Vasilii Marshev1
email: vasili.marshev@imt-atlantique.fr

Johanne Bolloc'

BsC Bsc Nico Pallamin4

Jean-Louis De Bougrenet De La Tocnaye1

PhD Beatrice Cochener5

PhD Vincent Nourrit1

Keywords: Impact de casque réalité virtuelle sur clignement des nictation, sécheresse oculaire, visiocasque, réalité virtuelle, LipiView, l'épaisseur de la couche lipidique blinking, dry eye, VR headset, virtual reality, LipiView, lipid layer thickness

HAL is

Introduction

In the last years, virtual reality (VR) head mounted displays (HMD) have been gaining popularity among the public, due to the arrival of several new and affordably priced commercial products. If VR HMDs are to replace the desktop screen (at least partially) in entertainment, as well as some professional applications, it is necessary to assess the possible implications they might bring in regard to user's experience and comfort. The issue of visual comfort has long been discussed in relation to computer screens, in particular their effect on blinking and eye fatigue [START_REF] Stern | Blink rate: a possible measure of fatigue[END_REF][START_REF] Maffei | Spontaneous eye blink rate: An index of dopaminergic component of sustained attention and fatigue[END_REF] and on the development of dry eye desease [START_REF] Nosch | Relationship between corneal sensation, blinking, and tear film quality[END_REF] ("a common condition that carries significant patient morbidity and healthcare cost" [START_REF] Zhao | Intra-observer and inter-observer repeatability of ocular surface interferometer in measuring lipid layer thickness[END_REF] ). Several studies have shown that observers exposed to the regular prolonged use of desktop screens become more susceptible to dry eye and computer vision syndromes, which may originate from regular reduction of blink frequency when using desktop screen [START_REF] Rosenfield | Computer vision syndrome: a review of ocular causes and potential treatments[END_REF] .

In a recent study, Kim et al. found that blink rate decreased during two minutes long session when using a VR HMD when compared to using a desktop screen [START_REF] Kim | Change of Blink Rate in Viewing Virtual Reality with HMD[END_REF] .

Blink rate is, however, a parameter that shows significant dependency on environmental and individual characteristics [START_REF] Stern | Blink rate: a possible measure of fatigue[END_REF][START_REF] Maffei | Spontaneous eye blink rate: An index of dopaminergic component of sustained attention and fatigue[END_REF] . For instance, while some studies observed increasing blink rate with the time spent on a task, which can be a measure of fatigue [START_REF] Maffei | Spontaneous eye blink rate: An index of dopaminergic component of sustained attention and fatigue[END_REF][START_REF] Fukuda | Changes in blink rate during signal discrimination tasks[END_REF][START_REF] Stern | The eye blink and workload considerations[END_REF] , others invalidated this effect [START_REF] Kim | No fatigue effect on blink rate[END_REF] . Contradictory results have also been reported with respect to the influence of mental load (Stert and Skelly 8 reported a decrease in blink frequency but not Yamada 10 ) or task difficulty (decreased blink frequency reported by Stert and Skelly 8 , whereas not by Cho et al. 11 ). For this reason, in this study, the goal of the first experiment was to compare the potential change in blink rate when using VR HMD to the one observed with a conventional desktop screen as a reference, as well as blink rate and blink duration change over 20 minutes of use. The performed measures also included questionnaires to take into account the potential effect of cybersickness and eye fatigue.

The details and results of the first experiment are described in Experiment 1 section . In addition, because blinking and dry eye condition are tightly linked to the tear film state [START_REF] Nosch | Relationship between corneal sensation, blinking, and tear film quality[END_REF][START_REF] Freudenthaler | Characteristics of spontaneous eyeblink activity during video display terminal use in healthy volunteers. Graefe's archive for clinical and experimental ophthalmology[END_REF] and particularly the most superficial layer of the tear film, i.e. the lipid layer [START_REF] Korb | Tear film lipid layer thickness as a function of blinking[END_REF][START_REF] Foulks | The correlation between the tear film lipid layer and dry eye disease[END_REF] , the goal of the second experiment was to measure lipid layer thickness (LLT) before and after a session of either VR HMD or desktop screen use. The associated methods and results are presented in Experiment 2 section.

Experiment 1

The goal of the first experiment was to assess the difference in blinking activity between two presentation methods: desktop screen (DS) (referred to as desktop condition) and VR HMD (referred to as helmet condition). While stimuli were designed to be as similar as possible in both conditions, several important aspects remained different due to peculiarities of the presentation methods: 1) ambient illumination (while in desktop condition, participants were seated in a dark room, in helmet condition, the stimuli were presented on a black background), 2) screen distance (see below), 3) image resolution (see below).

Methods

Apparatus

The HMD used in the study was a FOVE helmet (FOVE, Inc., frame rate 70 Hz, resolution 1280×1440 each, field of view 90-100°). The FOVE integrates two cameras for eye tracking (70 Hz), which is a relatively novel feature for VR HDM devices. The DS was the display unit of the Tobii TX300 eye tracker (frame rate 60 Hz, resolution 1920×1080, distance 60 cm, field of view 41.5°). Room temperature, humidity and lighting conditions, remained constant during the experiment. The HMD luminance and the DS luminance were adjusted to be as similar as possible (21.33 cd/m 2 in the helmet condition and 23 cd/m 2 in the desktop condition). When using the FOVE, the pupillary distance was not adjusted for each participant, as this feature was unavailable with this headset.

Participants

The required sample size was calculated using G*Power3 software [START_REF] Faul | Statistical power analyses using G* Power 3.1: Tests for correlation and regression analyses[END_REF] for rmANOVA. In the experiment, one group sample went through two conditions (the helmet and the desktop conditions) giving one two-level factor. Type I error value was set to 0.05 and type II error value was set to 0.9. Effect size index was obtained from the study by Freudenthaler et al.

who compared the blink frequency in two conditions: general conversation and visual display unit use [START_REF] Freudenthaler | Characteristics of spontaneous eyeblink activity during video display terminal use in healthy volunteers. Graefe's archive for clinical and experimental ophthalmology[END_REF] . The calculated value of effect size index of Cohen's d of 0,997 corresponded to effect size index Cohen's f of 0.5 [START_REF] Lenhard | Calculation of effect sizes[END_REF] . Other studies showing the dependence of blink rate on various parameters produced even higher effect size estimates. Given the abovementioned values, 13 subjects were necessary to achieve the required power. This number is also in agreement with previous studies [START_REF] Patel | Effect of visual display unit use on blink rate and tear stability[END_REF][START_REF] Kim | Influences of computer works on blink rate and ocular dryness in adolescents[END_REF] . 15 subjects were recruited for the experiment (26.8 years old; 95% CI: 21.7-32 years, 6 female and 9 male). All participants had best corrected visual acuity of 1 (in decimal) with or without correction and no record of cornea-related medical conditions or binocular vision issues.

Participants were allowed to use their regular glasses if required. The study was carried out in accordance with the tenets of the Declaration of Helsinki. Written informed consent was obtained from all participants.

