Lili Tong
email: lili.tong@insa-lyon.fr

Audrey Serna
email: audrey.serna@insa-lyon.fr

Sébastien George
email: sebastien.george@univ-lemans.fr

Aurélien Tabard
email: aurelien.tabard@insa-lyon.fr

Supporting Decision-making Activities in Multi-Surface Learning Environments

Keywords: Decision-making, collaboration, Computer Supported Collaborative Learning (CSCL), Computer Supported Cooperative Work (CSCW), Multi-Surface Environments

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

INTRODUCTION

Collaborative decision-making broadly consists of exploring alternative options, defining criteria, weighting options, and choosing one among them. Educators have highlighted the importance of collaborative decision-making skills in scientific education [START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF][START_REF] Grace | Developing high quality decisionmaking discussions about biological conservation in a normal classroom setting[END_REF][START_REF] Evagorou | Should we kill the grey squirrels?" A study exploring students' justifications and decisionmaking[END_REF], as it can help students to appropriating knowledge. Collaborative decision-making becomes even more relevant in multi-disciplinary education, such as when educators tackle socio-scientific issues [START_REF] Evagorou | Should we kill the grey squirrels?" A study exploring students' justifications and decisionmaking[END_REF], e.g., sustainable development. These issues are often ill-structured, and always involve consideration for technical, economical, and ethical aspects.

However, the literature [START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF][START_REF] Grace | Developing high quality decisionmaking discussions about biological conservation in a normal classroom setting[END_REF][START_REF] Evagorou | Should we kill the grey squirrels?" A study exploring students' justifications and decisionmaking[END_REF] emphasize that students struggle with such complex issues, especially with multi-dimensional analyses. The underlying problems lie in difficulties to: become familiar with the material, evaluate choices and reach a decision together, follow a process, know what others are doing and adjust behavior accordingly.

In the meantime, tabletops have demonstrated their ability to support collaborative activities [START_REF] Shen | Ubitable: Impromptu face-to-face collaboration on horizontal interactive surfaces[END_REF]. They can lead to greater awareness of group activities [START_REF] Rogers | Collaborating around vertical and horizontal large interactive displays: which way is best?[END_REF]. They afford the introduction of external regulation mechanisms [START_REF] Dimicco | Influencing group participation with a shared display[END_REF] through the design of applications or visual indicators of participation. Multisurfaces environments (MSE) seem suited to support decision-making and problem-solving activities [START_REF] Dillenbourg | Interactive tabletops in education[END_REF]. Large shared displays are excellent at providing an overview of information, while personal devices support individual activities and enable participants to conduct analytical tasks in parallel.

Our focus in this article is to better understand how digital devices and MSE can support learning decision-making process. We co-designed Pickit with teachers, a learning environment enabling students to explore various locations on a map on a shared display and decide which is the most appropriate regarding several criteria. Students can use personal devices to analyze the characteristic of each location. We conducted an in-situ study of Pickit with 12 students from a vocational school.

Our study shows that MSE is well suited for tightly-coupled collaboration and loosely-coupled parallel work in the decision-making process. Groups reached motivated decisions for their choices, while broadly following the decision-making process we implemented in our application. We outline the device use in MSE and link them to the behaviors in the decision-making process. We further derive a set of considerations for designing decision-making activities using MSE in classrooms.

RELATED WORK 2.1 Decision-making Process in Education

Decision-making is a process of gathering information, identifying and weighing alternatives, and selecting among various alternatives based on value judgments [START_REF] Uskola | The use of criteria in argumentation and the construction of environmental concepts: A university case study[END_REF]. Several models of decision-making processes have been introduced in the learning literature over the past years [START_REF] Janis | Decision making: A psychological analysis of conflict, choice, and commitment[END_REF][START_REF] Aikenhead | Collective decision making in the social context of science[END_REF][START_REF] Kraemer | Computer-based systems for cooperative work and group decision making[END_REF][START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF][START_REF] Roberto | The art of critical decision making[END_REF]. These models differ mostly in how they scope the decision-making process. They define however similar stages and all underline the non-linear nature of the process. The most generic model, proposed by [START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF], draws upon common elements in normative and descriptive decision-making models [START_REF] Janis | Decision making: A psychological analysis of conflict, choice, and commitment[END_REF]. This decision-making process consists of 6 stages that can be intertwined: 1) Listing options; 2) Identifying criteria; 3) Clarifying information; 4) Evaluating the advantages and disadvantages of each option according to the criteria previously identified; 5) Choosing an option based on the analysis undertaken; 6) Evaluating the decision-making process, and identifying any possible improvements. This process of critical analysis of information is widely used in basic scientific education and is well suited to the co-construction of knowledge [START_REF] Hong | Analysis of korean high school students' decision-making processes in solving a problem involving biological knowledge[END_REF][START_REF] Grace | Developing high quality decisionmaking discussions about biological conservation in a normal classroom setting[END_REF][START_REF] Evagorou | Should we kill the grey squirrels?" A study exploring students' justifications and decisionmaking[END_REF]. Making complex decisions in science courses involves many aspects of critical thinking, such as understanding procedures for rational analysis of a problem, gathering and using of available information, clarifying the concerns and values raised by the issues, or coordinating hypotheses and evidence [START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF][START_REF] Siegel | High school students' decision making about sustainability[END_REF]. Students evaluate the relevance and relativity of evidence and make choices by considering and respecting different viewpoints. Whenever a group makes a collective decision, each member of the group should reach the same decision individually [START_REF] Deneubourg | Collective patterns and decision-making[END_REF]. Students should develop their own judgment and understanding on the problem, and exchange opinions with the group.

To improve students' ability to make decisions, it is necessary not only to focus on the result of their discussions but also on how the students carry out the decision-making process, such as how they are able to evaluate and take into account the available information individually [START_REF] Uskola | The use of criteria in argumentation and the construction of environmental concepts: A university case study[END_REF]. Learning environments supporting decision-making processes should enable both collective and individual activities, including exploring and analyzing data, modeling, voting, or analyzing decisions.

Collaborative Learning with

Multi-surface Environments

Tabletops have been widely recognized as well suited to co-located collaborative activities [START_REF] Shen | Ubitable: Impromptu face-to-face collaboration on horizontal interactive surfaces[END_REF]. They provide shared spaces for organizing and controlling simultaneously information [START_REF] Dillenbourg | Interactive tabletops in education[END_REF], and support for cognitive offloading and shared awareness [START_REF] Judge | Studying group decision making in affinity diagramming[END_REF]. Former studies have shown that using tabletops in collaborative learning activities promotes higherlevel of thinking and more effective work [START_REF] Kharrufa | Digital mysteries: designing for learning at the tabletop[END_REF][START_REF] Higgins | Multi-touch tables and collaborative learning[END_REF]. Collaborative decision-making applications can thus leverage tabletop's properties: promoting equal access to all group members, and direct interaction with digital information displayed on an interactive surface (Rogers et al., 2004;[START_REF] Mccrindle | The design of t-vote: a tangible tabletop application supporting children's decision making[END_REF]. However, supporting the development of personal judgments in these shared environments can be a challenge [START_REF] Gutwin | Design for individuals, design for groups: tradeoffs between power and workspace awareness[END_REF][START_REF] Häkkinen | Shared and personal learning spaces: Challenges for pedagogical design[END_REF]. Introducing personal devices, such as tablets can be helpful to address that problem.

Multi-surface environments (MSE) typically expand shared tabletop or vertical surfaces with extra devices for personal data exploration. For instance, in Caretta [START_REF] Sugimoto | Caretta: A system for supporting face-to-face collaboration by integrating personal and shared spaces[END_REF], groups of students work together on urban planning tasks with a shared surface combined with several PDAs. The shared surface supports the city construction, on which students can manipulate physical objects and make decisions on the city evolution. PDAs are used as personal spaces where students can experiment ideas running simulations on different parts of the city.

