Philippe Boyer

The food euro: method and new results to analyze distribution of value in the French food chain

Keywords: final food consumption expenditure, value added, input-output matrix, food supply chain, agricultural income JEL Classification: M21 M41

The food euro" denotes the method and results of the decomposition of food consumption into values added, imports and taxes, by means of calculations on the input-output tables. The article explains the role of price ratios in the (low) level and (downward) evolution of the share of the agricultural branch in this distribution. The contributions of the various final demands to the formation of the agricultural income are also measured. The article begins with a presentation of the method and concludes with a discussion about the scope of this approach and its prospects and constraints for improvement.

Introduction

"The food euro" refers to the analysis of the distribution of food expenditure in France into value added, imports and taxes, inspired by the work on the "food dollar" of the Economic Research Service of the United States Department of Agriculture (Canning, 2011; Canning, Kelly, Weersink, 2016) and consisting of an application of calculations on input-output tables (IOT) of W. Leontief's "open model" (Leontief, 1936, 1986). These results complement by a macroeconomic view the microeconomic and sectoral analyses of the gap between agricultural and food prices carried out by the French "Observatory of the formation of prices and margins of food products" (OFPM, 2022). Compared to previous works (Boyer, Butault, 2012, 2013, 2014), this article presents more recent results, from a revised method integrating food-services consumption (restaurants, institutional catering, food to go, home delivered meals) and including 2018 data 1 .

Sources and methods

The symmetric input-output table and its adaptations

The main source used is the domestic symmetric input-output table (SIOT) at basic price produced by the French National Institute of Statistic and Economic Studies (Insee) for Eurostat, the European Union statistical service (Eurostat, 2008), and presented here in condensed version in Appendix A. It divides the use of each domestic product into intermediate consumption by the different industry groups (branches 2 ) and final demands: final consumption, exports and gross capital formation.

Output and its uses are at basic prices, i.e., the amount the producer receives from the buyer per unit of good or service he produced, less taxes on products and plus direct subsidies on products. For each product, the amount of the domestic resource is therefore equal to that of its uses, unlike the standard input-output table [START_REF] Bonnet | [END_REF] .

1 Former work based on 2017 data was presented at the "15th Days of Social Sciences Research -INRAE, SFER, CIRAD, Toulouse, France , 2021 December 9-10, Session about agricultural income" and published in French (Boyer, 2021). 2 In the French national accounts, the term "branch" (branched, in French) refers to a homogeneous unit of production, that is to say, which produces goods or service which belong to the same item of the classification of economic activity in question. (In this article, "industry groups" means "branches"). On the contrary, a "sector" groups together statistical units (enterprises, legal units) classified according to their main activity. [START_REF] Bonnet | [END_REF] For a description of the structure and the properties of the symmetric input-output table, different from that of the standard input-output table : Braibant, 2011, Eurostat, 2006 and Malherbe, 2018. The number of products is equal to the number of industry groups, which are moreover "pure", in one-to-one relation to the products (the type of the SIOT used is "product-by-product"). This symmetry makes it possible to perform calculations that use the inversion of matrices linking industry groups outputs to products inputs.

But first, the SIOT must be adapted.

In the SIOT, the consumption of food products bought in the retail trade by customers is included in the final consumption at home of the products of these three industry groups : Agriculture, Fishery and aquaculture, Food products and beverage processing industry. The consumption in restaurants is not included in the final consumption of the products of agriculture, fishery or food processing : it is computed as the final consumption of food services, aggregated in the Eurostat SIOT with accommodation services. To consider food services in food consumption requires adaptation of this SIOT to separate food services from accommodation services, in terms of intermediate and final uses of these services, and in terms of intermediate consumption, output and value added of their industry groups.

The distribution of the resource and its uses between food services and accommodation is based on the "Supply and Use Balance" tables of the national accounts, in which the two services are distinguished. Another source of national account, the "Accounts per Branches" gives the intermediate consumption of each industry group: food services and accommodation. The intermediate consumption of each branch is then broken down by type of input, based on the statistics by sector given by the Business statistics system of Insee.

This results in a SIOT in which food services industry group, its production and uses, are individualized and separate from accommodation. This adaptation, now carried out on SIOT available since 1995, is an innovation compared to previous work (Boyer, Butault, 2012, 2013, 2014).

The resulting SIOT has yet to be adapted for two more purposes (Boyer, Butault, 2014). These are: 1°) reallocate wine production to the agricultural industry group, in accordance with the French national accounts of that branch, and unlike the SIOT of Eurostat, which allocates wine production to the Food products and beverage processing industry. 2°) eliminate subsidies to products included in the amounts at basic prices of uses and resources. So: regarding uses, final consumption will be without subsidies, as is the actual expenditure of consumers; regarding resources, outputs, and therefore value added, will not include amounts not derived from effective expenditure of purchasers [START_REF] Bournay | Les séries longues des comptes nationaux. Retour sur la rétropolation des comptes[END_REF] .

Since 2008, the nomenclature of the SIOT aggregates food processing with tobacco products, and the impact of these non-food products on the results must be eliminated. The significant impact of tobacco margins and, especially, tobacco taxes, are corrected in the course of the calculations, and after, the otherwise minimal impact of the tobacco values excluding taxes and margins is eliminated by calibration on the final consumption of the products of the food processing industries excluding tobacco, given by the "Supply and Use Balance" tables of the national accounts.

After these adjustments, the SIOT (at basic prices less subsides) presents values which do not yet incorporate the trade and transport margins of final consumption, although they represent almost a quarter of its purchase value, nor consumption taxes (VAT, excise duties on alcohol, etc.). They shall be taken into account after the series of calculations at the basic price excluding subsidies, described below.

The equality between final demand and "domestic value added"

Domestic value added is the balance between output and intermediate consumption of domestic products (Appendix A). The overall equality between domestic value added and final demand is an accounting obviousness: since overall domestic value added is the difference between output and its intermediate uses, it is therefore the part of output that is subject to final use. This equality is the basis for the calculations of the decomposition of food consumption into induced value added in each of the industry groups of the national economy, imports and taxes.

The first stage of this decomposition consists in breaking down the above-mentioned overall equality into industry groups where domestic values added are formed, and into products, whose final demands induce these values added. A matrix calculation gives the coefficients of domestic value added induced by final demands: cf. Appendix C-1, Eq. ( 3).

The breakdown of final consumption at basic prices excluding subsidies

As a consequence of the assumption, inherent in the input-output analysis, of the uniqueness and linearity of the production function of a product whatever its uses, the abovementioned coefficients apply to any element of final demand for the same product and, applied to the final consumption of agrifood products, they provide the "domestic value added" induced in each industry group by this final consumption.

Using the SIOT data, these "domestic value added" are then broken down into value added, imported intermediate consumption, and taxes on intermediate consumption: cf. Appendix C-2, Eq. ( 6) to (8). Another Eurostat table, the "Importation input-output Table ", gives the final consumption of imported agri-food products, excluding margins and taxes.

