L Druette

F Jouanot

C Meurger

M C Rousset

IOPE: Interactive Ontology Population and Enrichment Guided by Ontological Constraints

Keywords: Ontology Engineering, Knowledge Acquisition, Automation Form Generation, Simulation-based Training in Medecine

In this paper, we focus on the construction of specialized ontologies that capture skills of experienced experts in a particular domain with the goal to share them with a larger community of trainees or less experienced experts in the domain. Our main contribution is the automatic construction of a Graphical User Interface (GUI), named IOPE, built from the ontological constraints of an input ontology, as the support of the controlled update process of the considered ontology. The resulting GUI functions as a guidance for the experts with no knowledge of OWL/RDFS, which enables them to easily explore and update their ontologies. We illustrate the functionality of IOPE on an ontology for simulation-based medical workshops called ONTOSAMSEI. In an extensive set of experiments, we discuss the effectiveness and efficiency of our proposed approach in a specialized medical domain.

Introduction

Ontologies are the backbone of many information systems that require access to structured knowledge. By their very nature, real world ontologies are dynamic artifacts that evolve both in their structure (the data model) and their content (instances). Keeping them up-to-date is a critical operation for most applications which rely on semantic Web technologies. Ontology updates encompass both enrichment and population. Ontology enrichment is the task of extending an existing data model of an ontology with additional concepts and semantic relations, while ontology population is the task of adding new instances of concepts to the ontology, using domain documentations. Ontology updates are typically performed in an exploratory and manual fashion, as the non-documented knowledge of the domain expert is required to be taken into consideration. However, these manual updates put burden on the experts and render the whole ontological ecosystem inefficient. In this paper, we advocate for an alternative and more effective approach, and propose to handle updates automatically through a few interactions with the expert, using a Graphical User Interface (GUI). The challenges associated to interaction-based automatic updates are two-fold:

• While ontologies are typically represented in the form of graphs, it is inherently difficult and counterintuitive to provide a graphical graph-based representation of ontologies for the consumption of experts. While there exist several methods to visualize a graph structure [START_REF] Henry | Nodetrix: a hybrid visualization of social networks[END_REF][START_REF] Fang | C-Explorer: Browsing communities in large graphs[END_REF], the outcome is often hard to digest by domain experts.

• It is unclear how experts should perform ontology updates through the interactions, without the prior knowledge of the formal syntax and the semantics of ontology languages.

In this paper, we propose IOPE (Interactive Ontology Population and Enrichment), a framework for the automatic construction of a Graphical User Interface (GUI) consisting of pre-filled Web pages. We leverage Web pages as a natural interaction means to tackle the challenge of counterintuitive ontology representations. IOPE generates the Web pages from ontological constraints, which support the controlled update process of a given ontology, and prefills the generated pages. While IOPE is generic and can be applied to ontologies from a variety of domains, we employ an ontology called ONTOSAMSEI [START_REF] Baghernezhad-Tabasi | OntoSAMSEI: Interactive ontology engineering for supporting simulation-based training in medicine[END_REF] as a use case, whose content helps the domain experts design teaching units for learning skills in simulation-based Medicine. ONTOSAMSEI is a hierarchy of classes and properties enriched by ontological constraints on those classes and properties, that convey the constraints that will have to be fulfilled by their future sub-classes, sub-properties or instances. ONTOSAMSEI contains 30 different types of simulation sessions formalized with properties such as the target audience, the aimed objectives, the prerequisites, the resources required (human, consumable, simulator, material), as well as the evaluation mode of prerequisites and objectives, to name a few. All these sessions have been defined with the help of many formal documentations, expert and teacher interviews, and analyses on all information from a teaching ingineer. ONTOSAMSEI is availabe in Perscido dataset storage: https:// perscido. univ-grenoble-alpes.fr/ datasets/ DS352. In this paper, we show how to exploit these ontological constraints as a source of guidance for (possibly less experienced) educators willing to design their own simulation sessions, hence addressing the challenge of expert noviceship. ONTOSAMSEI's IOPE GUI is accessible via the following link: http:// iope.tabasi.info.

The paper is organized as follows. Section 2 describes the formal background of the ontologies that we consider. Section 3 describes our methodology for the automatic construction of a GUI from an input ontology, and its usage for guiding its update (population and enrichment). Section 4 summarizes the evaluation conducted to assess the added value of the GUI for ontology updating. Section 5 is dedicated to related work, and Section 6 concludes the paper.

Formal Background

An ontology is a shared formalization of a domain of interest based on a structured vocabulary made of classes, properties and instances. Ontological constraints are declared on classes and properties to constrain their formal semantics to fit with their actual meaning in the domain of application. Then, factual statements can be added to describe specific entities as instances of classes with specific values for some properties. The ontological constraints are defined in RDFS 1 and OWL 2 , and described as RDF graphs.

RDF Format

Ontological Constraints

The ontological constraints that we consider are RDFS constraints and some OWL constraints (displayed in Table 1). These constraints form the main core for the most of domain ontologies and are sufficient for our application domains. Adding new ontological constraints will be studied in future works. Figure 1 displays part of the specialization hierarchies of properties and classes resulting from RDFS ontological constraints declared in ONTOSAMSEI.

Figure 2 shows the RDF graphs associated to two constraints declared in the ontology on the property 1 Resource Description Framework Schema (RDFS): https://www.w3. org/TR/rdf-schema 2 Web Ontology Language (OWL): https://www.w3.org/TR/ owl-features Classes samsei:Gesture samsei:Resource samsei:TeachingUnit samsei:Simula@onLearningUnit samsei:PortACathPlacement samsei:S@tch samsei:InfusionSupplies samsei:Protec@veSupplies samsei:Material samsei:HumanResources samsei:Simulator samsei:ElectronicSimulator samsei:Synthe@cSimulator samsei:Par@alManikin samsei:En@reManikin samsei:VenousChestSimulatorManikin samsei:KneeManikin samsei:simula@onSessionAudience samsei:hasTutor samsei:objec@ves samsei:prerequisites samsei:knowHowToAchieve samsei:toLearn samsei:toObserve samsei:toValidate samsei:resources samsei:equipmentSupplies samsei:humanResources samsei:simulatorRessources samsei:dura@on samsei:dura@onOfSimula@onSession samsei:numberOfLearner samsei:numberOfLearnerPerSimula@onSe samsei:forAcademicYear Proper@es owl:Thing for the class samsei:PortACathPlacement, which is a particular type of simulation learning unit that trains students to place a port or a catheter. The constraint graph in Figure 2(a) expresses that samsei:sterilecompress (which is an instance of Bandage material) is declared in the ontology as a mandatory value of the property samsei:equipmentSupplies.

The constraint graph depicted in Figure 2(b) expresses that at least one equipment of type samsei:protectiveSupplies is mandatory for simulating a placement of a port or a catheter.

Interactive Ontology Update

Our approach consists of transposing the RDF data and the ontological constraints of a given domain ontology into a graphical user interface (GUI) named IOPE GUI. The Web form templates on which the IOPE GUI is built are described using a Web form ontology called IOPE_Web that we have developed by adapting RaUL [START_REF] Haller | Raul: Rdfa user interface language -A data processing model for web applications[END_REF].

The IOPE_Web Ontology

The IOPE_Web ontology is shown in Figure 4. It is organized around 4 main classes IOPE:Page, IOPE:PageLayout, IOPE:Container and IOPE:Widget related by properties for modeling Web pages which are structured in containers with widgets and are associated with page layouts. The widgets act as a direct point of user interaction and provide access to the triples of the referenced RDF graph. The interaction with users can be done using several types of widgets such as LABEL, TREE-VIEW, LIST BOX, TEXT BOX and CHECK BOX, which leads to as many corresponding subclasses of the main class IOPE:Widget. They inherit of the standard properties for widgets that are described in IOPE_Web as datatype properties such as IOPE:name, :placeholder, IOPE:label, and others.

In our setting, the IOPE:dataSource property is used to assign an input data from a domain ontology that can be of type xsd:string, simple or nested list IOPE:list, or owl:Thing. The IOPE:value property is filled by the output value of the widget provided by a user. The boolean properties IOPE:hidden, IOPE:multiple, IOPE:readonly and IOPE:onclick are similar to HTML form attributes. A widget with the IOPE:required property as "True" will be rendered by a red asterisk to specify that the widget must be filled in by the user. Widgets can be grouped in a Web page within containers that can be nested using the IOPE:partOf property. In our setting, different types of specific containers are declared as subclasses of IOPE:Container to express that the different types of ontological constraints in our setting will be rendered in a specific manner in the IOPE GUI.

Ontology-Based GUI Construction

We have followed a declarative approach based on a set of mapping rules to generate automatically pre-filled Web pages, and on a set of binding rules to generate RDF graphs from entered values by users via widgets. Input: The input of GUI construction is a domain ontology in which the ontological constraints have been automatically saturated by a reasoning algorithm as detailed in [START_REF] Baghernezhad-Tabasi | IOPE: Interactive Ontology Population and Enrichment[END_REF]. Initialization: The GUI construction is initiated with the choice of one class of interest in the ontology by the user, which is called the focus class F. The set Constraints(F ) of the ontological constraints associated to the focus class F is decomposed in groups Group(P, F ) of all the constraints involving sub-properties of a given property P . For the focus class F , and for each group of properties Group(P, F ), an instance of a Web page is created with the page layout depicted in Figure 5, which sets up the organization within the page of the specific containers dedicated to the different types of constraints on subproperties p of P for which there exists constraints in Group(P, F ). The following instances of the IOPE:Container class are • IOPE:FocusClass F Container denotes the main container of the created Web page,

• IOPE:Group(P, F )Container denotes the container that will group all the containers corresponding to the constraints holding for F on sub-properties of P ,

• IOPE:ConstraintContainer p denotes the container that will display the restrictions of F on property p,

• IOPE:HasValueContainer p denotes the container that will display the hasValue restrictions of F on property p,

• IOPE:AlternativeValuesContainer p denotes the container that will display the alternative values restrictions of F on property p,

• IOPE:CardinalityContainter p, C denotes the container that will display the cardinality restrictions of F on property p and class C,

• IOPE:RangeContainter p, C denotes the container that will display the range restrictions of F on property p which is class C,

• IOPE:FreeEntryContainer p denotes the container for the user to add new classes involved in cardinality restrictions for the property p.