Other research on MSE applications in analytics or decision-making range from basin (oil/gas) exploration [START_REF] Seyed | Skyhunter: a multi-surface environment for supporting oil and gas exploration[END_REF], to emergency response planning [START_REF] Chokshi | eplan multi-surface: A multi-surface environment for emergency response planning exercises[END_REF]. In most cases, large shared displays support groups in prioritizing infor-mation, making comparisons, and structuring data that embodies the working hypotheses [START_REF] Wallace | Collaborative sensemaking on a digital tabletop and personal tablets: prioritization, comparisons, and tableaux[END_REF]. While auxiliary displays are used to simultaneously control and exploit additional information [START_REF] Seifert | Mobisurf: improving co-located collaboration through integrating mobile devices and interactive surfaces[END_REF].

Former work in decision-making support with tabletops and MSE focused mostly on the system design and collaboration results. This article focuses more precisely on how students pursue decisionmaking learning activities by using the combination of devices. To this end, we define below the behaviors relevant to decision-making activities derived from previous literature and teachers interviews.

APPLICATION DESIGN

Decision-making Behaviors Supported

To understand teachers' requirements and expectations regarding the design of an environment for learning decision-making processes, we organized several workshops with four teachers from a vocational high school. Based on the discussions and workshops, we found that the decision-making process was often too complex for our target students. Teachers emphasized the needs for developing students' analytical skills. Considering Ratcliffe's model, three stages (stage 3, 4 and 5) were particularly relevant to teachers' pedagogical concerns. These concerns are strengthening students' abilities to analyze and evaluate different options, weighing the benefits and drawbacks, expressing their own reasoning, considering others' opinions, and reaching group decisions. Other stages of the decision-making process such as defining criteria or searching for options [START_REF] Siegel | High school students' decision making about sustainability[END_REF] are not the main focus for the targeted learners. The knowledge about the activity, including the options, criteria and context would be developed in previous classes. Teachers would prepare these supporting material beforehand.

Our proposition thus focuses on supporting the analytical process in decision-making activities. In order to structure the design and evaluate the activity, we identified four broad categories of behaviors relevant to decision-making activities based on the literature and the discussions with the teachers: Exploring is mostly an individual behavior, with which students can develop their own opinions. Exploring consists of browsing content, running simulations or conducting data analyses. It corresponds to behaviors linked to clarifying information and surveying described in several models [START_REF] Janis | Decision making: A psychological analysis of conflict, choice, and commitment[END_REF][START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF].

Discussing is the main collaborative behavior in the decision-making process. It happens when students are talking about and exchanging their ideas. According to the different models [START_REF] Aikenhead | Collective decision making in the social context of science[END_REF][START_REF] Kraemer | Computer-based systems for cooperative work and group decision making[END_REF][START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF], this behavior occurs when participants are building common ground [START_REF] Clark | Grounding in communication[END_REF] on the options and collectively evaluating them. Ratcliffe identified several subcategories when analyzing discussing including discussing options, discussing criteria, discussing information, comparing options, and choosing with reasoning.

Awareness is necessary for collaborative activities to enable participants to adjust to the group progression. It involves being aware of the activity as it unfolds: its progress, what other people are doing and how the group is behaving as a whole [START_REF] Dourish | Awareness and coordination in shared workspaces[END_REF][START_REF] Hornecker | Collaboration and interference: awareness with mice or touch input[END_REF].

Regulation is built upon awareness and relates to people's ability to plan, monitor, and evaluate the joint activity [START_REF] Vauras | Shared-regulation and motivation of collaborating peers: A case analysis[END_REF][START_REF] Volet | Self-and social regulation in learning contexts: An integrative perspective[END_REF][START_REF] Rogat | Socially shared regulation in collaborative groups: An analysis of the interplay between quality of social regulation and group processes[END_REF]. It is important in group activities, even more so in a learning context, in which students are still in the process of developing collaboration skills [START_REF] Hadwin | Selfregulated, co-regulated, and socially shared regulation of learning[END_REF]. In a classroom environment, regulation can come from the teachers or the students themselves.

Scenario

The decision-making activity is part of a larger paperbased learning game focusing on a non-determinist and pluri-disciplinary pedagogical situation. The goal of the game is to set up a sustainable company breeding and selling insects. Students are split into groups of three people and must choose one kind of renewable energy and the family of insect to breed and sell.

Our application focuses on the selection of the best location to establish the insect farm. Students must analyze the geographical and abiotic data of four optional locations and decide which location is best.

To do so, they should consider the breeding and living conditions of their insects, logistics requirements, and sustainable development principles. Teachers defined six criteria before the session for students to help them analyze: 1) moisture for breeding the insect; 2) temperature for breeding the insect; 3) feasibility of using wind energy; 4) feasibility of using solar energy; 5) accessibility (transport, communication routes); and 6) neighborhood.

To support students' progress throughout the activity, but also to monitor and evaluate the analytical process, we decided to structure the activity around three steps:

1. Survey: students explore, analyze the data and rate the four locations before they can move to the next step. We merge clarifying information (stage 3) and evaluating option (stage 4) of Ratcliffe's model into this step because of the close relation between these two stages and the non-linear nature of the process.

2. Choice: students decide which location to choose. Once a location is picked, they can move to the final step. This step is based on choosing an option (stage 5) of Ratcliffe's model.

3. Justification: students produce an explanation of their choice, explaining how the location meets their requirements based on the criteria. This step is essentially required by the teachers for the evaluation of students analytical skills.

Application

Pickit, the application developed, uses the combination of a tabletop and tablets to support analytical decision-making process (Figure 1). The tabletop is mostly dedicated to viewing the decision-making context and the tablets are dedicated for browsing the data about each location, i.e. the options in the decisionmaking model. The tabletop displays a large map with four markers corresponding to the four locations to consider (Figure 2). To get the information about a location on their tablets, students need to tap a marker on the map, then tap their avatars in the pop-up box. An information button in the menu bar in the top left corner lets students get information about the energy and the insect they chose.

On their tablets, students can then see data about light intensity, wind strength, soil temperature, and humidity (Figure 3). The students can analyze each location based on six criteria defined by the teachers. Students must rate each location based on these criteria on a scale from one star to five stars. While exploring, they can also submit comments about the locations to help them build an argument and support later discussions. Such arguments can also be recorded to build a justification of the final decision. Each student has an individual color for their comments.

These evaluations appear as four cards representing the four locations to support group discussion (brown cards in Figure 2). On these cards, students can see each other's comments. When all the group members finish their rating, they can get the average of the group rating results on the cards. These cards can be dragged and scaled, which allows students to organize and compare different options when discussing. It also allows students to orient cards easily when sitting on the side of the tabletop.

We introduced several features to foster awareness and facilitate group regulation. For example, when a student picks a location to explore, the background color of his/her avatar on that option card will change on tablets in order to indicate who is exploring which location. Once a student has finished rating a location, a green checkmark appears on that option card next to his/her avatar as a sign of completion. On the menu bar, there are rating progress bars for each student and step-lists with the current step highlighted, to help students understand their progress and the ongoing task.

Table 1 shows the functionalities of the application that support these decision-making behaviors.

We used AngularJS to develop a Web application running on tabletops and tablets. All the devices connect wirelessly to an external server hosted on Heroku, and they communicate via Web sockets.

STUDY

We conducted the activity described above in the high school to study whether and how our application supported the four categories of behaviors that were defined before, and how the devices were used when students were performing those behaviors.

Participants

Four groups of three students from the same high school class took part in the activity (12 in total). The students were between 16 and 19 years old (mean: 17.5, SD: 0.78), including seven females and five males. They knew each other well and had already worked together as groups in their former classes. Two teachers joined us to follow groups and gave instructions on task. Teachers underlined that it was challenging for students from this class to collaborate.

