Nadine Chaurand
email: nadine.chaurand@ifsttar.fr

Floriane Bossart

Patricia Delhomme Ifsttar

Patricia Nadine Delhomme

Chaurand

Floriane Bossard

A Naturalistic Study of the Impact Of Message Framing on Highway Speeding

Keywords: Speeding, message framing, gain, loss, highway, variable-message sign

Speeding is the most common road violation, and is one of the main causes of crashes. To protect road users, authorities use sanctions and preventive measures to prompt drivers to observe speed limits.

However, the efficacy of prevention messages varies according to a number of factors, among which risk framing is important. We ran a study to test whether gain is more effective than loss (framing effect). Four anti-speeding messages were presented on variable-message signs, along one side of a busy 8-lane highway in France (speed limit: 130 km/h -80 mph), during 6 weekends. Within a between subject design, the messages differed in orientation (gain vs. loss vs. no message) and theme (crash vs. fuel consumption). The drivers' speed was recorded on the highway 2 km (1.25 miles) after the sign (6486 recordings of speed). The results showed that speed was lower when a message was displayed than in the control condition, and when the message was gain-framed rather than lossframed. These effects were stronger on the left lanes (overtaking lanes). Hence, gain framed messages are recommended for prevention campaigns at least when no risk factor is salient.

INTRODUCTION a. Speeding Rates and Role of Speeding in Crashes

Speeding is among the most commonly observed road violation in many countries. Estimations are that at any given time, about 40% to 50% of car drivers exceed the speed limits while on the road, and that about 10% to 20% exceed the limit by more than 10 km (6.25 miles) (OECD, 2006). Speeding behavior occurs mainly in overtaking lanes (the leftmost lanes in France).

Speeding has been identified as an important factor in crashes (particularly serious ones). Numerous studies have illustrated the link between speed and the occurrence of crashes, reporting that an increase in speed of 1 km (0.62 miles) per hour leads to an average increase of 3% in crashes [START_REF] Aarts | Driving speed and the risk of road crashes: a review[END_REF][START_REF] Elvik | Speed and road accidents: An evaluation of the Power Model[END_REF][START_REF] Finch | Speed, speed limits and crashes[END_REF][START_REF] Nilsson | Traffic safety dimensions and the power model to describe the effect of speed on safety[END_REF]OECD, 2006;[START_REF] Taylor | The effect of drivers' speed on the frequency of accidents[END_REF]. Because this relationship cannot be considered totally linear, researchers have developed formulae based on the principles of kinetic energy to model the role of speed in crash occurrence, which have then been validated on crash data from different countries [START_REF] Elvik | Speed and road accidents: An evaluation of the Power Model[END_REF][START_REF] Nilsson | Traffic safety dimensions and the power model to describe the effect of speed on safety[END_REF]. They have found that when speed is multiplied by 2, the rate of injury crashes is multiplied by 4, the rate of severe injury crashes is multiplied by 8, and the rate of fatal crashes is multiplied by 16.

b. Speeding Prevention

In order to avoid crashes caused by speeding, speed enforcement in most countries is done by the police force (often through the use of automatic radar devices). Sanctions are applied to drivers who exceed the speed limit, be it monetary fines, administrative sanctions (demerit point systems, driving license suspension), or legal action. Moreover, governments can set up prevention campaigns with messages that are broadcast on TV or radio, or through promptings displayed to drivers along the road, on variable-message signs (VMS). In order to increase road safety, any information provided via VMS would have to be quickly read and understood. Thus, a lot of work has been carried out on drivers' reading and comprehension of messages provided via VMS [START_REF] Dutta | Use of a driving simulator to evaluate andoptimize factors affecting understandability of variable message signs[END_REF]. It appears that motorists require about one second per word displayed on VMS or "4-units information (1-unit information = one word)" to accurately process and understand the information while paying attention to the driving activity [START_REF] Dudek | Manual on Real-Time Motorist Information Displays[END_REF][START_REF] Ullman | Advanced Notification Messages and Use of Sequential Portable Changeable Message Signs inWork Zones[END_REF]. The messages can be aimed at to the whole population or be targeted to specific groups. In the case of incentives displayed along the road, messages can be targeted to speeders by appearing only when speeding is detected.

Two possible issues with prevention campaigns are that they may not be evaluated and may not be based on theoretical knowledge about behavior modification. In answer to these issues, a growing number of research in various fields has focused on speeding prevention campaigns, in order to design campaigns derived from behavior modification theories, and test the efficiency of these campaigns (for example, see Algie & Rossiter, 2010; Delhomme et al., 2010; Delhomme et al., 2008; Falk and Montgomery, 2007; Hoekstra and Wegman, 2011; Poulter & McKenna, 2010; Rossiter & Thorton, 2004; Schulze and Kossmann, 2010; Stead, Tagg, MacKintosh, & Eadie, 2005; Tay, 2005a, 2005b, 2011; Tay & Ozanne, 2002; Tay & Watson, 2002; or Walton & McKeown, 2001). In particular, several studies have focused on messages broadcast on VMS, illustrating that such messages can help reduce drivers' speed [START_REF] Schramm | Effects of speeding and headway related variable message signs on driver behaviour and attitudes[END_REF][START_REF] Tay | Public perceptions of the use of dynamic message signs[END_REF], 2010).

In the field of social psychology, research on effective ways to get drivers to comply with speed limits has focused on different domains, including commitment [START_REF] Delhomme | The effect of the commitment to observe speed limits during rehabilitation training courses for traffic regulation offenders in France[END_REF], persuasion [START_REF] Goldenbeld | Effects of persuasive communication and group discussions on acceptability of anti-speeding policies for male and female drivers[END_REF], and fear arousal [START_REF] Castillo-Manzano | How many lives can bloody and shocking road safety advertising save? The case of Spain[END_REF]. Following persuasion models [START_REF] Petty | The elaboration likelihood model of persuasion[END_REF], it is also necessary that the population targeted by the campaign feel involved. Indeed, people who do not feel involved in the issue, the situation or the specific topic addressed in the campaign message are likely to discard it as irrelevant, and are therefore not likely to change their behavior. As a result, the target population has to be clearly defined and the features of the campaign (in terms of its theme, consequences displayed, media used, etc.) must be tailored to that target [START_REF] Cauberghe | Fear, threat and efficacy in threat appeals: Message involvement as a key mediator to message acceptance[END_REF][START_REF] Goldenbeld | Effects of persuasive communication and group discussions on acceptability of anti-speeding policies for male and female drivers[END_REF]Kaye, White & Lewis, 2014;Lewis et al., 2007;Lewis et al., 2008;Lewis et al., 2013). In particular, anti-speeding messages are more effective when displayed on the road than when displayed out of context, as drivers feel more involved in speed-and crash-related questions when they are actually driving than when they are not [START_REF] Phillips | Meta-analysis of the effect of road safety campaigns on accidents[END_REF].

