S Martinez

A Machard

A Pellegrino

K Touili

L Servant

E Bozonnet

A practical approach to the evaluation of local urban overheating-a coastal city case-study

In response to urbanization and global warming, which amplify heatwave effects and might lead to urban heat stress, this paper proposes a practical approach to characterize the local microclimate at the neighborhood scale. In this approach, the local urban climate is described using suitable indicators, to support the ecodistrict design process or refurbishment.

Experimental and numerical results illustrate the approach in a case study of a French coastal city, La Rochelle. In the first step, we set up urban and rural weather stations to characterize the local urban climate over a summer period and to identify local temperature differences.

The measurements highlighted a daytime urban cooling effect due to the local sea breeze.

While the Urban Weather Generator (UWG) simulation tool used for this study does not capture coastal effects, the results were consistent with the urban heat island (UHI) measurements. We proposed two indicators to quantify the local climate modifications: local UHI and overheating intensity. The parameters of the adaptation strategies were assessed through a sensitivity analysis for these two indicators. For this case-study, we identified vegetation cover, building height and road albedo as key parameters that can be used to mitigate local overheating.

Introduction

In recent decades, the expansion of cities and environmental constraints [START_REF] Seto | A Meta-Analysis of Global Urban Land Expansion[END_REF] have resulted in increasing challenges for urban planning, district renovation and building energy design.

Urban heat islands (UHI) are closely tied to the complex interactions between the urban canopy, buildings (envelope and system waste heat), and the occupants [START_REF] Santamouris | Energy and Climate in the Urban Built Environment[END_REF][START_REF] Kim | Urban heat island[END_REF]. In this context, and to adapt to increasing temperatures due to climate change, the decision process requires practical quantitative tools, and indicators to compare urban strategies and building design adaptations. In this paper, we combined an experimental and numerical approach to propose easy to interpret quantitative indicators. The results can be used to adapt the urban fabric to future UHIs and future urban heatwaves. Indeed, the occurrence of heatwaves will increase during the 21 st century, and studies have shown that the UHI effect is amplified during hot days and nights in dense cities [START_REF] Heaviside | Attribution of mortality to the urban heat island during heatwaves in the West Midlands, UK[END_REF][START_REF] Paravantis | Mortality Associated with High Ambient Temperatures, Heatwaves, and the Urban Heat Island in Athens, Greece[END_REF]. Our approach is illustrated through a case study of a coastal city (La Rochelle, France), which shows similarities with other coastal studies [START_REF] Hu | Influence of Synoptic Sea-Breeze Fronts on the Urban Heat Island Intensity in Dallas-Fort Worth, Texas[END_REF][START_REF] Long | Correlation between temperature and classification of urban fabric on Marseille during ESCOMPTE[END_REF][START_REF] Founda | Synergies between Urban Heat Island and Heat Waves in Athens (Greece), during an extremely hot summer[END_REF].

Indeed, under some conditions, the sea breeze may attenuate high daytime temperatures in summer.

On hot days, in the urban context, critical periods of thermal discomfort [START_REF] Ulpiani | On the linkage between urban heat island and urban pollution island: Threedecade literature review towards a conceptual framework[END_REF][START_REF] He | Localized synergies between heat waves and urban heat islands: Implications on human thermal comfort and urban heat management[END_REF] or thermal stress [START_REF] Kristensen | European Environment Agency, Climate change, impacts and vulnerability in Europe 2012: an indicator-based report[END_REF] may occur. During the 2003 European heatwave [START_REF] Kovats | in Europe: provisional estimates of the impact on mortality[END_REF], the UHI amplified the intense exposure to the heatwave and led to increased mortality, especially among vulnerable people. Seventy thousand deaths were correlated with the heatwave in Europe, and 15,000 in France, where the highest excessive mortality rate was recorded in Paris [START_REF] Robine | Death toll exceeded 70,000 in Europe during the summer of 2003[END_REF]. Laaidi et al. [START_REF] Laaidi | The Impact of Heat Islands on Mortality in Paris during the August 2003 Heat Wave[END_REF] showed that abnormally elevated night temperatures (26 °C on the warmest day of the heatwave at 6 am in Paris) were due to the UHI, and had a strong impact on the health of occupants in buildings. Old residential free-floating Parisian buildings are not adapted to heat, and the reduced cooling effect of the urban fabric at night could explain these elevated nighttime temperatures. In a recent study, an ecodistrict (i.e., an urban area with a reduced carbon footprint and a sustainable design [START_REF] The | A Vision Plan for a More Sustainable Future[END_REF][START_REF]AustinTexas[END_REF]) in Paris was modelled under a future intense heatwave around the mid-century, and the results indicated that the urban neighborhood would be subject to heat stress [START_REF] Machard | How to assess ecodistrict resilience to urban heat stress under future heatwaves? A case study for the city of Paris[END_REF]. This reinforces the need to adapt the urban fabric to climate change and implement effective mitigation strategies.

In this study, we focused on both exposure to overheating and microclimate modification due to the local UHI. Exposure to overheating (defined in section 2.4.1) is specifically related to summer thermal discomfort and potential heat stress within inhabited spaces. Although the proposed indicators are based on common UHI and overheating definitions, this approach quantifies the exposure in more detail, with two time-integrated quantitative indicators that account for both exposure duration and intensity. Unlike purely numerical or spatially averaged studies, our aim was to highlight the practical benefits and limitations of this approach, based on the very local differences that can be captured experimentally by these indicators, so that they can be used in adaptation strategy simulation and the decision-making process.

On the one hand, we installed two urban weather stations within a specific local climate zone (LCZ) [START_REF] Stewart | Local Climate Zones for Urban Temperature Studies[END_REF] to highlight and quantify very local urban effects, since urban simulation tools usually take into account the spatially averaged local climate (LCZ scale). Our analysis is specifically supported by data recorded during a 10-day heatwave.

On the other hand, we used the spatially broader modelling approach with the numerical Urban Weather Generator (UWG) model [START_REF] Nakano | Urban Weather Generator -a Novel Workflow for Integrating Urban Heat Island Effect within Urban Design Process[END_REF][START_REF] Salvati | Built form, urban climate and building energy modelling: case-studies in Rome and Antofagasta[END_REF]. This approach is useful for experimenting with various strategies to mitigate overheating, and with future weather conditions. Recent studies using this model [START_REF] Palme | From urban climate to energy consumption. Enhancing building performance simulation by including the urban heat island effect[END_REF][START_REF] Parker | The Leeds urban heat island and its implications for energy use and thermal comfort[END_REF][START_REF] Boccalatte | Microclimate and urban morphology effects on building energy demand in different European cities[END_REF][START_REF] Tsoka | A method to account for the urban microclimate on the creation of 'typical weather year' datasets for building energy simulation, using stochastically generated data[END_REF][START_REF] Santos | Evaluating approaches for district-wide energy model calibration considering the Urban Heat Island effect[END_REF] demonstrated its potential to assess UHI, thermal discomfort and health issues [START_REF] Santos | Climate-informed decision-making for urban design: Assessing the impact of urban morphology on urban heat island[END_REF]. The neighborhood architecture may also benefit from this approach, which takes into consideration different urban contexts using a modified weather file [START_REF] Salvati | Built form, urban climate and building energy modelling: case-studies in Rome and Antofagasta[END_REF].

The UHI parameters are well-known [START_REF] Chapman | Urban heat & critical infrastructure networks: A viewpoint[END_REF][START_REF] Oke | City size and the urban heat island[END_REF][START_REF] Santamouris | Recent progress on urban overheating and heat island research. Integrated assessment of the energy, environmental, vulnerability and health impact. Synergies with the global climate change[END_REF][START_REF] Santamouris | On the impact of urban heat island and global warming on the power demand and electricity consumption of buildings-A review[END_REF], and we analyzed the improvement in radiative properties such as increased albedo (e.g., cool roofs) and the implementation of evaporative cooling (e.g., green roofs) to decrease solar heat gain on the building fabric. Susca et al. [START_REF] Susca | Positive effects of vegetation: Urban heat island and green roofs[END_REF] reported a 2°C difference between sparse and well-vegetated areas in New-York. Bonafoni et al. [START_REF] Bonafoni | Sustainable strategies for smart cities: Analysis of the town development effect on surface urban heat island through remote sensing methodologies[END_REF] and Taha et al. [START_REF] Taha | Residential cooling loads and the urban heat island-the effects of albedo[END_REF], investigated the benefits of increased albedo on urban climate and air-conditioning cooling loads. In Montreal [START_REF] Touchaei | Energy savings potentials of commercial buildings by urban heat island reduction strategies in Montreal (Canada)[END_REF], cool roofs on commercial buildings could save up to 11% of cooling energy consumption. Various other advanced techniques are under development to mitigate urban heat with surface modifications [START_REF] Gago | The city and urban heat islands: A review of strategies to mitigate adverse effects[END_REF][START_REF] Santamouris | Using cool pavements as a mitigation strategy to fight urban heat island-A review of the actual developments[END_REF].

Through a sensitivity analysis, we analyzed the potential of these passive cooling solutions to mitigate urban heat and summer overheating. For this purpose, we used the defined quantitative indicators as objective functions. This method can be applied to other cities, which might identify different key solutions, depending on the location. This method is therefore positioned upstream of the decision-making process, and could be useful for the implementation of strategies at the building and the urban area design stage, and in identifying the main parameters responsible for urban overheating that could then be adjusted to achieve better climate adaptation.

Methodology

Case study and methodology overview

The neighborhood studied is located in La Rochelle, a city on the southwest coast of France.