Apparatus

Each group had a capacitive 27-inch horizontal touch screen with a resolution of 1920x1080 pixels, and a tablet per student (Galaxy Note 8 with protective covers). The touch-screens were positioned on round tables. Students all sat on the same side of the table and could rest the tablets on the table in front of the touchscreen (see Figure 1). All the devices were wirelessly connected to the network.

Task Organization

Each session lasted about 30 minutes. The study took place in the high school library. Two groups performed the task at the same time. A teacher followed each group to give instructions. Before the task, the teacher explained the application to the students, and let them play with the application to familiarize themselves with all the functionalities. Several bookshelves isolated the two groups, to avoid any external influence during the task. Competition or collaboration between groups was neither encouraged nor discouraged.

Data Collection / Recording

We used one camera set in front of the table to record the tabletop screen, students' interactions, gestures, and postures. We also collected logs to quantify interactions on the tabletop and tablets and complement the videos, e.g. know what was displayed on the tablets of the participants. After the experiment, students were asked to fill in a questionnaire containing 5-point Likert-scale and free-form questions about their perception of learning and their feelings on using the combination of devices to carry out the activity.

Analysis Method

We focused our analysis on the four behaviors identified earlier. We used two type of data sources, the recorded videos, and logs. The goal of the analysis was not to provide quantitative data of the activity but to give qualitative insights on how students behaved and collaborated in MSE. We tried to understand how the design of our application impacted activity and device usage, and contributed to the decision-making process. To do so, we defined a coding scheme for the analysis of videos based on the literature presented previously [START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF][START_REF] Hornecker | Collaboration and interference: awareness with mice or touch input[END_REF][START_REF] Rogat | Socially shared regulation in collaborative groups: An analysis of the interplay between quality of social regulation and group processes[END_REF].

Two coders analyzed the videos independently on different samples. They did an inter-rater reliability test with the result of 85% agreement. Then one researcher analyzed three groups and the other analyzed one group. Both of them went through the videos twice. The first time, they used the coding scheme and the second time, they noted down devices usage (for instance who was interacting on the shared display or how students used their tablets and the tabletop to discuss a specific option).

Video Coding Scheme

For exploring behaviors, we noted the sequence of exploring options of each student on a timeline. This timeline is used to analyse how students chose the options to explore, how long they spent on each option, and whether their exploration strategies were influenced by others.

To analyse discussing behaviors, we used the categories defined by Ratcliffe's [START_REF] Ratcliffe | Pupil decision-making about socioscientific issues within the science curriculum[END_REF] We coded awareness behaviors when they were directly linked to the MSE configuration and to the distribution of the interface among the different devices, for instance when someone was looking or taking a glance at one another to check what others are doing [START_REF] Rogers | Collaborating around vertical and horizontal large interactive displays: which way is best?[END_REF]:

AW. looking what others are doing.

We split regulation between group regulation (RG) and teachers initiating group regulation (RT). We coded regulation when observing monitoring and planning of the task, as in [START_REF] Rogat | Socially shared regulation in collaborative groups: An analysis of the interplay between quality of social regulation and group processes[END_REF].

RG-1. one group member reminds others of the time or the task progression; RG-2. one group member offers help to others; RT. teacher gives instructions on how to use the application or provides instruction/information to help students understand the decision they should make.

When analyzing these behaviors, we also observed how students were using the different devices. We observe device usage from two dimensions: the number of students involved in the activity, and the devices students focused on.

Log analysis

We focused our analysis on the number of actions on the large display including zooming and dragging the map or the location card, pressing buttons, selecting avatars, etc. We computed students' ratings to see whether their final choice was the location for which they gave the highest score. We also counted the number of comments and justifications of each student.

RESULTS

We now describe how the different groups performed the decision-making activity, focusing on the behaviors defined previously.

Overview of the Activity

All the groups succeeded in analyzing locations, making decisions and providing reasonable justifications. Groups spent different amount of time on their tasks (G1 = 38m14s, G2 = 25m37s, G3 = 31m33s, G4 = 23m02s). We were interested in observing how groups structured the analytical process and which behaviors were involved in the different steps. We observed that three groups (G1, G2 and G3) explored options and began to discuss and compare them at the same time, during the survey step. Discussions always happened when one student finished browsing an option and wanted to exchange ideas with others. Such discussions only happened when students were checking or had already checked the location. But if other students did not check the location yet, the discussion would not be initiated.

Group 4 acted differently. The students explored options individually and did not discuss during this step, which made it much shorter comparing to other three groups (time percentage of the survey step for each group: G1 = 65.4%, G2 = 77.7%, G3 = 77.8%, G4 = 55.1%). Group 4 also had fewer interactions on the shared display (G1 = 102, G2 = 156, G3 = 50, G4 = 35) but a higher amount of individual comments for each location (G1 = 14, G2 = 15, G3 = 16, G4 = 26).

G1, G2 and G3 spent a little time on the choice step as they already had discussions and changed their ideas in the former step. On the contrary, G4 began to discuss various options in the choice step, using the individual comments written on the previous step. Consequently, this step was longer than for the other groups (time percentage of the choice step: G1 = 1.6%, G2 = 6.5%, G3 = 3.2%, G4 = 14.3%).

Exploration

Exploration happened mostly during the survey step. Students checked the information about breeding requirements of their insects, their chosen energy and geography of locations on the shared surface, and browsed each option and criteria (such as the temperature for breeding the insect or the feasibility of using wind energy) on their tablet. In G1, G2 and G3, students did not double check options in the last two steps, which indicated they knew well about these options after the survey step. Only G4, who did not discuss during the survey step, re-visited some locations in the choice step. During the exploration, students acted individually when choosing a location to analyze on the map. We observed nevertheless implicit coordination in the choice of locations. From the figure 4 we can see that three groups (G2, G3 and G4) started the exploration with the same location. When a participant selected another location, s/he was later followed by the two others. According to the speed of exploration of each student, we can observe adjustments and switches in the exploration sequences. For instance, in G3, after the second location visited, students 2 and 3 broke the order chosen by student 1, who is quicker than the other two. They chose the location that student 1 was exploring at this moment so they could discuss together. We can find several periods in these three groups when students were checking the same location together. One reason for this could be they were influenced by the interface, choosing the marker that showed up on the display. The other reason could be that students wanted to evaluate together the same locations so they could discuss and share opinions. Only students of G1 adopted a different strategy.

They chose different locations to explore on purpose during the whole survey.

Discussion among group

Discussion in survey

We counted the number of discursive acts in the survey step and we observed how devices were used during the discussions. Options and criteria were mostly the main focus of discussions whereas discussing the context and comparing options occur few times in this step (Table 2). We observed mostly two participants focusing on one tablet during discussions followed by two or three students focusing on the shared display and hybrid chat using both shared display and tablet.

Students had most discussions dyadically and used tablets to discuss, especially when the discussions were related to options and criteria. They used tablets to check a specific option, analyzing the data according to the criteria and exchanging ideas. The shared display was often used when students discussed about the context and their preferences (example of a discussion in Table 3).

Regarding group coordination, groups that tended to explore the same options in parallel on their tablets (G2 and G3) preferred to discuss using their tablets. Group 1, where students explored the location independently on their tablets, used mostly the tabletop to discuss. Group 4 did not have discussion in this step.

Discussion in choice and justification

Discussions in the choice and justification steps were more concentrated in comparison to the survey step where they were fragmented. Therefore, we considered discussion durations instead of counting occurrences in our analysis (Table 4). Group 4 spent more time in these steps compared with other groups since they did not discuss during the survey. All the groups Table 3: An extract of G3 discussion on a location.

