Solar cells convert sunlight into electrical energy using the photo effect. With a mar-ket share of 60%, multicrystalline silicon (mc-Si) is the most frequently used absorber material. Standard mc-Si ingots are directionally solidified in a fused silica (SiO2) crucible, which exhibits a silicon nitride (Si3N4) inner coating. After the entire raw material has been melted, the nucleation takes place on the Si3N4 inner coating at the bottom of the crucible. This results in an inhomogeneous initial grain structure and an increased fraction of dislocation clusters in the upper part of the ingot, which decrease the quality of standard mc-Si. Therefore, the global goal is the development of a cost-effective technology that reduces the formation of clusters and enhances the quality of mc-Si ingots. One way of achieving that goal is to produce the so-called \"high performance multi crystalline silicon\" (HPM-Si). During the directional solidification silicon raw material remains unmelted at the bottom of the SiO2 crucible, whereby crystallization does start on the silicon feedstock a few millimeters above the crucible bottom. Compared to standard mc-Si, a finer grained structure with many small grains is formed, which are separated by so-called random grain boundaries. Since the movement of dislocations across this grain boundary type has rarely been observed, the risk of formation of dislocation clusters, which have a negative impact on the efficiency of solar cells, is greatly reduced for HPM-Si. However, the disadvantage of the HPM-Si compared to the mc-Si is the yield loss resulting from the unmelted raw material at the crucible bottom. Hence, the aim of the present work is to produce mc-Si with a fine-grained structure in combination with a high fraction of random grain boundaries without the disad-vantage of yield loss. In order to investigate the grain structure in dependence of the nucleation conditions G1 ingots having a mass of 14.5 kg and dimensions of 220x220x130 mm³ were directional solidified in a furnace. The analysis of the grain structure with respect to the grain size, grain orientation and the random grain boundary length fraction and the comparison with the HPM-Si reference crystal took place on horizontal wafers with a thickness of 3mm. One possibility to influence the grain structure of mc-Si could be the variation of the cooling conditions before the start of crystallization at the crucible bottom. In a first series of experiments, a gas-flowed cooling plate, positioned below the crucible, was used. An increased gas flow increases the axial heat flow downwards and the cooling rate below the crucible bottom in the same direction. The detected cooling rate, measured by a thermocouple in the silicon melt 5 mm above the crucible bottom, varied in a range between 0.06-1.5 K/min. An increased cooling rate increases the supercooling, with a maximum of 2K. The analysis of the grain structure shows that a reduction in the cooling rate in combination with the lowest supercooling minimizes the average grain size and increases the fraction of random grain boundaries. However, an HPM-Si like grain structure (grain size and fraction of random grain boundaries comparable to HPM-Si) could not completely produced. Furthermore, due to the extended process time, the wafer yield is reduced, whereby the reduction of the cooling rate is not a preferable method for the industrial process. In a second experimental series, which took place under constant cooling rates, the influence of an additional nucleation layer on the initial grain structure was investigated. For this purpose, the additional nucleation layer was applied on the already existing Si3N4 inner coating on the crucible bottom. In order to adjust a HPM-Si like grain structure, the contact angle of the silicon melt on the additional nucleation layer