Caroline Guibet
email: caroline.guibet-lafaye@ens.fr

Lafaye Centre

Maurice Halbwachs

ETHICS of INHERITANCE 1

Both in the U.S. and in France, inheritance is probably the main factor of wealth concentration among the richest part of the population, and of its intergenerational reproduction. In so far as wealth is an opportunity, a reform of inheritance tax could be a mean to ensure a fairer distribution of opportunities in the society. Many reforms of inheritance systems have been conceived at least since Bentham. The identification and the analysis of ethical properties of reforms as the ones designed by Mill, Rignano, Solvay, Huet and Haslett show that the latter is certainly the one which most satisfies the requirements of an ethics of inheritance.

Key words Bequest, equality, opportunity, tax, Haslett's quota.

Inherited wealth is generally quite unequally distributed: it is nearly as unequally distributed as wealth (generally considered) and a great deal more unequally distributed than income.

Inheritance is probably the main factor of wealth concentration among the richest part of the population, and of its intergenerational reproduction 2 . In the United States, inheritance is primarily responsible for the fortunes of no less than sixty-seven percent of men who qualifies as "ultrarich". In countries like France, inherited wealth accounts for a large part of all wealth 1 This paper has been started during my participation to the network "Applied Global Justice" (Fifth Framework Program, European Commission, HPRN-CT-2002-00231). I thank all its member and especially his coordinator, Jean-Christophe Merle. I also particularly thank Ayelet Banai for its careful review of the paper and the relevant remarks he suggested to me. Finally I thank my husband for the help he kindly provided to me while I wrote the paper.

2 Thus, more than half of American citizens who have died rich (the top 1%) have received a sizeable inheritance. The 10 th edition of World Wealth Report underlines the stake of intergenerational transfers of wealth and inherited wealth: 90%

possessed (generally estimated at around 40%) and represents the largest descending monetary transfer: three times as much as wealth received in the form of inter vivos gift for example 1 . In general, transfers of property by means of inheritances and gifts also play a very important role in the processes which determine the distribution of income and wealth. Therefore the problem of distribution lies, for an important part, in the accumulation of wealth, especially through inheritance.

Nevertheless, inheritance taxation remains a problematic issue. This taxation engenders a feeling of spoliation which impedes any attempt at reform. While inheritance is the main origin of the intergenerational reproduction of inequalities, no government will attempt to reform inheritance taxes -except in order to reduce them. The figures above however justify an inheritance tax reform and, moreover, require to treat of the inheritance tax issue not only as an economical question but also as an ethical one. In this way, the bequest issue appeals for an "ethic of inheritance". In fact, the values of freedom and equality -linked to the issue of inequality generated by inherited wealth -, the interpretation of equality, and the status of the family are among the main factors that influence the way one looks at inheritance. Furthermore, the unequal distribution of inherited wealth and bequests is a crucial vector of the inequality of opportunities. In fact, if one was born with a nice estate, one's opportunities are far greater, ceteris paribus, than those of the poor who was provided with barely for subsistence in his childhood.

For these reasons, the question of inheritance and inheritance tax is not one which can be tackled only by purely 'economic' arguments.

The current debate which opposes defenders of a reform of the right to inherit (Rawls, Haslett) and defenders of a limitation of the right to bequest (Nozick) brings about older propositions to reform inheritance system. Our aim will be to demonstrate that in so far as inheritance is not only an economical or fiscal issue, ethical arguments should be used to assess these propositions. In this investigation, the concern for a reduction of inequality of opportunities will play a crucial rule since inheritance is the main vector of intergenerational reproduction of wealth concentration. In other words, our point will be to identify the inheritance reform the most able to promote equality of opportunities. To lead this investigation, we will firstly analyse the main ethical claim defending the right to bequest: bequest is motivated by altruism. Then we will discuss some objections often raised against reform of inheritance tax.

Finally we will demonstrate why a reform of the right to inherit (i.e. to receive) bequests is more relevant and practicable, considered from an ethical point of view, than a reform of the right to bequest.

Is bequest altruistic?

Some authors such as Philippe van Parijs suggest that the prohibition of bequest, advocated by Roemer, "amounts in fact to make egoism as the only legitimate motivation of action" 1 . The political attempts to reform inheritance tax often raise a feeling of spoliation. The latter is motivated by the conviction that State should not intervene in private issues and by a longstanding idea that bequest was essentially an altruistic attitude, which expresses the desire to help one's own children at a particular moment of their life and which reflects filial feelings 2 . The stereotyped representation of inheritance corresponds to the model based on pure altruism, i.e. on parental love and filial piety. On these grounds, it seemed illegitimate to impose limits to altruism. Nevertheless, this traditional image of bequest and of its motivation as strictly altruistic seems wrong. In the American literature of the seventies and early eighties, altruism was the dominant hypothesis. Since then there has been a gradual change of opinions concerning the leading bequest model 3 .

In fact, there are at least three kinds of bequest. Bequest can be (1) accidental or unplanned bequests, (2) voluntary or planned bequests, (3) capitalistic or entrepreneurial. When the bequest is voluntary, its motivations can be altruistic, paternalistic, "retrospective", either grounded on mere exchange, or on various strategies 4 . This specification, quite remote from the traditional and popular picture of bequest, is specifically relevant because it allows us to identify (i) the vector of the bequest, (ii) the kind of relations existing within the family, (iii) the structure of preferences, (iv) the kind of information held by each member of the family, and finally (v) the characteristics, in terms of capabilities or life expectancy, of the family members. Let us describe the properties of these various kinds of bequest. Which motivations each one has in each case?

(1) When the bequest is accidental -and, therefore, unexpected -it does not express any desire of the parents but only their concern for themselves (i.e. precautionary savings) and a preference for deferred consumption. (2) When the bequest is voluntary and planned, it could be motivated by altruistic reasons but also by strategic or paternalistic reasons. [START_REF] See | The economic way of looking at behavior[END_REF] The "capitalist or entrepreneurial" bequest is the result of an accumulation for its own sake. The person who initiated this accumulation is the main beneficiary of it1 . Hence and although accidental bequests are typically limited to the consumer's life cycle, voluntary bequests are essentially based on family considerations. Finally, capitalist bequests generally have a horizon that extends over the lifetime of the wealth holder. They are not primarily motivated by family considerations -even though the dynastic family is used as the channel allowing for the perennity of the estate.

In this way, it is obvious that (a) not all bequests are motivated by altruism and (b) that among bequests that express familial concerns, not all bequests are grounded on generosity and filial solidarity. For instance, among the voluntary bequests and voluntary gifs, some are the result of an "exchange strategy" which can be in some case fair but, in other cases, unfair for some of the members of the same family. The level of altruism decreases gradually from altruistic and paternalistic bequests to bequests motivated by an "exchange strategy". For example, in the first case, when they make decisions on consumption and savings, parents take into account their children's preferences while anticipating their income and future needs. But when the bequest amounts to an exchange, it is less altruistic: parents take care of their children until they reached adulthood and promise to leave them an inheritance (often their work tools). In exchange, children promise to look after their parents once they reach old age, or even earlier in the event of failing health. Finally the strategic bequest is a step further remote from an altruistic bequest. In the procedures of a game-theory approach2 , strategic inheritance brings parents at the beginning of retirement face to face with their children who are just starting their working lives. The parents want each of their children to help them and pay additional attention to them. They extract the maximum from each of their children under the threat of disinheriting them.

These analyses obviously show that bequest can not be considered as an expression of altruism nor of filial devotion solely. It is not possible to invoke bequest motivations -not even altruism -in order to prohibit any limitation of inheritance. Moreover, we are also convinced that not all kinds of motivations are equally valid and respectable from an ethical point of view3 . For this reason, an ethical approach is relevant to the legitimacy of inheritance tax, and not only an economic one.

Limitation of the right to inherit vs. limitation of the right to bequest.

2.1 The right to bequeath an item should not be a transferable right.

The reform of inheritance tax is an old issue. Several models of inheritance tax have been proposed. Bentham, for example, proposed to widen the scope of the law of escheat, in combination with a limitation of the power to bequest1 . Nozick, for his part, suggested that the bequest has to be limited to one passing that cannot be repeated. This sets the principle according to which the right to bequeath an item is not transferable by bequest but adheres only to the original earner or creator2 . What people have not earned themselves, cannot be passed on by inheritance. Nozick's proposal, as he advocated in The Examined Life, constitute a simplified version of the Rignano-Solvay proposal.

