Liliana Braescu

Modern engineering needs of crystals with specified size for use as final products without additional machining. Moreover, the quality of a crystal depends on the distribution of both special added and detrimental impurities. A non-uniform distribution of such impurities along the crystal length and cross-section leads to non-uniform spatial, electrical and optical properties of the crystal. Variations of the concentration of impurities along the crystal length and cross-section are determined by the processes that take place during the crystal manufacturing. Mathematical models constructed for describing the evolution of the shape of the crystal and/or the distribution of impurities take into account such processes.The aim of our research is: -the study of the dependence of the crystal shape on the pulling rate, melt temperature at the meniscus base, pressure in the furnace, vertical temperature gradient in the furnace in the case of EFG method, in view of the choice of the optimal process parameters and to develop a mathematical model based control procedure of the crystal shape. -a model based evaluation of the impurities of the crystal grown form the melt by various techniques: edge-defined film-fed growth (EFG); Czochralski (Cz); Vertical Bridgman-Stockbarger (VBS); dewetted Bridgman, and find ways to reduce the non-uniformity of the distributions of impurities.For these complex and rigorous explorations, we use mathematical and numerical tools in order to obtain theoretical and numerical results comparable with experimental data.Software used:-COMSOL Multiphysics for coupling different application modes which use partial differential equations: Navier-Stokes, Convection-Diffusion, Moving Mesh, etc.-MathCAD and Mathematica for simulate the shape of the meniscus, the shape of the crystal and for other numerical data concerning the control, the regions of attractions, etc.-Table Curve 2D and 3D for fitting the obtained numerical data.

John Patrick University of Health and Applied Sciences, South Bend, IN, USA, .

E-mail: trimite un mesaj.

Pagina web a instituţiei: https://jpu.edu/

Urmareste linkul ResearcherID pentru toate articolele cercetatorului: A-9300-2010. Tabelul detaliat al articolelor este in josul paginii.

Nascut(a) in: 1967

Interese: ecuatii cu derivate partiale, ecuatii ordinare, teoria controlului, stabilitate, domeni de atractie, cresterea cristalelor, coagularea sangelui, modelare matematica

Detalii:
Ingineria moderna utilizeaza lamele (placi subtiri) si fibre (bare cilindrice subtiri) monocristaline de dimensiuni date, pentru a fi folosite ca atare, fara prelucrari mecanice suplimentare. Mai mult, calitatea cristalelor depinde si de distributia dopantilor; neuniformitatile dopantului in cristal determina neuniformitati ale proprietatilor electrice, optice, etc. Aceste neuniformitati ale concentratiei dopantului in cristal se datoreaza proceselor care au loc in timpul cresterii cristalului din topitura, cu una dintre urmatoarele metode: edge-defined film-fed growth (EFG); Czochralski (Cz); Vertical Bridgman-Stockbarger (VBS); dewetted Bridgman.

Se construiesc modele matematice care sa fie capabile sa descrie cat mai bine procesele care au loc in timpul cresterii.
Utilizand aceste modele matematice precum si tehnici de calcul numeric dorim sa estimam cat mai precis efectele parametrilor de proces din timpul cresterii asupra cristalului, astfel incat sa putem prezice inginerilor crescatori de cristale parametrii necesari in vederea obtinerii unui cristal de dimensiuni date, avand o calitate a formei si compozitionala cat mai buna.

Publicații selectate:

* L. Braescu, S. Epure, Th. Duffar , Mathematical and numerical analysis of capillarity problems and processes, John Wiley & Sons Ltd, Crystal growth processes based on capillarity: Czochralski, floating zone, shaping and crucible techniques, 2010.