Taking into account trade and transport margins and taxes

Margins are the value of services produced by trade and transport. In the SIOT, the use of these services by each industry group constitutes its intermediate consumption of trade and transport services, and the margins of final expenditure all domestic products together are included in final demands (including final consumption) in trade and transport. On the other hand, since the SIOT are at basic prices, final expenditure by product does not include trade and transport margins. Thus, the breakdown of final consumption obtained at this stage relates to expenditure which would have been done without margins. However, these margins correspond to a final consumption of trade and transport services, which induces, like any final demand, values added, imported intermediate consumption, and taxes on intermediate consumption.

The "Supply and Use Balance" gives margins on final consumption by product, domestic and imported. The components of these margins in values added, imported intermediate consumption and taxes on intermediate consumption are calculated and added member to member to composition without margins, obtained previously, to obtain the composition including margins (Appendix C-3). Final consumption taxes are estimated as the difference between final consumption including margins and final consumption at purchasers' prices (i.e., taxes included) provided by the "Supply and Use Balance" tables.

The calibration on effective food consumption

At this stage, the decomposition obtained relates to a consumption of agri-food products, assimilated to actual food products. However, final consumption of agri-food products includes that of non-food products, identifiable in the detailed national accounts by products in a more precise nomenclature.

For agricultural products, these a priori non-food products are flowers, plants and pets, which account for 18% of final consumption of agricultural products in 2018. Among the products of the food processing industry, pet food, which accounts for 2% of final food products consumption, is also to be excluded since only human consumption is concerned. [START_REF] Boyer | méthode et nouveaux résultats pour l'analyse de la répartition L'euro alimentaire -2021/4 n° 378[END_REF] The impact of these products is roughly corrected by recalibrating the results on the final consumption of only a priori food products, given by national accounts at a detailed level of nomenclature of products, then by a final calibration on the total amount of effective food consumption, given by national accounts of final consumption by function (Appendix B).

Notes on the calculation of the other results of the euro food

An equation of the same type as Eq. ( 4) in Appendix C-1, that giving induced output, provides the employment (in full time equivalent) induced in the branches by food consumption (Appendix C-5 ).

For the purpose of farm income analysis, we calculate the contribution to the formation of agricultural value added by different final demands for different commodities: food consumption, agrifood exports and fixed capital formation, other final demands for other products (for example: biofuel, textile…). The results are derived from a symmetrical calculation of the breakdown of final demands (Appendix C-6 ).

Retropolation of results obtained in previous databases

National accounts "change their base" periodically. These changes may affect the nomenclatures, the classification of transactions in the accounts [START_REF] Boyer Ph | La décomposition de « l'euro alimentaire » en revenus des différents facteurs en France en[END_REF] and evaluation methods [START_REF] Boyer Ph | L'euro alimentaire en 2005 dans vingt pays de l'Union européenne. 7 èmes Journées de recherches en sciences sociales[END_REF] . National accounts must also comply with the European System of Accounts (ESA), also periodically amended (CE, 2010).

There is no retropolation in new bases of formers SIOT published by Eurostat in previous bases, so the comparability of "food euro" results from different bases is compromised.

Thus, the results developed here relate with some exceptions to the years 2010-2018, calculated in base 2010 until 2014, then in base 2014. These two bases are under the ESA 2010 and the changes made by the 2014 base have a negligible impact on the euro food [START_REF] Boyer Ph | L'euro alimentaire en France et le partage des valeurs ajoutées[END_REF] .

Results

Distribution of food expenditure in value added, imports and taxes in 2018

In 2018, the food consumption (with food services) amounts to 255 805 M€ of which 71 5366 M€, or 27%, in food services. The Table 1 (next page) shows its distribution and the following explanatory ratios:

-the "production coefficient of food consumption": the ratio of the production induced by food consumption in a given industry group, in the food consumption, -the "value added ratio" : the ratio of the value added of the industry group in its production.

The share of the value added induced in agriculture by food consumption is low, with 6.9% of the food expenditure, due to production coefficient and value added ratio lower than the average for other industry groups.

The weight of food services, trade and other services is important compared to that of upstream industry groups: agriculture and food industry.

In 2018, the value added induced in trade represented more than 15% of food consumption and nearly a quarter of the value added induced by all branches. This refers to all trade activities, wholesale and retail, contributing directly or indirectly to the satisfaction of food demand, and not just food retailing.

Compared to the initial approaches of the euro food (Boyer, Butault, 2014), the share of other sectors is reduced by taking into account food services, where the value added induced is important: 13.6% of food consumption and 21.5% of the value added induced by all industry groups.

"Other services" cover a large number of industry groups where dominate, for more than 55% of the value added induced in these branches: legal, accounting, management consulting and head office services, real estate, employment services (including temporary work), financial and insurance activities.

The other very important aspect of the distribution is the weight of importations : they account for more than the quarter of food expenditures. They come from European Union for 61% all products combined, and for 69% for agri-food imports only. They break down as described in Table 2. Sources : author's calculation from Insee and Eurostat data.

Table 1. Content of food consumption in value added, importations and taxes in 2018

The weight of agri-food imports is normally high in the import content of food consumption. Food services is sometimes considered to make significant use of these imports, but according to Table 3 (next page), they represent 7.5% of the value of food services consumption. In comparison, agri-food imports for intermediate consumption alone represent 3.1% of food expenditure excluding food services, so less than in food services (7.3%), but 17.8% when final imports are added [START_REF] Braibant | La confection d'un TES symétrique pour Eurostat et d'un tableau de contenu en importation[END_REF] . A significant share of induced imports are services, of which trade and transport account for just under half.

In comparison, agri-food imports for intermediate consumption alone represent 3.1% of food expenditure excluding food services, so less than in food services (7.3%), but 17.8% when final imports are added . A significant share of induced imports are services, of which trade and transport account for just under half. The evolution of the share of agriculture in the food euro

The share of value added of an industry group in food consumption is the product of its ratio of value added in the output by its coefficient of production in food consumption. These two terms are associated with the two following relative prices: the agricultural price index in relation to the food price index [START_REF] Canning | A Revised and Expanded Food Dollar Series: A Better Understanding of Our Food Costs[END_REF] , involved in the variations in the coefficient of production, and the agricultural price index in relation to the intermediate consumption price index of this industry group [START_REF] Canning | Farm share of the food dollar: an IO approach for the United States and Canada[END_REF] , involved in the variations in its value-added rate.

Because of breaks in series due to national accounts base changes, the results since 1999 belongs to three non-homogeneous time series, allowing only comparisons on the direction of evolutions (Chart 1).

Chart 1. Evolution of induced value added and imports in food consumption

NB : (1) Series breaks are represented by breaks on the curves. ( 2) Taxes (fairly stable around 10%), fisheries and aquaculture (less than 1%), transport (3%) and non-agri-food industries (4%) are not represented.

Sources : author's calculation from Insee and Eurostat data.

The period 1995-2007 was studied in the initial article on the food euro (Boyer, Butault, 2014). Until 2005, the decrease of relative agricultural prices as a result of successive CAP reforms (which reduced support of agricultural prices support by bringing them closer to world prices), led to a decline in the share of agricultural value added. Added to this is the increase of imports, which also affects the share of other industry groups.