A total of three weather stations were installed. The two urban stations (ULR1 and ULR2) were set up in the university urban neighborhood located very close to the sea (500 m), and the rural station is about 10 km inland (Figure 1). Several studies suggest methods and guidelines to properly install and analyze data in an urban area [START_REF] Lowry | Empirical Estimation of Urban Effects on Climate: A Problem Analysis[END_REF][START_REF] Stewart | A systematic review and scientific critique of methodology in modern urban heat island literature[END_REF][START_REF] Pigeon | Urban Thermodynamic Island in a Coastal City Analysed from an Optimized Surface Network[END_REF] The methodology used in this research can be split into four parts: (i) Information on building typologies and GIS data was collected for two reasons: First, to map the urban area into LCZs, which are of interest to urban planners in understanding UHI risk and hot spots [START_REF] Perera | A "Local Climate Zone" based approach to urban planning in Colombo, Sri Lanka[END_REF][START_REF] Bechtel | Mapping Local Climate Zones for a Worldwide Database of the Form and Function of Cities[END_REF][START_REF] Gardes | Statistical prediction of the nocturnal urban heat island intensity based on urban morphology and geographical factors -An investigation based on numerical model results for a large ensemble of French cities[END_REF]. They are then used as input data for the urban climate model (UWG); (ii) The urban model is used to complement the meteorological stations (rural and urban) in order to understand and analyze the change in the local climate in the city; (iii) In order to facilitate the analysis of the data, two quantitative indicators were defined and calculated using the above.

The first indicator quantifies the intensity of the local urban heat island, which is related to urban climate change, while the second calculates the intensity of local overheating, which provides information on outdoor heat stress during heatwaves; (iv) Finally, the urban climate model was used to perform a sensitivity analysis of the different design parameters during urban planning, to determine the main mitigation and adaptation strategies for the coastal city under study. The overall goal was that the practical indicators enable the stakeholders to address overheating issues in a holistic approach that takes into account the related health impacts, energy poverty and social disparity in the population.

Mapping urban zones

Stewart and Oke [START_REF] Stewart | Local Climate Zones for Urban Temperature Studies[END_REF] defined the LCZ classification from urban parameters. These LCZ parameters include the urban morphology and thermophysical characteristics of urban zones.

Long et al. [START_REF] Long | Influence of the urban morphology on the urban heat island intensity: an approach based on the Local Climate Zone classification[END_REF] classified the LCZ for 42 French urban areas and highlighted a significant link to UHI intensity, defined here as the temperature difference between urbanized and nonurbanized temperature for the same location. These results were obtained from numerical simulations at a spatial resolution of 250 m using the Town Energy Balance (TEB) model coupled to the Méso-NH atmospheric model. In the MUSTARDijon project [START_REF] Richard | How relevant are local climate zones and urban climate zones for urban climate research? Dijon (France) as a case study[END_REF], the reliability of this LCZ classification was experimentally studied, including the establishment of a network of 47 meteorological sensors [START_REF] Richard | How relevant are local climate zones and urban climate zones for urban climate research? Dijon (France) as a case study[END_REF]. The authors compared both LCZ and Urban Climate Zone (UCZ) classifications [START_REF] Houet | Mapping urban climate zones and quantifying climate behaviors -An application on Toulouse urban area (France)[END_REF]48] with a 150 m grid resolution. These results showed that LCZ is the most applicable mapping method for the thermal clustering of urban areas.

The LCZ classification is based on the average values of morphological urban parameters, as defined by Oke [START_REF] Stewart | Local Climate Zones for Urban Temperature Studies[END_REF]. We extracted most of the morphological urban and building data required for LCZ identification from the detailed BD TOPO database in France (database from IGN, http://professionnels.ign.fr/bdtopo), and from OpenStreetmap [49]. Collecting precise data on green areas and identifying trees was more challenging. To tackle this problem, Haala and Brenner [START_REF] Haala | Extraction of buildings and trees in urban environments[END_REF] proposed an imagery data methodology for urban areas. We defined the main building typologies from local surveys and the TABULA project database (http://webtool.building-typology.eu/). The definition of thermal properties at this urban zone scale requires simplifications, especially given the strong variation in surface properties, such as the albedo. For anthropogenic heat release in the district, we used the typical value from the literature of about 8 W/m², which was measured in Toulouse, a city located in southwest France [START_REF] Pigeon | Anthropogenic heat release in an old European agglomeration (Toulouse, France)[END_REF][START_REF] Sailor | A review of methods for estimating anthropogenic heat and moisture emissions in the urban environment[END_REF].

According to the classification available online (mapuce.orbisgis.org), La Rochelle is characterized by low and mid-rise buildings. Most of the downtown buildings are low-rise residential constructions (height 3 to 6 m), while some suburban constructions are higher. We studied an urban area located around the university (Figure 3a,b), close to the city center. We delimited the area of the case-study neighborhood within a 200 m radius (Figure 3a) to extract morphological data from the BDTOPO database (GIS). No available database was available to determine green areas accurately and to provide all the necessary parameters. We therefore built a digital model enhanced with simple vegetation modelling (Figure 3b).

Finally, the case-study of the university neighborhood (Figure 3a,b) was determined as LCZ type 5. The main parameters computed for this case-study and their variation range for LCZ 5 are presented in Figure 4.

m

Figure 4: Range values for LCZ 5 and parameters calculated according to Oke [START_REF] Stewart | Local Climate Zones for Urban Temperature Studies[END_REF] We computed for this urban area a plan-area density of 27 %, defined as the ratio of building plan area to total plan area (%) [START_REF] Stewart | Local Climate Zones for Urban Temperature Studies[END_REF], and an average building height of 11.6 m. This first step characterizes an LCZ and the associated neighborhood UHI risk. Due to the lack of available data and tools to quantify several urban parameters, this estimation may have significant uncertainties. For example, green areas vary throughout the year, which was not taken into account in the model, and this may impact the pervious surface fraction. Leconte [START_REF] Leconte | Using Local Climate Zone scheme for UHI assessment: Evaluation of the method using mobile measurements[END_REF] recently highlighted similar limitations.

Measurement and urban model 2.3.1 Weather station technology

We collected weather data from the urban and rural weather stations (Figure 1) over the summer period from June 1 to September 1, 2019. The rural station, located in a residential area in the northeast of La Rochelle, served as a reference station and is approximately 10 km away from urban areas. Both urban weather stations (ULR1 and ULR2) in La Rochelle are in the LCZ type 5 defined in the previous section. These urban weather stations are close to the sea (500 m approximately). The ULR1 station is in an open field surrounded by trees and grass, while the ULR2 station is located in the courtyard of a building (Figure 5a); ULR2 is therefore shadier than ULR1 (Figure 5b). The weather stations are composed of Campbell Scientific dataloggers and sensors (Table 1).

The air temperature and humidity sensors were positioned at a height of 2 m. The suppliers provided the uncertainty of the solar shortwave and longwave sensors (Table 1).

We performed a specific calibration for the relative humidity and the air temperature sensors.

For the temperature, all the sensors were calibrated using a Fluke 7321 calibration bath that guarantees a 0.1 °C uncertainty between sensors. Similarly, humidity sensors were calibrated using LiCl and NaCl salts. Concerning other values, simultaneous recordings from all weather stations demonstrated that the instruments provided the same output values for the same input conditions.

Urban model

In order to complement the experimental analysis and further evaluate different passive cooling strategies, the UWG model was used [START_REF] Nakano | Urban Weather Generator -a Novel Workflow for Integrating Urban Heat Island Effect within Urban Design Process[END_REF]. This model predicts Finally, the direct normal irradiance and the solar position were estimated with the DISC algorithm [START_REF] Maxwell | A quasi-physical model for converting hourly global horizontal to direct normal insolation[END_REF] and the PyEphem package [START_REF] Rhodes | PyEphem: Astronomical Ephemeris for Python[END_REF].

The UWG model calculates the local UHI and overheating from a rural weather file. The model was validated in the cities of Toulouse (France), Basel (Switzerland) [START_REF] Bueno | Urban weather generator: a method to predict neighborhood-specific urban temperatures for use in building energy simulations[END_REF], Rome and Antofagasta (Italy) [START_REF] Salvati | Built form, urban climate and building energy modelling: case-studies in Rome and Antofagasta[END_REF]. Furthermore, a study of the 2003 urban heatwave in downtown Paris (France) gave a good correlation between UWG simulations and the measured temperatures [START_REF] Long | Correlation between temperature and classification of urban fabric on Marseille during ESCOMPTE[END_REF].

Urban planning strategies 2.4.1 Quantitative indicators

While no clear standard is available for urban planners, a large variety of tools and guidelines are available to policy makers, such as in the US [START_REF] Epa | Measuring Heat Islands[END_REF] and France [START_REF]Urban overheating diagnostic -Diagnostic de la surchauffe urbaine[END_REF], especially to answer community requests relative to urban overheating issues. However, the spatial and temporal results obtained from numerical simulations and measurements are too precise, and therefore inappropriate to efficiently support stakeholders' decision-making. Martilli et al. [START_REF] Martilli | Is the Urban Heat Island intensity relevant for heat mitigation studies?[END_REF] pointed out the importance of looking at thermal stress in preference to UHI intensity as way to propose heat mitigation strategies for urban stakeholders. While UHI intensity is useful complementary information that quantifies the anthropogenic contribution to local climate modification, the change in urban overheating in inhabited areas, especially during heatwaves, is also a crucial indicator. We therefore propose to convert the detailed scientific data into two easy-to-use indicators, initially to help fill the gap between the detailed evaluation and the decision process:

• UHI exposure at the neighborhood scale, related to local microclimate warming;

• Neighborhood overheating related to heat thermal discomfort.

UHI has been quantified using different indicators in many research articles. Schwarz et al. [START_REF] Schwarz | Exploring indicators for quantifying surface urban heat islands of European cities with MODIS land surface temperatures[END_REF] discussed the relevance of eleven different surface UHI indicators, and noted a weak correlations among them. UHI intensity is typically quantified by air or surface temperature difference at a specific time-step between urban and reference rural weather stations [START_REF] Magee | The Urban Heat Island Effect at Fairbanks, Alaska[END_REF][START_REF] Memon | An investigation of urban heat island intensity (UHII) as an indicator of urban heating[END_REF][START_REF] Martin-Vide | On the definition of urban heat island intensity: the "rural" reference[END_REF] (Eq. ( 1)). We decided to take into account UHI intensity rather than UHI exposure (UHIexp [°C.h], (Eq. ( 2)), which is a sum of positive differences between urban (Turb,t) and rural (Trur,t) air temperatures.

uhi( ) = ( , - , ) , , (1)
UHI = uhi( ) × Δ !" (2)
This cumulative intensity of UHI highlights the warming effect without the overstatements induced by maximum intensities at some specific periods.