In his first book 3 , Eugenio Rignano (1870-1930) proposed to consider the right to bequest according to the "origin" or "age" of the property involved. What is now known as the "Rignano principle" stipulates that the higher the number of transfers a piece of property has been subject to, the lesser the power of the owner to dispose of it by will. In other words, the rate of inheritance taxation levied at each transfer of property increases with the number of transfers, and after a limited number of transfers reaches the level of 100%. That is, when a man dies, his possessions have to be split up into different parts according to the number of times his possessions have been transferred (by means of inheritance or gift) to reach its present state. This means that a distinction is made between the goods and money which constitute the own savings of the deceased (0 transfers), the goods and money which he had inherited from other persons and which came from their own savings (1 transfer), the goods and money which he had inherited from other persons who in their turn had inherited them from others (2 transfers), etc. This reform comes down to the introduction of a new principle of progressiveness in inheritance taxation, i.e. the principle of an inheritance tax progressive through time. It obviously imposes limitations to property transfers. In fact, one of the aims of the alternative property regime, designed by Rignano, is to de-cumulate private fortunes fairly rapidly, so as to prevent the creation of large differences in private wealth.

At the same time, the Belgian industrialist Ernest Solvay (1838Solvay ( -1922) ) formulated a similar proposal: the inheritance tax should be made progressive with the number of generations between the original creator of property and its present owner1 . In the same spirit, François Huet (1814Huet ( -1869) ) proposed to change property rights in accordance with the distinction between 'selfcreated' property and 'inherited' property: property which has been accumulated by its owner may be bequeathed freely, but property which has been inherited by its owner will be confiscated by the State when the owner of it dies2 .

All of these proposals are relevant for our issue, firstly because the legal and fiscal frameworks in which these transfers take place have not changed drastically since the beginning of the 20 th century, nor have the arguments used in the inheritance tax debate of the 1920s 3 . Secondly, it seems more relevant, from our point of view, to concentrate on a limitation of bequest -rather than on an abolition of inheritance -because the former can be implemented more immediately and with less constraints. From this prospect, Rignano/Solvay proposal -and Haslett's one as we will see later -are the more conclusive. Finally, the introduction of a differential treatment for 'earned' and 'inherited' wealth involves important ethical issues we should explore to set an ethics of inheritance.

Objections to reforms of inheritance system.

a) Inheritance assessed from a "personal" and an "impersonal" standpoints.

There is a strong opposition to any limitation of bequest. The obstacles are either psychological, human, due to the desire of wealth accumulation and personal choices, or related to incentives. Most of the time, reforms are perceived as an injustice from the part of the State against individuals. Wealth is generally understood as the result of individual merit or of family deserve lead on several generations. Nevertheless we have to take into account the negative externalities resulting from the practice of allowing unrestricted gifts and, especially, the negative externalities in the field of opportunities, inequalities of wealth and so on, perpetuated by this practice.

Any possible answer to objections against reforms of inheritance tax requires to know whether such a reform is (aside from its public support) justifiable. A solution is provided by the distinction between "personal" and "impersonal" standpoints 1 . In this framework, one of the main objections to inheritance tax reforms is that the institutional settlement of a limit between "personal" and "impersonal" spheres prohibits the legitimate expression of preference for one's own family. Nevertheless, firstly it is not ineluctable to believe that the privilege to bequest to one's own children the means of an independent life reflects familial devotion, which absolutely does not depend on State's competences. Secondly, we could expect that this belief will change with time and along inheritance reforms, and that one day it will not go without saying that one is rich because his father was rich. Individual values will change if they face new situations 2 . In this respect, our goal is not to abolish the action of priority and preferences bestowed to one's family but to restrict their effects to the personal sphere and to limit its effects on wealth concentration and on the general distribution of opportunities within the society. In fact, we believe that the scope of the priority given by the family to its members should be institutionally defined.

Nonetheless the personal standpoint has to be taken into account. Indeed, one of the advantages of a reform of inheritance -as Rignano/Solvay's one -rather than a mere abolition of inheritance is that it considers the "familial preference" (the concern for one's own family). In this perspective, F. Huet's proposal should also be considered. An inheritance tax of 100% on the goods inherited from the grandfathers and, as Rignano suggests, a progressive tax (according to time) is a way to conciliate the requirements of personal and of impersonal standpoints. An excessive impartiality is not imposed on individuals. These kinds of proposal take into account the fact that, most of the time, the affective links are stronger between parents and children than between grandfathers and children. These proposals also avoid the capitalistic bequest, while preserving the familial and economical resources, belonging to the restricted familial sphere.

b) The incentive objection.

Another sharp objection to a progressive inheritance tax is that it will reduce people's incentives to be productive. Against this critic, several arguments are relevant but one is particularly crucial. Empirical studies 3 suggest that people with no children to inherit their wealth 1 See T. Nagel, Equality and Partiality, New York, Oxford University Press, 1991, p. 12. 2 Albert Hirschman defended the thesis of values cycle between a focus on the public and a focus on the private (A. Hirschman, Shifting Involvements, Princeton, University Press, 1982). 3 are certainly no less productive, on average, than those who do have children. People are motivated to be productive for many reasons other than merely that of leaving their money to their children. These reasons include, for instance, supporting one's children well while they remain dependent but, as well, saving for old age and enjoying their wealth by spending it on themselves. A fundamental reason for being productive is success and, thereby, gaining respect from others as well as self-respect. Many business executives, lawyers, engineers or research scientists try just as hard to "win".

But our opponents will still argue that even if a broad reform on inheritance tax would not decrease productivity by decreasing people's incentives to be productive, it will decrease productivity by decreasing people's incentives to save and invest. As D. Haslett underlined it, in the case of abolishing inheritance, no one really knows for sure in fact how -if at all -these reforms would affect savings and investment. There are reasons to believe, however, that the effect may not be serious. The economic structure is always such that as much of society's newcapital savings and investment today is corporate savings and investment, which will be unaffected by these reforms. Conversely, much savings and investment by the rich takes the form of trading in previously-issued stock, and therefore does not create new capital. We cannot assume that any given percentage drop in overall savings and investment by the rich will necessarily result in the very same percentage drop in new-capital savings and investment.

Moreover -and the argument is here conclusive -even if inheritance is abolished or if a high inheritance tax is set, people must continue to save for the future anyway, since no one knows for how many years and in what state of health, they or their spouse may have to live off these savings.

Likewise, it is plausible that even the abolition of inheritance will give rise to an important countertendency, often overlooked, in the form of increased savings and investment 1 . With no or less prospects for inheritance, the need for people to save for their own future will be greater than ever, and, accordingly, so too may be their savings. Even if inheritance is abolished, many, especially the ultrarich, will continue to hang on to their fortunes merely from pleasure, power, 1 Considering the case of an abolition of inheritance, D. Ascher shows that even if it results in an unacceptable decline in investments, there would be better ways of reinstating the previous level of investments (see M. L. [START_REF] Ascher | Curtailing Inherited Wealth[END_REF], "Curtailing inherited wealth", Michigan Law Review, 89, esp. pp. 102-11;[START_REF] Duff | Taxing Inherited Wealth: A Philosophical Proposal[END_REF], "Taxing inherited wealth: A philosophical proposal", Canadian Journal of Law and Jurisprudence,6,[28][29][30][31][32][33][34][35][36][37]. For a detailed answer to the savings and investment objection, see D. [START_REF] Haslett | Capitalism with Morality[END_REF], chap. 6. and prestige. Finally, governments have many measures at hand that can be used to motivate more savings and investment 1 .

c) The economical and social interdependence.

In response to the economic argument we should recall that, in the majority of cases and maybe in all cases, the wealth some people benefit is a result of the cooperative social structure.

The profits generated by the capital and the wealth accumulation depend on the social structure to which everyone participate. Therefore a redistribution of property or a redistribution of these profits at least seems justified. This argument has been often pointed out, for example by J.

Wedgwood, when he observed that "for a good deal of property is not the result of the owner's effort or thrift; and not all that is the result of his efforts represents an economic service to the community" 2 . Rawls also underlines this economic conjunction and the fact that in a wellordered society, the profits produced by the exploitation of individuals' talents should be redistributed. This requisite is summarized in the "principle of solidarity of talents", which considers "the distribution of natural talents as in some respect a common asset and to share in the greater social and economics benefits made possible by the complementarities of this distribution" 3 . In fact, the talents can be exploited by their holders only in the framework of a society, that is, in the framework of a set of social conventions and institutions.

