Frederic Martinez
email: frederic.martinez@ish-lyon.cnrs.fr

Jean-François Bonnefon

Julie Hoskens

Frédéric Martinez
email: frederic.martinez@ish-lyon.cnrs.fr.

Frédéric Martinez

GREPS Frédéric Martinez

Frédéric Martinez

Active Involvement, not

Keywords: Illusory Control, increases Risk Taking Choice, involvement and illusory control 3 Choice, involvement and illusory control 27

Active Involvement, not Illusory Control, increases Risk Taking in a Gambling Game

Would you wager less money at the roulette table if the dealer placed your bets for you? Would you spend less money on the slot machine if you could not pull the arm? That is, do Choice and Involvement increase the risks we are willing to take in a gambling game?

We define Choice as the possibility for the player to choose a gamble or another, rather than leaving that decision to another person (e.g., the dealer, the bank, another player). We define Involvement as the physical interaction with the gambling device, which triggers the (quasi-)immediate resolution of the gamble (e.g., spinning the wheel, throwing the dice, picking the ball from the urn). 1 Choice and Involvement are orthogonal dimensions of the gambling experience, although they have often been counfounded in experimental studies.

Remarkably, although the empirical evidence for the effects of Choice and Involvement on risk taking is at best mixed, and at worst flawed, there is a consensus that would these effects exist, they would operate through illusory control.

In this article, we question this postulate and show that (a) although Choice does increase illusory control, this influence does not translate in increased risk taking, and (b) although Involvement does increase risk taking, this effect is not mediated by illusory control. We first review the mixed empirical evidence for the links between choice, involvement, illusory control and risk taking in gambling games, which leads us to consider three potential models. We then report the results of a laboratory experiment testing these three models.

Choice, Involvement, and Illusory Control in Gambling

Choice and risk taking Prior data are inconclusive about the effect of Choice on risk taking in gambling games-either because of small samples, of inconsistent results, or because of confounds with Involvement. [START_REF] Dixon | Manipulating the illusion of control: Variations in gambling as a function of perceived control over chances Choice, involvement and illusory control 24 outcomes[END_REF] investigated risk taking in a game of roulette as a function of Choice. For each participant (five adult women), sequences of three trials with free choice (participants chose the location on the roulette board where they placed their bets) alternated with sequences of three trials with forced choice (participants gave their chips to the experimenter, who selected the location). Four of the five participants wagered a greater number of chips when they could place their bets Choice, involvement and illusory control 5 themselves. This study hints at an effect of Choice on risk taking, measured by the number of chips wagered; however, the small size of the sample makes it difficult to draw a definitive conclusion, and the [START_REF] Dixon | Manipulating the illusion of control: Variations in gambling as a function of perceived control over chances Choice, involvement and illusory control 24 outcomes[END_REF] article does not document the statistical significance of this effect.

Using a dice-throwing game, [START_REF] Dunn | When the stakes are high : A limit to the illusion control effect[END_REF] showed that participants who could choose their target number made larger bets than participants who were randomly assigned their target number. This effect, however, disappeared in higher-stakes games. In a study of computer blackjack, [START_REF] Chau | Effects of perceived control upon wagering and attributions in computer Blackjack[END_REF] awarded or denied 12 participants the ability to choose their dealer, as blackjack players are often found to switch to new tables after a streak of losses. This manipulation did not impact the size of participants' bets. [START_REF] Gilovich | Biased evaluations of randomly determined gambling outcomes[END_REF] showed that bingo players increased the size of their bets (after a win) when they could make choices during the game-more precisely, when they could choose the numbers on their bingo cards and when they could choose which of five computer keys to press to generate the random number that determined whether any space could be filled on the card. Note that Choice here is confounded with Involvement, because the choice of a computer key entails a physical interaction with the gambling device, which triggers the resolution of the gamble.

Involvement and risk taking

Support for the effect of Involvement on risk taking is less equivocal.

Previous studies strongly suggest that risk taking increases with active Involvement. From their observations of patrons playing craps in realworld casinos, [START_REF] Davis | Illusory personal control as a determinant of bet size and type in casino craps games[END_REF] concluded that higher bets were placed on patrons' own dice rolls than on other patrons' rolls.

Participants in the study of [START_REF] Ladouceur | The level of involvement and the timing of betting in roulette[END_REF] played a game of roulette where they were either actively or passively involved (either they threw the ball or the dealer did). Risk taking was assessed through a combination of the odds chosen by participants and the raw amount they waged, and was influenced by Involvement. [START_REF] Chau | Effects of perceived control upon wagering and attributions in computer Blackjack[END_REF] observed that computer blackjack players were likely to wager larger bets when they were playing for themselves (and got to press a key to draw a new card) than when they were betting on other players (and were passive spectators of the resolution of the gamble). Finally, Fernandez-Duque and Wifall (2007) presented participants a game in which they selected cards, one at a time, from a set of 10, after being instructed that nine cards won a dollar each and one lost all the money and ended the game. Some participants played the game (which implied active Involvement with the gambling device), others made their decisions while observing a confederate play the game. Involved participants took more risks (in this case, picked up more cards) than non-involved participants.

The role of illusory control

Whether or not it is real, the effect of Choice and Involvement on risk taking is traditionally considered from the perspective of illusory control. According to [START_REF] Langer | The illusion of control[END_REF], any condition that encourages participants in a game of chance to behave as if they were participating in a game of skill induces an illusion of personal control. Insofar as Choice and Involvement qualify as such conditions, it is expected that they will induce such an illusion, which will manifest itself in an inappropriate perception of one's chances to win. In turn, this inappropriate perception will translate into increased risk taking.

It seems reasonable to accept that Choice induces an illusion of control over the outcome of the game. Participants who can choose their bets likely maintain the illusion that their betting strategy can influence the outcome of the game. Indeed, all five participants in the study of [START_REF] Dixon | Engaging in illusionary control during repeated risk-taking[END_REF] decided to buy the right to choose the location of their bets in a roulette game, rather than betting on random locations. Accordingly, lottery players have a marked preference for choosing their own numbers rather than having them chosen at random [START_REF] Wohl | Temporal orientation and perceived control as determinants of risk-taking[END_REF], especially when they score high on 'desirability for control' [START_REF] Burger | The effects of desire for control in situations with chance determined outcomes: Gambling behaviour in lotto and bingo players[END_REF], and have higher expectations of success when they can do so. They also require more compensation to exchange their tickets (Langer, 1975, Exp. 2), even when the exchange ticket has a higher probability of winning (Langer, 1975, Exp. 3).

It is not clear, however, that Involvement promotes an illusion of control in gambling games. In particular, participants in the [START_REF] Ladouceur | Illusion of control: Effect of participant's participation and implication[END_REF] study did not manifest illusory control over the outcome of the game when they could throw the dice themselves instead of watching the dealer do it. Langer (1975), Exp. 4 showed an effect of Involvement on illusory control, but the task was not a gamble, and had all the appearances of a game of skill. [START_REF] Langer | Heads I win, Tails it's chance: The illusion of control as a function of the sequence of outcomes in a purely chance task[END_REF] observed an effect of Involvement on illusory control in a coin-tossing game, but since Choice was not manipulated orthogonally (and was offered to all participants), it is impossible to assess whether Involvement alone was responsible for increased illusory control. This skepticism is reinforced by the results of [START_REF] Wortman | Some determinants of perceived control[END_REF]: Participants blindly drew (or watched someone else drew) a colored marble from a can to determine which consumer item they won. Drawing the marble caused an illusion of control only when there was foreknowledge of which marble was associated with which prize (i.e., only when Choice was offered to participants as to which prize they were aiming at). Finally, it has not been firmly established that illusory control increases risk taking in gambling games, although illusory control does appear to encourage risk taking in other domains [START_REF] Horswill | The effect of perceived control on risk taking[END_REF]. Gambling studies rarely include simultaneous measures of illusory control and risk taking, and when they do [START_REF] Chau | Effects of perceived control upon wagering and attributions in computer Blackjack[END_REF], no causal model is tested. Previous results are thus inconclusive at best. In particular, [START_REF] May | Gambling-related irrational beliefs in the maintenance and modification of gambling behaviour[END_REF] exposed participants in a roulette game to messages aiming at increasing or decreasing illusory control; although messages did influence participants' level of irrational thinking, no significant difference was observed in gambling behavior.

Summary

Figure 1 displays the three models that seem the best candidates in light Choice, involvement and illusory control 10 of previous findings. From the data we have reviewed, it seems reasonable to assume that Choice impacts illusory control, and this link is therefore featured in all the models. It also seems reasonable to assume that Involvement impacts risk taking, and this link is featured (directly or indirectly) in all the models. Now, although Choice should have an effect on illusory control, previous data are not clear about whether this effect translates into increased risk taking. And although Involvement should have an effect on risk taking, previous data are not clear about whether this effect is mediated by illusory control.

Considering this various possibilities and constraints, we arrive at three potential models.

In the Half-mediation model, both Choice and Involvement lead to increased risk taking, but only the effect of Choice is mediated by illusory control. In the Full-separation model, only Involvement has an (unmediated) effect on risk taking; in this model, Choice promotes illusory control, but this does not translate in increased risk taking.

Finally, in the Full-mediation model, both Choice and Involvement lead to increased risk taking, and both effects are mediated by illusory control.

To discriminate between these models, we report an experiment where we independently manipulated Choice and Involvement, included several measures of perceived control, and assessed risk taking through several indices.

