Melt Flow Study EMF

The numerical and experimental study of
a melt flow under the influence of a
special type of electromagnetic field in a
model experiment
Ph.D. Student
Andrei-Radu Negrilă
Scientific coordinator
Prof. Dr. Daniel Vizman
West University of
Timişoara
Faculty of Physics

Many things are linked to a
vortex
•We are here ...

Outline
 Motivation
 State of the Art in Directional Solidification of Si DS for PV
 Model Experiment for the study of EMF stirring
 Numerical results and their experimental validation
 Flow structure analysis
 Flow structure engineering
 Conclusions & perspectives

Energy coming from the Sun
•The solar energy on the earth’s surface is 1000 times it annual energy usage (16
Tw-yr=504.6 Exajoules) !
Perez et al., 2009, International Energy Agency Update, “A Fundamental Look At Energy Reserves For The Planet”

So, why not plug in directly to
the Sun ?
•Human burning of fossil fuels is “the dumbest experiment in history” – Elon
Musk, billionaire entrepreneur and physicist

However, it all depends if PV is
commercially viable ….
•Levelized Cost of Electricity (LCOE) – here , in EUR per
kWh

The cost of PV is going down with
mass production and innovations
We are HERE
•Very good (perspective) evolution of
Levelized Cost of Electricity for PV
compared to fossil fuels by 2020
•Due to innovations reducing solar cell
costs and increasing their efficiency (our
technique is aspiring to be one of them)

Bloomberg Financial prediction
•It is no longer government policy sustaining the advancement of PV, but
by the economics of the process, as costs are driven down by
innovation and mass production

The dominant technology (> 90% of market)
Crystalline Silicon for solar cell manufacture
current conversion efficiency
for commercial cells 17-21 %; @23% for
back contact cells (ITRPV 2015)

Market Leader (60% out of 90%): Multicrystalline
Silicon Directional Solidification (DS)
The DS silicon Ingot
is cut into Brics
Courtesy of INES-CEA France, LMPS
Laboratory
Which are sliced into wafers
for Solar Cell fabrication
•The method has the
best cost/ efficiency
ratio in USD/W !

Costs can be reduced by increase of yield (useful
% of ingot volume) and of furnace throughput
•Predicted increase of mc-Si ingot mass will lead to a higher throughput per furnace

 There are thee main sources of impurities (C,N,O and
metals) in the ingots:
1. Impurity content in the feedstock
2. Crucible and crucible coating dissolution
3. Furnace environment (heating elements).
 When solubility limit is reached precipitates can form
 SiC and Si3N4 precipitates Catastrophical for
electromechanical proprieties
 Metal oxides precipitates Impede photovoltaic
(or dissolute metals) conversion
More Impurities in Silicon DS with
larger crucibles
•WITH INCREASING CRUCIBLE SIZE, more impurities can diffuse from the
crucible, coating or furnace atmosphere, because of higher melt surface areas and
solidification time.

Buoyant convection limitations in Si
DS
V. Pupazan, R. Negrila, O. Bunoiu, I. Nicoara, D. Vizman, Journal of Crystal Growth 401 (2014), 720-726.
•Impurities and precipitates accumulate in poorly mixed areas, between buoyant
convection loops
•Convective flows may become turbulent for high levels of S-L interface deflection

• two main convection zones: one due to the S-L interface deflection and one near the
melt free surface
• poorly mixed areas can be observed in between the convection loops, where precipitates
may form and be engulfed in the ingot
xOz section
Buoyant convection is even less
effective for larger ingots
A. Popescu, D. Vizman ,International Journal of Heat and Mass Transfer 54 (2011), 5540-5544

Race towards cost reduction :
With the need to maintain or increase Si ingot quality !
Two major trends for cost reduction in
DS solidification of mc-Si
Increasing
crucible size
•Avoiding detrimental
curvature of S-L
interface
•Increase in impurity
concentration from
crucible, coating or furnace
atmosphere, because of
higher melt surface areas
or crystallization time.
Cheaper feedstock of a
lesser purity
•Avoiding precipitate
formation or
morphological
destabilization of
growth interface
•Achievement of a total
mixing regime for
optimal distribution of
impurities through axial
segregation
• CHALLENGES with INCREASING CRUCIBLE SIZE and using a LOWER PURITY
FEEDSTOCK can be met by TAYLORING THE MELT CONVECTION !

