Rémy Le Boennec
email: remy.leboennec@univ-nantes.fr

Frédéric Salladarré

The impact of air pollution and noise on the real estate market The case

Keywords: air pollution, noise pollution, housing location, housing price

In this paper, we aim to demonstrate the way air pollution and noise may affect the well-being of the inhabitants of Nantes, France, designated the European Green Capital in 2013. We use a database compiling certain attributes of the houses that exchanged hands and their price. In order to understand the complex relationships that can exist between explanatory variables and housing price, we consider not only the direct effects of air pollution and noise on the price of around 3,000 houses sold in Nantes and its metropolitan area from 2002 to 2008, but also the way some location attributes of the dwellings may affect air pollution and noise. We demonstrate that even if air pollution may be affected by some location characteristics of the house, this variable has no significant impact on the price, in the end. Noise is affected by the location of the house and exerts some significant effect on housing price. However, whilst air pollution does not impact at a global level, people who have lived in an air polluted county before coming to Nantes are sensitive to air quality, whereas those who come from a low air polluted county tend to choose low noise exposure dwellings.

Introduction 1

Air and noise pollution can be considered as two environmental variables that may affect the well-being of inhabitants. 2 There is a large body of evidence about the health impacts of pollution: on the one hand, air pollution has adverse effects on the respiratory and cardiovascular systems as well as a range of other side effects (World Health Organization, 2013); on the other hand, noise exposure can induce hearing impairment, hypertension, annoyance and stress, sleep disturbance, and decreased school performance [START_REF] Passchier-Vermeer | Noise exposure and public health[END_REF]. Because they apply to specific geographical contexts, such annoyances can be assessed by the depreciation we observe on the real estate market. The effects of noise exposure as well as air pollution on housing values are still of interest, even if largely explored [START_REF] Anselin | Interpolation of air quality measures in hedonic house price models: spatial aspects[END_REF][START_REF] Bajari | A Rational Expectations Approach to Hedonic Price Regressions with Time-Varying Unobserved Product Attributes: The Price of Pollution[END_REF][START_REF] Nelson | Hedonic property value studies of transportation noise: aircraft and road traffic[END_REF].

In this paper, we concentrate our analysis on Nantes, France's sixth largest city. Even if its environmental conditions are as a whole acceptable, due to windy weather linked to its proximity to the Atlantic coast, Nantes is characterized by contrasted environmental conditions regarding noise and air pollution, according to which part of the city is being observed. Over the last two decades, the city of Nantes has developed several policies to make its environment cleaner. 3 Priority was given to a sustainable transport policy, especially public transport, walking and cycling. For instance, Nantes was the first city in France to re-introduce the electric tramway, in 1985. The policy of city-center development aims at minimizing car transport and 1 We thank the anonymous reviewers for their insightful comments and suggestions on the manuscript.

2 Concerning air pollution, see [START_REF] Evans | Psychological reactions to air pollution[END_REF], [START_REF] Lercher | Perceived traffic air pollution, associated behavior and health in an alpine area[END_REF], [START_REF] Forsberg | People can detect poor air quality well below guideline concentrations: a prevalence study of annoyance reactions and air pollution from traffic[END_REF], [START_REF] Klaeboe | Oslo traffic study-part 1: an integrated approach to assess the combined effects of noise and air pollution on annoyance[END_REF], [START_REF] Ambrey | Estimating the cost of air pollution in South East Queensland: An application of the life satisfaction non-market valuation approach[END_REF]. For noise, see [START_REF] Lercher | Behavioral and health responses associated with road traffic noise exposure along alpine through-traffic routes[END_REF], [START_REF] Klaeboe | Oslo traffic study-part 1: an integrated approach to assess the combined effects of noise and air pollution on annoyance[END_REF].

increasing pedestrian areas. Furthermore, in 2010/2011 long-term noise polices were implemented. Source: http://www.airpl.org/ As a result of this overall strategy, the levels of most of the main air pollutants have fallen since 2000 (Figure 1), according to the regional agency for air quality (Airpl). Most air pollution indicators (for instance, Carbon monoxide or benzene) remain at levels below the limits set by the European Directive (Directive 2008/50/CE) or the World Health Organization (WHO, 2006). Particulate matter, both between 2.5 and 10 micrometers (PM2.5 and PM10) have been relatively stable since 2000. However, some marked differences exist and remain between the different districts of the city. 4 Furthermore, people can be affected by air pollution even if the levels of pollution comply with current WHO guidelines [START_REF] Lercher | Perceived traffic air pollution, associated behavior and health in an alpine area[END_REF]).

4 For instance, the annual average level of NO2 varies according to the district from 10.53 to 42.41 µg/m3 in 2008 (Eval-PDU project, 2012). PM10 exhibit a similar and contrasting pattern, whereas PM2.5 are above the WHO Air Quality Guideline in almost all districts of the city.

Noise disturbance is a negative externality mainly due to transport and this especially occurs in cities near main road transport arteries (OECD, 2001;[START_REF] Who | World Health Organization: Guidelines for Community Noise[END_REF]. People respond differently to noise disturbance, although they generally tend to be affected negatively when noise levels reach a certain threshold [START_REF] Dekkers | Monetary valuation of aircraft noise: A hedonic analysis around Amsterdam airport[END_REF]. In Nantes, noise exposure reveals a similar contrasted pattern according to the dwelling location.5

Beyond the policies implemented at the public level, the objective of this paper is to study whether the prices of dwellings are influenced by air pollution and noise. Nantes is a city where employment growth is superior to population growth (INSEE, 2014). 6 The aim is to question whether inhabitants coming to Nantes consider air quality and noise as potential determinants of their housing location and as factors of their willingness to pay a premium for their dwellings.

For our purpose, we use the Perval notaries' database linking the price of 2,969 houses that were exchanged in Nantes and its metropolitan area (Nantes Métropole) in 2002, 2006 and 2008 respectively, with their intrinsic and extrinsic attributes (location and environmental quality).

We consider the facts that firstly, air pollution and noise exposure variables may directly affect the price of a dwelling in local contexts and secondly, that some location characteristics of the dwelling may simultaneously affect air and noise pollution levels. Furthermore, the impacts of these two annoyances are usually studied separately. 7 To our knowledge, very few studies concern the influence of noise and air pollution together on the prices of dwellings.8

We show the existence of a positive but weak relationship between noise and air pollution.

Moreover, despite the fact that location attributes affect air pollution levels, these levels do not in turn exert any significant influence on the price of houses that were exchanged in Nantes and its metropolitan area. We emphasize a different result considering noise pollution: it can be affected by some location characteristics of the house purchased, and it simultaneously constitutes a real estate depreciation factor. However, whilst the air pollution variable does not exert any effect at a global level, people who had lived in an air polluted county ('département') before coming to Nantes appear to be sensitive to air pollution level. Furthermore, people who come from a low air polluted county choose low noise exposure dwellings. Finally, the importance given to air quality when a house is being purchased tends to increase in line with the age of the inhabitants as well as their previous pollution experience.

This paper is structured in the following manner: in section 2 we present the assumptions.

Section 3 is dedicated to the data and the methodology we use, namely a simultaneous equation model. In section 4, we discuss our results and section 5 is devoted to our concluding remarks.

Research hypothesis

The way environmental variables may affect the well-being of the inhabitants of some local territories may be assessed by the hedonic pricing method. According to [START_REF] Rosen | Hedonic prices and implicit markets: product differentiation in pure competition[END_REF], housing price depends on intrinsic attributes of the dwelling (number of rooms, living surface area) and extrinsic ones, such as proximity to public transport, sources of amenities and pollution. The real estate market indirectly provides a monetary value of these attributes. However, the results that may be observed when using the hedonic pricing method appear to be strongly contrasted depending on the variables and the context [START_REF] Cavailhès | Le prix des attributs du logement[END_REF]. Whereas intrinsic attributes prove to exert comparable effects on the price of the dwellings regardless of the geographical context, this is no longer the case for location or environmental characteristics.

Concerning noise pollution, a large body of literature indicates that noise exposure has a detrimental impact on housing values.9 For example, the drop in prices is also about 0.5 per cent per additional decibel emitted by the rail network in Seoul, Korea [START_REF] Chang | Hedonic estimates of rail noise in Seoul[END_REF].

Similarly, apartments located in peaceful districts of Paris are worth 1.5 per cent more on average [START_REF] Bureau | Évaluation de l'impact des politiques[END_REF]. However, depending on the context, the level of noise exposure does not always constitute a significant variable, such as in Grenoble, France, [START_REF] Saulnier | Une application des prix hédonistes: influence de la qualité de l'air sur le prix des logements?[END_REF] and in the majority of the 287 French urban centers studied by [START_REF] Cavailhès | Le prix des attributs du logement[END_REF].