should be lower than on the Si3N4 inner coating. The theoretical basis for this hypothesis is the relationship between the contact angle and the nucleation energy, which states that a reduced contact angle lowers the nucleation energy and can ultimately lead to more nuclei. Furthermore, in order to avoid melting, the additional nucleation layer must have a higher melting point than silicon. Suitable materials for the application as a foreign seed sample are SiC, SiO2 and Al2O3, which are used in the form of particles with different sizes. The production of the additional nucleation layer was carried out by a spraying as well as by an embedding procedure. These layers exhibit different thermal conductivity as well as surface roughness. Embedded nucleation layers generate higher roughness values than sprayed nucleation layers. The analysis of the grain structure identified the surface roughness as the main influencing factor on the initial grain size. While an increased surface roughness (Rq>100μm) results in a fine-grained structure (average grain size: <2mm²) comparable to HPM-Si, the average grain size increases (>2 mm²) with a reduced surface roughness (Rq<100μm). However, the analysis of the grain boundary relationship shows that the fraction of random grain boundaries does not correlate with the average grain size. Only a ma-terial dependency was detected. All SiO2 nucleation layers generate an increased fraction of random grain boundaries, comparable to the HPM-Si material. In contrast, the fraction of random grain boundaries was reduced for all SiC nucleation layers. This result is probably established with the different thermal conductivities of the used materials. The increased thermal conductivity of the sample with the SiC nucleation layers increases the cooling rate, promoting dendritic growth. In contrast the lower thermal conductivity of the SiO2 nucleation layers reduces the cooling rate and dendritic growth is suppressed. Since dendrites exhibit a Σ3 grain boundary relationship in the center, the fraction of this grain boundary type increases for SiC nucleation layers and the fraction of random grain boundaries decreases. In this thesis, various possibilities for influencing the grain structure have been pre-sented. A SiO2 nucleation layer with a roughness value Rq> 200μm represents an industrially relevant solution for the production of mc-Si with comparable properties to the HPM-Si without the disadvantages of yield loss. Hence, it was possible to in-crease the yield with comparable material quality, whereby the production costs could be reduced. Some first crucible manufacturers have already transferred the use of the SiO2 nucleation layers on top of the already existing Si3N4 inner coating at the crucible bottom to production.

Diese Arbeit stellt einen Beitrag zur Modellierung der gerichteten Erstarrung von Silizium für die Photovoltaik dar. Es wurde basierend auf einem industriellen Prozesses ein Modellaufbau der Schmelze mit zwei Induktoren nach der Ähnlichkeitstheorie abgeleitet. Dieser ermöglicht, durch die Verwendung von niedrig schmelzenden Metallen, eine umfassende Messung der Strömungsgeschwindigkeiten mit Ultraschall-Velocimetrie. Basierend auf den experimen- tellen Daten wurde ein numerisches Modell zur Berechnung der Schmelzströmung unter Magnetfeldeinfluss validiert. Es wurden detaillierte Untersuchungen zu Strömungsstrukturen und beeinflussende Parameter durchgeführt, eine Methode zur Klassifizierung entwickelt und die Rotationskennzahl Ro eingeführt, mit welcher man in Abhängigkeit vom Magnetfeld und der Schmelzgeometrie die horizontale Rotation der Schmelzströmung in einem breiten Gültigkeitsbereich vorhersagen kann. Das validierte numerische Modell wurde zur Prozessoptimierung auf die Schmelzströmung des industriellen Prozesses angewendet.

No description available.