•Travelling magnetic fields
-Ch. Kudla et.al. , Crystallization of 640 kg mc-silicon ingots under traveling magnetic field by using a heater-
magnet module, J. Crystal Growth, 365 (2013), 54-58
-K.Dadzis et.al., Unsteady coupled 3D calculations of melt flow, interface shape, and species transport for
directional solidification of silicon in a traveling magnetic, J. Crystal Growth, 367 (2013), 77-87
•Other Magnetic fields (Alternating, Rotating, Carousel)
-N.Dropka et. al. Comparison of stirring efficiency of various non-steady magnetic fields during unidirectional
solidification of large silicon melts, J. Crystal Growth, 365 (2013), 54-58
•Mechanical stirring
-S. Dumitrica et.al., Numerical studies on a type of mechanical stirring in directional solidification method of
multicrystalline silicon for photovoltaic applications, J. of Crystal Growth, 360 (2012) 76-80
-B. Ubbenjans et al.,, Numerical analysis of the influence of ultrasonic vibration on crystallization processes
Crystal Research and Technology 47 (2012) 279-284.
•Electro magnetic (EMF) stirring
- C. Tanasie, D. Vizman, J. Friedrich, Journal of Crystal Growth 318 (2011) 293–297.
- D. Vizman, C. Tanasie, Journal of Crystal Growth 372 (2013) 1–8
Convection tailoring in the DS of mc-
silicon

Lorentz forcesTMF - inductors
22x22x22 cm


1
sSkin depth: For silicon at 50Hz δ=5cm
Limitations of Traveling magnetic field
in tailoring DS convection
•Same limitation for all types of time varying magnetic fields

Idea for Electromagnetic field
(EMF) stirring
Combined application of a vertical magnetic field
and electrical current for melt stirring
  BBUEFL


Radial electric current
from Electrodes at free
melt surface
Vertical magnetic field
Forced convection(stirring)
via the Lorentz Force

From EMF Simulation to
Model Experiment
Numerical simulations in D. Vizman, C. Tanasie, Journal of Crystal Growth 372 (2013) 1–8 of
EMF stirring performed using STHAMAS3D software
Two study
directions for this
Thesis
 Numerical Simulations of Si EMF need
to be validated by a Model Experiment
 Study of additional control parameters’
(I,B, electrode position) influence on
Flow Structure (STHAMAS3D)

Velocity measurements: Ultrasound Doppler Velocimeter
US-transducers
Model Experiment for EMF stirring.
UDV Technique
US-transducers Electrodes

Homogenous Vertical Magnetic field
in EM Gap Middle
•Magnetic field is quasi-homogenous (>90% of maximum value) in crucible
region
1
3
5
7
9
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8 9
10
Bz(%ofBzmax)
Vertical Magnetic Field measured with 3 Axis Hall
Magnetometer fixed on 3D movable support
(as % of 10 mT maximum value in center)
90-100
80-90
70-80
60-70
50-60
40-50
30-40
20-30
10-20
0-10
crucible position

The “perfect” model melt
An easy to handle, non-toxic, room temperature liquid melt with similar
proprieties with molten Silicon is needed in order to perform a relevant
model exeperiment for Si EMF validation
Physical property GaInSn Silcon Unit
Density, ρ 6360 2520 Kg/m3
Dynamic viscosity, μ 2.16 ∙10-3 7.56∙10-4
N·s/m2
Kinematic viscosity (η= μ/ρ) 0.34∙10-6 0.3∙10-6
m2/s
Electrical conductivity, σ 3.2∙106 1.29∙106
S/m

Optimized configuration
Uncertainties:
-Material properties of
Plexiglas compared to glass
(sound speed, acoustic
impedance)
-Poor wetting of Plexiglas
by GaInSn due to lower
density
-Electrode shape and current
distribution
-Self magnetic field
-Relative positions error for
old system
Non magnetic stainless steel hemispherically tipped
electrodes : lower self-magnetic field

 Pulsed ultrasonic echo technique to measure velocity profiles of flowing liquids:
 Gives velocity projection along the ultrasonic beam direction (depth) from a
specified number of volumes
Ultrasonic Doppler Velocimetry.
DOP3010 Velocimeter
Vy (mm/s)
Y (um)

 A transducer contains an emitter that sends periodically a short
ultrasonic bursts and a receiver that collects continuously echoes
from targets present in the path of the ultrasonic beam.
 Calculation of the autocorrelation function of the signal coming
from the same particles in a measurement volume, reflected from
different pulses separated in time by Tprf, in order to derive the
Doppler shift in frequency !
Ultrasonic Doppler Velocimetry.
Method principle
• average Doppler frequency is the
Fourier Transform of the
autocorrelation function of the echo
signal
• auto-correlation function is
estimated using the complex
envelope of the echo signal.