Design and procedure

The participants went through 20 minutes of playing a simplified version of the 2D game "Flappy bird" in 2D, in two conditions: while wearing a HMD and in front of a DS, 60 cm away. Several studies suggest that 20 minutes of use of a VR HMD are sufficient to induce discomfort [START_REF] Stanney | Aftereffects from virtual environment exposure: How long do they last?[END_REF] . This duration presented a good compromise between the need for having a task long enough to possibly observe a decrease in blink rate (BR), and practicalities. The choice of this game was motivated by two reasons. Firstly, it required a sustained attention. BR has been shown to reduce with effort [START_REF] Kim | No fatigue effect on blink rate[END_REF] , attention [START_REF] Sakai | Eda-Based Estimation Of Visual Attention By Observation Of Eye Blink Frequency[END_REF] , interest [START_REF] Hideoki | Eyeblink rates as a function of the interest value of video stimuli[END_REF] and in view of the relatively short experiment duration, the circumstances were organized as to facilitate BR reduction. Secondly, it would not produce any cybersickness and its simple interface and availability made it easy to implement in both conditions with limited differences.

In the helmet condition, the game was presented on a "virtual" screen on a black background. The monitor in the desktop condition was positioned at 60 cm away from the viewer, in the helmet condition, the game was presented at the same distance to ensure that the game's retinal projection was the same in both conditions. In addition, the game played on the DS was rendered at 640×480 (compared to 640×720 of each screen of the HMD) instead of the native screen resolution (1920×1080) to ensure similar pixel density per degree.

Although the game ("Flappy bird") used in this study was designed to avoid any induction of cybersickness, Simulator sickness questionnaire [START_REF] Kennedy | Simulator sickness questionnaire: An enhanced method for quantifying simulator sickness[END_REF] (SSQ) was used as a further precaution. The SSQ is a list of 16 questions to evaluate three categories of symptoms: nausea related symptoms, oculomotor symptoms and disorientation symptoms. In addition, the questionnaire developed by Bang et al. [START_REF] Bang | Assessment of eye fatigue caused by 3D displays based on multimodal measurements[END_REF] was also used to assess visual discomfort (VFQ). This questionnaire based on study by Heo et al. [START_REF] Heo | Quantitative measurement of eyestrain on 3D stereoscopic display considering the eye foveation model and edge information[END_REF] has the advantage of being short and easy to fill out. Just before the test and right after it, the participants were seated in front of the DS while answering orally the experimenter's questions (SSQ and VFQ).

During the pretest and posttest interview, blink activity was measured using the Tobii TX300 eye tracker. When playing "Flappy bird" on the DS or the FOVE, blinking was measured respectively with the TX300 or the eye tracker integrated into the FOVE. Blinks were derived from the eye tracker data. Control for the closing percentage of the eye lid was not available with the FOVE's blink detection algorithm. Therefore, the eye closure was assumed whenever the eye tracker failed to recognize both eyes. Two criteria were used to consider absence of a pupil as a blink based on its duration: 1) bottom limit of 83 ms (following [START_REF] Van Orden | Combined eye activity measures accurately estimate changes in sustained visual task performance[END_REF][START_REF] Benedetto | Effects of luminance and illuminance on visual fatigue and arousal during digital reading[END_REF] ), in order to filter out brief data losses, 2) top limit of 1 second (one of the criteria proposed by Stern et al. [START_REF] Stern | The endogenous eyeblink[END_REF] ) to exclude other irrelevant events.

In order to limit the number of subjects and due to significant individual variability of BR in people (see Introduction and Stern et al. [START_REF] Stern | Blink rate: a possible measure of fatigue[END_REF] ), a within-group design was chosen. To avoid any possible influence of the order of the tests, half of the participants went through the helmet condition first, the other half were tested with the DS first. Two experimental sessions for both conditions were taken on two separate days to avoid any possible cross influence.

To assess if the blinking data from the FOVE and TX300 are in agreement, two measurements with two participants were performed to compare the counted blinks estimated by the eye trackers to those made by a human observer during two minutes playing sessions. The observer would directly watch the subject's eyes when using the TX300 or watch the videos recorded by the cameras of the FOVE's eye tracker using the FOVE debug application on a separate screen. Results (see Table 1) show that measurements can differ from the ones measured by an observer, and the FOVE seems somewhat less consistent with the experimenter's observations than the Tobii. Various reasons can contribute to this discrepancy in blink count, such as different proprietary algorithms. Observer's blinks and judgements about whether a blink was complete (covered the whole pupil) can affect the observer's count. Another possibility could be that the quality of the eye tracking system built in the FOVE helmet may be of poorer quality than that of the TX300, thus widening the discrepancy in the measurements made by the observer and by the FOVE eye tracker. Yet, since eye trackers based analysis has been used lately in studies dedicated to blinking activity [START_REF] Freudenthaler | Characteristics of spontaneous eyeblink activity during video display terminal use in healthy volunteers. Graefe's archive for clinical and experimental ophthalmology[END_REF][START_REF] Benedetto | Effects of luminance and illuminance on visual fatigue and arousal during digital reading[END_REF] , this method was used to analyze blinking as well. To avoid misconclusions due to the possible bias in the eye trackers' measurements, the blink metrics measured by Tobii just before and immediately after the game session were compared (pretest and posttest comparison).

Analyses

Each test condition (helmet and desktop conditions) consisted of three phases: pretest (included a questionnaire-based interview), test (playing the game) and posttest (included a questionnaire-based interview). In each phase of the experiment, eye blinks were recorded. Therefore, the data included two subsets: blinking activity and questionnaire results.

Blinking was analysed in two aspects: BR and blink duration (BD). Blinking during the test phase was analysed in five minutes intervals (thus, four intervals). Average number of blinks per minute was calculated for each five minute interval Therefore, for the test, each participant's data were treated as four pairs of BR and BD averaged for each of the four five-minute intervals. Only the blinks recorded during the first two minutes were used in the analysis for the pretest and posttest interviews, as the duration of the interviews varied with participants. To compare BR in the pretest phase and the posttest phase in both conditions, the BR recorded in the pretest was substracted from the BR recorded in the posttest. For BD analysis, average BD recorded in pretest was substracted from that recorded in posttest.

Results

The data of three participants were excluded from the analysis, because their blink registration data were too noisy to efficiently distinguish actual blinks from data losses which occured during the tests and resulted in eye trackers' failure to register any blinks in long time intervals, such as three consecutive minutes.

BR for all participants during the game in both conditions (i.e., desktop and helmet data averaged together) was 14.9 blinks; 95% CI: 13.5-16.2 blinks (see Both parameters increased significantly with time (rmANOVA F(1,11) = 9.19, p = .01 for BR, rmANOVA F(1,11) = 6.4, p = .03 for BD), as illustrated, respectively, in Fig. 1 and Fig. 2. To support this observation, linear mixed-effects regression analysis was performed to model BR and BD as functions of time. To account for between-subject variance, a random intercept for each participant was included. To assess the effect of time, two models were compared: one with time as a fixed effect and one without. P-values were computed using Kenward-Roger approximation; this method was chosen due to the comparatively small sample size. The models confirmed an increase in BR (F ( Regarding the questionnaires measuring eye fatigue (VFQ) and discomfort (SSQ) induced by the use of HMD or DS, the difference between the posttest and the pretest scores was calculated to compare the conditions (helmet vs desktop) using the Wilcoxon paired test.