Furthermore, the choice of the campaign theme itself is also a factor of effectiveness. For example, a large number of campaigns stress that speed increases crash risks, so we may assume that people had already knowledge of risks associated to speed. It is thus possible that habituation occurs: people expect to see crash-related messages and pay less attention to them. By contrast, uncommon antispeeding messages, such as ones about fuel consumption or environmental pollution [START_REF] Delhomme | Reducing air pollution: A New Argument for Getting Drivers to Abide by the Speed Limit?[END_REF], are less expected, so they capture attention, are considered more informative, and thus have more probability to change people's behavior. In line with this research, the question of message content, and more particularly message framing has gained considerable importance.

c. Framing Theory

Message framing can concern different dimensions of the message [START_REF] Lindenberg | Normative, Gain and Hedonic Goal Frames Guiding Environmental Behavior[END_REF][START_REF] Steg | An Integrated Framework for Encouraging Pro-environmental Behaviour: The role of values, situational factors and goals[END_REF], one of which is goal framing. Indeed, a number of studies (Levin et al., 1998;[START_REF] Meyers-Levy | Exploring message framing outcomes when systematic, heuristic or both types of processing occur[END_REF][START_REF] Rothman | The systematic influence of gain-and loss-framed messages on interest in and use of different types of health behavior[END_REF][START_REF] Rothman | Shaping perceptions to motivate healthy behavior: The role of message framing[END_REF] showed that the framing of the message in terms of gains that adopting the promoted behavior will trigger, or in terms of losses that avoiding the promoted behavior will trigger, has an impact on the efficiency of the message and on the adoption rate of the behavior. Meta-analyses show that on average, gain framed messages have a larger effect than loss framed messages on modifying people's behavior [START_REF] O'keefe | The relative persuasiveness of gain-framed and lossframed messages for encouraging disease prevention behaviors: A meta-analytic review[END_REF], in domains such as health [START_REF] Banks | The effects of message framing on mammography utilization[END_REF][START_REF] Meyerowitz | The effect of message framing on breast selfexamination attitudes, intentions, and behavior[END_REF], consumer behaviors (Meyers-Levy and Maheswaran, 2004), pro-environmental behaviors (Stillwater and Kurani, 2012), or safety [START_REF] D'onghia | Effets du cadrage et de la présence d'une image dans les messages de prévention sur l'intention comportementale en faveur du respect des limitations de vitesse[END_REF][START_REF] D'onghia | Comment persuader les automobilistes à respecter les limitations de vitesse ? Effets du cadrage et de la présence d'une image sur les attitudes à l'égard du respect des limitations de vitesse et l'intention de les respecter[END_REF][START_REF] Delhomme | Reducing air pollution: A New Argument for Getting Drivers to Abide by the Speed Limit?[END_REF]Haddad and Delhomme, 2006;[START_REF] Meyer | Quand chacun pense être moins exposé que les autres aux risques mais plus réceptif aux messages de prévention pour la santé[END_REF]Millar and Millar, 2006). This framing effect is sometimes reversed though for some behaviors. Indeed, the framing effect is moderated by the risk (or uncertainty) associated with the advocated behavior, as proposed by the Prospect Theory (Kahneman and Tversky, 1979;[START_REF] Tversky | The framing of decisions and the rationality of choice[END_REF]. More precisely, when proposed a gain, people will choose non risky options (100% chances of saving 200 persons); when proposed a loss, they will choose more risky options (1/3 chances of letting 600 persons die) [START_REF] Tversky | The framing of decisions and the rationality of choice[END_REF]. This means that when the outcomes of the advocated behavior are certain and not risky, in other words when the behavior is meant for prevention, gain framed messages have more impact than loss framed ones; but when the outcomes of the promoted behavior are uncertain and undertaking it presents a risk, in other words when the behavior is meant for detection, loss framed messages have more impact than gain framed ones (O' Keefe and Jensen, 2007;[START_REF] Rothman | The systematic influence of gain-and loss-framed messages on interest in and use of different types of health behavior[END_REF].

In the domain of road safety, slowing one's driving speed is a prevention behavior, as it reduces one's risk to be involved in a crash, and thus should be better prevented by positive-framed messages.

Several studies tested this hypothesis, mostly by presenting people various framed messages and measuring afterwards speeding intentions [START_REF] D'onghia | Effets du cadrage et de la présence d'une image dans les messages de prévention sur l'intention comportementale en faveur du respect des limitations de vitesse[END_REF][START_REF] D'onghia | Comment persuader les automobilistes à respecter les limitations de vitesse ? Effets du cadrage et de la présence d'une image sur les attitudes à l'égard du respect des limitations de vitesse et l'intention de les respecter[END_REF]. However, conclusions are inconsistent, showing either a stronger effect for gain-framed messages [START_REF] D'onghia | Effets du cadrage et de la présence d'une image dans les messages de prévention sur l'intention comportementale en faveur du respect des limitations de vitesse[END_REF][START_REF] D'onghia | Comment persuader les automobilistes à respecter les limitations de vitesse ? Effets du cadrage et de la présence d'une image sur les attitudes à l'égard du respect des limitations de vitesse et l'intention de les respecter[END_REF]Millar and Millar, 2006), or loss-framed messages or even no framing effect [START_REF] Delhomme | Reducing air pollution: A New Argument for Getting Drivers to Abide by the Speed Limit?[END_REF]. Indeed, although participants from Delhomme et al.'s (2010) reported higher intentions to decrease speeding after seeing a message than in the control condition, there was no difference between those seeing the loss framed message and those seeing the gain framed one. This inconsistency may be in part due to the fact that the dependent variable is most often a behavioral intention and not an actual behavior on the road. Participants may thus be wrong when predicting their speeding behavior in driving context. Moreover, most often when the behavioral intention is measured, participants are not driving. Thus, it is likely that participants sitting on a chair during a study, feel less involved by the messages, and have more difficulties relating to the danger speeding represents, because they are not in context. Thus, it would be interesting to study whether the framing effect does appear with speeding prevention messages, by measuring actual speed in a road context.

d. Our study

We investigated the impact of anti-speeding framed messages, displayed on a variable-message sign on a highway. Participants' actual speeding behavior was measured. More precisely, we compared the impact of messages that were positively framed or negatively framed. As loss-framed messages are globally more frequent in health and speed risk communication, we chose a commonly used theme -crash rate-, and a less commonly used theme -fuel consumption-.