UDV parameters
US frequency 4.130 Mhz
Doppler angle 0°
Pulse repetition frequency 310.56 Hz
Speed of sound in GaInSn 2730 m/s
Measured depth 70 mm
Bursts per profile 64
Velocity resolution 0.2 mm/s
Time resolution (single profile) 750 ms
Number of gates (measurement volumes) 300
Number of profiles 900/1600
Spatial resolution (distance between two
measurement volumes)
0.228 mm
Axial spatial resolution of measurement
volume
2.184 mm
Minimum/Maximum US beam diameter 5 mm - 9.5 mm
Divergence /spread of the US beam 3.89° Half angle at (-6 dB) / 7.79°
spread

•Isothermal Melt: GaInSn
(melting point 11C)
• L=7 cm; h=5 cm;
•B=10mT, 3mT
•I=2A,5A,10A
US sensors
Symmetric configuration
Asymmetric configuration
U
B
h
L
I
Numerical Model employed
Combined application of current I and magnetic field B causes melt rotation
;

• Direct solution of Navier-Stokes equations using Finite Volume
method
• Consideration of Lorentz force by solving additional scalar potential
equation
• Higher efficiency for parallel version on a PC cluster
Simulations with STHAMAS3D
software

  0


i
i
u
y

     3,2,1








is
y
p
uu
y
u
t
u
i
i
ijji
j
i 
Fb+ Fs+ FL + FV
• Consideration of Lorentz force
by solving additional scalar
potential equation (current
continuity) at each time step
(MHD2 approximation)
Navier-Stokes Equations
j = σ (- + u x B)
j = 0 => ∆𝛷 = 𝜵 ∙ 𝒖 × 𝑩
𝜵| 𝑛 𝛷 = −
𝒋 𝒏
𝜎
𝒔 𝒖 = 𝑭 𝑳 = 𝒋 × 𝑩
• Current injected at
electrode positioning
• Conservation of Momentum :
• Conservation of mass:
• External forces:

Vortical melt rotation develops in the whole mass of the melt
Flow intensity increases with the increase of the electrical current
I=5A
Bottomview
I=2A I=10A
GeneralviewMelt flow in an Asymmetric
electrode configuration
B=10mT:

Flow structure changes to poloidal with by electrode position
Even a magnetic field of 3mT can produce a significant stirring effect
Bottomview
AC; B=10mT; I=10A
Generalview
SC; B=10mT; I=10A SC; B=3mT; I=10A
Melt flow in a Symmetric
electrode configuration
R. A. Negrila, A. Popescu, M. Paulescu, D. Vizman, Procedings of the 9th PAMIR International Conference, Riga, 2014, Volume 2, 205-208

Comparison of numerical and
experimental results
 A good agreement between numerical and experimental profiles
 Better agreement in the AC case due to simpler flow structure than in SC one
R. A. Negrila, A. Popescu, M. Paulescu, D. Vizman, Procedings of the 9th PAMIR International Conference, Riga, 2014, Volume 2, 205-
208

Phenomenological explanation of the flow
structure with the help of a Model Problem
•There are two Lorentz forces: an acceleration one, Fθ, and a damping one Fd
• Fd has a component opposing uθ and a component opposing up
•The flow around an electrode can be described by an azimuthal uθ and a poloidal up component
Fd_θ
Fd_p Bz

AC case – Vortex Formation
 an azimuthal rotation and a converging meridional flow form a “Vortex”
structure
 The flow is pointed towards the electrode