The rural reference definition impacts UHI intensity [START_REF] Hawkins | The Role of Rural Variability in Urban Heat Island Determination for Phoenix, Arizona[END_REF], and was studied by Vogel and Afshari in the context of a coastal city [START_REF] Vogel | Comparison of urban heat island intensity estimation methods using urbanized WRF in Berlin[END_REF]. They suggested different approaches:

The first approach is to locate both the reference rural and the urban weather stations at the same distance from the coast, as during sea-breeze events the coastal effect is also examined;

In the second approach, the reference is a virtual rural station located in an urban area without the city effects, which can be obtained only from simulations;

The third approach analyses an upstream rural reference station (related to wind direction), which gives similar results to the virtual reference method at nighttime.

In our approach, we used an inland reference rural weather station. Due to its location (see Figure 1), this reference is upstream during land breeze events. In contrast, during sea breeze events, the upstream reference station would be located in the sea, which is not relevant for our study since our aim was to characterize inhabited areas. Given that the purpose of this study was to determine the risk of an urban heat island for the inhabitants, we defined a rural station that could serve as a reference when the wind was inland (wind from the east). In this case, the city does not benefit from the refreshing marine breeze. Therefore, the positioning of the rural station makes it possible to evaluate the most unfavorable case concerning the risk of heat thermal discomfort.

For exposure to overheating, we adapted the Cooling Degree Hours indicator. This indicator, originally defined for the building energy sector, is also used to characterize local urban climate [START_REF] Kolokotroni | Heating and cooling degree day prediction within the London urban heat island area[END_REF]. Outdoor overheating affects both indoor and outdoor thermal comfort. We did not use thermal discomfort indexes (e.g., PMV, PET, or UTCI) due to the variety of locations and activities, and the vulnerability of urban inhabitants. As residents are usually indoors at night, the calculation of outdoor thermal discomfort is not relevant here. However, urban overheating during nighttime may be critical and lead to significant heat-related health impacts on the population.

The proposed overheating intensity was defined as the temperature difference between the air temperature (Turb,t) and a threshold temperature (Toverheat). This temperature threshold was set at 26 °C during daytime, which is the cooling set-point for conditioned buildings as defined by the French thermal regulation [START_REF] Carbone | Projet de documents méthode pour la Réglementation environnementale 2020 (RE2020)[END_REF]. Since nighttime-overheating exposure is more sensitive to the urban heat island, we also adopted a nighttime threshold of 21°C, a reference defined by the Heat Health Warning System heatwave for the city of La Rochelle. At each time step, the overheating intensity oh(t) was quantified by the positive temperature difference between the outdoor air temperature and the threshold temperature, Eq. (3). Overheating exposure OHexp, Eq. ( 4) is defined as the sum of the overheating intensities. (

) OH = oh( ) × Δ !" 3

Sensitivity analysis

In construction or renovation projects, the neighborhood adaptation strategies and design must be analyzed through a multi-criteria analysis, which often lacks quantitative criteria and objective levers of action. In order to further guide adaptation strategies, sensitivity analysis (SA) helps to improve the understanding of model interactions and to identify the most relevant urban parameters in order to mitigate outdoor overheating and local UHI. The Morris method [70] has been used frequently in building design [START_REF] Nguyen | A performance comparison of sensitivity analysis methods for building energy models[END_REF][START_REF] Tian | A review of sensitivity analysis methods in building energy analysis[END_REF][START_REF] Corrado | Uncertainty and Sensitivity Analysis for Building Energy Rating[END_REF].This method, also called the elementary effects method, is a screening method used to estimate the elementary effects of the input parameters roughly corresponding to a first-order partial derivative. For each parameter studied, the Morris method evaluates the absolute average of the effects (µ*) corresponding to the mean effect of the parameter, as well as the standard deviation of these effects (σ), which represents its interactions with the others parameters of interest (the sampling method is based on an iterative variation of the parameters). All parameters are then represented in the (σ-µ*) plan for the analysis of the results. We used a grid-jump of 6 (level of partition of the inputs domain) which was qualitatively estimated as sufficient to explore the domain of the parameter space.

The first step was to define the possible design parameters for the neighborhood studied and their bounds. In the literature, the morphological parameters have often been identified as prominent for UHI; however, in a refurbishment context, these parameters cannot be modified significantly. Other mitigation strategies have proven to be successful, such as an increase in cool and green surfaces, and a reduction of anthropogenic heat. We assessed the influence of five parameters, given fixed bounds: (i) road albedo (0.05 to 0.65); (ii) wall albedo (0.05 to 0.85); (iii) anthropogenic heat (2 to 20 W/m²); (iv) building height (7 to 13 m); and (v) vegetation cover (0 to 85 %). We varied the building height to determine if adding one or two floors to a building would impact the UHI intensity or overheating. Anthropogenic heat was modulated following the default UWG weekly and daily schedule for urban traffic.

For the Morris method used here [70], we used a 100-trajectory sample , which corresponds to 500 simulations with the specified parameters and their discretization steps (we used a gridjump = 6). However, the SA approach is inconsistent for correlated parameters such as vegetation cover and the average albedo of urban surfaces. To tackle this problem, we first analyzed the albedo impact as a UHI mitigation strategy, given both the impact of the average albedo for both roofs and walls. In the second step, we assessed the influence of vegetation cover, without albedo modifications for non-vegetated surfaces.

Results

Local microclimate -urban and coastal effect

This section presents and analyses the measurements made during the heatwave, from the 20 th to the 30 th July 2019. Figure 6 presents from top to bottom: air temperature, the temperature difference between the urban and rural stations, wind speed, and specific humidity. We compared the modelled temperatures (UWG) to the measurements, and we discuss the reliability of the model for our case study. It seems that the direction of the wind coming either from the sea or from the land affected the results, which is explained below. To understand the influence of the wind, the sea breeze periods (NNW 337° to SSW 202°) are highlighted in Figure 6 in blue, and the land breeze periods in red (NNE 22.5° to SSE 157.5°). In Figure 6a, the urban heat island is recognizable during nighttime, where higher temperatures were recorded at both urban stations (ULR1 and ULR2) than at the rural station.

A maximum of 4°C temperature difference was recorded during this period. The predicted urban night temperatures (UWG) were higher than the rural measurements but lower in comparison to the urban measurements. During the day the phenomenon was reversed, and the measured temperatures in the urban area were lower than in the countryside, as illustrated on Figure 6b. From July 20 th to July 25 th , the temperature difference between urban and rural areas was positive during nighttime and negative during daytime, up to almost 5°C cooler on the warmest days, July 23 and 24. The daily amplitude between temperature minima and maxima in the local neighborhood was, therefore, greatly reduced compared to the countryside. Daytime temperatures obtained from the UWG model were consistent with the rural weather station records. The model confirmed this trend during the night, but overestimated the temperature during daytime, especially on July 22 nd , 23 rd and 24 th . To explore this divergence, we analyzed the wind direction and intensity (Figure 6c). The sea breeze was more likely to occur at the end of the day. With evaporation effects, this sea breeze contributed to a decrease in the temperature of the urban area. These local mass flows due to the sea were not modelled by the UWG model, which contributed to the observed divergences during daytime. Other studies using the UWG model observed an overestimation of the heat island during the day [START_REF] Bande | Validation of UWG and ENVI-Met Models in an Abu Dhabi District, Based on Site Measurements[END_REF]. This overestimation may come from a poor assessment of the urban limit layer height, which is a challenging parameter to estimate. An improvement in the vertical model has been

proposed recently [START_REF] Moradi | The Vertical City Weather Generator (VCWG v1.3.2)[END_REF].

This divergence was further investigated by analyzing the difference in absolute humidity between urban and rural areas, as represented in Figure 6d. During sea breeze events, the absolute humidity increased in the urban area, which contributed to the decrease in temperatures (Figure 6d, see evenings on July 20 th , 23 rd , 25 th , 28 th and 29 th ). The phenomenon rarely occurred during land breeze events.

The influence of wind direction is more specifically addressed in Figure 7, during the hottest day of the heatwave under study (July 23 rd ). The coastline distance (Figure 7a) was defined for each weather station as the distance from the sea along the wind direction (from east and from west). The temperature values for specific periods of the day are represented for urban, suburban and rural areas, given the coastline distance (Figure 7b-c). At 5.4 km from the coastline (grey point), an additional suburban weather station was available in an industrial area north of La Rochelle (Figure 7a), identified as an LCZ 8. In Figure 7b, the temperatures were averaged over the three-hour interval in the afternoon, 3 PM to 6 PM, identified as a sea breeze event from the wind direction records. The arrows represent the minimum and maximum temperature intervals for this period. For the three-hour night period, from 3AM to 6 AM (Figure 7c), we observed a a.

b.

c.

land breeze event. During this night period, the air temperature decreased with the coastline distance from the urban, to the suburban, and to the rural stations. An average difference of 2°C was observed between the urban and rural areas during the night. The suburban air temperature increased slightly due to the stronger local UHI effect and the reduced sea cooling effect, reinforced by the absence of a sea breeze and the greater distance from the coast compared to the urban location.

Urban heat island and overheating intensity

In this section, we analyze the experimental and numerical results using the previously defined indicators.

First, for the UHI intensity (see 2. For the same period, Figure 9a presents the average daily temperature profile obtained from ULR1, ULR2, and the rural weather stations, and the modelled urban area with UWG. Figure 9b presents the temperature distribution during the same heatwave for the UHI at night. At night, the UHI effect observed by the model was close to the measurements, and the temperature in urban areas was 1.5 ℃ higher than in rural areas. (Figure 9a). The variation in UWG temperature was consistent with the measurement from 10 PM to 4 AM. However, as previously observed (Figure 6), the early morning temperatures were underestimated by the model, while the calculated temperatures did not represent correctly the observed daytime temperature decrease in an urban context, which was due to the coastal effects.