Then mapping rules are triggered for mapping components of each ontological constraints to the visual widgets in the prepared containers in order to fill each Web page guided by the ontology.

Mapping rules: Each mapping rule has a constraint graph pattern in its left-hand side and a IOPE_Web graph pattern in its right-hand side. The constraint graph pattern expresses a particular ontological constraint on the focus class and can be instantiated via the input data. The corresponding instantiation of IOPE_Web graph pattern in the right-hand side is a specification using the vocabulary of the IOPE_Web ontology of how to fill the corresponding widgets and containers in the corresponding Web page.

The mapping rules can be triggered in a forward-chaining manner and in any order. The resulting IOPE_Web graph provides the full RDF specification of the pre-filled Web pages that have to be created for the focus class chosen by the user. The effective implementation of the mapping rules is implemented using RDFLib and JSON libraries in Python 2.7.16 language. Our code is publicly available in [START_REF]IOPE implementation[END_REF]. The set of mapping rules are given in a companion report [START_REF] Baghernezhad-Tabasi | IOPE: Interactive Ontology Population and Enrichment[END_REF]. Here, we just give two of them in their instantiated form for clarity purpose.

Figure 6 shows a mapping rule for a value restriction (F p value v).

The specific container IOPE:HasValueContainer p is decomposed in two sub-containers defined as blank nodes whose types are IOPE:HasValueInstanceContainer and IOPE:HasValueClassContainer respectively. For these two sub-containers, widgets of type IOPE:LABEL are created as blank nodes with the property IOPE:dataSource filled by the corresponding labels of v and its class C in the domain ontology. The property IOPE:required is set to "True" for the first widget to refer that the value v is mandatory for the property p.

Figure 7 shows a mapping rule for a cardinality restriction (F p min n C) such that n > 0, where C has a hierarchy of sub-classes and a list of instances in the domain ontology.

The specific container IOPE:CardinalyContainer p, C is decomposed in two sub-containers defined as blank nodes whose respective types are:

• IOPE:CardinalityClassContainer

• IOPE:CardinalityInstanceContainer

For the former, a widget of type IOPE:TREEVIEW is created as a blank node with the property IOPE:dataSource filled by the tree view of subClasses(C), which denotes the hierarchy of the sub-classes of C in the domain ontology enriched with an additional item Other_C.

The property IOPE:required and IOPE:onClick are set to "True" for this widget to indicate that entering at least one value is mandatory for the property p, and this widget supports the interaction with users to display interactively the sub-class hierarchy.

For the latter, a widget of type IOPE:LISTBOX is created as a blank node with the property IOPE:dataSource filled by the list instances(C) of instances of the class C, the IOPE:label property set to "select existing item(s) or enter new item(s)" and the IOPE:hidden property set to "True" to make the widget invisible until the first interaction of the user through the widget of type IOPE:TREEVIEW. A widget of type IOPE:TEXTBOX is also created with the IOPE:placeholder property set to the value "Enter the new item(s) (separated by a comma)" in order to give users possibility to enter new instances. The other binding rules are given in [START_REF] Baghernezhad-Tabasi | IOPE: Interactive Ontology Population and Enrichment[END_REF].

Evaluation

The objective of our study is to evaluate the efficiency, the users' satisfaction and the effectiveness of the IOPE interface with the purpose of populating and enriching the ONTOSAMSEI ontology. The users involved in our user study are a subgroup of 22 experts in simulationbased training in Medicine. They are domain experts but they are not familiar with RDF and OWL. The user study was organized in two steps for each expert. In the first step, the expert logs in the system with her credentials, picks one simulation training session, and begins to observe and update the information in the pre-filled Web pages.

In the second step, she will be transferred to a survey form to evaluate some qualitative aspects of IOPE and ONTOSAMSEI ontology and reflect her viewpoint based on her interactions with the IOPE interface.

Evaluation of the IOPE GUI Efficiency

We first provide quantitative results on the time spent by users and their number of interactions with IOPE . Then, we compare these results with the time insight perceived by users and with the number of interactions required for Enter the new item a comma).

IOPE:placeholder

Select exis:ng item(s) or enter new item(s)

IOPE:label

Enter the new item(s) (separated by a comma) or give a minimal number of items

IOPE:placeholder

SimulaFon training session of Port-a-cath placement

Equipment and supplies: (*)

Other :

Provide the label(s) (separated by a comma).

Simple disposal drape Fenestrated disposal drape

Select exis@ng item(s) or enter new item(s):

Enter the new item(s) (separeted by a comma).

Resources

Sterile compress (Bandage material) (*)

Protec@ve supplies (*)

Disposable drape

Simulator-type resources: (*)

Venous-access chest simulator manikin (*) Provide item(s):

Enter the new item(s) (separeted by a comma) or give a minimal number of items.

Other :

Provide the label(s) (separated by a comma).

Warning! To save the informa/on entered on this page, you must click on "Save

SimulaFon training session of Port-a-cath placement

Equipment and supplies: (*)

Other :

Provide the label(s) (separated by a comma).

Simple disposal drape Fenestrated disposal drape

Select exis@ng item(s) or enter new item(s):

Enter the new item(s) (separeted by a comma). seconds (1.12 minutes). On average, their number of interactions with IOPE is 5.78, with a maximum of 14 and a minimum 3. The majority of interactions are with CHECK BOX widget (56.15%) followed by TEXT BOX widget (32.30%) and LIST BOX widget (11.53%). Table 2 shows the distribution of experts in two categories of groups. In terms of number of interactions, we have built the groups of "prolific" experts (having more than 6 interactions with IOPE), "active" experts ( having between 3 and 6 interactions), and "moderate" experts (with less than 3 interactions). In terms of interaction duration, we have built the groups of experts spending "short-time" (less than 2 minutes), "medium-time" (between 2 and 4 minutes), and "long-time" (more than 4 minutes). Table 3 reports the distribution of time groups for each interaction activity groups. We notice that more interactions do not necessary yield to more time spent to interact. This shows that IOPE helps experts to fulfill their task in a reasonable amount of time, even for prolific experts. 4.1.2 Time-to-Insight Users's Evaluation.

Resources

After they are done with using the IOPE interface for fulfilling their task, we ask the experts the following question to estimate the time-to-insight for a future interaction with IOPE : "how much time do you expect to take for setting up a new simulation training session with IOPE?". The response is in the form of a Likert scale from 1 to 5 where "1" means "very short time" and "5" means "very long time". Figure 11 shows the results. We observe that the majority of experts chose "short time" and "average time", i.e., options 2 and 3 in the Likert scale. Moreover, prolific experts and long-time perceive shorter expected time compared to the active and moderate experts. A possible interpretation is that more interactions and more time sent interacting with the system boosts the perception of faster delivery of required information. The goal of this experiment was to measure the addedvalue of IOPE compared to a standard ontology editor such as TOPBRAID [START_REF]Topquadrant topbraid composer[END_REF], in terms of number of interactions required to fulfill edition tasks mentioned in Table 4.

2 0 2 1 1 2 1 1 2 0 0 2 3 2 1 0 1 2 5 1 2 4 1 1 3 1 0 0 0 1 2 0 2 4
0 0 1 2 0 0 0 0 0 0 0 0 1 0 1 3 4 1 0 1 0 0 2 0 2 1 0 2 2 0 2 2 0 2 0 0 2 5 1 0 1 1 3 4 1 3 3 1 2 1 0 0 0 1 2 0 2 2

Easy-friendliness

The tasks are categorized into three levels of difficulty based on [START_REF] Dimara | A task-based taxonomy of cognitive biases for information visualization[END_REF]. TOPBRAID is a major IDE for knowledge graph management. It can play the role of a rich model, constraint, data and queries editing tool, and of a powerful querying and reasoning flexible. It is intensively used by many actors in the area of ONTOSAMSEI.

For the fairness of this experiment, since none of the Fill the number of trainees for X Medium Fill the target audience of X Difficult Fill the required resources for X domain experts have ever used TOPBRAID, the different tasks were fulfilled by the five authors of the paper who have a sufficient knowledge about the domain, as well as a sufficient experience using both IOPE and TOPBRAID. Figure 12 shows the average number of interaction steps to fulfil those tasks in IOPE and TOPBRAID. We observe

Easy task

How many participants are needed to setup X? 1.31 10.24

Medium task

What are the disciplines targeted for X? 1.62 164.17

Difficult task

What are the necessary resources to setup X? that for both tools, the number of interaction steps increases with the difficulty of the tasks. However, the IOPE's trend grows from average 3.00 steps for an easy task to average 5.72 steps for a difficult task, while using TOPBRAID grows from average 5.00 steps for an easy task to average 21.00 steps for a difficult task. This shows that IOPE , by weaving relevant information together using constraints, enables the experts to fulfill their tasks more rapidly than by using a standard editor.

Evaluation of IOPE Users' Satisfaction

We have measured on a Likert scale in the range 1 to 5 the assessment by users of three aspects of satisfaction, namely utility, usability, and adoption, through the questions of the three first rows of Table 5. The aggregated results are shown in the three first column of Figure 13. Utility. 82.35% of the participants have a positive view on the utility of IOPE. However, the prolific experts appreciate the utility more than active experts. This shows that more interactions increases the perception of utility, which is also confirmed by long-time experts who are entirely on the positive spectrum. Usability.

