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Continuous solidification of photovoltaic multicrystalline silicon from an inductive cold crucible
Journal of Crystal Growth 193 (1998) 230—240
Continuous solidification of photovoltaic multicrystalline silicon from an inductive cold crucible Gilles Dour!, Eric Ehret", A. Laugier", Dominique Sarti#, Marcel Garnier$, Francis Durand$,* ! Ecole des Mines, Albi-Carmaux, France " LPM INSA Lyon, France # Photowatt Int., Bourgoin-Jallieu, France $ EPM-Madylam, CNRS and INP Grenoble, ENSHMG, BP 95, F-38402 St. Martin d+Heres Cedex, France Received 12 December 1997; accepted 27 April 1998
Abstract An inductive cold crucible is used to melt photovoltaic granular silicon and to form massive multicrystalline billets by continuous pulling downwards. The cold crucible is noncontaminating. In the billet the impurity content is kept at the same low level as it is in the feed stock, even for copper, and somewhat lower for oxygen. Square billets are as easy to shape as circular ones. Continuous solidification gives the material uniform grain structure and properties, so that a considerable reduction in waste material is expected. Details are given on the experimental procedure and on measurements. For a given pulling rate, the optimal electrical conditions result from a fine compromise between the risk of a liquid leak, and the risk of nonmelting granules. Among the electrical and thermal measurements which were tested, the electrical frequency seems to give a possible gage for estimating the variation of the amount of liquid. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Multicrystalline silicon; Continuous solidification; Inductive cold crucible
1. Electromagnetic casting of photovoltaic silicon The photovoltaic energy conversion is now used in practical systems for providing electricity, not only in remote areas, but also for the domestic-scale consumption of large cities, as an effort to reduce the “greenhouse problem”. Economists [1] predict for the next two decades an increase in the solar cell
* Corresponding author. Fax: #33 4 7682 5249.
production by a factor 10, together with a corresponding decrease in the cell price by a proportion of 2—5, partly due to a scale effect and partly due to technological progress. For photovoltaic cells in the square meter scale, a significant part of the costs comes from the material. In the present state of the market, more than 25% comes from multicrystalline silicon, because it combines a fair conversion yield (11—15%) with low production costs. For the near future this part should increase to the detriment of the single
0022-0248/98/$ — see front matter ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 4 9 2 - 8
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crystal silicon (presently more than 55% of the market) because the higher production costs of the latter and the higher proportion of wasted material due to the crystal circular cross section are not compensated by its higher conversion yield (up to 24%). Presently, the larger part of multicrystalline silicon is prepared by directional solidification in ingot moulds [2]. Practically all moulds are lined with a thin “crucible” of high purity silica. Differences in the industrial techniques (“Silso” by Wacker [3,4], “HEM” [5], “Polix” by Photowatt [6]) come principally from the method for controlling heat transfer to insure a flat solid—liquid interface moving at a slow constant growth rate from the bottom to the top of the ingot. All techniques give massive ingots, multicrystalline with a grain structure formed of large columnar grains, ingots which are first sawn into blocks and then into thin wafers. These techniques all suffer from relatively high production costs associated with the crucible consumption, with the ingot manipulations, and with the long time of the cycle heating#melting# solidification. Moreover, due to the final transient regime of the ingot solidification, the upper part of the ingot has a lower quality and must be recycled so that the material yield is lowered [7]. These disadvantages are resolved by continuous casting using an inductive cold crucible. The application of an inductive cold crucible for processing silicon has been considered for many years [8—11]. The main advantage is that the material is not contaminated by the crucible. The continuous casting of metallic alloys using bottomless cold crucibles was developed in the early 1980s, initially using a slag as a protection [12], later without slag [13]. In 1985, Ciszek prepared silicon billets by continuous casting in an open-bottom crucible having a 26 mm]26 mm square confinement cross section with slightly octahedral corners [14]. In our lab, Delage et al. [15,16] developed studies on the electrical and thermal aspects of the process. Then with the French company Cezus we developed the so-called “4C-process” for recycling titanium scraps [17,18]. In this process, the metal forms a molten zone heated in a bottomless inductive cold crucible. It is fed with the titanium scraps. It is cast continuously in the form of billets. In 1989,
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in collaboration with the French company Photowatt, we applied this process to photovoltaic silicon. A major difficulty comes from the fact that induced currents develop only in the high temperature part of the material. For the theoretical analysis of this effect, a numerical software called “MALICE” was created, in which the electromagnetic phenomena treated using the integral method can interact with the finite element technique for the thermal calculations [19]. The solidification microstructure of the continuously cast material was presented first [20], then came some photovoltaic measurements [21—23]. More recently a theoretical model described the formation of thermal stresses during cooling, and their possible relaxation by dislocation multiplication and flow [24,25]. Independently, from 1987 a Japanese group led by Kyojiro Kaneko working under Osaka Titanium Co., now with Sumitomo Sitix Co., intensively applied the concept created by Ciszek to the production of photovoltaic multicrystalline silicon in square billets, initially 88 mm]88 mm, then 220 mm]220 mm, and they announced the billet size of 350 mm]350 mm. They pointed out the economical advantages (crucible costs eliminated, material handling much simpler2). They demonstrated the superior uniformity in microstructure and properties of this material [26—32]. They created the expression “EMC silicon” for “electromagnetically cast silicon”. The aim of this paper is to describe the operating conditions of the laboratory pilot equipment we call “Madylam Puller”, in its P3 version, in particular the limitations in the process parameters due to possible casting accidents, and the correlative interpretation.
2. Experimental equipment The active part of the process is a molten zone, heated by induction, from which a massive silicon billet is cast at a constant rate (Fig. 1). The molten zone is fed by raw silicon in a particulate form. In principle we use millimeter size granules fresh from the gas cracking production, but most of the setting up experiments were performed using crushed
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as a susceptor can be placed in the upper part of the crucible in order to control the final cooling of the liquid dome during the arrest regime. Coil, crucible, billet, silicon feed stock and the feeding system are placed in a vacuum tight chamber with double wall, watercooled. Prior to the experiment the chamber is evacuated, then filled with argon. A slight overpressure and an argon flow are maintained during the entire experiment.