Methods

Participants

Participants were 100 undergraduate psychology students at the University of Toulouse (89 women, mean age = 21.8, SD = 3.3), individually recruited by a research assistant. This research assistant (who was blind to the objectives of the study) also performed as the experimenter; we will refer to her as 'the dealer.'

Procedure

Participants took the task individually. The task consisted of a series of gambles (in fact, six; but participants did not know exactly how many gambles they would play, they just knew the game would last for some 15 minutes). Participants received an initial pool of 60 chips and were presented with three urns. Each urn contained 24 balls, with different proportions of white (winning) balls and red (losing) balls (12-12, 8-16, and 6-18, respectively). The three urns had different payments (2 to Choice, involvement and illusory control 12 1, 3 to 1, 4 to 1) as a function of the proportion of white balls they contained, in order for any bet on any urn to have an expected value of zero (e.g., a wager of 10 chips on the third urn had an expected value of .25×4×10-10=0).

Although this calculation was not explicitly shown to participants, each urn was clearly labelled with its proportion of winning balls and its payment, and no participant complained that he or she had not understood the payment scheme. A game turn consisted of (a) choosing an urn to bet on, (b) deciding on the amount of the bet, (c) drawing a ball from the urn, (d) possibly receiving some gains, and (e) putting back the ball in the urn. Participants were informed that a 20 voucher would be given (at random) to two of the five players finishing the game with the most chips.

Design

The game procedure depended on the experimental condition participants were assigned to, following a 2 × 2 between-subject design that manipulated Involvement (Player draws vs. Dealer draws) and Choice of urn (Free-choice vs. Forced-choice). In the player-draws condition, participants could draw the ball from the urn themselves, while it was a prerogative of the dealer in the dealer-draws condition.

Choice, involvement and illusory control 13

In the free-choice condition, participants could freely decide during each turn which urn they would bet on. In the forced-choice condition, the dealer made this choice for them. In fact, the sequence of urns imposed to a participant in the forced-choice condition was determined by the choices made by the previous participant, who was assigned to the free-choice condition. Thus, the 50 sequences of choice imposed by the dealer in the forced-choice condition exactly matched the 50 sequences of choice made by participants in the free-choice condition.

Measures

Once they had familiarized themselves with the rules, and before the game session began, participants answered to three preliminary questions, measuring illusory control: How many chips do you expect to have at the end of the game? Do you think that one has better chances to win the voucher if one can decide oneself on the urn to bet on? (yes or no) Do you think that one has better chances to win the voucher if one can draw the ball from the urn oneself? (yes or no). The latter two questions will only be used as a supplement to the first question, which will be our main measure of illusory control. Our four measures of interest are:

1. Expectation: The number of chips participants expect to leave Choice, involvement and illusory control 14 with at the end of the game. This is an implicit measure of their illusion of control.

Bet:

The number of chips wagered by participants, on average, during the six turns of play. This is a crude measure of risk taking.

Investment:

The ratio of the amount of chips wagered by participants to the amount of chips they currently have in their possession, on average, during the six turns of play. This is a more sophisticated measure of risk taking.

Luck:

The ratio of the numbers of white balls actually drawn to the number of white balls expected from chance. This measure of luck will be used as a covariate in some analyzes.

The choice of the risk taking measures was dictated by a concern of consistency with the extent literature on gambling: Almost all the articles we have reviewed in the introduction use Bet as a measure of risk taking. Another traditional measure of risk taking would address the players' preferences for low-probability gambles, but this measure is unavailable in the present design, because Choice is denied to half the players.

As indicated by a power analysis, with N=100, a linear regression including three uncorrelated predictors has a satisfactory power of .80

Choice, involvement and illusory control 15 to detect a small to moderate effect size (β=.25) at a significance level of .05 (one-tailed), assuming that the predictors and the errors from the regression model have a standard deviation of at most 1 (which is necessarily true of our Choice, Involvement, and Luck predictors, as well as of our Investment dependent variable).

Results series

The mean and standard deviations of Expectation, Bet and Investment in the four experimental groups are reported in Table 1. To test the three candidate models we identified, we performed a of regression analyzes (see results in Table 2 ). Note that we did not include the interaction term Choice × Involvement in the regression analyzes, for the sake of parsimony (there was no a priori theoretical motivation for that inclusion). We nevertheless checked that including the interaction term did not make any difference to the results of the regression analyzes.

We first regressed the hypothesized mediator (Expectation) on the predictors (Choice and Involvement). Next, we regressed each of the dependent variables (Bet and Investment) on the predictors plus their covariate (Luck). Finally, we regressed each dependent variable on the two predictors, the Luck covariate and the hypothesized mediator.

Mediation is achieved when inclusion of the mediator in the regression significantly decreases the contribution of one or several predictors to the dependent variables.

The broad picture is clear. First, illusory control (as measured by Expectation) increases when participants can choose the urns they bet on (Choice) but not when participants can draw the balls themselves (Involvement).

Results related to our two additional, explicit yes/no measures of illusory control confirm this finding. Overall, 58 of the 100 participants believe that one's chances are better if one can choose, whereas only 14 of the 100 participants believe that one's chances are better if one can draw, a large and significant difference (Z=6.1, p<.001, Cohen's h=0.96). Note that whether the participants could themselves choose or draw (depending on the experimental group they had been assigned to prior to responding) did not appear to make any difference to their answers to these two general, hypothetical questions: A multivariate analysis of variance did not detect any effect of Choice, Involvement or their interaction on these two answers (all Fs<1, all ps>.35).

Second, the risks participants are willing to take are impervious to Choice, involvement and illusory control 17 the Choice manipulation but not to the Involvement manipulation.

Involvement has a reliable influence on the number of chips participants wager, as well as the ratio of their resources this bet represents. Interestingly, the Luck covariate (negatively) affects Investment but not Bet: It appear that participants who where lucky with their draws (and consequently in possession of a comparatively large number of chips) did not substantially increase the size of their bets, which mechanically decreased the proportion of their resources they wagered. Third, it is remarkably clear from Table Erreur ! Source du renvoi introuvable. that Expectation does not serve as a mediator for the effect of Involvement on Bet or Investment. Indeed, the contribution of Involvement to Bet and Investment is strictly the same whether or not Expectation is included in the regression. Furthermore, Involvement is not in any case a significant predictor of Expectation. Two of the conditions for statistical mediation are thus violated. The same conclusion applies to Choice: the contribution of Choice to Bet or Involvement is not reduced by the inclusion of Expectation in the regression. Furthermore, although Choice does significantly increase the Expectation mediator, it has no detectable effect on Bet or Investment even before the mediator is included in the regression.

Again, two of the conditions for statistical mediation are violated.

Overall, results are entirely consistent with the full-separation model, and falsify both the full-mediation and the half-mediation models. Choice indeed has an effect on Expectation, but this effect on Expectation does not impact in turn Bet or Investment. On the other hand, Involvement does have an effect on Bet and Investment, but this effect is not mediated by Expectation-and in particular, Involvement has no detectable effect on Expectation.

General Discussion

Participants in our experimental gambling game played differently and had different expectations depending on whether they could choose the location of their bets, and whether they were actively involved in the mechanistic resolution of the gamble. Players who could choose the location of their bets expected to fare better than those who could not, but did not take larger risks. Players who could draw the balls from the urns took larger risks than those who could not, but did not expect to fare better. In other terms, a clear separation was observed between the effects of Choice (which impacted illusory control) and Involvement (which impacted risk taking). illusory control, and does not extend to risk taking, especially since illusory control has been shown to play a role in problem gambling [START_REF] Ginakis | Problem gambling: An exploration of the role of global personal hopefulness, short-term gambling hope, and illusion of control beliefs[END_REF]. We do not see however any contradiction between our results and the conception according to which illusory control is a key aspect of pathological gambling. Illusory control can influence gambling decisions in other ways than simply increasing wagers. For example, illusory control can be an encouragement to engage in a gamble in the first place; or an encouragement to adopt self-destructive attitudes such as chasing, that is, persistent gambling in the hope of making up for a series of losses [START_REF] Breen | Chasing in gambling behavior: personality and cognitive determinants[END_REF].

One reviewer suggested that participants in the Forced Choice condition may have had theories ranging from a benevolent to a malevolent dealer, because they were not told that their forced choices were actually that of the previous participant. If true, this may have watered down the effect of Choice on risk taking, as some participants (those who have illusions of control about Choice and believe in a benevolent dealer) could have wagered more in the Forced Choice condition. This, however, would imply greater variance in the Forced Choice, involvement and illusory control 20

Choice group, which is not found in our data-variance is in fact slightly greater in the Free Choice group, both for the Bet and Investment variables.

Another potential concern about our experimental design is that Expectation may reflect general optimism about future outcomes, over and above any effect of illusory control: Although perceptions of control imply optimism, the locus of optimism might be located outside illusory control. We acknowledge this possibility, but cannot think of any plausible reason for Choice to trigger optimism/pessimism about the results of the gamble that would not be due to perceptions of control. Furthermore, this concern is moot in the case of Involvement: Because Involvement does not impact Expectation, we can tentatively conclude that it has no effect on optimism, control-based or not.