In hedonic studies, air quality variables often play ambiguous roles. [START_REF] Decker | Residential Property Values and Community Right-to-Know Laws: Has the Toxics Release Inventory Had an Impact?[END_REF] highlighted the negative impact of high concentrations of restricted pollutants in Nebraska. Still, the same pollutants were not significant in Massachusetts [START_REF] Bui | Regulation and capitalization of environmental amenities: evidence from the toxic release inventory in Massachusetts[END_REF]. [START_REF] Saulnier | Une application des prix hédonistes: influence de la qualité de l'air sur le prix des logements?[END_REF] did not find any significant relationship between rents and NO2 levels in Grenoble. This absence of a significant link was generalized by [START_REF] Cavailhès | Le prix des attributs du logement[END_REF], who found a reduced and possibly zero influence of air pollution on rents in the urban centers studied.

We analyze housing transactions taking place in Nantes Métropole, an urban community grouping together 24 communes of the Loire-Atlantique region. It contains around 600,000 inhabitants, half of whom live in the central city of Nantes. At a national level, Nantes

Métropole is one of the most attractive places to live in the country: its population grew by 4,500 inhabitants each year between 2008 and 2012 (compared with +6,000 inhabitants between 1999 and 2007, according to the National statistical institute). Over the past decade, around one third of newcomers have come from Paris and the Parisian metropolitan area, being characterized by its stronger pollution levels (INSEE, 2014). Nantes was designated the "European Green Capital" in 2013 thanks to its good environmental results.

However in Nantes, unlike numerous other cities, Le [START_REF] Boennec | Nouvelles Centralités, Choix modal et Politiques de Déplacements: le Cas Nantais[END_REF] did not find any impact of air pollution on the housing values when using the spatial hedonic model. Such contrasted results concerning environmental variables explain why it may be important to look for more complex relationships between explanatory variables. To build location and environmental quality variables, each dwelling location was geo-referenced in the framework of the Eval-PDU project, regarding the environmental impacts of the 2000-2010 urban transport plan of Nantes Métropole. Using this original quantitative cross-sectional data, we carried out an econometric analysis based on simultaneous equation modelling. We analyzed the specific influence of some location attributes of the houses exchanged on air pollution and noise exposure levels, which in turn may constitute significant sources of depreciation of the dwelling.

More specifically, we tested the following hypothesis (Figure 2):

-The intrinsic characteristics of the houses exchanged directly influence their price [START_REF] Baudry | Formation des prix immobiliers et consentements à payer pour une amélioration de l'environnement urbain: l'exemple rennais[END_REF][START_REF] Bureau | Évaluation de l'impact des politiques[END_REF]. This is generally the case when regarding hedonic literature;

-Certain location characteristics simultaneously influence property values [START_REF] Brécard | Plans de déplacements urbains et capitalisation immobilière: le cas des appartements de l'agglomération nantaise[END_REF][START_REF] Dubé | Commuter rail accessibility and house values: The case of the Montreal South Shore, Canada, 1992-2009[END_REF] as well as the levels of noise and air pollution;

-Air pollution influences the price of the dwellings, and may as well be affected by location attributes of the houses exchanged;

-Noise pollution influences the price, and may as well be affected by location attributes.

The three last assumptions in particular better emphasize the way some variables exert an influence on housing price, transiting by specific interactions that are ignored when using the classic hedonic pricing method.

Material and Methods

Description of the data

The Perval notaries' database allows us to link the price of houses that were exchanged in Nantes Métropole with some specific characteristics (Figure 2). The database gives information on the transactions (price, date, type of negotiation, nature of the transfer, etc.), on location (district of the house, land registry reference, etc.) and on the intrinsic attributes of the accommodation (type of house, number of rooms, living surface area). Certain details concerning the purchasers are provided as well (age, and previous location).

After rationalizing the database, the analysis involved 2,969 house transactions. According to Regarding location, the geo-referencing included the geographical location of the dwellings and a large set of reference places (railway stations, green spaces, etc.). Several distances variables expressed in kilometers were retained: distance to the city center, central station, tram, campus, airport, commercial zone, green space or access to the ring road around the city. Furthermore, the number of bus stops within a distance of 100 meters was also taken into consideration. 10

The natural environment is generally of good quality. The mean distance from a green space is equal to 330 meters (Table A correlation matrix between theses distances is presented in Table 1. Some accessibility criteria are strongly correlated in the upper part of the matrix: distance to the city center, station, tram, or campus. 11 We considered the log mean value of these four variables to compile the distance to the city center. The noise exposure levels to road and rail noise were calculated from the traffic data. Each road was decomposed in homogenous parts in terms of noise emission. The traffic data were completed with speeds, acceleration or deceleration of cars, the surfacing and the slope of the road. From each homogenous part of the road, we calculated the standardized noise level in agreement with the Annex 1 of the European Directive 2002/49/CE relating to the assessment and management of environmental noise. 12 The minimum, mean and maximum noise values (respectively) were individually calculated on each of the three periods of the day (daytime, evening, night-time). Afterwards they were compiled to calculate the minimum, mean and maximum levels (respectively) of the synthetic noise index in the form and using the weights advocated by the Directive. Around 25% of houses are subject to disturbing and excessive noise 11 For these variables, the Cronbach's alpha statistic, which determines the internal consistency of items in a survey instruments to determine its reliability, is equal to 0.96. According to [START_REF] Nunnally | Psychometric Theory[END_REF], a score of 0.70 obtained on a substantial sample is an acceptably reliable coefficient.

(greater than 65 dB(A), [START_REF] Who | World Health Organization: Guidelines for Community Noise[END_REF]) at some point during the day (maximum noise over 24 hours, Figure 3). The mean noise level of the synthetic index was retained. Noise levels (dB(A))

Fig.3. Distribution of noise levels dB(A)

Note: Gaussian kernel function is used (bandwidth=2.5) Source: Eval-PDU

The air pollution levels around the dwellings subject to a transaction were calculated. The concentration of several airborne pollutants described in Table A.2 was simulated using the Atmospheric Dispersion Modelling System (ADMS Urban model). In this model, road traffic, residential and tertiary emissions are regarded as a major source of air pollution at urban scales.

The retained pollutants are Nitrogen dioxide (NO2), Nitrogen oxides (NOx), Particulate matter (PM10 and PM2.5), Carbon monoxide (CO), benzene (C6H6), Volatile organic compounds (VOC), and Sulphur dioxide (SO2). The pollutants of interest are in particular NOx, PM10 and PM2.5. They take into consideration the Euro5 (2011) and Euro6 (2015) standards for diesel vehicles and their controversial effectiveness on air quality. The ADMS Urban model for NOx chemistry includes reactions with ozone and hydrocarbons. 14 A Lagrangian trajectory model 13 For each of the 2969 observations (for which we know the mail address), we were able to obtained and identify the Nantes Métropole actual noise levels for 2008. The Spearman's rank correlation coefficient is equal to 0.78 (the conurbation uses an ordinal scale to characterize the actual noise levels). The null hypothesis of independence between actual and simulated noise levels is rejected at the .0001 level. The actual and simulated noise levels are highly correlated and we suppose that simulated noise levels reflect individual preferences.

14 More precisely, the NOx chemistry is modeled using the eight reaction Generic Reaction Set (for details, see [START_REF] Venkatram | The development and application of a simplified ozone modelling system (SOMS)[END_REF]. The NOx chemistry offers the possibility to get accurate predictions of NO2.

including the effects of emissions, chemistry, and deposition is used to calculate background concentrations for the air approaching the main modelling area.

The ADMS Urban model integrates lots of emission sources simultaneously. Road emissions were calculated for segments of roads, depending on the traffic flow and the mean speeds of different categories of vehicles, as well as the technical characteristics of the road (the effect of street canyons and traffic-induced turbulence). Residential and tertiary emissions were based on combustion and the use of solvents by households and firms' employees (depending on the population and the nature of the housing stock). Finally, a variety of meteorological data were taken into account to reflect seasonality (with for instance lower pollution levels during summer) (Figure 4). Most of air pollution mean values for the city of Nantes and its metropolitan area are under the annual Air Quality Guideline (AQG) of the WHO (2000WHO ( , 2006)): this is notably the case for the NO2 (the AQG equals to 40 μg/m 3 ) and the PM10 (20 μg/m 3 ). Only the PM2.5 mean value is above the AQG (10 µg/m 3 ). For the NOx, the French quality objective is equal to 30 µg/m 3 . In our sample, around 40% of the dwelling transactions took place where the air pollution level was above the AQG. As showed by Figure 4, the NOx concentration is characterised by a strong disparity. This dichotomy is also notable when considering the mean NOx concentration by district (Figure 5).