3. Experimental parameters and procedure For the process at the laboratory scale, the parameters are the following:
Fig. 1. Schematic diagram of electromagnetic continuous pulling equipment, in its “Madylam Puller” version (a). Grain structure of the multicrystalline silicon billet in longitudinal section and (b) transverse section.
recycled refuse of electronic grade silicon. Besides, according to our experience on metals, it should be possible to feed the molten zone by direct remelting of polycrystalline silicon rods fresh from the cracking production. The cross section of the billet is shaped by the inner surface of the cold crucible. Different crucibles have been used: initially a circular one, 100 mm diameter, then a square one 60 mm] 60 mm, more recently a circular one 120 mm diameter. All of them are segmented from the bottom to about 10 cm from the top. All the following experiments are related to the 120 mm diameter crucible. The crucible is surrounded by four turns of copper tube forming the inductive coil. Just below the crucible, the silicon billet enters an annealing sheath of preformed graphite fibers which controls the cooling conditions.The silicon billet is fixed on a graphite base. A pulling system ensures a constant solidification rate. A graphite disc acting
f the casting rate (1 mm/min in the runs presented here, comparable to the pulling rate in Czochralski technique, up to 3 mm/min in a first series on square billets); f the coil-crucible geometry, in particular the number of turns of the coil, its height, the position of the lower turn; f the electrical frequency (20—25 kHz) f the electrical voltage at the power generator, through which the Joule power induced in the charge can be controlled. The present generator has a nominal power of 100 kW, but in pulling conditions the power is around 30 kW. This section describes the successive steps of a casting experiment, together with the variation of the measured parameters, in particular the electrical parameters (Fig. 2). 3.1. Formation of the molten zone At the beginning of the experiment, preheating is necessary because induction currents can develop in silicon only at high temperature. The graphite base of the pulling system is placed 5 mm inside the crucible, so that it can be inductively heated to silicon melting temperature. Then the feeder is activated, and the silicon particles melt in contact with the base. Due to the electromagnetic forces, the liquid immediately takes the shape of a dome which moves randomly and very fast around the
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particles do not melt anymore. It is necessary to stop the feeding, and to apply extra power to remelt the crust, with the risk of liquid leak afterwards. The risk of the above accidents is particularly high during the transient regime occurring at the beginning of pulling, until temperatures below the crucible are stable, which corresponds approximately to cast a billet length of the order of the diameter. Beyond this, on condition that no mechanical or electrical breakdown occurs, something like a steady state regime is established after about approximately 500 mm billet length. The desired length of billet can be cast. 3.3. Arrest procedure
Fig. 2. Time variation of the electrical parameters in a typical experiment.
axis of the base. The dome grows with the particle feeding until it is nearly touching the crucible wall. At this stage the liquid surface hardly moves, except for small oscillations. 3.2. Continuous casting, and possible accidents When enough liquid is formed, the graphite base is pulled downwards. The feeding rate is adjusted in order to balance the selected pulling rate, typically 1 mm/min. The electrical voltage is reduced progressively to the steady-state value. The latter results from a compromise: f if the power is too high, a liquid leak occurs. If the leak is massive, or if it cannot be detected, the molten zone drains off, the process stops by itself, and the billet is lost. If the leak is weak and can be detected, the operator can use an emergency procedure: pulling is stopped, together with feeding, power is significantly lowered until the solid shell is restored. Then the casting operation can be restarted. f if the power is too low, the solid particles can accumulate on the dome in contact with the crucible wall and form a crust. The following
The laboratory equipment allows only 600 mm of billet length to be cast. At the end of the casting operation, special care must be taken to avoid a solid cap forming on the liquid free surface, because the volume expansion associated with the solidification of silicon would make the billet head split, and the cracks would propagate in the entire billet. The operator stops both feeding and pulling, keeps the power level constant and introduces the graphite susceptor into the crucible. When the disc is hot enough, the power input is progressively lowered, so that the temperature at 5 mm below the crucible outlet decreases at the rate 2—4°C/min, i.e. the cooling rate of a billet slice in continuous pulling. 3.4. Variation of the electrical parameters Fig. 2 shows typical variations of the electrical parameters during the dome formation and the pulling regime. The voltage is the only electrical parameter the operator can actually control during the experiment. It is high during the dome formation, and much lower in the following sequences. In the present working conditions, during pulling we use approximately 7700 V, giving a current of 3.7 A in the circuit, it means 28 kW power. A slow decrease can be noticed in the second sequence in Fig. 2 because the operator anticipated the heat loss reduction. As this latter slowly decreases to
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reach a steady-state value after 8 h, so does the voltage. In the last sequence, the voltage is manually lowered according to the cooling down criterion. 3.5. Temperature measurements Four thermocouples were placed at the internal surface of the annealing sheath, at 50, 200, 350 and 550 mm below the crucible outlet, respectively. They give information on the temperature distribution at the billet surface. In particular they give an indication of the relatively long response time of the thermal phenomena. For instance after the power was fixed at its steady state value, temperature records show a plateau only 210 min later at level !50 mm, and this change propagates along the billet. For a casting rate of 1 mm/min, approximately 500 mm of billet are necessary to get steady state casting conditions. Six thermocouples were inserted at different levels along a vertical line through the crucible wall. The temperature records (Fig. 3) give an idea of the fluctuations affecting the molten zone. The temperature of the two upper thermocouples fluctuates slightly around 100°C, because the small oscillations of the dome modify periodically the heat transfer. The two lower thermocouples give smooth cold records (200°C) except when a leak occurs. Periodic fluctuations appear on the records of the intermediate thermocouples, and this is used to detect the level of the solid/liquid/gas triple junction, and also to monitor feared leak departures.
orthogonal to the grain boundary lines (GB lines). It is concave towards the liquid phase, as in continuous casting processes. Different zones can be distinguished according to grain size and orientation: f in the skin layer, the grains are very thin (about 0.1 mm) and randomly oriented; f a transition zone is visible on the longitudinal section because the direction of growth changes rapidly, so the grain boundary lines show a strong curvature. f in the core zone, the grain boundaries are nearly parallel to the pulling direction. The grain diameter can reach 4—5 mm. It means that the grain transverse size increases by a factor 20 or more along 100 mm of a GB-line from the surface to the core zone, an expansion rate much lower than that is expected for a metallic alloy. The reason is that in silicon this expansion is probably controlled by differences in planar growth rate due to crystal or twin orientation, and not to a branching mechanism of secondary or tertiary dendrites like in alloys. 4.2. Cracks At the beginning of the program, all billets were severely damaged by cracks. In the present process,
4. “Madylam” silicon as a “future” photovoltaic material 4.1. Grain structure, mechanisms, development of grain size The grain structure of the silicon billets is entirely columnar (Fig. 1). Grains nucleated at the triple junction, i.e. the line along which solid, liquid and atmosphere are in contact. They grew from the outer surface towards the core following the heat flow lines [20]. Therefore, the shape of the solid— liquid interface can be visualized as the surface
Fig. 3. Time variation of the temperature of the thermocouples inserted at different levels along the internal wall of the crucible. The position is shown on the cross section Z, distance to the crucible bottom.
