bioul.ppt

7/18/2019 Bioul.ppt

http://slidepdf.com/reader/full/bioulppt 1/29

Optimization of the Czochralski silicon

growth process by means of

configured magnetic fields

F. Bioul, N. Van oethem, !. "u,B. #elsaute, $. $olinsky,

N. Van den Bogaert, V. $egnier, F. #upret

%ni&ersit' catholi(ue de !ou&ain

7/18/2019 Bioul.ppt


Bulk growth from the melt : basic

techniquesCzochralski (Cz),

Liquid Encapsulated

Czochralski (LEC)

Czochralski (Cz),

Liquid Encapsulated

Czochralski (LEC)

Floating Zone (FZ)

Floating Zone (FZ) Vertical Bridgman

Vertical Bridgman

7/18/2019 Bioul.ppt


Czochralski process

7/18/2019 Bioul.ppt


Factors affecting crystal quality

• Cylindrical shape(technological requirement)

• egularity of the lattice(reduction of defects : point defects! dislocations! twins")

• #mpurities(o$ygen in %i growth)

• Crystal stoichiometry&dopant concentration(reduction of a$ial and radial segregation)

7/18/2019 Bioul.ppt


'umerical modeling goals

• Better understanding of the factors affecting crystal quality

• rediction of : crystal and melt temperature e*olution solid+liquid interface shape melt flow residual stresses dopant and impurity concentrations defects and dislocations

• rocess design impro*ement

• rocess control and optimization

7/18/2019 Bioul.ppt


rincipal aspects of the problem

• Coupled! global→ interaction between heat transfer in crystal andmelt! solidification front deformation and o*erallradiation transfer

• 'on+linear

→ physics of radiation! melt con*ection andsolidification

• ,ynamic→ critical growth stages: seeding! shouldering! tail+

end! crystal detachment! post+growth

• #n*erse→ natural output is prescribed (crystal shape)! while

natural input is calculated (heater power or pull rate)

7/18/2019 Bioul.ppt


-elt con*ection

. %ignificant heat transfer mechanism defect and dislocation densities

growth striations

interface shape

. ,ominant mechanism for dopant and

impurity transfer dopant and impurity (o$ygen) distributions

7/18/2019 Bioul.ppt


/ypical flow pattern

-elt con*ection is due to

• Buoyancy (0)

• Forced con*ection

+ Coriolis (1)

+ Centrifugal pumping (2)

• -arangoni effect (3)

• 4as flow (5)

01

23

5crystal

melt

Ωs

Ωc

crucible

7/18/2019 Bioul.ppt


6uasi+steady a$isymmetric models

• 7b8ecti*eCoupling with quasi+steady and dynamic

global heat transfer models

• ,ifficulties

%tructured temporal and azimuthal oscillations

(2, unsteady effects) 9 superposed chaotic

oscillations (turbulence)

a&erage modeling re(uired

7/18/2019 Bioul.ppt


-elt flow model

Renolds equations !

→ µ", k " ! additional #iscosit and conducti#it

Renolds equations !

→ µ", k " ! additional #iscosit and conducti#it

Hypotheses : $ncompressi%le &e'tonian luid Boussinesq approimation

*uasi+stead, tur%ulent or laminar lo'

Hypotheses : $ncompressi%le &e'tonian luid Boussinesq approimation

*uasi+stead, tur%ulent or laminar lo'

7/18/2019 Bioul.ppt


t t- t. t/ t0 t1 t2 timet3

Cone

gro'th

Bod

gro'th

4ail+end

stage

*uasi+stead simulations

'ith melt lo'

*uasi+stead simulations

'ith melt lo'

4ime+

dependentsimulation

'ith

interpolated

lo' eect

4ime+

dependent

simulation

'ith

interpolated

lo' eect

4ime+dependent

simulation can pro#ide

quasi+stead sourceterms equi#alent to

transient terms

4ime+dependent

simulation can pro#ide

quasi+stead sourceterms equi#alent to

transient terms

4eneral dynamic strategy

7/18/2019 Bioul.ppt


-elt con*ection

• ow to modify the flow;<arge electrical conducti*ity of semiconductor melts

=se of magnetic fields to control the flow

• >*ailable magnetic fields ,C or >C >$isymmetric : *ertical or configured /rans*erse (horizontal) otating

• ,ifficulties orizontal fields (2, effects) 'umerical problems (artmann layers") 1, turbulence (;)

7/18/2019 Bioul.ppt


igid magnetic fields

5hm6s la' !

Conser#ation o charge !

5hm6s la' !