What is left to explain is why Involvement increases risk taking, and why this effect is not mediated by illusory control. In the rest of this discussion, we suggest that the lack of mediation by illusory control rules out an explanation in terms of belief in the deployability of personal luck, and that the effect of Involvement is best explained by the increased arousal it may deliver. [START_REF] Wohl | Temporal orientation and perceived control as determinants of risk-taking[END_REF] expanded on Langer's model of illusory control to include perception of personal luck as a source of illusory control. In a first study, they showed that letting participants choose themselves a scratch-and-win lottery ticket enhanced both their perception of personal luck and their perceived chance of winning. In further studies, they demonstrated that participants behaved as if luck was a personal quality that could be transmitted to the gambling device by mechanisms akin to sympathetic magic. One might then consider that our participants behaved as if they could 'magically' enhance their chances of winning by drawing the ball from the urn, and that this belief encouraged them to wager larger amounts of chips. This account, however, would predict an effect of Involvement on Expectation, and an effect of Expectation on risk taking-neither of which is detected in the present study.

One reviewer suggested that the timing of the control measure might be responsible for the lack of an Involvement effect on illusory control.

It could be that, unlike that of Choice (which is immediate), the effect of Involvement on illusory control builds up as a result of actually taking action, and requires measurement through out the game. We acknowledge that possibility, and the methodological challenge of finding a nonintrusive measure of illusory control that would not Choice, involvement and illusory control 22 disrupt the continuity of the gambling task.

We believe, though, that an explanation in terms of arousal gives the most consistent account of our results. Gambling is physically arousing [START_REF] Meyer | Casino gambling increases heart rate and salivary cortisol in regular gamblers[END_REF], and higher levels of arousal increase one's inclination to accept a higher risk level; for example, aroused individuals are willing to pay more for lotteries and less for insurance [START_REF] Mano | Risk taking, framing effects, and affect[END_REF]. In parallel, [START_REF] Coventry | Arousal, erroneous verbalizations and the illusion of control during a computergenerated gambling task[END_REF] did not observe any link between arousal and illusory control in a gambling task. Thus, our results can be readily explained by postulating that active involvement results in higher arousal (see also [START_REF] Fernandez-Duque | Actor/observer asymmetry in risky decision making[END_REF], for a similar intuition): Participants who can draw the balls experience higher arousal, and therefore take greater risks, but they do not feel greater control over the outcome of the gamble.

Illusory control has been legitimately identified as a key aspect of gambling-but we should be careful in assessing both its determinants and its behavioral consequences. Our findings emphasize that the quantitative risks players are willing to take (arguably a critical feature of gambling) are increased by their active involvement in the mechanistic aspects of the gamble, independently of the illusion they maintain over the control they exert. Further investigations will likely

Figure 1 .

 1 Figure 1. Three theoretical models for the effect of Choice and

Notes

1. Note that our notion of (active) Involvement as physical interaction with the gambling device is different from [START_REF] Langer | The illusion of control[END_REF] notion of 'passive' involvement. Passive involvement basically consists of delaying the gamble, for example by postponing its resolution, or by giving players their lottery numbers in instalments rather than at a single point in time.


Jan Behrends
email: jan.behrends@helmholtz-berlin.de

Alexander Schnegg

Matthias Fehr

Andreas Lambertz

Stefan Haas

F Finger

Bernd Rech

Klaus Lips

Electrical Detection of Electron Spin Resonance in Microcrystalline Silicon pin Solar Cells

Keywords: conductivity, defects, EPR, microcrystalline silicon, photovoltaics solar cells, electron spin resonance solar cells, photovoltaics, conductivity, defects, microcrystalline silicon, electron spin resonance

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Today's solar cell technology is mainly based on crystalline silicon (c-Si) wafers. The high efficiencies that can be reached with wafer-based technologies, however, come along with the energy and cost intensive wafer production process. In contrast to that, solar cells made from hydrogenated amorphous silicon (a-Si:H) and its microcrystalline counterpart (µc-Si:H) can be deposited directly on inexpensive substrates like glass and have the potential to be superior with regard to material consumption and cost effectiveness. The production of these thin-film devices, which are usually realised in a pin configuration, was made possible by the pioneering discovery by W.E. Spear and P.G. LeComber in 1975 that amorphous silicon can be doped during deposition [1]. Unfortunately, a-Si:H and µc-Si:H suffer from an inferior electronic quality compared to crystalline silicon. This is due to defect states in the band gap of the material resulting from silicon dangling bonds (db) as well as band tail states close to the band edges. In thin-film solar cells, trapping and recombination at localised defects are the main limiting factors for the cell performance. Due to the fact that these defects are often paramagnetic (in the case of db) or can be made paramagnetic by light excitation (in the case of tail states), electron spin resonance (ESR) can reveal quantitative as well as structural information [2][3][4]. For instance, ESR on powder samples is routinely being used to optimise the deposition parameters for a-Si:H and µc-Si:H growth [5]. Although a correlation between material quality as determined by ESR and efficiency of resulting solar cells is well established, it still remains questionable if the defect properties of the thin-films in the device and in powder samples are indeed identical, since the boundary conditions for the layer growth are different. Attempts to extend ESR studies to fully processed thin-film solar cells are restricted by two major limitations. Firstly, the detection sensitivity of conventional X-band ESR is typically too low for the spin concentrations found in state-of-the-art thin-film solar cells, and secondly, paramagnetic centres in contact layers and the substrate may introduce additional ESR signals, which do not influence the solar cell efficiency. To overcome the limitations of conventional ESR, we applied electrically detected magnetic resonance (EDMR) (for a review see [6] and references therein). This technique allows the investigation of paramagnetic states influencing transport and recombination through spin-dependent processes in thin films [7][START_REF] Schiff | AIP Conf. Proc[END_REF][START_REF] Street | [END_REF] and devices [10,11] at ultra high sensitivity [12,13]. Since EDMR is based on photocurrent measurements, it is inherently only sensitive to defects influencing the conductivity of the solar cell and therefore its performance and efficiency. The uniqueness of EDMR originates from its capability to directly relate the microscopic properties of current limiting paramagnetic states with macroscopic transport in the device. Probing the sample properties by spin interactions, defect states may be assigned by their position in the EDMR spectrum. Further on, EDMR line shape analysis yields highly desired information about the microscopic defects. Though conventional cwEDMR proved to provide valuable information about defect states in the material, a complete picture of the transport mechanisms in the solar cell may only be obtained by time-resolved EDMR techniques. Employing state-of-the-art pulsed ESR instrumentation in combination with sensitive current detection, we recently succeeded in the development of several pulsed (p)EDMR detection schemes providing 2D resonance field vs. evolution time EDMR spectra [14][15][16]. Extending the capabilities of EDMR into time domain, pEDMR allows assigning defect states to complex transport mechanisms.

In this paper, we exploit pEDMR to identify paramagnetic centres in µc-Si:H solar cells. Despite its capabilities, pEDMR spectra from samples containing many layers of different material typically contain overlapping signals, which may only be identified by combining appropriate pEDMR techniques with a systematic variation of the sample morphology. While the types of localised defect states that are present in either µc-Si:H or a-Si:H are similar, the fingerprints of their respective ESR signals (most importantly the g value) show significant differences between both morphologies [6]. All measurements were performed at T = 10 K in order to benefit from the enhanced signal-to-noise ratio at low temperatures which is indispensable for a thorough analysis of the EDMR signals and the assignment to the respective defect states. However, it is worthwhile noting that mechanisms that govern the spin-dependent transport at T = 10 K differ significantly from the performancelimiting processes at normal solar cell operating conditions. Nevertheless, this study constitutes the starting point for prospective investigations of charge transport at higher temperatures up to 300 K.

In the following, we will first describe our pEDMR setup and outline the requirements the sample has to meet in order to be analysed by pEDMR. Subsequently, we will focus on measurements employed to a series of thin-film solar cells with a microcrystalline absorber layer in which the morphology (µc-Si:H or a-Si:H) of the doped layers in the pin structure was systematically altered. The aim of this study is to discriminate between different processes involving various types of defect states in the individual layers of the solar cell. This is an extension to a first study comparing only two different cell structures [16]. The results will be discussed in the light of information about a-Si:H and µc-Si:H powder samples previously obtained by ESR.

Samples

All µc-Si:H pin solar cells investigated in this study are based on the layer sequence shown in figure 1. The samples were deposited on quartz substrates using plasma enhanced chemical vapour deposition (PECVD) at the Forschungszentrum Jülich with a process that was shown to reach efficiencies above 10% on areas of 1 cm 2 [17]. Four series of solar cells were prepared, where the p-(boron) and ndoped (phosphorus) layers were either composed of amorphous or microcrystalline silicon keeping the deposition conditions for the intrinsic absorber layer unchanged. The solar cells were grown on Al-doped ZnO, always starting with the thin p-doped silicon layer. A ZnO/Al layer stack was used as back reflector and contact. Note that the chosen cell structure was not optimised for high solar cell conversion efficiency but was solely designed for the purpose to reliably study the influence of the various contact layers on the EDMR behaviour.

To discriminate between pEDMR signals arising from the intrinsic µc-Si:H absorber or the highly doped layers, four samples with the layer sequence described in table 1 were prepared. It should be noted here that different thicknesses of the ZnO layer were used for the four samples. However, we believe that this does not affect the pEDMR signals originating from the silicon pin structures. Throughout this article the sample structures will be referred to as sample A, B, C, and D. Schematic energy-band diagrams of all cells neglecting the ZnO as well as metal layers are depicted in figure 2.