The results did not show significant differences between the conditions (helmet vs desktop) for both questionnaires (SSQ: V = 46, p = .62; VFQ: V = 15.5, p = .13, see Fig. 3).

In view of the absence of differences between the two conditions and the importance of individual variations in blinking (see previous sections), individual results were analyzed to see if for some of the participants BR varied more significantly than for others, depending on the test conditions (see Table 3). In this analysis, 20 BR values (for each minute) were taken for each participant to obtain more reliable datasets. False discovery rate correction for multiple comparisons was used. The data show that among 12 subjects, who participated in the experiment, four demonstrated significantly more blinks in the helmet condition, seven subjects showed significantly more blinks in the desktop condition, and in one participant, no significant difference was found in BR between the conditions.

In order to see if questionnaire scores reflected this individual variability, questionnaire score change and BR differences were tested between the conditions for correlation with Spearman correlation coefficient. No significant correlation was found for both questionnaires (SSQ: rs = .29, p = .35; VFQ: rs = -.16, p = .61).

Experiment 2

In Experiment 2 LLT before and after a video game session was measured. The lipid layer "is the outermost layer of the tear film" [START_REF] Zhao | Intra-observer and inter-observer repeatability of ocular surface interferometer in measuring lipid layer thickness[END_REF] and its thickness has been shown to depend on blinking frequency [START_REF] Korb | Tear film lipid layer thickness as a function of blinking[END_REF] and to correlate with dry eye symptoms severity [START_REF] Blackie | The relationship between dry eye symptoms and lipid layer thickness[END_REF] . Lipid layer is thought to slow down the tear film evaporation rate, therefore, reduced LLT or inconsistency of its spread across the cornea due to BR decrease can lead to dry eye symptoms [START_REF] Foulks | The correlation between the tear film lipid layer and dry eye disease[END_REF] . Subjects were divided into two groups, one of which played the game wearing the FOVE HMD (the helmet condition) and the other played the game in front of a DS (the desktop condition).

Methods

Apparatus

The same FOVE helmet was used as in Experiment 1. The instrument used to assess LLT was the LipiView® ocular surface interferometer (TearScience Inc, Morrisville, NC). During the measurement, the participant is seated in front of the apparatus and places his head on a chin rest. The built-in multi-wavelentgh light sources emit light into the participant's eye while the built-in cameras capture a picture of the eye. The light reflected from the tear film is used to compute the light interference patterns to infer the thickness of the outmost lipid layer of the tear film [START_REF] Korb | Ocular surface interferometry (OSI) methods for imaging and measuring ocular tear film layer thickness (es)[END_REF] . Measurements which exceeded the maximum value accessible by the apparatus (100 nm) were discarded from the analysis. All the measurements were performed by the same specialist at the Brest Regional Hospital-University Centre.

Design and procedure

Participants played the game "Flappy bird" for 20 minutes as described in Experiment 1.

Two groups of subjects participated in this experiment. One group played the game on a DS, the other group played it wearing the FOVE HMD. LLT (both eyes) was measured by the same trained orthoptist right before (pretest) and right after (posttest) playing the game. Only right eyes data were used in the study.

To double check the repeatability of the data provided by the apparatus, a small study was carried out with four subjects (including one author) (25.5 years old; 95% CI: 18.4-32.6 years, 3 female, 1 male) who were tested by the same observer four times during the day between 10 a.m. and 4 p.m. with two hours intervals in same conditions (same room, same lighting, with humidity and temperature controlled by an airconditioner). Data of one participant were excluded (LLT value exceeded the maximum accessible by the apparatus (100 nm)). Coefficient of repeatability was 9 nm for the left eye and 8 nm for the right eye.

These results are in agreement with another study [START_REF] Zhao | Intra-observer and inter-observer repeatability of ocular surface interferometer in measuring lipid layer thickness[END_REF] which showed that "when a single observer repeated the imaging on the same day, the coefficient of repeatability was 16 nm and the 95% limits of agreement were between -11 nm and 18 nm".

Participants

The desktop group consisted of 12 subjects (including 3 authors) (31.3 years; 95% CI: 25.5-37.2 years, 6 female and 6 male). The helmet group consisted of 12 subjects (including 3 authors) (32.8 years; 95% CI: 25.9-39.7 years, 6 female and 6 male). Data of two subjects were discarded from the helmet group due to value of LLT exceeding the maximum value measurable with LipiView (100 nm). In order to even out the sizes of the samples in the two groups, data of two randomly chosen participants in desktop group also were not included into the analysis.

The required sample size was calculated using G*Power3 software [START_REF] Faul | Statistical power analyses using G* Power 3.1: Tests for correlation and regression analyses[END_REF] for 2×2 betweenwithin subject ANOVA. The within-subject factor was represented with the measurement stage (pretest or posttest). The between-subject factor was represented with the condition (helmet or desktop). Type I error value was set to 0.05 and type II error value was set to 0.9. In absence of studies with similar designs, methods and conditions that could be used as reference for expected effect size estimation, the effect size was considered big (Cohen's f of 0.5) due to high test-retest reliability of the used measuring technique and the precision of the apparatus. The calculated sample size necessary to find the significant interaction of the two factors was 20. It corresponds to the resulting 20 participants (10 in each condition) whose data that were analyzed.

All participants had normal or corrected to normal vision and no record of cornea-related medical conditions. Participants were allowed to use their regular glasses if required. The study was carried out in accordance with the tenets of the Declaration of Helsinki. Written informed consent was obtained from all participants.

Results

Initial LLT (before the experiment) was 57.2 nm; 95% CI: 53.3-61.1 nm and it reached 66.5 nm; 95% CI: 62.25-70.8 nm afterwards, which was a little lower than data reported previously [START_REF] Isreb | Correlation of lipid layer thickness measurements with fluorescein tear film break-up time and Schirmer's test[END_REF] (average 89.8 nm with standard deviation 42.5). Mixed effects ANOVA was used to test the effect of the experiment phase (pretest or posttest) and condition (helmet or desktop) on LLT.

The results showed a significant interaction between phase and condition (F(1,18) = 9.35, p = .02). Further analysis revealed significant increase in LLT in both conditions (helmet: F(1,9) = 26.18, p < .001, desktop F(1,9) = 14.22, p = .004). Also, it showed comparable initial values of LLT between the conditions (pretest: F(1,18) = 0.77, p = .39) and significant difference after 20 minutes of the session (posttest: F(1,18) = 11.03, p = .004) with a higher LLT value found in the helmet condition (58.8 nm in desktop condition, 76.2 nm in helmet condition) (see Fig. 4).