In terms of outdoor overheating (defined in 2. comparing the rural and the ULR2 weather stations; ULR2 was selected because it is in a more urbanized location than URL1 and has a higher risk of overheating. The hourly temperature variation is presented at the top of Figure 10. The periods are highlighted in yellow for daytime (7 AM to 10 PM, Figure 10a) and in blue for nighttime (10 PM to 6 AM, Figure 10b). During daytime (Figure 10a), the rural area was more vulnerable to the heatwave than the urban area (ULR2). On July 23 rd (daytime), the maximum overheating intensity reached +10 °C at the rural station, while that of urban stations close to the coast and cooler than the rural stations was only + 7 ° C. In contrast, nighttime overheating was higher in the urban area, where it increased up to +6.3 °C, compared to +4 °C at the rural station. This maximum nighttime overheating (Figure 10b) was observed two days later (July 25 th ). For the hottest day (July 23 rd ), urban nighttime overheating remained much lower than rural overheating. Over the period, urban (ULR2) daytime overheating (OHexp = 140 °Ch) was 45 % lower than that in the rural area (OHexp = 249 °Ch). Nighttime a. b.

overheating for the urban area was well quantified by the same OHexp indicator, which was 95 % higher than the rural indicator, 126 °Ch and 64 °Ch, respectively.

Table 2 summarizes the UHIexp and OHexp indicators for daytime and nighttime as well as for different urban/rural areas and the UWG model. Within the same LCZ 5 neighborhood (ULR1 and ULR2 weather stations), the UHIexp was amplified from day to night by a factor of about seven. However, significant UHIexp differences were observed between ULR1 and ULR2, with 25 % for daytime and 39 % for nighttime, respectively (Table 2). This can be explained by the vegetated area surrounding the ULR1 weather station, which was also more exposed to winds, while the ULR2 weather station was located within a courtyard surrounded by buildings. While the simplified UWG model was not consistent with daily urban temperature variations (grayed in Table 2), this approach gave a good representation of the nighttime variations.

Overheating exposure was much more homogeneous within the neighborhood under study, as observed for ULR1 and ULR2, with a 5 % OHexp difference for daytime, and a 18 % OHexp difference for nighttime (Table 2). As expected, the simplified modelling approach (UWG) significantly overestimated daytime overheating. However, this model (UWG) gave a good assessment of nighttime overheating compared to the urbanized area, represented by the ULR2 station, where the overestimation of the nighttime OHexp was only about 6%.

Therefore, the modelling approach and the proposed indicators were further analyzed during nighttime for the UHI intensity and overheating effects.

Neighborhood design parameters

The key urban parameters for this case study, for both the intensity of outdoor overheating and UHI (OHexp and UHIexp), were identified using the sensitivity analysis (SA) results

(Figure 11). The SA objective functions (OHexp and UHIexp) were numerically determined with the UWG model, over the nighttime summer period from June 1 st to September 1 st .

Indeed, we excluded the daytime periods as they include sea breeze events not taken into account by the model. This was observed in the experimental comparison of OHexp and UHIexp (Table 2). The SA model inputs are the urban design parameters, and its output The results for UHI exposure for the nighttime summer period (Figure 11a,c) for variations in both albedo and vegetation cover, suggest that the parameters are independent, with an almost linear effect. The height of the buildings, anthropogenic heat and vegetation cover were the parameters that had the most impact, regarding the absolute values μ*. This means that, of the parameters studied, these have the highest potential to mitigate urban heat stress. The road and wall albedo had a smaller effect, which could be due to the lower impacts of daily solar heat gain over the nighttime period for this case study. For the overheating exposure OHexp during the nighttime summer period (Figure 11b,d), the key parameter sensitivities were similarly classified, except road albedo (orange point, Figure 11) and vegetation cover (green point, Figure 11), which had a relative increased sensitivity. While the impacts of vegetation on the urban microclimate are well documented, this approach highlights possible differences depending on the indicator of interest. The importance of urban morphology parameters was also emphasized by Salvati et al. [START_REF] Salvati | Built form, urban climate and building energy modelling: case-studies in Rome and Antofagasta[END_REF] using the UWG model. While the use of the Morris method requires a certain expertise, the results can easily be used by city stakeholders to rank the impact of the parameters on urban overheating. These help to identify the main strategies that should be implemented to mitigate the hot spots of a city previously identified during the mapping of the urban zones (Figure 2). Therefore, this method helps establish priorities in the plans of action.

Discussion

For this coastal city case study, the measurements revealed a cooling sea breeze effect during the daytime. Although both ULR1 and ULR2 weather stations were close to each other and had similar variations in temperature, significant differences were obtained for both UHI and overheating exposure. These results highlight the impact of the thermal heterogeneity of the urban environment. Moreover, beyond the usual characterization of a LCZ, the indicators obtained show that the evaluation of the risk of overheating in inhabited places may require multiplying the measurement points within this LCZ.

Similarly to our case study, the littoral urban microclimate was characterized in Sydney by Khan et al. [START_REF] Khan | Exploring the Synergies between Urban Overheating and Heatwaves (HWs) in Western Sydney[END_REF] during a heatwave in 2017. A significant difference of 10 °C was measured between urban and rural areas. Wind intensity and direction were identified as key parameters for the advective heat fluxes. It was observed that the humidity difference between the urban zone and the rural surroundings was also an important factor affecting the urban microclimate. Unlike our case study, Khan et al. observed a higher UHI intensity during daytime, which they explained by the surrounding desert of Sydney. Yet, the same coolingdown effect was observed at the end of the night at the coastal stations. Founda and Santamouris [START_REF] Founda | Synergies between Urban Heat Island and Heat Waves in Athens (Greece), during an extremely hot summer[END_REF] observed sea breeze effects on the urban air temperature and humidity for the Mediterranean city of Athens, Greece. They underlined the fact that the water heat capacity dampens the daily temperature variations and the daytime UHI, as in Figure 9a. This phenomenon was also noted by Long et al. [START_REF] Long | Correlation between temperature and classification of urban fabric on Marseille during ESCOMPTE[END_REF] during the ESCOMPTE project for the Mediterranean city of Marseille, France. While our measurements confirm the tendencies found in other studies, the main findings of this case study concern the variations in exposure (Table 2), especially between day and night. The comparison of this evaluation process for other locations and cities will give a better understanding of the variation in amplitude of these exposure indicators.

From a modelling point of view, UWG is a practical tool for comparing urban design options, based on a reduced number of inputs. However, as a counterpart to the simplicity of this onenode model at the neighborhood scale, it cannot englobe the spatial heterogeneity for a deeper analysis within the zone, nor account for the regional surroundings, such as large bodies of water. Indeed, a comparison of the two urban stations revealed episodic differences. More complex models could be used [77], with a refined spatial resolution to access urban fabric temperature distribution, more realistic shadow effects, and wind patterns. Yet, such a detailed analysis is not suitable for decision support for stakeholders in the initial steps of the design stage. So, determining the tendencies of the impacts of these simple design parameters, such as vegetation cover, will then guide urban planners for much more detailed plans, given the complex urban constraints that cannot be taken into account in the extensive sensitivity analysis. In a further step, new or innovative greening techniques could, for example, be used to maximize the vegetation effects identified here.

The adaptation strategies suggested by the SA results are highly dependent on the period of investigation, the indicators, and the range of variation of the input parameters. The proposed SA was restricted to the nighttime periods, which was relevant for this case-study as the UHI intensity was higher at night. The results showed that vegetation cover, the height of the buildings, and anthropogenic heat had the most impact on the variations in UHIexp and OHexp.

The results may differ for other cities with higher daytime UHI effects or other indicators, such as the surface UHI effect.

Conclusions

We propose a methodology that meets the need to characterize the UHI effect at the neighborhood scale. This methodology was used in a coastal case-study of the university neighborhood in La Rochelle, close to the city center. An extended study including additional weather stations within the city is ongoing. While the coastal effect demonstrated a mitigation effect during the daytime, the UHI was more pronounced during nighttime, which is expected in French cities. The measurements revealed a nocturnal UHI effect, with an average temperature increase of +2 °C, which reached +8 °C on the warmest days. This high increase during a heatwave stresses the importance of this work, which is designed to provide key indicators and general guidelines for stakeholders to reduce urban heat stress during future heatwaves. Both UHI and overheating intensities were studied and quantified through UHIexp and OHexp indicators, which we defined to assist the analysis of the results. The UHI intensity increased by seven from day to night for both urban locations. The urban outdoor overheating exposure, quantified by the sum of urban hourly air temperatures above specific daytime and nighttime thresholds, was higher during daytime. The experimental part of this research work highlighted the pitfalls to avoid in order to improve measurement reliability. The methodology could be enriched with a more detailed urban microclimate model.

The analysis highlighted non-negligible differences in these indicators between the two urban weather stations, located within the same LCZ. These results are limited to a single case study, yet they are consistent with more extensive studies on temperature variation within LCZs [START_REF] Long | Influence of the urban morphology on the urban heat island intensity: an approach based on the Local Climate Zone classification[END_REF]. While the LCZ scale is a useful initial approach to roughly classify a city into zones with UHI or overheating risks, as proposed in our methodology (see Figure 2), and to analyze the various neighborhood scale strategies (see section3.3), urban planners need to assess more precisely the risk of overheating at the building or inhabitant scale. The experiments confirmed the ability of both aggregated and simple indicators to capture local variations. They have the potential to be a convenient tool for the evaluation of urban strategies. Furthermore, this emphasizes the need to be cautious when using LCZ-scale results in implementing urban cooling strategies.