<p>Crystal growth has been recognized as a paradigm for non-equilibrium pattern formation for decades. Scientific interest in this field has focused on the growth rates and curvature of branches in snow flake-like structures patterned after a solid's crystallographic orientations. Similar patterns have been extensively identified in solidification of metals and organic metal analogues and are known as dendrites, which is originated from a Greek word "dendron" meaning tree.</p> <p>Dendritic spacing and morphology established during casting often sets the final microstructure and second phase formation that develops during manufacturing of alloys. This is particularly true in emerging technologies such as twin belt casting of aluminum alloys, where a reduced amount of thermomechanical processing reduced the possibility of modifying microstructure from that determined at the time of solidification. Predicting and controlling these microstructure of cast alloys has thus been a driving force behind various studies on solidification of materials.</p> <p>Mg-based alloys are another class of materials gaining importance due to the high demand for weight reduction in the transportation industry which accordingly reduces the gas consumption. While the solidified microstructure and its effect on the material properties have been the subject of intensive studies, little is known about the fundamental mechanisms that determine dendritic microstructure in Mg alloys and its evolution under directional growth conditions.</p> <p>This thesis investigates the relationship between the microstructure and cooling conditions in unsteady state upward directional solidification of Al-Cu and Mg-Al alloys. The four-fold symmetry of Al-Cu alloys are used to study the dynamical spacing selection between dendrites, as the growth conditions vary dynamically, whereas, the Mg-Al system with a six-fold symmetry is used to study a competition between neighbouring, misoriented grains and the effect of this as the resulting microstructure. Mg-Al also presents a situation wherein the cooling conditions dynamically vary from the preferred crystallographic growth direction. Analysis of phase field simulations is used to shed some light on the morphological development of dendrite arms during solidification under transient conditions. Our numerical results are compared to new casting experiments.</p> <p>Chapter three studies spacing selection in directional solidification of Al-Cu alloys under transient growth conditions. New experimental results are presented which reveal that the mean dendritic spacing versus solidification front speed exhibits plateau-like regions separated by regions of rapid change, consistent with previous experiments of Losert and co-workers. In fact, The primary spacing of a dendritic array grown under transient growth conditions displays a distribution of wavelengths. As the rate of change in solidification front velocity is decreased, the evolution of the spacing follows the prediction of the geometrical models within a band of spacing fluctuations. The width of the band is shown to highly depend on the rate of the solidification front velocity acceleration, such that the higher the rate, the wider the band of available spacings. Quantitative phase field simulations of directional solidification with dynamical growth conditions approximating those in the experiments confirm this behavior. The mechanism of this type of change in mean dendrite arm spacing is consistent with the notion that a driven periodically modulated interface must overcome an energy barrier before becoming unstable, in accord with a previous analytical stability analysis of Langer and co-workers.</p> <p>In chapter four, it is demonstrated both computationally and experimentally that a material's surface tension anisotropy can compete with anisotropies present in processing conditions during solidification to produce a continuous transition from dendritic microstructure morphology to so-called seaweed and fractal-like solidification microstructures. The phase space of such morphologies is characterized and the selection principles of the various morphologies explored are explained. These results have direct relevance to the microstructure and second phase formation in commercial lightweight metal casting.</p> / Doctor of Philosophy (PhD)

Nous avons étudié in situ et en temps réel la structure de grains du silicium multi-cristallin issue de la solidification dirigée en utilisant l’imagerie X synchrotron. La radiographie X permet de suivre l’évolution de l’interface solide/liquide et de caractériser sa dynamique et sa morphologie. La topographie X nous donne des informations sur la structure de grains formée, les contraintes et les défauts issus de la solidification. Nous avons montré l’importance la préparation de l’état initial de la solidification en particulier pour les expériences de reprise sur germe. L’analyse de la morphologie de l’interface solide/liquide nous a permis de caractériser la surfusion cinétique du front de solidification, de comprendre l’évolution des sillons de joints de grains et d’analyser les mécanismes de compétition de grains ainsi que de révéler l’impact des impuretés sur la structure de grains formée à l’issue de la solidification. Le phénomène de maclage a aussi été observé dans nos expériences et nous avons démontré que les macles dans le silicium multi-cristallin peuvent être des macles de croissance. Deux types de macles ont été identifiés et le phénomène de compétition de grains en présence de macles étudié. / We studied in situ and real-time the grain structure of multi-crystalline silicon from directional solidification using synchrotron X-ray imaging techniques. X-ray Radiography gives information on the evolution, dynamics and morphology of the solid/liquid interface. X- ray Topography gives more information on the grain structure, strains and defects that occur during solidification step. We showed the importance of the preparation of the initial stage of solidification in particular in the experiments where solidification is initiated from seed. The analysis of the solid/liquid interface morphology allowed us to characterize the kinetic undercooling of the solidification front, to understand the evolution of the grains boundary grooves and to analyze the mechanisms of grain competition and also to reveal the impurities impact on the grain structure formed at the end of the solidification. We also observed twinning phenomenon in our experiments and we demonstrated that twins in multi-crystalline silicon can be growth twins. Two kinds of silicon twins have been identified and the grain competition phenomenon with twins studied.