Discussion

Computer vision syndrome is defined by the American Optometric Association as the combination of eye and vision problems associated with the use of computers [START_REF] Portello | Blink rate, incomplete blinks and computer vision syndrome[END_REF] . These problems include eyestrain, tired eyes, irritation, redness, blurred vision and diplopia. One of the possible causes of computer vision syndrome is the reduction of the BR that contributes to a poor tear film quality and temporary stress of the cornea. Most studies concerning computer vision syndrome focused on the use of conventional computer screens [START_REF] Rosenfield | Computer vision syndrome: a review of ocular causes and potential treatments[END_REF] but little is known about the risk of computer vision syndrome symptoms when using VR HMD. Kuze and Ukai 33 conducted a pretest-posttest questionnaire study to compare the visual fatigue effect of HMD and DS use, but their system used 3D stimuli on the contrary of this study. In the present study, the choice of the 2D stimuli instead of 3D stimuli was dictated by the need to investigate the possible outcomes of the presentation circumstances and to isolate them from the influence of 3D presentation aftereffects, such as vergence-accomodation conflict and cybersickness.

In Experiment 1, the goal was to investigate the impact of HMD use on BR, BD, cybersickness and eye strain and compared it to that of DS use. In terms of BR and BD, the present results are in agreement with litterature 2 with respect to the fact that BR and BD increase with time spent on a task. However, the change in BR and BD after the game compared to the base level (pretest-posttest comparison) was not statistically significant.

In the present study, the game presentation time was comparable to other studies [START_REF] Kuze | Subjective evaluation of visual fatigue caused by motion images[END_REF] , but, perhaps, too short to allow observing a significant change in BR increase between the two conditions.

On the contrary to Kim et al. [START_REF] Kim | Change of Blink Rate in Viewing Virtual Reality with HMD[END_REF] , the present results did not highlight any significant impact of the viewing method on BR and BD. This discrepancy may be explained by the different procedures: 1) the screen distance (0.6 m here and 1 m in the study by Kim et al. [START_REF] Kim | Change of Blink Rate in Viewing Virtual Reality with HMD[END_REF] ), 2) the stimuli (here, participants performed a task that required them to pay attention to the scene to fulfill the task), 3) the algorithm used to count blink, and, perhaps, most of all 4) the test duration (20 minutes here and 2 minutes in Kim et al. [START_REF] Kim | Change of Blink Rate in Viewing Virtual Reality with HMD[END_REF] ). However, the results of the present study are in agreement with Kuze and Ukai 33 who did not find differences in terms of induced eye fatigue (assessed by questionnaire scores) despite using a possibly more tiring stimulus (stereoscopic). Significant individual variations in BR between the conditions occured in 11 of 12 subjects suggesting that personal recommendations are needed when regular use of any of the presentation techniques is considered. At the same time, according to the correlation analysis, questionnaire scores did not follow these individual variations, suggesting that questionnaires used in this study may not be sensitive enough to measure these individual susceptibilities. (The questionnaires were filled out in the first five minutes past viewing (according to Ames et al. [START_REF] Ames | The development of a symptom questionnaire for assessing virtual reality viewing using a head-mounted display[END_REF] ), which allowed to rule out the possibility that symptoms had dissipated by the time the subjects filled the questionnaires.)

The goal of experiment 2 was to measure the change in eye tear film LLT after DS and HMD use. According to the present results, LLT increased in both conditions, whereas no change was expected (following the results of experiment 1) or a reduction (e.g., due to reduced BR). A possible explanation would be that participants, having deprived themselves from blinking while playing, felt necessary to blink intensively after the experiment, producing excessive LLT reinforcement before the second measurement was made, as extensive blinking has been shown to cause significant increase in LLT [START_REF] Korb | Tear film lipid layer thickness as a function of blinking[END_REF] . Secondly, the experiment revealed higher degree of change of LLT after HMD use compared to DS use. In this study, the temperature and humidity conditions were not measured, but controlled by providing same environment for all participants. These environmental factors have been shown to have the influence on tear film state and, in particular, on LLT. For instance, Abusharha and colleagues [START_REF] Abusharha | Effect of ambient temperature on the human tear film[END_REF] conducted an experiment varying the temperature in a controlled chamber and showed increase in LLT and evaporation rate as a consequence of increase of temperature. Korb et al. [START_REF] Korb | Effect of periocular humidity on the tear film lipid layer[END_REF] measured the effect of humidity on LLT. They compared the LLT in an eye in the room humidity (40-50% of relative humidity) to that in an eye isolated with goggles with 10 drops of saline added onto the mounting to increase humidity. The results [START_REF] Korb | Effect of periocular humidity on the tear film lipid layer[END_REF] showed that in the eye presented with higher humidity, LLT increased significantly compared to the eye in the room humidity both during the period of different humidity and as far as 60 minutes after removing the goggles. Presumably, the isolated chamber of the HMD might preserve higher temperature and humidity because of the face skin and sweat evaporation, which might produce similar effect to that in the two studies [START_REF] Abusharha | Effect of ambient temperature on the human tear film[END_REF][START_REF] Korb | Effect of periocular humidity on the tear film lipid layer[END_REF] . It may also be an evidence for a more apparent manifestation of a reactive mechanism protecting the ocular surface from exposure to blink reduction, however this claim would require a thorough experimental clarification.

In conclusion, the present study addressed the issue of blinking during use of VR HMD.

On the contrary to a recent study [START_REF] Kim | Change of Blink Rate in Viewing Virtual Reality with HMD[END_REF] , the present results did not show any statistically significant differences between DS and HMD in terms of blinking. However, strong individual variations were observed in all subjects but one. In view of these results, further investigation considering longer exposure time and more "natural" use (i.e. in the design used here the two conditions were as similar as possible, but in practice, VR games tend to be more visually demanding than the ones played at the DS) would be of interest, also considering additional tear film statistics [START_REF] Choi | The influences of smartphone use on the status of the tear film and ocular surface[END_REF] .

Figure 1:

Blink rate throughout the game session in the two conditions. Number of blinks per minute (blink rate, BR) averaged for five-minute intervals across the participants (N = 12) while playing a game in two conditions (while using a virtual reality headset and desktop screen) with regression lines is plotted. No significant difference between the conditions was found. Blink rate increases with time. Dots indicate mean blink rate for the previous 5 minutes across all the participants for the helmet condition, and triangles indicate blink rate for the desktop condition. The dashed and solid vertical lines represent the 95% confidence intervals for the helmet and desktop conditions, respectively. Also, linear models were fitted for the helmet (dashed) and the desktop (solid) conditions. minutes of playing the game wearing virtual reality headset (helmet) and in in front of a desctop screen is plotted. Lipid layer thickness increased significantly with time. Also, it increased at a higher rate with the virtual reality headset. Lipid layer thickness is scaled on the ordinate axis, the measurements done before the experiment (pretest, left) and after 20 minutes of playing the game in virtual reality headset (posttest, right). The data in the desktop condition is plotted with a solid line, and the data in the helmet condition is plotted with a dashed line.