Advantages of Rignano/Solvay's proposal.

Some of the main objections to an inheritance tax reform are now put aside. The next step is to suggest the best way to design this reform. It requires to consider: (i) the beneficiaries of the transfer; (ii) the resources transferred; (iii) the bequest at stake and, in particular, the capitalistic bequest in so far as we know that while accidental inheritance touches all classes of society, capitalistic bequest concerns only the well-to-do.

(i) Any inheritance reform should answer the first question: "who is concerned by inheritance?". Most of the proposals we known distinguish between the bequeathers. In the same spirit that Rignano, Solvay and Huet's proposals, the American Richard T. Ely (1854Ely ( -1943)), for 1 D. Haslett, for example, suggests to use the amounts collected from abolishing inheritance to subsidize investments or, if the amounts thus collected are insufficient, to use instead amounts collected from ordinary taxes (D. Haslett, "Distributive Justice and Inheritance", in Erreygers & Vandevelde (eds.), 1997, p. 146 example, wanted the inheritance tax to be progressive, graduated according to the degree of relationship and to the amount inherited. He even suggested that "the state or the local political unit -as town or city -must be recognized as a co-heir entitled to a share in all inheritances" 1 . In general, we can admit -as a result of common sense and of a concern of a well-understood partiality -that surviving spouse and children should benefit from a special treatment regarding the capitalist bequest. By the way, the personal point of view will be taken into account2 .

(ii) Secondly, we have to consider the resources transferred. As we have seen before -in particular in Rignano's model -it seems relevant to distinguish between: (α) property which an owner has accumulated as a result of his or her own efforts (i.e. 'self-created' property) and (β) property which he or she has inherited from others (i.e. 'inherited' property). The Rignano proposal is meant to encourage individuals to work and save. To achieve this aim individuals have the right to own and bequeath private property, but only insofar as it is necessary and sufficient to make people work and save 3 . The possibility to bequest the accumulated goods, acquired by work, thus reply to the disincentive objection and to the objection advocated the merit one had in his life and the legitimacy to keep the results of his work. For these reasons, Rignano's proposal, which differentiates the right of bequest according to the 'origin' or 'age' of the property to be bequeathed, is one of the most interesting. But in this reform, the impersonal standpoint prevails4 .

Why should we prefer an inheritance reform rather than a bequest reform?

Even if the reform of the progressiveness of inheritance tax according to its origin seems to be one of the best ways to reform inheritance tax, we ought to consider an alternative option which takes more into account the personal standpoint, i.e. a reform of the right to inherit (i.e. to receive) bequests. This reform has the advantage not only to fight wealth concentration but also to enhance equality of opportunity. This "limitation of the right of inheritance" is stood up by Mill who was nevertheless a defender of private property and bequest 5 . Mill advocated high and The Haslett's quota presents several advantages. (α) First, the quota would break up the fortunes of the ultrarich people 1 and would disperse the estates of the wealthy -more widely than a quota on how much any given person may give 2 . In fact and since a strict lifetime inheritance quota precludes people from receiving huge sums of wealth through inheritance, it will certainly result in a distribution of wealth more equally. (β) Secondly, a quota goes a long way toward avoiding the potential savings and investment objection 3 . (γ) Moreover this quota will not prevent the passing of family heirlooms, homesteads and small family businesses from one generation to the next as argued by opponents to an inheritance abolition 4 . In this way, Haslett's proposal avoids the objection which emphasizes family and filial links or feelings. (δ) Finally the quota will avoid some of the insidious loopholes that a progressive inheritance tax will necessarily face.

This proposal might be associated to other propositions. For example we could imagine that only some kind of goods could be bequest (for instance houses, in a limit of a precise valuable amount) and other not 5 . The individuals would be allowed to choose the goods they will bequest and the goods they will not. This clause will also be a mean to take into account the personal standpoint. Finally the limit on the value which can be inherited could be introduced from the existing inheritance tax in country as the United States, Great-Britain or France. But the main difficulty remains to set the maximum amount which could be transferred.

How an inheritance reform can enhance equality of opportunity?

3.1 Dispersing wealth.

The assessment of reforms of inheritance tax in the prospect of an "ethics of inheritance" ought to refer not only to the balance between personal and impersonal standpoints, involved in these reforms, but also to their ability to correct inequalities of opportunities due to morally 1 Gifts and bequests are mainly concentrated among the richest households. In the United States today, inheritance is primarily responsible for the fortunes of no less than sixty-seven percent of the "ultrarich" people. Based upon DGI-Insee, 1987 French estate data, the share of total bequest of the bottom decile is 0,7% while the total share of the top 10 decile is 51,2%. The proportion is more than half among the top 1% of the bequest distribution. This privileged group (the top 1%) accounts for 19% of total bequests, but for more than 54% of the total amount of gifts while the bottom decile receive 0,1% of this total amount. 2 We recall that the share of inherited wealth, in total saving, amounts to 40%. 3 See D. Haslett, "Distributive Justice and Inheritance", p. 149. For instance, for those who know a number of eligible people to whom they want to leave some wealth, the quota provides more motivation for savings. 4 This is especially true if this quota is combined with regulations that [START_REF] Van Parijs | Qu'est-ce qu'une société juste ?[END_REF] give first opportunity to purchase them to family members who have been designated by the decedent in his or her will, and that (2) also give these same family members lenient, long-term credit terms.

5 With a specific care to the survival spouse and the minor children.

arbitrary factors. But in this perspective, we face a major difficulty: on the one hand, the bequest is not compatible with equality of opportunity but, on the other hand, an inheritance tax reform could enhance inequality of opportunity rather than diminishing it. Therefore, we will now demonstrate how restriction on inheritance tax could enhance equality of opportunity or, at least, enhance equity in choices for a great diversity of life prospects.

The equality of starting points or of initial endowments involves, practically, the prohibition of any kind of gifts because there is no difference between inheriting a company at the age of 40 years old or at birth 1 . In fact, inequality of opportunity is strongly associated with inequalities of wealth. In some respect, "wealth opportunity": "those who inherit large fortunes have, as a result, significantly more opportunities than those who do not" 2 . Do high progressive inheritance tax -as designed by Rignano -or a restriction on the right of inherit -advocated by Haslettare adequate devices to enhance equality of opportunity?

If bequests and gifts are allowed, we have to recognize as legitimate inequalities which result from previous inequalities of opportunities, and the more inheritance there is, the less equal people's opportunities will be. But, from an ethical point of view, people do not deserve to profit differentially from the luck of the birth lottery, which distributes valuable assets (skills, parents, citizenship, etc.) in an arbitrary and highly unequal way. In this respect, an inheritance tax reform helps equalizing starting points: an excessive concentration of wealth in the hands of very few people will impede the implementation of equity of opportunity 3 .

Furthermore even if people have justly earned (under conditions of equal opportunity) their estates, it does not follow that they have the right to exacerbate differential opportunities in the next generation by distributing their estates to favoured individuals. We should here not only consider the current allocation of opportunities but their distribution in the future. The requirement of equality of opportunity for the next generation may well trump such a right. Secondly, even if inheritance tax is not the best mean, on its own, to guarantee equality of opportunity, it is obvious that the actual inheritance practices, at least in France, largely contribute to the 1 The average age at which inheritance is received during a given year is around 48 in France (see L. Arrondel, A. Masson and P. Pestieau, "Bequest and Inheritance: Empirical Issues and France-U.S. Comparison", in G. Erreygers and T. Vandevelde, 1997, p. 101), while gifts are naturally received earlier: at 38 on average [START_REF] Laferrère | Héritiers et héritages[END_REF]1991).

2 D. Haslett, "Distributive Justice and Inheritance", p. 141-142. Huge fortunes are often put in trust, not for children, but for grandchildren. These funds then become available to the grandchildren upon their reaching age 21, enabling them to get their inheritance at the start their careers after all. This device is common among rich Americans. 3 For this reason, Meade suggests to impose a high and progressive tax on gifts received during one's life (see J. E. Meade, Efficiency, Equality and the Ownership of Property, p. 54-58). Rawls also underlines the importance of preventing excessive accumulation of property and wealth (Theory of Justice, p. 63) because the fair equality of opportunity and freedom are put in jeopardy when inequalities of wealth exceed a certain limit (p. 246). reproduction of social inequalities1 . Both in the U.S. and in France, inheritance is probably the main factor of wealth concentration among the richest part of the population, and of its intergenerational reproduction. Therefore, some limitations on the amount individuals are entitled to receive during their life should be settled.