Before investigating the role of these two factors on the price of houses, we have to analyze the potential link between noise and air pollution, as road traffic induces most of air pollution and noise. As expected, Figure 5 shows an upward sloping noise/air pollution relationship by district (NOx concentration). This relationship is obtained through a kernel smoother. Yet the R 2 is only 0.3. Finally, the correlation matrix is presented in Table A.2 to take into account the potential links between these pollutants. According to Table A.2, the air pollution criteria are strongly correlated. The Cronbach's alpha statistic was computed and is equal to 0.99. Finally, we consider the mean value of all normalized pollution criteria to construct the air pollution variable. 15

Methods

The price of the house was retained as the dependent variable (in a logarithmic form). From the descriptive analysis of the data, we postulate that the price can be explained by several factors. 16 We introduce in a simultaneous equation model the effect of certain intrinsic characteristics, some location attributes (see above distance variables), and environmental variables (the air pollution construct and the log of mean noise level variable). Using such a model, we are willing to take into account the path analysis and recursive nature of the relationships between the 15 The coefficient of correlation between the noise variable and the air pollution construct is equal to 0.36. Even if air and noise pollution are mainly an effect from road traffic, their coefficient of correlation is low because their propagation models are different (wave mechanics for noise vs fluid mechanics for air). 16 The hedonic literature alternately consider rents or housing prices as a dependent variable. Comparable results may be noticed concerning in particular intrinsic attributes (number of rooms, parking facilities…). See for example [START_REF] Cavailhès | Le prix des attributs du logement[END_REF] for rents in 287 French cities or [START_REF] Bureau | Évaluation de l'impact des politiques[END_REF] for housing prices in Paris.

variables (Figure 2). 17 This is useful for testing multiple sets of associations between variables simultaneously. The model can be written as:

i i i i i i Y Z W X P             (1) i i i W Z       (2) i i i W Y       ( 3
)
where Pi is the vector of prices (in logarithm) that vary between transaction i. Xi is a vector of intrinsic characteristics, Wi a vector of location attributes, Zi a vector of atmospheric characteristics, Yi a vector of noise characteristics. α, μ, ν, γ, β, δ, , λ, and φ are the corresponding parameters to estimate. εi, ωi, υi are residual error terms (expected to be uncorrelated with the explanatory variables).

A correlation matrix on the independent variables was performed (Table A.3). As several variables are correlated (for instance, noise and air pollution or air pollution and distance to the city center), the Variance inflation factor (VIF) statistics were calculated. They show that the model does not suffer from multicollinearity as all VIF statistics are lower than 5 which is often taken as threshold [START_REF] Chatterjee | Regression Analysis by Example[END_REF].

The presence of spatial dependency was tested in our set of data. The Moran's I statistics is equal to 1.66 (exactly the 10% significance level). We conducted afterwards both the Spatial Error Model (SEM) and the Spatial Autoregressive Model (SAR). In the latter case, it appeared that the value of the spatial parameter never significantly differed from zero. For the SEM estimation, the likelihood ratio test comparing the non-constricted and the constricted models 17 This path analysis model is treated as a seemingly unrelated regression which allows for the simultaneous estimate of the coefficients and carries out estimates of the standard errors that take into account the contemporaneous correlations.

generally concluded to the absence of significant spatial autocorrelation between the independent variables. 18 Given the global results obtained respectively to the Moran-s I statistics and to the likelihood ratio tests, we concluded to the absence of significant dependency in our sample.

Furthermore, as residuals are heteroscedastic and not normally distributed, the Huber-White standard errors were used and the model was estimated with quasi-maximum likelihood estimation. Moreover, the independent variables are by assumption measured without error. As both air pollution and noise are simulated data, the presence of measurement error may lead to biased and inconsistent parameter estimates [START_REF] Fuller | Measurement Error Models[END_REF]. In our case, we tested an error-invariables regression model in presence of independent variable measured with error. The significance levels are similar to the model measured without error.

Results

The results for the whole model are presented in Table 2. In Table 3, several variables linked to buyers' characteristics are used.

In hedonic studies, the intrinsic attributes such as living surface area, the number of rooms or parking spaces, the age of the building usually influence the price of houses or apartments [START_REF] Baudry | Formation des prix immobiliers et consentements à payer pour une amélioration de l'environnement urbain: l'exemple rennais[END_REF][START_REF] Bureau | Évaluation de l'impact des politiques[END_REF][START_REF] Cavailhès | Le prix des attributs du logement[END_REF]. For Nantes Métropole, the results show that the living surface area not surprisingly plays a positive role on the price.

Furthermore, the average room area, the two-storey houses (compared to single-storey house), 18 The result of the test was usually between 0 and 2.23, to be compared to the 5% significance level for the Chisquare test with one degree of freedom: 3.84. Only two specific calibrations of the neighborhood matrix performed a test comprised between 3.40 and 3.89.

and the age of the houses (for houses built after 1991 compared to houses built before 1948) are on average conversely linked to the price as well as the distance to the city center.

The original result of the paper consists in the explanation of air pollution and noise exposure levels. These two variables are assumed to explain the price of the house. In the second and third columns of Table 2, the variables at stake in such an explanation are analyzed. The influence of air pollution in the formation of house prices in Nantes is not as evident, probably because of the satisfactory level of air quality. Air pollution regarded as the dependent variable can be explained by the distance to the city center: the closer the house exchanged is located to the center, the poorer air quality. This is also the case when the house is located near a commercial zone. In such areas, the high level of airborne pollutants (excluding ozone) is due to the numerous cars circulating during peak hours that aggravates air pollution. This is also the result of the simultaneous presence of industrial firms. The presence of diesel light delivery trucks at other times of the day constitutes another source of aggravated air pollution.

The number of bus stops exerts a significant impact on air pollution. Those areas also see a high number of cars circulating. Such reconfigured areas may have contributed to diminish the mean speed of the remaining cars. Indeed the large initial place devoted to cars has often been transferred to public transport and clean transport modes. Yet traffic jams prove to add to air pollution.

Surprisingly, the proximity to the ring road leads to the opposite result. The relative quality of air around the city is probably due to the fact that the road network in the less densely populated areas is less built-up. In the absence of congestion, cars travelling at higher speed on the ring road (rather than more slowly on inner streets) may be considered less pollutant as well.

The case of noise pollution is more interesting. According to our results, the amplitude of the effect of noise on housing price remains low: 1% increase in dB(A) should induce a decrease equal to around 0.035% of the price.

When noise is regarded as the dependent variable, it would seem worthwhile to compare the same potential explanatory variables as for air pollution. Being located next to the city center constitutes a significant factor for aggravation of noise pollution: cars, buses, trams, but also pedestrians shopping or having leisure time in coffees or restaurants prove to be numerous sources of noise from the morning to late at night. Surprisingly, this is no longer the case for the proximity to a commercial zone, as it was emphasized for air pollution: a house located next to a mall appears to be less affected by noise than the same house located farther. This could be the result of specific peak hours for consumer activities in such areas (mostly in the evening). Such a pattern would have an impact on the maximum noise level, but not on the mean level, considering parallel and majoritarian calm hours during the rest of the day and at night.

As expected, the number of bus stops in the neighborhood, as for air pollution, exerts a positive effect on the average noise level. The coefficient is higher than for air pollution because buses are particularly loud when they leave stations compared to cars (whereas in Nantes they tend to pollute less than cars because they use natural gas instead of fuel). This is also the result of high concentrations of people waiting for the bus, especially schoolchildren which may be regarded as unruly by the inhabitants early in the morning. The distance to the ring road, to the nearest green space or to the airport have no significant impact on the mean noise level. 19 Source: Eval-PDU 19 Concerning the ring road, the positive impact of being remote from the city center and having less built-up road and tram networks is offset by the proximity to a major road, where fast cars appear to be loud on average (with the exception of peak hours). The expected quietness of green spaces is offset by car-parking in the neighborhood and by numerous households living elsewhere. For the airport, only a very small part of our sample is located in the air corridor. For all the other dwellings, the mean noise level due to air traffic proved to be below the disturbance limit.

Finally, we use two variables linked to buyers' characteristics: their age and whether their last dwelling was situated in a polluted county. 20 Table 3 gives the coefficients of air pollution and noise estimated in the same simultaneous model as before, conditioned to certain characteristics.

Young people appear to pay more attention to noise levels when they buy a house, whereas old people seem to be more sensitive to air pollution. This result is partly in line with the results from [START_REF] Menz | Population aging and environmental preferences in OECD countries: the case of air pollution[END_REF], which show that the preferences for air quality are U-shaped in age with epidemiological evidence on the age-specific health consequences of air pollution.

Furthermore, people who lived in air polluted counties before coming to Nantes (especially Paris) appear to be more sensitive to air pollution levels, whereas those who come from low air polluted counties are more inclined to choose a house with low noise exposure. This result confirms the result from [START_REF] Menz | Do people habituate to air pollution? Evidence from international life satisfaction data[END_REF] which showed, in an environmental valuation, that past pollution levels increase the value of clean air.

Concluding remarks

In this paper, we tested the assumption of the way environmental variables could be simultaneously affected by specific attributes of the houses exchanged in Nantes and its metropolitan area, and could affect housing price. We showed that air pollution had no significant impact on the price, whereas noise pollution does have an impact. Air pollution still depends on the proximity to the city center or to a commercial zone, and on the structure of the individual or public transport network. The relationships between such characteristics and noise pollution prove to be more complex: noise strongly depends on the proximity of the city center 20 The Perval database gives information on the age and the municipality of residence. For each municipality of residence belonging to a county, we have used the National Atmospheric index scaled from 1 to 5 (high pollution refers to an index superior to 3).

or the number of bus stops in the neighborhood. This seems to reinforce the depreciation impact noise pollution significantly exerts on housing price in Nantes Métropole.