For the pEDMR samples a special contact structure consisting of 50 mm long, 0.5 mm wide and 100 nm thin Ag strip lines was used to establish an electrical connection to contact pads that are positioned outside the microwave (mw) res- onator. Through this design the perturbation of the eigenmodes of the dielectric mw resonator by the electric circuitry is minimized. Details of the contact scheme and its influence on the pEDMR measurement can be found elsewhere [START_REF] Boehme | The investigation of charge carrier recombination and hopping transport with pulsed electrically detected magnetic resonance techniques, in Charge transport in disordered solids with applications in electronics[END_REF]. The patterning of the contacts as well as the confinement of the active solar cell area to 1 mm 2 was realised by laser scribing techniques. Figure 1 depicts a photograph of a completely processed sample, clearly showing the structure of the EDMR samples and the contact pads opposite to the solar cell.

E C E V E C E V E C E V E C E V sample A sample B sample C sample D n-a-Si:H i-µc-Si:H p-µc-Si:H n-µc-Si:H i-µc-Si:H p-µc-Si:H n-a-Si:H i-µc-Si:H p-a-Si:H n-µc-Si:H i-µc-Si:H p-a-Si

Experimental details

The pEDMR setup is based on a commercial X-band ESR spectrometer Bruker Elexsys E580 which was upgraded by the equipment for electrical detection. The sample is mounted in a dielectric resonator and cooled using a continuous flow helium cryostat with optical access. All EDMR measurements described in the following were carried out at T = 10 K under illumination through the quartz substrate with a cold light source at approximately 50 mW cm -2 . Figure 3 shows current voltage curves obtained under these experimental conditions. Note that the low-temperature I-V curves differ significantly from those one would obtain at ). All EDMR measurements were carried out at a constant voltage U = -1 V (reverse bias regime of the solar cell). This point is indicated in the plot by a vertical line.

room temperature. At positive voltages this can primarily be attributed to barriers -in particular the heterobarrier between a-Si:H and µc-Si:H -which hinder the charge transport in the device. This is in line with the observation that the I-V curve of sample B (µc-Si:H n-and p-layers) varies markedly from the other curves in the forward bias regime.

For the EDMR measurements, a battery-based constant voltage source (Stanford Research SIM928) was used to apply a reverse bias voltage of U = -1 V to the sample. Due to the different current-voltage-characteristics of the respective samples A to D (cf. figure 3), this corresponds to photocurrent densities between -1.3 and -3.3 mA cm -2 . At this voltage the qualitative behaviour of the illuminated I-V curves was the same for all samples, and in none of the samples the saturation regime of carrier extraction was reached. We believe that at U = -1 V the current extraction mechanism is the same for all specimens under study and is dominated by drift in the electric field of the intrinsic µc-Si:H layer.

Two-dimensional mappings of the spin-dependent processes were obtained by recording the transient photocurrent changes ∆|I ph | following a mw pulse excitation as a function of the external magnetic field. While the mw pulses have a length of typically several 10 to a few 100 ns, the detection of ∆|I ph | is carried out for some 100 µs. We used a current/voltage converter (Elektronik-Manufaktur Mahlsdorf) that was especially designed for transient photocurrent detection in pEDMR measurements and that allows for a good trade-off between bandwidth and noise. The EDMR setup is schematically shown in figure 4. This instrument consists of three main components as indicated in figure 4. In the transimpedance amplifier the current signal is converted into a voltage which is then filtered by a bandpass with lower cut-off frequency of 1 Hz to remove the DC-component of I ph . The upper cut-off frequency can be varied in order to control the time resolution of the detection setup. The resulting signal is then amplified to a level that is suitable for the transient recorder (Bruker SpecJet).

The time evolution of the photocurrent after mw excitation (in the following referred to as pEDMR transient) is determined by the rate coefficients of the spindependent microscopic processes as described in refs. [14,[START_REF] Boehme | The investigation of charge carrier recombination and hopping transport with pulsed electrically detected magnetic resonance techniques, in Charge transport in disordered solids with applications in electronics[END_REF]. However, it is generally difficult to determine these coefficients directly from the pEDMR transients since RC time constants of the detection electronics or the dielectric relaxation times of the sample dominate the experimentally obtained pEDMR transients. To demonstrate this, figure 5 shows two pEDMR transients of sample A that were obtained using two different current/voltage converters under otherwise identical conditions. The transient labelled with 'SR570' was measured using a Stanford Research SR570 current amplifier which is often used for pEDMR. The transient labelled 'EMM' was recorded with the current/voltage converter described above (Elektronik-Manufaktur Mahlsdorf) with the bandwidth set to a value corresponding to a rise time of 2 µs. Both transients clearly exhibit markedly different dynamics, although the experimental conditions were the same. The rise and fall times of the 'SR570'-transient are slower and the sign reversal of the transient is shifted to longer times. This difference is simply due to the lowpass filtering by the SR570 current amplifier. This can be demonstrated by numerical lowpass filtering of the 'EMM' data with the response time of the SR570 amplifier taking into account the RC equivalent circuitry as indicated in figure 4. As shown in figure 5, the filtered 'EMM' data becomes identical with that of 'SR570'. To elucidate the influence of the sample (not necessarily of the microscopic processes) on the transients, it can be helpful to model the pEDMR transients. Assuming that the transients are determined by two exponential functions with two time constants linked to the spin-dependent process under observation and further taking into account the RC time constants induced by the current detection setup and the sample itself, good fits to the experimentally obtained data can be achieved. This is demonstrated in figure 5 for the unfiltered 'EMM'-transient. Regardless of the strong influence of the detection electronics on the pEDMR dynamics, the pEDMR dynamics can be used to deconvolute spectrally overlapping signals as will be shown in this article.

The geometry of solar cells to be analysed by pEDMR is inherently limited by the dimensions of the mw resonator which in turn is determined by the wavelength of the microwave. For X-band (ν ≈ 10 GHz, wavelength 3 cm), a solar cell area of 1 × 1 mm 2 (cf. figure 1) has proved to be reasonably small to yield a homogeneous mw amplitude over the whole active area of the solar cell. We have carefully checked that defects induced by the preparation and processing -in particular defects located at the edges -do not affect the experiments by comparing results obtained from cells with different geometries. This is particularly important when studying coherent effects by means of pEDMR. Since the active area of solar cells studied with EDMR is rather small, additional defects induced by the preparation and processing -especially defects located at the edges -can significantly affect the experiments. To exclude that the EDMR spectra are dominated by such defects, we prepared sample D with two different solar cell geometries with clearly varying edge length as shown by the optical micrographs in figure X. The respective pEDMR spectra, i.e. ∆|I ph | as a function of magnetic field, are shown in figure X. Within the accuracy of the measurement, the normalised spectra are identical, indicating that the same underlying microscopic processes are involved. It is therefore safe to assume that no new types of defects are introduced by the specific processing of the solar cells for pEDMR measurements. The signal-to-noise ratio is significantly reduced for the 2 × 0.5 mm 2 sample which is attributed to the smaller photocurrent (and consequently also smaller ∆|I ph |) resulting from the fact that the illumination condition was optimised for a square-shaped active area. All following experiments have been carried out on square-shaped solar cells.

Results and discussion

The pEDMR datasets obtained from samples A to D differ with respect to both their spectral shape as well as their transient behaviour. In the following, we will first identify the defect states by their resonance position in the pEDMR spectra.

Combining these pieces of information with the dynamics and Rabi oscillations of the respective spectral components, we will, in a second step, conclude on the underlying transport and recombination mechanisms.

Identification of defect states

Figure 6 shows the pEDMR spectra of samples A to D recorded at t = 2.2 µs after applying the mw pulse. The insets display spectra taken from the same samples on a broader magnetic field range. Common to all samples is that they contain a narrow component centred around the g value of the free electron and, in addition, a broad (> 20 mT) component with lower intensity. Beside these similarities, further inspection of the spectra unravels that the narrow component as well as the broad line consist of several EDMR signals which, in addition, differ from sample to sample.

For the identification of the defects contributing to the pEDMR spectra, we analysed the resonances by fitting Lorentzian and Gaussian functions to the narrow spectra. The line shapes (Gaussian or Lorentzian) were chosen to achieve best fits to the experimental data. Note that the mw power in pEDMR is considerably higher than in cwEDMR. As a result, mw power broadening of the lines can lead to deviations between line shapes and line widths obtained from cw-and pEDMR experiments. This applies especially to narrow lines. The results of the least square fits can be summarised as follows: Best fits to the experimental spectra can be obtained when assuming a resonance at g CE = 1.9975( 5) for all samples. Additionally, we find a signal at g e = 2.0049(5) in samples A and C (amorphous n-layer) as well as a line at g h = 2.011(1) in samples C and D (amorphous p-layer).

The broad spectra reveal an additional pair of lines separated by 25 mT, indicating the presence of hyperfine interaction in samples A and C (amorphous n-layer). Both lines are symmetric to g P ≈ 2.003. This feature is absent in samples B and D (microcrystalline n-layer). Instead, in samples B and D an asymmetric broad signal is uncovered. For an unambiguous assignment of the microscopic origin of this line we will discuss its spectral shape in more detail below. In the following, we will assign the resonance positions to defect states in the samples based on findings from previous EDMR and ESR studies on thin films as well as powder samples.