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Fig. 3. Continued.
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cracks can result from two different mechanisms. (a) Cracks resulting from the final solidification transient step. For this reason we added the graphite disc which acts as an upper heater to orientate the final solidification from the pool bottom to the free surface. (b) Cracks from thermal contraction [24,25]. In continuous casting, a slice of material is traveling through a field of isotherms, concave inside the crucible, then progressively more and more planar. During this transformation, nonuniformity in thermal contraction creates elastic stresses which can be relaxed by multiplication of dislocations flowing plastically. For silicon, it is known that this plastic flow can occur only at high temperature, say more than 700°C. The practical conclusion was to make planar the isotherms above this temperature, which was done by using a convenient insulating sheath. In the present stage of the procedure, all runs performed according to the above rules give crack free billets which can be cut in wafers distributed to the partners for characterization. 4.3. Dislocations The dislocation distribution as revealed by etch pits is highly nonuniform [20,33]. In some grains the density is low, the etch pits are aligned along crystallographic directions, suggesting some slow plastic flow process. In other grains, the density is much higher, the etch pits are arranged into cells, suggesting some complex interaction mechanism. Crowded areas appear in some grains, the shape of which suggests an intense local deformation mechanism creating dislocation tangles. Outside such tangled areas, the mean density of etch pits ranges from 30]104 to 50]104 cm~2. It is higher in the skin area of the billet (150]104 cm~2). Probably the present cooling conditions give rise to some residual thermal contraction occurring in the medium temperature range, sufficiently hot to avoid crack formation, but not enough to promote creep relaxation [25]. 4.4. Impurities and dopant All metallic impurities were below the detection limit of the atomic absorption technique. In par-
ticular this was true for copper in the billets and also in the feed stock. The only contamination noted was due to the use of an improper feeding system which had a crushing effect and contaminated with iron an intermediate series of billets. This was corrected by the setting up of a new feeder in the more recent tests. In the present program the feed particles were crushed refuse of doped “Polix” silicon. Resistivity measurements on cast billets gave 0.7$0.1 ) cm, practically constant, the variation from center to edge of the wafer, or variation along the billet being less than 0.1 ) cm [33]. As regards oxygen and carbon, the measurements reported here were performed by Fourier transform infrared spectroscopy (FTIR) [33]. Such measurements give information on oxygen and carbon atoms in solid solution only, and not on the possible oxide or carbide particles. Measurements on “total” content were not performed at this stage of the program. The results are the following: f there is practically no variation in the oxygen content according to the position in the billet, neither radial, nor axial; f the oxygen content in Madylam Si as in EMC Si from Osaka Titanium Sitix is significantly lower (from 0.4 to 1.2 ppm) than in the Polix material; f the carbon content is below the detection limit in the EMC-OTC-Si. It is practically uniform (7 ppm) in Madylam Si. 4.5. Diffusion length The photovoltaic quality of the material itself is evaluated from photocurrent measurements performed on simplified cells which do not require either heat treatments or surface treatments [21—23]. The photocurrent resulting from a local light input is a measure of the local value of the diffusion length of the minority carriers. A low value means that the carriers are trapped. The diffusion length varies along a diameter as shown in Fig. 4a. The diffusion length in the central zone is very homogeneous and is the highest. This zone seems to correspond to the core zone of the grain structure. The peripheral zone has a much poorer response [33].
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Fig. 5. Photovoltaic module fabricated from Madylam multicrystalline silicon in the Photowatt workshops.
Fig. 4. Diffusion length of the minority carriers, on a typical Madylam billet. (a) Transverse variation, (b) axial variation
As expected from the continuous casting process, the properties are very uniform along the billet (Fig. 4b). A similar uniformity was reported on the EMC Sitix material. The plateau value of the diffusion length is 45 lm for the Madylam Si, to be compared to 70 lm for the Sitix Si, a value significantly lower than what is measured on the Polix material (from 90 lm to more than 100 lm). Undoubtedly the EMC material must be considered as a new material, on which research efforts can give significant improvements.
Fig. 6. Conversion efficiency of the 30 cells of the module on Fig. 4.
100 mm) are rounded by the circular section of the billets (120 mm). The conversion efficiency ranged from 10 to 11.5% and was remarkably uniform along the billet (Fig. 6). These numbers are very close to what was published for the Sitix material, which is a surprising result considering the difference in diffusion length. As compared to Polix cells (efficiency 13—15%) it is clear that the Madylam material is at an early stage of development and should be improved.
5. Discussion 4.6. Measurements on solar cells A series of 31 solar cells was fabricated by Photowatt from one of the Madylam billets. A photovoltaic module was built (Fig. 5). The origin of the wafers is visible because the square cells (100 mm]
5.1. Fleeting contact between material and cold crucible On the lateral surface of the billets, it is difficult to detect the position of the crucible slits because
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there is no external protrusion. This means that the electromagnetic forces were sufficient to repell the liquid and to prevent it penetrating into the slit. In front of the segment walls, the skin seems to be made from successive waves frozen against the crucible wall. Their periodicity is relatively long, a few mm, so they reflect a slow fluctuation, with a periodicity comparable to that of the temperature fluctuations (Fig. 3). These waves build the upper lip of the shell. As soon as the latter has a sufficient thickness to counterbalance the hydrostatic pressure, a gas edge forms between the billet surface and the crucible wall because of thermal contraction and moreover of the taper machined in the lower part of the crucible wall. If fluctuation waves happen to put the liquid in contact with the crucible wall, this contact is local and short. Taking into account the low temperature of the copper surface, if some copper atoms migrate, this migration lasts a very limited time and is rapidly frozen.