Moreover, whereas noise is directly perceptible, the reason for which air pollution has no effect on house prices may be due to: first, the largely invisible and intangible nature of air quality (except for instance when it is odorous or visible, like for certain industrial smokes, or when its effects are tangible for people who suffer from coughs or other forms of irritation); and second, to the fact that air quality is seen as being ephemeral (even though the effects of air pollution on health are tangible). Even if French urban citizens have begun to be suspicious about invisible pollution since the end of the 19 th century [START_REF] Massard-Guilbaud | Culture, technique, gestion de l'espace. Une histoire sociale de la pollution industrielle dans les villes françaises, 1789-1914[END_REF], air pollution resulting from traffic or industry may be thought of as impossible to tackle as it is anonymous, permanent, and linked to modernity [START_REF] Barraqué | Le bruit, question de santé ou de qualité de vie[END_REF]. Furthermore, the process of measuring invisible and toxic pollution remained in the technical domain until recent years, over which atmospheric pollution have steadily become a political issue [START_REF] Frère | Les pollutions atmosphériques urbaines de proximité à l'heure du Développement Durable[END_REF].

As Nantes is a dynamic city, the housing demand has seen important growth since the 2000s.

Prospective purchasers may have fewer options for choosing property and may not have the choice between different dwellings with similar attributes but with significant differences in noise or air pollution levels. For instance, as noted by [START_REF] Blanco | Property prices in urban areas affected by road traffic noise[END_REF], the advantages of living in noisier or more polluted areas closer to specific facilities (closer to the city center or a commercial zone for instance) outweigh the assumed negative effects of the consequently higher noise or air pollution levels. If purchasers are prepared to accept higher pollution levels as unavoidable consequences of living closer to facilities, then there might be no reason for the price to be affected [START_REF] Blanco | Property prices in urban areas affected by road traffic noise[END_REF]. As we have no information about the motivations, perceptions, and preferences of the buyers, a study taking these elements into account should contribute to better understand the impact of environmental variables on the real estate market. Note: the number of observations is equal to 2969. Source: Eval-PDU

Annex

Fig. 1

 1 Fig.1 Annual air pollutant concentrations in Nantes (µg/m3, except for CO) Note: Carbon Monoxide (CO) is in 100µg/m3; VOC: Volatile Organic Compounds (here BTEX). The annual average values are based on the mean values of active measurement stations at this moment: for instance, 13 stations were used for PM10 in 2015.

Fig

  Fig.2. The hypothesized relationships between the variables

Fig. 4 .Fig. 5 .

 45 Fig.4. Box plot of NOx concentration (µg/m 3 ) by months Fig.5. Average noise level (dB(A)) and NOx concentration (µg/m 3 ) by district Note: The dashed line represents the mean. The upper/lower limit is the largest/lowest value not greater than third/first quartile +/-1.5 × Interquartile range. Source: Eval-PDU Note: The curve is obtained by symmetric nearest neighbor linear smoother.

  (9) 0.193 0.059 -0.091 0.033 0.098 -0.102 0.020 -0.184 1.000 House built between 1970 and 1980 (10) -0.121 -0.016 0.072 -0.038 0.035 -0.014 -0.032 -0.189 -0.257 1.000 House built between 1981 and 1991 (11) -0.157 -0.053 -0.053 -0.121 -0.013 0.082 -0.122 -0.194 -0.265 -00.018 -0.007 -0.020 0.017 0.010 -0.027 0.031 0.072 0.012 -0.021 -0.005 -0.100 -0.030 -0.082 0.033 0.025 1.000 Distance to airport (18) -0.155 -0.039 0.101 -0.006 -0.111 0.130 -0.047 -0.133 -0.096 0.065 0.115 0.061 0.311 0.084 -0.003 0.017 -0.133 1.000

Table A

 A

.1, the houses have a mean living surface area equal to 112.82 square meters with an average room area equal to 21.84 square meters. More than 65% of the houses are two-storey houses and 22% of the houses were built between 1981 and 1991.

Table 1 . Accessibility criteria correlation matrix (in kilometers)

 1

			(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	City center	(1)	1.000
	Railway station	(2)	0.967	1.000
	Tram	(3)	0.909	0.890	1.000
	Campus	(4)	0.819	0.875	0.818	1.000
	Airport	(5)	0.416	0.281	0.340	-0.042	1.000
	Commercial zone	(6)	0.395	0.366	0.390	0.315	0.173	1.000
	Green space	(7)	0.089	0.067	0.064	-0.003	0.210	0.152	1.000
	Ring road	(8)	0.322	0.334	0.312	0.306	0.083	0.091	-0.006	1.000

Note: the number of observations is equal to 2969. Source: Eval-PDU

  13

	Density	.03			Excessive noise
		.02
		.01
		0
		0	20	40	60	80

Table 2 . Estimation results Price Environmental variables Air Noise Environmental variables

 2

	Air pollution	0.071
		(0.103)
	Noise	-0.035**
		(0.018)
	Intrinsic characteristics
	Living surface area	0.950***
		(0.024)
	Average room area	-0.009***
		(0.002)
	Single-storey house (reference)	Ref.
	Two-storey house	-0.055***
		(0.012)
	Three-storey house or higher	0.003
		(0.023)
	House built before 1948 (reference)	Ref.
	House built between 1948 and 1969	-0.047**
		(0.018)
	House built between 1970 and 1980	-0.024
		(0.018)
	House built between 1981 and 1991	-0.024
		(0.019)
	House built after 1991	0.098***
		(0.018)
	Location attributes
	Distance to city center	-0.112***	-0.143***	-0.087***
		(0.016)	(0.002)	(0.010)
	Distance to commercial zone	-0.010	-0.013***	0.022***
		(0.008)	(0.002)	(0.007)
	Number of bus stops	0.003	0.002**	0.012***
		(0.004)	(0.001)	(0.004)
	Distance to ring road	0.007	0.004**	-0.004
		(0.007)	(0.002)	(0.008)
	Distance to green space	-0.0003	-0.0005*	-0.001
		(0.001)	(0.0002)	(0.001)
	Distance to airport	0.075***	-0.010***	-0.013
		(0.011)	(0.002)	(0.012)
	Constant	8.278***	1.558***	4.592***
		(0.206)	(0.026)	(0.139)
	Temporal effects (monthly effects)	Yes	Yes	Yes
	Number of observations		2969
	Pseudo Log-Likelihood		-37584.818
	Note: Robust standard errors are in parenthesis. * p<0.1, ** p<.05, *** p<0.01.
	Source: Eval-PDU

Table 3 . Estimation results to certain characteristics of purchasers

 3

		Air pollution	Noise
		Coeff	SE	Coeff	SE	N	PLL
	Total	0.071	0.103	-0.035**	0.018	2969	-37584.82
	Age
	Less than 40 years	0.125	0.135	-0.070***	0.026	1485	-18247.69
	40 to less than 55 years	0.202	0.173	-0.054	0.031	980	-12353.77
	55 years and more	-0.387**	0.189	0.065	0.043	504	-6312.63
	Anterior air pollution level
	High	-0.630**	0.314	-0.003	0.047	199	-1954.61
	Low	0.099	0.108	-0.035*	0.107	2770	-35222.20
	Note: *p<0.1, **p<.05, ***p<0.01. SE: Standard errors, N: Number of observations, PLL: Pseudo-
	LogLikelihood.

Table A .1. Descriptive statistics

 A Note: the number of observations is equal to 2969. SD: standard deviation. Source: Eval-PDU

		Mean	SD	Min	Max
	Intrinsic attributes
	Living surface area (square meters)	112.82	42.26	32.00	650.00
	Average room area (square meters)	21.84	6.00	7.50	125.00
	Single-storey house	0.26	0.44	0	1
	Two-storey house	0.66	0.47	0	1
	Three-storey house or higher	0.08	0.27	0	1
	House built before 1948	0.19	0.39	0	1
	House built between 1948 and 1969	0.20	0.40	0	1
	House built between 1970 and 1980	0.21	0.41	0	1
	House built between 1981 and 1991	0.22	0.41	0	1
	House built after 1991	0.18	0.39	0	1
	Location attributes (kilometers)
	Distance to city center	6.55	3.46	0.35	19.92
	Distance to station	6.67	3.63	0.35	20.94
	Distance to tram	2.74	2.57	0.03	13.70
	Distance to campus	5.17	3.52	0.29	19.97
	Distance to airport	9.61	3.88	0.83	23.67
	Distance to commercial zone	0.76	0.61	0.01	5.23
	Distance to green space	0.33	0.27	0.01	1.92
	Distance to ring road	2.18	1.21	0.15	8.69
	Number of bus stops	1.84	1.43	0	7
	Atmospheric pollution (μg/m 3 )
	Nitrogen dioxide (NO2)	19.85	4.41	10.53	42.41
	Nitrogen oxides (NOx)	28.35	9.13	12.70	121.05
	Particulate matter (PM10)	16.81	0.83	15.33	24.68
	Particulate matter (PM2.5)	11.37	0.66	10.17	17.54
	Carbon monoxide (CO)	470.20	31.54	425.40	732.63
	Benzene (C6H6)	0.23	0.15	0.02	1.52
	Volatile Organic Compounds (VOC)	8.90	4.90	1.32	49.41
	Sulphur dioxide (SO2)	1.29	0.51	0.27	4.06
	Noise pollution (dB(A))
	Max	54.77	12.62	5.48	80.34
	Mean	49.12	11.71	4.69	74.50
	Min	32.52	14.76	0.02	73.86