Intrinsic µc-Si:H

In intrinsic and n-doped µc-Si:H an ESR resonance at g = 1.997 -1.998 is reported in various studies which is associated with shallow localised states in energetic proximity to the conduction band, typically referred to as CE states [2,[START_REF] Hasegawa | [END_REF][20][21][22][23]. It was demonstrated by cw-and pEDMR measurements on µc-Si:H films that these states are involved in hopping transport at low temperatures as well as in tunnelling recombination between CE and dangling bond states [3,22]. Hence, we assign the signal at g CE = 1.9975 (5), that was observed in all samples, to originate from CE states in the intrinsic microcrystalline absorber layer.

n-doped a-Si:H

Both samples that contain an a-Si:H n-layer (samples A and C) show signals at g e = 2.0049(5) and g P ≈ 2.003, which are absent in samples B and D. This is a strong indication that these resonances are related to localised states in n-a-Si:H. In the case of line at g P (in the following referred to as 'P signal'), this interpretation is supported by the fact that the EDMR signal consists of a pair of Gaussian lines with equal intensity that are split by 25 mT. This splitting is well known to arise from hyperfine (hf) interaction between phosphorus electron and nuclear spins in amorphous silicon [24] and was shown to also exist in the cw-and pEDMR spectra of phosphorus-doped a-Si:H [25,26]. It is worthwhile noting here that phosphorus is only incorporated in the thin n-doped layer and that for phosphorus-doped µc-Si:H neither the 4.2 mT hyperfine splitting known from c-Si nor the abovementioned 25 mT split hf lines are observed [2,27]. This is consistent with our observations. The signal at g e is presumably associated with conduction band tail states in the n-a-Si:H layer and is also observed in n-a-Si:H/c-Si solar cells [26]. EDMR investigations at temperatures between 100 and 150 K have revealed that a signal at g = 2.0044 may be associated with hopping of electrons among band tail states in a-Si:H (known as 'e signal') [25,28]. However, LESR measurements have shown an increase of the g value with decreasing temperature [29]. Thus, the discrepancy between g = 2.0044 and g e = 2.0049(5) -as it was found in our measurements at T = 10 K -might be explained by the temperature difference. This is also in line with low-temperature pEDMR results for hopping via a-Si:H tail states in a-Si:H/c-Si solar cells [START_REF] Boehme | The investigation of charge carrier recombination and hopping transport with pulsed electrically detected magnetic resonance techniques, in Charge transport in disordered solids with applications in electronics[END_REF]26].

p-doped a-Si:H

Analogous to electron hopping described before, hopping of holes via valence band tail states in boron-doped a-Si:H can also contribute to the photocurrent. The corresponding resonance ('h signal') has been investigated in the past using EDMR [25,28,30] and optically detected magnetic resonance (ODMR) revealing g = 2.011 to 2.013 [31][32][33]. In the solar cells C and D (a-Si:H p-layer) we found a signal at g h = 2.011 which we assign to valence band tail states in a-Si:H. No evidence of boron acceptor states could be found.

The CH signal

In the pEDMR spectra of samples B and D (µc-Si:H n-layer) the 25 mT splitting of the phosphorous signal is absent. Further inspection of these spectra unravels an asymmetric signal of different shape (see figure 6). Figure 7a gives an enlarged view of the pEDMR spectrum of sample B with a range covering the first 10% of the ordinate range of the plot in figure 6. The line shape of the resonance resembles the powder pattern of an asymmetric g tensor. The dashed curve in figure 7a depicts the results of a simulation (simulation program EasySpin [34], simulation parameters: g = 2.15, g ⊥ = 1.995, field-dependent inhomogeneous broadening ∆g = 0.2, ∆g ⊥ = 0.01). Note that field-dependent inhomogeneous broadening has been reported in many cases concerning disorder in amorphous silicon [4,35,36]. Asymmetric broad lines in echo-detected field-sweep spectra obtained by pulsed ESR have been reported in literature to be associated with holes in localised valence band tail states (referred to as CH signal) in undoped and boron doped µc-Si:H [27]. Therefore, it seems to be justified to assign the asymmetric signal described above to CH states in the intrinsic absorber layer which is present in all samples. The CH signal is indeed visible in the spectra of all samples, however, in samples A and C it is almost completely hidden underneath the high-field hf-satellite which has a higher intensity. We can exclude that this line originates from the a-Si:H layers because the ESR signature from valence band tail states in a-Si:H is different (cf. h signal described before) [30]. It should be noted that it is complicated to resolve broad lines in cwEDMR. In pulsed ESR and EDMR, however, one benefits from a flat baseline which facilitates the observation of broad spectral components. Further examination of figure 7a reveals an additional spectral component with Gaussian line shape at g sd = 1.9675(5) (FWHM = 2.5 mT) which is represented by a dotted curve in figure 7a. The fact that this line (referred to as 'sd signal') is not part of the asymmetric resonance becomes clear when evaluating the time evolution of the pEDMR spectra. This is illustrated in figure 7b where three spectra taken between 2.8 and 6.0 µs after the mw excitation are shown. The position of g sd is marked by a solid vertical line. The central lines have been cut in order to facilitate the analysis of the weaker signals. The plot unambiguously shows that the sd signal has a distinctively different time dependence as compared to the asymmetric line, indicating that both signals arise from different paramagnetic centres and microscopic processes. While the asymmetric line having qualitatively identical shape was found in all four samples, the sd signal could exclusively be observed in sample B.

To the best of our knowledge, no ESR or EDMR signals caused by paramagnetic states at g sd = 1.9675 (5) have been reported for either a-Si:H or µc-Si:H. However, resonances at similar g values were obtained from shallow donors in ZnO [37,38]. Here, the observed g value critically depends on the morphology (crystallite size) of the respective ZnO material. The photogenerated charge in all solar cells investigated traverses the ZnO layers on both sides of the pin structure which are both degenerately doped with aluminium. We therefore assign the sd signal to originate from either of the ZnO layers. Its g value and the fact that this resonance is only observed in sample B suggests that it is connected to a shallow donor state resulting from Al incorporated in the ZnO layer on the p-µc-Si:H side or at the interface between these two layers. From this argumentation, the sd resonance should also appear in sample A, but here the line may be buried below the broad and rather intensive hf satellites. We can exclude that the resonance is connected to transport at or through the ZnO/n-µc-Si:H interface since the sd signal is not visible in the spectrum of sample D.

In summary, the line parameters of the individual signals and the associated paramagnetic defects in the respective layers are listed in table 2.

Assignment to microscopic transport and recombination mechanisms

In order to fully describe the involvement of different defect states in charge transport processes, information obtained from line shape analyses have to be combined with the information extractable from pEDMR transients and Rabi oscillations.

In general, EDMR signals are due to changes in the probability for spindependent transitions between paramagnetic states. All signals observed in this study can be explained within the framework of a spin pair model in which the transition probability depends on the relative spin orientation of both spin partners of the pair [14,39,40]. Upon application of a strong mw pulse which is in resonance with either of the participating states, the transition probability generally increases, leading to an increase of the corresponding transition rate. However, this rate change of a microscopic process can influence the macroscopic photocurrent of a pin µc-Si:H solar cell in different ways, depending in a complicated way on the microscopic mechanism, the device physics, and, in the particular case of pin solar cells, on the bias voltage applied to the sample [START_REF] Lips | IEE Proc. -Circ. Dev. Syst[END_REF][START_REF] Brammer | [END_REF].

In the present case all experimental data has been obtained in the reverse bias regime (U = -1 V) where the photocurrent is negative. In this situation, the pEDMR transient exhibits a relative enhancement of the photocurrent (∆|I ph | > 0) immediately after the mw pulse for a spin-dependent hopping process, implying an improvement of carrier extraction due to the selective mw excitation. The resonant mw pulse leads to an increase of the hopping rate and thus can be considered to enhance the mobility in the hopping transport path. It has been shown that mobility modulations in thin-film silicon solar cells can strongly affect the conductivity, in particular at low temperatures [43,44]. In contrast to that, one would expect an initial quenching of the photocurrent (∆|I ph | < 0) for spin-dependent recombination or trapping. In this case, the conductivity is altered by a spin-resonant change of the charge carrier concentrations. Note that the abovementioned spindependent processes can be connected to other charge extraction limitations such as transport over energy barriers at contacts, recombination in a space charge region, space charge limited currents or trap assisted tunnelling through barriers.

In such a case it is difficult to predict the sign of the photocurrent change since these processes can coexist and influence the current response of the device in a rather complex manner. However, irrespective of the spin-dependent transport limitation, theory predicts that the pEDMR transient shows a sign reversal when non-vanishing triplet transition probabilities are present [14,[START_REF] Boehme | The investigation of charge carrier recombination and hopping transport with pulsed electrically detected magnetic resonance techniques, in Charge transport in disordered solids with applications in electronics[END_REF]. To discriminate between various mechanisms, additional information is needed which we may obtain from the dynamics of the pEDMR signals as well as from coherent spin motion experiments.