Overall, the experts perceived usability positively. However, there is a vivid contrast between moderate experts versus active and prolific experts, where the former group seems to not enjoy the usability of IOPE. We conjecture that moderate experts got lost early in the process, and abandoned their task. There is also a subset of long-time experts who assessed low usability. They probably spent too much time to fulfil their tasks and got lost in the process also. Adoption. The choice over adoption is from 1 to 5, where 1 means "never" and 5 means "always". Most of the experts voted to adopt IOPE in the future.

Effectiveness of IOPE for Enriching the ONTOSAMSEI Ontology

In this part of the experiment, we measure the expert's assessment of accuracy and completeness of the ONTOSAMSEI ontology through its presentation to the experts by IOPE GUI. We do it by asking the experts the questions in the two last rows of the Table 5. The aggregated results (on the Likert scale from 1 to 5) are shown in the two last columns of Figure 13.

Accuracy. The majority of the participants are positive on accuracy, while 11.76% are negative. Short-time and moderate experts express more negative votes on accuracy compared to long-time and prolific experts, respectively. This is presumably because less investigations in the former groups did not enable them a precise view of the ontology.

Completeness.

76.46% of the participants find ONTOSAMSEI complete enough. However, prolific experts appreciate completeness less than the overall population. We found out that they prominently interact with text-boxes, which shows that they use IOPE to effectively enrich the ontology. The entire long-time expert group votes positively, which means that spending more time to go into the details of the simulation training sessions convinces them of their completeness.

Related Work

In the literature, ontological updates are often performed using ontology editing tools, such as PROTÉGÉ [START_REF] Noy | Creating semantic web contents with protégé-2000[END_REF], TOPBRAID [START_REF]Topquadrant topbraid composer[END_REF], and ONTODIA [START_REF] Mouromtsev | The simple webbased tool for visualization and sharing of semantic data and ontologies[END_REF]. However, these systems require a basic understanding of the RDF notation and of the OWL semantics to edit the ontology consistently. Graph-based editing approaches alleviate this limitation by leveraging shapes graphs in the form of SHACL standard3 [START_REF] Wright | Schímatos: A shacl-based web-form generator for knowledge graph editing[END_REF][START_REF] Valdestilhas | Voceditor an integrated environment to visually edit, validate and versioning rdf vocabularies[END_REF]. While shapes graphs are well adapted for editing complex data, they require the definition of such graphs for each ontology. In contrast, IOPE abstracts all RDF/OWL technicalities and seamlessly enforces the ontological constraints as a strong guidance for the experts to update the ontology, using the pre-filled forms. WebVOWL [START_REF] Wiens | Webvowl editor: Device-independent visual ontology modeling[END_REF] is a web application for the interactive graph-based visualization of ontologies which employs the Visual Notation for OWL Ontologies (VOWL) [START_REF] Lohmann | Visualizing ontologies with VOWL[END_REF]. However, WebVOWL does not visualize the instances but only the OWL part of a (possibly populated) ontology. Also, the graphs displayed by the tool tend to become quickly illegible when their size increases. In IOPE, we employ Web forms as a more widespread medium for visualizing information, and we support the update of instances and of ontological constraints. Forms are also used in [START_REF] Maillot | Nested forms with dynamic suggestions for quality RDF authoring[END_REF] in a nested structure to capture relational aspects of knowledge graphs and update RDF data. However, the nested structure introduces increasing complexity and hence lacks intuitiveness. Moreover, the focus in [START_REF] Maillot | Nested forms with dynamic suggestions for quality RDF authoring[END_REF] is solely on the population part and the approach does not extend to OWL constraints. In [START_REF] Butt | Activeraul: Automatically generated web interfaces for creating rdf data[END_REF], Web forms are generated from ontologies (using a User Interface ontology, called RaUL) by interpreting ontology assertions as rules. While the approach only incorporates individual assertions (ontology population), IOPE serves both ontology enrichment and population, through interactions with the experts. IOPE stresses on ontological constraints as first-class citizens and renders pre-filled forms to provide a more aggregated view for the experts, which is, to the best of our knowledge, nonexistent in the literature.

In [START_REF] Wright | Schímatos: A shacl-based web-form generator for knowledge graph editing[END_REF], Web forms generation are very close to ActiveRaul approaches. Constraints are expressed using SHACL language as SHACL shapes. The SchÍmato application manages the web form generation, the end-user interaction and the ontology engineer enrichement. While end-user interactions are limited to add and update instances of a knowledge graph, IOPE allows end-users to enrich the knowledge graph by updating classes and some constraints on data. IOPE has been applied and evaluated on a complex domain and is able to generate a sequence of web pages that structures the knowledge graph for the end-users, and not only a simple web form generator.

Conclusion

In this paper, we have presented the interactive IOPE framework for enrichment and population of specialized ontologies.Given any input ontology, IOPE exploits the ontological constraints and a set of mapping rules to generate a set of user-friendly Web pages which assist the experts in editing the ontology. Binding rules are then used to derive the RDF graphs corresponding to the updates entered by the experts. We have conducted an extensive set of experiments on the domain of simulation-based medical education, for measuring IOPE's efficiency, effectiveness, as well as the experts' satisfaction in fulfilling their tasks using IOPE . In the future, we plan to improve the explainability of IOPE to reduce the number of abandoned editing tasks and increase its usability by domain experts not familiar with ontology engineering.

Figure 1 :

 1 Figure 1: A part of hierarchy of properties and classes in ONTOSAMSEI

Figure 2 :

 2 Figure 2: Two constraint graphs (a) and (b) on the property equipmentSupplies for the class PortACathPlacement

Figure 3 :

 3 Figure 3: Overview of IOPE workflow

Figure 4 :Figure 5 :

 45 Figure 4: The IOPE Web form ontology

Figure 8 -

 8 Figure8-left shows one of the resulting pre-filled Web pages generated by the HTML implementation of the IOPE_Web specification resulting from the application of the mapping rules to the ONTOSAMSEI's ontological constraints. Figure8-right shows the effect of a user interaction through the widget of type the IOPE:TREEVIEW to select the sub-class DisposableDrape from the ProtectiveSupplies sub-class hierachy. As a result of this interaction, the instance container corresponding to the selected sub-class becomes visible to let the user select an instance or enter a new one. User interaction are guided by constraints on properties based on the mapping rules, which allow to check cardinality, domain and codomain. The input entered by the user must be bound to RDF data corresponding to new instances or new constraints submitted to populate or enrich the domain ontology. This binding mechanism is based on a set of binding rules that are triggered on IOPE_Web graphs to generate RDF graphs built on the domain ontology. Binding rules: Each binding rule is defined as a diagram with a IOPE_Web graph on the left side and the corresponding generated triples in the form of RDF graph on the right side. The binding rule shown in Figure9is triggered when a focus class F is chosen. This rule simply creates an instance f of the focus class F . The other binding rules are triggered when the IOPE:value property is filled by an input provided by the user through an interactive widget. Figure10shows the binding rule for the textbox widget in the free entry container of a property p for the focus class F . Its application generates a new constraint graph expressing a new cardinality constraint for F on the property p and a new class. The other binding rules are given in[START_REF] Baghernezhad-Tabasi | IOPE: Interactive Ontology Population and Enrichment[END_REF].

Figure 6 :

 6 Figure 6: Mapping rule for a value restriction (F p value v) where v rdf:type C cardinality model 1 and 2-V 3

Figure 7 :

 7 Figure 7: Mapping rule for a Cardinality constraint where subClasses(C) and instance(C) are not empty

Figure 8 :BindingFigure 9 :Figure 10 :

 8910 Figure 8: Left: HTML Web page generated from the outcome of the application of mapping rules on ONTOSAMSEI ontological constraints. Right: HTML Web Page changes after user interaction by the widgets.

Figure 11 :

 11 Figure 11: Time-to-insight results.

1

 1

Figure 12 :

 12 Figure 12: Comparative number of interactions between IOPE and TOPBRAID.

Figure 13 :

 13 Figure 13: Satisfaction and effectiveness metrics results.

Table 1 :

 1 RDFS and OWL constraints considered in this paperIt functions as a guidance for domain experts to easily explore the ontology and update it through interactive graphical widgets. The input entered by domain experts through the IOPE GUI is transformed into RDF triples that must be verified by a specialist in knowledge management, to maintain ontology correctness, before being added effectively in the domain ontology. Figure3is an overview of our interactive IOPE system.

	Type		Shortened syntax	Semantics
	Class specialization	(C rdfs:subClassOf D)	∀ i ((i rdf:type C) ⇒ (i rdf:type D))
	Property specialization	(p rdfs:subPropertyOf q)	∀ i ∀ j ((i p j ) ⇒ (i q j))
	Domain restriction	(p rdfs:domain C)	∀ i ∀ j ((i p j ) ⇒ (i rdf:type C))
	Range restriction	(p rdfs:range D)	∀ i ∀ j ((i p j ) ⇒ (j rdf:type D))
	Value restriction	(C p owl:hasValue v)	∀ i ( (i rdf:type C) ⇒ (i p v))
	Alternative values restriction (C p owl:oneOf [v1, ..., vn])	∀ i ( (i rdf:type C) ⇒ k∈[1..n] (i p vk))
	Cardinality restriction	(C p min k D)	∀ i ( (i rdf:type C) ⇒ ∃o 1 , ... o k ( i,j∈[1..k] o i = o j
				∧ j∈[1..k] (o j rdf:type D) ∧ (i p o j ))
	INPUT
	RDF Data	Ontological Constraints
		(1) Decode
	User Interface	Interac.ons
	Updated RDF Data	Updated Ontological Constraints

(4) Encode Domain expert

HasValue InstanceContainer IOPE:HasValue ClassContainer IOPE:Cardinality ClassContainer IOPE:Cardinality InstanceContainer IOPE:Range ClassContainer IOPE:Range InstanceContainer IOPE:FreeEntry Container IOPE:Alterna:ve ValuesContainer

	IOPE:PageLayout	IOPE:has	IOPE:Page
					IOPE:contain	IOPE:partOf
					IOPE:Container
					IOPE:hasWidget
	xsd:string		xsd:boolean		xsd:string	xsd:string xsd:int ∪	IOPE:
	IOPE:placeholder	IOPE:readonly	IOPE:name	IOPE:value
	xsd:boolean	IOPE:required		IOPE:hidden	xsd:boolean
					IOPE:Widget
		IOPE:onClick		IOPE:mul.ple
	xsd:boolean					xsd:boolean
						IOPE:dataSource
		IOPE:label
	xsd:string				rdfs:subClassOf	xsd:string IOPE:list owl:Thing ∪ ∪
	IOPE:LABEL IOPE:TREE VIEW	IOPE:LISTBOX	IOPE:CHECKBOX	IOPE:TEXTBOX

rdfs:subClassOf

Table 2 :

 2 Distribution of expert groups

		moderate	active	prolific
	Expert population	22.73%	50%	27.27%
		short-time medium-time long-time
	Expert population	50%	31.82%	18.18%

Table 3 :

 3 Distribution of interaction time groups for interaction volume groups.

			Interaction volume groups
			moderate active prolific
	Interaction	short-time	0.80	0.46	0.33
	time	medium-time	0.00	0.27	0.67
	groups	long-time	0.20	0.27	0.00

Table 4 :

 4 Tasks descriptions

	Task	Description (Given the simulation training session X ...)
	Easy

Shapes ConstraintLanguage (SHACL): https://www.w3.org/TR/shacl/

Table 5: Measure definitions and corresponding questions asked in the survey.