The consistency of the UWG model in representing nighttime UHI and overheating intensities, in comparison with the measurements made it possible to study the sensitivity of several urban design parameters during the extended summer period. The results showed that anthropogenic heat release, vegetation cover and the height of buildings were key design parameters that need to be taken into account in order to mitigate the local microclimate air temperature in a given neighborhood. The adaptation strategies we identified could help to define strategies to mitigate the expected increase of UHI and outdoor overheating, while the precise detection of hot spots will provide insights into where it is most efficient to implement these strategies.

  such as the positioning of the reference station, different methods to calculate UHI, and in particular the positioning of the weather stations. The two weather stations were installed close to each other (approximately 200 m) to (i) estimate local overheating and UHI, and (ii) highlight the local differences due to urban heterogeneity within the same LCZ zone.

Figure 1 :

 1 Figure 1: La Rochelle case study and weather station location

Figure 2 :

 2 Figure 2: Overview of the proposed methodology

Figure 3 :

 3 Figure 3: Aerial view (a), and digital model (b) for the neighborhood studied in La Rochelle.

Figure 5 :

 5 Figure 5: ULR1 (a) and ULR2 (b) weather stations

  the effects of the local UHI for a specific urban zone. The physical UWG model is divided into four sub-models: (i) a rural station model for heat flux calculation at a rural site; (ii) a vertical diffusion model for vertical air profiles at the rural site; (iii) an urban boundary layer model for the calculation of air temperature above the urban canyon; and (iv) a representative street canyon model to compute the urban canopy and building energy sensible heat fluxes. Each sub-model is represented by one node, and the street canyon model evaluates the average temperature modification in an urban neighborhood. The model output is an urban weather file with modified values of urban air temperature and relative humidity from a rural weather file. The required input weather data, from the measurements at the rural weather station, include ambient dry bulb temperature [°C], relative humidity [%], wind direction [°] and speed [m/s],and rainfall [mm]. The horizontal direct and diffuse solar irradiances [W/m²] were calculated using the horizontal global solar irradiance measurements and the python pvlib library[START_REF] Holmgren | pvlib python: a python package for modeling solar energy systems[END_REF].

Figure 6 :

 6 Figure 6: (a) Air temperature at the rural weather station for both urban weather stations during heatwave days in La Rochelle and predicted by the UWG model (b) Temperature differences between rural/urban areas both measured and predicted by the UWG model (c) Wind speed (d) Measured humidity

Figure 7 :

 7 Figure 7: Day and night temperature distribution for 4 urban, suburban and rural weather stations, during the hottest day of the heatwave (July 23 rd , 2019)

Figure 8

 8 Figure8for the summer (from June 1 st to September 1 st , 2019). Figure8-a represents the rural

Figure 8 :

 8 Figure 8: Daily rural temperature (a), daily maximum/minimum UHI temperature difference (b), and hourly UHI temperature difference (c) for the La Rochelle University location, obtained with the UWG model, from June 01 to September 01.

Figure 9 :

 9 Figure 9: (a) Daily temperature profile for ULR1, ULR2, the rural weather station and UWG (from July 20 to 30, 2019), (b) The probability distribution for nighttime temperature and (c) The UHI distribution for ULR1, ULR2 and UWG

4 . 1 )

 41 , and focusing on the hottest days (from July 21 st to July 26 th , 2019), Figure10shows the hourly variation of the OHexp for both the rural and urban weather station ULR2. The figure shows the temporal series of ULR1, ULR2, the rural stations and UWG. In addition, we chose to present heatmaps of the indicators,

Figure 10 :

 10 Figure 10: Hourly temperature variation (top), and hourly overheating variation for rural and urban (bottom)during daytime (a) and nighttime (b) -from July 21 st to July 26 th

  objective function is either the indicator UHIexp, or OHexp. The UWG model was run several times through the Morris design matrix to identify the most influential parameters. The SA results provided the average variation μ* [°Ch] (x-axis) and the standard deviation σ [°Ch] (yaxis) of the elementary effects for each parameter. A parameter effect is considered as almost linear if σ / μ* < 0.1, quasi-monotonic if 0.5 < σ / μ* < 1, and non-monotonic (i.e., interactions with other parameters) if σ / μ* > 1. If σ / μ* < 0.5, the parameter can be considered as independent from the other parameters.

Figure 11 :

 11 Figure 11: sensitivity analysis for UHI intensity (left) and overheating (right) -for albedo strategies (top) and vegetation (bottom) -from July 20 th to 30 th , 2019.

Table 1 :

 1 Weather parameters and sensors for weather stations

	Parameter	Sensor

Table 2 :

 2 UHIexp and OHexp indicators for daytime and nighttime, obtained from the urban weather stations (ULR1 and ULR2) and the model (UWG), for the heatwave period (July 20 th to 30 th , 2019)

		ULR1	ULR2	UWG	rural
	UHIexp [°C.h]	Day	20	25	29	-
		Night	153	213	128	-
	OHexp [°C.h]	Day	133	140	248	249
		Night	107	126	134	64

Acknowledgements

This study was partially funded by the EQL'ORE project supported by the Region of Nouvelle Aquitaine, and the European FEDER project PEDOBUR. We acknowledge M.

Burlot for his contribution and his great expertise in the sensor calibration and weather station selection. We also acknowledge the UWG software developers and the developers of the Python SALib library.


Ndèye Saly

Olivier Simonetti
email: olivier.simonetti@univ-reims.fr

Thien-Phap Nguyen

Louis Giraudet

Generation-recombination in disordered organic semiconductor: application to the characterization of traps

Keywords: organic semiconductors, traps, DLTS, Gaussian density of states, generation recombination

The presence of traps in organic semiconductor based electronic devices affects considerably their performances and their stability. The Shockley-Read-Hall (SRH) model is generally used to extract the trap parameters from the experimental results. In this paper, we propose to adapt the SRH formalism to disordered organic semiconductors by considering a hopping transport process and Gaussian distributions for both mobile and trapped carriers. The model is used to extract multiple trap parameters from charge based Deep Level Transient Spectroscopy (Q-DLTS) spectrum. Calculation of the charge transients are given in detail. The model predicts that the activation energy of the trap should not follow an Arrhenius plot on large temperature ranges. Also, the charge transients are no longer exponential when considering Gaussian trap distributions, enlarging the Q-DLTS peaks. The model fits the Q-DLTS spectra measured on organic diodes with a limited number of trap contributions with a good agreement. It is found

Introduction

The use of organic semiconductors (OSCs) in electronic devices is challenging. Organic photovoltaics (OPV), organic light emitting diodes (OLED) and organic thin-film transistors (OTFT) are used in applications such as solar energy, sensors and biosensors, flat panel displays and e-paper and circuits [START_REF] Moser | Challenges to the Success of Commercial Organic Photovoltaic Products[END_REF] [2] [3] [4] [START_REF] Torsi | Organic field-effect transistor sensors: a tutorial review[END_REF] [6] [START_REF] Paterson | Recent Progress in High-Mobility Organic Transistors: A Reality Check[END_REF] [START_REF] Gelinck | Organic Transistors in Optical Displays and Microelectronic Applications[END_REF]. Device performances are affected by the presence of traps in many ways. Traps can be located in the bulk of the semiconductor or at material interfaces and are believed to be responsible for several limitations such as instabilities or low conductivity, which then restrain their use in mainstream applications [START_REF] Haneef | Charge carrier traps in organic semiconductors: a review on the underlying physics and impact on electronic devices[END_REF] [10] [START_REF] Bisoyi | A comprehensive study of charge trapping in organic field-effect devices with promising semiconductors and different contact metals by displacement current measurements[END_REF] [START_REF] Bobbert | Operational Stability of Organic Field-Effect Transistors[END_REF] [13] [START_REF] Nicolai | Unification of trap-limited electron transport in semiconducting polymers[END_REF] [START_REF] Zuo | General rule for the energy of waterinduced traps in organic semiconductors[END_REF]. However, the trap formation and charge carrier trapping processes in OSC are not fully understood yet despite numerous investigations [START_REF] Haneef | Charge carrier traps in organic semiconductors: a review on the underlying physics and impact on electronic devices[END_REF].

To study traps, the processes of emission and capture of carriers must be studied. Transient spectroscopy techniques have been reviewed recently by A. R. Peaker et al. [START_REF] Peaker | Tutorial: Junction spectroscopy techniques and deep-level defects in semiconductors[END_REF]. One of the most efficient techniques is the Deep Level Transient Spectroscopy (DLTS). It was proposed for the first time in 1974 by D. V. Lang [START_REF] Lang | Deep-level transient spectroscopy: A new method to characterize traps in semiconductors[END_REF] and consists in studying the emission of trapped charges (after a filling phase of the traps) recorded as a capacitance transient (C-DLTS). The technique allows to determine the activation energy of the traps and their capture cross section . In the frame of the Shockley-Read-Hall (SRH) model developed for inorganic materials, charge transients are exponential functions of time, the activation energy can be clearly defined as the difference in energy between the trap level and the closest transport energy level in the conduction or in the valence band. In this work we will establish that these statements will not hold when considering organic semiconductors.

In a first section, the SRH model will be briefly exposed and the parameters determining the charge transient properties will be introduced.

In a second section, we consider some specific properties of disordered OSCs: a Gaussian density of states (DOS) and a hopping transport process. In OSCs, the capture probability of a charge carrier strongly depends on its mobility [START_REF] Kuik | Trap-Assisted Recombination in Disordered Organic Semiconductors[END_REF] [START_REF] Pope | Electronic Processes in Organic Crystals and Polymers[END_REF]. The mobility model proposed by Oelerich et al. [START_REF] Oelerich | How to Find Out the Density of States in Disordered Organic Semiconductors[END_REF] [21] is introduced, which appears as one of the most advanced mobility model for disordered OSCs [START_REF] Simonetti | Transport models in disordered organic semiconductors and their application to the simulation of thin-film transistors[END_REF]. First, we consider a Gaussian DOS for mobile carriers (the LUMO DOS) and a discrete energy level for traps. This hypothesis, which does not reflect the complexity of disorder materials, is nevertheless used to illustrate the influence of the disordered material properties on the trap characterization process.