II. METHOD a. Participants

The speeds of 6486 vehicles were measured. In order to have a homogeneous sample, and to avoid participants with a poor knowledge of French language or road legislation, only cars, with a French license plate, were considered. Drivers were not aware that an experiment was conducted.

b. Messages

The prevention messages were the same as the ones used by [START_REF] Meyer | Quand chacun pense être moins exposé que les autres aux risques mais plus réceptif aux messages de prévention pour la santé[END_REF]. They presented the gains associated with non speeding or losses associated with speeding, in regard to 2 themes, crashes and fuel consumption. The length of the messages displayed on a variable-message sign is limited to 60 characters, so that drivers can read the message quickly without allotting too much attention to it. As such, the messages we used had to be short and "slogan like".

The 4 messages were "respected speed limit = less crashes" (crash gain), "exceeded speed limit = more crashes" (crash loss), "speed limit respected = less fuel consumption" (fuel gain), and "speed limit exceeded = more fuel consumption" (fuel loss). In the control condition, the variable-message sign displayed the time.

c. Location

The study took place on a highway section close to a tollbooth about 55 km south west of Paris. The highway comprises 4 lanes in each direction. Following legal rules, speed is limited at 130 km per hour (about 80 mph). Traffic comprises vehicles of all sorts and sizes allowed in highways.

The study was run on about 20 weekend days between September and November 2010. Only days where weather was nice (no rain, wind or fog) and that did not correspond to holiday rushes were considered, leaving 12 weekend days (6 Saturdays and 6 Sundays). There was one measurement timeslot per day. Measurement timeslots were from 9:30 to 11:05 am on Saturdays, and from 3:00 to 4:35 pm on Sundays. These timeslots were chosen based on official statistics (COFIROUTE), as traffic was fluid (about 800 vehicles per hour) and the tollbooth was not clogged up at these times, in order to be able to measure free-flow speed.

Authorizations to display the messages on highway variable-message signs and to record speeds were obtained from public road safety authorities, police forces, as well as the highway operator.

d. Procedure

We used a quasi-experimental design. On six of the study days (3 Saturdays and the 3 following Sundays), only fuel related messages were displayed; on the other six (again 3 Saturdays and the 3 following Sundays), only crashes related messages were displayed.

To avoid biases caused by road conditions, environment, or weather, each timeslot contained the 3 different message conditions (positive, negative and no message), with the "no message" condition serving as a baseline. Each timeslot was divided in three 25 minutes sections. On Saturdays, the 25minutes sections times were 9:30-9:55, 10:05-10:30, and 10:40-11:05; on Sundays, they were 3:00-3:25, 3:35-4:00, and 4:10-4:35. In a given timeslot, each of the three messages was allocated a section, and thus broadcast for 25 minutes. The order of the messages during the timeslots was counterbalanced. There were 6 possible orders; each order was attributed to one of the 6 days with fuel related messages and to one of the 6 days with crashes related messages.

The prevention messages were displayed 2 kilometers after the tollbooth on a variable-message sign above the 4 lanes. Speed was assessed 2 kilometers after the variable-message sign (which corresponds to around 1 minute at 130 km/h -80 mph), using a laser speed gun. The laser speed gun belonged to the set of devices the police forces used for assessing speed and thus fining speeders. It emits electro-magnetic waves and uses the Doppler effect to determine the speed of a car. By law, the margin of error of such speed guns cannot exceed 5%, and the devices are regularly checked to control their reliability. This specific laser speed gun did not take pictures of the cars, and as such, did not emit flashes. Each measure took 0.36 seconds, and the minimum interval between 2 measures was 3 seconds. Using a laser speed gun operated by an experimenter on the side of the highway had to be preferred to more automatic solutions (such as using traffic sensors and recorders) due to financial and time constraints. The experimenter was stationed in a place hidden from drivers' view.

As the first lane is largely used by slow vehicles (such as trucks), this lane was not used in the measures. Moreover, preliminary observations revealed that the 4 th lane was relatively rarely used. As such, speeds measured in this lane were combined with speeds measured in the 3 rd lane. Then, speed was measured for cars in the 2 nd and in the 3 rd and 4 th lanes.

There was only one experimenter for the entire experiment. She was blind to the experimental conditions and did not know which message, at a particular time in a particular timeslot, was broadcast.

She stood down the side of the road, such that highway users on both sides could not see her. During each timeslot section, she would randomly select a car on the second lane, measure its speed, and report the speed and the lane number on the data sheet (identified with the timeslot section and the date). She would then without delay randomly select a car on the third or fourth lane, measure and report its speed, and switch back to the second lane for the next measure. Time between 2 measures was kept as short as possible.

These speed measures only served research aims, and were not used to fine or sanction drivers.

III

IV. RESULTS

We ran analyses using speed (continuous variable) and exceeding speed limit (yes/no, dichotomous) as DVs. We first ran a 2*2*3 between-subjects ANOVA to study the effect on speed on theme (crashes vs. fuel), lane (2 vs. 3/4), framing (goal vs. loss vs. control) and their interactions. This ANOVA revealed no effect of theme: speed in the crashes theme (m=128.28) was the same as in the fuel theme (m=128.48, F(1,6472)<1, p>.54). As could be expected, speed was significantly higher on lanes 3 and 4 (m=132.45) than on lane 2 (m=122.85, F(1,6472)=2197.749, p<.001, partial η 2 =.253).

Moreover, speed was significantly higher in the control condition (m=129.32) than in the loss framing condition (m=128.27), which was itself significantly higher than in the goal framing condition (m=127.53, F(1,6472)=36,801, p<.001, partial η 2 =.006). This framing effect was moderated by lane (F(1,6472)=29.823, p<.001, partial η 2 =.005), and was stronger on lanes 3 and 4 than on lane 2. More precisely, simple effect analyses reveal that the framing effect is indeed statistically significant for lanes 3 and 4 (F(1,6472)=77.707, p<.001, partial η 2 =.010),

but not for lane 2 (F(1,6472)<1, p>.68). These results are represented in Figure 1. No other interaction reached significance.

Speed was then recoded, with speeds higher than 130 km/h -80 mph -coded as exceeding speed limit, and speeds 130 km/h -80 mph -or lower coded as non exceeding speed limit.