Measures

Definition Question asked in the survey utility [START_REF] James | Illuminating the Path: The Research and Development Agenda for Visual Analytics[END_REF][START_REF] Albert | Measuring the user experience: collecting, analyzing, and presenting usability metrics[END_REF] The usefulness of the method to fulfil a given task.

How do you evaluate the utility of IOPE for setting up simulation training sessions? usability [START_REF] Rahman | Evaluating interactive data systems[END_REF][START_REF] Albert | Measuring the user experience: collecting, analyzing, and presenting usability metrics[END_REF] The easiness of interactions with the method To which degree do you find IOPE easy-to-use?

adoption [START_REF] James | Illuminating the Path: The Research and Development Agenda for Visual Analytics[END_REF] The usefulness of the method for future similar tasks How often will you employ IOPE for setting up and describing a new simulation training session in the future?

accuracy [START_REF] Omidvar | Data pipelines for user group analytics[END_REF][START_REF] Rahman | Evaluating interactive data systems[END_REF] The precision of information based on expert's prior knowledge.

How do you evaluate the accuracy of IOPE's pre-filled information for describing simulation training sessions?

completeness [START_REF] Rahman | Evaluating interactive data systems[END_REF] The retrieval exhaustiveness of the necessary and required information.

How do you evaluate the sufficiency of IOPE's pre-filled information for describing simulation training sessions?


Gheorghe Taran
email: gheorghe.taran@kit.edu

Edgar Bonet
email: bonet@grenoble.cnrs.fr

Wolfgang Wernsdorfer
email: wolfgang.wernsdorfer@kit.edu

Decoherence measurements in crystals of molecular magnets

Decoherence processes in crystals of molecular magnets are prototypical for interacting electronic spin systems. We analyze the Landau-Zener dynamics of the archetypical TbPc2 complex diluted in a diamagnetic monocrystal. The dependence of the tunneling probability on the field sweep rate is evaluated in the framework of the recently proposed master equation in which the decoherence processes are described through a phenomenological Lindblad operator. Thus, we showcase low temperature magnetic measurements that complement resonant techniques in determining small tunnel splittings and dephasing times.

Introduction.-The coherent dynamics of an ensemble of weakly coupled spin systems is central to both the development of mesoscopic quantum physics 1,2 and to the fast advancing field of quantum engineering [3][4][5] . Amongst solid state electron spin systems that are researched as potential quantum bits, (e.g. semiconductor quantum dots 6 , nitrogen vacancies centers in diamond 7 , molecular magnets, phosphorus or bismuth in silicon 8 ), molecular magnets proved to be especially useful model systems. Thus, many purely quantum phenomena like ground state tunneling 9 , phonon and photon assisted tunneling transitions 10,11 , spin parity and quantum phase interference 12 , phase coherence and Rabi oscillations 13 were analyzed in great detail in these systems. When it comes to the study of decoherence, the common ground between different qubit systems is found in the description of the environment by standardized models like oscillatory or spin baths 1 . The main advantages of molecular magnets arise from their diversity and chemical tunability of the spin ground state and the intra-and intermolecular interactions (e.g. through the appropriate choice of the organic ligands) 14,15 . Thus, one of the best characterized molecular system, the Fe 8 complex 16 , was used to validate the theory of environmental decoherence against experiment 2 . In the above experiment as well as the breakthrough achievements like the first measurements of the spin relaxation times 17 and the observation of millisecond coherence time and Rabi oscillations at room temperature [18][19][20] , electron paramagnetic resonance (EPR) was the technique of choice. However, the stringent requirement for a system to be susceptible to EPR investigation is a large coherence time 21 . Through this work we show that using incoherent Landau-Zener tunneling dynamics 22 we are able to determine the intrinsic tunneling time and the decoherence rate, thus complementing the resonance techniques and providing a new tool to probe the quantum properties of molecules that could be candidates for implementing quantum bits.

We analyze the magnetic response characterizing a diluted crystal of terbium(III) bis(phtalocyanine) (TbPc 2 ) lanthanide single ion molecular magnets (SIMMs). Amongst already numerous example of SIMMs, the TbPc 2 complex makes its claim to fame through events central to the development of both the field of single molecule magnets and molecular spintronics. First, the analysis of its magnetic bistability proved that a molecular complex with a single magnetic center can exhibit a large effective energy barrier 23 . Second, the possibility to dilute the TbPc 2 molecules in a isostructural diamagnetic matrix and the strong hyperfine interaction, characteristic of lanthanide ions, allowed to experimentally evidence the resonant quantum tunneling between mixed states of electronic and nuclear origin 24 . Furthermore, the planar structure of the molecule made possible its deposition on different substrates, and thus subsequent inclusion in spintronics devices 25,26 . The last point is especially relevant in the race to develop quantum information processing devices 4 . An example of the symbiotic relationship between the fundamental research and technological application is given by the TbPc 2 single molecule spin transistor. It was first used to read out and control both the electronic and the nuclear spin 27 , then to successfully implement quantum algorithms 28 . The same device provided the experimental means to explore how the effective character of the resonant tunneling changes when the dephasing of environmental or measurement origin is taken into account 22 .

We start by reviewing the low temperature magnetic properties of the TbPc 2 complex and the Landau-Zener formalism in which it's dynamics is studied. Then, we describe the novel method by which we obtain the dependence of the tunneling transitions on the sweeping rate, alongside presenting the first experimental evidence of the thermalization of the 159 Tb nuclear spins. Finally, the phenomenological model proposed in Ref. 22 is used to motivate the dynamics of the molecular spin and to study it quantitatively leading to experimental estimates of both the intrinsic tunneling time and the dephasing time.

Theory.-The magnetic properties of the TbPc 2 molecule are dominated by the coupling between the spin arXiv:2004.09011v1 [cond-mat.mes-hall] 20 Apr 2020 Energy (K)

B z (T)
FIG. 1. a) A zoom on the magnetic hysteresis loop of a crystal containing TbPc2 SIMMs diluted in a diamagnetic, isostructural matrix formed by YPc2 molecules, with [TbPc2]/[YPc2] ratio of 1%, measured by microSQUID technique 29 . The insets show: (left) a zoom of a level anticrossing between two hyperfine states and (right) the entire hysteresis loop. b) Hyperfine structure of the lowest doublet, mJ = ±6, as a function of an applied magnetic field.

(S = 3) and orbital (L = 3) angular momentum of the Tb 3+ ion, resulting in a total ground state angular momentum, J = L + S = 6, separated from the first exited multiplet, J = 5, by 2900 K. The interaction with the phtalocyanine (Pc) planes further splits the energy levels in the ground multiplet. The strong uniaxial character of this interaction leads to a ground doublet, m J = ±6, separated by about 600 K from the first exited doublet, m J = ±5. As we work at subkelvin temperatures, the system is confined to the two lowest states, m J = ±6, and thus the electronic spin can be treated as an effective Ising spin 1/2. In a classical world the two orientations of the molecular spin would describe two metastable states that are separated by a large energy barrier (∼ 800 K) 23 . However, this is not the case as non-axial interactions mix the m J = ±6 states, with the resulting eigenstates separated in energy by an amount called tunnel splitting (∆ -Fig. 1). Thus, transitions between different spin orientations can occur not only through spin lattice processes but also through quantum tunneling 30 .

The coupling of the molecular spin to an external magnetic field applied along the easy axis is described by the Zeeman interaction: H Z = g eff µ 0 µ B H z σ z , where g eff = 18 is the effective g-factor, and σ z is the z-Pauli matrix. For a spin 1/2, the non-axial interactions can be modelled by an effective transverse field, H x = ∆/(g eff µ 0 µ B ), so the total Hamiltonian is:

H = g eff µ 0 µ B (H z σ z +H x σ x ).
The time evolution of the magnetic moment under a changing magnetic field is given by the following master equation for the density matrix (ρ):

dρ dt = i [ρ, H] (1)
Thus, the spin reversal probability, for the case when the magnetic field is swept at a constant rate, is given by the Landau-Zener expression [31][START_REF] Zener | Proc. R. Soc. Lond. A[END_REF][START_REF] Stückelberg | [END_REF] :

P LZ = 1 -exp - π∆ 2 2 µ 0 µ B |δm|α (2)
where α is the field sweep rate and δm is the change of the angular momentum upon tunneling. At this point, two important observations need to be made. First, the Tb 3+ ion has a nucleus with a nonzero spin, I = 3/2. The strong interaction between the electronic shell and 159 Tb nucleus is described by the hyperfine term, (A hyp I • J), and the quadrupolar term, (P quad I 2 z ), added to the total Hamiltonian. The resulting hyperfine structure is shown in Fig. 1b. Thus, tunneling transitions within the doublet m J = ±6 happen between the hyperfine states |+6, m I and |-6, m I , with m I and m I taking values between -3/2 and 3/2. However, in a first approximation, we consider that tunneling transition events at different crossings are independent of each other, that is, tunneling dynamics at a specific anticrossing affects only the populations of the two levels that form it.