Subjec

  1,83) = 4.3, p = .04, β = .36) and in BD (F(1,83) = 13, p = .001, β = .35) with time. Pretest and posttest BR comparison (the BR in pretest substracted from the BR in posttest) did not reveal any significant differences (rmANOVA F(1,11) < .001, p = .98) between the helmet condition (1.2 blinks; 95% CI: -3.5-+5.8 blinks) and the desktop condition (1.3 blinks; 95% CI: -4.2-+6.7). The comparison of BD (the BD in pretest substracted from the BD in posttest) also did not show significant difference (F(1,11) < .001, p = .92) between the helmet condition (-4.67 ms; 95% CI: -34.8-+25.4 ms) and the desktop condition (-7.23 ms; 95% CI: -75.7-+61.2).

Figure 2 :

 2 Figure 2: Blink duration throughout the game session in the two conditions. The duration

Figure 3 :

 3 Figure 3: Questionnaire scores change after the game session in the two conditions. The

Figure 4 :

 4 Figure 4: Lipid layer thickness measurements before and after the game session in the

Table 2 )

 2 , BD was 198.8 ms; 95% CI: 195.3-202.3 ms, which is similar to what has been reported in previous studies 28 .

	Repeated measures ANOVA was used to investigate how BR and BD varied in both
	conditions and with time on experiment (2 (conditions) × 4 (five-minute intervals)) during
	the test phase. The analysis did not show significant difference in BR (rmANOVA F(1,11) =
	.01, p = .92) between the helmet condition (15.1 blinks; 95% CI: 12.6-17.6 blinks) and the
	desktop condition (14.6 blinks; 95% CI: 13.6-15.7 blinks). Neither the difference in BD
	between the helmet condition (205.75 ms; 95% CI: 200.9-210.6 ms) and the desktop
	condition (202.82 ms; 95% CI: 198.2-207.5 ms) was significant (rmANOVA F(1,11) =
	4.534, p = .06).

Table 3 :

 3 Participants-wise analysis of the difference between the conditions

		F	Corrected P	Mean BR; 95% CI (Helmet / Desktop), blinks
	t		(False
			Discovery Rate)
	1	22.11	< .001	3.88-7.12 / 2.35; 1.8-2.9
	2	16.72	< .001	45; 33.56-56.35 / 21.6; 20.09-23.11
	3	64.2	< .001	56.65; 47.59-65.71 / 21.15; 19.6-22.7
	4	22.15	< .001	2.4; 1.59-3.21 / 8.8; 6.08-11.52
	5	18	< .001	23.35; 20.06-26.64 / 15.6; 13.92-17.28
	6	63.71	< .001	3.75; 1.97-5.53 / 11.7; 10.56-12.84
	7	72.21	< .001	10.35; 9.11-11.6 / 29.05; 24.91-33.19
	8	<	> .99	14.25; 11.24-17.26 / 14.25; 12.3-16.2
		0.0001
	9	80.54	< .001	6.75; 5.1-8.4 / 18.6; 16.61-20.6
	10	14.53	.001	9.1; 6.46-11.74 / 14.45; 12.52-16.39
	11	100.44 < .001	2.15; 1.27-3.03 / 8.5; 7.18-9.82
	12	30.62	< .001	1.95; 1.25-2.65 / 9.55; 6.88-12.23

Table 3 .

 3 Participants-wise analysis of the difference between the conditions.

Acknowledgements

This research was partially funded by the Brittany region and FHU Tech-San.

Disclosure of interest

The authors declare that they have no conflict of interest concerning this article. This research was partially funded by the Brittany region and FHU Tech-San.


Y Si Abderrahmane

A Menad

F Boutaiba

N Benyahia

A Zaoui
email: azaoui@polytech-lille.fr

M Ferhat

Insights into structural and dynamical characteristics of III-V Boron polytypes

Keywords: DFT, III-V Boron semiconductors, crystal polytypes 3C and 2H

III-V boron materials are a class of semiconductors with a wide range of outstanding properties and applications. In this paper, the density functional theory is used to explore the structural phase stability, atomic structure, electron band structures and dynamics properties of cubic (3C) and hexagonal (2H) polytypes of boron III-V compounds. We show that polytypism has generally a weak impact on electronic and lattice dynamics properties of BP, BAs, BSb, and BBi.

We find small total energy difference between cubic and hexagonal boron-V compounds (∼18.7meV/atom, ∼15.8meV/atom, ∼6.9meV/atom, and ∼15.8meV/atom for BP, BAs, BSb and BBi respectively). Accurate quasiparticle (modified Becke-Johnson (mBJ) potential, and local density approximation-1/2) schemes predicted indirect bandgap for 3C and 2H phases of BP, BAs and BSb. Interestingly, BBi evidence narrower direct bandgap for both cubic (∼0.38eV) and hexagonal (∼0.19eV) crystal polytypes, which makes BBi compound a promising candidate for optoelectronic applications such as infrared sources and detectors.

The dynamical stability of 2H boron compounds has also been studied to unravel the possible feasibility of experimental realizations of these compounds. Moreover, we find that the phonon properties of boron III-V compounds contrast considerably with other III-V materials, such the overbending of the transverse optical branches, the bunching of the acoustic branches, the weak LO-TO splitting, and the atypical negative Born effective charges.

2

I. Introduction

Boron based III-V semiconductors (BP, BAs, BSb, and BBi) and their alloys have recently become highly studied materials in the context of both fundamental investigations and their wide range of possible thermal [1][2][3], transport [4], and electronic properties .

BP, BAs, BSb, and BBi usually have the zinc-blende (ZB) crystal structure. Whereas boron nitride (BN), which posses exceptional properties, can stably exists in many polymorphs, such as hexagonal graphite like structure (h-BN), wurtzite-like phase (w-BN), and also cubic diamond-like phase (c-BN). BN share many of its electronic structure properties with group-III nitride compounds (GaN, AlN and InN). For example, BN shows wide gap energies [6,8,9,13,30,31], high bulk modulus and elastic constants [9], and a relatively high ionic bonding [32]. In contrast BP, BAs, BSb, and BBi show narrow band gap energies [8,13,15,19], strong covalent bonding [5,12,13,15] and unusual dynamical properties [16] compared to BN.

With the recent progress in nanowires (NWs) growth, a structural novelty was recently demonstrated in semiconductors-NWs based on various cubic-ZB III-V-compounds, which is their unexpected favored crystallization in the hexagonal-wurtzite (WZ) phase. The WZ crystal is not observable at ambient conditions in bulk of any III-V materials except for III-V nitrides.

For instance, a wide number of WZ III-V NWs such as GaAs [33], AlAs [34], GaP [35],

InP [36], InAs [37], InSb [38], InGaAs [39], and InAsSb [40] have been grown by modern epitaxial techniques including molecular beam epitaxy (MBE), chemical beam epitaxy, metal organic vapor phase epitaxy (MOVPE), and other techniques. Interestingly, the coexistence of different polytypes (i.e., different crystal phase such as WZ and ZB can coexist in a single NWs) can dramatically modifies the electronic structure properties. For instance indirect ZB semiconductors such as AlAs [34], GaP [35], and GaSbP [41] may evince drastic change of their electronic properties when transformed from the cubic to the wurtzite crystal phase with direct band-gap.