In a third section, we consider a Gaussian DOS for both mobile and trapped carriers and study the influence of the distribution of trapped charges on the determination of the trap parameters.

The choice of a Gaussian DOS for both mobile and trapped charge carriers is driven by previous studies [START_REF] Nicolai | Unification of trap-limited electron transport in semiconducting polymers[END_REF] [23] [START_REF] Nenashev | Theoretical tools for the description of charge transport in disordered organic semiconductors[END_REF]. In this section, we show that the charge transient does not remain exponential, broadening the DLTS peaks and modifying the trap parameter extraction process.

Furthermore, we show that the activation energy of a trap cannot be strictly defined due to the complex temperature dependence of the emission frequency, and that an Arrhenius plot would not be appropriate when considering extended experimental temperature ranges. Finally, trap parameters of experimental Q-DLTS spectra [25] [26] are extracted and discussed.

Characterization of trap capture and emission: the SRH model and the DLTS method

To describe the emission and capture processes, the SRH model was proposed in 1952 to study silicon generation-recombination in silicon-based devices [START_REF] Shockley | Statistics of the Recombinations of Holes and Electrons[END_REF]. This formalism is often used to characterize traps in inorganic semiconductors but also in OSCs [START_REF] Nguyen | Defects in organic electronic devices[END_REF] [28] [START_REF] Yang | Deep-level defect characteristics in pentacene organic thin films[END_REF] [30] [START_REF] Stuchlikova | Defect Analysis of Pentacene Diode[END_REF]. In this study, we consider only one type of mobile charge carriers (electrons). The processes of capture and emission of charge carriers is shown for electrons in Fig. 1. In this figure, is the emission frequency (in Hz) of an electron from the trap energy level to the LUMO band, is the capture frequency (in Hz) of a mobile electron by a trap site. and are respectively the density of mobile and trapped charge carriers. is the total density of trap sites. To characterize a trap level , one needs to calculate the emission and capture frequencies.

The emission and capture rates, respectively and (expressed in s -1 .cm -3 ), are given by Eq.

1 and Eq. 2:

Eq. 1 ,

Eq. 2 .

The capture frequency can be expressed as (Eq. 3):

Eq. 3 .

The parameter depends on the capture process and the type of semiconductor, as discussed later. At thermal equilibrium, in a steady state, the number of electrons emitted from a given trap level is equal to the number of electrons captured by that trap:

Eq. 4 .

According to Eq. 4, it is then possible to express the emission frequency as follows:

Eq. 5 .

The concentration of mobile charge carriers is given by: Eq. 6 , where is the density of states of mobile charge carriers and

!"#$% &'& ( )* +
is the Fermi-Dirac distribution for electrons, , is the Fermi energy level,is the Boltzmann constant and . is the absolute temperature.

In the case of a discrete trap energy level is given by: Eq. 7 , where A * is the effective mass of an electron,

? the bottom of the conduction band and ђ, the reduced Planck constant [START_REF] Sze | Physics of semiconductor devices[END_REF].

In this case, an analytical expression is obtained for the concentration of mobile charge carriers:

Eq. 8 ? exp %

D = + E/7
is the effective density of states of the conduction band.

In the SRH model, the parameter , characteristic of the trap capture process in Eq. 3, can be expressed as:

Eq. 9

〈H D 〉,
where 〈H D 〉 J E56 : * is the average thermal velocity of the mobile carriers in the conduction band, and is the trap capture cross section. By replacing in Eq. 5 the expressions of (Eq. 8), (Eq. 7), and , one obtains the emission frequency (Eq. 10):

Eq. 10 + for a set of temperatures, called the "Arrhenius plot". The plot is linear since the trap emission process is exponentially dependent of the activation energy:

the slope of the plot actually allows for determining the activation energy . The capture cross section is extrapolated from the intersection of the Arrhenius plot with the y-axis.

In the Q-DLTS technique [START_REF] Lang | Deep-level transient spectroscopy: A new method to characterize traps in semiconductors[END_REF] [25] [START_REF] Carr | Deep defects and the attempt to escape frequency in organic photovoltaic materials[END_REF], during the relaxation phase of the experiment (i.e. when the trapped charges are released), providing no capture occurs thanks to an appropriate biasing sequence of the device, the emitted charge a during a time interval b can be expressed as a a b b, where a b is the remaining trapped charge. For a given temperature, the emission frequency (Eq. 10) does not depend on the concentration of trapped carriers and is constant with time. Consequently, the previous equation can be integrated and the relaxation of the trapped charges a b follows an exponential evolution with time b as given in Eq. 12:

Eq. 12 a b a c exp b , where a c is the initial trapped charge, for a given temperature and biasing sequence. In practice, at a given temperature, the Q-DLTS spectrum ∆a is plotted. ∆a a b a b 7 is the charge released during the time interval eb , b 7 g. This technique is relevant in that it transforms an exponential transient into a response peak. For this, a new variable, call the time-window, is defined by: h = 4 @ ij% = @ + . Usually, one takes b 7 2b giving h @ ij 7 . Then ∆a takes the form: Eq. 13 ∆a h a c kl ln 2 h e1 kl ln 2 h g, which reaches its maximum (∆a : m a c 4 ⁄ ) for h 1 ⁄ [START_REF] Nguyen | Defects in organic electronic devices[END_REF]. The trap density is given by: Eq. 14

p q r ,
where is the electronic charge, s is the active area of the device, and is the sample thickness.

In summary, the measurement of the charge transient and the plot of ∆a h gives the emission rate from the position of the peak maximum, at a given temperature [see Fig. 9 for an illustration of a simulated Q-DLTS peak]. Repeated experiments at various temperatures give the Arrhenius plot and finally the trap parameters ( , ) (see Fig. 4 for an example). Of course, in real devices trap energy levels are not discrete and one obtains multiple maxima and complex spectra, depending also on the bias sequence. However, this method appears to be relevant for the study of defects in inorganic semiconductors and has been successfully used in organic devices.

The assumptions of the SRH model are well adapted for crystalline inorganic semiconductors but should be discussed when applied to OSCs.

Adaptation of the model to organic semiconductors having a discrete trap level

To characterize traps in OSCs, the classical SRH formalism must be adapted due to the specific trap density of states of disordered organic semiconductors , and to the specific charge carrier transport mechanisms [START_REF] Baranovskii | Mott Lecture: Description of Charge Transport in Disordered Organic Semiconductors: Analytical Theories and Computer Simulations[END_REF] [33] [START_REF] Tessler | Charge Transport in Disordered Organic Materials and Its Relevance to Thin-Film Devices: A Tutorial Review[END_REF]. Gaussian and exponential trap distributions are commonly used to characterize traps in organic semiconductors [START_REF] Dacuña | Estimation of the spatial distribution of traps using spacecharge-limited current measurements in an organic single crystal[END_REF] [36] [37] [38] [39] [START_REF] Campbell | Space-charge limited conduction with traps in poly(phenylene vinylene) light emitting diodes[END_REF]. The energetic distribution of mobile carriers is not determined generally but it is commonly considered to be a Gaussian [41] [33] or exponential [42] [43]. In this work a Gaussian DOS was considered, based on the work of Baranovskii [44] [24], stating that the Gaussian distribution is the one which makes it possible to explain the evolution of the mobility with the density of charge carriers.

In this part, we first considered a Gaussian DOS for the mobile carriers and discrete trap levels to study the charge trapping dynamics and the resulting characterization of traps using Q-DLTS spectra. Gaussian DOS for both mobile and trapped carriers will be treated after.

In the SRH model, the capture frequency is expressed as (Eq. 3) with is given by Eq. 9. Mobile charges are assumed to be delocalized and at thermal equilibrium in the conduction band. As discussed by Kuik et al. [START_REF] Kuik | Trap-Assisted Recombination in Disordered Organic Semiconductors[END_REF], this assumption cannot stand for semiconductors with a low carrier mobility, due to their hopping transport: considering delocalized charge carriers with a thermal velocity expressed by 〈H D 〉 J E56 : * does not make sense in this case. To adapt the SRH model, Kuik et al. [START_REF] Kuik | Trap-Assisted Recombination in Disordered Organic Semiconductors[END_REF] compared the trap-assisted recombination to a biomolecular Langevin recombination [START_REF] Pope | Electronic Processes in Organic Crystals and Polymers[END_REF]. This recombination process can be described as the drift of the charge carrier towards a trap (with opposite charge) driven by the Coulomb force. To avoid capture, the thermal energy of the charge carrier must be high enough to overcome the Coulombic attraction produced by the trap [START_REF] Pope | Electronic Processes in Organic Crystals and Polymers[END_REF]. Following their assumption, and considering a single trap contribution, the parameter in Eq. 3 becomes t u, where u is the mobility of charge carriers, and v are the elementary charge and the dielectric constant of the OSC respectively. To extend the approach of Kuik et al. to systems with multiple trap contributions, one must discuss the expression of the parameter , since the proposed expression of the capture frequency does not depend on any of the given trap physical properties. It seems unrealistic that traps originating from various physical or chemical surroundings, would all show a single capture frequency. Consequently, we state that a parameter should be defined for each trap contribution. We then introduce the dimensionless parameter w related to a given trap contribution in the parameter expression:

Eq. 15 w t u.

The capture frequency (Eq. 3) of a trap contribution becomes:

Eq. 16 w t u .