Student A and B have the same location on their tablets: -A: "What do you think about the humidity?" (A looks at B.) -B: "It's too humid." (B looks at his own tablet.) -A:"Too humid? What about the wind speed?" (A takes a look at her tablet, then looks at B.) -B: "We don't care about wind, we use solar energy." (B looks at A.) -A: "Yes, but the light intensity is also not good enough." (A looks again at her tablet, then looks at B.) -B: "No, it only has 1017 lux." (B looks at his tablet.)

Discussion

G1 G2 G3 G4

Comparing locations 142s 20s 37s 184s Choosing with reasoning 12s 16s 11s 53s discussed around tabletop. This tends to indicate that the shared display supported groups in synchronizing opinions and reaching a decision. In group 4, we also observed one student looking at the tabletop while two others looked at their tablets, when they had difficulty deciding which option was better and needed to check the data on their tablets again. Possibly, tablets served as supportive tools for debating during discussion when more information was needed.

Location cards played an important role during the discussion. The ratings on the cards helped students to quickly find the options with the highest scores. Students could zoom out and put aside the options with lower scores and only focus on the best ones. We observed several times students were organizing the cards on the shared display together to compare options. The comments they added to the cards also reminded them of their reasoning and supported them in building justifications. In the end, each student submitted his/her justifications through his/her tablet. We observed two ways students used for submitting their justifications. In two groups, students submitted the group justification that they discussed and agreed upon. In two other groups, students distributed their justifications, each one submitting the justifications that concerned some specific aspect. From the logs, we saw that members of a group did not always have the same preferences, but all groups chose the option that had the highest average score.

Awareness and Regulation

Awareness and regulation behaviors happened mainly in the survey step, when students were individually exploring options. The maintenance of awareness was subtle. For example, when one student chose an option on the tabletop, other students working on their tablets would take a glance at the tabletop. This slight head movement indicated that students could be aware of others actions on the tabletop. In group 2 and 3, although we did not observe students explicitly looking at each other, they still knew which option their partners were exploring and talked with them about that option. Awareness was mainly maintained by the shared surface, such as one student looking at another's interaction on the tabletop.

We did not observe many regulation behaviors in which students reminded others of their progress or time (RG-1) (mean = 1.25, SD = 0.96). In contrast, regulation in the form of supporting one another (RG-2) happened more frequently (mean = 17, SD = 10.7). For example, in group 1, student A was looking at the location card on the tabletop and saw student B dragging the map looking for the next location to explore. A pointed at a location card and said to B: "This one you haven't evaluated." Such behaviors happened mostly over the tabletop when they were tapping avatars for others, showing others the picture of a location on the map, or passing location cards. At a more minor level we also observed regulation behavior while students shared a tablet.

Teachers intervened mostly at the beginning of each step to regulate the activity. It mainly involved explaining the task and the application functionalities. They also answered students' questions about the criteria and the decision-making context, ensuring relevance of students' analysis.

Learning Experience

After the activity, we gathered students' feedback (Figure 5). They were all positive about their learning experience and the skills developed during the activity. In particular, they felt more competent in collaborating with others, analyzing problems and taking reasonable decisions at the end of the activity. Besides that, they also enjoyed the activity (see Figure 6). Most of them thought using a personal tablet with a shared display helped them collaborating.

We also interviewed teachers after the activity. They were all satisfied with the activity progress. Teachers were positively surprised to see that students collaborated well and could listen to others opinions as they used to have problems on collaborating.

DISCUSSION

We compare Pickit with former systems supporting decision-making that mentioned in the related work (Table 5). Some of these systems do not focus on decision-making processes, but still support some decision-making stages, such as Caretta [START_REF] Sugimoto | Caretta: A system for supporting face-to-face collaboration by integrating personal and shared spaces[END_REF] and ePlan [START_REF] Chokshi | eplan multi-surface: A multi-surface environment for emergency response planning exercises[END_REF].

Main Findings

Our study showed that the analytical process conducted during decision-making activities in classroom can benefit from MSE properties. The combination of devices enabled tightly-coupled collaboration and loosely-coupled parallel work in the decision-making process, avoiding free-riding situations. The shared display seemed to increase students' awareness of the ongoing activity, and led students to explore the same option synchronously, but with a high level of freedom and without interfering with each other. In this sense, the tablets improved independent exploration of options within groups. Students were able to develop their own judgments on the various options using criteria. And hence increased their understanding. During discussions, the shared display supported students in synchronizing opinions and reaching a decision whereas tablets served as supportive tools for debating when more information was needed.

From an educational point of view, according to teachers, students all succeeded in making reasonable decisions and providing justifications to support their decisions. Students learned to argue and to structure better a decision-making activity. Teachers also underlined the positive effects of the application on students' cross-disciplinary skills. They were more inclined to collaborate with others even though they usually have great difficulties to listen to others and consider other opinions. Former studies have demonstrated that prior friendship had a significant, large negative impact on group performance [START_REF] Maldonado | When is collaborating with friends a good idea? insights from design education[END_REF]. Our findings suggest that MSE may address this issue as using Pickit allows students to collaborate better than in a classic classroom situation.

6.2 Implication for Design

Structuring Decision-making Applications and Taking Advantages of MSE

The design of decision-making activities should take into account the properties of MSE to balance individual and collaborative work and to help students in structuring their analytical process.

As underlined by previous literature [START_REF] Roberto | The art of critical decision making[END_REF], we observed that according to the groups, the stages of the analytical process could be strongly intertwined. Many times students were discussing during the individual exploration building gradually their choice. The structure promoted more independent analytical work nonetheless. Students rated their options independently and were able to construct their personal opinions. We did not observe free-riding be-haviors in class that was prone to it according to the teachers. We attribute this partly to the design of the application: the analysis being connected to each participant through their tablets, which made everyone accountable in a way.

In addition, distributing content on tablets enabled to avoid conflicted viewing and analyzing, especially in our case where the information was abundant and challenging to display at once.

Supporting Discussion

Overall, tablets became supportive tools for debating, and supported discussions. Tablets also enabled students to freely analyze options at their own pace. However, analyzing different options in parallel tended to impede discussion. We observed how confusion could arise from students discussion a specific criteria but not referring to the same option/location.

We also hypothesize that group 4 did not discuss at all in the survey stage, because one student did not let others look at her tablet. We assume that letting students going through options together may promote more discussions. Moreover, giving an overview of analysis elements on the shared surface can support students in comparing options. We observed several times that students were organizing the cards according to the scores of options. The comments added during the survey and displayed on the cards also supported students in building justifications.

Better Supporting Awareness

In our application, we distributed the controls between the shared display and tablets. For instance, in order to control what was displayed on their tablet, students needed to use the tabletop. An alternative could have been to offer tabs on the tablets so that all the locations would be directly available. However, we noticed that our strategy led to a good awareness of students' actions, status and progress. Students could notice when their partners finished one location and switched to the next. In addition, the features designed in the application, such as avatars showing who is exploring which option, progress bars and step-list, contributed to maintaining a good level of awareness.

Limitations

The design of Pickit was focused on the analytical process in decision-making activities. In agreement with the teachers, we decided to not support several aspects of the process, such as searching for options, and identifying criteria. We assume that more features would be required in the application when supporting the whole process of decision-making. Also, we should investigate deeper whether the design of the application could influence or introduce some bias in the behaviors we analyzed. In particular, it remains difficult to establish if the sequences of location explored during the survey followed a specific strategy or if it was a consequence of the interface, displaying the last location chosen by someone.

CONCLUSION

We presented Pickit, an application supporting decision-making process for multi-surface environments. Our application design is grounded in workshops with teachers and an in-depth analysis of the literature on decision-making process. Based on these dual requirements from teachers and the literature, we focused on the analytical process of the decisionmaking activity, which involves four broad categories of decision-making behaviors: exploring, discussing, awareness and regulation.