Analysis of pEDMR transients

To exploit in which way the different signals affect the charge transport in the device, we deconvoluted the pEDMR signals in time domain by taking the line parameters from the spectra shown in figure 6 (cf. table 2) as fixed parameters and their relative intensities as fit parameters. Thus, we were able to independently study the time behaviour of the spectrally overlapping signals. In this way we obtained the integrated peak intensities A of all resonances. In order to cross-check the validity of the spectral fits (see figure 6), the three lines at g CE (FWHM = 1.8 mT), g e (FWHM = 1.8 mT) and g h (FWHM = 2.9 mT) were taken into account for all samples. The deconvolution procedure was applied to the experimental data obtained with narrow magnetic field range (cf. figure 6). The g values and line widths were assumed to be identical for all samples. Details of the deconvolution procedure are described in the text.

traces shown it is obvious that the three pEDMR signals CE, e and h exhibit different dynamics. This indicates that none of the paramagnetic states associated with these resonances belong to the same spin-dependent process. In this case one would expect that both peak intensity and dynamics of two lines are correlated. Beside the different rise and fall times, all three signals show the same behaviour with respect to the observed sign of the mw induced effect (enhancing signal), except for the line at g e in sample B which shows a photocurrent decrease after the mw excitation (quenching signal). The small dip at short times (t < 3 µs) of this quenching signal is a measurement and data processing artefact. Although the g value of the quenching signal in sample B (see figure 6) seems indistinguishable from the g value of signals at g e in sample A and C, we ascribe this quenching signal to a different paramagnetic state, namely dangling bond states in the intrinsic absorber layer. This argumentation is supported by the fact that we are able to resolve a small g value shift between the enhancing lines of samples A and C as compared to the quenching signal in sample B. In addition, the quenching signal exhibits different dynamics and can easily be separated from the CE line in sample B by evaluating the time evolution of the spectra. Figure 9 shows a comparison between two spectra recorded at t = 2.2 and 4 µs after the mw pulse excitation. One can clearly observe the quenching contribution at t = 4 µs which can easily be fitted separately. From this analysis we find g db = 2.0045(5) which slightly differs from g e as it was found for samples A and C. Within the experimental uncertainty this agrees with the g values reported for Si dangling bonds in µc-Si:H (g = 2.0042-2.0058 depending on the deposition conditions) [5,45]. Note that despite of the difference between g db and g e , the temporal evolution of the quenching signal (figure 8) is reflected by the line at g e = 2.0049 (deduced from the enhancing signal found in samples A and C, cf. figure 6). At present it is not clear why this quenching . pEDMR spectrum of sample B recorded 4.0 µs after the mw pulse. Two lines with different g values and opposite signs can clearly be distinguished (solid line: experiment; dashed line: result of a fit with two Lorentzian lines; dotted lines: both separate contributions to the fit). Note that the spectrum has been multiplied by a factor of two to allow for a better comparison with the spectrum recorded at 2.2 µs which is also included in the plot.

signal is not also observed in samples A, C and D. Either this signal is associated with the specific interface of the intrinsic and the doped layers or the signal is simply masked by the strong signals related to the doped a-Si:H layers.

To evaluate the dynamics of the 25 mT hf split lines that show up in the spectra of samples A and C, the deconvolution procedure on these samples was additionally carried out using the pEDMR datasets with broad magnetic field range. Here, we assumed the same parameters as described before for the CE and e signals but, for the sake of simplicity, omitted the line at g h . The P signal was taken account of by assuming a pair of symmetric Gaussian lines with equal intensity that are split by 25 mT and have their centre-of-gravity at g P = 2.003. Figure 10 shows the results of this analysis.

While the time dependence of the CE and e signals resembles that given in figure 8, we observe a clear correlation between the rise and fall times of the lines at g e and g P for both samples. For this to occur, both centres must either be involved in the same microscopic process or two different processes involving the two paramagnetic centres separately, but influence I ph in a similar way [46]. Based on the experimental results we cannot unambiguously discriminate between both possibilities, but in any case the correlation between the pEDMR transients supports the interpretation that both signals stem from spin-dependent processes in the n-a-Si:H layer.

Coherent spin motion

Further information about charge transport mechanisms and the involvement of the defects assigned above may be obtained by analysing Rabi oscillations of the observer spins localised at the respective defect states. In particular, one can distinguish a spin-dependent transition (recombination or tunnelling) that involves only one paramagnetic centre -like direct capture recombination at silicon dan- The deconvolution procedure performed using the two-dimensional pEDMR datasets with wide magnetic field range (cf. main plots in figure 6). The hyperfine signal that is visible in the respective spectra was taken into account by assuming a pair of Gaussian lines that are symmetric to g P = 2.003. Note that the ordinate scale is normalised to facilitate the comparison of the dynamics.

gling bonds or a hopping process among tail states -from a process in which the spin-dependent transition takes place between two centres having different g values [39,40,46]. In the latter case, one can address the spins of the charge carriers in both states separately by choosing the resonance condition according to the g value of the respective spin. The frequency of the coherent spin motion is given by the Rabi frequency of the paramagnetic centre which is in resonance, provided that the driving field γB 1 (B 1 denotes the amplitude of the mw magnetic field and γ is the gyromagnetic ratio) is small compared to the Larmor separation δω = (ω a -ω b ) of the two respective centres [47,48]. Here, ω a and ω b are the Larmor frequencies of the two centres a and b, respectively. On the contrary, when the Larmor separation of two participating centres is smaller than the driving field (δω γB 1 ), theory predicts a Rabi frequency that is higher by a factor of two [14,49,50].

To observe Rabi oscillations in pEDMR, the charge Q(τ ) resulting from the integration of ∆|I ph | over several microseconds after the mw excitation is recorded as a function of the pulse length τ [15]. Figure 11 illustrates the charge response Q(τ ) obtained on two different spectral positions (indicated by the g values as given in the legend) for each sample. The insets show fast fourier transformations (FFT) of Q(τ ) clearly indicating similar Rabi frequencies (Ω/2π = 12-15 MHz) for all signals. Under the experimental conditions used in the experiment this corresponds to the Rabi frequencies we expect for a spin-dependent transition between weakly coupled spins that can be resolved in the pEDMR spectrum (δω γB 1 ). It should be stressed that, unfortunately, the weak peak intensities of the broad lines (hf and CH) do not allow us to determine their Rabi frequencies.

Assuming that all EDMR signals found in this study can be explained by the spin pair model [39], in which the relative spin orientation of both partners of a spin pair determines a microscopic transition rate, two spectrally distinguishable paramagnetic states are involved in each spin-dependent transition such as recombination or hopping process. When the spectral positions and/or line widths of these resonances differ significantly, which is true for the signals e and P in samples A and C, the frequency measured in the coherent spin motion experiment reflects the Rabi oscillation of the centre which is in resonance (e signal in this case) [14]. In the opposite case, when the spin pair consists of two paramagnetic centres with similar g values and homogeneous broadening, only one line appears in the pEDMR spectrum. However, in this case it is impossible to manipulate only one spin partner without influencing the other (often referred to as the case of strong light-field coupling) [47,48], and thus, one measures a Rabi frequency which is predicted to be higher by a factor of two as compared to the case before [14,49,50]. Only if the lines of both spins are strongly inhomogeneously broadened, the spectral overlap between individual spin packets of both lines may be small enough to form a weakly coupled spin pair. All Rabi measurements presented here indicate spin-dependent transitions between paramagnetic centres which do not overlap in the EDMR spectra. This, however, raises the question which EDMR resonance line represents the respective recombination or hopping partner. For the EDMR signals which could be assigned to the n-a-Si:H layer, this puzzle may be answered referring to the transients of the EDMR signals shown in figure 6. Both signals e and P have the same dynamics and their resonances in the pEDMR spectrum are clearly separated. Hence, they may constitute a weakly coupled spin pair, where the spin partners may be excited independently by the microwave pulse, resulting in the observed Rabi frequencies. This indicates a spin-dependent process between the two respective centres. Following the previous interpretation of the centres, we assign the spin-dependent process to hopping between band tail and phosphorous states in a-Si:H [46].

For the signals related to the µc-Si:H absorber layer this question remains an obstacle because the transients depicted in figure 8 exhibit completely different time constants. At present it is not clear how these paramagnetic centres are related to microscopic transport or recombination processes. A straightforward explanation of the observed Rabi behaviour can only be delivered if we assume that in the case of the signals CE, CH and db the respective pair partners are not visible in the pEDMR spectra due to the fact that their lines are strongly inhomogeneously broadened or that the signals arise from a microscopic process involving more than two spins. The paramagnetic centres that were identified by the pEDMR analyses described above are summarised in figure 12.

E C E V E C E V E C E V E C E V sample A

Conclusion and outlook

The preceding pEDMR study demonstrates that an identification of paramagnetic defect states and charge transport processes may be obtained in completely processed pin solar cells. The complexity of the problem to assign the defect states to materials and interfaces in a multi-layer solar cell made a systematic alternation of the morphology of the highly doped n-and p-layers mandatory. We could show that by combining the information obtained from pEDMR spectra and from the time evolution of the spin-dependent photocurrent transients the spectral resolution may be significantly enhanced. As a result, valuable additional information about transport mechanisms could be obtained as compared to conventional ESR and EDMR investigations.

Thereby we succeeded in identifying electron hopping processes between conduction band tail states and phosphorus donor states in the n-a-Si:H layer. Similarly, spin-dependent processes involving holes in valence band tail states in the p-a-Si:H layer could be observed. Presumably, these states are involved in a hopping or tunnelling process, however, the details of these mechanisms are at present unclear. Paramagnetic states in the intrinsic µc-Si:H absorber, which was present in all samples, give rise to pronounced resonances. A strong signal related to localised electrons in the conduction band tail (CE) was observed in the i-µc-Si:H layer. In addition, we found a signal which we assign to holes localised in the valence band tail (CH). These states give rise to an asymmetric and broad line that could be simulated assuming a strongly asymmetric g tensor and asymmetric line broadening. Signals related to dangling bonds in the µc-Si:H absorber could only be observed for the sample with microcrystalline n-and p-layers. This is of particular importance for prospective studies which address the investigation of spin- dependent recombination via dangling bonds in the absorber layer created though the Staebler-Wronski effect [51]. Our findings indicate that the strong EDMR signals caused by tail states in the highly doped layers can be suppressed by using microcrystalline n-and p-layers.

Besides this, we were able to detect a pEDMR signal at g = 1.9675 (5) in the µc-Si:H pin solar cell with p-and n-doped µc-Si:H layers which we associate with shallow donor states in the Al-doped ZnO. Here, more work is needed on thin ZnO layers and devices, in which the ZnO is replaced by other transparent conducting oxides, to further investigate the microscopic nature of this resonance.