Table A .2. Air pollution concentrations correlation matrix

 A

			(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Nitrogen dioxide	(1)	1.000
	Nitrogen monoxide	(2)	0.947	1.000
	Particulate (PM10)	(3)	0.942	0.997	1.000
	Particulate (PM2.5)	(4)	0.944	0.996	0.999	1.000
	Carbon monoxide	(5)	0.913	0.969	0.976	0.977	1.000
	Benzene	(6)	0.909	0.966	0.973	0.974	0.998	1.000
	Organic compound	(7)	0.914	0.967	0.973	0.974	0.992	0.993	1.000
	Sulphur dioxide	(8)	0.971	0.926	0.927	0.930	0.927	0.926	0.933	1.000
	Note: the number of observations is equal to 2969.
	Source: Eval-PDU

Table A .3. Correlation matrix of the variables included in the model

 A

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9) (10) (11) (12) (13) (14) (15) (16) (17) (18)
	Air pollution	(1) 1.000
	Noise	(2) 0.366 1.000
	Living surface area	(3) 0.069 0.023 1.000
	Average room area	(4) 0.100 0.032 0.455 1.000
	Single-storey house	(5) -0.197 -0.062 -0.295 -0.013 1.000
	Two-storey house	(6) 0.023 0.033 0.130 -0.027 -0.823 1.000
	Three-storey house or higher	(7) 0.276 0.042 0.248 0.067 -0.177 -0.413 1.000
	House built before 1948	(8) 0.254 0.036 -0.067 0.083 -0.038 -0.059 0.164 1.000
	House built between 1948 and 1969

The city of Nantes adopted an air quality management plan in 2002, and a climate plan in 2007 whose objective is to reduce greenhouse gas emissions by 30% in 2020 and by 50% in 2025.

The mean noise exposure varies from around 5 to 75 dB(A), with

dB(A) the daily value threshold before noise annoyance becomes noticeable[START_REF] Who | World Health Organization: Guidelines for Community Noise[END_REF]. Around 25% of dwellings are above this level.6 According toINSEE (2014), Nantes has the second employment growth at the country level (the first for the executives and managers) and the third population growth of the country between 2006 and 2011.

An exception is[START_REF] Klaeboe | Oslo traffic study-part 1: an integrated approach to assess the combined effects of noise and air pollution on annoyance[END_REF], but the aim of the paper is to assess the combined effects of noise and air pollution on annoyance.

See for instance Le[START_REF] Boennec | Nouvelles Centralités, Choix modal et Politiques de Déplacements: le Cas Nantais[END_REF], but they use a spatial model approach and the impact of location characteristics on air and noise variables is not taken into account.

See Taylor et al. (1982),[START_REF] Hughes | Traffic externalities and single-family house prices[END_REF],[START_REF] Theebe | Planes, trains, and automobiles: the impact of traffic noise on house prices[END_REF],[START_REF] Dekkers | Monetary valuation of aircraft noise: A hedonic analysis around Amsterdam airport[END_REF],[START_REF] Chen | Impact of high-speed rail on housing values: an observation from the Beijing-Shanghai line[END_REF]. Furthermore, see[START_REF] Nelson | Hedonic property value studies of transportation noise: aircraft and road traffic[END_REF] for a review of hedonic property value studies of transportation noise.

http://www.developpement-durable.gouv.fr/IMG/pdf/Texte_de_la_Directive-2002-49_CE-2.pdf

Acknowledgments

This study has been financed by the Agence Nationale de la Recherche (National Research Agency), as part of the "Evaluation of environmental impacts of different UTPs scenarios and their socio-economic consequences in Nantes Métropole" (Eval-PDU), as part of its sustainable cities program (ANR-08 VILL-0005).


J P Landesman

N Isik-Goktas

R R Lapierre

C Levallois

S Ghanad-Tavakoli

E Pargon

C Petit-Etienne

J Jiménez

Low temperature micro-photoluminescence spectroscopy of microstructures with InAsP/InP strained quantum wells

Keywords: InAs x P 1-x /InP quantum wells, micro-PL, reactive ion etching

Ridge microstructures were prepared by reactive ion etching (RIE) of a series of stacked InAs x P 1-x quantum wells (QWs) with step graded compositions grown on InP by molecular beam epitaxy. These microstructures were characterized by low temperature micro-photoluminescence. The photoluminescence (PL) emission associated with each of the QWs was clearly identified and a model for their line shape was implemented. PL line-scans were measured across etched ridge stripes of various widths in an optical cryostat, with a spatial resolution of 1 µm. The model for the PL spectra allowed accurate extraction of the local PL integrated intensities, spectral positions and line widths. Two different RIE processes, using CH 4 /H 2 and CH 4 /Cl 2 , were investigated. The PL line-scans showed strong variations of the integrated PL intensities across the etched stripes. The PL intensities for all QWs increased gradually from the edge to the center of the ridge microstructures, over a length scale of 10 to 20 µm. On the other hand, the spectral peak position of the PL lines remained constant (0.2 to 0.4 meV, depending on which QW was considered) across the microstructures. These observations are discussed in terms of the mechanical stress induced by the RIE processes, the relaxation of the biaxial built-in compressive stress in the InAsP QWs (induced by the free surfaces at the vertical etched sidewalls), and also by the non-radiative recombination at these sidewalls. Altogether, this study illustrates the contribution that specially designed test structures, coupled with advanced spectroscopic characterization, can provide to the development of semiconductor photonic devices (e.g. lasers or waveguides) involving RIE processing.

Introduction

Given the amount of published work based on nanostructures, there is still a need for tools and methodologies to accurately determine material properties at local scales. Characterizing and understanding the optical properties on a local scale of two-dimensional, one-dimensional and zero-dimensional semiconductor heterostructures deserves specific attention. The confinement geometry by itself is a source of modification of the local optical properties [1], but the synthesis technique as well as the processing of the material to elaborate micro-and nanostructures may also have nonnegligible impact on the material properties [2]. For example, the photoluminescence (PL) signal measured from quantum well (QW) samples patterned into micro-or nanoobjects may differ from that of the as-grown QW material [3]. Processing of QW samples to form building blocks for photonic devices, such as ridge waveguides, may also affect the PL properties [4]. In this work, we investigate the changes in the PL emission from InAs x P 1-x QWs when ridge structures are fabricated by reactive ion etching (RIE). Low temperature micro-PL (µPL) allows us to identify different trends, indicating that the luminescence emission of the QWs is sensitive to the etching process. In particular, the local PL intensity is affected by the mechanical stress within the stripes. First, as was demonstrated recently, the RIE process itself can introduce some mechanical stress, probably due to diffusion and implantation of ions and reactive radicals near the etched sidewalls [5]. Secondly, as the InAs x P 1-x QWs were grown with compressive built-in stress, stress relaxation occurs near the etched sidewalls which are free surfaces. Moreover, the local PL intensity may also be affected by non-radiative recombination due to creation of the etched sidewalls and the change in the surface recombination velocity (SRV) resulting from the etching process. The information produced by such µPL experiments can be useful from two points of view. First, it helps to understand the fundamentals of the interactions of etching plasmas with the semiconductor material. This remains still an active field of research, particularly because new plasma chemistries and etching processes are being used [6,7,8,9]. The specific design of our graded QW samples contributes to improving the knowledge gained on this kind of interaction. Secondly, it can provide a methodology to better monitor the perturbation undergone by the active material during processing of photonic structures such as waveguides, especially when the critical dimension of these structures is reduced and the device performance can be affected by the material changes or degradation. Altogether, the evolution of the PL intensity can be an indicator of possible damage to the material during the processing of photonic devices which can limit the performance of components such as laser diodes or passive waveguides.