We conducted a study with 12 high school students to understand how our application would support in a complex decision-making scenario, involving the consideration of multiple options, criteria and background information. A second purpose of the study was to understand how students interact with personal and shared devices in such an environment. Our results show that the proposed MSE application supported the analytical decision-making process. It helps students develop their own ideas and makes free-riding more difficult. Students were all succeed in making reasonable decisions and providing justifications to support their decisions.

  group and activity awareness; 4. Regulating the activity.

Figure 1 :

 1 Figure 1: Three students using Pickit.

  Functionalities of the application to support decision-making behavior. Behaviors Functionalities Exploring (tabletop) -Information button to show the decision making context (energy and insect) -Map to show the geographical condition of locations Exploring (tablet) -Showing data of locations -Rating tool based on criteria provided -Writing comments and arguments Discussing (tabletop) -Sharing everyone's comments -Providing average of the group's rating result -Showing location cards for comparison Awareness & Regulation (tabletop) -Showing who is exploring what -Progress bars for the rating processes -Check marker for the location that has been rated -List of steps in the menu bar

Figure 2 :

 2 Figure 2: Pickit on tabletop. A screenshot of the survey stage.

Figure 3 :

 3 Figure 3: Pickit on one student's tablet, from the top to bottom showing the location title, location information, rating, comment for the location, and comment in general.

  : D-O. discussing options; D-C. discussing criteria; D-I. discussing context (background knowledge or information); D-CMP. discussing benefits and drawback of options (comparing); D-R. choosing with reasoning.

Figure 4 :

 4 Figure 4: Location analysis sequence of each student based on the timeline. Four colors represent four locations.

Figure 5

 5 Figure 5: 5-point Likert questionnaires on learning results: do you feel more competent in collaborating with others (top), analyzing problems (middle), and taking reasonable decisions (bottom).

Figure 6

 6 Figure 6: 5-point Likert questionnaires on learning experience: enjoy the activity (top) and using a personal tablet with a shared display helps collaboration (bottom).

Table 1 :

 1

Table 2 :

 2 Discussion in survey: the number of discussions on locations, criteria, context and comparing locations by each group (expect group 4 who did not discuss in this step).

	Discussion	Group 1 Group 2 Group 3
	Locations	12	8	14
	Criteria	5	3	10
	Context	6	1	2
	Comparing locations	1	3	1

Table 4 :

 4 Duration of discussions in choice and justification on: comparing locations and choosing with reasoning.

Table 5 :

 5 Comparison of Pickit with former systems supporting decision-making. For the systems that use MSE, we also clarify the role of devices.

	Systems Convince me (Siegel, 2006) Argue-WISE (Evagorou et al. 2012) T-vote (Mccrindle et al. 2011) Finger talk (Rogers et al. 2004) Caretta (Sugimoto, et al. 2004)	Apparatus PC PC Tabletop Tabletop Calendar design Application context Science and sustainability issues Socioscientific issues Finding a shared topic of interest in a Museum MSE Urban planning	Stages of decision-making supported and associated functionalities 1) Listing options 2) Identifying criteria 3) Clarifying information 4) Evaluating options 5) Choosing an option 6) Evaluating decision Listing options and evidences -Linking hypotheses and evidence Evaluating evidence and belief -Obtaining feedback of evaluation --Browsing information Writing arguments -Writing arguments ---Voting for topics ----Browsing images Choosing images ---Browsing information (individual) Simulating plans (individual) Agreement button (shared) Backtracking (shared)	Summary Making individual decisions, no collaboration Mainly focusing on building arguments Not supporting the analytical process Not supporting the analytical process No clear decision-making flow
	ePlan (Chokshi, et al. 2014)	MSE	Emergency response planning	-	-	Browsing / sharing information (shared); annotating (individual)	-	-	Focusing on analysis rather than taking decisions
	Pickit (our study)	MSE	Pluri-disciplinary sustainability issues	-	-	Browsing information (shared & individual); writing notes (individual)	Rating options based on criteria (individual)	Rating averages, validation (shared)	Writing arguments (individual)	Focusing on the analytical process and collaboration in a decision-making activity with a defined flow

ACKNOWLEDGEMENTS

This research would not have been possible without the teachers Cerise, Pascaline, Xavier, Cécile, Sébastien and Caroline who participated to the design and made the activity possible, as well as the amazing students from LPA la Martellière in Voiron. This work was partially funded by the China Scholarship Council PhD program and the ANR project JENlab (ANR-13-APPR-0001).


V I Zubkov
email: vzubkovspb@mail.ru

A V Solomnikova

J E Post

E Gaillou

J E Butler

Characterization of electronic properties of natural type IIb diamonds

Keywords: Natural diamond, boron, admittance spectroscopy, charge carrier concentration, activation energy

Precision admittance spectroscopy measurements were carried out over wide temperature and frequency ranges for a set of natural single crystal type IIb diamond samples. Peaks of conductance spectra vs. temperature and frequency were used to compute the Arrhenius plots, and activation energies were derived from these plots. The capacitance-voltage profiling was used to estimate the majority charge carrier concentration and its distribution into depth of the samples. Apparent activation energies between 315 and 325 meV and the capture cross section of about 10 -13 cm 2 were found for samples with uncompensated boron concentrations in the range of 1 to 5 x 10 16 cm -3 (0.06-0.3 ppm). The obtained boron concentrations are in good coincidence with FTIR results for the samples. Also, the reason the difference between the observed admittance activation energy and the previously reported ionization energy for the acceptor boron in diamond (0.37 eV) is proposed.

I. Introduction

Natural (mined) diamonds may contain several impurity elements in the crystal lattice which can affect their optical, electrical and other physical properties. [START_REF] Field | The Properties of Natural and Synthetic Diamond[END_REF] Nitrogen is the most common impurity found and can occur as a substitutional atom in the lattice, or as more complicated clusters of nitrogen atoms and lattice vacancies. As a result, natural diamonds are generally classified as Type I, if they contain sufficient nitrogen as detected by infrared absorption spectroscopy (IR), and Type II, if nitrogen related defects are undetectable by IR. Type II diamonds, with no IR detectable nitrogen, generally make up less than 2% of all mined diamonds. Other impurity atoms found in natural diamonds are hydrogen, boron, and silicon. More complicated mineral inclusions are also found in natural diamonds and are important indicators of the diamond genesis environment. The type II class of diamonds is further divided into type IIa, where neither nitrogen nor boron is detectable by IR, and type IIb, where only boron related defects are detectable by IR. [START_REF] Field | The Properties of Natural and Synthetic Diamond[END_REF] Amongst the rarest and most valuable of natural diamonds ($ per carat) are the blue, type IIb boron containing diamonds. While almost all diamonds are electrical insulators, the type IIb diamonds are electrically conductive and may be considered as possessing the properties of semiconductor. Thanks to the boron impurities, the optical hue of these diamonds can range from light grey/blue to a dark steely-blue. Some famous examples of these blue natural diamonds are the Hope Diamond, the Blue Heart Diamond, the Blue Moon, the Wittelsbach-Graff Diamond, and others. Having the deep level boron impurity of relatively high concentration, these diamonds also show interest-ing fluorescence and phosphorescence properties when exposed to ultraviolet light and have been the subject of several recent investigations. [START_REF] Gaillou | Boron in natural type IIb blue diamonds: Chemical and spectroscopic measurements[END_REF][START_REF] Eaton-Magana | Using phosphorescence as a fingerprint for the Hope and other blue diamonds[END_REF][START_REF] Gaillou | STUDY OF THE BLUE MOON DIAMOND[END_REF][START_REF] Gaillou | Quantifying boron in natural type IIb blue diamonds[END_REF][START_REF] Gaillou | NOT CUT FROM THE SAME ROUGH[END_REF] Knowledge of the relative concentration of N and B in diamonds would be of great interest to the understanding the competition in nature between those two elements during diamond growth. A detailed understanding of the electrical properties of boron in diamond is especially important to the exploitation of semiconducting diamonds for electronic applications. [START_REF] Balmer | Unlocking diamond's potential as an electronic material[END_REF][START_REF] Gurbuz | Diamond semiconductor technology for RF device applications[END_REF][START_REF] Thonke | The boron acceptor in diamond[END_REF][START_REF] Butler | Exceptionally high voltage Schottky diamond diodes and low boron doping[END_REF] The purpose of this study was to comprehensively investigate the main properties of the electronic spectrum of rare, natural blue diamonds with moderate concentrations of boron. A non-destructive techniquea complex of temperature admittance spectroscopy (TAS) together with frequency admittance spectroscopywas employed to study the electrical response of diamonds with boron. The experimental apparatus used in this study was a purpose built computer-controlled admittance spectroscopy setup which covers a temperature range 20 -450 К and frequency range 1 kHz -2 MHz. [START_REF] Zubkov | Analysis of the electrostatic interaction of charges in multiple InGaAs/GaAs quantum wells by admittance-spectroscopy methods[END_REF][START_REF] Kucherova | Nondestructive Diagnostics of Nanoheterostructures with InGaN/GaN Multiple Quantum Wells by Thermal Admittance Spectroscopy[END_REF][START_REF] Zubkov | Admittance Spectroscopy as a Method for Investigating Relaxation Processes in Quantum-Sized Heterostructures[END_REF] By measurement and appropriate simulations, full characterization of electronic properties for boron impurity in 4 natural type IIb diamonds has been obtained, including the distribution of majority charge carrier concentrations and the thermionic emission characteristics.