Precisely, the more efficient way to spread huge fortunes could be -as Haslett suggests it -to institute a ceiling for how much a person can, throughout his or her life, receive from all sources.

By the way, great fortunes2 would tend to be broken up -whether by increased personal spending or by this tax -and, thereby, it will bring about a more equal distribution of wealth in the next generation. Haslett's quota will achieve greater equality of opportunity by spreading fortune among more people.

As we have seen above, the quota is set at the average value, today, of an adult's estate at the time of his or her death3 . It will conveniently contribute to a wealth fragmentation and to an improvement of equality of opportunity because most people know at least five people for whom they really care and who will not yet have received any, or much, of their quota -children, grandchildren, great grandchildren, friends, close relatives, the children of close relatives, loyal employees, and the like 4 -that is at least five times the value of the average estate. Therefore with this measure we can expect that, in the next generation, wealth become more equally distributed.

If everyone profit from this redistribution, the reform would greatly increase the opportunities for self-realization and individual welfare, and for example opportunities to pursue one of the higher-paying occupations, such as doctor, lawyer, business entrepreneur, and so on. This argument -focused on the long run -is also an answer to the objection according to inheritance tax reform as negative effects on the distribution of educative opportunities. Some economists as Becker and Kothkoff 5 , and others as Bracewell-Milnes 6 , emphasize that a direct correlation between an increase of inheritance tax and an improvement of equality of opportunities seems problematic, because restrictions on the amount of material wealth parents can donate or bequeath to their children will lead them to spend more on the education of their b) Familial links.

Moreover, a reform of inheritance system will induce an evolution of family links. One of the perverse consequences of current inheritance systems is to give a pre-eminent importance to material assets in what is hung from parents down to children. In fact, many people seem to view what parents can give to their children primarily in terms of wealth. But there are far more important things that parents can give to their children, such as their time and love, skills, capacities and values that will enable their children to succeed in life on their own. By reforming drastically inheritance system, perhaps parents will then concentrate more on giving their children not mere wealth, but what is more important to experience, the deep satisfaction of succeeding on their own: love, capacities, values and strength of character. The implementation of Haslett's quota, for example, will reinforce the fact that the most important part of this bequest is immaterial. By this way, the ability the parents will demonstrate in providing properly their children to face life will be fairly assessed. This will contribute to contradict the common idea according to it is fair and admissible that one is rich because his father was rich.

Conclusion

The prior examination of some reforms of inheritance tax was aimed to draw the main lines of an ethics of inheritance, devoted to reduce equalities of opportunity and especially the ones involved in current inheritance tax systems. Our approach was ethical rather than economical. Its objective was not to abolish the familial preference but to limit its social effects and especially its undesirable consequences on wealth and opportunities distributions. From this point of view, two propositions of inheritance reform are particularly relevant: Rignano/Solvay's proposition and Haslett's quota, in so far as they redesign the scope of influence of the familial preference.

The reforms considered -which would introduce radical transformations of current inheritance tax systems -have the advantage, without requiring from individuals an excessive impartiality, to relieve two of the worst consequences of these systems: the reproduction of social inequalities (especially of wealth inequalities) and the lack of sense of community between citizens.

If inheritance is not only an economical topic -as we showed it -but should give rise to an ethics of inheritance, ethical arguments plead for the implementation of Haslett's proposal, i.e. a quota on the amounts people are allowed to receive from bequests and gifs during all their life. In fact, Haslett's proposal would certainly contribute to reduce inequality of opportunity in so far as opportunities are conditional to wealth. This reform also seems to be the most able to induce and develop a deeper sense of community.

  See D. C. McClelland, The Achieving Society, Princeton, NJ (Van Nostrand), 1961, pp. 234-5, and S. Fiekowsky, On the Economic Effects of Taxation in the United States, Cambridge, MA (Harvard University), unpublished dissertation,1959, pp. 370-1.

See the results exposed in the table 3.1 by A. Masson and P. Pestieau, "Bequests Motives and Models of Inheritance…", p. 58-59.

See Bernüeim and al. (1985), "The Strategic Bequest Motive", Journal of Political Economy, 93.

On this point, see E. Schokkaert, "Bequests and Inheritance Taxation: A Comment", in G. Erreygers & T. Vandevelde (eds.), 1997, p. 131.

He brought up the law of escheat, i.e. a law of feudal origin, which stipulated that in the absence of legal heirs an estate becomes public property.

By analogy, the right to vote and citizenship are also rights that are not transferable.

E.[START_REF] Rignano | Di un Socialismo in Accordo colla Dottrina Economica Liberale[END_REF], Di un Socialismo in Accordo colla Dottrina Economica Liberale, Torino, Fratelli Bocca Editori.

E.[START_REF] Solvay | Etude sur le progrès économique et la morale sociale[END_REF], "Etude sur le progrès économique et la morale sociale", Annales de l'Institut des Sciences sociales, 3(6).

F. Huet, Le Règne Social du Christianisme (1853), Paris/Bruxelles, Firmin Didot Frères/Librairie Polytechnique Decq. The interest of Huet's proposal for equality of opportunities is that everything which is confiscated by the State, in a given year, is then equally distributed among all the young people of a given age, so that all dispose of a certain amount of 'basic capital'. For more details, seeHuet (1853), pp. 263-303;[START_REF] Ferrero | A Blueprint for Intergenerational Socialism[END_REF], pp.

3-5;[START_REF] Cunliffe | The Liberal Case for a Socialist Property Regime: the Contribution of François Huet[END_REF];[START_REF] Cunliffe | Basic income? Basic capital!' Origins and Issues of a Debate[END_REF].[START_REF] See | The economic way of looking at behavior[END_REF] In the mid-twenties there was, in the British Policy Debate, a lot of support from economists for some aspects of the Rignano proposal.

R.T.[START_REF] Ely | The Inheritance of Property[END_REF], "The inheritance of property", North American Review, 153, pp. 54-66. This measure is grounded on the following principle: "All inheritances of every sort should be taxed, provided the share of an heir exceeds a certain amount" (p. 61).

Mill, for instance, also recognized the claims of children to the property of their parents as "real and indefeasible" but he did not consider that the children of the deceased should always inherit the whole estate.

E. Rignano, Di un Socialismo in Accordo colla Dottrina Economica Liberale, p. 63.

A strict imposition of the impersonal point of view would be implemented through a mere abolition of bequest.

J. Mill (1888), Principles of Political Economy, London, Longmans,Green and Co., 1965, p. 225.

See L. Arrondel and al., "Bequest and Inheritance: Empirical Issues and France-U.S.Comparison", in Erreygers & Vandevelde (1997).

The persons who will be affected by the quota are the ultrarich, who have literally millions at their disposal, and the moderately rich.

D. Haslett, "Distributive Justice and Inheritance", p. 149.

It will also be a device to develop others kinds of relationships with persons close to us. The necessity to find, at least, five persons to whom bequest will expand a kind of benevolence far away from motivations inherent to capitalist bequest.

See G. S. Becker, A Treatise on the Family, Cambridge, Harvard University Press, 1991; L. J.Kotlikoff, Generational Accounting. Knowing Who Pays, and When, For What We Spend, New York, Free Press, 1992.

B. Bracewell-Milnes, "The Hidden Costs of Inheritance Taxation", in G.Erreygers & T. Vandevelde (1997).

M.Friedman, Capitalism and Freedom, Chicago, University of Chicago Press, 1962, p. 163-5.

progressive inheritance taxation 1 , explicitly, to reduce wealth inequalities or, at least, the greatest one 2 . Mill suggested to set a limit on what any one may acquire by the mere favor of others. For this reason and from an ethical point of view -as we will see later -, it seems to be the most relevant inheritance reform. Unfortunately, Mill never specified precisely how high the maximum amount of property a person would be entitled to acquire by inheritance. While Mill did not assume the originality of his own proposal 3 and did not propose any precise solution to establish a threshold beyond which the individuals would not be allowed to receive any bequest or any gift, Haslett, more recently, ventured a figure.