Sample preparation

The sample structure is illustrated in figure 1. The As composition in the QWs is step graded, with QW8 (closest to the substrate) having the highest As composition and QW1 (closest to the surface) having the lowest As composition. This controls the energy gap of the different QWs such that the PL emission from the deeper QWs is not absorbed as it travels through the upper-lying QWs, which are transparent to this PL emission. The sample was grown by gas source molecular beam epitaxy (MBE) on an ntype InP (100) substrate using a solid source for In and a gas cracker for PH 3 /AsH 3 gases (producing P 2 /As 2 ). The growth temperature was 470 °C. The InP buffer thickness was 300 to 400 nm. No dopant was included during growth of the buffer and QW structure. The design included a constant thickness for the QWs, made possible by keeping the In flux and the duration of each QW growth sequence constant. The QW thickness was 7.5 nm. Careful calibration of the As and P sources, prior to sample growth, yielded a linear variation of the As to P composition ratio along the 8 QWs. The As/(P+As) atomic composition was 0.5 for QW8 and 0.35 for QW1. Microstructures made of ridges with a rectangular cross-section were then etched on these samples. A silicon nitride (SiN x ) mask thin film (500 nm thick) was first deposited by plasma-enhanced chemical vapor deposition at 250 °C. Stripes of various widths, from 1 to 50 µm, and a length of several mm, were defined by optical lithography in this mask. Finally, the ridges were fabricated by RIE using two different processes. In process # 1, a capacitively coupled RIE reactor (Alcatel 300) with a chamber 300 mm in diameter was used. The gaseous species involved are CH 4 , H 2 , and Ar with the following respective flow rates: 6.4 sccm / 50 sccm / 8.4 sccm. The total pressure was maintained at 30 mTorr during the process and the applied RF power was 40 W leading to a DC self-bias of 360 V. Under these conditions a moderate etch rate of 20 nm/min is reached but smooth sidewalls are obtained for the patterns formed. As this etching rate is low, to avoid heating during long etching steps, samples were attached to a water-cooled holder (water temperature between 10 and 15 °C). In process # 2, an industrial inductively coupled plasma reactor accepting 200 mm wafers (DPS+ from Applied Materials) with Cl 2 /CH 4 /Ar gas mixture was used [START_REF] Pargon | Plasma etching processes for the integration of InP based compounds on 200mm Si wafer for photonic applications[END_REF]. This reactor is equipped with a hot cathode whose temperature can be tuned from 150 °C to 250 °C. The reactor chamber walls are coated with Al 2 O 3 . The chamber walls are kept at 80 °C and the ceramic dome is maintained at 60 °C. The III-V samples are thermally glued with a thermal paste on a 200 mm SiO 2 carrier wafer. The plasma conditions used in this study were : 20 sccm Cl 2 / 100 sccm Ar / 32 sccm CH 4 , pressure chamber 20 mTorr, source power 800 W, bias power 200 W, chuck temperature 200 °C. The resulting etch rate was 900 nm/min. The samples were etched to a depth of 2 µm to ensure the etching of all the QWs. After the semiconductor etching process, the remaining SiN x mask was etched away using a solution of hydrofluoric (HF) acid.

Low temperature micro-photoluminescence measurements

The µPL experiments were performed at 10 K in an optical cryostat. Details of the set-up have been previously reported [START_REF] Haapamaki | Growth of InAs/InP Nanowires by Molecular Beam Epitaxy[END_REF]. The excitation wavelength was 1064 nm, with a spot size of approximately 1 µm. This wavelength generates electron-hole pairs in the InAs x P 1-x QWs but not in the InP buffer, substrate and barrier layers. The excitation power density was approximately 10 6 W/cm 2 but a small part of this pump power is used for the QWs excitation since absorption occurs only in the QWs. µPL line-scans across the etched ridges could be performed with a step size of 5 µm, using high accuracy piezo-electric nano-positioners on the sample holder inside the cryostat. The spectrometer resolution was 0.025 nm. Figure 2 illustrates the PL spectrum from the as-grown sample. Eight emission lines can be clearly identified. A simple best-fit procedure was used to extract the spectral parameters from this PL spectrum. This procedure assumes a Gaussian shape for each line, with adjustable central wavelength, full width at half maximum (FWHM) and amplitude for each peak. The calculated PL intensity as a function of wavelength I P L (λ) is given by :

I P L (λ) = 8 i=1 A i • exp - (λ -λ i ) 2 2 • F W HM 2 i (1)
where, for each of the eight PL lines, A i denotes the amplitude, λ i the central wavelength and F W HM i the full width at half maximum. The agreement between the experimental data and best-fit procedure is acceptable as shown in figure 2-a (determination coefficient R 2 = 0.997). The first observation is that a single transition from each QW contributes to each line. This can be explained by the light hole (LH) to heavy hole (HH) energy levels separation in the InAs x P 1-x QWs induced by compressive stress, which was estimated to be of the order of 0.1 eV [START_REF] Monier | [END_REF]13]. Only transitions from the electron to the HH level are observed, the LH level lying too high in energy to significantly contribute to the PL spectrum. The second observation is the sharpness of the PL lines. The FWHM of each line is approximately 4.8 nm (4.2 meV) for QW1 -QW7, and 6.7 nm (5.1 meV) for QW8. The slightly higher FWHM for QW8 may be due to the proximity of the buffer / substrate interface, with some residual impurities. Altogether, the FWHM values are indicative of very high-quality material [START_REF] Monier | [END_REF]13]. The third observation is the almost linear variation of the QW transition energies versus QW composition (figure 2-b). The fluctuations of the PL line wavelength across the 2" wafer were less than 1 nm. The short-scale fluctuations (calculated over distances of 30 µm) were smaller than 0.2 nm for QW1 -QW7, and 0.4 nm for QW8. These fluctuation values were used to estimate the standard deviation on the QW transitions energies, giving 0.2 meV for QW1 -QW7 and 0.4 meV for QW8. Taking into account these small values, error bars were not displayed on the data of figure 2-b. Figure 3 shows the evolution of the integrated PL intensities of the QW lines measured on the reference sample, along a 30 µm wide line-scan starting at a cleaved edge. This plot will be used as the reference for similar line-scans measured across etched ridges in the following section.

RIE results

Figure 4 shows a schematic diagram of the excitation laser beam scanned across the etched ridge to produce µPL line-scans. We first observe in figure 5 the superposition of spectra recorded from the reference (un-etched) sample and samples etched by the two different processes. The spectra for the etched samples were taken at the center of 50 µm wide stripes, as far as possible from the influence of the etched sidewalls. The PL lines for the etched samples have a higher intensity than for the reference sample. The origin for the higher intensity observed in the un-etched region of the samples was investigated by performing the entire process (SiN x mask deposition, exposure to the RIE plasma, mask removal) on samples without stripe definition. The step causing the increase in PL intensity appears to be the SiN x mask deposition and removal. The SiN x layer was kept in the HF solution long enough to etch the entire thickness, but we could not check for the possible presence of a residual very thin passivation layer (1 or 2 nm). We will come back to this in section 5. Small blue shifts of the PL lines also appear for the two etched samples compared to the reference sample, which we will also discuss later.

Next, we discuss the results obtained from µPL line-scans recorded across a 30 µm wide stripe etched with the two processes. The integrated PL intensities and spectral positions (peak wavelengths) are shown in figure 6. These data were obtained with the same best-fit procedure as described for the analysis of the spectrum on the reference sample. We checked that the determination coefficient was always higher than 0.95. Integrated intensities for each line were computed using the amplitude and FWHM parameters produced by the best-fit procedure, without any need for baseline subtraction. The integrated intensities (figures 6-a and 6-c) show a gradual increase Exp. data ref.

Exp. data process #1

Exp. data process #2

Figure 5. PL spectrum measured at 10 K with 1064 nm excitation on the reference sample after epitaxial growth (blue curve), on the sample after etching with process #1 (green curve) and on the sample after etching with process #2 (red curve). The spectra for the etched samples were measured at the center of a 50 µm wide stripe.

from the edges to the center, with the same trend for all QWs. This intensity increase is not related to the spatial resolution of the µPL setup, which is in the µm range. The peak wavelengths (figures 6-b and 6-d) indicate a detectable blue shift for QW1 and QW2. This blue shift remains within the spectral resolution, throughout the ridge. The blue shifts are illustrated in figure 7, as a function of the depth location for each QW. Similar trends were observed for 50 µm wide ridges.

Discussion

PL lineshapes

We first note that the evolution of the peak positions during etching of the stripes is a homogeneous effect, in the sense that the spectral peak positions appear nearly constant across the stripes etched with both processes. A trend for a small blue shift is observed for all QWs (figure 7), with a maximum for the QWs closest to the surface. The PL linewidths displayed in figure 8 show a tendency to decrease after the etching processes, again homogeneously (no observation of position-dependent FWHM changes across etched stripes). This FWHM reduction is more pronounced for process #1, and for QW1 and QW2, located closest to the surface, and also for QW8, located closest to the substrate. RIE in general is expected to increase the PL linewidths [14] through the generation of some disorder at QW interfaces. The small blue shift (with a maximum value for QW1 and QW2), together with the linewidth reduction, may suggest a reduction of the quantum confined Stark effect [15] caused by the residual built-in electric field present in the sample. The residual built-in electric field is the result of the Fermi level pinning at the sample surface after MBE growth. One should note that the residual built-in electric field causing the quantum confined Stark effect is actually also conditioned by the presence of the photo-generated carriers due to PL excitation and the non-radiative recombination at the surface. Thus we propose that a passivation of the InP surface occurs due to the SiN x mask deposition and remains even after removal of this mask layer by the HF etching. This surface passivation reduces the SRV, increasing the PL intensities (as illustrated e.g. in the paper by Casey and Buehler [16]), and simultaneously reducing the built-in electric field.

PL intensities

As shown in figures 6 and 9 (for 50 µm wide stripes), integrated PL intensities vary strongly across etched stripes. The evolution of the PL intensities can be described by the superposition of a homogeneous change, affecting the overall intensities in the unetched areas, and an inhomogeneous change which results in the intensity distribution 3 (integrated intensity profiles on a line-scan measured from a cleaved edge on the reference sample) illustrates these two different trends. The homogeneous change could be the result of the surface passivation produced by the SiN x mask deposition and removal process whereas the intensity variation across the stripes (inhomogeneous change) could be the result of the RIE process itself. Table 1 summarizes the maximum of the integrated PL intensities recorded for the different QWs in both types of stripes, and for both etching processes.