From 2006, deregulated agricultural prices were exposed to volatility, in an upward trend which follows that of raw materials and energy, between 2005 and 2008, in a context of climatic hazards, low stocks, speculation and increased demand (Huchet-Bourdon, 2011; Voiturier, 2009). This led to the increase of agriculture share in 2007.

The national accounts base change in 2008 leads to a second and short series of results, (2008-2010), characterized by the decrease of the share of agriculture in 2009, due to that of agricultural prices [START_REF] Canning | A Revised and Expanded Food Dollar Series: A Better Understanding of Our Food Costs[END_REF] Index of the price of agricultural production, in the national accounts per branch ; index of the food consumption prices, including "restaurant," canteen, cafes" (Insee). The third series covers the years 2010 [START_REF]Système européen des comptes -SEC 2010 Luxembourg[END_REF] -2018. Imports are increasing and, correspondingly, the shares of value added are on a downward trend, more or less regular depending on the branch, including restaurants, trade, and services. During this period, the downward trend in the share of agricultural value added is given by the decrease in the agricultural production coefficient after 2012 and in the value added rate from 2011, which also contributes to yearly short run variations (Chart 2).

Chart 2. Share of agricultural value added in food consumption, agriculture value added ratio and agricultural production coefficient in food consumption

Sources : author's calculation from Insee and Eurostat data.

The ratio of agricultural prices to food prices, which is involved in the production coefficient, tends to decline after 2012 and thus reduces the share of value added in agriculture (Chart 3, next page).

The impact of variations of the prices of agricultural products reported to food prices is reduced or amplified by variations of the prices of agricultural products reported to those of their intermediate consumption, the downward trend of the latter report being less marked since 2010 than in the previous ten years (Insee, 2020).

On Chart 4 (next page), the variations of the ratio of intermediate consumption in volume to agriculture production in volume are , sometimes in phase, sometimes in phase opposition to those of price ratios, accentuate or cushion the impact of the latter on the share of value added.

From 1999 to 2018, observed over each period of homogeneous basis, the coefficient of agricultural production in food consumption (in value) tends to decrease : from 20% to 18% on 1999 -2007, from 17% to 16% on 2010 -2018. This decline is mainly due to that of agricultural prices reported to food prices: -9% per year by average over 2003-2018, but also to the growth of imports that replace domestic resources. Added to this is the quality effect of the increasing incorporation in volume of nonagricultural elements in food expenditure: industrial processing, packaging, services (advertising, marketing, health safety). These elements obviously do not replace the agricultural raw material but they are added to it and modify the composition of the "basket" of the food supply.

This trend is slower than that of price ratios. It is perceptible over 1999-2018, through the decrease of less than 1% per year on average in the coefficient of agricultural production estimated in volume.

12 2010 is the only year for which an input-output table is available in the new and the former base.

Share of agricultural value added in food consumption and relative prices

Sources : author's calculation from Insee and Eurostat data.

Chart 4. Share of agricultural value added in food consumption and relative volumes

Sources : author's calculation from Insee and Eurostat data.

The formation of the agricultural income by the various final demands

In 2018, the gross income of the agriculture branch breaks down as follows, in terms of contributions of final demand and subsidies (Table 4):

-Food consumption contributes 40% to the "gross value added at factors costs" (GVAFC) of the branch. The contribution of food services alone is much lower (5.7%) than its share in food consumption (28%). This results from lower coefficients for domestic agricultural and agroindustrial products in consumption of food services (8% and 22% respectively) than in food consumption excluding food services (19% and 48%). -A quarter of the value added of the agriculture branch comes from exports of agricultural products and goods of food processing and beverages industry. -Gross capital formation (GCF) in agri-food products covers the final demand represented by the storage of these products or their fixed assets (e.g. perennial plantations in agriculture) which constitute gross fixed capital formation.

9

-"Other final demands for goods and services" include domestic consumption, GCF or exports of products other than agri-food, but incorporating intermediate consumption with agricultural origin: demand for bio-based materials and energy (biofuels) and goods or services whose production incorporates these products. The evolution of the contributions of the various final demand to the agricultural Gross Value Added at Factors Costs (GVAFC) is shown on Chart 5, it is not very marked over the period considered.

Chart 5. Contributions of final demand and subsidies to gross value added at factor cost of the agriculture industry

Sources : author's calculation from Insee and Eurostat data.

The contribution of a final demand to the agriculture GVAFC depends on the amount of that final demand and the share of agriculture value added induced in this final demand. Changes in the value of these items are shown in Charts 6a and 6b (next page) for the two major demands on agriculture: agrifood exports (6a) and food consumption (6b).

The trends in the shares of agricultural value added in food consumption and in agri-food exports are very similar, which is normal: agricultural products are exported more (32% of their final demand) than products of the food industries (26%) but, because of the hypothesis inherent in SIOT, the coefficients of value added induced by the demand final for a given product are identical whatever this demand (consumption, export or GCF). These shares of value added in food consumption and in exports are variable and trending downwards. Their evolution contributes to the decline and variations in the contribution of these two final demands to the agriculture GVAFC, but their impact on the contribution of these final demands to the agricultural GVAFC is mitigated by the increase of these demands. Unlike exports, the increase is fairly steady for final consumption, whose prices (and of course volumes) are less volatile, the downstream margins in food chains cushioning the impact on consumer prices of changes in agricultural prices (OFPM, 2020). On the other hand, the weight of "commodities" in agri-food exports exposes them to the volatility of world prices. The variability of the contribution of food consumption to agricultural GVAFC is thus less than that of exports.

39%

Chart 6a. Evolution of agri-food exports, share of agriculture value added in agri-food exports and contribution of agri-food exports to agricultural

Discussion: scope of results, limitations, outlook

Scope of results: contribution to debates about sharing or creation of value

The old question of the distribution of value in food chains has been revived by the disarmament of agricultural market regulation policies and the strengthening of competition rules, with their questionable application to the agricultural sector (Prieto, 2018), in a context of price volatility (Huchet-Bourdon, 2011) and concentration of food distribution (Allain, Chambolle, Turolla 2016).

It is in this context that the OFPM is developing a sectoral approach by chain of products, aimed at breaking down the prices of various food goods into the value of the agricultural raw material incorporated and downstream "margins" [START_REF]Analytical factsheet for France: Nine objectives for a future Common Agricultural Policy[END_REF] , followed by an analysis of the costs contained in these components.

Compared to this approach, the "food euro" completes in some way the decomposition of costs down to their content in primary factors incomes and, as a result, involves all industry groups in the distribution of value, and not only these considered in the vertical chain of agri-food products.