Second, when describing the physics of crystals of SIMMs, Eqs. 1 and 2 have a limited domain of applicability, adequately describing the experimental reality only when the characteristic time of the experiment (the time the system is driven through resonance) is considerably smaller than the characteristic time of the environmental perturbation (e.g. dephasing time). The deviations from the Landau-Zener formalism are thus due to both elastic (dephasing) and inelastic (relaxation and excitation) processes. The problem was recently analyzed using measurements performed on a single TbPc 2 molecule in a spin transistor geometry 22 and it was concluded that, in the limit of small probing currents, the dephasing processes dominates the system's dynamics. The observed behaviour was successfully modeled by a phenomenological Lindblad operator:

L(t) = 1 τ av t+τav t-τav η 2 √ τ d [| 1 (t) 1 (t)| -| 2 (t) 2 (t)|]dτ (3) where | 1,2 (t) are the time-dependent eigenstates of H, η = 1 (t)| σ z | 1 (t)
, τ d is the characteristic dephasing time representing the efficiency of the dephasing process. The time constant, τ av , was introduced as an interpolation parameter between the two limiting cases in which the environment affects the superposition of the diabatic or the adiabatic states 22,34 . The dephasing process acts through the term (2LρL † -L † Lρ -ρL † L) added to the right hand side of Eq. 1. It should be noted that, previous treatments of the dissipative Landau-Zener problem are known to theory 35 , however the main advantage of the above presented formalism lies in the ability to study the decoherence process without requiring the detailed knowledge of the coupling between the molecular spin and the environmental degrees of freedom.

Results.-With the above considerations in mind, we can start to analyze the magnetic hysteresis loop of a crystal containing TbPc 2 SIMMs diluted in a diamagnetic, isostructural matrix formed by YPc 2 molecules, with [TbPc 2 ]/[YPc 2 ] ratio of 1%, measured by mi-croSQUID technique 29 (Fig. 1a). Starting with a saturated sample, at a large negative magnetic field, and sweeping through the zero field hyperfine resonances (the level anticrossings in Fig. 1b), approximatively 85 % of the TbPc 2 SIMMs undergo quantum tunneling transitions, seen as sharp steps in the magnetization curve.

The remaining SIMMs reverse their magnetic moment at larger magnetic fields by a direct relaxation process [START_REF] Ganzhorn | Molecular Magnets[END_REF] . Quantum tunneling transitions take place between mixed states of nuclear and electronic origin, thus both spin projections can change. There is no relaxation step at zero field as the I = 3/2 nuclear spin couples to the J = 6 electronic spin resulting in a half total integer spin and, according to Kramer's theorem, the states |+6, m I and |-6, -m I , which cross at zero field, are degenerate [START_REF] Wernsdorfer | [END_REF] .

The rest of the transitions can be labeled by the change in the nuclear magnetic moment (∆m I = 0, 1 and 2, shown in Fig. 1b as a square, circle and triangle, respectively).

The step heights depend both on the initial population of the hyperfine levels and on the tunneling probability. From the Zeeman diagram in Fig. 1 one can see that the strong hyperfine and quadrupolar interaction result in exited states separated from the ground state by 122 mK, 284 mK and 476 mK. These spacings are larger than the lowest temperature of about 25 mK reached with our dilution cryostat. This suggests that any initial distribution of the nuclear spin population should evolve towards the equilibrium Boltzmann distribution.

To show this experimentally, we first sweep the field back and fourth in the region where tunneling transitions are observed (∼ [-0.05, 0.05] T) so that the nuclear spins are heated up. We then saturate the sample in a field of -1.3 T and wait for the nuclear spins to thermalize. Finally, we test the nuclear distribution by sweeping the zero field transitions once more. As the waiting time increases one observes that the steps that correspond to transitions starting from an excited state gradually diminish and then disappear (Fig. 2a). At the lowest temperature of the cryostat of ∼ 25 mK a waiting time larger than 5000 s is needed in order for the system to be completely thermalized, while for temperatures above 100 mK, a waiting time of about 2000 s is sufficient (Fig. 2). Thus, if we thermalize the sample, we know the distribution of the spins on the hyperfine states and we can use the height of the relaxation steps to obtain the tunneling transition probabilities at different crossings.

The usual approach to investigate tunneling dynamics in molecular magnets is to measure the sweeping rate dependence of the relaxation steps. Figure 3a shows the TbPc 2 's magnetization curves obtained after a waiting time of 2000 s at the cryostat temperature of 200 mK for 3 distinct sweeping rates. To extract the transition probabilities and compare it to the Landau Zener formalism we fit the magnetization curves. The model assumes an initial Boltzmann distribution and that relaxation processes around zero field are entirely described by tunneling spin flip transitions that occur with probability P i (corresponding to ∆m I = ±i). The 3 tunneling parameters, P i , are the only fit parameters used to model the magnetization curves (Fig. 3a). The relation between the magnetization steps and the tunneling probabilities is:

P i = ∆M/(2M in )
where M in is the initial magnetization corresponding to the two levels that form the anticrossing and ∆M is the step height. Thus, sweeping over a level anticrossing formed by two states, |+6, m I and |-6, m I , with initial relative populations n i and n j , modifies the population of the hyperfine levels in accord with the following relation:

n i,j = n i,j ∓ P |m I -m I | (n i -n j ).
There are 2 additional factors that come into play when modeling the measured magnetization curves. First, the steps are broadened due to dipolar interactions in the system (from experimental curves this is taken to be around ∆H 2 dip = 1 mT). Note that, if the dipolar field is quasistatic during the relaxation process of the individual molecular spins (as it is the case for diluted samples and small relaxation steps), the effect of the dipolar coupling is just to shift the time origin of the Landau-Zener process, with no effect on the dephasing process. Then, the steps are artificially broadened due to the time constant of the feedback loop of the measurement process 29 . Taking into account the above two factors results in an almost perfect fit of the experimental curves, as seen in Fig. 3a. The determined transition probabilities are shown in Fig. 3b. It is important to notice that at very slow sweeping rates (dB/dt 5 mT), the model for the magnetization curves starts to fail because the characteristic time of the experiment approaches the electronic and nuclear spin lattice relaxation times. Thus, we work in the sweeping rate range in which the tunneling dynamics dominates the direct relaxation process.

In order to characterize the dephasing process, we solve numerically the above presented phenomenological master equation and fit the spin flip transition probabilities using a nonlinear least-square algorithm with three time constants: τ ∆ , τ d and τ av . As seen in Ref. 22, if we are far from the coherent Landau-Zener dynamics, then τ d /τ ∆ and τ av /τ ∆ parameters are uniquely defined by the shape of the P (dB/dt) characteristic, while a variation of the tunneling time, τ ∆ , results in a horizontal shift along the sweeping rate axis. Additionally, to reduce the number of fit parameters, we make the requirement for τ d and τ av to be the same for ∆m I = ±1 and ± 2 transitions.

The transitions that conserve the nuclear spin (∆m I = 0) are independent on the sweeping rate (in the range tested experimentally). The plateau at P 0 = 0.5 is char-acteristic of a dephasing process that comes from a strong interaction between the system and its environment, so that the Lindblad operator is mostly constructed from the diabatic states 22 . The ∆m I = 1 and 2 transitions are well fitted by using tunneling times, (τ ∆ ≡ /∆), τ ∆ = 4.78 and 3.47 µs, respectively, and with the same dephasing (τ d = 0.33 µs or alternatively a decoherence rate γ d = 1/τ d ≈ 3 MHz) and averaging time (τ av = 93.7 µs). The sweeping rate range for which the plateau of P 0 = 0.5 is observed for ∆m I = 0 means that the tunnel splitting for this anticrossing is at least 10 times larger than the other 2 transitions (the fit curve is not uniquely defined for ∆m I = 0 transition).

The study in Ref. 22 and the present work share the same molecular complex but which is placed in very different environments. Thus, it is worthwhile to compare the measured low temperature dynamics. For the TbPc 2 molecule in a spin transistor geometry, tunneling events are observed only at the crossings that conserve the nuclear spin while for TbPc 2 in a single crystal environments, all the transitions except the ones at zero field are evidenced experimentally 24,38 . This clearly shows that the molecules in the two samples are acted upon by different transverse terms. Also, the measured P (dB/dt) characteristics differ significantly between the two experiments proving that the dynamics of a molecular spin driven though an avoided level crossing is strongly dependent on the coupling to its environment. In the former study, the conduction electrons that tunnel through the ligand quantum dot are expected to play the dominant role in the decoherence process, while for a molecular crystal at very low temperatures, the incoherent dynamics is caused mainly by the surrounding spin bath comprised of nuclear and other molecular spins. Establishing the connection between the phenomenological model that uses Lindblad operators and a microscopic description that includes explicitly the environmental degrees of freedom is an important outlook of the present study.

Conclusions.-Even though there still remain a number of open questions regarding decoherence in mesoscopic systems 1 , both theoretical and experimental progress has been reported 2,39 . This article represents another step towards understanding the complex dynamics of an ensemble of interacting quantum systems, so that we can get closer to functional devices that make use of their properties. We show that the incoherent Landau-Zener dynamics can be used to infer relevant information regarding the quantum dynamics in crystals of molecular magnets. The combination of low temperature magnetometry with appropriate theoretical tools has the potential to complement the resonant techniques used so far.

ACKNOWLEDGEMENT

We acknowledge the Alexander von Humboldt Foundation and the ERC advanced grant MoQuOS No. 741276.

