Bulk Growth of Semiconductor Crystals in a Magnetic Field: A Study of Dopant Transport

Our model for the unsteady transport of a dopant during the entire period of time required to grow a crystal assumes that the externally applied magnetic field is sufficiently strong that inertial effects and convective heat transfer are negligible. We divide the semiconductor melt into (1) mass-diffusion boundary layers where convective and diffusive mass transfer are comparable, and (2) a core region where diffusion is negligible, so that the concentration of each fluid particle is constant. A Lagrangian description of motion is used to track each fluid particle during its transits across the core between diffusion layers. The dopant distribution in each layer depends on the concentrations of all fluid particles which are entering this layer. The dopant distribution is very non-uniform throughout the melt and is far from the instantaneous steady state at each stage during crystal growth. Our transient model is the first model to predict the dopant distribution in the entire crystal. The predictions of this asymptotic model are confirmed by a numerical solution to the full mass transport equation.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Ma, Nancy

Contributors dc:contributor

• Walker, J.S.

• Engineering, Materials Science

Language dc:language

eng

Identifier

(MiAaPQ)AAI9717303

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/83949