Au cours de cette thèse, nous avons étudié in situ la solidification du silicium à l’aide de l'imagerie X-synchrotron. Les deux techniques utilisées lors de la solidification sont la radiographie et la diffraction de Bragg, elles permettent de caractériser: la dynamique des mécanismes de croissance, la cinétique de croissance, la nucléation et la compétition de grains, la déformation du réseau cristallin et les champs de contraintes liés aux dislocations. Ces observations sont combinées avec des caractérisations ex situ pour étudier l'orientation cristallographique, les déformations du réseau cristallin ainsi que les concentrations d'impuretés légères telles que le carbone et l'oxygène.La complémentarité de ces techniques permet d'étudier et de mieux comprendre : les phénomènes physiques liés à la formation de la structure de grain finale. Les résultats concernant la cinétique de croissance de l'interface solide-liquide et des facettes {111}, l'établissement de la structure de grain, l'importance du maclage, l'effet des impuretés légères, le champ de contrainte lié à la croissance et la compétition de grains et les dislocations sont discutés dans le manuscrit. / During this thesis, we studied in situ the solidification of silicon with X-synchrotron imaging. The two techniques used during solidification are radiography and Bragg diffraction and they allow characterizing: dynamic growth mechanisms, growth kinetics, grain nucleation and competition, lattice deformation and dislocation related strain fields. These observations are combined with ex situ characterizations to study the crystallographic orientation, the deformations of the crystal lattice as well as the concentrations of light impurities such as carbon and oxygen. The complementarity of these techniques makes it possible to study and to better understand: the physical phenomena related to the formation of the final grain structure. Results concerning the growth kinetics of the solid-liquid interface and of the {111} facets, the establishment of the grain structure, the importance of twinning, the effect of light impurities, the strain field related to growth and grain competition and dislocations are discussed in the manuscript.

A proposta da modificação química da superliga MAR-M247 através da substituição do Ta pelo Nb (em átomos) foi baseada nas seguintes informações: (1) O Nb desempenha funções muita parecidas com as do Ta nas superligas à base de Ni, como endurecedor via solução sólida da fase ? e elemento formador de fases secundárias (?? e carbonetos); (2) O Brasil tem as maiores reservas de Nb do mundo e (3) O Nb já é adicionado em diversas classes de superligas à base de Ni - fundidas convencionalmente e solidificadas direcionalmente e monocristalinas. Neste trabalho o objetivo principal foi de avaliar a viabilidade da substituição do Ta pelo Nb na superliga à base de Ni MAR-M247. As amostras da MAR-M247 e da liga modificada - MAR-M247[Nb] utilizadas na caracterização microestrutural foram obtidas por solidificação direcional no forno a vácuo do tipo forno Bridgman (Lab. de Solidificação/FEM-UNICAMP) nas seguintes condições de processamento: v = 5, 10 e 18 cm/h e G = 80°C/cm. As simulações de cálculo termodinâmico utilizando o programa Thermo-Calc foram realizadas com o objetivo de se avaliar se as temperaturas de transformação mudariam com a substituição do Ta pelo Nb. Para avaliação das propriedades mecânicas em alta temperatura e a estabilidade estrutural da superliga MAR-M247[Nb] foram realizados ensaios de fluência a 750 e 850 °C nas tensões de 840, 780 e 440 MPa. A estabilidade microestrutural da MAR-M247[Nb] foi testada por meio de ensaios de oxidação isotérmica a 1000 °C no intervalo de tempo de 30 minutos a 100 h. A substituição do Ta pelo Nb promoveu mudanças significativas principalmente nas temperaturas de formação do eutético ?/??, solvus - ?? e de fusão incipiente. As microestruturas das ligas após os experimentos de solidificação direcional a v = 5, 10 e 18 cm/h eram constituídas por dendritas da fase gama - ? e precipitados coerentes da fase gama linha - ?? (morfologia cuboidal). Na região interdendrítica da MAR-M247 e MAR-M247[Nb] solidificadas a v = 5 e 10 cm/h foram encontrados os eutéticos ?