For process #1, on average, the maxima of the PL intensities are similar for 50 µm wide stripes as compared to 30 µm wide stripes. For process #2, the maxima of the PL intensities are approximately twice as high for 50 µm wide stripes as compared to 30 µm wide stripes. For the 50 µm stripes, PL intensities are higher by 80% after process #2 compared to process #1.

The spatial variation of the PL intensity across the etched stripes could originate from three kinds of mechanisms. #1: non-radiative recombination at the vertical etched sidewalls (due to defects introduced on these surfaces by the etching process), #2: non-radiative recombination due to point defects diffusing laterally from the etched walls (these defects would result from interaction with the etching plasma), and #3: local modification of the electronic structure, for example crystal deformation due to mechanical stress. A theoretical description of the effect of non-radiative recombination at the limiting surface of a semi-infinite semiconductor has been proposed by Van Roosbroeck [17] and applied experimentally to various cases for determining the surface recombination velocity at various kinds of structures [18]. In this description, the length scale for the spatial variation of the PL line intensities is determined by the diffusion length of photo-generated carriers. Spatially resolved optical measurements, similar to what is described here, have been used to determine minority carrier diffusion length in various III-V semiconductor-based materials and heterostructures [19]. The diffusion lengths obtained are typically in the range of a few microns for the highest quality materials [19,20]. In our measurements, the PL line intensities vary over lengths of 15 to 20 µm (figures 6 and 9), significantly longer than the diffusion lengths reported; therefore, the non-radiative recombination at the vertical etched sidewalls alone cannot account for the luminescence intensity profiles recorded. Non-radiative recombination at some point defects diffusing laterally from the vertical etched walls, as a result of the interaction of the etched material with the plasma, would also require defect diffusion lengths of at least 15 to 20 µm to explain our observations, which is not realistic either. Therefore, we suggest that the reduction of the PL intensities is caused predominantly by a local modification of the electronic band structure within the QWs, resulting from a crystal deformation due to mechanical stress introduced by the etching process. The occurrence of mechanical stress during RIE of stripes in GaAs and InP has been demonstrated recently by Landesman et al [5]. The origin of this mechanical stress could be related to the ion bombardment taking place during exposure to the etching plasma. As previously described in [5], the resulting crystal deformation consists mainly of a hydrostatic volume compression taking place at the vertical etched sidewalls and extending several microns inside the stripes. Such volume compression should change the band gap, which was actually observed by both µPL and spatially resolved cathodoluminescence. The fact that the PL peak positions do not significantly vary near the edges of the stripes in the present study indicates that this local crystal deformation close to the etched sidewalls cannot be dominant. However, another crystal deformation contribution must be taken into account: due to the creation of free surfaces at the vertical etched sidewalls, the initial biaxial compressive stress within the InAs x P 1-x QWs has to relax partially. This kind of relaxation has been investigated in detail both experimentally and theoretically [21,22]. In our sample, it should consist mainly of a uniaxial tensile deformation perpendicular to the stripe length, and parallel to the wafer surface (x direction in figure 4). This kind of relaxation can extend over distances up to several µm away from the stripe edge.

The resulting local electronic structure within the QWs, in particular the location of the different hole sub-bands and sub-band mixing, should affect both PL intensities and peak positions. A quantitative computation requires solving the local electronic band structure for the QWs taking into account a coupling with the elastic crystal deformation describing the relaxation phenomenon as well as the effect of RIE. Surface non-radiative recombination should also be included. This is outside the scope of this paper and will be considered in the future. A simple approach is presented below.

To emphasize the variations of PL intensities in the etched stripes we have performed a best-fit procedure to the experimental data. As an analytical model for the dependence of the PL intensity versus the distance to the edges, we have tried on the first hand a formula with exponential variation (such as would result from non-radiative recombination at the etched sidewalls [18,17]) and on the second hand a formula with erf c-type variation (which would quantify the impurity concentration variation near the etched sidewalls as a solution to the first Fick's law [23]). These are two extreme physically possible assumptions for the observed variations of the PL intensities. However, both models yield acceptable agreement with the experimental data. Our choice here is to illustrate the best-fit procedure using the first choice, based on the formula:

I P L (x) = A [1 -Bexp(-α • x) -Bexp(-α(W -x))] (2)
where I P L (x) is the PL intensity measured at location x within the stripe. A and B are constants: A holds for the PL intensity in an area infinitely far from the etched sidewalls, and A • (1 -B) is the PL intensity which would be measured exactly at the etched sidewalls (in other words, B is the fraction of the intensity reduction caused by the sidewalls). W is the stripe width. α is a coefficient accounting for the intensity variation from both stripe edges. The best-fit curves are shown in figure 6 (a) and (c) for 30 µm wide stripes and in figure 9 (a) and (b) for 50 µm wide stripes. As mentioned earlier the fact the PL line intensities vary over lengths of 15 to 20 µm away from the etched sidewalls tells us that the coefficient α cannot be related to non-radiative surface recombination as would suggest the analytical model we used for the best-fit procedure. The observations on the PL line intensities demonstrate a strong spatial modulation driven by the different effects suggested. Comparison of the evolution of the PL line intensities across 30 and 50 µm wide stripes, etched with the two different processes, indicates a significant difference between the two etching processes. From the potential mechanisms contributing to PL intensity variations, biaxial stress relaxation associated with the formation of the sidewall free surfaces should be similar for both etching processes. However, one has to consider the stress generation by the etching process itself, as well as the non-radiative recombination at the sidewalls, and these two factors are certainly very different for the two etching processes. Solving this issue requires the complete numerical quantitative approach which will be addressed in a separate article.

Conclusion

The results described illustrate the potential of low temperature µPL measurements for a careful assessment of microstructures based on QW designs. The details of our study reveal the complex physics resulting from the etching processes. Thanks to the high quality of the QW samples, the PL lines for each QW could be measured individually with high accuracy and line-scans were performed across ridge stripes etched with different RIE processes. Two trends of changes of the integrated PL intensities were observed: one homogeneous and one inhomogeneous. For the homogeneous change we proposed a mechanism of surface passivation by the SiN x mask, which persists after the removal of this mask. This surface passivation mechanism may be due to a remaining very thin layer (1 -2 nm) after removal of the SiN x mask, or to the effect of the HF etching (H passivation ?). For the inhomogeneous change, we proposed three origins: non-radiative recombination (mainly at the vertical etched sidewalls), compressive volume change near the etched sidewalls generated by ion bombardment from the plasma, and uniaxial relaxation of the built-in compressive stress in the asgrown QWs. A significant difference in the behavior for PL line intensities was observed between the two studied etching processes. Whereas for the 30 µm wide stripes, the PL intensities are similar for both etching processes, for the 50 µm wide stripes these intensities are approximately 80% higher for process #2 as compared to process #1. A detailed quantitative analysis is required to explain this difference. Uniaxial relaxation of the built-in compressive stress in the QWs should be identical in magnitude for both etching processes. The other two mechanisms (compressive volume change near the etched sidewalls, non-radiative recombination at the sidewalls) may lead to strong differences between the two etching processes. At this stage, we suggest that the different magnitude of these mechanisms explains the difference observed on the PL intensities. The temperature involved during the etching process (higher for process #2 than for process #1), or the amount of hydrogen present (higher for process #1) might be some of the origins. Future work will perform quantitative simulations of the PL line intensities, using a coupled model taking into account local electronic band structure within the QWs, the associated optical transitions, and the effect of elastic strain relaxation. The electronic band structure calculation will be performed using either a full ab-initio approach or a more simple k • p hamiltonian description. The spectral shifts of the PL lines display a homogeneous behavior. These line shifts appear constant with a high accuracy for each QW across the etched stripes, suggesting that the mechanisms responsible for PL intensity variations do not produce any spectral shift, or that some compensation takes place leading to overall negligible peak shift.

Figure 1 .

 1 Figure 1. Epitaxial sample structure. Each InAs x P 1-x QW has the same thickness (7.5 nm). The As/(P+As) composition is step graded, from 0.5 for QW8 to 0.35 for QW1.

Figure 2 .

 2 Figure 2. (a) PL spectrum measured at 10 K with 1064 nm excitation after epitaxial growth (sample structure shown in fig. 1). Black symbols ( ): experimental data; full line (red): best-fit with the model described in text. (b) PL line energy versus QW composition. The full line in (b) is a linear best-fit to the PL energies.

Figure 3 .Figure 4 .

 34 Figure 3. Integrated intensity of the PL lines measured along a 30 µm line-scan from the cleaved edge on the reference sample. The cleaved edge is located at the position 0 µm.

Figure 6 .Figure 7 .

 67 Figure 6. Spectral characteristics of the PL lines measured across a 30 µm wide ridge. (a) Process #1, integrated intensities. (b) Process #1, spectral positions. (c) Process #2, integrated intensities. (d) Process #2, spectral positions. The reference lines in (b) and (d) indicate the spectral position of the corresponding QW measured on the un-etched reference sample (cf. fig. 2). Full lines in (a) and (c) are the best-fits to the experimental line intensity data using the model described in the text.

Figure 9 .