Radial pressure gradients description of
poloidal flow generation
The forcing around one electrode is similar to that in these
studies
•A radial pressure gradient oppoeses the centrifugal force
•As long as the angular momentum is an increasing
functions from the axis of rotation, the flow is
centrifugally stable
Centrifugal pumping: axial variation
of radial pressure gradients in the core
flow generate a poloidal flow
Ekman pumping: axial variation of
radial pressure gradients (in the
boundary layer) generate a poloidal flow
P. A. Davidson, J. C. R. Hunt - Journal of Fluid Mechanics 185 (1987), 67
P. A. Davidson Journal of Fluid Mechanics 245 (1992), 669-699

SC cases considered here
present another flow structure
•The vortex is resupplied by a converging meridional recirculation (as for AC) but
a secondary “Poloidal” structure is observed

41
•Melt: GaInSn (melting point 10C)
• L=7 cm; h=5 cm (aspect ratio close to
G1 silicon ingot)
•B=5mT, 10mT, 20mT, 30mT
•I=0.1A, 0.5 A, 1A, 2A, 5A,10A, 15A,
20A, 25A, 30A, 35A, 40A, 45A
Simulations with STHAMAS3D software on symmetrical configuration of
electrodes
Change of flow structure with electromagnetic
parameters – SC parametrical study
Parametrical Study for array of currents I and magnetic fields B to understand,
quantify and predict flow structure

42
The flow structures: “Vortex” and
“Poloidal” dominated
(a) I = 0.1 A; B = 10 mT (b) I = 45 A; B = 10 mT
(c) I = 0.1 A; B = 30 mT (d) I = 45 A; B = 30 mT
Flow structure changed from “Vortex” to “Poloidal” flow domination with the increase of the intensity
of electrical current for any magnetic field
Particle tracking of
flow structure
BLUE FROM TOP
OF VORTEX;
RED FROM
BOTTOM OF
VORTEX
R. A. Negrila, A. Popescu, D. Vizman, European Journal of Mechanics B/Fluids 52 (2015), 147-159.

The flow structure transition
Particle tracking of flow structure for different electrical current I and magnetic field B pairs
(a) I = 0.1 A; B = 30 mT (b) I = 10 A; B = 30 mT
(c) I = 20 A; B = 30 mT (d) I = 45 A; B = 30 mT

Dependence of possible flow structures
on an integral energy constraint
Flow
scaling
case
Secondary poloidal flow
Energy Dissipation around
streamlines lengthscale
(a)
Generated by centrifugal pumping
(usually in a deep crucible)
Torrodial structure closing inside the
core of the flow
Long enough so that energy diffuses to the
wall where destroyed by shear forces
(b)
Generated by Ekman pumping (usually
in a short crucible)
Poloidal structure passing through the
boundary layer (suppressing centrifugal
pumping )
Streamline lengthscale short as Ekman
pumping flushed them through the wall
boundary layer where energy is destroyed
by shear forces
(c)
May be generated by pumping both
mechanisms.
At wall but also by magnetic damping
inside the melt volume

Streamline structure
(a) 0.1 A 30 mT; Z=1mm (b) 45A 30 mT; Z=1mm
(g) 0.1 A 30 mT; Z= 49.9 mm (h) 45A 30 mT; Z= 49.9 mm
•Streamlines passing close to the electrode and the bottom are flushed by Ekman
pumping through boundary layer for the “Vortex” case

Streamline structure
•For the “Vortex” case streamlines in the bulk flow are centrifugally pumped
•For the “Poloidal” case streamlines adopt a longer lenghtscale to dissipate the flow
(c) 0.1 A 30 mT; Z= 20 mm (d) 45A 30 mT; Z= 20 mm
1
(e) 0.1 A 30 mT; Z= 40 mm (f) 45A 30 mT; Z= 40 mm

Confirmation of “Vortex” and
“Poloidal” flow structure for SC case
•The plane at 6 mm close to the bottom of crucible – area of interest for DS
•GaInSn poor wetting material - limits of “no-slip” condition imposed in
simulation for Ekman flushed streamlines

Quantification of the flow structure
transition. The parameter - LStruct
The competition between the vortex driven flow and the poloidal one characterised by LStruct
- the distance along the diagonal where the two opposing flows balance at the bottom,
marked by a dark arrow
I = 0.1A, (vortex flow) I = 1A, (vortex flow) I = 5 A, (transition)
I = 25A, (poloidal flow) I = 35 A, (poloidal flow) I = 45A, (poloidal flow)
B=20mT