Coherent spin motion measurements revealed the signature of spin-dependent transitions in which both spins of the respective spin pair can be addressed separately. In the case of the hopping signals originating from the n-a-Si:H layer, this is in agreement with the pEDMR spectra, provided that we indeed observe a hopping process from a phosphorus donor state to a band tail state or vice versa. In the case of the resonances that stem from the p-a-Si:H and i-µc-Si:H layers, no such correlation between two signals could be found in the pEDMR spectra and transients. This indicates that either the missing spin partners cannot be observed in the spectra or that the spin pair model cannot account for the underlying microscopic mechanisms. Due to its strong inhomogeneity, spin-dependent processes through the CH states could serve as the missing link in the interpretation of the Rabi oscillations. To connect the CH states to a specific process, the dynamic behaviour of this line has to be studied in greater detail which, however, is difficult in view of the relatively small signal amplitude.

The present study was performed at a temperature of T = 10 K where charge transport dynamics are distinctively different from the dominating mechanisms at room temperature, i.e. under operating conditions of solar cells. However, the identification of defect states and transport mechanisms at low temperatures constitutes the basis for studies focusing on the temperature dependence of these mechanisms. It shall be mentioned here that due to instrumental improvements in our lab, pEDMR experiments are no longer restricted to the low-temperature range. Benefiting from these improvements we recently succeeded in performing pEDMR measurements (photocurrent relaxation as well as coherent experiments) at room temperature, which will pave the way to study spin-dependent transport in multi layer solar cells at room temperature in the near future.

Further on, the identification of defects and transport mechanisms obtained in the present work is an inevitable step towards multi-frequency and multi-resonance pEDMR studies of individual paramagnetic centres. Here, our aim is to combine the sensitivity and specificity to charge transport mechanisms of pEDMR with the spectral resolution of advanced EPR techniques [START_REF] Schweiger | Principles of pulse electron paramagnetic resonance[END_REF] to shed light on the functionstructure relationship of individual defect states and transport pathways.

Figure 1 .

 1 Figure 1. Left: layer structure of the superstrate µc-Si:H pin solar cells. Four different samples which differ in the morphology (amorphous or microcrystalline) of the n-and p-doped layers were investigated. Right: photograph depicting the pEDMR sample geometry. The solar cell (active area of 1 × 1 mm 2 ) is electrically connected by 5 cm long thin-film wires that extend to contact pads on the opposite side of the substrate.

Figure 2 .

 2 Figure 2. Schematic representation of the energy-band diagrams at room temperature without illumination for samples A to D. The morphology of the doped layers can be identified by the different band gaps. Localised defect states are sketched for all layers without taking into account the difference in their density of states with respect to energy, doping concentration and layer morphology. Note that the ZnO and metal layers have been omitted. In all measurements presented here, the cells were illuminated through the substrate (p-side of the pin structure).

Figure 3 .

 3 Figure3. Low-temperature current-voltage characteristics of samples A to D under illumination (50 mW cm -2 ). All EDMR measurements were carried out at a constant voltage U = -1 V (reverse bias regime of the solar cell). This point is indicated in the plot by a vertical line.

Figure 4 .

 4 Figure 4. Sketch of the pEDMR setup based on a commercial Bruker Elexsys E580 X-band ESR spectrometer. The sample is located in a microwave resonator which is placed in a He-cryostat with a window for optical access. A constant voltage source is used to apply a voltage U S to the sample and thus establishing a steady-state photocurrent I ph . Changes of the photocurrent, ∆|I ph |, are recorded as a function of time using a current detection unit shown in the lower part. The equivalent circuitry of the solar cell can be considered as a parallel circuit consisting of current source, resistor, and capacitor. Thus, it inherently acts as a lowpass filter for changes of the photocurrent and therefore limits the time resolution. The signal ∆|I ph | is converted into a voltage, filtered, and amplified to a level that is sufficient for the transient recorder of the ESR-spectrometer.

Figure 5 .

 5 Figure 5. pEDMR transients obtained from sample A. Two different current amplifiers as described in the text were used in order to demonstrate their influence on the transient dynamics. The curve labelled with 'EMM filtered' was generated by applying a numerical lowpass filter to the data of 'EMM'. The curve 'EMM fit' represents a least square fit of a model function consisting of two exponential functions (time constants τ 1 and τ 2 ) and taking into account lowpass filtering (time constant τ RC ) to the experimental data 'EMM' (fit results: τ 1 = 0.75 µs, τ 2 = 65 µs, τ RC = 4 µs). The inset shows an enlarged view of the first 20 µs of the transients.

Figure 6 .

 6 Figure 6. pEDMR spectra of samples A to D taken at t = 2.2 µs after the mw excitation at T = 10 K using a pulse length τ of 320 ns (solid line: experiment; dashed line: fit to the experimental data; dotted lines: individual spectral components as obtained from the fit). The resonance positions are indicated by vertical dotted lines. The insets show spectra on a broader magnetic field range measured under the same experimental conditions except for a mw power increased by 9 dB in order to enhance the broad spectral components. In addition, τ was set to values between 50 and 60 ns, which in all cases corresponds to a spin flip angle of φ = Ω • τ = π, with Ω being the Rabi frequency.

Figure 7 .

 7 Figure 7. Asymmetric line that was found in samples B and D (µc-Si:H n-layer). (a) Enlarged view of the pEDMR spectrum of sample B as shown in figure6with an ordinate range covering the first 10% of the maximum signal amplitude (solid line: experiment; dashed line: results of a simulation consisting of an inhomogeneously broadened line with parameters given in the text and a symmetric Gaussian line at g sd = 1.9675(5); dotted lines: both spectral components separately). (b) pEDMR spectra of sample B for several delays after the mw excitation. The solid vertical line serves as a g value marker. Note that the time behaviour of the asymmetric line and the sd resonance is considerably different.

Figure 8 Figure 8 .

 88 Figure 8. Time-dependent integrated peak intensities A of the deconvoluted pEDMR signals of samples A to D. The deconvolution procedure was applied to the experimental data obtained with narrow magnetic field range (cf. figure6). The g values and line widths were assumed to be identical for all samples. Details of the deconvolution procedure are described in the text.

Figure 9

 9 Figure 9. pEDMR spectrum of sample B recorded 4.0 µs after the mw pulse. Two lines with different g values and opposite signs can clearly be distinguished (solid line: experiment; dashed line: result of a fit with two Lorentzian lines; dotted lines: both separate contributions to the fit). Note that the spectrum has been multiplied by a factor of two to allow for a better comparison with the spectrum recorded at 2.2 µs which is also included in the plot.

Figure 10 .

 10 Figure 10. Integrated peak intensities for samples A and C (cells with a-Si:H n-layer). The deconvolution procedure performed using the two-dimensional pEDMR datasets with wide magnetic field range (cf. main plots in figure6). The hyperfine signal that is visible in the respective spectra was taken into account by assuming a pair of Gaussian lines that are symmetric to g P = 2.003. Note that the ordinate scale is normalised to facilitate the comparison of the dynamics.

Figure 11 .

 11 Figure 11. Results of pEDMR measurements of coherent spin motion carried out at two spectral positions for each sample A to D. The mw pulse length was varied from 0 to 450 ns with an increment of 2 ns. The oscillations reflect the coherent spin motion of the spin pair ensemble during the mw pulse. Fast fourier transformations of the data are depicted in the insets. The oscillation frequencies Ω/2π lie in the range from 12 to 15 MHz which corresponds to the Rabi frequency of a spin 1/2 under the conditions used in the experiment.

Table 1 .

 1 Structure of the silicon-layers for the µc-Si:H pin solar cells investigated in this study.

		n-layer	i-layer	p-layer
	sample A	a-Si:H	µc-Si:H	µc-Si:H
	sample B	µc-Si:H	µc-Si:H	µc-Si:H
	sample C	a-Si:H	µc-Si:H a-Si:H
	sample D	µc-Si:H	µc-Si:H a-Si:H

Table 2 .

 2 g values, line shapes and line widths obtained from least-square fits to the pEDMR spectra with narrow and wide magnetic field range (see figure6). Details are given in the text.

			sample A sample B	sample C sample D	paramagnetic state
	CE	g CE (Lorentzian) 1.9975(5) FWHM CE (mT) 1.8(1)	1.9977(5) 1.8(1)	1.9974(5) 1.8(1)	1.9977(5) 1.9(1)	cond. band tail µc-Si:H
	e	ge (Lorentzian) FWHMe (mT)	2.0049(5) 2.3(1)		2.0049(5) 1.8(1)		cond. band tail a-Si:H
	h	g h (Gaussian) FWHM h (mT)			2.011 2.9	2.011 2.9	val. band tail a-Si:H
		g P (Gaussian)	2.003		2.003
	P		hf split.: 25 mT		splitting: 25 mT		phosph. donor a-Si:H
		FWHM P (mT)	11.3		11.3
	sd	g sd (Gaussian) FWHM sd (mT)		1.9675(5) 2.5			shallow donor ZnO
	db	g db (Lorentzian) FWHM db (mT)		2.0045(5) 1.3(1)			dangling bond µc-Si:H
	CH	g CH (asym.) FWHM CH (mT)		g = 2.15 g ⊥ = 1.995 5 (Lorentz.) ∆g = 0.2			val. band tail µc-Si:H
				∆g ⊥ = 0.01

  Sketch of energy-band diagrams at room temperature without illumination for samples A to D. The paramagnetic centres that were found to be involved in spin-dependent processes in the respective samples are shown schematically. Details can be found in the text.

				sample B
			hn hn			CE	hn hn
		CE
	e,P	CH			CH	db
	n-a-Si:H	i-µc-Si:H	p-µc-Si:H	n-µc-Si:H	i-µc-Si:H	p-µc-Si:H
	sample C		sample D
			hn hn				hn hn
		CE				CE
	e,P	CH	h		CH		h
	n-a-Si:H	i-µc-Si:H	p-a-Si:H	n-µc-Si:H	i-µc-Si:H	p-a-Si:H
	Figure 12.

