Mohammed M'Hamdi

Thermo-Mechanical Analysis of Directional Crystallisation of Multi-Crystalline Silicon Ingots

Multi-crystalline silicon ingot casting using directional crystallisation is the most costeffective technique for the production of Si for the photovoltaic industry. Non-uniform cooling conditions and a non-planarity of the solidification front result, however, in the build-up of stresses and viscoplastic deformation. Known defects, such as dislocations and residual stresses, can then occur and reduce the quality of the produced material. Numerical simulation, combined with experimental investigation, is therefore a key tool for understanding the crystallisation process, and optimizing it. The purpose of the present work is to present an experimental furnace for directional crystallisation of silicon, and its analysis by means of numerical simulation. The complete casting procedure, i.e., including both the crystallisation phase and the subsequent ingot cooling, is simulated. The thermal field has been computed by a CFD tool, taking into account important phenomena such as radiation and convection in the melt. The transient thermal field is used as input for a thermo-elasto-viscoplastic model for the analysis of stress build-up and viscoplastic deformation during the process. Numerical analysis is employed to identify process phases where further optimisation is needed in order to reduce generated defects.

Modeling of Lifetime Distribution in a Multicrystalline Silicon Ingot

Lifetime distribution of a multicrystalline silicon ingot of 250 mm diameter and 100 mm height, grown by unidirectional solidification has been modeled. The model computes the combined effect of interstitial iron and dislocation distribution on minority carrier lifetime of the ingot based on Shockley Read Hall (SRH) recombination model for iron point defects and Donolato’s model for recombination on dislocations. The iron distribution model was based on the solid state diffusion of iron from the crucible and coating to the ingot during its solidification and cooling, taking into account segregation of iron to the melt and back diffusion after the end of solidification. Dislocation density distribution is determined from experimental data obtained by PVScan analysis from a vertical cross section slice. Calculated lifetime is fitted to the measured one by fitting parameters relating the recombination strength and the local concentration of iron

Tensile Properties and Hot-Tearing Tendencies of 3xxx Alloys

A set-up for tensile testing in the mushy zone allowing for studies of semi-solid mechanical behavior is available at SINTEF. A hot-tearing experimental set-up has recently been developed allowing for investigation of the hot-tearing susceptibility of industrial aluminium alloys and effects of e.g. alloying composition and grain-refiner. Load and temperature are registered during constrained solidification giving information on the mechanical behavior of the alloy during solidification. Two crack-prone alloys in the 3xxx-series (A and B) have been investigated using both techniques and the results analyzed using information about solidification path from a thermo-physical model. Alloy B is found to be mechanically weaker in the interval most susceptible to hot-tearing in agreement with cast-house experience. This study shows that the experimental techniques combined with thermo-physical modeling and characterization allow for a better understanding of the hot-tearing sensitivity of the alloys.

Modelling of micro- and macrosegregation for industrial multicomponent aluminium alloys

Realistic predictions of macrosegregation formation during casting of aluminium alloys requires an accurate modeling of solute microsegregation accounting for multicomponent phase diagrams and secondary phase formation. In the present work, the stand alone Alstruc model, a microsegregation model for industrial multicomponent aluminium alloys, is coupled with the continuum model ALSIM which calculates the macroscopic transport of mass, enthalpy, momentum, and solutes as well as stresses and deformation during solidification of aluminium. Alstruc deals with multicomponent alloys accounting for temperature dependent partition coefficients, liquidus slopes and the precipitation of secondary phases. The challenge associated with computation of microsegregation for multicomponent alloys is solved in Alstruc by approximating the phase diagram data by simple, analytical expressions which allows for a CPU-time efficient coupling with the macroscopic transport model. In the present work, the coupled model has been applied in a study of macrosegregation including thermal and solutal convection, solidification shrinkage and surface exudation on an industrial DC-cast billet.

Numerical analysis of Oxygen control during growth of Czochralski silicon single crystals

In the present work, a set of 2D global furnace simulations accounting for oxygen dissolution and transport have been used to predict Oi content along the produced Silicon crystal. It is shown that Oi content is sensitive to several growth parameters (melt level, crucible rotation, etc.). Results indicate Oxygen tends to increase at the end of the crystal due to a combination of weakening of turbulence and planar velocity in addition to decrease of the melt free surface. Crucible rotation is the most influencing parameter at low melt level. Argon gas pressure and flow have a limited impact at low melt level.

Modelling of Micro- and Macrosegregation in Multicomponent Aluminium Alloys Accounting for Secondary Phase Formation

Realistic predictions of macrosegregation formation during solidification of aluminium alloys require an accurate modeling of solute microsegregation accounting for multicomponent phase diagrams and secondary phase formation. In the present work, the stand alone ALSTRUC model, a microsegregation model for industrial multicomponent aluminium alloys, is coupled with the continuum model ALSIM which calculates the macroscopic transport of mass, enthalpy, momentum, and solutes during solidification of aluminium. Alstruc deals with multicomponent alloys accounting for temperature dependent partition coefficients, liquidus slopes and the precipitation of secondary phases. The challenge associated with computation of microsegregation for multicomponent alloys is solved in ALSTRUC by approximating the phase diagram data by simple, analytical expressions which allows for a CPU-time efficient coupling with the macroscopic transport model. In the present work, a coupling strategy is proposed where macroscopic transport quantities such as the enthalpy and the solute compositions are used as input to the microsegregation model which then returns the temperature, solid fraction and the compositions in the solid and the liquid phases. The coupled solidification model is then applied in a case study to illustrate the effect of secondary phase precipitation on macrosegregation formation due to shrinkage induced flow.

Analysis of the impact of macrosegregation on hot tearing conditions during DC casting of aluminium alloys

Abstract It is well known that the chemical composition has a strong impact on the hot tearing susceptibility of aluminium alloys. Macrosegregation formation during DC casting of aluminium may lead to large variations of the alloy composition. Assessments of the cracking susceptibility during DC-casting do not take into account composition variations within the ingot. A two-phase model where the main phenomena associated with the formation of hot tears are accounted for, i.e., the lack of feeding at the late stages of solidification and the localization of viscoplastic deformation, has recently been proposed by the authors. In the present study, the two-phase model is extended to allow for the computation of macrosegregation and its interaction with hot tearing formation. The impact of macrosegregation on mechanical fields often associated with the cracking tendency is assessed through case studies where both macrosegregation and the mechanical analysis are computed simultaneously. The case studies are carried out for the start-up of the DC casting process.