50
The flow structure transition with
electromagnetic parameters
•Lstruct as a characteristic length defining the “Vortex” to “Poloidal” structure
transition for the different electrical currents I and magnetic fields B

51
Scaling analysis of the flow
governing equations
by defining characteristic values for the length 𝐿 = 𝐿0 𝐿′
, velocity u= 𝑢0 𝑢′, time 𝑡 = 𝑡0 𝑡′
=
𝐿0 𝑢0 𝑡′
, pressure 𝑝 = 𝑝0 𝑝′
= (𝜌𝑢0
2
)𝑝', Lorentz Force 𝐹𝐿 = 𝐹𝐿0
𝐹𝐿′, and operators ∇= ∇′ 𝐿0,
∆= ∆′ 𝐿0
2
𝜕𝒖′
𝜕𝑡′
+ 𝒖′
𝜵′
𝒖′
= − 𝜵′
𝑝′
+
1
𝑅𝑒
∆′
𝒖′
+
𝐹𝑒𝑚 #1
𝑅𝑒2
𝑬′
× 𝑩′
+
𝐹𝑒𝑚 #2
𝑅𝑒2
𝒖′
× 𝑩′
× 𝑩′
𝑅𝑒 =
𝑢0 𝐿0 𝜌
𝜇 𝐹𝑒𝑚 #1 =
𝐼0 𝐵0
𝐿0
2
𝐿0
3
𝜌
𝜇2
=
𝐼0 𝐵0 𝐿0 𝜌
𝜇2 𝐹𝑒𝑚 #2 =
𝜎𝑢0 𝐵0
2
𝐿0
3
𝜌
𝜇2
F1_Re F2_Re
Flow structure and Re = functions of (Fem#1, Fem#2, boundary conditions,
electrode positioning)

Reynolds number
𝑅𝑒 = 1.2278 𝐹𝑒𝑚 #1
0.5232
Re number depends on Fem#1, as
the accelerating Lorentz force
is balanced in the core by the
inertial force

Flow structure depends on
dimensionless numbers ratios
𝐹1_𝑅𝑒 = 𝐹𝑒𝑚 #1 𝑅𝑒2𝐹2_𝑅𝑒 = 𝐹𝑒𝑚 #2 𝑅𝑒2
•Vortex” structure depends on ratio of the second Lorentz number
•“Poloidal” structure tends to depend more on the ratio of first Lorentz number
• in the “Transition” region both ratios have an important influence on the flow solution

Structure “phase” diagram
•A flow structure “diagram” can be imagined for sets of Lorentz ratios values

MHD damping of poloidal flow
• for same Fem#1= 9.52E+05 ~ IB product, damping parameter Fem#2 ~ uB2 differs:
2.99E+05 4.78E+06

0.5 A, 20 mT2 A, 5 mT
•The flow in the forced region is more azimuthal for the “Vortex” case

the MHD interaction parameter F2_Re =σB2/ρ∙L0/U0 = (1/τ)∙(L0/U0) ) = tp/τd
Z=45 mm Z=5 mm
2 A, 5 mT; F2_Re = 0.104 0.5 A, 20 mT; F2_Re = 1.79

Isothermal Silicon melt EMF flow structure
conservation with dimensionless numbers
“Vortex” case of I=0.1 A B=30 mT for GaInSn EMF vs. I=0.03 A B=0.0279 mT
for Si EMF
(a) plane with electrodes GaInSn (b) plane with electrodes Si
(c) plane containing diagonal between
electrodes GaInSn
(d) plane containing diagonal between
electrodes Si
(a) plane with electrodes GaInSn (b) plane with electrodes Si
(c) plane containing diagonal between
electrodes GaInSn
(d) plane containing diagonal between
electrodes Si
“Poloidal” case of I=45 A B=5 mT for GaInSn EMF vs. I=14.91 A B=4.656 mT
for Si EMF

59
•Melt: GaInSn (melting point 10C)
•I=45A ; B=30mT
•same aspect ratio as for L=7 cm; h=5
cm: L=10 cm, h=7 cm; L=15 cm,
h=11cm; ; L=25 cm, h=18cm; ; L=35
cm, h=25 cm.
Simulations with STHAMAS3D software on symmetrical configuration of
electrodes
Change of flow structure with up-scaling the crucible
size - SC parametrical study for varying (L) at I, B =
const
Parametrical Study for variation of crucible size to understand, quantify and predict
flow structure