We ran logistic regression analyses, where we regressed topic, lane and message type on this dichotomous variable, The Wald χ 2 values associated with each variable are reported. Results replicated the ones from the previous analyses. Indeed, speeding was no more likely when the message was crashes related (36.9%) than fuel related (36.6%; χ 2 = .501, p>.48). There was a significant effect of lane, the odds of speeding compared to non speeding was 8.069 times higher on lanes 3 and 4 (where speeding represents 54.1% of cases) than on lane 2 (13.2% of cases; χ 2 = 999.126, p<.001). There was a significant effect of the message (χ 2 = 14.997, p<.001). The odds of speeding compared to non speeding for drivers in the control condition (41.1% of cases) was 1.246 times higher than for drivers in the loss framing condition (36.0% of cases; χ 2 = 7.426, p<.001), and 1.343 times higher than for drivers in the goal framing condition (33.0%, χ 2 = 13.923, p<.001). However, the odds of speeding compared to non speeding for drivers in the loss condition did not differ from the odds for drivers in the goal framing condition (χ 2 = 0.873, p>.350). Again, this message effect was moderated by lane (χ 2 = 10.558, p<.001, and was significant for lanes 3 and 4 (χ 2 =47.087, p<.001), but not for lane 2 (χ 2 =.385, p>.825). Speeding rates are indicated in Table 1. Finally, we studied the impact of message on extreme speeding by coding speeds higher than 150 km/h -93 mph -as extreme speeding and speeds 150 km/h -93 mph -or lower as not extreme speeding. As there were no extreme speeding cases on lane 2, we only analyzed lanes 3 and 4. Again, analyses replicated the results. Extreme speeding was no more likely when the message was crashes related (1.9%) than fuel related (2.2 %; χ 2 = .310, p>.58).

There was a significant effect of the message (χ 2 = 15.419, p<.001). The odds of speeding compared to non speeding for drivers in the control condition (5.4% of cases) was 1.781 times higher than for drivers in the loss framing condition (3.0% of cases; χ 2 = 7.595, p<.006), and 2.224 times higher than for drivers in the goal framing condition (2.4%, χ 2 = 12.736, p<.001).

However, the odds of speeding compared to non speeding for drivers in the loss condition did not differ from the odds for drivers in the goal framing condition (χ 2 = 0.794, p>.373).

Extreme speeding rates are indicated in Table 1.

Speeding, among the most common causes of road crashes, particularly on highways, has been for years one of the main target of prevention campaigns. The literature in social and cognitive psychology has demonstrated that the framing of the messages used to promote safe behaviors, such as reducing one's speed, influences the efficiency of the message. Gain framed messages should be more efficient in promoting this behavior than loss framed ones.

However, this framing hypothesis had rarely been tested in context, while people are driving.

We ran a study by measuring the speed people drove on a highway, after seeing speedingprevention messages that were either gain-, loss-, or control-framed. Results confirm our framing hypothesis: speed is lower in the gain-framed condition, followed by the loss-framed condition, and finally by the control condition. This result is consistent with literature about the framing effect and the documented stronger impact of gain-framed messages. It is even more interesting in that it was obtained by measuring actual behaviors in a naturalistic driving environment, and as such presents more validity than previous studies on speeding intentions [START_REF] D'onghia | Effets du cadrage et de la présence d'une image dans les messages de prévention sur l'intention comportementale en faveur du respect des limitations de vitesse[END_REF][START_REF] D'onghia | Comment persuader les automobilistes à respecter les limitations de vitesse ? Effets du cadrage et de la présence d'une image sur les attitudes à l'égard du respect des limitations de vitesse et l'intention de les respecter[END_REF][START_REF] Delhomme | Reducing air pollution: A New Argument for Getting Drivers to Abide by the Speed Limit?[END_REF]. However, although speeding rates (exceeding the speed limit) are greater in the control condition than in the messages conditions, we cannot conclude that these speeding rates differ between gain-and loss-framed conditions.

As could be expected, the framing effect is stronger on the overtaking lanes. Indeed, speeding is more common on left-side lanes (the overtaking lanes in France) than on the right-side lane (the regular driving lane in France). Right -side lanes are used by vehicles with a large range of speeds, high and low, while left-side lanes are only used by vehicles that are overtaking slower vehicles, and that have as such a higher average speed than on the right-side lane. As such, vehicles on the right-side lane may not feel as involved in anti-speeding messages as vehicles on the left-side lanes, which could lead to a floor effect.

Interestingly, the theme of the message (crashes or fuel consumption) had no effect, which may imply that the framing effect we observe is not influenced by people's familiarity with the theme, or that participants considered both themes to be equally familiar and relevant to their speeding behavior. In an applied perspective, this means that given both themes have the same efficacy, they could be used simultaneously in an anti-speeding campaign, which would allow to avoid habituation and reactance.

The framing effect that appears in our study implies that actions at low cost can help decrease speeding rates, which is likely in turn to decrease crash rates. One may object that the effect size for this relationship is quite small, at η 2 =.010 for the left-side lanes (used for overtaking), but even though small, any significant effect size can be interesting in driving behavior.

Indeed, according to previous research (Elvik et al., 2004; Nilsson, 2004), such a decrease in speed of 3 km/h -1.875 mph -could lead to a decrease of up to 8.5% of crash rate. A costbenefit analysis of such an action would thus put in perspective the low implementation costs (the messages are short, easily displayed to large numbers of drivers, and do not imply identification and targeting of specific categories of drivers), and the small but significant expected benefits. A possible drawback should however be taken into account, in that there may be potential negative side effects of using VMS for anti-speeding campaigns [START_REF] Tay | Public perceptions of the use of dynamic message signs[END_REF]. Nonetheless, given the low implementation costs, the results of this study could be of interest for stakeholders.

Our study suffers from some limitations. Indeed, drivers were exposed to the messages only once, and it is likely that seeing these messages multiple times may lead to different results.

Moreover, we measured speed 2 km -1.25 mile -after the variable-message sign. As such we cannot tell whether framing has a long-term impact or only a short-term one. Moreover, although the experimenter stood on the side of the road so as not to be seen by automobilists on the highway, it is possible that some automobilists spotted her and, not knowing the speed measure would not be used for fining purposes, reduced their speed to avoid a fine. Thus, the following automobilists, cued by the previous driver slowing down, may have reduced their own speed accordingly. The proportion of cyclists who spotted the experimenter should be low, and should not differ across the experimental conditions. However, the slowing down behavior should be more likely from automobilists who were speeding beforehand, which could cause a small bias in our results. Future research could thus benefit from developing more discrete ways to measure speed.

Finally, the setting of the study prevented us from measuring a number of complementary variables, such as message perception and processing, baseline speed, individual and personality characteristics such as goal orientation, etc. In the same vein, variability of driving conditions (fog, raining, previous crashes, presence of police, fuel price, etc.) may add a lot of additive and no additive effects. Being able to take into account these variables in future studies will be necessary to identify the conditions in which the framing effect is the most efficient, as well as the population most receptive to this effect.

VI. CONCLUSION

The impact of message framing on speeding had never been studied by measuring speeding behavior in an actual driving context. Our research filled this gap and revealed that driving speed decreased after seeing a gain-framed message than a loss-framed message, or than a control message. Such a result could be used by authorities to set up non costly efficient antispeeding interventions.

FIGURE CAPTIONS Figure 1 .

