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

Process: Vertical Gradient Freeze (VGF) growth of InP

Task: Substrates with low dislocation density without additional dopands for lattice hardening

Problem: Generation of dislocations during the relaxation of thermal stresses

Possible Solution: Usage of time dependent magnetic fields to control convective heat transferèChange the shape of the solid liquid interface in order to minimize the von Mises StressèOptimization using numerical modeling

Motivation Motivation

Melt

Crystal

Crucible

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)

Insulation

Inert gas

9 Heating zones

Crucible support

Steel autoclave

Boron-oxide Melt cover

InP Crystal

No significant influence on the bending of the interface and the resulting von Mises stress

Process time

Applying RMF to the standard growth processApplying RMF to the standard growth process

Bending (b) of the solid liquid interface for different process times.

Max. von Mises stress at solid liquid interface for different process times.

Melt

Crystal

concave convex

b>0b<0

Interface

Upward configuration

Downward configuration

Standard Process

1,2 MPa

2,0 mm

4,6 mm/s

2,1 MPa0,6 MPaMax. von Mises stress at the phase boundary

2,1 mm1,6 mmBending of the solid liquid interface

9,6 mm/s5,3 mm/sMaximum velocity in the melt.

Only the down-ward configuration is useful

Applying TMF to the standard growth process – Applying TMF to the standard growth process – influence of the orientation of the Lorentz-forceinfluence of the orientation of the Lorentz-force

Aspect ration: 0.5

IsothermsdT = 1k

Streamlines

• Function of the velocity in z direction has a minimum• The bending of the solid liquid interface changes from concave to concave-

convex shape (hat or W-shape)

Applying TMF – Influence of the strength of the Applying TMF – Influence of the strength of the magnetic induction on the flow pattern 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.

è Minimum of the von Mises stress at 5,5 mT, but the phase boundary has a W-shape.

è Two contradicting optimization criteria:a) Minimization of the bending of the phase boundaryb) Minimization of von Mises stress at the phase boundary

PG.max

PG.max PG

.max

MPaPG 93,0.max MPaPG 57,0.max MPaPG 33,0.max

Applying TMF – Resulting von Mises stress at the solid Applying TMF – Resulting von Mises stress at the solid liquid interface liquid interface

Comparison of the results for RMF and TMFComparison of the results for RMF and TMF

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)

Conclusions –Part IConclusions –Part I

transversal axial cusp

Czochralski growth of Si crystalsCzochralski 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

Optimization of the seeding phase by reducing Optimization of the seeding phase by reducing diameter fluctuations diameter fluctuations

Magnetic field

with without

Magnetic field

with

without

Magnetic field

with

without

Hirmke, Study Work 2001

Dia

met

erT

empe

ratu

re 5K

1mm

Time in sec

(in collaboration with Siltronic)

Czochralski growth of Si crystals under the influence of Czochralski growth of Si crystals under the influence of steady magnetic fieldssteady magnetic fields

Determination of the temperature distribution in the melt and at the crucible wall by using a special thermocouple set-up

Gräbner, Proc. EMRS 2000

Measured temperature distribution at the wall (lines) compared with calculated values (point).

x = -20rpm, c = 2rpm

x = -20rpm, c = 5rpm

Experiment 2D - Simulation

Axial Field 128mTx = -20rpm, c = 5rpm

Cusp Field 40mTx = -20rpm, c = 5rpm

Experiment 2D - Simulation

Czochralski growth of Si crystals under the influence of Czochralski growth of Si crystals under the influence of steady magnetic fieldssteady magnetic fields

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

3D view

Crystal rotation: x = -15rpmCrucible rotation: c = 4rpm

Side view

300mm

Czochralski growth of Si crystals under the influence of Czochralski growth of Si crystals under the influence of steady magnetic fieldssteady magnetic fields

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

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

Conclusions –Part IIConclusions –Part II

Acknowledgement 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