FIG. 2 .

 2 FIG.2. a) Magnetization curves when the cryostat temperature is 25 mK, as a function of the time the sample is kept saturated in an external field of 1.3 T (cooling time). As the nuclear spins relax towards the ground state the steps that correspond to crossing involving an excited level gradually diminish and eventually disappear. b) Equilibrium magnetization curves at different cryostat temperatures obtained after the sample was kept polarized in 1.3 T for 4000s.

  FIG.3. a) Magnetization curves for different sweeping rates, at 200 mK, fitted by theoretical curves (black lines). The fitting procedure leads to the spin flip probability corresponding to the 3 types of anticrossings (∆mI = 0, 1 and 2). The curves were shifted vertically for a better visualization. b) Spin flip probabilities fitted to the dephasing model outlined in the text, leading to tunneling times of 4.78 and 3.47 µs for ∆mI = 1, 2, respectively and a dephasing time of 0.33 µs.


domain: phys spi

text:
Sergi Cuesta

Lou Denaix

) Le

Si Dang

Eva Monroy

Decorrelation of internal quantum efficiency and lasing threshold in AlGaN-based separate confinement heterostructures for UV emission

In this paper, we study the internal quantum efficiency and lasing threshold of AlGaN/GaN separate confinement heterostructures designed for ultraviolet laser emission. We discuss the effect of carrier localization and carrier diffusion on the optical performance. The implementation of graded index separate confinement heterostructures results in an improved carrier collection at the multi-quantum well, which facilitates population inversion and reduces the lasing threshold. However, this improvement is not correlated with the internal quantum efficiency of the spontaneous emission. We show that carrier localization at alloy inhomogeneities results in an enhancement of the radiative efficiency but does not reduce the laser threshold, more sensitive to the carrier injection efficiency. a) S. Cuesta and L. Denaix contributed equally to this work.

AlGaN is a promising material to for the fabrication of ultraviolet (UV) lasers in the range of 200-365 nm. 1 However, the implementation of AlGaN laser diodes has encountered technical challenges to achieve efficient current injection and p-type doping, which lead to high threshold devices. An alternative approach is to pump directly the semiconductor structure with a pulsed laser [2][3][4] or a high energy electron beam 5,6 , obviating the need of doping or contacts. In this context, there is a strong interest in designing new architectures with reduced lasing threshold. Thinking of an edge emitting laser consisting of a separate confinement heterostructure (SCH), the quantum wells and the waveguide must be treated as a whole. The waveguide must be designed to provide a high optical confinement factor in the wells, and its structural quality is important to minimize the internal losses due to light scattering. Additionally, the waveguide structure should provide a good carrier transfer to the quantum wells. The quantum wells should present high radiative efficiency and spectrally narrow emission. Finally, the SCH ensemble should provide high optical gain. Being able to address properly such issues should help to improve the performance of the next generation of AlGaN lasers, which are still outperformed by InGaN lasers in terms of efficiency.

In this paper, we analyze optical properties of AlGaN-based SCHs designed for the implementation of electron beam pumped UV lasers. We study their photoluminescence under various injection levels and compare the internal quantum efficiency (IQE) of the spontaneous emission and the lasing threshold power density, to determine the limiting factors. We discuss the effect of carrier localization and carrier diffusion on the device performance.

The samples were grown by plasma-assisted molecular beam epitaxy on bulk GaN substrates. 7 The three samples under study consist of a 10-period of GaN/Al0.1Ga0.9N multiquantum well (MQW) inserted in an Al0.1Ga0.9N/Al0.2Ga0.8N waveguide to form an SCH. A schematic description is presented in Fig. 1(a), and the dimensions of the layers are listed in Table 1. Sample S1 presents chemically sharp heterointerfaces (Al mole fraction profile in Fig. 1(b)), whereas the Al0.1Ga0.9N/Al0.2Ga0.8N heterointerfaces in sample S2 are linearly graded along 35.2 nm (profile in Fig. 1(c)) to implement a graded index separate confinement heterostructure (GRINSCH). Finally, the sample S3 consists of an asymmetric GRINSCH, where the top cladding layer has higher Al content and the top graded region is larger, reaching the top of the MQW (profile in Fig. 1(d)). The GRINSCH design aims to decrease the bandgap bending due to spontaneous and piezoelectric polarisation at the Al0.1Ga0.9N/Al0.2Ga0.8N interface in order to promote the diffusion of carriers to the MQW. The asymmetric GRINSCH was implemented to force the carriers generated in the top cladding layers to diffuse to the MQW. A more detailed explanation of the designs with simulations of the band diagrams were reported elsewhere. 7 In particular, we studied the confinement of the optical mode in the waveguide using a commercial finite-element analysis software (Comsol Multiphysics). The refractive indices used as input parameters were extracted from refs. 8,9 . The resulting mode distribution profiles are displayed in Figs. 1(b-d), superimposed to the Al content profiles. The optical mode profiles are very similar for S1 and S2, whereas the mode is slightly shifted towards the substrate in S3 due to the higher Al content in the top cladding layer. If we consider the 10 quantum wells as active elements, the optical confinement factors are 3.84%, 3.73%, and 3.79% for S1, S2, and S3, respectively. If the integration is extended along the MQW (including the barriers), the optical confinement factors are 36.3%, 36.5%, and 35.3%, respectively. These values, summarized in Table 1, confirm the optical similarity of the three samples.

Photoluminescence (PL) spectroscopy under low injection conditions was measured by excitation with a continuous-wave frequency-doubled solid-state laser (λ = 244 nm), with an optical power of 10 μW focused on a spot with a diameter of  100 μm. PL measurements under pulsed excitation used a Nd-YAG laser (266 nm, 0.5 ns pulses, repetition rate of 8 kHz).

In all the cases, the luminescence was collected by a Jobin Yvon HR460 monochromator equipped with a UV-enhanced charge-coupled device (CCD) camera.

For lasing threshold measurements, the samples were mechanically cleaved along m planes of the GaN substrate, to form laser bars with a resonator length of 1 mm. Excitation was provided by the Nd-YAG laser. A cylindrical lens was inserted in the optical path to shape the laser beam into a 100-µm-wide stripe perpendicular to the sample facets. In this configuration, the lateral confinement of light is obtained by gain guiding, i.e. the populationinverted region is determined by the width of the pumping laser stripe, which generates a gradient of gain and refractive index. The emission was collected from the edge of the laser bar. This characterization is described in detail in ref. 7 . The values of lasing threshold obtained from such measurements are listed in Table 1.

The performance of a UV emitter can be described by its external quantum efficiency (EQE), which is the ratio between the number of photons detected and the number of photons (optical pumping) or electrons (electrical pumping) injected in the device. In an LED, the EQE can be expressed as the product of the injection efficiency (inj, ratio of carriers reaching the light-emitting region), the radiation efficiency (rad, radiative recombination ratio) and the light extraction efficiency (ext, ratio of photons coming out of the sample). Note that the above-defined inj is different than the injection efficiency generally used in laser diodes, which describes the fraction of current above the threshold that results in radiative recombination. Also in the case of a laser, a relevant parameter is the differential EQE, EQE, extracted from the slope of the output power vs. pumping power curve above the lasing threshold. However, if we want to assess the material properties, it is more interesting to refer to the internal quantum efficiency, which is defined as IQE = inj  rad. Unlike the EQE and EQE, the IQE is independent of the geometrical properties of the laser, such as the cavity length or the ridge width. Hence, it is a good parameter to compare the material quality. The IQE is generally extracted from temperature-dependent PL measurements. It is often assumed that the IQE at a certain temperature (T) can be calculated as

IQE(T) = I PL (T) I PL (T = 0K) (1)
where IPL(T) is the integrated PL intensity at T. This estimation is based on the hypothesis that the PL intensity saturates at low temperature, since carrier freeze out prevents them from reaching non-radiative recombination centers.

To obtain the intrinsic IQE, associated with the material properties, the excitation should introduce as little perturbation as possible. Therefore, we have performed low-injection temperature-dependent PL measurements, with the results presented in Figs. 2(a-c) for S1, S2

and S3, respectively. To understand the spectra, we must keep in mind the penetration depth of the pumping laser: In view of the absorption coefficient of GaN, 80% of the absorption occurs in the TOC+TIC layers, and carriers have to diffuse towards the MQWs. Therefore, the observed transitions can be assigned to recombination in the TOC and TIC layers, in the MQW, and to a low energy band due to donor-acceptor recombination (DAP), as indicated in the figures. In the three samples under study, the ratio of integrated PL intensity from the MQW at room temperature and at low temperature is systematically lower than 1%. Such low values are generally observed in GaN-based MQWs measured under low injection conditions. 10,11 Looking at the PL line assigned to the MQW in Fig. 2, the spectral evolution of the PL peak presents an S shape, outlined with dashed lines in the figures. This behavior is assigned to the localization of carriers in potential fluctuations in the QWs, 12 which can be due to fluctuations of the QW thickness or alloy inhomogeneities in the QW barriers. Figure 2(d) shows the evolution of the MQW PL peak energy as a function of temperature for the three samples, and the high temperature trend was fitted with Varshni's equation. 13 The deviation from this trend observed at low temperature provides an estimation of the carrier localization energy, which varies from Eloc = 40±2 meV for S1 to 20±1 meV for S2 and 17±1 meV for S3.

A similar study applied to the TIC line, assigned to recombination in the Al0.1Ga0.9N inner cladding, leads to Eloc = 42±4 meV for S1 to 37±4 meV for S2 and 19±3 meV for S3. This points to the fact that carrier localization in the MQW is induced by alloy inhomogeneities in the barriers rather than thickness fluctuations of the wells. We note also that the localization energy in the TOC layers, with higher Al content, increases to the range of 44-53 meV in all the samples, which hinders the diffusion of carriers towards the MQW at low temperature and explains the presence of the TOC-related lines in all the spectra in Figs. 2(a-c).