This going beyond the sectoral analysis and also distinguishes the "food euro" from the study of the distribution of added value in the agri-food chain carried out by the European Commission (EC, 2018), consisting in measuring the share of each agri-food sector in the total value added of all these sectors: in this distribution, French agriculture receives about 20% of the value added (of the agrifood sectors), instead of about 10% of the value added (induced in all industry groups by food demand) in the "food euro". [START_REF]Analytical factsheet for France: Nine objectives for a future Common Agricultural Policy[END_REF] Trade margins in wholesale and retail trade and, by extension, in the agri-food processing industries: difference between processed production and its intermediate consumption of agricultural origin. The comparison between value added and labour induced by food consumption shows that agriculture represents 10% of the value added induced by all industry groups for 15% of induced units of employment measured in full-time equivalent (average 2010-2018).

This refers to certain debates of the OFPM: according to some, the level of agricultural prices result from market structures unfavorable to agriculture and do not make it possible to remunerate agricultural work at the level of its contribution to the creation of value ; for others, on the contrary, prices reveal the values created by each industry, and the distribution unfavorable to agriculture would reflect, above all, the still insufficient productivity of the sector (despite its strong increase in labour productivity, cf. Dechambre 1994, Veysset, Lherm, Boussemart, Natier 2017).

The decomposition of food expenditure into primary factors incomes puts the question of the distribution of value in the agri-food sector into the larger debate about the sharing of value added between labour and capital (Cotis, 2009). However, both data and method constraints limit here the approach to a breakdown in terms of gross incomes.

The limits of the "food euro"

The SIOT does not allow to go beyond a distribution of gross income: wages, and gross operating surplus including the gross mixed income of capital and self employed labour. The "Overall economic table" of National Accounts gives the decomposition of gross operating surplus into remuneration of owners of capital, net transfers14 , saving and income and wealth taxes, for the three institutional sectors [START_REF] Cotis | Partage de la valeur ajoutée, partage des profits et écarts de rémunérations en France -Rapport au Président de la République[END_REF] .

To carry out such a breakdown branch-by-branch for gross operating surplus induced by food consumption would require additional data and the distribution of gross operating surplus including mixed income of the SIOT into gross operating surplus at stricto sensu and remuneration of selfemployment.

The same constraints would apply to the continuation of the decomposition up to the "cost and extra-cost of capital", distinguishing the "normal" remuneration of capital and rents derived from its property (Cordonnier et al., 2013; Garnier, Mahieu, Villetelle, 2015).

The nomenclature of the SIOT aggregates all agricultural products into a single product. Therefore, the SIOT does not allow analysis by chain of food product (meat, milk, fruits and vegs, etc.). If this were the case, the "food euro", by giving the income obtained from food expenditure by each industry group for each chain of food product, could replace the current sectoral approach of the OFPM.

A fraction of "physiological" food consumption escapes the "food euro". This is the part of the food services demand included in intermediate consumption by industry groups (business meals) and which is therefore not found in (final) food consumption. About 25% of food services production is used for intermediate consumption, for an amount that would increase food consumption by 9% if it were to be included. The calculation of the "food euro" with food consumption thus enlarged would require a transfer from intermediate consumption of food services to final consumption of these services, thus increasing the value added of the user branches.

As has already been pointed out, the insufficiently detailed nomenclature of the SIOT and its hypothesis of fixed coefficients determine the results of the euro food. The same applies to the treatment of subsidies to products, excluding them from basic prices.

Outlook

The breakdown of value added down to the cost and extra-cost of capital remains a possible objective, but rather in the context of a study than an annual review.

In terms of annual review, it would be useful to reconstruct a long series of results in the new base of national accounts. This requires redoing the calculations for previous years on SIOT "retropolated" (backcasted) in new base, with the support of Insee, which had built a tool for this purpose. (Bournay, Khelif, 2012).

The feasibility of a food euro per food product chain should be studied, in particular drawing inspiration from the SIOT adaptation work carried out in a study of employment induced by the agricultural sectors of Brittany (Bonnet et al., 2016 [1], [2]).

Another goal could be to extend the approach to other countries. A test was carried out on twenty European countries for the year 2005 (Butault, Boyer, 2013), which showed significant differences in the composition of national food euros, in terms of the weight of upstream agri-food branch compared to imports or services. The comparison with the food dollar of the United States (Canning, 2011) needs to consider the food euro excluding final imports because the USDA only breaks down the consumption of domestic products (even manufactured with imported inputs). The food dollar differs mainly from the domestic food euro by a greater weight of the food services (31% vs 17%, in 2018), resulting from very different food models and habits, and a smaller share of intermediate imports (6% vs 18%), probably due to greater energy autonomy of the USA. In addition, the shares of agriculture are significantly different. (5.6 % in USA vs 8.4% in France).

Conclusion

The " à la Leontief " calculations are an old macroeconomic method but still relevant for value analysis in the agri-food chain, highlighting the contributions of all activities beyond those that usually define the food chain, and by measuring the revenues they derive from our food expenditures.

This calls for a development of these works, as well as of the complementary studies on transfers of productivity gains in the agri-food sector, by the means of "surplus accounting method", applied to macroeconomic national accounts (Dechambre, 1994) or to microeconomic sources (Veysset, Lherm, Boussemart, Natier, 2017)… and also argues for the maintenance of homogeneous statistical series over a long period.

Note 1:

The SIOT actually used has 65 branches and products, and:

(1) It distinguishes agriculture from fisheries and aquaculture;

(2) It does not distinguish, before author's adaptation, food services from accommodation;

(3) It distinguishes 3 branches and products for trade (retail except vehicles, retail and wholesale of vehicles, wholesale except vehicles) and 4 branches and products for transport (by land, by air, by water, warehousing);

(4) It distinguishes 29 branches and products in services and 24 branches and products other than food, beverages and tobacco products;

(5) It breaks down value added into gross wages, gross operating surplus including mixed income, and subsidies less taxes;

(6) It details the "Other final demands" in "Exportation" and "Fixed capital formation" detailed into "Gross fixed capital formation" and "Changes in inventories and valuables".

(a) Importations are detailed by product an using branch in the "symmetric input-output

& V $ !" ! & $'( = FD % (1)
Without exposing here the demonstration (see Leontief, 1936, 1986), we have :

!V !" # = 〈v〉[I -A] )( 〈FD〉 (2)
with: § 〈v 〉 diagonal square matrix of the ratios of domestic values added in the output of branches j, § [I -A] )( inverse of square matrix of difference between the square identity matrix [I] and [A] the square matrix of domestic technical coefficients of the SIOT formed by the ratios of intermediate consumption of each domestic product i in the production of each branch j. § 〈FD〉 diagonal square matrix of final demands in domestic products i, Each term of the square matrix:

[I -A] )(
is the output of branch j necessary for (or induced by) one euro of final demand of domestic product i.

Each term of the square matrix:

[w] = 〈v〉[I -A] )( (3)
is the coefficient of domestic value added in the branch j induced by one euro on the final demand of the domestic product i.

Note:

[I -A] )( 〈FD〉 = !P !" # (4)

with %P !" ' the square matrix of productions (in row) induced by final demand of products (in column).