The phenomenon polytypism has been also observed in many II-VI [42][43] and oxide semiconductors such BeO [44] and CaO [45] which crystallizes in the wurtzite structure, unlike the other members of their family (i.e., alkaline-earth oxides: MgO, SrO, and BaO).

In the nanomaterial regime, BN show rich unusual crystalline phases, including, nanotube (1D, BNNTs) [46,47], hexagonal graphite-like (2D-, h-BN) [48], and 2D nanostructure (including nanosheets [49,50], nanoribbons [50], and nanomeshes [50]). Moreover, recent DFT calculations addressed the electronic structure properties of two-dimensional hexagonal structure of BN, BP, BAs, and BSb [51], and planar molecules of BN [52][53]. Because of the low dimensionality and the induced confinement effects, 2D B-V materials would offers a plethora of applications. First principles study [51] shows that 2D-h BN, BP, BAs and BSb are mechanically and dynamically stable, and are found semiconductor. Their band-gaps are reduced compared to their 3D-bulk forms, however BN(PB, BAs, BSb) still have wide(narrow) band-gaps. Moreover, 2D-h BN shows strong in-plane stiffness compared to 2D-h BP, BAs, and BSb.

The small ground-state total energy differences (< 25meV) between ZB (3C) and WZ (2H) phase found for III-V phosphides [54], arsenide and antimonide compounds, lead one to ask the question about the stability of boron III-V materials in the WZ phase. Knowledge on the materials properties of the bulk phase of boron compounds is the step towards the optimization of device performances and the design of new Nws-based devices. Moreover, the knowledge regarding WZ electronic structure properties of B-V materials is quite limited in the literature. To address these questions, we present here the detailed calculations of structural, energetic, electronic and dynamical properties of hexagonal WZ-2H polytype phase in comparison to the well-known unstrained ZB-3C structure of III-V boron compounds (BP, BAs, BSb and BBi), using state-of-the-art first-principles pseudopotential calculations.

II. Computational methods

The ab initio calculations based on density functional theory (DFT) [55] have been performed using the plane-wave pseudopotential approach as implemented in the Quantum ESPRESSO Package [56]. The exchange-correlation functional of the many-body electron-electron interaction is approximated by its local version, explicitly, the local density approximation (LDA) as parameterized by Perdew and Zunger [57]. Relativistic effects, including spin-orbit coupling (SO) were fully included in the present calculations using the all-electron projectoraugmented wave (PAW) scheme [58].

We used a plane-wave cutoff energy of80 Ry, and an energy cut-off of 600 Ry was included for charge density. The Brillouin zone (BZ) was sampled within a 8×8×8 (3C) and 8×8×6 (2H) k-points grid according to Monkhorst and Pack [59]. Structural optimizations for cell geometry and atomic positions were performed energy were converged to within 10 -5 Ry/cell, and the remaining force acting on the atoms are less than 5 10 -4 RyÅ -1 .

The phonon properties are performed using density functional perturbation theory (DFTP) [60]. A 4 × 4 × 4 (3C) and 4 × 4 × 3 (2H) q-points MP sampling were employed to perform inverse Fourier transformation.

III. Results and discussions

A. Structural properties

The equilibrium structural parameters of the 3C and 2H polytypes of boron III-V compounds are obtained by minimizing the total-energy with respect to the lattice constant a (3C) and the lattice constants a and c and the internal-cell parameter u for the WZ-2H phase. The crystalpolytype types are depicted in Figure 1. The resulting minimum energy surface E(c, a, u) is illustrated in Figure 2.

In Table I, we compare the calculated equilibrium structural parameters of 3C and 2H B-V compounds (V = P, As, Sb, and Bi) with available theoretical and experimental results. The theoretical 3Clattice constants a are in excellent agreement with experimental values, being within ∼1%, 0.6% and 1.7% of the measured value for BP, BAs and BSb respectively. To the best of our knowledge no experimental data are available for structural parameters of 3C-BBi and 2H boron III-V semiconductors. Nevertheless, the present work is in good agreement with previous calculations [19,65]. Interestingly, the bulk modulus B0 is indifferent with crystallographic phase that can adopt boron III-V materials.

The calculated ratio typically deviates from the ideal value of ~1.633 of III-V metastable WZ semiconductors ( ~1.645(GaAs), 1.64(InP), AlP(1.642)) [54]. These findings agree with the empirical rule of Lawartz [66], which states that materials compounds with ZB ground state should have ratios larger than the ideal value of their 'unstable' WZ phase.

This rule is also supported by earlier first-principles calculation [42][43]54] for metastable WZ III-V and II-VI compounds. In addition, the calculated cell-internal parameter u for 2H crystal departs from its ideal value = = 0.375. Stable WZ III-V and II-VI compounds show u>u0 [42,[66][67]; while metastable WZ III-V [54] and II-VI [42][43] materials have the opposite trend (i.e., u<u0). We conclude that there is a close correlation between ratio, internal cell parameter u and 3C-versus-2H ground-state-stability.

B. Energetic stabilities

The volume dependence of total energy of 3C and 2H polytypes are shown in Figure 3.

Clearly the ground state phase of III-V boron compounds is the zinc-blende crystal structure.

This means that the cubic (3C) polymorphs are the energetically lowest, agreeing with experimental observations and previous calculations. The stability of the polytype (ZB versus WZ) is described by the total energy difference ∆ between 2H and 3C phases (∆ = 2 -3 . ∆ is ∼18.7meV(BP), ∼15.8meV(BAs), ∼6.9meV(BSb), and ∼15.8meV(BBi). From an energetically point of view, the minimum found in ∆ for BSb, compared to BP/BAs/BSb, indicates that WZ BSb crystal can be grown close to equilibrium; whereas that would be relatively more difficult for BP, BAs and BBi. The calculated ∆ agrees well with previous DFT calculations [14] from which 20meV, 15.76meV, 6.74meV, and 15.56meV were derived for BP, BAs, BSb and BBi respectively. The total energy difference ∆ is quite small, thus it costs low energy to change the sequence of the stacking layers 3C→2H, which might be taken as a strong tendency of polytypism in boron III-V compounds. Consequently, under specific temperature and crystal growth conditions, we can expect (or not expect) that BP, BAs, BSb and BBi would have good chance to be synthesized in the wurtzite crystal structure.

C. Electronic structure It is well known that very often, DFT-LDA fails to predict correctly the energy gaps of semiconductors and insulators, and typically Kohn-Sham gaps underestimates excited states of solids by 50%-100%. The underestimation of the excitation energies is fundamentally attributed to the inherent lack of derivative discontinuity of the exchange-correlation functional. In the last years, an efficient method based on Hedin's GW approximation [68] has been developed [69]. Unfortunately, GW methods are rather computer-time consuming.