II. Methods of characterization

The main measurement technique presented in this study is admittance spectroscopy. Admittance spectroscopy is the combination of conductance (G) and capacitance (C) measurements, carried out during one temperature cycle. By scanning different electric parameters of p-n junction or Schottky barrier as function of temperature, applied bias (V) and the frequency ω of the bias, one can propose a set of methods for quantitative characterization of semiconductor materials and structures, Fig. 1. Admittance spectroscopy allows one to characterize the following parameters for natural diamond samples: free charge carrier concentration, its distribution over the sample, the activation energy of deep levels a E , their capture cross section, emission and capture rates, their dependence on temperature and other parameters. Admittance measurements were carried out by means of computer-controlled setup, the main parts of which are RLC-meter Agilent E4980A, closed-cycle helium probe station Janis CCR-10, and temperature controller LakeShore 336. [START_REF] Zubkov | Analysis of the electrostatic interaction of charges in multiple InGaAs/GaAs quantum wells by admittance-spectroscopy methods[END_REF][START_REF] Kucherova | Nondestructive Diagnostics of Nanoheterostructures with InGaN/GaN Multiple Quantum Wells by Thermal Admittance Spectroscopy[END_REF][START_REF] Zubkov | Admittance Spectroscopy as a Method for Investigating Relaxation Processes in Quantum-Sized Heterostructures[END_REF] A deep trap like boron in single crystal diamond can be characterized by emission rate of charge carriers to the corresponding band (valence band in our case): [START_REF] Blood | The electrical characterization of semiconductors: majority carriers and electron states[END_REF] exp

a p A th p V E e g N kT      , (1)
where N V is the effective density of states, th v is the thermal velocity for holes, p  is the hole capture cross section, and A g is the degeneracy factor for the acceptor level. Tak- ing in mind the temperature dependence of the pre-exponential factors, one usually rewrites (1) in the form

2 exp a p E e AT kT     , (2)
where factor A is independent on temperature. When a small ac signal of frequency ω is applied to the sample with fabricated Schottky and Ohmic contacts, a trap with the emission rate (1) generates a conductance (and capacitance as well) response of the form: [START_REF] Vincent | CONDUCTANCE AND CAPACITANCE STUDIES IN GAP SCHOTTKY BARRIERS[END_REF]      

12 2 0 22 2 eT eN N p A T G T S pV eT p          . (3)
In expression (3) N T is the trap concentration, and p is the free charge carrier concentration. The square root term, multiplied by the Schottky contact area S, has the meaning of the sample barrier capacitance at the applied bias V. At the maximum of conductance spectrum, the following relation is fulfilled:

p e . (4)
The processing of measured conductance spectra includes building the Arrhenius plots in coordinates ln(e/T 2 ) vs. 1/T and derivation of apparent activation energy and capture cross sectionthe key characteristics of deep level. The term "apparent activation energy" here means the dynamic activation energy obtained in non-equilibrium capacitance or admittance measurements, in the presence of ac electric field. Together with the dynamic characteristics of the deep center, conductance spectra give (via N T /p relation) the explicit information about the concentration of the trap under investigation.

Additional modeling of conductance (and capacitance) spectra according to (2) and (3) may reveal extra information about the possible energy broadening of the deep center.

Furthermore, for determination of free carrier concentration the capacitancevoltage (C-V) profiling was used. The majority charge carrier (hole) concentration profile is obtained by derivation of measured C-V characteristics:

  1 3 2 0 CV C dC pw dV eS       . ( 5
)
At this, the charge depletion width, corresponding to the barrier capacitance at a given bias, is

0 S w C   . ( 6
)
In case of the Schottky barrier the whole width is related to space charge region (SCR) of the semiconductor. Taking into account that the charge increment takes place only at the SCR edge, one can associate the width, derived from ( 6), with the current coordinate of the space charge region edge at a given bias, assuming the Schottky barrier location as a reference point (x = 0).

Note that C-V profiling gives the concentration of free charge carriers in the sample. This is an even more important characteristic for a wide bandgap semiconductor like diamond (ΔE g = 5.45 eV) than the impurity concentration N A , because only free carriers (electrons and holes) produce the electric current through the semiconductor device, providing its desirable electronic properties. But, owing to the large activation energy of boron, only less than 1% of the impurity is ionized at room temperature). [START_REF] Zubkov | Temperature admittance spectroscopy of boron doped chemical vapor deposition diamond[END_REF] Due to the peculiarities of the capacitance-voltage technique, the measured concentration of free charge carriers may differ from the impurity concentration, which will be further discussed in Section V.

III. Samples under investigation

A total of 4 natural blue type IIb diamonds were investigated in this study. The natural diamond samples were on loan from the Smithsonian Institution of Washington DC. The samples Apollo Blue and Steinmetz are double side polished. The sample Blue Pear (H26) is faceted as a gem. And the sample 111 has the major surfaces as cleaved <111> surfaces.

FTIR measurements were performed both at the Smithsonian Institution and at University LETI. The estimated FTIR concentrations of boron are presented in Table 1 The key challenge for admittance measurements is the fabrication of two types of contacts -Ohmic and Schottky. For wide bandgap diamond this is a very difficult task, and considerable time and effort was spent to work out the appropriate technology and geometry of contacts to achieve reliable results. The side, to which the contacts were deposited, was chosen on the basis of surface quality inspection. The Ohmic and Schottky contacts for electrical investigation were deposited at different temperatures. The Pt large Ohmic contact was deposited at T = 300 ºC, and smaller, round Pt Schottky contacts were deposited at 150 ºC. The diameters of the Schottky contacts were from 350 to 450 μm for various samples, Fig. 2. The resulting contact area was taken into account in the concentration measurements. Special holders for samples Blue Pear and Steinmetz were fabricated, since their bottom sides are not flat.