Particle tracking of flow structure
(BLUE FROM TOP OF VORTEX;
RED FROM BOTTOM OF
VORTEX) for I=45A ; B=30mT and
different characteristic lengths with
same aspect ratio
(a) x=7cm, y=7cm, z=5cm (b) x=10cm, y=10cm, z=7cm
(c) x=15cm, y=15cm, z=11cm (d) x=25cm, y=25cm, z=18cm
(e) x=35cm, y=35cm, z=25cm
R. A. Negrila, A. Popescu, B. Barvinschi, M. Paulescu and D. Vizman, GaInSn melt flow structure
variation with crucible size in an isothermal electromagnetic stirring configuration, to be published in
AIP Conference Proceedings

61
quantification
Lstruct as a parameter defining the “Vortex” to “Poloidal” structure transition for for I=45A ; B=30mT
for the different characteristic lengths with same aspect ratio that have been numerically simulated

Reynolds number variation
with up-scaling

Flow structure depends on MHD
interaction parameter F2_Re
•“Vortex” to “Poloidal” structure transition depends on ratio of the second Lorentz
number; this can be generalized for any I and B pair

Electrode positioning influence
on Poloidal structure formation
(a) SC case; electrodes at 1/3 and 2/3
of the diagonal
(b)AC case; electrodes at 1/2 and 5/6
of the diagonal
(c) AC case; electrodes at 1/2 of the
diagonal and corner volume element
on the diagonal
(d) AC case; electrodes at 1/2 of the
diagonal and adjacent volume
element to the right on the diagonal
•“Poloidal” flow structures structure seems to be favored if the intersection of the
two vortices around the electrodes is close to the diagonal between them

65
Outline
 Motivation
 State of the Art in Directional Solidification of Si DS for PV
 Model Experiment for the study of EMF stirring
 Numerical results. Flow structure analysis
 Experimental results for validation of the numerical model
 Conclusions & perspectives

A dreamer may ask:
"Sometimes do you think
that crystals grow better
if you grow'em with Jazz ?"
A laughing man answers:
"It depends on the Jazz atmosphere pressure“
with a contribution from Zbignev Kowalski (the laughing
man :) )
The link between the advancement of PV
and the work of this thesis
THE ELECTROMAGNETIC CONTROL
OF A MELT FLOW CAN CREATE A
“JAZZY” ATMOSPHERE FOR
growing a better PV Si ingot, being an
innovation that could lead to a
reduction in solar cell costs and an
increase in their efficiency

Conclusions
 The combination between an vertical magnetic field and an electrical
current is an interesting option in the control of melt convection in the
DS growth of silicon ingots
 Good qualitative agreement between experimental and numerical
results
 The results prove the potential of numerical simulation to support the
process development. Numerical experiments are much less more
expensive than real ones.
 It was shown that even small values of the magnetic field and electrical
current can improve the level of mixing in the melt
 The flow structure can be changed through electrode AC or SC
positioning, electrical current or magnetic field variation

Conclusions
 The resulting flow structure was analyzed and described in terms of a
"Vortex“, respectively a “Poloidal” flow domination on the flow structure
 Quantification of flow structures through a dedicated parameter
 A scaling analysis of the flow governing equation, was done indentifying a
direct correlation between ratios containing dimensionless forcing parameters
and the Reynolds number or the flow structure parameter
 By increasing the crucible size and conserving the electromagnetic
parameters I and B, the transition a “Poloidal” to a “Vortex” flow structure
is observed
 The apparition of a “Poloidal” flow structure seems to be related to the
distance between the intersection of the vortices surrounding each electrode
and the diagonal lying between them.
 The same flow structures will be obtained for a Si melt as for GaInSn by
conserving the Reynolds and forcing parameters

Perspectives
 The forcing parameters must be adapted to be able to predict the
influence of changing the aspect ratio of the crucible on the flow
structure
 A full description of the application of EMF to DS flow must take into
account the Grashof number for buoyant convection as an
independent variable
 A correlation must be made between the flow structure and impurity
concentration and growth interface deflection through the employment
of some additional numerical simulations and experimental
characterization work, for Si DS