the above conditions, a slight increase (approximately 0.5%) in the generator voltage is sufficient to trigger a leak. As regards the heat extracted from the billet surface, the crucible outlet makes a major discontinuity, because the insulating sheath limits the radial heat flow to a very low value. Now, considering an accidental increase in Joule power, at a given level the shell thickness first tends to decrease. If the level considered is inside the crucible, this thickness decrease results in an increase in extracted heat so that the front can find a stable position. On the contrary, if the level considered is below the crucible, the extracted heat is only weakly related to the distance to the surface, the front position is much less stable, the risk of leak is considerably greater [34]. This is a difference in comparison to the continuous casting of alloys, because in this latter case the billet cooling is increased when the material comes out of the mould. 5.3. The electric frequency, the most sensitive gage
5.2. Liquid leaks and the limited stability of the solid shell Considering a billet cross section, the core zone should be favored because of its better photovoltaic performances. It means that the skin zone and the intermediate zone should be confined approximately in the 10 mm external layer of the billet. Taking account of the grain mechanism, we have modified the solidification procedure in order to make the solid—liquid front as shallow and as flat as possible. At least for the low pulling rate (1 mm/ min) we succeeded in keeping the front inside the crucible, the pool bottom being close to the level of the crucible outlet. In fact the front originates at the triple junction, the level of which is correlated to the lower level of the induction coil because the magnetic flow lines are channelled into the electromagnetic penetration layer at the liquid free surface, which makes a localized heat source. Starting from this point, the front profile is an isotherm, the shape of which depends on the balance between the Joule power input, the heat transported in the pulled material, and the heat extracted from the external surface of the billet [34]. This balance is very sensitive. Particularly in
From an electrical point of view, the whole system Mgenerator#capacitor#coil# crucible# material chargeN can be considered as an oscillating circuit, the model of which was proposed by Delage and Ernst [15]. The capacity C is equal to that of the capacitor box (presently 20 lF). The equivalent resistance R is the sum of the component resistances, for the coil, the crucible, and the charge, respectively: In the inductance ¸, the coil inductance is lowered from the contribution of the crucible and of the material. According to this model and knowing the generator is aperiodic, the frequency of the electrical signal is the fundamental frequency of the equivalent circuit, f"1/ (2p(¸C)1@2). The frequency is affected by any change in the dome shape, but it does not depend on the voltage (or just through the dome shape). In the first sequence, in Fig. 2 the frequency increases linearly with time, and then with the amount of liquid. This increase is explained by a decrease in the equivalent inductance ¸, a decrease due to the increasing contribution of the melt inductance. As soon as the steady state regime is obtained, the frequency does not vary more than 10 Hz.
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In the relationship between voltage and current predicted by the model, the charge is expected to act in two different directions via inductance and resistance so that the interpretation is not straightforward. Moreover, the sensitivity of the recorded values seems to be much lower. As mentioned in Section 3, the transition from the molten zone formation to the continuous pulling regime needs careful control of the electrical power, in relation to the volume of the liquid zone. Temperature measurements are easy at points of the billet surface below the crucible outlet, but their information is damped by the relatively long distance to the critical points of the solid shell. On temperature measurements performed through the crucible the fluctuation noise is high so they cannot be used for control purpose. On the contrary the electrical frequency measurements give a reproducible behavior which can be supported by the electrical model [15], so we consider it could be used as a measure of the liquid zone extension.
6. Conclusions (1) Continuous pulling gives the multicrystalline silicon material very uniform grain structure and properties. An important reduction in waste material can be expected from the application of the process. (2) The cold crucible does not contaminate the material. In particular the copper content is kept at the same low level as in the feed stock. The oxygen content is somewhat reduced with respect to the feed stock. (3) As in alloy continuous casting, the container for the liquid is in fact the solid shell freezing against the crucible and below. Its shape is concave towards the liquid. New crystals nucleating along the triple junction are not geometrically eliminated, they grow towards the billet core. The increase in grain cross section results only from the differences in growth rate related to crystal orientation, as in the silicon ingot solidification. (4) The cold crucible acts as a shaping tool giving its external surface to the material, in particular a square cross section, favorable to the building of large photovoltaic systems. This is an advantage
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with respect to single crystal pulling systems, Czochralski or floating zone. (5) As compared to alloy continuous casting, the inductive cold crucible acts not only as the shaping tool for casting the billet, but also as the melting tool. These two functions are antagonistic, because a too low electrical power leads to the formation of a crust stopping the incorporation of feed granules, whereas a very high power makes the solid—liquid front deeper and more concave, leading to liquid leaks. The optimal operating conditions result from a fine compromise, particularly if the coil is kept in the lower position.
Acknowledgements The authors gratefully acknowledge the financial support of the French Government via the ADEME and CNRS-ECODEV programs since 1990, and of the European Community in the JOULE program since 1996. They wish to express their appreciation of the competence and reliable support of A. Claverie and Y. Marfaing, delegate managers of the French photovoltaic public program. The characterization of the “Madylam” silicon was performed by the partners of the program, i.e. Gilles Goaer, Le Quan Nam at Photowatt, Santo Martinuzzi, Isabelle Pe´richaud at Universite´ d’AixMarseille, Jean Claude Muller at CNRS-Phase, Strasbourg, Dominique Ballutaud at CNRSMeudon. Many thanks to them for their contributions and advice.