In most OSCs, the mobility is low because of the molecular disorder. The transport of charge carriers occurs via localized states and is described as a hopping process. The mobility then depends on the temperature, the charge carrier concentration, the shape of the DOS and the electric field [START_REF] Baranovskii | Mott Lecture: Description of Charge Transport in Disordered Organic Semiconductors: Analytical Theories and Computer Simulations[END_REF] [22] [START_REF] Tessler | Charge Transport in Disordered Organic Materials and Its Relevance to Thin-Film Devices: A Tutorial Review[END_REF] [44] [START_REF] Simonetti | Effective mobility in amorphous organic transistors: Influence of the width of the density of states[END_REF]. Many approaches have been developed to describe the charge carrier transport in OSCs with Gaussian DOS [START_REF] Simonetti | Transport models in disordered organic semiconductors and their application to the simulation of thin-film transistors[END_REF]. In this study, we have used the advanced mobility model of Oelerich et al. [20] [21]. The model is based on the transport energy concept and considers the percolation nature of the hopping transport. The mobility model is carrier concentration dependent and is valid only at low electric field. It is well adapted to the disordered organic semiconductors under consideration. Following Oelerich et al. [START_REF] Oelerich | How to Find Out the Density of States in Disordered Organic Semiconductors[END_REF] the expression of the mobility is given by: Eq. 17 u ≈ y c 56

Ez B , &{ |8 }T3 ~V •€•' × exp ƒ 7z B @/> " …T † V 3 ~43 ( 56 ‡
where y c is the attempt-to-escape frequency of the hopping process, and taken equal to y c 10 7 Hz, ˆ 0. 215 Š‹OE• 4 /E is the localization length of the charge carriers and Ž ? 2.735 is related to the percolation nature of the hopping transport [START_REF] Nenashev | Theoretical tools for the description of charge transport in disordered organic semiconductors[END_REF]. Š‹OE• is the concentration of the localized states, typically between 10 20 cm -3 and 10 21 cm -3 . Interested readers should refer to [START_REF] Baranovskii | Mott Lecture: Description of Charge Transport in Disordered Organic Semiconductors: Analytical Theories and Computer Simulations[END_REF] for the concept of transport energy † and the expression of the distance between localized states with energies below † , …T † V, and refer to [START_REF] Roichman | Generalized Einstein relation for disordered semiconductors-implications for device performance[END_REF] for • 3• which is related to the generalized Einstein relation. Some parameters of the Gaussian disorder model depend on the actual OSC considered [START_REF] Lee | Parametrization of the Gaussian Disorder Model to Account for the High Carrier Mobility in Disordered Organic Transistors[END_REF]. In the present work, due to the lack of data regarding the DOS width, the value of the attempt-to-escape frequency, or the localization length, typical values are considered. In the transport energy concept, the charge carriers occupying energy levels above † are mobile.

Below this energy, carriers do not move efficiently and are considered as trapped. The concentration of the trapped charge carriers in the LUMO band is then given by Š‹OE• 3 4'

, and the concentration of mobile charge carriers in the LUMO :Š‹OE• is given by: Eq. 18

:Š‹OE• !' 3 ~.
In the framework of the transport energy level, † , the activation energy, , of a trap energy level, , can be defined as:

Eq. 19 †

.

As the transport energy † depends on temperature [START_REF] Baranovskii | Mott Lecture: Description of Charge Transport in Disordered Organic Semiconductors: Analytical Theories and Computer Simulations[END_REF], the activation energy depends on temperature as well. Consequently, a single trap level cannot be associated with a discrete activation energy as assumed in the SRH model (Eq. 10 and Eq. 11). To the best of our knowledge, this feature has never been reported before.

Let us first consider a Gaussian DOS within the LUMO and several discrete traps. The density of mobile carriers is given by Eq. 18 with

S / •€•' " •€•' √78 exp " 343 •€•' = 7" •€•' = •, where Š‹OE• is
the width of the Gaussian, indicative of the degree of disorder in the OSC. The higher the material disorder, the larger the LUMO width ( Š‹OE• . A representation of the DOS is given in Fig. 2 with only one trap.

Replacing in Eq. 5 the expressions of :Š‹OE• from Eq. 18, from Eq. 7 and from Eq. 16, one obtains the expression of the emission frequency: Eq. 20

:Š‹OE• w t u -1 + exp % 3 43 ( 56 +-.

For a given temperature, the emission frequency is constant with time; we still have an exponential decay of the trapped charges as in Eq. 12. Consequently, the shape of the Q-DLTS peaks will remain unchanged compared to that proposed by the SRH approach.

Calculating ln % Q 6 = + from Eq. 20 will not result in a linear dependence with % 6 + as with the SRH approach given by Eq. 11, and therefore, an Arrhenius plot would not be correctly obtained.

Consequently, it is not possible to extract the trap parameters by a simple linear regression as in the classical method. In this work an optimization technique was used to extract the trap parameters from the Q-DLTS spectra. In other words, the plots of ln % Q 6 = + vs % 6 + is non-linear but this non-linearity is not visible for a reduced range of temperatures.

Fig. 4 Fit of the "Arrhenius plots" from [START_REF] Nguyen | Defects in organic electronic devices[END_REF] using our model.

To highlight the influence of the LUMO DOS on the trap parameters determined by the experiment using our model, the extracted results were compared to those of reference [START_REF] Nguyen | Defects in organic electronic devices[END_REF] based on usual SRH. The trap activation energies shown Fig. 5 have been extracted for Š‹OE• 80 meV. The trap parameters extracted for each trap level (see reference [START_REF] Nguyen | Defects in organic electronic devices[END_REF] for details) using the SRH model are given in Fig. 6 (dashed constant lines) as well as those extracted with our model for various LUMO Gaussian widths. As can be observed Fig. 6, the model predicts that the trap energy levels depend on the degree of disorder of the material. The trap energy levels are closer to the transport band when the degree of disorder is high, i.e., when Š‹OE• is high. In practice, the dependence of the extracted trap energy on the transport band width is a difficulty since the Gaussian width of disordered materials is generally unknown. Also, it should be noted that by following this model, obtaining an Arrhenius trace is rather unexpected in organic devices when the experiment covers a wide temperature range. To conclude this section, considering the strong dependence of the extracted trap energies on the material DOS width, it appears mandatory to consider an appropriate model to characterize traps in organic semiconductor devices.

Capture and emission processes in organic semiconductors with trap Gaussian DOS

It is unlikely that a trap level could be discrete and well defined in a disordered energetic landscape. Traps are then likely to be distributed in energy in disordered OSCs [START_REF] Abbaszadeh | Electron Trapping in Conjugated Polymers[END_REF] [48] [START_REF] Borsenberger | Hole trapping in tri-ptolylamine-doped poly(styrene)[END_REF] [50]. To be more relevant we now consider Gaussian distributions for both the mobile and the trapped charges, as illustrated Fig. 7. Due to the Gaussian distribution of the trapped charges, the expression of the emission frequency of the trap distribution is no longer given by Eq. 20. To calculate the emission frequency, our approach is to consider the trap Gaussian distribution as a "quasi-continuum" of discrete traps ™ š › (Fig. 8). The index oe represents the oe D "discrete trap". Let we define a c T š V as the initial amount of trapped charged at each š during the filling stage, it is given by: Eq. 21

a c T š V p q " √78 exp • T3 ž 43 q V = 7" = Ÿ T š V
where a c , and c are defined for a particular trap distribution and are respectively the initial trapped charge during the filling phase, the width of the trap distribution, and the distribution central energy (see Fig. 8).

T š V !"#$ƒ & ž '& ( ¡ )* ‡
is the Fermi-Dirac distribution for the electrons, where , ¢ is the Fermi level position during the filling phase. The amount of initially trapped charges given in Eq. 21 depends on the capture probability of mobile carriers which is constant for a given temperature. We suppose that the Fermi level was set appropriately during the filling phase, i.e., above all the trap sites to ensure efficient capture.

Within a Gaussian distribution the discrete trap sites will be considered to have the same probability to capture a mobile carrier, which is equivalent to consider that T š V ≈ 1. In other words, the trap Gaussian distribution is considered as uniformly occupied after the filling phase.

During the relaxation phase, each "discrete trap" level, š , can release aT š , bV charges following:

Eq. [START_REF] Simonetti | Transport models in disordered organic semiconductors and their application to the simulation of thin-film transistors[END_REF] aT š , bV a c T š V expT T š V. bV, where T š V is the emission frequency of an electron from the "discrete trap" level š to the LUMO and is given by Eq. 20 with replaced by š :

Eq. 23

T š V :Š‹OE• w t u -1 + exp % 3 ž 43 ( 56 +-.
Finally, considering Eq. 21 and Eq. 22 with T š V ≈ 1 the total released trapped charges of a particular trap contribution is given by: Eq. 24

a b £ p q " √78 exp • T3 ž 43 q V = 7" = Ÿ expT T š V. bV š !' 4' .
A Gaussian trap contribution is then characterized by three parameters: the Gaussian width of the trap distribution, , the maximum of the trap distribution, c , and the dimensionless parameter w introduced in Eq. 15.

In order to test the model represented by Eq. 24, we use previously published experimental Q-DLTS spectra [START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF] (Fig. 10). The experimental Q-DLTS spectra used in this study were recorded from a perovskite based N-I-P solar cell structure from 250 to 320 K [START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF]. The SRH model was used to extract six discrete trap contributions in PBTTTV-h (see the Table 4 in the reference [START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF]). The PBTTTV-h is a thiophene-based two-dimensional conjugated polymer of poly{3-(5,5"di(2-ethylhexyl)-2,2':5',2"-terthienyl-3'-vinyl)-thio-phene-alt-thiophene} (insert in Fig. 10).

Our approach consisted in calculating the Q-DLTS spectrum for a number of Gaussian trap contributions using Eq. 24, to fit the data. A standard non-linear optimization technique was used to extract the trap parameters.

The following list details the fitted parameters and their initial values:

-As can be seen in Fig. 10, the amplitudes of the various Q-DLTS peaks, corresponding to the various trap distributions, vary with temperature. This is partly due to variations of the initial amount of trap charges a c over the various trap distributions after the filling phase. This charge a c depends both on temperature, filling time (see Fig. 3), and generally on the sample biasing history. Despite the filling phase being set so as to minimize these fluctuations, some variations remain. Therefore, the amount of initial trapped charges in each trap distribution and at each temperature a c were fitted parameters. Initial values were set by manual adjustment to obtain an initial approximate agreement.

-The central energy of each trap distribution c is a fitting parameter. Initial values were set based on the activation energies obtained in [START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF].