/?? e ?/Ni5(Hf,Zr). Na v = 18 cm/h a região interdendrítica era constituída apenas do eutético ?/??. A exposição a 1250 °C por 15 e 30 dias promoveu a decomposição total e a re-precipitação de carbonetos do tipo MC. No entanto, devido à contaminação por oxigênio e nitrogênio durante os tratamento térmicos, não foi atingido o equilíbrio termodinâmico em decorrência de mudanças das composições dos carbonetos MC. Nos ensaios de fluência a 750 °C, os tempos de ruptura foram de 49 h para MAR-M247 e de 39,4 h para MAR-M247[Nb] apesar dos elevados valores das tensões terem sido superestimados. A 850 °C o tempo de ruptura da MAR-M247[Nb] (trup = 359 horas) foi reduzido em 32 % em relação ao valor observado para MAR-M247 (trup = 476 horas). Os resultados dos ensaios de oxidação a 1000 °C da superliga MAR-M247[Nb] mostraram que o período transiente foi de 20 h com ganho de massa expressivo. A partir de 50 h o efeito do descolamento das camadas oxidadas durante o resfriamento das amostras foi significativo e promoveu uma variação de massa importante no intervalo de tempo de 50 a 100 h. Ensaios de oxidação em tempos mais longo deverão ser feitos para determinação da estrutura de formação das camadas e seus respectivos constituintes. / The chemistry modification in the Ni-based superalloy MAR-M247 through the replacing all Ta by Nb was based on in these statements: (1) Nb does the same function in Ni-based superalloys as Ta does, solid solution strenghtening and ?? e carbides element formers, (2) Brazil has the major ores of Nb in the world and (3) Nb has been added in all classes of Ni superalloy conventional casting, columnar and single crystal processed by directional solidification. In this study the main focus was to evaluate the feasibility of replacing Ta by Nb in the Ni - based superalloy MAR-M247. The samples of MAR-M247 and the Nb modified MAR-M247[Nb] were produced by directional solidification in a Bridgman vacuum furnace at the Solidification Research Lab/FEM - UNICAMP) in the following processing conditions: v = 5, 10 and 18 cm/h and G = 80 °C/cm. The thermodynamic simulations using Thermo-Calc program were performed to evaluate whether or not the transformation temperatures would change with the replacing of Ta by Nb. For the evaluation of mechanical properties at high temperature were performed creep rupture tests at 750 and 850 °C under the stress values of 840, 780 and 440 MPa. The isotermal oxidation tests at 1000 °C were done during the time interval of 30 min to 100 h. The replacing of Ta by Nb promoted some changes in eutectic-?/??, ??-solvus and incipient melting temperatures. After the directional solidification experiments at the v = 5, 10 and 18 cm/h the microstructural characterization has shown that for all condition the microstructures were composed by dendrites - ? and ?? - cuboidal precipitates in it. In the interdendritic region was observe the ?/?? and ?/Ni5(Hf,Zr) eutectics for v = 5 and 10 cm/h and only the ?/?? eutectics for v = 18 cm/h. The exposure at 1250 °C for the extended times promoted the formation of fine MC carbides but the equilibrium compositions have not been achieved due to the oxygen and nitrogen contamination. In the creep rupture tests at 750 °C the MAR-M247[Nb] have shown more shorter lifetime than the MAR-M247 even with overestimated tensile stress. At 850 °C the lifetime for MAR-M247[Nb] (trup = 359 h) was reduced by 32 % compared to the MAR-M247 (trup = 476 h). It was discussed that the changes in the composition of the ? phase induced Ta by Nb replacing which would led to the weakness of matrix in the MAR-M247[Nb]. The samples were oxidized at 1000 °C showed 20 h to the transient period and significant weight gain in that time. However at the extended period the weight gain had changed significantly and was precluded to predict the structure formation of oxides layer properly.