The electronic band structure is first performed using the full-potential linearized augmented plane-wave (FP-LAPW) as implemented in the Wien2k code [START_REF] Blaha | WIEN2k: An Augmented Plane wave plus Local Orbitals Program for Calculating Crystal Properties[END_REF] within the recent developed modified Becke-Johnson (mBJ) exchange potential [START_REF] Tran | [END_REF] within the LDA. The mBJ exchange potential has been applied to a large variety of solids and was able to deliver accurate excitations energies in close agreement with experiment. In addition, we also apply pseudopotential LDA-1/2 technique [72], which is less computationally expensive, compares well with the popular many-body GW quasiparticle (QP) approach [69] and have shown to work well for a variety of types of semiconductors and insulators [72,73].

The mBJ band structures, including spin-orbit coupling of B-V compounds in the ZB and WZ crystal structures are displayed respectively in Fig. 4 and Fig. 5 along the high-symmetry points of the BZ. The various band parameters such as direct and indirect band gaps and spinorbit coupling are given in Table II (3C) and Table III (2H). All 3C band structures of III-V boron compounds, except BBi, show a minimum of the lowest conduction band near the X point. Earlier QP-GW calculations [8] qualitatively support our findings with minimum indirect(direct) band gaps of 1.90eV (4.4eV) and 1.60eV (4.2eV) for BP and BAs respectively. The calculated fundamental (minimum) band-gaps of ∼1.8 eV (BP) and ∼1.7 eV (BAs) are in good agreement with the available experimental measurements of ∼2 eV for BP [74], and 1.46 ±0.02 eV for BAs [75]. The few existing experimental minimum band gapsfor BSb are probably not reliable, they yield values of 0.46-0.55eV [63] and ∼0.51eV [76] close to the earlier underestimated LDA-bandgap calculations of ∼0.53eV [11]. The calculated minimum band-gap for BSb is ∼0.94eV in good agreement with the recent FP-LAPW calculations [77] in which an indirect-gap of ∼1eV was obtained.

The trend concerning the indirect nature of the band-gap of 3C BP, BAs and BSb is violated for BBi. 3C-BBi has a direct band-gap semiconductor at Γ point. Interestingly, the calculated direct narrow energy band gap of 3C-boron bismuth (∼0.38eV) corresponds to mid-infrared spectral range of electronic spectrum (λ∼3.27µm), which makes BBi a good of choice for many optoelectronic applications such as infrared sources and detectors.

Clearly the band structures of BP, BAs and BSb compounds for 2H and 3C crystals reveal several similarities. All three compounds have indirect band gap. In contrast, all polytypes, the band structure of BBi exhibits a direct band-gap character. 2H-BBi also shows a narrower direct band-gap of ∼0.19eV; whereas the indirect gap is ∼0.7eV (Γ→M). For 2H polytypes BP, BAs and BSb are also indirect semiconductors, the conduction band minimum is found near the K point for BP and near the M point for BAs ad BSb.

Intriguingly, the indirect band gaps of 3C and 2H polytypes of PB, BAs and BSb are similar.

The calculated Eg(ZB)-Eg(WZ) difference is ∼0.15eV, ∼0.15eV and ∼-0.15eV for PB, BAs and BSb respectively. Whereas the direct band gap difference between WZ and ZB crystals highly differs (i.e., Eg(ZB)-Eg(WZ) ∼0.7eV(BP), ∼0.84eV(BAs) and ∼1.14eV(BSb)).

Note that without spin orbit coupling the VB maximum of ZB boron III-V compounds is a threefold degenerate state with Γ symmetry. In the presence of the SO coupling, the Γ states splits into fourfold-degenerates Γ and twofold-degenerate Γ . The corresponding ∆ ! = " Γ -" Γ is 0.038eV, 0.194eV, 0.324eV and 1.13eV for BP, BAs, BSb and BBi respectively; whereas ∆ # = " Γ $ -" Γ is 0.046eV(BP), 0.37eV(BAs), 0.36eV(BSb) and 1.23eV(BBi). The calculated ∆ ! are close to FLAPW-calculations [78] of 0.041eV, 0.216 eV and 0.366 eV for BP, BAs and BSb respectively. Clearly the strength of ∆ is rather insensitive with respect to polytype structure.

For all polytypes, the SO splitting increase monotonically when anion atomic number increases, i.e., along the anion row P→As→Sb→Bi. However, the SO coupling for B-V materials is significantly smaller than that for their corresponding common-anion compounds (∆ ! = 0.086 eV(GaP), 0.34 eV(GaAs), 0.73eV(GaSb), 2.15eV(GaBi)) [78], because boron III-V semiconductors show stronger covalent bonds compared to other III-V materials [5-6, 10-13, 15].

D. Dynamical properties

The phonon dispersion curves and phonon density of states (PhDoS) for boron compounds in the 3C and 2H crystal phases are illustrated respectively in Fig. 6 and Fig. 7. The phonon frequencies at high-symmetry points are displayed in Table IV (3C) and TableV (2H). The phonon spectra of boron-V compounds have atypical characteristics when compared to other III-V materials. This can be outlined as follows: (i) Longitudinal (LO) and transverse (LO) optical branches are not clearly separated, in particular for BP and BAs, which is typical for IV-IV semiconductors but not for III-V compounds. (ii) The TO-phonon branches overbend at the X (3C) and M(2H) points for BAs, BSb and BBi, i.e., region in the BZ where the LO mode has higher frequency than at zone-center Γ point. (iii) Bunching of the acoustic branches around K point, contrasting from what occurs for III-V group semiconductors, i.e., the acoustic branches are closer to each other. (4i) Unusual weak LO-TO (3C) splitting at Γ point, with gap-frequencies of ∼7cm -1 , 3.7cm -1 , ∼17cm -1 and ∼8cm -1 for BP, BAs, BSb and BBi respectively. These unusual features are related to the strong covalent bonding of boron-V family.

The phonon spectrum of c-BN [32] is very different from those of BP, BAs, BSb, and BBi due to nearly equal mass of B and N atoms. For c-BN, there is no clear gap between acoustic and optical phonon modes, moreover, there is no sharp peak in the PhDoS due to the LO phonon modes, and the transverse acoustic (TA) branches are not flat. For cubic BP, BAs, BSb, and BBi, the reverse is true.

The calculated (3C) TO (∼821cm -1 ) and LO (∼828cm -1 ) values for BP agree well with experimental values of ∼820cm -1 (TO) [79], ∼834cm -1 (LO) [79], and∼829cm -1 (LO) [80].

Moreover, Raman peaks located at ∼595 cm -1 [63] could be associated to LO phonon mode for 3C-BSb.

The calculated 2H phonon band structure of boron III-V semiconductors (Figure 7) have no soft imaginary phonon frequencies in the whole BZ, suggesting the dynamical stability of wurtzite crystal phase of B-V compounds. The Raman active E2(high), which can be used for distinguishing the two polytypes 3C and 2H, is about ∼777cm -1 , ∼673cm -1 , ∼595cm -1 and ∼517cm -1 for BP, BAs, BSb and BBi respectively. The L point in the BZ is folded onto the Γ point in the 3C BZ of the 2H, thus reducing the LO, TO, LA and TA phonon modes at L point of the BZ (3C) to respectively B1 H , E2 H , B1 L and E2 L at Γ point of the BZ in 2H phase.