2) Values added induced by final consumptions without margins

!V !* # = [w]〈FC〉 (5)
is the square matrix of domestic values added induced in the branches by the final consumption in products, which terms, as in Eq. ( 1), verify :

& V $ !* ! & $'( = FC % (6)
From the SIOT, we have (cf. appendix A) :

V $ = VA $ + IC + $ + T ,* $ (7) With : § V $ : domestic value added of branch j ; § VA $ : value added of branch j ; § IC + $ : intermediate consumptions of branch j in imported inputs : § T ,* $ : taxes on intermediate consumption of branch j.

The structure of domestic value added from Eq. ( 7) applies to the part of this domestic value added which is induced by the final consumption : from Eq. ( 6) and Eq. ( 7) is therefore derived the composition of the final consumption of any product i in values added, imported intermediate consumptions and taxes on intermediate consumptions, induced in the various branches j by the final consumption of i, then :

For the index i corresponding to the agri-food products and food services, equation [8] gives the decomposition of the finals consumption of said domestic products and services, in values added, imported inputs and taxes on inputs induced in the n branches.

3) Takin into account margins

The "Supply and Use Balance" tables give MF % , domestic margins of the final consumption of domestic and imported products i. Let VA $ -! ! , CI + $ -! ! and T *,$ -! ! , the components of MF % to be added term to term to those of Eq. ( 8), and such that :

MF % = & VA $ -! ! & $'( + & IC + $ -! ! & $'( + & T ,*$ -! ! & $'( (9)
VA $ -! ! , CI + $ -! ! and T *,$ -! ! are obtained by weighting with MF % FC .&. 7 , (FC .&. being the final consumption of trade and transport given by the SIOT), each of the following terms :

VA $ !* "&" , IC +$ !* "&" and T ,* $ !* "&" , obtained from V $ !* "&" : domestic value added induced by the final consumption of trade and transport, given by !V !* # (cf. Eq. ( 5) ) and broken down by applying Eq. ( 7).

4) Alternative méthode

It is possible to calculate the matrix [w] of Eq. (3) from the SIOT maintained at basic prices (i.e., including subsidies to products), and to apply it as before to final consumption excluding product subsidies.

Then, compared with former results, the components of final consumption are: § 8VA $ !* ! + S 0 $ !* $ :, values added at basic price, thus including subsidies to products S 0 $ !* $ ; § IC + $ !* $ , imported intermediate consumption, term without change. § 8T ,1$ !* ! -S ,1$ !* $ :, taxes on intermediate consumption, less their subsidies to products.

The share of value added in the food euro is thus increased, but by elements of subsidies not included in consumer expenditure (but indirectly induced by it). The share of the taxes is reduced. The calculation at basic price leads to consider that a part of the taxes included in consumer expenditure, ultimately paid by him to the State, finances the subsidies received by the producer, paid to them by the State, and therefore ultimately by consumers-taxpayers.

5) Employments induced by final consumption

They are obtained by a calculation of the type of Eq. ( 4):

!L !* # = [𝑙] [I -A] )( [FC] (10)
L an 𝑙 being respectively employments in full-time equivalent and employment ratio in the input of the branch.

  Agricultural production coefficient in food consumptionAgriculture value added ratioShare of agricultural value added in food consumptionThe food euro: method and new results to analyze distribution of value in the French food chain. Philippe Boyer. "15th Days of Social Sciences Research -INRAE, SFER, CIRAD, Toulouse, France , 2021 December 9-10, Session about agricultural income"

GVAFC Chart 6b .

 6b Evolution of food consumption, share of agriculture value added in food consumption and contribution of food consumption to agricultural GVAFC Sources : author's calculation from Insee and Eurostat data.

  exports Share of agriculture VA in agri-food exports Contribution of agri-food exports to agriculture GVAFC of agriculture VA in food consumption Contribution of food consumption to agriculture GVAFC

FC

Table 2 .

 2 Structure of the import content of food consumption in 2018

	Food services	Food consumption	Total food
	consumption	at home	consumption

Which final import : (a) : 9,2% et (b) : 33,7%.

Table 3 .

 3 Weight of agri-food imports in food consumption in 2018

	Food services	Food consumption at	Total food
	consumption	home	consumption

  [START_REF] Canning | Farm share of the food dollar: an IO approach for the United States and Canada[END_REF] Index of the prices of intermediate consumption of agriculture branch, in the national accounts per branch(Insee). 15%) or reported to those of intermediate consumption (-9%); this decrease of relative agricultural prices in 2009 results of an excess in supply in response to the previous price increase.

	reported to food prices (-
	% food consumption	15% 20% 25% 30%																					Agriculture Food and beverage manufacture Food services
		10%																					Trade
		5%																					Other services
		0%
		1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2010	2011	2012	2013	2014	2015	2016	2017	2018	Final and intermediate importations

Table 4 .

 4 Contribution of final demands and subsidies to gross factor income of the agriculture branch in 2018

	Value added	Gross operating surplus and mixed income	Compensation of employees
	M €	%	M €	%	M €	%

Sources : author's calculation from Insee and Eurostat data.

B. From final consumption of agri-food products to food consumption

  Taxes on intermediate subsidies : compared with the initial SIOT (before adaptations), this line is no longer corrected by the subsidies to products included in the value at basic prices of the intermediate consumption, because the deduction has been operated in the line per product. !" # the square matrix with n branches and products, which terms are V $ !" ! , domestic value added induced in the branch j by the final demand of the product i : FD % such that (cf. Appendix A,

	C. Matrix calculation
	1) Domestic values added induced by final demands
	Let !V note 2) :
				table of
	importations" (Eurostat).
	(b) Note 2: Overall equality between total domestic value added and total final demand (at basic prices
	excluding product subsidies):
	Total domestic value added
	= total production -total intermediate consumption of domestic products (4 178.0 -1 556.8 = 2
	621.2)
	= total final consumption + total other final demands (1 532.9 + 1 088.3 = 2 621.2) = total final
	demand
	Note 3: Components of domestic value added per branch:
	Domestic value added
	= value added + intermediate importations + taxes on intermediate consumption
	Example for Agriculture branch:
	47,6
	= 34,8 + 10,8 + 2,0
				Effective consumption
		Final consumption	Final consumption of a	by function : food,
	At purchaser's prices	of products	priori food products	food service.
	Year 2018	(SIOT and supply-	(National Accounts,	Excluding territorial
	Unit : 10 6 €	use tables)	detailed nomenclature)	correction (*)
				(National Accounts)
	Products of agriculture, fisheries, aquaculture	34 301	28 499	28 021
	Products of food and beverage manufactures	161 830	158 914	156 247
	Food services	70 718	70 718	71 536
	Total « food including food services »	266 849	258 131	255 805
	(*) territorial correction : the expenses of residents abroad (import) minus the expenses of non-residents in France (export).
		Source : Eurostat, Insee

However, it is possible to make calculations with production maintained at basic prices: then, food consumption induces value added with subsidies to the products included. See Annex C-4.

Food stuffs for farm cattle are also food processing industries products, but, unlike pet-food, bought by households, they are not computed in final consumption: their domestic use is intermediate consumption, bought by agriculture industry group.

For example, expenditures of firms for research and development, formerly classified as intermediate consumption, are reclassified since base 2010 as investment, that increases the value added.