Acknowledgements

We are grateful to M.A. Gluba and O. Astakhov for helpful discussions. This work was partially funded by the German Federal Ministry of Education and Research (BMBF network project EPR-Solar 03SF0328A).


Laetitia Patural
email: patural@emse.fr

Alexandre Govin

Philippe Grosseau

Bertrand Ruot

Olivier Deves

O Devès

Effect of cellulose ethers on water retention in freshly-mixed mortars

Keywords: cellulose ethers, consistency, mortar, water retention

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Introduction

The factory made mortar industry produces today more than 100 types of mortars in Europe. These mortars are found in different forms and offer chemical and mechanical properties and characteristics specially fitted to very differing building and civil engineering constructions. Depending on the applications, factorymade mortars are mainly composed of mineral binders (cement, lime and/or gypsum), sands, aggregates and additives (e.g. fillers). To these major ingredients, different kinds of admixtures, mostly organics, are added in order to bring some particular properties to the mortar, from the fresh paste to the hardened material [START_REF] Bertrand | Proceedings of the 11th International Congress on Polymers in Concrete[END_REF][START_REF] Ghio | [END_REF][3][4][START_REF] Ruot | Proceedings of the VII SBTA (7° Symposio Brasileiro de Tecnologia das Argamassas)[END_REF]. Water retention is the property of a mortar that prevents the rapid loss of water to masonry units of high suction and prevents "bleeding" or "water gain" when the mortar is in contact with relatively impervious substrate. Water retention is an important property of mortar and affects workability and bond (durability, completeness, and strength) between mortar and masonry units. Water retention is affected by the formulation of the mortar (both cementitious and aggregate) and may be increased through the use of some organic admixtures. Cellulose is a common material in plant cell walls and it is the most abundant form of living terrestrial biomass. These polymers are widely used in many fields of application. The hydroxyl groups of cellulose can be partially or fully reacted with various chemicals to provide derivates, such as cellulose ethers, with useful properties. Among them, hydroxyethyl methyl cellulose (HEMC) are widely used in food industry, pharmaceutical industry and building materials. These admixtures constitute one of the most suitable molecules to improve mortar water retention [START_REF] Green | [END_REF]7], and its workability while they induce hydration delay. The mechanism by which the cellulose ethers affect the cement hydration was reported in literature [8,9]. However, the effect of such polymers on the mortar properties at the fresh state (water retention and consistency) is not well understood.

The objective of this paper is to evaluate the effect of HEMC on mortar water retention and its consistency. The consistency was assessed using Consistor Baronnie method and steady rate rheology. A correlation between both methods was attempted.

Experimental Materials

Experiments were performed using a laboratorymade mortar, called "CEReM mortar", composed of Portland CEM I 52.5 R cement (30% wt.), siliceous sand (65% wt.) and calcareous filler (5% wt.), to which CE was added (0.27% wt. in addition to the above dry mix). Cellulose ethers (CE) are water-soluble polymers derived from cellulose. Nowadays, they are systematically introduced into mortar formulations, in order to improve both water retention and workability of the fresh paste. Among the wide variety of existing CE, three types are mainly used in mortar manufacturing: hydroxypropyl-methyl cellulose (HPMC), hydroxyethyl-methyl cellulose (HEMC) and hydroxyethyl cellulose (HEC). Such polymers are characterised by three parameters: the molecular weight (noted as Mw) and two substitution degrees: DS (degree of substitution, the average number of hydroxyls substituted per anhydroglucose units) and MS (molecular substitution, the average mole substituents per anhydroglucose units). In our paper, eleven CE have been studied: four HEMC, noted as C and seven HEC, noted as H. Their molecular weights and the contents of substitution groups are detailed in Table 1.

Water retention measurements

Water retention was measured following two different standards: DIN 18555-7 Standard [START_REF]Testing of mortars containing mineral binders; part7: Determination of water retentivity of freshly mixed mortar by the filter plate method[END_REF] and ASTM C91 Standard [START_REF]Standard C91 section 7.2 and 7.3 -Specification for masonry cement: determination of water retention and air content[END_REF]. For the first one, experiments had to be performed 5 minutes after mixing and consisted in measuring the lost water of a mortar in contact with a filter paper. For the second one, the test was performed using the apparatus described in the ASTM C.91 Standard. 15 minutes after mixing, the mortar was subjected to vacuum (50 mmHg) for 15 minutes (Fig. 1).

Consistency measurements

Mortar consistency was assessed by two methods: the Consistor Baronnie method [START_REF]Certification CSTB des enduits monocouches d'imperméabilisation -Modalités d'essais[END_REF] and the steady rate rheology. The first one consisted in 10 stainless tubes with diameters ranging from 10 to 55 mm. They were marked from 1 to 10 and the aim of the experiment was to find the largest tube for which the paste did not slide before 5 seconds. Mortar consistency was given by the number which corresponded to the largest tube. This method need to be confirmed with more rigorous rheological measurements. For the rheometry tests, experiments were carried out with a Rheometrics Fluid Spectrometer RSFII with Vane geometry [13]. Rheograms represented the evolution of shear stress () versus the shear rate (), and were fitted with Herschel Bulkley model [14]:

n K        0 (1)
where: K represents the consistency coefficient,  0 the yield stress and n is the flow behaviour index. When n = 1, the formula reduces to the Bingham model. The shear-thinning behaviour associated with 0 < n < 1, and the unusual shear-thickening behaviour with n > 1.

Results and Discussion

First, a correlation between the results from two standards was established (Fig. 2). CE improved mortar water retention. Indeed, the ASTM retention capacity of the non-admixed mortar in next to 65%. Both methods were well correlated (r² = 0.99). Moreover, the results obtained with ASTM method slightly overrated the DIN ones. Then, the effect of molecular weight was studied using two different panels of molecules. For HEMC C, substitution degrees were roughly constant among the group, thus only one parameter varied: Mw. For HEC H, we consider that MS variations were less important than the Mw variations. Therefore, with this group, the water retention was also studied as a function of CE molecular weight. For HEMC C, while Mw increased from 80kDa to 380kDa, mortar water retention increased from 93.6% to 98.3% and mortar consistency increased from 1 to 3. As a result, for HEMC, an increase in polymer molecular weight leads to an improvement of both mortar water retention and consistency. Concerning HEC family, when Mw increased from 45kDa to 790kDa, mortar water retention increased from 95.1% to 98.8% and mortar consistency was improved. Consequently, for both CE families, the higher polymer molecular weight, the better the mortar water retention and its consistency. This can be explained by the CE capacity to form with water an aqueous phase with a higher viscosity [7,15], [16]. Consequently, a high molecular mass admixture would lower the water mobility with the result that the water retention would be increased. A correlation was attempted between Consistor Baronnie results and consistency coefficient obtained with rheometry (Fig. 3). With Consistor Baronnie method (CBM), the consistency c ranged from 1 (for C1) to 3 (for C4), while the consistency coefficient K varied from 1.92 (for C1) to 37.4 (for C4). Variations of the consistency c and the consistency coefficient K were similar, thus confirming the validity of the use of our method, CBM. Moreover, the correlation between both methods was established and the correlation coefficient was equal to 0.99 (Fig. 3). Consequently, BCM can be used to estimate mortar consistency. Besides, this method is very easy and quick to set up.

Conclusions

This paper reviewed the effect of cellulose ether molecular weight on mortar water retention and its consistency. The results demonstrated that the molecular weight is a crucial parameter in a given polymer family. It was noted that, as the molecular increased, both water retention and consistency were improved. Moreover, it has been shown that consistency assessed with the Consistor Baronnie method was wellcorrelated to the rheological parameter (more particular, to the consistency coefficient).

Fig. 1

 1 Fig. 1 ASTM test device to determine water retention of mortars. 1: fresh mortar; 2: perforated dish; 3: funnel; 4: tap; 5: flask; 6: to air vacuum.

Fig. 2

 2 Fig. 2 Correlation between water retention standard methods.

Fig. 3

 3 Fig. 3 Correlation between Consistor Baronnie method and rheometry.

Table 1

 1 Molecular parameters of the selected cellulose ethers.

	Cellulose ether	Mw (KDa)	DS	MS
	MHEC C1	80	1.8	0.15
	MHEC C2	180	1.7	0.15
	MHEC C3	310	1.7	0.15
	MHEC C4	380	1.7	0.15
	HEC H1	45	-	1.9
	HEC H2	140	-	2.0
	HEC H3	275	-	2.2
	HEC H4	430	-	2.3
	HEC H5	720	-	2.4
	HEC H6	770	-	2.4
	HEC H7	790	-	2.4

Acknowledgements

The authors would like to acknowledge all the industrial and academic CEReM members for their financial and technical support (http://cerem.cstb.fr). The authors also extend to thank Philippe Marchal (GEMICO, ENSIC, Nancy) for his help to perform and analyse rheological experiments.