Conser#ation o charge !

igid magnetic field appro$imation :induced magnetic field is negligible

#mposed steady a$isymmetric magnetic field :

igid magnetic field appro$imation :induced magnetic field is negligible

#mposed steady a$isymmetric magnetic field :

7/18/2019 Bioul.ppt


>nalytical solutionsFrom 8ellming ? @alker! 0AA2

$istence of a free shear layer :plays an important role in o$ygen andimpurity transfer

ypotheses :

igh artmann number :

#nertialess appro$imation (*alid if BDE1/) :

ypotheses :

igh artmann number :

#nertialess appro$imation (*alid if BDE1/) :

7/18/2019 Bioul.ppt


Case # : Case ## :

'o magnetic field lines incontact with neither thecrystal nor the crucible

-agnetic field lines incontact with both the crystaland the crucible

B

Crystal

-elt

Crucible

B

Crystal

-elt

Crucible

Free shear layer

>nalytical solution

7/18/2019 Bioul.ppt


6uasi+steady numerical results

Material and geometrical parameters :

7ilicon crstal diameter ! - mm

Cruci%le diameter ! / mm8olecular dnamic #iscosit ! 9:..e+0 kg;m:s

Process parameters :

Crstal rotational rate ! + . rpm (+ .:< rad;s)

Cruci%le rotational rate ! = 1 rpm (= :1./ rad;s)

>ull rate ! -:9 cm;h (1:e+2 m;s)

Material and geometrical parameters :

7ilicon crstal diameter ! - mm

Cruci%le diameter ! / mm8olecular dnamic #iscosit ! 9:..e+0 kg;m:s

Process parameters :

Crstal rotational rate ! + . rpm (+ .:< rad;s)

Cruci%le rotational rate ! = 1 rpm (= :1./ rad;s)

>ull rate ! -:9 cm;h (1:e+2 m;s)

FEMAG SoftwareFEMAG Software

7/18/2019 Bioul.ppt


-agnetic field lines

Bma$.DED2/ Bma$.DE/

-agnetic field generated by

1 coils with same radius

(GDD mm)

/urbulence -odel :

>dapted -i$ing <ength

B.D/

%tokes stream function

7/18/2019 Bioul.ppt


-agnetic field lines

-agnetic field generated by 1

coils with different radii

(GDD mm and 5 mm)

/urbulence model :

>dapted -i$ing <ength

Bma$.DE1/ Bma$.DEA/

%tokes stream function

B.D/

7/18/2019 Bioul.ppt


Run A

5pposite crstal and cruci%le

rotation senses

7ilicon

8iing length model

µ ? 9:..1 -+0 kg;m:s

Ωc? :1. s+-

Ωs? +.:5< s+-

V pul ? 1: -+2 m;s

Run A

5pposite crstal and cruci%le

rotation senses

7ilicon

8iing length model

µ ? 9:..1 -+0 kg;m:s

Ωc? :1. s+-

Ωs? +.:5< s+-

V pul ? 1: -+2 m;s

Run B

7ame as " 'ith a #ertical

magnetic ield

B ? :/. 4esla

Run B

7ame as " 'ith a #ertical

magnetic ield

B ? :/. 4esla

)n&erse dynamic simulations of silicon growth

FEMAG! softwareFEMAG! software

7/18/2019 Bioul.ppt


BB

AA

*tream function for runs + and B*tream function for runs + and B

7/18/2019 Bioul.ppt


emperature field for runs + and Bemperature field for runs + and B

BB

AA

7/18/2019 Bioul.ppt


7/18/2019 Bioul.ppt


7ff+line Control

• Ob-ecti&e/o determine the best e*olution of the process

parameters in order to optimize selected process

*ariables characterizing crystal shape and quality

<ong+term time scales are considered (instead of

short+term time scales for on+line control)

• ethodology,ynamic simulations are performed under super*ision

of a controller

7/18/2019 Bioul.ppt


7ff+line Control

4ime+dependent

simulator

4ime+dependent

simulator

5+linecontroller 5+line

controller

@o process #aria%les

satis the control

o%Aecti#es

7tartne' time step 'ith

updated process

parameters

7/18/2019 Bioul.ppt


Conclusions

• >ccurate quasi+steady and dynamic simulation modelsare a*ailable using F->4+1 software

• %imulations are in agreement with theoretical predictions

• /urbulence modeling must be *alidated and impro*ed ifnecessary

• 'umerical scheme should be able to control mesh

refinement along boundary and internal layers

• 7ff+line control is a promising technique for optimizingthe magnetic field design

7/18/2019 Bioul.ppt


k+l turbulence model

• ow to modify the flow;

"dditional #iscosit !

"dditional conducti#it !

! mean tur%ulent kinetic energ

'here

"ur#ulent $inetic energy e%uation

! parameters o the model

! additional >randtl num%er

From /hE @etzel

7/18/2019 Bioul.ppt


,imensionless parameters

cruci%le Renolds num%er

(related to Coriolis orce)

crstal rotation Renolds

num%er

(related to centriugal orce)

rasho num%er

(related to natural con#ection)

>randtl num%er

Dartmann num%er

cruci%le Renolds num%er (related to Coriolis orce)

crstal rotation Renolds

num%er

(related to centriugal orce)

rasho num%er

(related to natural con#ection)

>randtl num%er

Dartmann num%er

bioul.ppt

Documents