 9 Figure 9. PL integrated line intensities measured across a 50 µm wide ridge etched using (a) process #1, and (b) process #2. Full lines are the best-fits to the experimental line intensity data using the model described in the text.

Table 1 .

 1 Maximum of the integrated PL intensity (arb. units) for each QW, for both types of stripes and for both etching processes.

	QW Etching process #1	Etching process #2
		30 µm 50 µm	30 µm	50 µm
	1	3.1	2.9	2.7	6.0
	2	4.7	3.8	4.0	8.8
	3	5.3	5.1	4.4	9.3
	4	5.8	5.7	4.5	9.9
	5	9.3	7.6	7.3	15.3
	6	7.9	7.6	6.6	14.0
	7	7.7	8.0	6.5	13.7
	8	8.4	10.2	7.3	15.2
	across the stripes. Comparison of figures 6 and 9 with figure

Acknowledgments

JPL and CL acknowledge support from the NanoRennes platform, affiliated to RENATECH+, the French national facilities network for micro-nanotechnology. RRL and NIG acknowledge support from the Natural Sciences and Engineering Research Council of Canada (NSERC), Grant RGPIN-2018-04015 and RGPAS-2018-522624. JJ was funded by Junta de Castilla y León (Project No. VA283P18) and MINECO (Project No. RTI2018-101020-B-I00).


Sleimane Nasser
email: sleimane.nassereldine@geeps.centralesupelec.fr

El Dine

Xavier Mininger
email: xavier.mininger@geeps.centralesupelec.fr

Caroline Nore
email: caroline.nore@limsi.fr

Frédéric Bouillault
email: frederic.bouillault@geeps.centralesupelec.fr

Impact of Magnets on Ferrofluid Cooling Process: Experimental and Numerical Approaches

Keywords: Cooling, Ferrofluid, Finite Element Method, Magnet, Power Transformer, Thermomagnetic Convection

The cooling performance of a prototype immersed coil with magnetic fluid is evaluated in this paper, in order to estimate the heating process in a power transformer. For this purpose, thermocouples are inserted at several positions in the experimental setup. A magnetic fluid (Midel vegetable oil -FeCo2O4 Cobalt ferrite magnetic fluid) with nanoparticles volume fraction of 7% is used to improve cooling efficiency. The impact of a radial ring magnet located close to the ferrofluid tank is studied. The magnetic suspension proposed for solenoid cooling is influenced, in addition of the heat source magnetic field, by the magnet location around the tank. The temperature reduction in the coil, due to thermomagnetic convection, has been already assessed in a previous study. Experimental results match with numerical ones performed with a 2D axisymmetric model of the setup, using the finite element method. It is shown hence that the magnet reinforces the temperature decrement.

I. INTRODUCTION

P OWER TRANSFORMER excessive heating is one of the commun severity problems that may risk sustainability of these devices. In order to enhance the heat transfer rate within the transformer, a new cooling fluid is proposed: Ferrofluid. A ferrofluid is a colloidal stable suspension of ferromagnetic nanoparticles dispersed in a non magnetic carrier liquid. In our study, cobalt ferrite nanoparticles have been seeded in Midel vegetable oil to form the ferrofluid. Naturally, at constant magnetic field, a hot ferrofluid is less permeable than a cold one [START_REF] Petit | Etude expérimentale d'un système statique de génération de pression magnétothermique[END_REF]. The dependence ferrofluid magnetization-magnetic field is taken into account by using the assumption of linear magnetic material for ferrofluids [START_REF] Zanella | Natural convection of a ferrofluid in a cylindrical container heated by a solenoid inside[END_REF]:

M = χ(T )H, ( 1
)
where M is the ferrofluid magnetization, T the temperature, H the magnetic field and χ the magnetic susceptibility of the ferrofluid defined by:

χ(T ) = φµ 0 πd 3 M s,p (T ) 2 18K B T , M s,p (T ) = M 0 (1 -( T T c ) 1.5 ) (2)
where φ is the volume fraction of magnetic material, µ 0 the vacuum magnetic permeability, d the particle average diameter, M s,p (T ) the particle magnetization depending on the temperature, K B the Boltzmann constant, M 0 the particle magnetization at saturation, and T c the Curie temperature. Hence, the heated ferrofluid loses its magnetization at the windings, and is pushed up by the magnetic relatively cooler fluid from the surrounding. So, heat is transferred, through the warmer fluid, to the tank border then to the ambience [START_REF] Patel | Prevention of hot spot temperature in a distribution transformer using magnetic fluid as a coolant[END_REF]. Thus, a magnetic force is added to the buoyancy force, and changes the convection flow pattern into the tank. After losing its heat, the magnetic fluid regains its magnetization.

The fluid convection related to the magnetic field is called the magnetoconvection. Therefore, the need to an external mechanical pumping system is avoided. This magnetic force can be modelled by the Helmholtz one (N/m 3 ) given by:

F = -µ 0 H 2 2 ∇χ(T ) (3)
This force connects the magnetization variation with the thermal gradient. We first present a numerical simulation using the finite element method, to solve the fluidic thermal magnetic coupling. In particular, we study the impact of a radial ring magnet on the cooling process. Secondly, we perform an experimental test to validate the numerical results and make some comparisons.

II. EXPERIMENTAL SETUP AND GOVERNING EQUATIONS

The experimental setup studied is based on a Copper coil immersed in ferrofluid, the total is set into an Aluminium tank, tighty closed at the top by a PVC cap as shown in Fig. 1. A radial ring magnet is located close to the tank border, to study its impact on the cooling process.

∇ • u = 0, ρ l Du Dt + ∇p -ρ l ν∇ 2 u = ρ l βg(T -T 0 )e˙z + F, (4)
with Du Dt the material derivative, u the velocity vector, p the pressure, ν the kinematic viscosity, ρ l the density of the magnetic fluid, g the acceleration of gravity, β the thermal expansion coefficient, T 0 the reference temperature. The two last terms at the right side of the Navier-Stokes equation are respectively the buoyancy thermal force and the magnetic force. The heat transfer process that occurs in the ferrofluid is described by the following heat equation:

ρ l C p ( ∂T ∂t + (u • ∇)T ) = ∇ • (λ∇T ) + Q, ( 5
)
where C p is the specific heat capacity at constant pressure, λ the thermal conductivity and Q the volumic heat source dissipated by the Joule effect at the coil and given by 1 σ J 2 s (where σ is the copper electrical conductivity, and J s the current density in the coil).

The computed electromagnetic field is assumed to be quasisteady harmonic, and the ferrofluid magnetization is considered as instantaneously aligned with the magnetic field (see [4, p. 22-23]). The pyromagnetic coefficient is neglected. The magnetostatic equations are given by:

∇ × H = J, ∇ • (µH) = 0, µ = µ 0 (1 + χ(T )) (6)
with J = Jse θ , µ the magnetic permeability of the ferrofluid, and B the magnetic induction. The applied boundary conditions are : q 0 n = h(T ex -T )n at the tank top and lateral wall, q 0 n = 0 at the bottom, u = 0 at the fluid domain borders, A × n = 0 at the tank exterior borders. Initially, we assume that U 0 = 0, T = T 0 , A 0 = 0 with null reference pressure P 0 = 0, where n is the unit normal vector, A the magnetic potential vector, and h the global heat exchange coefficient (tank-air).

The parameters are φ = 7 %, d = 10 nm, ρ l ν = 0.1 P a.s as ferrofluid characteristics, where ρ l ν is the dynamic viscosity. The electrical current in the coil is I = 4 A with a density J s = 3, 35.10 6 A.m -2 , B r = 0.3 T (magnet residual induction), T 0 = 293 K and h = 8 W/m 2 .K(for natural convection). The setup dimensions are given in We study the fluid behavior when hanging a magnet to the tank wall. For this first test, the magnetic field of the coil is canceled (see [4, p. 129-130]), and we have only the magnet effect in the model. After 250 minutes of applying the magnet, it is removed. We record temperature at 2 locations, on the coil and in the fluid (see Fig. 2). We note that without the coil magnetic field, the solenoid temperature increases when the magnet is removed, by a variation of about 1 K. At the same moment, the fluid temperature decreases. Fig. 2: Experimental temperature measurements when applying/removing magnet The same process is numerically tested: the magnet impact is deactivated at t = 250 min, to see the crenelation reproduced numerically. As shown in Fig. 3, the numerical results are qualitatively and quantitatively in good agreement with experimental ones. The numerical results (data not shown) show that when the magnet is applied, the distribution of the magnetic force within the ferrofluid is changed. As a result, the fluid flow around the coil is modified, such that new recirculations arise and enhance the coil cooling.

Fig. 1 :

 1 Fig. 1: Experimental setup using ferrofluid cooling

Fig. 3 :

 3 Fig. 3: Numerical results of temperature when activating/deactivating magnet effect

TABLE 1 .

 1

	Parameter	Ht	Rt	e w1	e w2	e w3	H 0
	Value (cm) 12.5 3.1	1	2	1	3.9
	Parameter	L 0	R i	Re	Rc	e c1	e c2
	Value (cm)	2.1	0.8 1.175	2.6	2	1

TABLE 1 :

 1 Experimental setup dimensions III. RESULTS AND COMPARISONS