IV. Experimental data

A. Capacitance-voltage profiling

In order to examine the electrical properties of the samples, we used Schottky and Ohmic contacts. Measurements of their current-voltage (I-V) characteristics were performed at various temperatures. At T < 180 K the boron impurity is practically unionized. The I-V characteristic looks like that of a resistor. With temperature increasing the current-voltage characteristics become rectifying, and diamond possesses semiconductor properties. Typical I-V characteristics for the Apollo Blue sample at various temperatures are presented in Fig. 3. Rectification starts from about +2V, and we saw very low leakage currents at reverse biases up to 10-20 V. What is interesting is that the minimum in I-V characteristics was shifted from U = 0 for T < 210 K, at the temperatures where the emission from boron deep level begins take place (see next Section). At present there is not a clear explanation for this, but we note that this is a deviation from well-known Shockley theory. [START_REF] Sze | Physics of Semiconductor Devices[END_REF] Apollo Blue Capacitance-voltage characteristics of the samples were measured at several test signal frequencies over a wide temperature range (200 -400 K). The obtained 1/С 2 -V characteristics are linear in bias range from -10 to 0 V. At forward biases there is significant current across the structure, and the RLC-meter cannot properly balance the measurement scheme. At relatively low temperatures (< 250 K) a dependence of the capacitance-voltage characteristics on frequency is observed. This is the case of so-called non-quasistatic type of C-V measurements , Fig. 4a vs. 4b. [START_REF] Blood | The electrical characterization of semiconductors: majority carriers and electron states[END_REF] This is due to the fact that the boron acceptor level is located deeply in the forbidden gap and is only partially ionized. The specific feature of capacitance technique is the additional ionization of impurity with applied ac bias. The concurrence between the frequency of the induced ac bias and the deep center recharge velocity results in a frequency dependent ionization degree of the deep center under investigation. This leads to different values of charge and, hence, capacitance vs. test frequency, detectable in the experiment. Our experimental setup provides a wide range of test signal frequencies, thus controlling the ionization degree at a given temperature. At higher temperatures (> 300 K), when quasistatic C-V measurements are fulfilled (Fig. 4b) for all examined samples, no frequency dispersion of capacitance is observed.

B. Temperature and frequency admittance spectroscopy

Measurements of temperature dependent conductance (G/ω-T) and capacitance (C-T) spectra were carried out in the temperature range 20 -450 К and frequency range 1 kHz -2 MHz, Fig. 5. Care was taken to obtain accurate measurements of diamond temperature, so the temperature ramp rate was as slow as 0.5 K/min. Temperature scanning was performed with rising and falling temperature, and the obtained spectra displayed practically no hysteresis.

Temperature conductance spectra at U = 0 V for all samples were in general quite similar. Their peak amplitudes (G/ω) did not depend on frequency and fell into the temperature interval 175 -290 K. We observed the permanent frequency transformation of a single peak, which belongs to a deep boron center. An expected shift of conductance curves towards the higher temperatures with frequency increasing was observedthis is the distinctive feature of thermionic emission. So, from the temperature admittance spectra the activation energy of charge carriers from the impurity level can be evaluated in the usual manner via the Arrhenius plot, using the temperatures of conductance peak maxima, [START_REF] Blood | The electrical characterization of semiconductors: majority carriers and electron states[END_REF] (see Section V). Another measurement technique used in this study was frequency admittance spectroscopy. These measurements are performed by fixing the temperature and obtaining the capacitance and conductance response in interval of frequencies. The Arrhenius plots are created in a similar manner using the frequencies of the G/ω-f peaks maxima. This technique is sometimes more convenient than temperature admittance spectroscopy, allowing one to obtain the same set of dynamic characteristics of the examined deep level. This technique was used to study the Apollo Blue and Blue Pear samples. The Blue Pear G/ω-f spectra were obtained in the whole RLC-device frequency range (1 kHz -2 MHz), Fig. 6. The Steinmetz diamond exhibited slightly different behavior. Its peaks in conductance spectra are shifted towards low temperatures and the peak maxima drop to about 1 pF, Fig. 7. Such a decrease in conductance is in good agreement with the obtained hole concentration for this sample, which is smaller than for others.

V. DISCUSSION

A. Carrier concentration profiles

The carrier (hole) concentration profiles at various temperatures for the examined samples were obtained via derivation of C-V characteristics. Note, that this method measures the thermionic activation of the dopant at the edge of the space charge region (SCR). The dependence of net hole concentration on signal frequency was investigated for samples Steinmetz and Apollo Blue at various temperatures. At relatively low temperatures (< 250 K), when the C-V characteristics are non-quasistatic and the boron acceptor level is only partially ionized, we see strong dependence of apparent carrier concentration on frequency, see Fig. 8 for the Steinmetz. At higher temperatures (> 300 K) the quasistatic C-V measurement conditions are fulfilled (see Fig. 4b), and the derived carrier concentration p CV is independent of frequency. Similarly for the Apollo Blue sample, the average concentration of charge carriers at high temperatures is higher and about 2.5•10 16 cm -3 . At higher frequencies the apparent C-V concentration falls down to 1•10 At high temperatures the calculated concentration profiles for Apollo Blue, Blue Pear and 111 diamonds are almost the samewe see small variation of concentration from 2•10 16 cm -3 to 4•10 16 cm -3 while the space charge region width is about 1.35-1.50 μm, (Fig. 9 for Blue Pear). In general, these data are in good agreement with uncompensated boron concentration, obtained by FTIR.

For Steinmetz the p CV concentration is (4.5-5)•10 15 cm -3 at the maximum ionization and it decreases to 2•10 14 cm -3 at high frequencies and reduced temperatures. The concentration slightly increases with depth in the sample from 3•10 15 to 5•10 15 cm -3 , the corresponding coordinate (space charge region width) sweeps from 2.7 to 3.0 μm. We found that the charge carrier concentration for Steinmetz is less than for the other investigated samples, and the obtained charge carrier concentration doesn't match with the FTIR measurement for uncompensated boron.

The average hole concentrations obtained from the C-V characteristics for the samples are presented in Table 1. They are in reasonable coincidence with FTIR results.

B. Activation energies

The Arrhenius plots for all samples were created using the temperatures (for Steinmetz, Apollo Blue, 111) or frequencies (for Apollo Blue and Blue Pear) of conductance peak maxima. The apparent activation energy of charge carriers from the impurity level was obtained according to (2) as a slope of the line plotted in coordinates ln(e/T 2 ) vs. 1000/T. The activation energies and capture cross sections are presented in Table 1. For samples Apollo Blue and 111 the experimental points of the Arrhenius plots are fit linearly with high accuracy for the entire temperature range, Fig. 10. For these samples the Arrhenius plots give practically the same activation energies 322±2 and 320±1 meV; the capture cross section are 1.5•10 -13 cm 2 and 2.2•10 -13 cm 2 , respectively. The derived activation energies were the same for conductance measurements with increasing and decreasing temperatures. The slope of Arrhenius plot for Steinmetz is significantly different, resulting in E A ~ 285±10 meV. Its capture cross section is several times less.

Note, that the activation energies obtained for the natural diamond samples are similar to those measured for boron doped CVD grown diamond samples with B/C < 600 ppm. [START_REF] Zubkov | Temperature admittance spectroscopy of boron doped chemical vapor deposition diamond[END_REF] As can be seen, the mean square error (MSE) for the activation energy of the natural boron doped diamonds is less than 2 meV. One should note that the E A MSE is the criterion of crystal perfection, and for the CVD-epitaxial diamond layers, which we studied previously, the MSE was 2-3 times larger.

We have simulated the temperature conductance spectra for samples using the measured activation energies and factor A values from Table 1. The calculated curves fit very well the experimental spectra, and the estimated broadening is less than 1%, Fig. 7.