For example, since 1995 : evaluation of the production at basic price (including subsides to products, les taxes), instead of delivery price (without net subsidies to products).

The results obtained in base 2010 have been recalibrated on the amounts of final demands of agri-food products in base 2014, very little different from those in the previous base.

There are no final imports of food services, but only imports of inputs for the production of such services.

Benefits received minus contributions paid, indemnification minus insurance premiums.

& %'( + S $(12)

Appendix

A. Symmetric input-output table (SIOT) at basic prices excluding subsidies to products, branches and products aggregated

Année 2018 Agriculture, fisheries, aquaculture See notes next page.

Source : Eurostat, Insee ; adaptation : author.

6) Contributions of final demands to agricultural gross income

The Gross Value Added at Factors Costs (GVAFC) of branch j is given by :

with VA $ : value added without subsidies to product, and S $ : all operating subsidies less all taxes on production.

The values added induced in the branches j by exportations and gross capital formation in products i (VA $ 2+ $ and VA $ 3! ! ) are calculated as was calculated VA $ !1% . And, the value added of any branch (which agriculture) being induced by the final demands to which the branch contributes to serve, we have :


S Mahjoubi

N Bitri

E Aubry

F Chaabouni

P Briois

Back contact nature effect on the CZTS/ZnS based heterojunction

Keywords: Thin films, Spray, Cu2ZnSnS4, Back contact, Heterojunction, solar cells. Experimental

This work contributes to the discussion on the influence of the back contact on the electrical properties of Cu2ZnSnS4 (CZTS) based solar cells. Devices with noble metals back contact (Au, Ag and Pt) such as FTO/ZnS/CZTS/Au, FTO/ZnS/CZTS/Pt and FTO/ZnS/CZTS/Ag were investigated by means of the current voltage characteristic in the dark (FTO = fluorine-doped tin oxide). The originality of this work is that all active layers (absorbing and buffer layers) are deposited by the same system using spray pyrolysis technique. The metallic back contacts are sputter deposited. X-ray diffraction (XRD) and UV-visible spectrophotometry were used to investigate the main structural and optical properties of different layers constituting the solar cell. The electrical characterization achieved by I-V characteristic proves that all synthesized heterojunctions exhibit a rectifying behavior. Furthermore, the ideality factors of Au, Pt and Ag back contacts were estimated to 1.6, 2.4 and 2.8, respectively. The lower saturation current and series resistance are measured in the heterojunction using Au as a back contact. From this study, it is shown that Au back contact could be an alternative of Mo in CZTS based solar cell prepared by spray pyrolysis.

Introduction

Cu2ZnSnS4 (CZTS) thin films is considered to be a promising candidate for low cost and high efficiency thin film solar cells with record device efficiencies of about 12 % [1].

The elements of CZTS thin films is abundant in the earth crust, non-toxic and encouraging photovoltaic device performances Contrary to CdTe and CIGS absorbing layer, CZTS is a quaternary compound having p-type semiconductor behaviour with the kesterite crystal structure space group I-42m. It shows a relatively high absorption coefficient higher than 10 4 cm -1 and a direct band gap in the range of 1.4-1.5 eV [2, [START_REF] Ziti | Study of kesterite CZTS thin films deposited by spin coating technique for photovoltaic applications, Philippe Thevenin[END_REF]4]. These features make it a highly suitable material as an absorber thin film for low-cost thin film solar cells.

In addition to its application in conventional thin film solar cells, CZTS is widely used in others application such as gas sensor and photocatalytic [START_REF] Wang | Polyoxometalate electron acceptor incorporated improved properties of Cu2ZnSnS4-based room temperature NO2 gas sensor[END_REF][START_REF] Gurav | Cu2ZnSnS4 (CZTS)-based room temperature liquefied petroleum gas (LPG) sensor[END_REF][START_REF] Sampath | Structural, optical and photocatalytic properties of spray deposited Cu2ZnSnS4 thin films with various S/(Cu+Zn+Sn) ratio[END_REF]. Yuting Wang et al [START_REF] Wang | Polyoxometalate electron acceptor incorporated improved properties of Cu2ZnSnS4-based room temperature NO2 gas sensor[END_REF] have synthesized a Cu2ZnSnS4 (CZTS)-based gas sensor incorporated by polyoxometalate (POMs) electron acceptor by hydrothermal method. They confirm that the incorporation of POMs can form a shallow electronic trap, accelerate the electron transfer and enhance the performance of CZTS. Gurav et al [START_REF] Gurav | Cu2ZnSnS4 (CZTS)-based room temperature liquefied petroleum gas (LPG) sensor[END_REF] have invesigated the sensing liquefied petroleum gas (LPG) properties of p-CZTS/n-ZnO heterojunction.

Sampath et al have [START_REF] Sampath | Structural, optical and photocatalytic properties of spray deposited Cu2ZnSnS4 thin films with various S/(Cu+Zn+Sn) ratio[END_REF] studied the structural, optical and photocatalytic properties of spray deposited Cu2ZnSnS4 thin films with various S/(Cu+Zn+Sn) ratio. They founded that the presence of secondary phase significantly affects the photocatalytic performance of CZTS thin films.

In the literature, the structure of the solar cell based CZTS is directly copied from those used in Cu(In,Ga)Se2 (CIGS) technology such as p-type absorber (CZTS) and n-type buffer (ZnS) thin films constituting the heterojunction inserted between two electrodes. CdS thin film is the most buffer layer used in CZTS solar cells [START_REF] Washio | 6% Efficiency Cu2ZnSnS4-based thin film solar cells using oxide precursors by open atmosphere type CVD[END_REF][START_REF] Zhou | Fabrication of Cu2ZnSnS4 screen printed layers for solar cells[END_REF]. However, the toxicity, high cost of cadmium and its relative narrow band gap (around 2.41 eV) [10, 11] are considered obstacles for solar cells application.

For this reason, new semiconductors are studied to replace CdS. Among them, ZnS has attracted great attention as a promising buffer layer for solar cells owing to its tunable and direct band gap (3.65 eV) and earth-abundant elements [START_REF] Wi | Photovoltaic Performance and Interface Behaviors of Cu(In,Ga)Se2 Solar Cells with a SputteredZn(O,S) Buffer Layer by High Temperature Annealing[END_REF][START_REF] Al-Diabat | Growth of ZnS Thin Films using Chemical Spray Pyrolysis Technique[END_REF].

Numerous studies done on the electrical properties of the back contact in solar cells have shown that they strongly influence the solar cell performances. Mo film is the commonly used back contact. However, Mo back contact may be due to the formation of MoS2 at the interface.

Mo/CZTS back contact is associated to a MoS2 layer behaving as a blocking back contact. In this work, the effect of the nature of the metal back contact on the electrical properties of CZTS/ZnS based heterojunction prepared by spray pyrolysis is studied and the originality of this work is that all active layers (absorbing and buffer layers) are deposited by the same system using spray pyrolysis technique. contact layer. FTO coated on glass substrates is used as transparent front contact layer. It admits a sheet resistance in the range of 6-8 Ω square and has a thickness of about 500 nm.