A proposta da modificação química da superliga MAR-M247 através da substituição do Ta pelo Nb (em átomos) foi baseada nas seguintes informações: (1) O Nb desempenha funções muita parecidas com as do Ta nas superligas à base de Ni, como endurecedor via solução sólida da fase ? e elemento formador de fases secundárias (?? e carbonetos); (2) O Brasil tem as maiores reservas de Nb do mundo e (3) O Nb já é adicionado em diversas classes de superligas à base de Ni - fundidas convencionalmente e solidificadas direcionalmente e monocristalinas. Neste trabalho o objetivo principal foi de avaliar a viabilidade da substituição do Ta pelo Nb na superliga à base de Ni MAR-M247. As amostras da MAR-M247 e da liga modificada - MAR-M247[Nb] utilizadas na caracterização microestrutural foram obtidas por solidificação direcional no forno a vácuo do tipo forno Bridgman (Lab. de Solidificação/FEM-UNICAMP) nas seguintes condições de processamento: v = 5, 10 e 18 cm/h e G = 80°C/cm. As simulações de cálculo termodinâmico utilizando o programa Thermo-Calc foram realizadas com o objetivo de se avaliar se as temperaturas de transformação mudariam com a substituição do Ta pelo Nb. Para avaliação das propriedades mecânicas em alta temperatura e a estabilidade estrutural da superliga MAR-M247[Nb] foram realizados ensaios de fluência a 750 e 850 °C nas tensões de 840, 780 e 440 MPa. A estabilidade microestrutural da MAR-M247[Nb] foi testada por meio de ensaios de oxidação isotérmica a 1000 °C no intervalo de tempo de 30 minutos a 100 h. A substituição do Ta pelo Nb promoveu mudanças significativas principalmente nas temperaturas de formação do eutético ?/??, solvus - ?? e de fusão incipiente. As microestruturas das ligas após os experimentos de solidificação direcional a v = 5, 10 e 18 cm/h eram constituídas por dendritas da fase gama - ? e precipitados coerentes da fase gama linha - ?? (morfologia cuboidal). Na região interdendrítica da MAR-M247 e MAR-M247[Nb] solidificadas a v = 5 e 10 cm/h foram encontrados os eutéticos ?/?? e ?/Ni5(Hf,Zr). Na v = 18 cm/h a região interdendrítica era constituída apenas do eutético ?/??. A exposição a 1250 °C por 15 e 30 dias promoveu a decomposição total e a re-precipitação de carbonetos do tipo MC. No entanto, devido à contaminação por oxigênio e nitrogênio durante os tratamento térmicos, não foi atingido o equilíbrio termodinâmico em decorrência de mudanças das composições dos carbonetos MC. Nos ensaios de fluência a 750 °C, os tempos de ruptura foram de 49 h para MAR-M247 e de 39,4 h para MAR-M247[Nb] apesar dos elevados valores das tensões terem sido superestimados. A 850 °C o tempo de ruptura da MAR-M247[Nb] (trup = 359 horas) foi reduzido em 32 % em relação ao valor observado para MAR-M247 (trup = 476 horas). Os resultados dos ensaios de oxidação a 1000 °C da superliga MAR-M247[Nb] mostraram que o período transiente foi de 20 h com ganho de massa expressivo. A partir de 50 h o efeito do descolamento das camadas oxidadas durante o resfriamento das amostras foi significativo e promoveu uma variação de massa importante no intervalo de tempo de 50 a 100 h. Ensaios de oxidação em tempos mais longo deverão ser feitos para determinação da estrutura de formação das camadas e seus respectivos constituintes. / The chemistry modification in the Ni-based superalloy MAR-M247 through the replacing all Ta by Nb was based on in these statements: (1) Nb does the same function in Ni-based superalloys as Ta does, solid solution strenghtening and ?? e carbides element formers, (2) Brazil has the major ores of Nb in the world and (3) Nb has been added in all classes of Ni superalloy conventional casting, columnar and single crystal processed by directional solidification. In this study the main focus was to evaluate the feasibility of replacing Ta by Nb in the Ni - based superalloy MAR-M247. The samples