 CAPTIONS1 FIGURE CAPTIONS

  Sunday, during the crash theme, no message condition, on lanes 3 and 4. Suppressing these 2 outliers led to acceptable normality values of raw data in each of the 6 messages by lane conditions, as indicated by raw skewness and kurtosis scores (given the size of our sample, we rely on raw values for these indicators, as suggested byWest et al., 1996). More

	represented 34.7% of the sample (2249 observations). Extreme speeding (speeds higher than 150 km/h
	-93 mph, usually sanctioned by 135€ fines) represented 2.1% of the sample (135 observations).
	b. Distribution
	We examined our data following recommendation by Judd, McClelland & Ryan (2009).
	Normality and heteroscedasticity tests applied on raw data showed problems with outliers.
	We identified 2 main outliers, with speeds respectively of 211 and 207 km/h, both measured
	on a Among the 6484 speeds left, total average speed was 128.38 km/h (79.77 mph) (SD = 9,53;
	Min: 92; Max: 183). Speeds exceeding the limitation (130 km/h -80 mph) represented
	. 36.7% of the sample (2382 observations). Among these, "moderate speeding" represented DATA ANALYSIS
	a. Data description 34.6% of the sample (2249 observations). Extreme speeding represented 2.1% of the sample
	Among the 6486 speeds recorded, 3442 were measured after crashes messages (gain: 1195; loss:
	(133 observations).
	1088; control: 1159) and 3044 after fuel messages (gain: 981; loss: 1023; control: 1040). Moreover,
	2435 were measured on a Saturday and 4031 on a Sunday. Finally, 2756 were measured in the 2 nd
	lane and 3733 in the 3 rd and 4 th lanes.
	Total average speed was 128.40 km/h (79.78 mph) (SD = 9.634). Speeds exceeding the limitation

(130 km/h -80 mph) represented 36.8% of the sample (2384 observations). Among these, "moderate speeding" (speeds between 130 and 150 km/h -80 and 93 mph, usually sanctioned by 68€ fines) specifically, it led to acceptable normality values (again indicated by raw skewness and kurtosis scores), as well as acceptable homoscedasticity (as indicated by homogeneity of residuals among predicted values) for residuals in the ANOVA. Thus, we discarded the 2 outliers and ran ANOVAs.

Table 1 .

 1 Speeding and extreme speeding rates by message and lane

			Speeding		Extreme speeding
	Message	Lane 2	Lanes 3/4	Total	Lane 2	Lanes 3/4	Total
	Control	13,68%	61,52%	41,16%	0,00%	5,38%	3,09%
	Loss	12,73%	52,72%	36,05%	0,00%	3,01%	1,75%
	Gain	13,23%	47,94%	33,00%	0,00%	2,42%	1,38%
	Total	13,22%	54,11%	36,76%	0,00%	3,62%	2,08%

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M Montigaud

Y Boinet

Cohin

Thomas Barrès
email: thomas.barres@saint-gobain.com

B Tribollet

O Stephan

H Montigaud

M Boinet

Y Cohin

Characterization of the porosity of silicon nitride thin layers by Electrochemical Impedance Spectroscopy

Keywords: Electrochemical Impedance Spectroscopy, Transmission Electron Microscopy, Porosity, Silicon Nitride, Thin Layer

  L'archive ouverte pluridisciplinaire

Introduction

Dielectric thin films have found many applications,including as insulators or diffusion masks inmicroelectronics [1]and antireflection coatings, beam splitters or polarizing elements in optical elements [START_REF] Lissberger | Optical Applications of dielectric thin films[END_REF]. Their use is widespread as stacks of functionalized glazing layers inthe glass industry [START_REF] Bach | Thin Films on Glass[END_REF]to adjust the optical properties, prevent corrosion or act as barrier layersto diffusion. Silicon nitride thin layers are widely usedfor their good barrier properties [START_REF] Powell | Amorphous silicon-silicon nitride thin-film transistors[END_REF][START_REF] Elmiger | Recombination at the silicon nitride/silicon interface[END_REF],and we focus on this material for our study.

The deposition of silicon nitride layers can be performed using several techniques. Dense and homogeneous layerscan be obtained by Plasma-Enhanced Chemical Vapor Deposition (PECVD) [START_REF] Jeon | I-V characteristics of electron-cyclotron-resonance plasma-enhanced chemical-vapor-deposition silicon nitride thin films[END_REF], but suffer hydrogen inclusion related to the precursors which are involved.

Magnetron sputtering is extensively used in the glass industryand furnisheshigh-quality silicon nitride thin layers on large substrates (3.2 x 6m²) with reduced costs [START_REF] Awan | Electrical conduction processes in silicon nitride thin films prepared by r.f. magnetron sputtering using nitrogen gas[END_REF].

However, SiNx thin layers deposited by magnetron sputtering turn out to be porous at the nanometricscale [START_REF] Kim | Microstructure and properties of silicon nitride thin films deposited by reactive bias magnetron sputtering[END_REF]. The determination of this porosity is crucial to understanding the barrier properties of the layer. In the case of larger pores (micrometric scale), Ahnet al.have given a quantitative description of through-coating porosity using Electrochemical Impedance Spectroscopy (EIS) [START_REF] Ahn | A study on the quantitative determination of throughcoating porosity in PVD-grown coatings[END_REF].

The aim of this study is to give a quantitative description of the structure at the nanometer scale of these silicon nitride thin layers deposited by magnetron sputtering. The investigation of the porosity is carried outby Electrochemical Impedance Spectroscopy (EIS). We combineEIS with local observations by Transmission Electron Microscopy (TEM) allowing us to determine the morphology of the pores in order to validate the electrochemical model.

Experimental

Material deposition

The working electrode studiedwas composed of a Glass/SiNx/NiCr/Au/SiNxmultilayer deposited on glass by magnetron sputtering.The base pressure in the chamber was 2 x 10 -6 mbar. The under layers of silicon nitride and nickel chromium prevent the diffusion of alkali from the glass and promote the adhesion of gold respectively. The gold layer is deposited by magnetron sputtering using a high purity gold target under a total pressure of 8 μbar of Ar. Its thickness is set to 10 nm. The deposition of 30 nm of SiNxon the gold is executed by reactive magnetron sputtering in the same chamber as for the gold. A2%-aluminum-doped silicon target is sputtered in a gas mixture of Ar and N 2 at a total pressure of 14 μbar with fluxes of 180 sccm and 52sccm respectively (5.4 W/cm², 100 kHz). Thealuminum-doped targets do not crack under sputtering and generate fewer undesired particles in the chamber, thus reducing the brittleness of SiNx. Widely used in industrial production lines, they generateSiNx layers whose properties do not change from the case of deposition using a pure silicon target. [START_REF] Ruske | Properties of SiO 2 and Si 3 N 4 layers deposited by MF twin magnetron sputtering using different target materials[END_REF] The SiNx thin film characteristics such as layer thickness, composition, surface roughness and optical index have been measured. The layer thickness was estimated by masking a part of the substrate then measuring the step obtained after deposition by Atomic Force MicroscopyAFM (ICON Bruker). We measured a thickness dof 30 nm for the SiNx layer. The surface roughness was also evaluated by AFMto have anRMS value of 1.6 nm on a 500x500 nm area.