The optical properties of the boron acceptor level are well known and give an optical ionization energy for the boron acceptor of 373 meV. [START_REF] Walker | Optical absorption and luminescence in diamond[END_REF] In this study, we have very precisely measured the apparent activation energy of the boron acceptor as between 315 and 325 meV for three natural diamond samples with uncompensated boron in the range of 2.5 to 4 x 10 16 cm -3 -Apollo Blue, Blue Pear, and Diamond 111. This is significantly lower than the optical ionization energy A E , and also lower than the thermal acti- vation energy of 0.37 eV determined by dc electrical transport measurements on natural and synthetic type IIb diamonds (see, for instance [START_REF] Collins | PHOTOTHERMAL IONIZATION AND PHOTON-INDUCED TUNNELING IN ACCEPTOR PHOTOCONDUCTIVITY SPECTRUM OF SEMICONDUCTING DIAMOND[END_REF][START_REF] Lightowlers | ELECTRICAL-TRANSPORT MEASUREMENTS ON SYNTHETIC SEMICONDUCTING DIAMOND[END_REF]). The reason for the difference is the physics underlying the different measurement techniques. The free charge carrier concentration, measured using the dc electrical transport technique with ohmic contacts, corresponds to the well-known expression for partially ionized acceptor impurity A N  :

    1 1 exp A A A A F N N g E E kT      , (7)
where A g is the degeneracy factor for boron, and F E is the Fermi level. The admit- tance method, in contrast to dc electrical measurements of conductivity, is carried out under non-equilibrium conditions (due to the applied electric field) and is based on the resonant nature of the measurements. Here the ionized concentration is registered at ac frequency in vicinity of the space change region edge (that is coordinate dependent) and has an additional ionization, forced by the ac test signal: One may rewrite the expression in the form

          1 1 exp A A A A F dc ac N Nx g E E e x e x kT           . ( 8
        1 1 exp A A A A F N Nx g E E kT M x      . (9)
Here the factor

        exp dc ac M x e x e
x kT        is coordinate-dependent and divides the sample into three parts: 1) the space charge region near the rectifying barrier, where the impurity is totally ionized (small x); 2) an intermediate region where the acceptor level crosses the Fermi level; and 3) the electroneutrality region, where M(x) tends (strives) to 1 and the equilibrium carrier distribution described by [START_REF] Balmer | Unlocking diamond's potential as an electronic material[END_REF] The degree of compensation for the Apollo Blue and the Blue Pear (H26) can be estimated from the previously reported values measured by time-of-flight secondary ion mass spectroscopy (ToF SIMS) and FTIR absorption, see Table 5 in [START_REF] Gaillou | Boron in natural type IIb blue diamonds: Chemical and spectroscopic measurements[END_REF]. In that study, the ToF SIMS measurements were conducted on micron sized areas and gave a large variability from point to point, while the FTIR measurement was averaged over mm sized areas. It is not surprising to find significant inhomogeneities in natural diamond due to their often complicated growth history. Yet comparison of the uncompensated boron, measured by FTIR, and the total boron, measured by SIMS, suggests that the Apollo Blue and the Blue Pear (H26) are much less compensated than the Steinmetz sample.

VI. CONCLUSIONS

For the first time precision admittance measurements were carried out for a set of four rare, natural type IIb diamond samples in wide temperature and frequency ranges. The peaks in temperature and frequency conductance spectra were used to compute the Arrhenius plots, and the apparent activation energies for boron deep level were obtained from these plots. It was shown that G/ω-T and G/ω-f spectra give the same activation energies. Three samples (ApolloBlue, Diamond 111 and Blue Pear) showed quite similar conductance spectra, and the obtained activation energies for these samples were 320±2 meV and 315±5 meV. These energies correspond to low doped CVD-grown diamond samples with B/C < 600 ppm. Capture cross sections were generally in the range of 10 -13 cm 2 . For the Steinmetz sample the apparent activation energy is 285±10 meV, and its capture cross section is several times less.

The capacitance-voltage profiling was used to estimate the majority charge carrier concentration. Obtained carrier concentrations are in the range (1-5)•10 16 cm -3 (0.06-0.3 ppm) for three of the samples, and are in good coincidence with FTIR results. For the Steinmetz sample, the concentration is considerably lessabout 4•10 15 cm -3 .

Fig. 1

 1 Fig. 1 Admittance techniques

Fig. 2

 2 View of investigated samples with sputtered contacts and measuring probes: a -Apollo Blue, b -Diamond 111, c -Blue Pear, d -Steinmetz

Fig. 3

 3 Fig.3 Typical I-V characteristics for the natural Apollo Blue diamond sample at various temperatures (abs value for I is used)

  С 2 -V characteristics for the Steinmetz blue diamond sample at: a) 250 Knon-quasistatic condition; b) 310 Kquasistatic condition

ApolloBlueFig. 5 C

 5 Fig.5 C-T (a) and G/ω-T (b) spectra, Apollo Blue

Fig. 6 G

 6 Fig.6 G/ω-f spectra for Blue Pear

SteinmetzFig. 7

 7 Fig.7 Experimental (solid line) and modeled (dashed line) G/ω vs. T spectra for Steinmetz sample at various frequencies

Fig. 8

 8 Fig. 8 Apparent concentration vs. frequency for Steinmetz sample; T = 210 and 310 K. Error bars are shown

Fig. 10 Fig. 11

 1011 Fig.10Arrhenius plot for Apollo Blue from G-T and G-f spectra It is important that the points of the Arrhenius plot from G/ω-f measurements are in good coincidence with that ones for G/ω-T measurements, Fig.10, and in fact, the apparent activation energies, obtained from G-T and G-f measurements for Apollo Blue, are not significantly different.The Arrhenius plots for all 4 samples are shown in Fig.11. It is seen that the Arrhenius plots for Apollo Blue, Diamond 111 and Blue Pear are nearly parallel to each other, as their apparent activation energies are almost the samebetween 315 meV (for Blue Pear) and 325 meV (Apollo Blue, Diamond 111). The shifts among their Arrhenius plots originate apparently from differences in capture cross sections.



  is the dc potential applied to the sample by the dc bias (it is used for shifting the point of observation); the test signal of RLC-device produces, in turn, the ac part of potential   ac x. Here x is the distance from the Schottky barrier.

  takes place. The ac part of potential   ac x  , acting in the intermediate region, causes here the recharging of the deep boron center and produces the ac current in the outer circuit, proportional to the local carrier concentration at the edge of SCR.

Table 1 .

 1 . Characteristics of investigated samples

		Steinmetz	Apollo Blue	111	Blue Pear
	Uncomp. B from FTIR, ppm	0.15-0.20	0.21 -0.19	0.09	0.27 -0.30
	recalculated in atoms/cm 3	(2-3)•10 16	3•10 16	1.6•10 16	(4.5-5)•10 16
	p from C-V, cm -3	5•10 15	2.5•10 16	3.5•10 16	4•10 16
	G/ω peaks ampl., pF	1	2.3	3.5	2.1

  14 cm -3 for both samples.

			Blue Pear
		6e+16
	-3 p, cm	4e+16		300 K 350 K
		2e+16		400 K
				450 K
		1350	1400	1450	1500
				x, nm

Fig.9 Carrier concentration profiles at different temperatures, Blue Pear diamond

ACKNOWLEDGEMENTS

This work was supported by Act 220 of the Russian Government (Agreement No. 14.B25.31.0021 with the host organization IAP RAS). The Steinmetz blue sample was generously provided to the Smithsonian Institution by the Steinmetz company.

The authors give thanks to Dr. D. Chigirev for contacts fabrication, Dr. O. Kucherova for assistance in admittance measurements, and Dr. M. Panov (all from LETI) for FTIR measurements. They also thank Prof. Alan Collins (King's College London, UK) for valuable and useful discussions.