In fact, D. Haslett -taking into account a principle of distributive justice and a concern for equality -proposes a social policy which is a lifetime inheritance (i.e. gift and bequest) quota rather than an inheritance tax 4 . This quota firstly is "to be set at an amount that is small enough to break up large fortunes yet large enough not to impede most giving and receiving among people of ordinary means", but a giving and receiving not likely to create dramatic inequalities of opportunity that have a major effect upon how justly wealth is distributed. For any given country, Haslett estimates that "an amount somewhere around the current, average (i.e. mean) value of the estates of all people in that country who die over age twenty-one might be appropriate" 5 . In the United States, for example, Haslett suggested in 1997 that the quota might be of $100,000.

Haslett adds several restrictions to his proposal. Thus are excluded, from the obligation one has to report all gifts and bequests received each year: (a) unlimited gifts and bequests between spouses 6 ; (b) secondly, "everyone is to be able to support, as luxuriously as they please, their minor children and other genuine dependants 7 ". (c) The final exception to the quota concerns unlimited gifts and bequests for genuine charitable organizations or purposes. But once one's reportable gifts and bequests, throughout one's lifetime, reach the quota, then one is no longer eligible to receive further reportable gifts or bequests from anyone.

1 J. Mill, Principles of Political Economy, pp. 811-2. 2 J. Mill, Principles of Political Economy, p. 226. Rawls suggests to introduce -through the distribution branch -a taxation of inheritance and income at progressive rates, but also to impose a number of inheritance and gifts taxes and to set restrictions on the right to bequest (see Theory of Justice, p. 245). As suggested by Meade, Rawls recommends to apply the progressive principle at the beneficiary's end (J. E. Meade, Efficiency, Equality and the Ownership of Property, Londres, Allen & Unwin, 1964, p. 56 sq.). 3 Mill was aware of the fact that the public might not be prepared to accept all aspects of his reform proposal at once. 4 D. Haslett, "A Reply to Bracewell-Milnes", in Erreygers & Vandevelde (eds.), 1997, p. 216. 5 Another, perhaps better, benchmark for the amount of a country's quota is the average (i.e. mean) net wealth of all individuals in that country over age twenty-five. In any case, once the amount of the quota is set, it should then be 'indexed' so as to change automatically with (very substantial) changes in average wealth throughout the country. 6 In order to prevent marriages for purposes of avoiding the quota, this unlimited exception may have to be qualified. A relevant way of doing so is to evaluate prior to marriage, each person's assets.

7 D. Haslett, "Distributive Justice and Inheritance", pp. 147-148.

children 1 . And education is more important for success in life than an inheritance received at the age of 45. We can argue that even if any constraint on inheritance will induce rich people to spend more on the education of their children and will increase, in the short run, inequalities, in the long run, this taxation could increase equality of opportunity or, at least, reduce these inequalities.

Only in the long run will inheritance tax lead to a fairer distribution of wealth and hence to more equality of opportunity. Even if the Rignano/Solvay proposition tries to balance personal and impersonal points of view in inheritance tax, it gives a priority to the impersonal point of view. On the other hand, Haslett's proposal is more attractive because it largely preserves the expression of personal standpoint and offers some relevant ethical properties.

The dispersal of assets and wealth induces by Haslett's quota is a mean to share social and economical benefits of natural skills and capacities of all participants to the social structure and is a device to correct the arbitrary distribution of skills among them. In fact, without the social cooperation, those better situated would not obtain the greater advantages they actually enjoyed.

By this way, Haslett's quota -as the Rignano/Solvay proposition -will contribute to implement the Rawlsian principle of "solidarity of talents".

But contrary to the Rignano/Solvay proposal, the wealth dispersal produced by Haslett's quota could lead to a valorization of social links and could also avoid the exclusive focus on family relationships. The current inheritance system discloses an obvious lack of community between citizens. Even if today it is possible, in some States, to bequest his wealth to others persons than his relatives, a child can not be disinherited and the taxes imposed on this atypical bequest are very high. The obligation to bequest beyond the restricted family sphere will change the way one will consider other members of the society and probably give rise to kinds of generosity far different from the ones associated to capitalistic bequests. For example, the most privileged could improve educative and health opportunities or well-being of children from less advantaged strata of society.

For sure, an inheritance tax reform is not the only device needed for increasing equality of opportunity 1 . Reforms that make educational opportunities more available for all, that equalize health care and provide every family with access to at least bare necessities, are also needed. But

Haslett's quota has the advantage to promote equality of opportunity by breaking down wealth concentration but also to take into account the "personal standpoint" without implacably imposing the "impersonal standpoint". For these reasons and especially because of its ethical properties previously Haslett's quota could be the most attractive reform of inheritance system.


Nesrine Boussaada
email: n.boussaada@net.estia.fr

Alvaro Llaria

Guillaume Terrasson

Octavian Curea

Image compression for WSN applied to the process supervision in Industry 4.0

Wireless Sensor Network (WSN) applications in the industrial sector are in permanent evolution due the emergence of the Industry 4.0 concept. Considering this context, Wireless Image Sensor Networks (WISN) appeared as a solution to supervise production processes. In this specific type of WSN, the size of the data to process and to transmit constitutes an important constraint that could cause network congestion and impact node lifetime. Thus, the goal of this paper is to study and evaluate a typical image compression algorithm as a solution to optimize the energy consumption and communication traffic in a WISN, dedicated to control a chemical industrial process.

Introduction

The concept of Industry 4.0 has emerged in the last years thanks to the full evolution of digital solutions, along with the raising of Cyber-Physical Systems, which could provide new knowledges to manufacturers concerning their production processes. These knowledges can be collected, among other techniques, by means of distributed wireless sensors. Considering this context, specific Wireless Sensor Networks based on cameras, called Wireless Image Sensor Networks (WISN), are frequently deployed for process supervision purposes. In these WISN, one of the main challenges is to process and transmit images or videos, that represent high size data, ensuring, at the same time, the availability of the network and an acceptable network lifetime.

Therefore, to reduce the impact of this high quantity of data on the overall WISN performances, many research works are being carried out about the image processing and compression. As an example, one way considered in the scientific literature to reduce the communication network congestion is to execute image processing tasks at the WISN level, and to transmit only the labelled features to the server, as proposed in [START_REF] Wu | Real-time human posture reconstruction in wireless smart camera networks[END_REF]. In this case, the energy consumption due to data transmission decreases, while the energy consumption related to computation in the node increases. Other research works have opted to reduce the images size before transmitting them through the network. In [START_REF] Ghorbel | Images Compression in WSN: Performance Analysis[END_REF], the reduction of the energy consumption has been achieved using image compression before transmission. Considering the state of the art, image compression can be considered an appropriate solution to optimize both energy consumption and communication network availability in WISN.

Therefore, the aim of this work is to propose and evaluate solutions to improve data compression algorithms regarding the performance required for the supervision, in a chemical industry process, of a liquidliquid interface using WISN. The JPEG standard is one of the most widespread data compression algorithms in the literature [START_REF] Ferrigno | Balancing computational and transmission power consumption in wireless image sensor networks[END_REF], and its performance is evaluated using the MATLAB environment. As in future work experiments will be conducted to test the proposed solutions for data compression, an overview of the physical prototype architecture is also described.

JPEG standard evaluation by simulations 2.1. Applied methodology

To evaluate its performance using the MATLAB environment, the JPEG compression is applied considering the following steps: a) decomposition of the image in blocks of 8x8 pixels; b) application of the Discrete Cosine Transform (DCT) for each block in order to pass from the spatial to the frequential domain, resulting in a matrix containing the high and low frequencies separately; c) quantification, which is a multiplication with decreasing weights to eliminate the high frequencies which are invisible for the human eye. The result of this quantification gives a matrix containing positive values on the top left corner, and zeros or almost zeros values elsewhere. Therefore, the information on the image is finally concentrated in the top left corner. The size of the top left corner to be considered is determined by the details of the original image to be conserved.

Then, to reproduce more precisely the considered context, the compression phase is applied to an image composed of horizontal layers with different grey levels, representing the liquid-liquid interface to be supervised, and followed by a simulation of a noisy wireless transmission. For that, Zigbee frames are considered in which the data field size is equal to 80 bytes. In this scenario, one of the worst situations is considered: due to the noise, one random bit is changed in each packet sent through the WISN.