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[23] S. Martinuzzi, I. Pe´richaud, L. Clerc, M. Bacon, F. Floret, D. Sarti, G. Dour, Quan-Nam Le, G. Goaer, F. Durand, Proc. 25th PVSC-IEEE Conf., Washington DC, USA, 1996, pp. 617—620. [24] G. Dour, F. Durand, Y. Bre´chet, in: M. Cross, J. Campbell (Eds.), Proc. MCWASP VII, The Minerals, Metals and Materials Society, 1995, pp. 295—302. [25] G. Dour, F. Durand, Y. Bre´chet, Thermal-visco-plastic stress analysis in continuous casting, Application to silicon, Modeling Simul. Mater. Sci. Eng. (1997) 275—288. [26] K. Kaneko, T. Misawa, K. Tabata, Osaka Titanium Co., Proc. 6th Int. Iron and Steel Congress, Nagoya, Japan, 1990, pp. 254—259. [27] K. Kaneko, T. Misawa, K. Tabata, Proc. PVSEC-5, Kyoto, Japan, 1990, pp. 201—204. [28] K. Kaneko, R. Kawamura, T. Misawa, Sumitomo Sitix Co., Proc. 1st WC-PEC-IEEE, Hawaii, USA, 1994, pp. 30—33. [29] R. Kawamura, K. Sasatani, T. Onisuka, K. Kaneko, Sumitomo Sitix Co., Proc. 1st WC-PEC-IEEE, Hawaii, USA, 1994, pp. 1652—1655. [30] R. Kawamura, K. Sasatani, T. Onizuka, K. Kaneko, Sumitomo Sitix Co., Proc. PVSEC-9, Miyazaki, Japan, 1996, paper B2-1. [31] K. Sasatani, R. Kawamura, T. Onizuka, K. Kaneko, Sumitomo Sitix Co., Proc. PVSEC-9, Miyazaki, Japan, 1996, paper P1D-9. [32] T. Onizuka, R. Kawamura, K. Sasatani, K. Kaneko, Sumitomo Sitix Co., Proc. PVSEC-9, Miyazaki, Japan, 1996, paper P1D-10. [33] E. Ehret, Caracte´risation du silicium multicristallin e´labore´ en creuset froid inductif: influence des parame`tres de croissance et des traitements thermiques ulte´rieurs sur les proprie´te´s e´lectriques du mate´riau, Doctorate Thesis, INSA Lyon, 1996. [34] G. Dour, Tirage semi-continu de silicium photovoltaı¨ que multicristallin en creuset froid inductif, expe´rimentation et caracte´risation, Doctorate Thesis, INP Grenoble, 1996.
Continuous solidification of photovoltaic multicrystalline silicon from an inductive cold crucible Gilles Dour!, Eric Ehret", A. Laugier", Dominique Sarti#, Marcel Garnier$, Francis Durand$,* ! Ecole des Mines, Albi-Carmaux, France " LPM INSA Lyon, France # Photowatt Int., Bourgoin-Jallieu, France $ EPM-Madylam, CNRS and INP Grenoble, ENSHMG, BP 95, F-38402 St. Martin d+Heres Cedex, France Received 12 December 1997; accepted 27 April 1998
Abstract An inductive cold crucible is used to melt photovoltaic granular silicon and to form massive multicrystalline billets by continuous pulling downwards. The cold crucible is noncontaminating. In the billet the impurity content is kept at the same low level as it is in the feed stock, even for copper, and somewhat lower for oxygen. Square billets are as easy to shape as circular ones. Continuous solidification gives the material uniform grain structure and properties, so that a considerable reduction in waste material is expected. Details are given on the experimental procedure and on measurements. For a given pulling rate, the optimal electrical conditions result from a fine compromise between the risk of a liquid leak, and the risk of nonmelting granules. Among the electrical and thermal measurements which were tested, the electrical frequency seems to give a possible gage for estimating the variation of the amount of liquid. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Multicrystalline silicon; Continuous solidification; Inductive cold crucible
1. Electromagnetic casting of photovoltaic silicon The photovoltaic energy conversion is now used in practical systems for providing electricity, not only in remote areas, but also for the domestic-scale consumption of large cities, as an effort to reduce the “greenhouse problem”. Economists [1] predict for the next two decades an increase in the solar cell
* Corresponding author. Fax: #33 4 7682 5249.
production by a factor 10, together with a corresponding decrease in the cell price by a proportion of 2—5, partly due to a scale effect and partly due to technological progress. For photovoltaic cells in the square meter scale, a significant part of the costs comes from the material. In the present state of the market, more than 25% comes from multicrystalline silicon, because it combines a fair conversion yield (11—15%) with low production costs. For the near future this part should increase to the detriment of the single
0022-0248/98/$ — see front matter ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 4 9 2 - 8
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crystal silicon (presently more than 55% of the market) because the higher production costs of the latter and the higher proportion of wasted material due to the crystal circular cross section are not compensated by its higher conversion yield (up to 24%). Presently, the larger part of multicrystalline silicon is prepared by directional solidification in ingot moulds [2]. Practically all moulds are lined with a thin “crucible” of high purity silica. Differences in the industrial techniques (“Silso” by Wacker [3,4], “HEM” [5], “Polix” by Photowatt [6]) come principally from the method for controlling heat transfer to insure a flat solid—liquid interface moving at a slow constant growth rate from the bottom to the top of the ingot. All techniques give massive ingots, multicrystalline with a grain structure formed of large columnar grains, ingots which are first sawn into blocks and then into thin wafers. These techniques all suffer from relatively high production costs associated with the crucible consumption, with the ingot manipulations, and with the long time of the cycle heating#melting# solidification. Moreover, due to the final transient regime of the ingot solidification, the upper part of the ingot has a lower quality and must be recycled so that the material yield is lowered [7]. These disadvantages are resolved by continuous casting using an inductive cold crucible. The application of an inductive cold crucible for processing silicon has been considered for many years [8—11]. The main advantage is that the material is not contaminated by the crucible. The continuous casting of metallic alloys using bottomless cold crucibles was developed in the early 1980s, initially using a slag as a protection [12], later without slag [13]. In 1985, Ciszek prepared silicon billets by continuous casting in an open-bottom crucible having a 26 mm]26 mm square confinement cross section with slightly octahedral corners [14]. In our lab, Delage et al. [15,16] developed studies on the electrical and thermal aspects of the process. Then with the French company Cezus we developed the so-called “4C-process” for recycling titanium scraps [17,18]. In this process, the metal forms a molten zone heated in a bottomless inductive cold crucible. It is fed with the titanium scraps. It is cast continuously in the form of billets. In 1989,
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in collaboration with the French company Photowatt, we applied this process to photovoltaic silicon. A major difficulty comes from the fact that induced currents develop only in the high temperature part of the material. For the theoretical analysis of this effect, a numerical software called “MALICE” was created, in which the electromagnetic phenomena treated using the integral method can interact with the finite element technique for the thermal calculations [19]. The solidification microstructure of the continuously cast material was presented first [20], then came some photovoltaic measurements [21—23]. More recently a theoretical model described the formation of thermal stresses during cooling, and their possible relaxation by dislocation multiplication and flow [24,25]. Independently, from 1987 a Japanese group led by Kyojiro Kaneko working under Osaka Titanium Co., now with Sumitomo Sitix Co., intensively applied the concept created by Ciszek to the production of photovoltaic multicrystalline silicon in square billets, initially 88 mm]88 mm, then 220 mm]220 mm, and they announced the billet size of 350 mm]350 mm. They pointed out the economical advantages (crucible costs eliminated, material handling much simpler2). They demonstrated the superior uniformity in microstructure and properties of this material [26—32]. They created the expression “EMC silicon” for “electromagnetically cast silicon”. The aim of this paper is to describe the operating conditions of the laboratory pilot equipment we call “Madylam Puller”, in its P3 version, in particular the limitations in the process parameters due to possible casting accidents, and the correlative interpretation.
