Sino-German Workshop on Electromagnetic Processing of Materials,
11.10 – 13.10.2004 Shanghai, PR China
Magnetic Field Control of Heat and Mass Transport
Processes in Industrial Growth of Silicon and III-V
Semiconductors Crystals
J.Dagner, P. Schwesig, D. Vizman, O. Gräbner, M.Hainke, J.Friedrich, G.Müller
Outline:
•
Time dependent magnetic fields applied to growth process of InP
• Stationary magnetic fields in large scale Czochralski facilities
Motivation
Process: Vertical Gradient Freeze (VGF) growth of InP
Task: Substrates with low dislocation density without additional dopands for
lattice hardening
Crucible
Problem: Generation of dislocations during the
relaxation of thermal stresses
Melt
Crystal
Possible Solution: Usage of time dependent
magnetic fields to control convective heat
transfer
èChange the shape of the solid liquid interface
in order to minimize the von Mises Stress
èOptimization using numerical modeling
Numerical modeling
Furnace Setup :
• Existing VGF setup located at the
Crystal Growth Laboratory in
Erlangen (currently used for R&D
activities for S-doped InP)
• Already optimized thermal field using
numerical modeling
Numerical Modeling:
• Global model of the complete setup
for heat transfer with CrysVUn
(conduction radiation and melt
convection)
• Quasistationary calculations for
different position of the phase
boundary
• Investigated field types:
Rotating magnetic fields (RMF)
Traveling magnetic fields (TMF)
Inert gas
Boron-oxide
Melt cover
InP Crystal
9 Heating zones
Insulation
Crucible support
Steel autoclave
Applying RMF to the standard growth process
Process time
Melt
b<0
b>0
Crystal
concave
convex
Interface
Bending (b) of the solid liquid interface
for different process times.
Max. von Mises stress at solid liquid
interface for different process times.
No significant influence on the bending of the interface and the resulting von Mises
stress
Applying TMF to the standard growth process –
influence of the orientation of the Lorentz-force
Streamlines
Isotherms
dT = 1k
Aspect ration: 0.5
Standard Process
Downward
configuration
Upward
configuration
4,6 mm/s
5,3 mm/s
9,6 mm/s
Bending of the solid
liquid interface
2,0 mm
1,6 mm
2,1 mm
Max. von Mises stress
at the phase boundary
1,2 MPa
0,6 MPa
2,1 MPa
Maximum velocity in the
melt.
Only the downward configuration is
useful
Applying TMF – Influence of the strength of the
magnetic induction on the flow pattern
Streamlines for different magnetic induction at a aspect ration of 0.9. Only half of
the computational domain is show.
• Function of the velocity in z direction has a minimum
• The bending of the solid liquid interface changes from concave to concaveconvex shape (hat or W-shape)
Applying TMF – Resulting von Mises stress at the solid
liquid interface
PG
 max
.
PG
 max
.  0,93MPa
è
è
PG
 max
.
PG
 max
.  0,57 MPa
PG
 max
.
PG
 max
.  0,33MPa
Minimum of the von Mises stress at 5,5 mT, but the phase boundary has a Wshape.
Two contradicting optimization criteria:
a) Minimization of the bending of the phase boundary
b) Minimization of von Mises stress at the phase boundary
Comparison of the results for RMF and TMF
Conclusions –Part I
Rotating magnetic fields (RMF):
•
•
Only small influence on the bending of the phase boundary and the resulting
von Mises stress(< 15%)
Higher growth velocities have no advantages, in contrast to prior studies on
GaAs (Hainke et al. Magnethydrodynamics 39:513-519 2003)
Traveling magnetic fields (TMF):
•
•
•
Reduction of the resulting von Mises stress while maintaining a flat phase
boundary
Further reduction is possible if a W-shape interface does not create additional
problems in the growth process
Major drawback for the practical application: The integration of an inductor for
generating a TMF in a high pressure and high temperature vessel with
corrosive atmosphere (Phosphor vapor) is complicated and expensive.
(Schwesig et al. Journal of Crystal Growth 226:224-228 2004)
Czochralski growth of Si crystals
Objectives for using magnetic fields:
• Stabilization of convection
• Reduction of temperature fluctuations
• Control of oxygen transport and interface shape
Field strength:
• several mT up to several hundreds of mT
transversal
axial
cusp
Optimization of the seeding phase by reducing
diameter fluctuations
Magnetic field
Temperature
without
with
without
5K
Magnetic field
Diameter
with
1mm
with
without
Magnetic field
Time in sec
Hirmke, Study Work 2001
Czochralski growth of Si crystals under the influence of
steady magnetic fields
Determination of the temperature
distribution in the melt and at the crucible
wall by using a special thermocouple setup
Measured temperature distribution at the
wall (lines) compared with calculated
values (point).
(in collaboration with Siltronic)
Gräbner, Proc. EMRS 2000
Czochralski growth of Si crystals under the influence of
steady magnetic fields


wx = -20rpm, wc = 2rpm


wx = -20rpm, wc = 5rpm
Experiment
2D - Simulation
Axial Field 128mT
wx = -20rpm, wc = 5rpm
Cusp Field 40mT
wx = -20rpm, wc =
5rpm
Experiment
2D - Simulation
Temperature distribution in a Si melt with 20kg under different process conditions –
stationary numerical simulations with fixed shape of the melt pool; low Reynolds
number k- model (CFD-ACE); magnetic fields by FZHDM1.
[1] Mühlbauer et. al. J.o.Cryst.Growth 1999 pp 107
Czochralski growth of Si crystals under the influence of
steady magnetic fields
Crystal rotation:
Crucible rotation:
wx = -15rpm
wc = 4rpm
300mm
3D view
Side view
Shape of solid/liquid interface under the influence of a horizontal magnetic field.
Calculations (magnetic and flow field) with STHAMAS 3D. Free melt surface. The
temperature is color-coded.
Vizman, PAMIR 2002
Conclusions –Part II
Static magnetic fields:
• Widely used for large scale Czochralski process
• Measurement techniques for obtaining temperature values in the melt
are available
• Comparing this measured data to values obtained by numerical
simulations show a qualitative agreement
• Simulation of Czochralski process is still a matter of intense research
Acknowledgement
This work is financially supported by the German federal ministry of
education and research and Humbolt foundation.
The calculations with CFD-ACE were performed at SILTRONIC,
Burghausen, Germany