of MAR-M247 and the Nb modified MAR-M247[Nb] were produced by directional solidification in a Bridgman vacuum furnace at the Solidification Research Lab/FEM - UNICAMP) in the following processing conditions: v = 5, 10 and 18 cm/h and G = 80 °C/cm. The thermodynamic simulations using Thermo-Calc program were performed to evaluate whether or not the transformation temperatures would change with the replacing of Ta by Nb. For the evaluation of mechanical properties at high temperature were performed creep rupture tests at 750 and 850 °C under the stress values of 840, 780 and 440 MPa. The isotermal oxidation tests at 1000 °C were done during the time interval of 30 min to 100 h. The replacing of Ta by Nb promoted some changes in eutectic-?/??, ??-solvus and incipient melting temperatures. After the directional solidification experiments at the v = 5, 10 and 18 cm/h the microstructural characterization has shown that for all condition the microstructures were composed by dendrites - ? and ?? - cuboidal precipitates in it. In the interdendritic region was observe the ?/?? and ?/Ni5(Hf,Zr) eutectics for v = 5 and 10 cm/h and only the ?/?? eutectics for v = 18 cm/h. The exposure at 1250 °C for the extended times promoted the formation of fine MC carbides but the equilibrium compositions have not been achieved due to the oxygen and nitrogen contamination. In the creep rupture tests at 750 °C the MAR-M247[Nb] have shown more shorter lifetime than the MAR-M247 even with overestimated tensile stress. At 850 °C the lifetime for MAR-M247[Nb] (trup = 359 h) was reduced by 32 % compared to the MAR-M247 (trup = 476 h). It was discussed that the changes in the composition of the ? phase induced Ta by Nb replacing which would led to the weakness of matrix in the MAR-M247[Nb]. The samples were oxidized at 1000 °C showed 20 h to the transient period and significant weight gain in that time. However at the extended period the weight gain had changed significantly and was precluded to predict the structure formation of oxides layer properly.

La plupart des modules photovolta¨ıques produits sont `a base de silicium.L’efficacit´e de ces modules d´epend fortement de la qualit´e cristalline du siliciumutilis´ee ainsi que de la quantit´e d’impuret´es pr´esente dans le lingotd’origine d’o`u sont issus les modules. Les lingots de silicium sont obtenus aucours d’un proc´ed´e de solidification, durant lequel les impuret´es sont extraitespar ph´enom`ene de s´egr´egation. Le processus de s´egr´egation est influenc´e parl’´ecoulement dans le liquide durant l’´etape de solidification. L’utilisation d’unchamp magn´etique externe permet le contrˆole de l’´ecoulement dans le bainliquide. Dans cette ´etude, l’effet d’un ´ecoulement forc´e sur le processus des´egr´egation est ´etudi´e. Pour cela un dispositif exp´erimental (VB2) et unmod`ele num´erique ont ´et´e d´evelopp´es dans le but de comprendre le rˆole del’´ecoulement sur la forme de l’interface et sur la s´egr´egation des impuret´es. / The photovoltaic modules are generally produced using silicon wafers. Theirelectrical efficiency is related to the crystal quality, which is influenced bythe presence of pollutants in the ingots from which the wafers are cut. Siliconingots are obtained as a result of solidification processes, which implygrowing a crystal from melt. During this solidification process, impurities areseparated from the silicon. The segregation process is greatly influenced bythe melt velocity during the solidification process. The control of the meltflow during the crystallization process can be achieved using external magneticfields. This thesis presents the results of the study on the influence ofthe forced convection induced by a travelling magnetic field (TMF) duringthe solidification process, using both an experimental set-up (VB2) and anumerical model.