The calibration of the deposition and the control of the reproducibility were provided by optical measurements (optical absorption and reflection spectrometry in the [250, 2500 nm] wavelength range). A density of 2.9 g/cm 3 was obtained for the sample via X-Ray Reflectometry (Bruker D5000, CuKα(1,2) / scintillator, XRR). Finally, the composition of the film was determined by Electron Probe Micro Analysis (CamecaSXFive) on the same layer deposited on a Ge wafer; the layer composition is the following: 54.6 at.% N, 40.9 at.% Si, 3.2 at.% Al, and 1.3 at.% O.

Electrochemical measurements

A three-electrode electrochemical cell, filled with 0.5 M Na 2 SO 4 , was used in the electrochemical impedance measurements. The cell consists of a cylinder of PMMA (poly(methyl methacrylate))fixed on the sample surface,providing a working electrode area of 10 cm². The electrical contact is made through SiNx on the gold layer by ultrasonic welding. A sheet resistance of 2.6 Ω/sq was measured using a four-point probe. The imperfect transport of electrons in the 10 nm gold layer can induce a rather low resistance value which adds on to the electrolyte resistance value. A mercury-mercurous sulfate electrode and a 10 cm² platinum cylindrical sheet are used as reference and counter electrode respectively. A Pt wire is inserted in series with a 47 nFcapacitor connected to the reference electrode to avoid artefacts at high frequency due to the high impedance of the reference electrode [START_REF] Tran | Artefacts in electrochemical impedance measurement in electrolytic solutions due to the reference electrode[END_REF].The impedance measurements were performed using a Biologic SP 300 device, operating in potentiostat mode at the corrosion potential.We used a 14 mV peak-to-peak sinusoidal potential perturbation (10 mV RMS) whose frequency range extends from 100 kHz to 1 mHz with 11 points per decade. The sample was immersed 24 hours before the acquisition of the impedance spectra. The surface state of the sample was investigated by optical microscopy after measurement and showed no corrosion points or delaminated areas. (1) With 𝑛𝑓the number of frequencies in the experimental spectra, 𝑍 𝑒 and 𝑍 𝑐 the experimental and calculated impedance respectively, and the 0.005 coefficient standing for an acceptable error of 0.5% between the experimental and the calculated spectra.

The reproducibility of the measurements was tested. Deviations from reproducibility can be observed between several deposited samples and the inhomogeneity of the deposition can be measured by EIS on the sample itself. Thus, the samples presented in this study come from the same batch and the tendencies emerging from the experimental results exceed the reproducibility errors.

Transmission Electron Microscopy

The SiNx layers were observed in cross section by Transmission Electron Microscopy (TEM) in bright-field mode after preparation of a thin lamella by Focused Ion Beam (FIB). These observations were carried out on an Akashi Topcon EM-002B microscope at 100 kV with under-focused conditions (up to 50 nm in defocus).

The deposition of silicon nitride on commercial membranes (15 nm of silicon nitride support film deposited on a silicon wafer with nine windows of 100x100 μm²) allowed us to observe the layers in plan view. Scanning Transmission Electron Microscopy (STEM) measurements were performed in planview with a spherical aberration-corrected NION USTEM 200 instrument operated at an accelerating voltage of 100 kV. High-Angle Annular Dark-Field (HAADF) images were acquired.

Theory

The impedance of a dielectric layer can be represented by the series connection of several sets of Voigt elements (a resistor in parallel with a capacitor). [Figure 1]The schematic representation in figure 1 shows that the impedance tends towards a resistance at low frequency and towards a pure capacitance at high frequency. To each of these Voigt elements is associated a slice of a given thickness𝑑𝑥. Thus the local resistance can be written as a function of the local resistivity 𝜌(𝑥)and of the thickness of the correlated slice, while the local capacitance can be expressed as a function of the local permittivity 𝜀(𝑥), the vacuum permittivity𝜀 0 , and of the thickness of the slice (equation2). The variable 𝑥 is set equal to 0 at the electrode/layer interface.

𝑅 𝑛 = 𝜌(𝑥)𝑑𝑥 𝐶 𝑛 = 𝜀 𝑥 𝜀 0 𝑑𝑥 (2)
The local impedance can be written as afunction of the local resistivity and permittivity, and then the global impedance Zis deduced for a layer of thickness 𝑑(equation 3).

𝑑𝑍 = 𝜌(𝑥)𝑑𝑥 1+𝑗𝜔𝜌 (𝑥)𝜀(𝑥)𝜀 0 𝑍 = 𝜌(𝑥)𝑑𝑥 1+𝑗𝜔 𝜌(𝑥)𝜀(𝑥)𝜀 0 𝑑 0 (3)
If the permittivity is independent of position, the impedance becomes:

𝑍 = 𝜌(𝑥)𝑑𝑥 1+𝑗𝜔 𝜌(𝑥)𝜀𝜀 0 𝑑 0 (4)
The impedance depends of the resistivity distribution in the layer. Two main distributions of resistivity are commonly presented in literature: the Young model [START_REF] Young | Anodic oxide films. Part 4.-The interpretation of impedance measurements on oxide coated electrodes on niobium[END_REF] and the power-law distribution which was proposed by Hirschornet al. [START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films I. Theory[END_REF][START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films II. Applications[END_REF].

Young proposed an exponential decay of the resistivity as a function of the local position along the direction normal to the surface𝑥. The resistivity for𝑥 = 0 corresponds to the intrinsic value of the material 𝜌 0 and a characteristic length 𝑙 is introduced(equation 5).

𝜌 𝑥 = 𝜌 0 exp (-𝑥 𝑙 ) (5)
With this distribution the integral can be written in the analytical form called the Young model (equation 6). This expression was used first by Schilleret al. [START_REF] Schiller | The evaluation of experimental dielectric data of barrier coatings by means of different models[END_REF] for the study of coatings and later by Nguyenet al. [START_REF] Nguyen | Impedance analysis of the distributed resistivity of coatings in dry and wet conditions[END_REF].

𝑍 𝑐 (𝜔) = -𝑙 𝑗𝜔 𝜀𝜀 0 𝑙𝑛 1+𝑗𝜔 𝜀𝜀 0 𝜌 0 𝑒 -𝑑 𝑙 1+𝑗𝜔 𝜀𝜀 0 𝜌 0 (6)
Since the Young model presents a variable phase across the range of frequency, this model cannot explain theConstant Phase Element (CPE) behavior found in some experiments. Thus Hirschornet al. [START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films I. Theory[END_REF][START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films II. Applications[END_REF] proposed another model based on a power-law distribution of resistivity in the layer. The resistivity is expressed as a function of the thickness of the layer 𝑑, the depth𝑥 in the layer and the limit values of the resistivity 𝜌 0 and 𝜌 𝑑 at the interfaces 𝑥 = 0 and 𝑥 = 𝑑 respectively (equation 7).