It is known that the IQE of III-nitrides is strongly dependent on the injection intensity. 14- 16 Under operating conditions, the carrier density in the structure is high enough to saturate non-radiative recombination paths and screen potential barriers associated with defects or interfaces. Emulating such conditions requires high pumping densities. Therefore, we have studied the IQE of the SCH as a function of temperature and excitation power density using the method described by Yamada et al. 17 :

IQE SCH (T) =  PL (T) max[η PL (T = 0K)] (2)
where  PL is the PL efficiency, defined as the integrated PL intensity divided by the excitation power. The PL spectra were measured for various excitation powers, as presented for S1 at 6 K and 300 K in Figs. 3(a) and (b). The narrow lines labeled "*" that appear at high excitation power are assigned to stimulated emission. Such a phenomenon is not expected in a sample without cleaved facets, but it occurs due to the feedback provided by reflection at cracks, 18 which appear due to the strong lattice mismatch between different layers.

The calculation of IQE SCH considers the integrated intensity of the whole PL spectrum.

However, the contribution of recombination in the cladding layers to the total intensity can be important, particularly at low temperature, due to poor carrier diffusion to the MQW. In view of lasing, radiative recombination in the cladding layers should be considered as losses.

Therefore, we have calculated IQEMQW integrating only the optical signal from the MQW, which can be extracted using a Lorentzian fit to remove the other contributions, with the maximum PL efficiency still given by the integrated PL over the whole spectrum at low temperature, i.e.

IQE MQW (T) =  PL MQW (T) max[η PL (T = 0K)] (3)
where  PL MQW is the integrated PL intensity of the MQW divided by the pumping power and  PL is the total integrated PL intensity divided by the pumping power. Comparing IQESCH and IQEMQW, we can extract information about the efficiency of the carrier transfer from the waveguide to the MQW. Figure 3(c) displays the results of IQESCH and IQEMQW for S1. There is a significant deviation at low temperature, but the two values are very close at room temperature due to the thermally enhanced carrier diffusion towards the MQW.

Figures 4(a-c) show IQEMQW as a function of pump power and temperature for the three architectures under study. At 6 K, the highest IQEMQW is about 49%, 56% and 85%, for S1, S2

and S3, respectively (data summarized in Table 1). Note that the highest IQESCH at low temperature is considered to be 100%, so that the highest IQEMQW gives direct information on the efficiency of the carrier transfer to the MQW. The difference between samples can be explained by their band diagram 7 : The GRINSCH in S2 and S3 promotes the diffusion of carriers along the growth axis towards the MQW, which is one of the factors that limit the IQEMQW at cryogenic temperatures. However, at 300 K, the IQEMQW is about 22%, 11% and 5% for S1, S2 and S3, respectively, i.e. the trend is reversed compared to that at 6 K. This suggests that the higher carrier mobility at room temperature promotes not only carrier collection in the MQW, due to the enhanced diffusion length along the growth axis, but also their trapping in nonradiative centers, due to the enhanced in-plane diffusion length. As the acceleration of non-radiative processes is higher in samples with lower carrier localization, the performance of S3 is penalized with respect to S2 and S1.

To get a deeper insight into this issue, we have studied the variation of the maximum IQEMQW as a function of temperature in the three samples, with the result illustrated in Fig.

4(d).

The IQEMQW remains constant at low temperature, and drops sharply for higher temperature due to the activation of non-radiative recombination paths. It is interesting to note that the most severe thermal quenching is observed in sample S3, which features the highest IQEMQW at 6 K (see Fig. 2).

The dashed lines in Fig. 4(d) are fits assuming the dominance of a monoexponential nonradiative process, so that the variation with temperature is described by 19

IQE(T) = IQE(T = 0) 1 + A exp(-E a /kT) ( 4
)
where Ea is the activation energy of the non-radiative process, A is a fitting parameter that is determined by the ratio between the radiative and the non-radiative recombination times, 19 might indicate a higher density of point defects in the structure, which could be explained by the higher aluminum content in the upper layers.

Comparing the values of IQEMQW and lasing threshold at room temperature, summarized in Table 1, we observe that these two parameters are not correlated. Higher IQEMQW at room temperature seems to be associated with higher carrier localization in the MQW, which is explained by the fact that potential fluctuations prevent carriers from reaching non-radiative centers. A decorrelation of the lasing threshold and the IQEMQW is expected in samples presenting potential fluctuations in the wells, since they lead to inhomogeneous broadening of the gain spectrum. 20 In that case, higher pumping is required to attain a high-enough gain to overcome the losses, consequently increasing the lasing threshold, even if the MQW is more radiative efficient. Inhomogeneous spectral broadening of the gain generally manifests as inhomogenous broadening the photoluminescence. However, this is not the case here. If we compare the full width at half maximum (FWHM) of the MQW PL peaks in Figs. 2(a-c) with the lasing power density threshold, displayed in Table 1, the values do not follow the same tendency (e.g. S2 has a narrower emission line than S3 in spite of having the same lasing threshold).

The lasing threshold depends on more factors, namely the attainment of a carrier concentration high enough to ensure population inversion and a gain level that compensates the optical losses. In the three structures under study, the waveguide was designed to present similar optical confinement. The laser bars were cleaved in the same manner and the cavity length was the same, long enough to ensure that the distributed mirror losses are relatively small. Therefore, the variation of the threshold should not be associated with the optical properties of the waveguide, but rather to the difference in carrier injection and material quality.

To gain further insight into the role of the carrier mobility and localization on the device performance, Fig. 4(e) displays the variation of the lasing threshold as a function of temperature in the three samples. The decrease of the threshold when reducing the temperature is similar in samples S1 and S2, where an exponential fit (expected empirical dependence [START_REF] Pankove | Optical Processes in Semiconductors, Unabridged republication, with slight corr[END_REF] ) reveals an activation energy Eth = 12-13 meV, whereas it increases to Eth = 38 meV for S3. To understand the high threshold of S3 at low temperature, we must remind most of the absorption occurs in the TOC+TIC layers. Therefore, the higher losses that appear when cooling down can relate to the alloy fluctuations and higher density of non-radiative point defects in the Alrich topmost AlGaN layers. In contrast, at high temperature, carriers have enough energy to follow the potential ramp created by the GRINSCH and diffuse efficiently to the MQW.

In summary, this work discusses the different trends between internal quantum efficiency and power density lasing threshold in AlGaN-based separate confinement heterostructures. To assess the performance of these structures, it is important to analyze both the radiative efficiency and the carrier injection. At room temperature, carrier localization in the quantum wells leads to an enhancement of the radiative efficiency. However, our results show that the lasing threshold is more sensitive to the injection efficiency than to the radiative efficiency.

Therefore, designs including graded alloys result in a reduction of the lasing threshold, in spite of their lower internal quantum efficiency.

  and kT is the thermal energy. In the figure, Ea = 22±5 meV, 16±9 meV, and 14±2 meV for samples S1, S2 and S3, respectively. Even if the energy values are smaller than the carrier localization energy extracted in Fig.2(d), which can be explained by the different excitation conditions, the trend obtained here is consistent with the trend of the carrier localization energy extracted from the variation of the PL peak energy with temperature. On the other hand, the values of A extracted from the fits are A = 2.4±0.6, 6±3, and 12±3 for samples S1, S2 and S3, respectively.Even if the error bars are large, the trend points to an acceleration of non-radiative phenomena in sample S2 and particularly in sample S3 with respect to S1, which might indicate a higher density of point defects behaving as non-radiative recombination centers. These results suggest that the enhanced mobility of carriers at room temperature in S2 and S3 promotes not only carrier collection in MQWs but also their reaching non-radiative traps, which are more effective due to the reduced localization in the MQW. The particularly high value of A in S3

Figure 1 .

 1 Figure 1. (a) Scheme of the samples. Bottom to top: Bulk GaN substrate, bottom outer

Figure 2 .

 2 Figure 2. PL spectra recorded at low injection conditions for samples (a) S1, (b) S2 and (c)

Figure 3 .

 3 Figure 3. For sample S1, variation of the PL spectrum as a function of excitation power,

Figure 4 .

 4 Figure 4. IQEMQW as a function of the excitation power density at different temperatures,

Figure 1 Figure 2 Figure 4

 124 Figure 1

TABLETable 1 .

 1 Description of samples under study: thickness and Al content of the layers, following the general design in Fig.1(a). Optical confinement factor integrating the optical mode in the wells (OCFW) and along the whole MQW structure (OCFMQW). Lasing power density threshold at room temperature (RT). Maximum IQEMQW at 6 K and room temperature and maximum IQESCH at room temperature (note that the maximum IQESCH at 6 K is considered to be 100%). Lasing threshold measured in mechanically cleaved 1-mm long cavities when optically pumped with a Nd-YAG laser.

		S1	S2	S3
	TOC	44.4 nm Al0.2Ga0.8N 26.4 nm Al0.2Ga0.8N 44.2 nm Al0.3Ga0.7N
	Graded	--	35.2 nm	48.7 nm
	TIC	59.5 nm Al0.1Ga0.9N 41.4 nm Al0.1Ga0.9N --
	MQW	10×(1.4 nm GaN /9.8 nm Al0.1Ga0.9N)	10×(1.3 nm GaN /9.7 nm Al0.1Ga0.9N)	10×(1.3 nm GaN /9.7 nm Al0.1Ga0.9N)
	BIC	35.5 nm Al0.1Ga0.9N 17.6 nm Al0.1Ga0.9N 17.7 nm Al0.1Ga0.9N
	Graded	--	35.2 nm	35.4 nm
	BOC	355 nm Al0.2Ga0.8N 332 nm Al0.2Ga0.8N 334 nm Al0.2Ga0.8N
	OCFW (%)	3.84	3.73	3.79
	OCFMQW (%)	36.3	36.5	35.3
	RT Lasing threshold (kW/cm 2 ) 210	180	180
	max[IQEMQW(T = 6 K)] (%)	49	56	86
	max[IQEMQW(T = 300 K)] (%)	22	11	5.0
	max[IQESCH(T = 300 K)] (%)	26	13	5.5

ACKNOWLEDGEMENTS

This work is supported by the French National Research Agency via the UVLASE program (ANR-18-CE24-0014), and by the Auvergne-Rhône-Alpes region (PEAPLE grant).