2. Experimental equipment The active part of the process is a molten zone, heated by induction, from which a massive silicon billet is cast at a constant rate (Fig. 1). The molten zone is fed by raw silicon in a particulate form. In principle we use millimeter size granules fresh from the gas cracking production, but most of the setting up experiments were performed using crushed
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as a susceptor can be placed in the upper part of the crucible in order to control the final cooling of the liquid dome during the arrest regime. Coil, crucible, billet, silicon feed stock and the feeding system are placed in a vacuum tight chamber with double wall, watercooled. Prior to the experiment the chamber is evacuated, then filled with argon. A slight overpressure and an argon flow are maintained during the entire experiment.
3. Experimental parameters and procedure For the process at the laboratory scale, the parameters are the following:
Fig. 1. Schematic diagram of electromagnetic continuous pulling equipment, in its “Madylam Puller” version (a). Grain structure of the multicrystalline silicon billet in longitudinal section and (b) transverse section.
recycled refuse of electronic grade silicon. Besides, according to our experience on metals, it should be possible to feed the molten zone by direct remelting of polycrystalline silicon rods fresh from the cracking production. The cross section of the billet is shaped by the inner surface of the cold crucible. Different crucibles have been used: initially a circular one, 100 mm diameter, then a square one 60 mm] 60 mm, more recently a circular one 120 mm diameter. All of them are segmented from the bottom to about 10 cm from the top. All the following experiments are related to the 120 mm diameter crucible. The crucible is surrounded by four turns of copper tube forming the inductive coil. Just below the crucible, the silicon billet enters an annealing sheath of preformed graphite fibers which controls the cooling conditions.The silicon billet is fixed on a graphite base. A pulling system ensures a constant solidification rate. A graphite disc acting
f the casting rate (1 mm/min in the runs presented here, comparable to the pulling rate in Czochralski technique, up to 3 mm/min in a first series on square billets); f the coil-crucible geometry, in particular the number of turns of the coil, its height, the position of the lower turn; f the electrical frequency (20—25 kHz) f the electrical voltage at the power generator, through which the Joule power induced in the charge can be controlled. The present generator has a nominal power of 100 kW, but in pulling conditions the power is around 30 kW. This section describes the successive steps of a casting experiment, together with the variation of the measured parameters, in particular the electrical parameters (Fig. 2). 3.1. Formation of the molten zone At the beginning of the experiment, preheating is necessary because induction currents can develop in silicon only at high temperature. The graphite base of the pulling system is placed 5 mm inside the crucible, so that it can be inductively heated to silicon melting temperature. Then the feeder is activated, and the silicon particles melt in contact with the base. Due to the electromagnetic forces, the liquid immediately takes the shape of a dome which moves randomly and very fast around the
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particles do not melt anymore. It is necessary to stop the feeding, and to apply extra power to remelt the crust, with the risk of liquid leak afterwards. The risk of the above accidents is particularly high during the transient regime occurring at the beginning of pulling, until temperatures below the crucible are stable, which corresponds approximately to cast a billet length of the order of the diameter. Beyond this, on condition that no mechanical or electrical breakdown occurs, something like a steady state regime is established after about approximately 500 mm billet length. The desired length of billet can be cast. 3.3. Arrest procedure
Fig. 2. Time variation of the electrical parameters in a typical experiment.
axis of the base. The dome grows with the particle feeding until it is nearly touching the crucible wall. At this stage the liquid surface hardly moves, except for small oscillations. 3.2. Continuous casting, and possible accidents When enough liquid is formed, the graphite base is pulled downwards. The feeding rate is adjusted in order to balance the selected pulling rate, typically 1 mm/min. The electrical voltage is reduced progressively to the steady-state value. The latter results from a compromise: f if the power is too high, a liquid leak occurs. If the leak is massive, or if it cannot be detected, the molten zone drains off, the process stops by itself, and the billet is lost. If the leak is weak and can be detected, the operator can use an emergency procedure: pulling is stopped, together with feeding, power is significantly lowered until the solid shell is restored. Then the casting operation can be restarted. f if the power is too low, the solid particles can accumulate on the dome in contact with the crucible wall and form a crust. The following
The laboratory equipment allows only 600 mm of billet length to be cast. At the end of the casting operation, special care must be taken to avoid a solid cap forming on the liquid free surface, because the volume expansion associated with the solidification of silicon would make the billet head split, and the cracks would propagate in the entire billet. The operator stops both feeding and pulling, keeps the power level constant and introduces the graphite susceptor into the crucible. When the disc is hot enough, the power input is progressively lowered, so that the temperature at 5 mm below the crucible outlet decreases at the rate 2—4°C/min, i.e. the cooling rate of a billet slice in continuous pulling. 3.4. Variation of the electrical parameters Fig. 2 shows typical variations of the electrical parameters during the dome formation and the pulling regime. The voltage is the only electrical parameter the operator can actually control during the experiment. It is high during the dome formation, and much lower in the following sequences. In the present working conditions, during pulling we use approximately 7700 V, giving a current of 3.7 A in the circuit, it means 28 kW power. A slow decrease can be noticed in the second sequence in Fig. 2 because the operator anticipated the heat loss reduction. As this latter slowly decreases to
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reach a steady-state value after 8 h, so does the voltage. In the last sequence, the voltage is manually lowered according to the cooling down criterion. 3.5. Temperature measurements Four thermocouples were placed at the internal surface of the annealing sheath, at 50, 200, 350 and 550 mm below the crucible outlet, respectively. They give information on the temperature distribution at the billet surface. In particular they give an indication of the relatively long response time of the thermal phenomena. For instance after the power was fixed at its steady state value, temperature records show a plateau only 210 min later at level !50 mm, and this change propagates along the billet. For a casting rate of 1 mm/min, approximately 500 mm of billet are necessary to get steady state casting conditions. Six thermocouples were inserted at different levels along a vertical line through the crucible wall. The temperature records (Fig. 3) give an idea of the fluctuations affecting the molten zone. The temperature of the two upper thermocouples fluctuates slightly around 100°C, because the small oscillations of the dome modify periodically the heat transfer. The two lower thermocouples give smooth cold records (200°C) except when a leak occurs. Periodic fluctuations appear on the records of the intermediate thermocouples, and this is used to detect the level of the solid/liquid/gas triple junction, and also to monitor feared leak departures.