Conferences
1. 4th European Conference on Crystal Growth, 7-12 Iunie 2012, Glasgow, Marea Britanie: D. Vizman, C.Tanasie, R. Negrila -
Novel method for melt flow control in unidirectional solidification of multi-crystalline silicon (Poster)
2. The 7th International Conference On Advanced Materials (ROCAM), 28-31 August 2012:R. A. Negrila, D. Vizman - Numerical
and Experimental Studies on Melt Flow in a Model Experiment for Electromagnetic Stirring, Brașov, România (Poster)
3. 6th International Workshop on Crystalline Silicon Solar Cells (CSSC6), 8-11 Octombrie 2012, Aix-les-Bains, Franța : D.
Vizman, C. Tanasie, R. Negrila - A new type of electromagnetic stirring in directional solidification of mc-Si (Poster)
4. 7th International Workshop On Modeling In Crystal Growth, 28-31 Octombrie 2012, Taipei, Taiwan: D. Vizman, C. Tanasie, R.
Negrila - Numerical studies on a type of electromagnetical stirring in directional solidification method of multicrystalline silicon,,
(Oral)
5. Physics Conference TIM-12, 27-30 Noiembrie 2012, Timișoara, România :R. A. Negrilă, A. Popescu, M. Paulescu, D. Vizman -
Melt stirring based on a combination of electrical current and magnetic field(Oral); V. Pupăzan, R. A. Negrila, M. Bunoiu, M.
Stef, I. Nicoara, D. Vizman - Impurity distribution study in multi-crystalline silicon grown by Bridgman method (Oral)
6. A Treia Sesiune Națională De Comunicări Științifice A Doctoranzilor, 10-12 Iunie 2013, Timișoara, România:R.-A. Negrila -
Experiment model al unei noi configurații de stirring electromagnetic într-o topitură de GaInSn (Oral)
7. The 19th American Conference on Crystal Growth and Epitaxy, 21-26 Iulie 2013, Keystone, Colorado, Statele Unite ale
Americii: D. Vizman, R. Negrila - Numerical and experimental studies on a special type of electromagnetic stirring, (Oral);V.
Pupazan, R. Negrila, O. M. Bunoiu, I. Nicoara, D. Vizman - Growth and characterization of multi-crystalline silicon obtained by
Bridgman technique (Poster),
8. 17th International Conference on Crystal Growth and Epitaxy - ICCGE-17, 11-16 August 2013, Varșovia, Polonia: R.-A.
Negrila, M. Paulescu, A. Popescu, D. Vizman - Model experiment on a special type of electromagnetical stirring in a GaInSn
melt (Oral); V. Pupazan, R.-A. Negrila, M. Stef, M. O. Bunoiu, I. Nicoara, D. Vizman - Effects of crucible coating on the quality
of multi-crystalline silicon grown by a Bridgman technique (Poster); R.-A. Negrila, V. Pupazan, M. O. Bunoiu, D. Vizman -
Study of resistivity and lifetime profiles in highly polluted multi-crystalline silicon grown in a graphite crucible by a Bridgman
technique (Poster);
9. 7th International Workshop on Crystalline Silicon Solar Cells, 22-25 Octombrie 2013, Fukuoka, Japonia R. Negrila, S.
Dumitrica, A. Popescu, D. Vizman Model experiments on some melt stirring techniques in a rectangular crucible (Oral):