Evaluation criteria

In the considered context, the tradeoff to reach applying a compression method is to reduce the quantity of data while ensuring the image quality. Therefore, to validate our results, the Compression Ratio (CR) is firstly used to verify the information quantity gain. On the other hand, the Peak Signal to Noise Ratio (PSNR) and the Structural SIMilarity (SSIM) are used to confirm the compressed data quality allowing their interpretation [START_REF] Al-Najjar | Comparison of Image Quality Assessment: PSNR, HVS, SSIM, UIQI[END_REF]. PSNR, a mathematical metric and SSIM, a human visual system-based metric, are used both to measure the similarity between an image and a reference image. When this similarity increases, PSNR value goes towards +∞, and SSIM goes towards 1. Otherwise, the two metrics go towards 0. In our case, PSNR and SSIM values greater than 16 and 0.7 respectively, are considered satisfying.

Simulation results

Figure 1 presents the original image (a) along with the decompressed images obtained without transmission (b) and with noisy transmission (c).

Figure 1. Visual results of JPEG compression

The obtained values of CR, PSNR and SSIM for JPEG compression (JC) and decompression (JD), with and without noisy transmission (NT), are exposed in Table 1. Thanks to the JC, the quantity of data sent in the transmission channel is reduced to 25% of the initial quantity. Moreover, even with NT, PSNR and SSIM values are still within the acceptable limits. These results confirm that, in our context, data compression constitutes a solution to reduce the amount of data to be transmitted while ensuring the usability of the decompressed image.

Proposed physical prototype

To test improvements of compression method, a node prototype, based on a Raspberry Pi 4 (RP) as processing and transmission unit, is in preparation. The capacity to program RP using source languages, such as Python [START_REF] Kamath | Raspberry Pi as Visual Sensor Nodes in Precision Agriculture: A Study[END_REF], and to interface it to other nodes using different communication technologies explains this choice. As illustrated in Figure 2

Conclusion

This paper proposed an optimization way, by using data compression methods, to reduce the network congestion and energy consumption in WISN dedicated to process supervision. Considering CR, PSNR and SSIM criteria, simulation results have validated, using JPEG, data quantity reduction and acceptable image quality after compression and noisy transmission. The last section described the prototype that will be used in future work to experimentally validate our improvement proposals.

  , this prototype is also composed of:  RP Camera Module V2.1 to perform image capture,  WS2812 LED-based light source with configurable colors to enhance the details of the image,  PIC18F1320 nano-Watt technology microcontroller to activate periodically the DC/DC converter and the RP but also to control the light source,  Real Time Clock (RTC) to keep date and hour of the RP when the DC/DC converter is stopped.

Figure 2 .

 2 Figure 2. Prototype architecture

Table 1 .

 1 JPEG evaluation results.

	Result	CR	PSNR	SSIM
	JC + JD	75%	31.54	0.87
	JC + NT + JD	75%	17.21	0.62

Acknowledgement

This work is financially supported in the frame of the European project H2020 HYPERCOG.


Sylvain Finot

Corentin Le Maoult

Etienne Gheeraert

David Vaufrey

Gwénolé Jacopin
email: gwenole.jacopin@neel.cnrs.fr

Surface recombinations in III-nitride micro-LEDs probed by photon-correlation cathodoluminescence

III-nitride micro-LEDs are promising building blocks for the next generation of high performance micro-displays. To reach a high pixel density, it is desired to achieve micro-LEDs with lateral dimensions below 10 µm. With such pixel downscaling, sidewall effects are becoming important and an understanding of the impact of non-radiative surface recombinations is of vital importance. It is thus required to develop an adapted metric to evaluate the impact of these surface recombinations with a nanoscale spatial resolution. Here, we propose a methodology to quantitatively assess the influence of surface recombinations on the optical properties of InGaN/GaN quantum wells based on spatially-resolved time-correlated cathodoluminescence spectroscopy. By coupling this technique to a simple diffusion model, we confirm that the combination of KOH treatment and Al 2 O 3 passivation layer drastically reduces surface recombinations. These findings emphasize the need for nanoscale time-resolved experiments to quantify the local changes in internal quantum efficiency of micro-devices.

After more than 30 years of development, IIInitride-based light emitting devices (LEDs) are now widely used for general lighting. Thanks to their high efficiency, this technology is now considered as a promising candidate for µLED display applications. However, the size reduction brings various challenges that are currently preventing their commercialization. In particular, as the surface-to-volume ratio increases, non-radiative surface recombinations at the sidewalls become significant, which limit the efficiency of µLEDs. [START_REF] Olivier | Shockley-Read-Hall and Auger non-radiative recombination in GaN based LEDs: A size effect study[END_REF] To mitigate such effects, different passivation techniques have been proposed such as thermal annealing, 2 chemical treatment [START_REF] Boroditsky | Surface recombination measurements on III-V candidate materials for nanostructure light-emitting diodes[END_REF][START_REF] Choi | Sidewall passivation for InGaN/GaN nanopillar light emitting diodes[END_REF][START_REF] Wong | Size-independent peak efficiency of III-nitride micro-light-emittingdiodes using chemical treatment and sidewall passivation[END_REF] and oxide deposition. [START_REF] Wong | Size-independent peak efficiency of III-nitride micro-light-emittingdiodes using chemical treatment and sidewall passivation[END_REF][START_REF] Wong | High efficiency of III-nitride micro-light-emitting diodes by sidewall passivation using atomic layer deposition[END_REF] Due to the reduced dimensions of such µLEDs, dedicated optical characterization techniques have been specifically implemented.

First, the optical properties have been probed by micro-photoluminescence (µ-PL), [START_REF] Boroditsky | Surface recombination measurements on III-V candidate materials for nanostructure light-emitting diodes[END_REF][START_REF] Otto | Micro-pixel light emitting diodes: Impact of the chip process on microscopic electro-and photoluminescence[END_REF] and electroluminescence (EL) spectroscopies. [START_REF] Olivier | Shockley-Read-Hall and Auger non-radiative recombination in GaN based LEDs: A size effect study[END_REF][START_REF] Tian | Size-dependent efficiency and efficiency droop of blue InGaN micro-light emitting diodes[END_REF][START_REF] Ley | Revealing the importance of light extraction efficiency in InGaN/GaN microLEDs via chemical treatment and dielectric passivation[END_REF] In addition, cathodoluminescence (CL) spectroscopy has been used to study precisely the edge effects with an excellent spatial resolution. [START_REF] Xie | Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging[END_REF] However, if these techniques are well suited to characterize the variation in external quantum efficiency (EQE), they do not allow to disentangle changes in internal quantum efficiency (IQE), light extraction efficiency (LEE) or injection efficiency (IE). Thus, to directly estimate the influence of size reduction on Shockley-Read-Hall recombinations and to be only sensitive to IQE variation, time-resolved photoluminescence (TR-PL) spectroscopy [START_REF] Olivier | Shockley-Read-Hall and Auger non-radiative recombination in GaN based LEDs: A size effect study[END_REF][START_REF] Boussadi | Investigation of sidewall damage induced by reactive ion etching on AlGaInP MESA for micro-LED application[END_REF] have been employed. The spatial resolution of such technique, however, does not allow to directly quantify the surface recombination velocity.

Therefore, there is a need for a characterization technique that combines both high spatial and high temporal resolution, in order to assess the changes in IQE induced by the sidewalls without being influenced by changes in injection [START_REF] Olivier | 25-4: Investigation and Improvement of 10µm Pixel-pitch GaN-based Micro-LED Arrays with Very High Brightness[END_REF] or light extraction efficiency. [START_REF] Ley | Revealing the importance of light extraction efficiency in InGaN/GaN microLEDs via chemical treatment and dielectric passivation[END_REF][START_REF] Jin | InGaN/GaN quantum well interconnected microdisk light emitting diodes[END_REF][START_REF] Choi | Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes[END_REF] In this paper, we studied the optical properties of InGaN/GaN MQW µLEDs grown by metal-organic chemical vapor deposition (MOCVD). First, depth-dependent CL spectroscopy is presented to emphasize the importance of possible artefacts of standard CL spectroscopy. Then, thanks to a spatially resolved time-correlated CL setup (SRTC-CL), [START_REF] Meuret | Nanoscale Relative Emission Efficiency Mapping Using Cathodoluminescence g(2) Imaging[END_REF] we probe the carrier lifetime in a InGaN/GaN multiple quantum wells (MQW) near a mesa edge with a spatial resolution of 100 nm and a time resolution better than 50 ps. This enabled us to quantify the impact of surface recombinations on a single µLED with a nanoscale resolution. Finally, the robustness of this technique is demonstrated by comparing samples with different surface treatments.