The ZnS buffer layer has been grown on FTO substrates using chemical spray technique at 400°C for 30 min. The solution for ZnS layer was prepared from a solution composed with a mixture of Zinc chloride hexahydrate ZnCl2(6 H2O) (0.1 M) and of thiourea SC(NH2)2 (0.05 M) and has a thickness of 100 nm. The Cu2ZnSnS4 absorbing layer has been synthesized with the chemical spray process using the "Spray Sandwich" technique consisting in the deposition of three successively layers: ZnS/SnS2/Cu2S. The starting solutions were composed of zinc chloride hexahydrate ZnCl2(6 H2O) (0.01 M), tin chloride dihydrate SnCl2(2 H2O) (0.01 M), copper chloride dihydrate CuCl2(2 H2O) (0.04 M), mixed respectively with thiourea SC(NH2)2 (0.01 M) as chemical precursors. The CZTS thin films were obtained by spraying three solutions, starting by the deposition of the solution containing a ZnS, the following solution contains a SnS2 and the last solution contains Cu2S respectively at 420°C, 400°C and 300°C of the substrate temperature. The solutions were sprayed at the rate of 2ml/min. All chemicals were purchased from Sigma-Aldrich. The CZTS thin film has a thickness of 800 nm. The scheme of the heterostructure and cross-sectional micrograph of the solar cell based CZTS are given in Fig. 1.

Three metals are tested as back contact namely gold (Au), platinum (Pt) and silver (Ag).

All back contacts were deposited by direct current magnetron sputtering. Three different contacts (Pt, Ag, and Au) using masks are deposited successively of the top surface of the device (as shown in figure 1) in order to have the same heterojunction. The metallic coatings have been deposited by sputtering of metallic targets in pure argon atmosphere. Pulsed DC supplies powered the platinum (Pt, purity 99.95%), or silver (Ag, purity 99.5%) or gold (Au, purity 9.95%) targets mounted on balanced magnetrons, respectively an Advanced Energy Pinacle+ pulsed at a fix frequency of 100 kHz. The reactor was a 90-litre cylinder pumped down with a turbo molecular pumping system allowing a base vacuum of less than 10 -4 Pa before refilling with argon at the convenient pressure. The argon flow rate introduced in the deposition chamber was controlled by a Brooks flowmeter and his value is fixed at 50 sccm. In this condition, the total pressure was 0.5 Pa and was measured using a MKS Baratron Gauge.

The targets, 50 mm in diameter and 3 mm in thickness, are parallel to the substrate-holder and are spaced by 120 mm from each other. Their distance from the substrate holder (DT-S) has been fixed at 60 mm. During the deposition stage, the different substrates have been regularly rotated (20 RPM). The Pt, Au discharge current has been fixed at 0.2 A and 0.1A for Ag target.

The deposition time was 2 minutes for all coatings.

Characterization methods

The thickness of the layers has been determined by modelling the transmittance spectra of the translucent metallic coatings deposited on glass substrate (Scout software) [START_REF]WTheiss Hardware and software for optical spectroscopy[END_REF]. The total transmittance was measured by spectrophotometry with a Shimadzu UV-3600 spectrometer equipped with ISR-3100 integrating sphere (220-2600 nm), standard white board was used for the baseline. It has to be noticed that no effective medium approximations were necessary to obtain a satisfying model (deviation less than 4 10 -4 ) meaning that the metallic coatings were relatively smooth with a good surface coverage. The thicknesses of the Ag, Au and Pt layers are estimated at 50  2 nm, 35  1 nm and 50  1 nm, respectively.

In order to characterize the physical properties of the prepared layers, the layers were also sprayed on the glass substrates. The structure of the films was examined by high-resolution Xray diffraction (XRD, X'pert PRO, Philips) with monochromatic CuKα radiation (λ = 1.541874 Å) at 40 kV and 30 mA in -2 configuration from 10 to 70° with a step of 0.05°. UV-Vis spectrophotometer (Shimadzu UV 3100S) were studied to ascertain the transmittance and reflectance measurements for determining the optical parameters such as the absorption coefficient and the optical band gap energy. The optical absorption coefficient (α) is evaluated from the transmittance (T) and reflectance (R) measurements using the following relation:

𝛼 = ( 1 𝑑 ) × ln( (1 -𝑅) 2 𝑇 )
The optical band gaps are estimated from the extrapolation of linear region of the plots of (αhν)2 versus hν curves. the optical band gap energy (Eg) is obtained according to the Tauc's relation

αhv = A(hv -Eg) n
where α is the absorption in semiconductor, hυ is photon energy, Eg offered the bandgap energy, n depends on the transition probability, it takes the value of ½ or 2 correspondings to indirect and direct bandgaps, respectively

The electrical properties were studied using current voltage (I-V) characteristic in the dark with a sourcemeter Keithley 2400. and (220) planes of the cubic phase, respectively (JCPDS Card no. 05-0566) with a space group F-43m. Furthermore, in addition to the ZnS phases, the presence of ZnO phase is noticed. As shown in Fig. 4, the plane (101) of hexagonal wurtzite ZnO structure is clearly visible. This is related to the fact that the preparation of the layers by spray is done in air and in aqueous solution which do not sufficiently prevent from the oxidation of the as-grown layer [21].

ZnS buffer layer properties

The ZnS film exhibits a medium transmittance value in the visible (~ 30-35 %) and a relatively high transparency (> 80 %) in the near infrared region for wavelength higher than 1400 nm (figure 5a). From the transmittance spectrum, the optical band gap energy of the ZnS thin film has been estimated using the Tauc plot method. The band gap energy value is 3.3 eV (Figure 5b).

ZnS film deposited has a band gap equal to 3.34eV, which is narrower than ZnS pure. This gap value has been found by several authors [START_REF] Deepa | Highly transparent ZnS buffer layer prepared by ultrasonic spray pyrolysis for photovoltaic applications[END_REF][START_REF] Ke | Effect of temperature on structural and optical properties of ZnS thin films by chemical bath deposition without stirring the reaction bath[END_REF] and who have shown that: more the temperature of the substrate increase, more the gap energy is lower than of pure ZnS [START_REF] Ke | Effect of temperature on structural and optical properties of ZnS thin films by chemical bath deposition without stirring the reaction bath[END_REF]. ZnO thin film has a gap energy of around 3.2eV [START_REF] Mondal | Effect of Al doping on microstructure and optical band gap of ZnO thin film synthesized by successive ion layer adsorption and reaction[END_REF]. Thus, more the layer interacts with oxygen, there is a formation of the ZnO phase and the energy of the gap is lower than of pure ZnS. This may explain the presence of the ZnO phase in the X-ray diffraction spectrum obtained. The optical band gap of CZTS film was calculated from the linear extrapolation plot of (h) 2 vs h with the h-axis (Fig. 7). The value is closed to 1.48 eV, which seems consistent with the ideal CZTS thin film for solar cells application.