orthogonal to the grain boundary lines (GB lines). It is concave towards the liquid phase, as in continuous casting processes. Different zones can be distinguished according to grain size and orientation: f in the skin layer, the grains are very thin (about 0.1 mm) and randomly oriented; f a transition zone is visible on the longitudinal section because the direction of growth changes rapidly, so the grain boundary lines show a strong curvature. f in the core zone, the grain boundaries are nearly parallel to the pulling direction. The grain diameter can reach 4—5 mm. It means that the grain transverse size increases by a factor 20 or more along 100 mm of a GB-line from the surface to the core zone, an expansion rate much lower than that is expected for a metallic alloy. The reason is that in silicon this expansion is probably controlled by differences in planar growth rate due to crystal or twin orientation, and not to a branching mechanism of secondary or tertiary dendrites like in alloys. 4.2. Cracks At the beginning of the program, all billets were severely damaged by cracks. In the present process,
4. “Madylam” silicon as a “future” photovoltaic material 4.1. Grain structure, mechanisms, development of grain size The grain structure of the silicon billets is entirely columnar (Fig. 1). Grains nucleated at the triple junction, i.e. the line along which solid, liquid and atmosphere are in contact. They grew from the outer surface towards the core following the heat flow lines [20]. Therefore, the shape of the solid— liquid interface can be visualized as the surface
Fig. 3. Time variation of the temperature of the thermocouples inserted at different levels along the internal wall of the crucible. The position is shown on the cross section Z, distance to the crucible bottom.
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Fig. 3. Continued.
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cracks can result from two different mechanisms. (a) Cracks resulting from the final solidification transient step. For this reason we added the graphite disc which acts as an upper heater to orientate the final solidification from the pool bottom to the free surface. (b) Cracks from thermal contraction [24,25]. In continuous casting, a slice of material is traveling through a field of isotherms, concave inside the crucible, then progressively more and more planar. During this transformation, nonuniformity in thermal contraction creates elastic stresses which can be relaxed by multiplication of dislocations flowing plastically. For silicon, it is known that this plastic flow can occur only at high temperature, say more than 700°C. The practical conclusion was to make planar the isotherms above this temperature, which was done by using a convenient insulating sheath. In the present stage of the procedure, all runs performed according to the above rules give crack free billets which can be cut in wafers distributed to the partners for characterization. 4.3. Dislocations The dislocation distribution as revealed by etch pits is highly nonuniform [20,33]. In some grains the density is low, the etch pits are aligned along crystallographic directions, suggesting some slow plastic flow process. In other grains, the density is much higher, the etch pits are arranged into cells, suggesting some complex interaction mechanism. Crowded areas appear in some grains, the shape of which suggests an intense local deformation mechanism creating dislocation tangles. Outside such tangled areas, the mean density of etch pits ranges from 30]104 to 50]104 cm~2. It is higher in the skin area of the billet (150]104 cm~2). Probably the present cooling conditions give rise to some residual thermal contraction occurring in the medium temperature range, sufficiently hot to avoid crack formation, but not enough to promote creep relaxation [25]. 4.4. Impurities and dopant All metallic impurities were below the detection limit of the atomic absorption technique. In par-
ticular this was true for copper in the billets and also in the feed stock. The only contamination noted was due to the use of an improper feeding system which had a crushing effect and contaminated with iron an intermediate series of billets. This was corrected by the setting up of a new feeder in the more recent tests. In the present program the feed particles were crushed refuse of doped “Polix” silicon. Resistivity measurements on cast billets gave 0.7$0.1 ) cm, practically constant, the variation from center to edge of the wafer, or variation along the billet being less than 0.1 ) cm [33]. As regards oxygen and carbon, the measurements reported here were performed by Fourier transform infrared spectroscopy (FTIR) [33]. Such measurements give information on oxygen and carbon atoms in solid solution only, and not on the possible oxide or carbide particles. Measurements on “total” content were not performed at this stage of the program. The results are the following: f there is practically no variation in the oxygen content according to the position in the billet, neither radial, nor axial; f the oxygen content in Madylam Si as in EMC Si from Osaka Titanium Sitix is significantly lower (from 0.4 to 1.2 ppm) than in the Polix material; f the carbon content is below the detection limit in the EMC-OTC-Si. It is practically uniform (7 ppm) in Madylam Si. 4.5. Diffusion length The photovoltaic quality of the material itself is evaluated from photocurrent measurements performed on simplified cells which do not require either heat treatments or surface treatments [21—23]. The photocurrent resulting from a local light input is a measure of the local value of the diffusion length of the minority carriers. A low value means that the carriers are trapped. The diffusion length varies along a diameter as shown in Fig. 4a. The diffusion length in the central zone is very homogeneous and is the highest. This zone seems to correspond to the core zone of the grain structure. The peripheral zone has a much poorer response [33].
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Fig. 5. Photovoltaic module fabricated from Madylam multicrystalline silicon in the Photowatt workshops.
Fig. 4. Diffusion length of the minority carriers, on a typical Madylam billet. (a) Transverse variation, (b) axial variation
As expected from the continuous casting process, the properties are very uniform along the billet (Fig. 4b). A similar uniformity was reported on the EMC Sitix material. The plateau value of the diffusion length is 45 lm for the Madylam Si, to be compared to 70 lm for the Sitix Si, a value significantly lower than what is measured on the Polix material (from 90 lm to more than 100 lm). Undoubtedly the EMC material must be considered as a new material, on which research efforts can give significant improvements.
Fig. 6. Conversion efficiency of the 30 cells of the module on Fig. 4.
100 mm) are rounded by the circular section of the billets (120 mm). The conversion efficiency ranged from 10 to 11.5% and was remarkably uniform along the billet (Fig. 6). These numbers are very close to what was published for the Sitix material, which is a surprising result considering the difference in diffusion length. As compared to Polix cells (efficiency 13—15%) it is clear that the Madylam material is at an early stage of development and should be improved.