The InGaN/GaN MQW LED structure was commercially grown on c-plane GaNon-sapphire template. The LED stack consists of a 2 µm-thick n-GaN, followed by an In 0.15 Ga 0.85 N/GaN MQW active region emitting around 440 nm. The p-type region consists of a 20-nm thick Al 0.15 Ga 0.85 N electron blocking layer (EBL) and 180-nm thick p-GaN cap. To define the µLED mesa, 1 µm of SiO 2 has been deposited to be used as a hard mask. Squared mesas with lateral sizes ranging from 2 to 100 µm have been then defined by inductively coupled Cl 2 /Ar plasma (ICP) etching. A typical SEM image of a 4 × 4 µm 2 LED after dry etching is depicted in Figure 1 (a).

We first probed the optical properties by CL spectroscopy at 10 kV and room temperature. A CL spectrum obtained from a region containing both the mesa and the etched area is displayed in Figure 1 (b). Three spectral regions could be identified. First, the GaN near band edge emission (NBE) is located around 363 nm. Then, the CL contribution centered at 440 nm is attributed to the InGaN/GaN active region. Finally, the broad luminescent band emitting between 500 and 600 nm is ascribed to the GaN defect band (Yellow band). [START_REF] Reshchikov | Luminescence properties of defects in GaN[END_REF] These assignments are further confirmed by the fact that the GaN NBE and YL mainly arise from the etched region while the MQW CL comes from the mesa itself. To ensure to probe mainly the luminescence originating from the active region, a bandpass filter (λ = 450 ± 50 nm) is then used, corresponding to the spectral range within which the MQW emission occurs.

In CL spectroscopy, the incident electron energy defines the interaction volume. This interaction volume not only sets the penetration depth but also limits the spatial resolution. In order to study the luminescence of the active region, a substantial number of electrons must overcome the EBL. There is therefore a tradeoff between spatial resolution and the MQW luminescence intensity. In Figure 2 (a)-(d), normalized CL images at the MQW energy are shown for different acceleration voltages. Below 7 kV, most of the MQW CL intensity originates from the mesa edges. Indeed, in the center of the mesa, the EBL prevents the carriers generated in the p-GaN to diffuse to the MQW region. On the other hand, when the electron beam reaches the sidewalls which deviate by 8°f rom the vertical, it becomes possible to directly inject carriers into the active region (see the inset of Figure 2 (e)) and thus to collect the MQW CL signal from the edges.

By increasing the acceleration voltage, the penetration depth of the primary electrons in- To confirm these interpretations, we performed 3D Monte Carlo simulations [START_REF] Demers | Threedimensional electron microscopy simulation with the CASINO Monte Carlo software[END_REF] of the trajectories of the incident electrons near the sidewalls. Figure 2 (e) shows the normalized electron-hole pair generation probability in the active region for different acceleration voltages as a function of edge distance. These results suggest that the creation of electron-hole pairs depends on the geometry of the sample and the position of the electron beam. Thus, because of the change in excitation probability, the CL intensity does not necessarily capture the influence of surface recombination near the sidewalls but could also reflect local variations of injection or extraction efficiencies.

In order to be sensitive only to the local change of IQE, a more suitable approach is to probe the QW carrier lifetime itself. 17 Thus, we carried out SRTC-CL measurements to directly probe the carrier dynamics near the mesa edges. [START_REF] Meuret | Lifetime Measurements Well below the Optical Diffraction Limit[END_REF][START_REF] Finot | Carrier dynamics near a crack in GaN microwires with AlGaN multiple quantum wells[END_REF] As illustrated in Figure 3 (a), a Hanbury-Brown and Twiss interferometer is thus used to measure the CL photon autocorrelation function (g 2 ). Thanks to the specificity of the electron-matter interactions, g 2 measurements allow to retrieve the local carrier lifetime with the same spatial resolution as standard CL spectroscopy. In addition, the acceleration voltage is kept to 10 kV to efficiently probe the MQW region while having the best possible spatial resolution. The probe current has been set to 4 pA. More details on the SRTC-CL setup can be found in ref. 19.

We first investigated the carrier lifetime evolution across a single mesa. Figure 3 shows the SEM image (b) of a 3-µm large mesa together with its simultaneously acquired CL image (c). In analogy to time-resolved measurements, we display normalized autocorrelation functions for positive delays in Figure 3 (d). The corresponding scanning spots are colorcoded and indicated in Figure 3 (b). To extract quantitative information, we then fitted the g 2 decays by a stretched exponential:

g 2 (t) = 1 + g 0 exp (-(|t|/τ ) γ ) (1)
where τ represents the average CL lifetime and γ is the stretching exponent. [START_REF] Pophristic | Time-Resolved Photoluminescence Measurements of InGaN Light-Emitting Diodes[END_REF] The CL lifetime across the mesa is displayed in Figure 3 (e). The CL lifetime is maximum in the center of the mesa where it reaches ≈ 12 ns. This value is kept on a plateau of ≈ 1 µm. As the electron beam approaches the sidewalls, the CL lifetime decreases over a characteristic length of ≈ 1 µm. Near the sidewalls, the carrier lifetime is less than 5 ns, highlighting the detrimental role of non-radiative surface recombinations, as it will be discussed in the following.

It should be noted, however, that the left and right edges do not seem to behave in the same way. The left edge appears to impact on a wider band the carrier lifetime. This effect can be linked to the inherent spatial fluctuations of CL intensity of MQWs (Figure 2 (c)). Indeed, even in the absence of any etching, the internal quantum efficiency of the active area can vary locally due to the presence of non-radiative centers such as dislocations or point defects (see SI section I.2 for a CL image at the center of a 2 × 2 mm 2 mesa presenting similar fluctuations). Due to the nanoscale resolution of SRTC-CL, this may locally modify the probed CL lifetime.

In order to average these fluctuations without compromising the spatial resolution, it is necessary to average the signal in the parallel direction to the sidewalls. Thus, instead of measuring the CL lifetime point by point, it is requested to integrate the CL signal parallel to an edge.

In view of an accurate analysis of non-radiative recombinations at an etched surface, we now focus our investigation on the center of a single edge of a 100-µm large mesa. Figure 4 shows a SEM image (a) with its simultaneously acquired CL image (b) near a sidewall. As discussed above, we noticed a local CL intensity enhancement when the e-beam is on the sidewall, due an increase of electron-hole pair generation in the active region. In addition, we observed the random spatial fluctuation in the mesa itself due to the presence of non-radiative defects. On Figure 4 (c), we thus average both the CL and the secondary electron (SE) signals in the transverse direction. As a result, intensity fluctuations are smoothed out and surface related effects are becoming more apparent. First, we observe that the maximum of the CL intensity is reached in the vicinity of the sidewall. More precisely, it matches a dip in the SE signal. This dip is assigned to the presence of the AlGaN EBL. As expected from our MC simulations, this corresponds to the situation where the overlap between the interaction volume and the active region is maximum. Even after averaging, the CL signal still shows some small fluctuations in intensity away from the edge but these are limited to ±5 %. Finally, we observed that from a distance of about 450 nm from the edge, the CL signal decreases due to surface recombinations.

For SRTC-CL measurements, in order to maintain the spatial resolution while averaging along the transverse direction, we shaped the e-beam in a rectangle with a width of 100 nm First, we observe that the CL intensity recorded in the SRTC-CL setup is in excellent agreement with the results obtained on Figure 4 (c). Concerning the CL lifetime, two regimes can be identified. First, far from the edge, the variations of CL lifetime is correlated with CL intensity variations. In this region, both the CL lifetime and CL intensity reflect the local change in internal quantum efficiency. However, in a 1-µm band close to the etched surface, the situation is different. Indeed, between 450 nm and 1 µm from the edge, the CL lifetime decreases while the CL intensity remains almost unaffected. Only when the distance from the e-beam to the edge is less than 450 nm, the CL intensity decreases significantly.

Thus, it is clear that in the region of interest, i.e. near the surface, the CL intensity and CL lifetime do not carry the same information.

To understand this, it is useful to clarify their relation with efficiencies :

I CL ∝ η inj × η IQE × η LEE (2)
τ CL = η IQE × τ rad (3)
where η inj is the injection efficiency, η IQE the internal quantum efficiency, η LEE the light extraction efficiency and τ rad the radiative lifetime. From Equation 2, we can see that a change in CL intensity could be attributed to either a local change of η LEE , η IQE or η inj . On the other hand, τ CL only depends on η IQE and τ rad . Hence, the observed decrease of τ CL could be linked to a reduction of radiative lifetime or IQE near the surface.