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding authors upon reasonable request.


Thomas Aichele
email: thomas.aichele@physik.hu-berlin.de

Adrien Tribu

Catherine Bougerol

Kuntheak Kheng

Régis André

Serge Tatarenko

Defect-free ZnSe nanowire and nano-needle nanostructures

We report on the growth of ZnSe nanowires and nano-needles using molecular beam epitaxy (MBE). Different growth regimes were found, depending on growth temperature and the Zn-Se flux ratio. By employing a combined MBE growth of nanowires and nano-needles without any post-processing of the sample, we achieved an efficient suppression of stacking fault defects. This is confirmed by transmission electron microscopy and by photoluminescence studies.

Semiconductor nanowires (NWs) have attracted much attention in recent years because of their properties and potential use in a variety of technological applications. NW heterostructures are interesting candidates for the development of well-located and size-controlled quantum dots (QDs) [1]. Due to the narrow lateral size, QD heterostructures in NWs can be directly grown on very defined positions and without the necessity of selfassembly. This is an especially interesting feature for II-VI materials, where self-assembled island formation occurs only within narrow windows of growth conditions [2]. Recently, II-VI compound semiconductor NWs have been synthesized by Au-catalysed metal-organic chemical vapour deposition (MOCVD) and molecular-beam epitaxy (MBE) methods [3,4]. An obstacle towards the growth of optically active NW heterostructures are donor-acceptor pairs that form in defects [5]. These cause a strong spectral background which competes with the excitonic emission in the QDs. Ref. [6] reports the efficient reduction of this spectral background after annealing of the NW samples in Zn-rich atmosphere.

When developing NW heterostructures, annealing or other post-growth processing of the sample is often unfavourable as it may also influence the designed form of the heterostructure through inter-diffusion of the constituents. Instead, growth methods, that directly avoid the formation of defects are desired. In this letter, we report a growth recipe for ZnSe NWs, where the amount of stacking fault defects is strongly reduced. This was achieved by a combined growth of NWs and nano-needles without any post-growth processing of the sample.

The ZnSe NWs were grown in the vapour-liquid-solid growth mode with gold particles as catalysts. For comparison, GaAs(001) and Si(001) substrates were used. Degased surfaces for MBE growth were obtained after annealing in ultra-high vacuum at 580 • C. In the case of GaAs, the effect of an epitaxial GaAs buffer layer was also investigated. Interestingly the structural properties of the NWs depend very little on the utilized substrate.

Next, a thin gold film with thickness of 0.2-0.5 nm was deposited on the GaAs substrates inside an electron beam metal deposition chamber. The gold film was dewetted to a droplet-like surface by annealing the sample at 600 • C for 5 min. ZnSe MBE growth was then performed with varying growth conditions. The sample transfers between the MBE-and metal deposition chambers happened under ultra-high vacuum.

When growing under an excess of Se (Zn (Se) flux: 2.5 (7.5) ×10 7 torr) and a sample temperature of 350-450 • C, a dense carpet of narrow NWs with high aspect ratios covers the substrate. The NWs have a uniform diameter of 20-50 nm and a length up to 2 µm after a growth of one hour (fig. 1(a)). Additionally to the NWs, the as-grown substrate is covered with highly irregular nano-structures. Fig. 1(b) shows a transmission electron microscopy (TEM) image of one NW. The crystal structure of the NWs are predominantly wurtzite. However, the NWs are systematically intersected with regions of zinc blende phase. We account for the formation of such defects and the presence of highly irregular structures by non-ideal growth conditions at the initial stages of the growth process. Possible reasons are the presence of non-uniform gold agglomerations instead of small gold beads and the insertion of impurities during the gold deposition process. The presence of both wurtzite and Zn-blende shows, that at the utilized growth conditions both phases are allowed. Although, the observation of wurtzite structure is in contrast to the Zn-blende that naturally occurs in bulk ZnSe, it is not an uncommon behaviour for NWs, as discussed in ref. [7].

When, on the other hand, growing at low temperature (300 • C) or with inverted Zn:Se flux ratio, needle-shaped NWs are formed (fig. 2(a)). Hereafter we will refer to those nanostructures as nano-needles to distinguish them from the narrow NWs described previously. By TEM (fig. 2(b)) we determined that the nano-needles have a wide base (80 nm in diameter) and a sharp tip (5-10 nm). We also observed darker and lighter regions which again indicate the presence of stacking fault defects. The formation of nano-needles instead of NWs is well accounted for by the slower adatoms mobility expected at low temperature or at low Se flux. The slower mobility promotes nucleation on the sidewalls before reaching the gold catalyst at the nano-needle tip. Moreover, we observed that the nano-needles are predominantly wurtzite, as for NWs, but the wire axis is here perpendicular to the c-axis instead of being parallel. In contrast also to the long NWs (in fig. 1), the defect planes are here disoriented with respect to the nano-needle axis. It seems that this disorientation hinders the propagation of defects in the growth direction, especially for lower diameters. Defects zones are rapidly blocked on the side walls, providing a high structural quality towards the nano-needle tip.

To carry out single-NW studies, the sample is put in a methanol ultra-sonic bath for 30 s in order to detach some NWs from the substrate. Droplets of this solution are next placed on a fresh substrate, leaving behind a low density of individual NWs. Ensemble spectra were taken on the as-grown sample. All spectra in this paper were measured at a sample temperature of 5 K. The photoluminescence (PL) of individual NWs were excited with a cw laser at 405 nm via a microscope objective.

Both for NWs and nano-needles, we observe a broad spectral distribution within 500-600 nm, as seen in figs.

4(a) and (b). Even in the case of a single nano-needle, the spectrum is dominated by many intense spectral lines, which we attribute to emission from excitons localized at the defect zones in the NW [5]. In contrast to the observations in ref. [6] on MOCVD-grown NWs, we do not see an enhancement of the ZnSe band edge emission (443 nm at 5 K [8]) when growing under Zn-rich conditions. The intense emission with 500-600 nm instead suggests that in both cases (NWs and nano-needles), point defects effectively capture the excited charge carriers and quench the band edge emission, as also reported in Ref. [9]. This is in agreement with the high density of stacking fault defects observed by TEM. The observation of a decreasing defect density from the base towards the top in the nano-needles motivated us to modify the growth recipe in the following way: In the first partf, the sample is grown with excess of Zn for 30 min, leading to the formation of nano-needle struc- tures. Next, the Zn-and Se-flux was inverted and NWs were grown for another 30 min on top of the nano-needles. Thus, the growth at the side-walls was aborted and regrowth started on defect-free and strain-relaxed nanoneedle tips, where the high structural quality of the crys-tal lattice can be preserved along the narrow NW that is now formed in this second growth step. Fig. 3 shows results obtained from this sample. The structures have a broad base that tapers after a few ten nanometers to thin NWs with thickness of 10-15 nm. As symbolized in the sketch in fig. 3(a) we expect that stacking faults reduce towards the thin part of the NW, which is indeed the case, as seen in TEM images of a single NW, fig. 3(c).

The suppression of defects has a strong effect on the PL of these nano-structures (fig 4). Due to the low density of defects, the spectral emission between 500-600 nm that was observed before from the samples in figs 4(a) and (b) is strongly reduced, leaving behind only a small bunch of intense spectral lines between 450-500 nm. The weak and broad distribution between 500-600 that remains in the ensemble PL, fig 4(c), is due to excitons localized in defects in the thicker NW base. In the spectrum of a single NW that broke off behind the thicker base, fig 4(d), this broad background is now globally suppressed. In spite of this, no PL is observed at the ZnSe band-edge. A possible reason is that, due to the very thin diameter of the NWs, additional surface states may form in the bandgap [10] and introduce non-radiative decay channels that quench the band-edge PL. The remaining narrow PL peaks around 470 nm in fig. 4(d) can very likely be assigned to residual impurities responsible for donoracceptor pair emission and their related phonon replica [11].

In summary we have reported on MBE growth of ZnSe NWs. Depending on growth temperature and Zn-Se flux ratio, we can tailor the structures between thin NWs with homogeneous thickness of 20-50 nm, and nano-needles with broad base and a sharp tip with 5-10 nm thickness. By combining nano-needle and NW growth, we achieved the growth of mostly defect-free structures, without any post-growth treatment of the sample. This is confirmed by TEM and PL measurements. In the latter, the emission of excitons localized in the defect zones was strongly reduced. The suppression of defects is an important pre-condition for developing QD heterostructures inside NWs. In a next step, we included CdSe zones into the NW in order to form QDs. This will be reported in a subsequent publication.

Figure 1 :

 1 Figure 1: Data obtained from NWs grown at 400 • C: (a) SEM image of the as-grown sample at the border of the gold-coated region. The right side shows the dense carpet of NWs. On the left, individual NWs reach into the uncoated zone. (b) TEM image of a single NW. The arrows indicate wurtzite and Zn-blende zones.

Figure 2 :

 2 Figure 2: Data obtained from nano-needles, grown at 300 • C at Se excess: (a) SEM of the as-grown sample. (b) TEM image of a single nano-needle. The inset shows a zoom to the region around the tip.

Figure 3 :Figure 4 :

 34 Figure 3: Data obtained from combined growth of NWs on nano-needle tips. (a) SEM image of the as-grown NW/nanoneedle sample. (b) SEM of an isolated NW that broke off behind the thicker base. (c) TEM image of two close-by NWs.

Acknowledgments

We are grateful to V. Zwiller for inspiring discussions. T.A. acknowledges support by Deutscher Akademischer Austauschdienst (DAAD).