In dieser Arbeit werden Möglichkeiten zur Homogenisierung von Widerstandsprofilen entlang von phosphordotierten, gerichtet erstarrten, multikristallinen Silizium (mc-Si) Blöcken für PV-Anwendungen untersucht. Die im Rahmen der Dissertation durchgeführte analytische Untersuchung konzentriert sich auf den Phosphortransport in der Siliziumschmelze, an der Grenzfläche zwischen Kristall und Schmelze, an der Schmelzenoberfläche und in der Gasphase oberhalb der Schmelze. Es wurden drei Prozessparameter identifiziert, die den stärksten Einfluss auf die Phosphorverteilung in multikristallinen Blöcken haben: die Durchmischung der Schmelze, der Gesamtgasdruck in der Anlage und der Gasfluss über der Schmelze. Variationen in der Stärke der TMF sind sinnvoll, um die Phosphorverteilung entlang der Barrenhöhe zu beeinflussen. Ein schwaches TMF bewirkt eine gleichmäßigere Dotierstoffverteilung und führt zu einem verringerten spezifischen Widerstand des Blocks in den Anfangsstadien der Kristallisation, während ein starkes TMF einen signifikanten Effekt auf die Phosphorverdampfung hat und zu einem Anstieg des spezifischen Widerstandes zum Ende des Blocks hin führt. Die Ergebnisse der Experimente zeigten, dass die Verringerung des Gasdrucks zu einer deutlich verstärkten Phosphorverdampfung von der freien Schmelzenoberfläche führt und damit den spezifischen Widerstand des erstarrten Blocks erhöht, vor allem gegen dessen Ende hin. Die während der Studie gewonnenen Erkenntnisse wurden für die Optimierung der typischen G1-Wachstumsrezeptur verwendet. Die mit diesem Rezept gezüchteten G1 mc-Si Blöcke zeigen eine gleichmäßigere Widerstandsverteilung als solche, die mit einem typischen Rezept gezüchtet wurden. Die Widerstandsvariation wurde auf 55 % verringert und erfüllte den von der Marktspezifikation vorgegebenen Zielbereich von 3,0 - 1,0 Ω·cm. Die entwickelte Rezeptur wurde erfolgreich für die gerichtete Erstarrung mit Keimvorgabe übertragen. / The research described in this thesis is focused on homogenization of resistivity profiles along phosphorus-doped directionally solidified multicrystalline silicon (mc-Si) ingots for PV application. The analytical study conducted within the framework of the thesis is focused on phosphorus transport in the silicon melt, at the crystal-melt interface, at the melt surface and in the gaseous phase above the melt. Three process parameters were identified to have the most dominant influence on phosphorus distribution in multicrystalline ingots: melt mixing, furnace ambient gas pressure and gas flow above the melt. It was found that variations in strength of TMF could be used to control the phosphorus distribution along the ingot’s length. Weak TMF provokes more uniform dopant distribution and results in decreased ingot resistivity at the initial stages of crystallization, while strong TMF has more prominent effect on phosphorus evaporation that leads to the increase of resistivity towards the ingot’s end. The results of experiments demonstrated that reduction of ambient gas pressure leads to significantly intensified phosphorus evaporation from the free melt surface and increases the resistivity of the solidified ingot, especially towards its end. The findings obtained during the study were used for the adjustment of the typical G1 growth recipe. Conventional G1 mc-Si ingots grown using this recipe show more uniform resistivity distribution than those grown using a typical one. Resistivity variation was reduced to 55% and met the target range of 3.0 – 1.0 Ω·cm set by market specification. The developed recipe was successfully replicated for directional solidification seeded growth.