𝜌 𝜌 𝑑 = 𝜌 𝑑 𝜌 0 + (1 - 𝜌 𝑑 𝜌 0 )( 𝑥 𝑑 ) 𝛾 -1 (7)
For a frequency 𝑓 < 2𝜋𝜀𝜀 0 𝜌 𝑑 -1 , the corresponding impedance is expressed as:

𝑍 𝑐 (𝜔) = (1 + 2.88𝛾 -2.375 ) 𝑑𝜌 𝑑 1 𝛾 (𝜌 0 -1 +𝑗𝜔𝜀 𝜀 0 ) (𝛾 -1) 𝛾 (8)
This expression shows a CPE behaviorwith a coefficient 𝛼 = 𝛾 -1 𝛾 in the frequency domain 2𝜋𝜀𝜀 0 𝜌 0 -1 < 𝑓 < 2𝜋𝜀𝜀 0 𝜌 𝑑 -1 .

Results and discussion

The Nyquist and Bode diagrams of the impedance measurements of SiNxfilms on gold are presented in figure 2[Figure 2]. The Bode diagram obtained shows a slow decrease in the phase across the [100 mHz, 1 kHz] frequency range. The electrolyte resistance value was determined by the intersection of the Nyquist plot with the real axis (insert in figure 2a).

Cole-Cole plot

In order to obtain the permittivity of the SiNx, the layer was considered as a complex capacitance and studied in a Cole-Cole representation [START_REF] Cole | Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics[END_REF]. The Cole-Cole plot presented in figure3 [Figure 3] was obtained from the impedance spectra and the electrolyte resistance determination (equation9). The extrapolation of the real part of the capacitance to high frequency leads to a value of 0.24μF/cm². The thickness of the layer is well determined from the calibration of the deposition (30 nm), so the permittivity value is easily deduced from the capacitance using equation 10. [START_REF] Benoit | Comparison of different methods for measuring the passive film thickness on metals[END_REF] 𝜀 = 𝑑𝐶 ∞ 𝜀 0 [START_REF] Ruske | Properties of SiO 2 and Si 3 N 4 layers deposited by MF twin magnetron sputtering using different target materials[END_REF] with 𝜀 the permittivity of the layer,𝜀 0 the vacuum permittivity,𝑑the thickness of the layer, and 𝐶 ∞ the extrapolation at high frequency of the capacitance.

𝐶 𝜔 = 1 𝑗𝜔 (𝑍 𝜔 -𝑅 𝑒 ) (9)
We found a permittivity of 8.1 for this 30 nm SiNx layer, which is in good accordance with the literature. [START_REF] Awan | Electrical conduction processes in silicon nitride thin films prepared by r.f. magnetron sputtering using nitrogen gas[END_REF][START_REF] Sze | Current Transport and Maximum Dielectric Strength of Silicon Nitride Films[END_REF]

0 000E+0 05E-8 10E-8 15E-8 20E-8 20E-8 40E-8 60E-8 -C(Im) / F cm -² C(Re) / F cm -² C ∞

Electrical equivalent model

Since the phase across the [100 mHz, 1 kHz] frequency range is not constant and does not correspond to a CPE, the Young model seems to be more appropriate than a power-law model to fit the our datain this frequency range. Thus, the global model used is composed of a Young impedance in parallel with a branch composed of a pore resistance in series witha CPE representing the electrical double layer at the bottom of the through-pores.

The first branch of the model is described by the Young impedance. This impedance is related to a resistivity gradient due to the distribution of non-through-pores in the axial direction 𝑥in the layer (equation 5).

The second branch of the model describes the impedance in the through-pores, using a CPE (Q dl , α dl ) for the double layer at the bottom of the pores in series with a pore resistance.

[Figure 4].The gold electrode is considered as a blocking electrode since the value of the charge transfer resistance is substantially higher than the impedance of the CPE in the frequency range of the measurements. The experimental data and the result of the fittingmodel of the impedance arerepresented in a Bode plot (Figure 2b): the model is in good agreement with the data,with a𝜒² value of1.08.

Au

The high frequency region (from 10 kHz to 100 kHz) is less compatible with the model, since the bump on the phase is not well fitted. However, the impedance modulus corrected for the ohmic drop tends to zero at high frequency, which implies a concomitant reduction of the signal-to-noise ratio. Hence, the confidence in the goodness of the fit in the high frequency region is hard to evaluate due to these low values of the impedance modulus.

The parameters used in the regression are given in the table 1. [Table 1] The value of 4.1 10 14 Ω cm determined for the intrinsic resistivity corresponds to those found in literature for magnetron-sputtered Si 3 N 4 [START_REF] Vila | Electrical behavior of silicon nitride sputtered thin films[END_REF]. The pore resistance shows a relatively low value which may indicate a high through-porositysee next section. All the other parameters are fitted with the electrical equivalent circuit presented in figure 4. The value of 𝜒² is obtained for an estimated error of 0.5 %. The effective value of the electrical double layer determined with the Brug formula is reported in the last column.

d (nm) R e (Ωcm²) ε ρ 0 (Ωcm) l (cm) Q dl (Ω -1 cm -2 s α ) α dl R p (Ωcm²) χ² C dl (F.

Quantification of the through-porosity

The CPE used for the double layer model is assumed to correspond to a surfacevariation of the time constant. Indeed, the electric double layer is located at the bottom of throughporosity on the conductive accessible electrode surface. Thus, the formula proposed by Brug et al. [START_REF] Brug | The analysis of electrode impedance complicated by the presence of a constant phase element[END_REF] can be applied to this system in order to extract the effective capacitance value of the electric double layer. By dividing the effective capacitance value obtained at the bottom of the through-pores by the value determined on the gold electrode without the layer, we are able to give the fraction of electrode accessible due to through-porosity.

EIS measurementswere made on the gold electrode without the SiNx layer. [Figure 5] The Bode diagram is presented across the frequency range [0.01; 100 Hz]. The frequency domain was selected in order to model the electrical double layer formed on the gold electrode. Furthermore, the high frequency limit was set such that the measured modulus value corresponds to the electrolyte resistance, to avoid any artefact. The result is a constant phase in this frequency range which is modelled by a CPE for the electric double layer. We applied the following Brug formula on gold with and without the SiNx layer, neglecting the charge transfer resistance in the system.