According to the above, the estimated value of B1 H , E2 H , B1 L and E2 L are in close agreement with calculated modes of Table V, i.e., the deviation does not exceed ∼0.6% for B1 H ,∼1% for E2 H , ∼0.4% for B1 L , and ∼4% for E2 L . By considering the splitting at Γ point, ∆w(E1, A1) = w(LO)-w(TO) , we found for ∆w(E1(A1)) mode : ∼7cm -1 (∼8cm -1 ) for BP, ∼5cm -1 (∼4cm -1 ) for BAs, ∼17cm -1 (∼18cm -1 ) for BSb, and ∼9cm -1 (∼10cm -1 ) for BBi. 2H boron III-V compounds show rather weak LO-TO splitting compared to high ionic 2H III-V nitrides (∆w(E1)=∼232 cm -1 for AlN [81], ∆w(E1)=∼228 cm -1 for BN [32]) and metastable 2H III-V materials (∆w(E1) =51cm -1 (AlP) [82]). Once again the calculated weak ∆w(E1, A1) for 2Hborides may be related to the strong bonding behavior of these compounds.

As found for the cubic B-V compounds, lattice dynamics of h-BN and boron family differs considerably, in particular h-BN [32], and shows a considerable overlap between the acoustic and optical phonon branches, and flatness of the optical modes (i.e., there is only one clear peak in the PhDoS).

The ratio

% &' ( ) *% &' + ) % &' ( )
can be used as a measure of the strength of crystal anisotropy of WZ crystal, for which the obtained values are 0.012(BP), 0.008(BAs), 0.009(BSb) and 0.01(BBi). Therefore 2H boron III-V materials evidence weak crystal anisotropy.

To deal with the macroscopic electric field associated with atomic displacements in polar semiconductors, we report in Table VI, the Born effective charge (BEC) Z*and highfrequency dielectric ε(∞) tensors for B-V compounds. In the case of 3C polytype, ε(∞) (Z*) has a diagonal form and possesses only one independent component. For the 2H crystal phase, ε(∞) (Z*) is composed of two independent components: one corresponding to the direction parallel to the c axis (||), and the other being characteristic for the hexagonal plane perpendicular to the c axis (⊥). The average , ∞ = -., ∞ / * = -. * 1 is also reported.

The III-V boron exhibit rather striking and unusual properties, and appear to be very different from conventional III-V semiconductors. Several features of the data in Table VI confirm this statement. (i) B-V compounds display negative BEC value, unlike trends observed in III-V compounds (i.e., Z*(GaAs) =2) [82]. (ii) Although Z* have no rigorous relation to nominal ionicity, the ratio

|3 * | 3 456
(where 7 8 = 3 is the nominal ionic charge) is weak (0.2(BP), 0.17(BAs), 0.43(BSb), and 0.37 for BBi) compared to III-V compounds (∼0.66 (GaAs)) [82] and strong ( ∼0.94 (InN) [81], ∼0.64 (BN) [32]) ionic III-nitrides compounds. Note that these compounds 'violated' chemical intuition, instead to be the 'cation', boron atom plays the role of 'anion' with respect to the calculated effective charge in BP, BAs, BSb and BBi. . Z* is weakly sensitive to polytypism, since the Z* value of B-V compounds for both WZ and ZB structures are rather similar, and they differ by less than ∼0.1% for BP and BAs, and ∼6% for BSb, and BBi.

Finally, we calculate the spontaneous polarization Ps of 2H-crystal structures of B-V compounds within the modern Berry-phase approach [83]. Our calculations give Ps )) [84], and BN (-32 10 -3 C/m 2 )) [85], but reveal comparable spontaneous polarization with 'unstable' 2H III-V compounds (Ps = 7 10 -3 C/m 2 for AlP) [84]. The relatively large value of Ps found for BP can be related to volume effect [67], accounted by 1/a 2 . In particular, the lattice constant of BP is weaker than those of typical III-V compounds.

IV. Conclusion

To summarize, we have presented a first-principles study regarding structural phase stability, electronic, and lattice dynamics properties of boron III-V compounds in the cubic zinc-blende (3C) and hexagonal wurtzite (2H) crystal phases. There is a small total energy difference between 3C and 2H polytypes, suggestinga tendency of polytypism in boron III-V materials.

Accurate electronic band structures including spin-orbit coupling has been calculated using

Figure Captions

Figure1: Crystal structure of the 3C and 2H polytypes of boron III-V compounds.

  Moreover, 2H B-V compounds show weak anisotropy in their Z* (∆ * = )(∆, ∞ = :; || < *; ⊥ = > ; <

( 10 - 3 C

 103 /m 2 ) = 14.84, 8.75, 12.0, 9.76 for BP, BAs, BSb and BBi respectively. Apart BP, 2H boron compounds show modest Ps compared to 2H III-V nitrides compounds such as AlN (-40 10 -3 C/m 2

Figure 2 :

 2 Figure 2: Iso-energy lines of total energy E(c, a) of 2Hpolytypes of boron III-V compounds.

Figure 3 :Figure5:Figure6:

 3 Figure 3: Total energy versus volume of boron III-V compounds.

Figure 7 :

 7 Figure 7: 2H-Phonon band structure and phonon density of states (PhDoS) of boron III-V compounds.

Figure 1 Figure 2 3

 12 Figure 1

Figure 3 21

 3 Figure 3

)

  the modified Becke-Johnson exchange potential. The excited states are in close agreement with available experimental measurements. BP, BAs, and BSb polytypes have indirect band gap. However, heavier BBi compound evidences direct nature of the band gap in both 3C and

	2H crystal polytypes, with a narrower gap-energies of (∼0.38eV) (3C) and (∼0.19eV) (2H),
	which makes BBi compounds promising candidates for optoelectronic applications such as
	infrared sources and detectors.
	The lattice dynamics of boron III-V contrast noticeably that of other III-V compounds such as
	the overbending of transverse optical branches and bunching of acoustic branches. Moreover,
	contrary to most III-V semiconductors, 3C and 2H boron III-V materials manifest weak LO-
	TO splitting. Finally, the marked covalent bonding of these compounds yields atypical
	negative Born effective charge as well as dielectric isotropy of the 2H crystal.

Table Captions Table I :

 CaptionsI Calculated equilibrium structural parameters, bulk modulus(B0) and its pressure derivative (B'0)for the 3C and 2H polytypes of boron III-V compounds.

Table II :

 II Calculated minimum direct and indirect gaps, and spin-Orbit interaction (ΔSO) of 3C boron III-V compounds.

Table III :

 III Calculated minimum direct and indirect gaps, and spin-Orbit interaction (ΔSO) of

	2H boron III-V compounds

Table IV :

 IV Calculated phonon frequencies (cm -1 ) at high symmetry points of the BZ of 3C boron III-V compounds.

Table V :

 V Calculated phonon frequencies (cm -1 ) at high symmetry points of the BZ of 2H boron III-V compounds.

Table VI :

 VI Calculated Born effective charge Z* and high-frequency dielectric constant ε(∞) of 3C and 2H polytypes of boron III-V compounds