First, concerning the radiative lifetime, τ rad could be affected by a local change in the internal electric field induced by the strain relaxation. To quantify this effect, we performed 6 x 6 k.p simulations, taking into account the strain relaxation and the electric field with nextnano3. [START_REF] Birner | nextnano: General Purpose 3-D Simulations[END_REF] The parameters used for the simulations can be found in ref 22. We observed that the change in spatial electron-hole overlap is limited, with on average, a maximum variation of 20% within the first 200 nm from the edge depending on the QW (see SI Section II for more details). This cannot explain the trend followed by τ CL . Thus, we conclude that the variation of τ CL is mainly dominated by non-radiative re-combinations at the sidewall surface. From the CL lifetime profile near the edge, it is clear that surface recombination plays a role up to 1 µm which already gives an estimation of the lateral diffusion length in the MQW region.

Therefore, if the IQE is decreasing near the sidewall, in order to explain the near constant CL intensity between 450 nm and 1.1 µm from the edge, either η inj or η LEE has to increase in this region. However, no local variation of η inj is expected from our Monte-Carlo simulations (Figure 2 (e)). As a result, the different trend between CL lifetime and intensity in this region certainly arises from a local increase in light extraction efficiency. The origin of this increase could be explained by light scattering at the sidewalls, [START_REF] Choi | Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes[END_REF] increased sidewall emissions [START_REF] Ma | Strong light-extraction enhancement in GaInN light-emitting diodes patterned with TiO2 micro-pillars with tapered sidewalls[END_REF] or total internal reflections which could redirect the light at a more favorable angle for extraction. We then develop a 1D diffusion model taking into account non-radiative surface recombinations to extract quantitative information from our experimental results (see SI section III for more details). This model assumes a Gaussian electron beam characterized by a 150 nm standard deviation and a CL effective lifetime far from the edge of about 12 ns. Thus, the remaining fitting parameter are the diffusion co-efficient D and the surface recombination velocity S. As observed in Figure 5 (a), the surface recombination velocity S mainly determines the magnitude of the near-surface lifetime while the diffusion coefficient D defines the lateral extension over which the surface plays a role (see SI section III). Thus, the parameters S and D are almost independent and can be adjusted separately, which ensures the robustness of the fit.

In order to validate our method and model, a room temperature KOH etching has been performed to reduced plasma damages followed by an Al 2 O 3 deposition by atomic layer deposition. [START_REF] Ley | Revealing the importance of light extraction efficiency in InGaN/GaN microLEDs via chemical treatment and dielectric passivation[END_REF] As expected, we observed on Figure 5 (b) that the lifetime near the surface increases from 6 ns for the reference sample to 8 ns for the sample after KOH and Al 2 O 3 treatment.

A statistical study has been then performed on 7 different sidewalls for both the reference and the treated samples. We then applied the fitting procedure to extract D and S (Table 1). As expected, we observed that only the surface recombination velocity changes from about 5.6 × 10 3 for the reference sample to about 3.1×10 3 cm s -1 for the sample after KOH and Al 2 O 3 treatment while the diffusion coefficient remains around 0.33 cm 2 s -1 . These values are in line with previously published data obtained with other experimental techniques. Typical values of D can be found between 0.1 and 2 cm 2 s -1 . 24-26 S has been previously reported in the [10 3 -10 4 ] cm.s -1 range for etched III-nitride µLEDs. [START_REF] Bulashevich | Impact of surface recombination on efficiency of III-nitride light-emitting diodes. physica status solidi[END_REF][START_REF] Bulashevich | Effect of Die Shape and Size on Performance of III-Nitride Micro-LEDs: A Modeling Study[END_REF] From our results, we can draw some guidelines to the development of efficient µLEDs. First, in µLEDs with a diameter below 5 µm, non-radiative surface recombinations play an important role and cannot be neglected. However, from our model and experimental results, there are several direc-tions to mitigate the detrimental role of the surface. First, starting with the most obvious, one way to improve the efficiency is to reduce the surface recombination itself by developing optimized surface treatments or implementing damage free etching techniques. [START_REF] Zhu | Near-Complete Elimination of Size-Dependent Efficiency Decrease in GaN Micro-Light-Emitting Diodes[END_REF] Then, another way to reduce the influence of the surface is to reduce the diffusion length, defines as L ∝ √ Dτ . Therefore, one can consider to decrease the diffusion coefficient D by engineering the potential fluctuation landscape. [START_REF] Shen | Three-dimensional modeling of minority carrier lateral diffusion length in InGaN blue/green and AlGaN ultraviolet C single quantum wells including random alloy fluctuations[END_REF] Finally, the last option is to enhance the recombination rate. This could be achieved by reducing the QW thickness, [START_REF] Weatherley | Imaging Nonradiative Point Defects Buried in Quantum Wells Using Cathodoluminescence[END_REF] increasing the driving current [START_REF] David | Long-Range Carrier Diffusion in (In,Ga)N Quantum Wells and Implications from Fundamentals to Devices[END_REF] or by using semi-polar or non-polar structures. Additional simulations, showing the impact of these parameters on the IQE, are presented in SI Section III. Regarding all these aspects, core-shell microwire LEDs could also be an attractive solutions to produce efficient µLEDs with dimensions below 5 µm.

In conclusion, we studied the impact of etched sidewalls in µLEDs, which reduces the efficiency of InGaN/GaN QWs. We first demonstrate that CL intensity mapping can be affected by local changes in light extraction or injection efficiencies. Then, by combining SRTC-CL and a 1D diffusion model, we develop a methodology to quantitatively assess the precise role of surface recombinations. We finally demonstrate that the combination of KOH treatment and Al 2 O 3 passivation layer drastically reduces surface recombinations.

Figure 1 :

 1 Figure 1: (a) Bird's-eye view SEM image of a 4 × 4 µm 2 LED after ICP dry etching and hard mask removal. The scale bar is 1-µm long. (b) CL spectra obtained at 10 kV with and without bandpass filter (λ = 450 ± 50 nm).

igure 2 :

 2 (a)-(d) CL images of the same pixel at the quantum well energy (440±35 nm) for different acceleration voltages. The scale bar is 2 µm long. (e) Normalized electron-hole pair generation probability in the active region simulated with CASINO. (inset) Schematic of the interaction volume at low (orange) and high acceleration voltage (green). creases, allowing the generation of electron-hole pairs in the MQW from the top surface. Additional spectra for different acceleration voltages showing the optical contribution of each layer are available in section I of the supporting information (SI). However, this increase in penetration depth is accompanied by a decrease in spatial resolution. Indeed, by increasing the acceleration voltage from 10 kV to 20 kV, the CL spatial fluctuations become blurred (Figure 2 (c)-(d)).

Figure 3 :

 3 Figure 3: (a) Schematics of the SRTC-CL experimental setup. (b) SEM image of a 3-µm large mesa and (c) the corresponding CL image at MQW energy. The scale bar is 1-µm long. (d) Normalized g 2 for different positions on the mesa. (e) CL lifetime as a function of the position across the mesa.

Figure 4 :

 4 Figure 4: (a) SEM image near an edge of a 100-µm large mesa and (b) the corresponding CL image at MQW energy (440 ± 35 nm). The scale bar is 1-µm long. (c) SE and CL profiles averaged perpendicular to the edge. (d) Simultaneously acquired normalized CL intensity (black squares) and CL lifetime (red circles) as a function of the distance from the edge.

8

 8

Figure 5 :

 5 Figure 5: Lifetime profile of the untreated sample (a) and treated with KOH + Al 2 O 3 (b) (black circle). 1D diffusion simulations for different surface recombination velocities are also shown as dotted line.

Table 1 :

 1 Extracted model parameters for the reference sample (Ref) and passivated (KOH) sample. The uncertainty corresponds to one standard deviation.

		τ ef f (ns) S (10 3 cm s -1 ) D (cm 2 s -1 )
	Ref	11.8 ± 0.4	5.6 ± 1.4	0.33 ± 0.06
	KOH 11.8 ± 0.3	3.1 ± 0.6	0.33 ± 0.06

Acknowledgement This work is supported by the French National Research Agency in the framework of the "Investissements d'avenir" program (ANR-15-IDEX-02) and with the help of the "Plateforme Technologique Amont" de Grenoble, with the financial support of CNRS Renatech network. The authors would like to thank Fabrice Donatini for his help in the development of the SRTC-CL setup.

Supporting Information Available