𝐶 𝑒𝑓𝑓 = 𝑄 𝑑𝑙 1/𝛼 𝑅 (1-𝛼)/𝛼 (11)
R stands for the electrolyte resistance (R e ) in the case of the gold electrode without coating and for the pore resistance (R p ) in the case of the silicon nitride-coated electrode.

We found effective capacitances of 3.9.10 -8 F.cm -2 and 8.9.10 -6 F.cm -2 for coated and uncoated gold respectively, corresponding to 0.44 % of accessible surface of the electrode at the bottom of through-pores.When considering the pore resistance value of 280 Ω cm² and the This value is rather high compared to the electrolyte resistivity in the rest of the cell (around 7

Ω cm), probably due to a lower ionic concentration in the pores than in the solution expected for systems of nanometric size.

The nanostructure of the layeris clear from STEM-HAADF images acquired in plan-view mode [Figure 6]. The diameter of pores was estimated with a good precision and is comprised between 0.5 and 2.0 nm. Additionally, the porous surface is estimated from such images by applying an intensity threshold which corresponds to the absence of the nitride layer: the obtained valueis between 1% and 2% of the total surface. Since the fraction of pores which reach the electrode cannot be measured in plan-view observation, the porous surface calculated from STEM acquisition is certainly higher than the accessible surface of the electrode. with the same thickness and from the same deposition conditions were measured by EIS and fitted with the same model as previously. The resistivity values obtained from the fit were compared in order to give a standard deviation for the resistivity parameter and to provide the error bars presented in figure 7. For each depth value, a gap separates the profiles of the thinnest layers (10 and 20 nm) from the others (30 to 100 nm), while the profiles seem superimposed between 30 and 100 nm. Higher values of resistivity for thicker layers at a given depth could mean that the ionic concentration in the pores is lower. Increasing the thickness of the layer from 20 to 30 nm appears to block the ions' access to the electrode. This specific area near the substrate highlighted by EIS was investigated using TEM. The cross section bright-field observation of an FIB-prepared lamella from a 60 nm SiNx layer is presented in the following figure [Figure 8]. In this mode of acquisition, the voids or pores in the layer appear in lighter shades than the matter. The layer seems to be particularly inhomogeneous in the thickness direction. Indeed, at least three areas of different porosity seem to be distinguished across the thickness. The first 10 nm exhibit a dense nanostructure 1E-2 1E-1 1E+0 0,01 0,1 1 10

Normalized resistivity

Thickness / nm 10 nm 20 nm 30 nm 50 nm 100 nm while the 10 nm to 30 nm area seems highly porous. From 30 nm to 60 nm, the pores appear fewer. This TEM observation qualitatively confirms the discontinuity of pores ascertained from impedance measurements between 20 and 30 nm, moving from a highly porous zone to a less porous zone.

Conclusions

This study shows that impedance spectroscopy is a technique well suited to giving a global description of nanometer-scale pores in silicon nitride thin layers. Quantitative physical parameters are obtained by means of EIS, such as the intrinsic resistivity and the permittivity of the SiNx layer, the electrolyte resistivity in the through-pores and the accessible electrode surface area at the bottom of the pores. The layer is represented by an equivalent model composed of a Young impedance representing non-through-pores in parallel with the charge transfer at the bottom of the through-pores.The impregnation of the non-through-pores of the layer by the electrolyte is described by an exponential gradient of resistivity. The quantification of the accessible electrode fraction was realized using the Bruget al. formula [START_REF] Brug | The analysis of electrode impedance complicated by the presence of a constant phase element[END_REF] with the parameters of the electrical double layer and gives a value of accessible electrode area of 0.44 % for a 30 nm SiNx layer deposited on gold.A STEM HAADF observation in plan view of the layer was used to determine a diameter of the pores ofbetween 0.5 and 2.0 nm and showedan upper value of 2 % for the global porosity, compatible with the accessible surface area determined by EIS.

Additionally, the representation of the resistivity profile for layers with different thicknesses highlighted a specific area in the layers near the electrode. This result was confirmed by TEM bright-field observation of the cross section of a 60 nm layer showing discontinuous pores in the layer.

  Data modeling was carried out using non-commercial software developed at the LISE CNRS, Paris, based on a simplex strategy. The program minimizes the function𝜒² given below (equation 1). 𝜒² = 𝑅𝑒(𝑍 𝑒,𝑖 )-𝑅𝑒(𝑍 𝑐,𝑖 ) 0.005. 𝑍 𝑒 ² + 𝐼𝑚 (𝑍 𝑒,𝑖 )-𝐼𝑚 (𝑍 𝑐,𝑖 ) 0.005. 𝑍 𝑒 ² 𝑛𝑓 𝑖=1

Figure 1 -

 1 Figure 1 -Electrical circuit modelling the impedance of a dielectric layer. On the left is represented a

Figure 2 -

 2 Figure 2 -Impedance spectra for 30 nm SiNx on gold obtained in 0.5 M Na 2 SO 4 at the corrosion

Figure 3 -

 3 Figure 3 -Cole-Cole plot obtained from the impedance measurement of a 30 nm SiNx layer

Figure 4 -

 4 Figure 4 -Equivalent circuit used to describe the impedance of a 30 nm SiNx layer. The Young

Figure 5 -

 5 Figure 5 -Bode plot of the measured impedance spectra in 0.5 M Na 2 SO 4 of a 10 nm gold layer

  layer (30 nm), the accessible surface of the electrode determined by Brug allows us to calculate an electrolyte resistivity value inside the through-pores of 4.2 10 4 Ω cm.

Figure 6 -

 6 Figure 6 -HAADF-STEM image of 30 nm SiNx deposited on a silicon nitride commercial

Figure 7 -

 7 Figure 7 -Resistivity normalized by the intrinsic resistivity ρ 0 vs depth x in log-log representation for

Figure 8 -

 8 Figure 8 -TEM image in bright-field mode of a cross section of a 60 nm SiNx layer. The pores

Table 1 -

 1 Results of the measured impedance fitting for SiNx in 0.5 M Na 2 SO 4 . The layer thickness was measured by AFM, the electrolyte resistance was determined from the Nyquist diagram and the permittivity was obtained from the extrapolation of the Cole-Cole representation at high frequency.

	cm -
	2 )

Acknowledgements

The authors gratefully acknowledge the support of Saint-Gobain Recherche (Aubervilliers, France), the "Laboratoire Interfaces et SystèmesElectrochimiques" (UMR 8235, Paris, France), the "Laboratoire de Physique des Solides" (UMR 8502, Orsay, France)and the ANR -"Programmeinvestissementd'avenir" with the Equipex TEMPOS-NANOTEM (for the FIB preparation).

[1] K.H. Zaininger, C. Wang, Thin film dielectric materials for microelectronics,Proceedings of the IEEE, 57 (1969),p. 1564-1570,