CZTS absorbing layer properties

Operating electronical characteristics of the solar cell devices

The metal/semiconductor heterojunctions prepared with different back contacts were investigated using the current-voltage (I-V) characteristic in the dark. The current-voltage (I-V) characteristics device yields to important information about junction parameters such as series resistance (Rs), diode ideality factor (n) and saturation current (Is).

Fig. 8 shows the current-voltage curves of the FTO/ZnS/CZTS/M, with M = Au, Ag or Pt, solar cells in the dark. It is clear that no noticeable difference between the three characteristics can be observed. All heterostructures exhibit a rectifying behavior meaning that the barrier potential formed by the contact of the metal and semiconductor is high enough to not conduct the current in both directions. Theory of thermionic emission was used to express this behaviour. According to this theory, the current is expressed by the following equation:

𝐼 = 𝐼 0 [exp ( 𝑞𝑉 𝑛𝑘𝑇 ) -1] (Eq. 1)
Where I is the measured current intensity in A, V is the applied voltage in V, I0 is the saturation current (A), k is the Boltzmann constant (J. K -1 ), q is the elementary electric charge (C), n is the ideality factor and T is the absolute temperature in K. The ideality factor n is given by the following equation:

𝑛 = 𝑞 𝑘𝑇 ( 𝑑𝑉 𝑑(𝑙𝑛𝐼) ) (Eq. 2)
The factor is determined from slope of the linear part of forward bias ln(I)-V plot. The plots of forward bias ln(I)-V characteristics of different heterojunction structure are shown in Fig. 9.

According to Sah-Noyce-Shockley theory [28], the ideality factor is closed to 1 if the forward current is dominated by the recombination in the quasi-neutral regions of the p-n junction (far from the p-n contact region), while it would be about 2 for a forward bias current dominated by the recombination in the space charge region (p-n contact region). In table 1 The origin of the large value of n may be due to the metal/CZTS contact. Indeed, when the contact is not ohmic, the heterojunction can be modeled as a series of diodes and resistors in series. According to Shah-Li-Schubert, the ideality factor is the sum of ideality factor of each diode. Al and Ag back contacts can be used to form Schottky contact with CZTS, contrary to Au, which can have ohmic contact with CZTS.

The series resistance Rs is very important parameter in the performance of the solar cell. Indeed, a too high series resistance considerably reduces the form factor and consequently decreases the efficiency of the cell. The series resistances were calculated from I-V curve at high bias, their values are in the order of Ω, as reported in

Conclusion

In this study, CZTS/ZnS based heterojunctions were produced by thermal spray pyrolysis technique. Three different back metal contact (Pt, Au and Ag) were deposited on the absorbing layer by magnetron sputtering. Three different solar cells according to the metal nature of the back contact were tested to investigate its influence on the device electronic properties in order to find an alternative of the commonly used Molybdenum.

The devices electronical characterization exhibits a rectifying behavior. The electrical parameters prove that the Au metal can be efficiently used as back contact for CZTS based heterojunction solar cells as an alternative to Mo.

Indeed

  Scragg et al. [14] recommended reexamining the choice of molybdenum at CZTSSe|Mo. Patel and Ray [15] numerically simulated the current-voltage (I-V) characteristics of a Al:ZnO/i-ZnO/CdS/CZTSSe/BC solar cell trying to find the optimum BC (back contact) which would give the best cell performances. In this context, three different metals (Au, Pt and Ag) are tested as back contact instead of commonly used Mo.

Fig. 1 Fig. 2 XFig. 3

 123 Fig.1 Heterostructure and cross-sectional of the solar cell based CZTS

Fig. 4

 4 Fig.4shows the X-ray diffractogram of the ZnS thin film deposited on glass substrate. The ZnS film crystallizes in both cubic and hexagonal structures. The hexagonal structure is marked by the presence of diffraction lines at 11.31° and 46.48°, which are assigned to (0007) and (1023) planes according to the JCPDS file (83-2336) with a space group P3m1. The cubic phase is observed by the presence of diffraction lines at 28.46° and 47.55° corresponding to the (111)

Fig. 4 XFig. 5

 45 Fig.4 X-ray diffractogram of ZnS thin film synthesized by spray pyrolysis

Fig. 6

 6 Fig.6 shows the X-ray diffractogram of Cu2ZnSnS4 (CZTS) thin films deposited by spray sandwich technique on glass substrate. It can be seen three diffraction peaks at 2= 28.52°, 47.53° and 56.38° which are attributed to the kesterite Cu2ZnSnS4 thin films (JCPDS00-026-0575), space group I-42m. The three peaks correspond to the (112), (220) and (312) planes of Cu2ZnSnS4 structure, respectively, with the direction [112] as preferential orientation. It is noteworthy that no other peak related to any secondary phase are observed, despite rather oxidizing spray conditions, which is in agreement with the previously published structural results [25].

Fig. 6 X

 6 Fig.6 X-ray diffractogram of CZTS thin film by spray pyrolysis

Fig. 7

 7 Fig. 7 Plot of (αhν) 2 versus photon energy (hν) of CZTS thin film

Fig. 8 I

 8 Fig.8 I-V characteristics of different CZTS/ZnS heterojunctions prepared with different back contact metals.

  are reported the calculated values of the ideality factor, in addition to the series resistance and to the saturation current. As it can be seen, the ideality factors calculated in the realized heterojunctions are depending on the nature of the used metal contact. They are respectively equal to 1.6, 2.4 and 2.8 for Au, Pt and Ag contact, probably meaning that the forward bias current would be mainly controlled by the charge carrier recombination in the space charge region formed by the p-n contact which exhibits an electric field. It can be observed that the lowest value of ideality factor is obtained using Au as metal contact. This result is in agreement with that found by Boutebakh et al[START_REF] Boutebakh | Electrical properties and back contact study of CZTS/ZnS heterojunction[END_REF]. They observed a similar low value of n obtained with Au back contact, as well as large value of n for the Ag and Al back contacts.

table 1 .

 1 These values can explain the obtained large ideality factor as mentioned above. The resistance series is lower when using Au as back contact. This can be due to the high work function of Au by comparison to other metals. These results are in good agreement with those found by Boutebakh et al[START_REF] Boutebakh | Electrical properties and back contact study of CZTS/ZnS heterojunction[END_REF], where they showed that the Au can be used as an alternative to Mo in CZTS-based heterojunctions.The saturation current is obtained by extrapolating the linear part of the logarithmic plot of equation (Eq.1) to V = 0. The saturation current values for heterojunctions (Au, Pt or Ag back contact) are shown in Table1. It is clear that the heterojunction prepared with Au as back contact has the lowest value. Several authors report that the open circuit voltage in a solar cell is better with a low saturation current.

Table . 1

 . Electrical parameters of heterojunctions prepared with different metal back contact measured in dark: n ideality factor, I0 saturation current and Rs series resistance.

	Heterojunction	Ideality factor n	Series resistance Rs (Ω)	Saturation current
	structure			I0˟(10 -5 A)
	Ag/CZTS/ZnS/FTO	2.8	39	11
	Pt/CZTS/ZnS/FTO	2.4	29	9.5
	Au/CZTS/ZnS/FTO	1.6	25	6.5