5. Discussion 4.6. Measurements on solar cells A series of 31 solar cells was fabricated by Photowatt from one of the Madylam billets. A photovoltaic module was built (Fig. 5). The origin of the wafers is visible because the square cells (100 mm]
5.1. Fleeting contact between material and cold crucible On the lateral surface of the billets, it is difficult to detect the position of the crucible slits because
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there is no external protrusion. This means that the electromagnetic forces were sufficient to repell the liquid and to prevent it penetrating into the slit. In front of the segment walls, the skin seems to be made from successive waves frozen against the crucible wall. Their periodicity is relatively long, a few mm, so they reflect a slow fluctuation, with a periodicity comparable to that of the temperature fluctuations (Fig. 3). These waves build the upper lip of the shell. As soon as the latter has a sufficient thickness to counterbalance the hydrostatic pressure, a gas edge forms between the billet surface and the crucible wall because of thermal contraction and moreover of the taper machined in the lower part of the crucible wall. If fluctuation waves happen to put the liquid in contact with the crucible wall, this contact is local and short. Taking into account the low temperature of the copper surface, if some copper atoms migrate, this migration lasts a very limited time and is rapidly frozen.
the above conditions, a slight increase (approximately 0.5%) in the generator voltage is sufficient to trigger a leak. As regards the heat extracted from the billet surface, the crucible outlet makes a major discontinuity, because the insulating sheath limits the radial heat flow to a very low value. Now, considering an accidental increase in Joule power, at a given level the shell thickness first tends to decrease. If the level considered is inside the crucible, this thickness decrease results in an increase in extracted heat so that the front can find a stable position. On the contrary, if the level considered is below the crucible, the extracted heat is only weakly related to the distance to the surface, the front position is much less stable, the risk of leak is considerably greater [34]. This is a difference in comparison to the continuous casting of alloys, because in this latter case the billet cooling is increased when the material comes out of the mould. 5.3. The electric frequency, the most sensitive gage
5.2. Liquid leaks and the limited stability of the solid shell Considering a billet cross section, the core zone should be favored because of its better photovoltaic performances. It means that the skin zone and the intermediate zone should be confined approximately in the 10 mm external layer of the billet. Taking account of the grain mechanism, we have modified the solidification procedure in order to make the solid—liquid front as shallow and as flat as possible. At least for the low pulling rate (1 mm/ min) we succeeded in keeping the front inside the crucible, the pool bottom being close to the level of the crucible outlet. In fact the front originates at the triple junction, the level of which is correlated to the lower level of the induction coil because the magnetic flow lines are channelled into the electromagnetic penetration layer at the liquid free surface, which makes a localized heat source. Starting from this point, the front profile is an isotherm, the shape of which depends on the balance between the Joule power input, the heat transported in the pulled material, and the heat extracted from the external surface of the billet [34]. This balance is very sensitive. Particularly in
From an electrical point of view, the whole system Mgenerator#capacitor#coil# crucible# material chargeN can be considered as an oscillating circuit, the model of which was proposed by Delage and Ernst [15]. The capacity C is equal to that of the capacitor box (presently 20 lF). The equivalent resistance R is the sum of the component resistances, for the coil, the crucible, and the charge, respectively: In the inductance ¸, the coil inductance is lowered from the contribution of the crucible and of the material. According to this model and knowing the generator is aperiodic, the frequency of the electrical signal is the fundamental frequency of the equivalent circuit, f"1/ (2p(¸C)1@2). The frequency is affected by any change in the dome shape, but it does not depend on the voltage (or just through the dome shape). In the first sequence, in Fig. 2 the frequency increases linearly with time, and then with the amount of liquid. This increase is explained by a decrease in the equivalent inductance ¸, a decrease due to the increasing contribution of the melt inductance. As soon as the steady state regime is obtained, the frequency does not vary more than 10 Hz.
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In the relationship between voltage and current predicted by the model, the charge is expected to act in two different directions via inductance and resistance so that the interpretation is not straightforward. Moreover, the sensitivity of the recorded values seems to be much lower. As mentioned in Section 3, the transition from the molten zone formation to the continuous pulling regime needs careful control of the electrical power, in relation to the volume of the liquid zone. Temperature measurements are easy at points of the billet surface below the crucible outlet, but their information is damped by the relatively long distance to the critical points of the solid shell. On temperature measurements performed through the crucible the fluctuation noise is high so they cannot be used for control purpose. On the contrary the electrical frequency measurements give a reproducible behavior which can be supported by the electrical model [15], so we consider it could be used as a measure of the liquid zone extension.
6. Conclusions (1) Continuous pulling gives the multicrystalline silicon material very uniform grain structure and properties. An important reduction in waste material can be expected from the application of the process. (2) The cold crucible does not contaminate the material. In particular the copper content is kept at the same low level as in the feed stock. The oxygen content is somewhat reduced with respect to the feed stock. (3) As in alloy continuous casting, the container for the liquid is in fact the solid shell freezing against the crucible and below. Its shape is concave towards the liquid. New crystals nucleating along the triple junction are not geometrically eliminated, they grow towards the billet core. The increase in grain cross section results only from the differences in growth rate related to crystal orientation, as in the silicon ingot solidification. (4) The cold crucible acts as a shaping tool giving its external surface to the material, in particular a square cross section, favorable to the building of large photovoltaic systems. This is an advantage
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with respect to single crystal pulling systems, Czochralski or floating zone. (5) As compared to alloy continuous casting, the inductive cold crucible acts not only as the shaping tool for casting the billet, but also as the melting tool. These two functions are antagonistic, because a too low electrical power leads to the formation of a crust stopping the incorporation of feed granules, whereas a very high power makes the solid—liquid front deeper and more concave, leading to liquid leaks. The optimal operating conditions result from a fine compromise, particularly if the coil is kept in the lower position.
Acknowledgements The authors gratefully acknowledge the financial support of the French Government via the ADEME and CNRS-ECODEV programs since 1990, and of the European Community in the JOULE program since 1996. They wish to express their appreciation of the competence and reliable support of A. Claverie and Y. Marfaing, delegate managers of the French photovoltaic public program. The characterization of the “Madylam” silicon was performed by the partners of the program, i.e. Gilles Goaer, Le Quan Nam at Photowatt, Santo Martinuzzi, Isabelle Pe´richaud at Universite´ d’AixMarseille, Jean Claude Muller at CNRS-Phase, Strasbourg, Dominique Ballutaud at CNRSMeudon. Many thanks to them for their contributions and advice.
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