CRM-McGill Applied Math Seminar
Tuesday Mar 4, 2008, 3:35pm
McGill, Burnside Hall Room 1205

Speaker: Sean Bohun
University of Ontario Institute of Technology

Title:
Modelling the Czochralski Growth of Type III-V Binary Semiconductors

Abstract:
Group III-V binary semiconductors (GaAs, InP, GaSb, InAs, InSb, etc.)
are materials that are characterized by a high electron mobility and a
low energy band gap which make them excellent candidates in the
manufacturing of infrared detectors, and fast (> 250 GHz) transistors.
These highly desirable properties are a result of a loosely bound crystal.
This weak crystalline structure is exactly the reason that these materials 
so difficult to grow without the formation of defects.

There is an extensive literature for the modelling of Czochralski growth
for cylindrical crystals but until recently little progress has been made
in the case of a non-cylindrical profile which is the preferred technique
for III-V compounds in the crystal growth industry.  A semi-analytical 
solidification model for crystals with a non-cylindrical profile will 
be briefly described.

This model has been recently extended in two directions:

1) Accounting for the change in the thermoelastic stress when a crystal 
forms facets.  A geometric model is used to predict the location of 
facets for a given crystal orientation.

2) Including the cubic anisotropy of the elasticity tensor.  A new technique
is described where the anisotropic problem is replaced by a sequence of
isotropic problems.  This technique can be shown to converge for any
stable crystal with cubic anisotropy which extends previous methods that
required weak anisotropy.