-The dimensionless parameter w introduced in Eq. 15 is a fitting parameter. Initial values are also chosen based on reference [START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF]. With Eq. 9 and Eq. 15 the initial guess w c is calculated with the formula:

w c t † 〈H D 〉.
-The Gaussian width of each trap distribution was optimized as well. Initial values were taken around 100 meV. As expected, the trap distribution width modulates the width of the Q-DLTS peaks. This is illustrated Fig. 9 in which, Q-DLTS peaks are simulated for different Gaussian widths. The width of the Q-DLTS peak increases with the trap width . A narrow Gaussian distribution behaves as a discrete trap (dashed line in Fig. 9). Fig. 9 Illustration of the influence of the Gaussian width of a trap distribution on the Q-DLTS peak, and comparison with a discrete trap (dashed line). Increasing the trap distribution width broadens the Q-DLTS peak.

The following parameters are also required (see Tab. 1):

-The Gaussian width of the DOS of the mobile carriers Š‹OE• is set to 50 meV. This value, actually unknown in the sample under study, is typical of disordered organic semiconductors [START_REF] Bässler | Charge Transport in Organic Semiconductors[END_REF].

-The total density of states in the LUMO Š‹OE• is taken equal to 10 7c cm -3 .

-The Fermi level , Š‹OE• during the relaxation phase is set to 1.5 eV.

The results of the optimizations are given in Fig. 10 and Tab. 2. A correct fit can be obtained considering three Gaussian trap distributions instead of six in the reference [START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF] when using the SRH model. This is due to the enlargement of the Q-DLTS peaks when considering trap Gaussian distributions. Several comments can be made on the results.

The trap energy levels are close to each other and very close to the LUMO. To our knowledge this behaviour is not usual. This might be because the SRH method is used in the literature to extract trap parameters [25] [51] or because a single discrete trap contribution is considered as in the technic which uses SCLC measurements [START_REF] Mathijssen | Dynamics of Threshold Voltage Shifts in Organic and Amorphous Silicon Field-Effect Transistors[END_REF]. In comparison with previous studies, our approach is thought to give a more realistic view of the trap behaviour in organic semiconductors.

The attempt-to-escape frequency values, y c :Š‹OE• w t u, of traps can be calculated from the fitted w parameter. The calculated values are consistent with the range of values found in the literature [START_REF] Mathijssen | Dynamics of Threshold Voltage Shifts in Organic and Amorphous Silicon Field-Effect Transistors[END_REF]. However, we must emphasize that only a weak confidence can be given to these values, due to the limited experimental temperature range (here 250-320 K), since over a limited temperature range both c and y c have similar effect on the Q-DLTS peaks and are strongly correlated: both parameters translate the Q-DLTS spectra along the relaxation time axis. To evaluate a confidence interval, from the optimum fit, a range of values achieving an acceptable error was determined and are indicated in Tab. 2. The threshold of the relative error increase was set to 50%, with almost no observable effect (by eye) on the spectra. From Tab. 2 one can evaluate the relatively large variation range of each optimized parameter.

Unfortunately, due to device stability issues, the experimental temperature range can hardly be extended and one has to rely on these confidence interval. The evolution in temperature of the initially trapped charges for each trap distribution is given in Fig. 11. The amount of trapped charges a c increases with temperature. This behaviour is coherent with the physics of the trapping processes and the mobility temperature dependence in disordered materials. The capture frequency (Eq. 16) depends on the carrier mobility following w t u . As in disordered semiconductors the transport is hopping based, the carrier mobility is activated by temperature. Therefore, the capture process is accelerated during the filling phase when increasing the temperature, increasing in turn the trapped charge density and consequently the corresponding Q-DLTS peaks. This is experimentally observed (Fig. 3 and Fig. 10). The energetic distribution of the three trap contributions is given Fig. 12, figuring the uncertainty intervals as described above. From these distributions, we calculated the density of trap sites given in Tab. 2 using Eq. 14. The diode active area is s 0.07 cm 2 and the semiconductor thickness is 80 nm [START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF]. The trap densities are in agreement with the values obtained in [START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF]. This agreement is obviously required since the trap densities are directly linked to the amplitude of the charge transients, these experimental facts are independent of the model used. From the various extractions, it appears that mainly the material rate of disorder, (i.e. the LUMO width), impacts directly the extracted trap energies: increasing the rate of disorder brings the extracted trap distribution closer to the LUMO. The other extracted trap parameters are mostly independent of the material intrinsic DOS. To enhance the reliability of extracted trap parameters, in particular the trap energies, it is of prime importance to the study of the density of states of organic semiconductors. Other techniques such as the fractional thermally stimulated current (TSC) [START_REF] Schmechel | Electronic traps in organic transport layers[END_REF] or the thermally stimulated luminescence (TSL) [START_REF] Stankevych | Density of States of OLED Host Materials from Thermally Stimulated Luminescence[END_REF]. could be usefully considered to complementally probe the DOS.

We have developed a model to characterize trap parameters in organic semiconductors. The model considers the specific transport mechanisms in organic semiconductors and the Gaussian shape of the DOS for the mobile and trapped charges as well. We have accurately fitted the experimental data with a limited number of trap distributions. Limitations of the method have been studied. A larger temperature range would allow de-embedding c and w (or y c ), however such experiments are not possible due to device stability issues. Also, in order to more precisely assess the trap distribution energies c , a good knowledge of the density of states of organic semiconductors is mandatory.

Conclusion

In this study, a model for the characterization of traps in disordered organic semiconductors has We have highlighted the importance of considering the shape of the density of states for both mobile and trapped carriers instead of the SRH model established for inorganic semiconductors.

A first model has been derived considering the LUMO Gaussian DOS and discrete trap energies, allowing a number of statements to be established. It was shown that the concept of activation energy should be discussed. Indeed, if the activation energy is defined as the difference between the transport energy and the trap level, it has been established that the activation energy of the trap should not be constant with temperature. This is due to the variation of the transport energy with temperature in disordered semiconductors. Consequently, an Arrhenius plot over an extended temperature range should not be observed in disordered semiconductors. Also, evidence was given of the dependence of the position of the traps with the LUMO Gaussian width, often unknown. This first model did not allow to reproduce the large Q-DLTS peaks experimentally observed, since for a single trap level the charge detrapping transient is still exponential at a given temperature even with a Gaussian LUMO DOS.

It appeared then necessary to develop a more advanced approach considering Gaussian DOS for both the LUMO and the trap distributions. This model is believed to better describe the trap energetic landscape in disordered semiconductors. With this advanced model, the Q-DLTS spectra could be well fitted with only three trap contributions instead of six discrete levels using the SRH approach. This could be mainly due to the broadening of the Q-DLTS peaks resulting from the energy spreading of the traps within their respective distributions.

For each trap distribution, a number of parameters were extracted. The reliability of the extracted values was discussed with respect to various unknown parameters of the sample or due to the limited temperature range of the experiment. It was shown that the LUMO width, i.e.

the rate of disorder of the organic material, is the most sensitive parameter in the process of extracting trap data from Q-DLTS spectra. The width of the LUMO density of states influences the positions of the trap energy levels but not their own distribution widths. The trap distributions are found closer to the transport band when the degree of disorder is high. Finally, the extraction process revealed trap distributions close to the LUMO edge, with relatively large DOS.

Fig. 1

 1 Fig. 1 Schematic representation of emission and capture processes of

Fig. 2

 2 Fig. 2 Representation of the Gaussian DOS for the mobile carriers (here electrons), figuring the transport energy level † , a discrete trap level , and the Fermi energy level , during the relaxation of traps.

Fig. 3 Q 5 Tab. 1

 351 Fig. 3 Q-DLTS spectra in an ITO/PEDOT/(PF-N-PH)/Al diode for different charging times tc at . 300 K [25].

Fig. 5 a

 5 Fig. 5 a) Evolution of the extracted activation energies with the temperature for each trap contribution. b) Evolution of the transport energy † with temperature for low carrier concentration and the mean † with Š‹OE• in the inset.

Fig. 6

 6 Fig. 6Comparison between the activation energies extracted from[START_REF] Nguyen | Defects in organic electronic devices[END_REF] using

Fig. 7

 7 Fig. 7Schematic of the energy distributions for electrons in OSC: a Gaussian

Fig. 8 A

 8 Fig.8A discretized Gaussian trap distribution.

Fig. 10

 10 Fig. 10Experimental (circles) from[START_REF] Hsieh | Analysis of Defects and Traps in N-I-P Layered-Structure of Perovskite Solar Cells by Charge-Based Deep Level Transient Spectroscopy (Q-DLTS)[END_REF] and simulated Q-DLTS response

Fig. 11

 11 Fig. 11 Evolution of a c of each contribution obtained after the optimization of the data with the temperature.

Fig. 12

 12 Fig. 12Representation of the DOS of the three trap contributions at 320 K

  been adapted from the conventional Shockley-Read-Hall formalism and from previous developments for organic low mobility materials. The model considers the main specificities of disordered OSCs: Gaussian density of states and hopping transport. The charge transport model considered is the mobility model developed by Oelerich et al. The model is applied to the analysis of previously published measurements using the Q-DLTS technique.

Acknowledgment

This work was financially supported by the Grand-Est region and the European Community through the FEDER project POLCA. Some of the experiments were carried out within the Nanomat platform (www.nanomat.eu ) supported by the Ministère de l'Enseignement Supérieur et de la Recherche, the Région Grand Est, and FEDER funds from the European Community.

Considering the high density of trap states (10 17 cm -3 ), should these traps be considered as tail

states is an open question.

To conclude, a new model is proposed to describe defect states in disordered organic semiconductors considering a Gaussian distribution for both mobile and trapped carriers. Good agreement with experimental data is obtained by the Q-DLTS technique. Analysis of the reliability of the extracted trap parameters emphasized the need of a better knowledge of the LUMO characteristics in these materials. The present model is expected to help understanding some experimental results of disordered semiconductor materials.