Conferences
10.Al XV-lea Simpozion „Tinerii și cercetarea multidisciplinară”, 14-15 Noiembrie 2013, Timișoara, România: M. O. Bunoiu, R. A.
Negrila, D. Vizman - Materiale fotovoltaice și dezvoltarea de procese industriale pentru promovarea energiei solare prin
scăderea costurilor de producție(Oral)
11.TIM-13 Physics Conference, 21-24 Noiembrie 2013, Timișoara, România: R. A. Negrilă, A. Popescu, M. Paulescu, D. Vizman,
B. Barvinschi - Comparaison between numerical and experimental results in the case of a special type of electromagnetical
stirring for conducting melts (Oral); R. A. Negrilă, V. Pupăzan, O. M. Bunoiu, D. Vizman - Influence of process time on
electrical proprieties of highly polluted multi-crystalline silicon grown by bridgman technique (Poster)
12.E-MRS 2014 Spring Meeting, 26-30 Mai 2014, Lille, Franţa: R. Negrila, A. Popescu, D. Vizman – Novel electromagnetic
stirring technique in a direct-solidification configuration (Oral)
13.9th PAMIR International Conference on "Fundamental and Applied MHD, Thermo acoustic and Space technologies", Riga, 16-
20 Iunie, 2014: R. A. Negrila, A. Popescu, M. Paulescu, D. Vizman - Control of convective flows in a rectangular crucible by a
special type of electromagnetical stirring (Poster),
14.Physics Conference TIM14, 20 - 22 Noiembrie 2014, Timişoara, România: R. A. Negrila, A. Popescu, B. Barvinschi, M.
Paulescu and D. Vizman - GaInSn melt flow structure variation with crucible size in an isothermal electromagnetic stirring
configuration (Oral)
15.CSSC-8 / Crystalline Silicon for Solar Cells / May 5-8 2015, Bamberg, Germany: R. A. Negrilă, V. Pupăzan , A. Popescu, D.
Vizman - Influence of process time on electrical proprieties of highly polluted multi-crystalline silicon grown by the Bridgman
technique (Poster); R. A. Negrilă, A. Popescu, D. Vizman - Melt flow structure variation with crucible size in an isothermal
electromagnetic stirring configuration for Silicon Directional Solidification (Poster)
16.8th International Conference on Advanced Materials, ROCAM 2015, 7-10 July 2015, Bucharest, Romania: R. A. Negrilă, V.
Pupăzan , A. Popescu, D. Vizman - The influence of varying growth parameters on the quality of multi-crystalline silicon grown
by a Bridgman technique (Oral), R. A. Negrilă, A. Popescu, D. Vizman - Up-scaling of an electromagnetic stirring configuration
for silicon directional solidification (Oral)
17.5th European Conference on Crystal Growth, 9-11 September 2015, Bologna, Italy: R. A. Negrilă, A. Popescu, D. Vizman -
Numerical modeling and experimental validation of electromagnetical stirring in unidirectional solidification of multicrystalline
silicon (Oral); R. A. Negrilă, V. Pupăzan , A. Popescu, D. Vizman - Influence of growth parameters on electrical proprieties of
highly polluted mc-Si grown by the Bridgman technique with various crucible-coating combinations (Poster)

Published articles
1. V. Pupazan, R. Negrila, O. Bunoiu, I. Nicoara, D. Vizman - Effects of
crucible coating on the quality of multicrystalline silicon grown by a
Bridgman technique, Journal of Crystal Growth 401 (2014), 720-726. (IF:
1.698, AIS: 0.401)
2. R. A. Negrila, A. Popescu, D. Vizman - Numerical and experimental
modeling of melt flow in a directional solidification configuration under the
combined influence of electrical current and magnetic field, European
Journal of Mechanics B/Fluids 52 (2015), 147-159. (IF: 1.656, AIS: 0.701)
3. R. A. Negrila, A. Popescu, B. Barvinschi, M. Paulescu and D. Vizman,
GaInSn melt flow structure variation with crucible size in an isothermal
electromagnetic stirring configuration, în curs de publicare în AIP
Conference Proceedings
4. R. A. Negrila, A. Popescu, M. Paulescu, D. Vizman - Control of convective
flows in a rectangular crucible by a special type of electromagnetical stirring,
Procedings of the 9th PAMIR International Conference on "Fundamental
and Applied MHD, Thermo acoustic and Space technologies", Riga, 2014,
Volume 2, 205-208

Acknowledgments
 All the mc-Si team at Physics Faculty, West University of Timisoara for
continuous help and crucial discussions
 I would like to thank Prof. Dr. Daniel Vizman, who set me up with a very
challenging PhD position and for his practical advice in professional and
personal matters
 I would like to thank all the members of the PhD advisory and defense
commission for support and for accepting to review my thesis.
 For the financial support : the work was supported by a grant of the
Romanian National Authority for Scientific Research, CNCS – UEFISCDI,
project : “Control of melt flow in a directional solidification configuration
using an electromagnetic field” number PN-II-ID-PCE-2011-3-0789
 This work was supported by the strategic grant POSDRU/159/1.5/S/137750,
”Project Doctoral and Postdoctoral programs support for increased
competitiveness in Exact Sciences research” cofinanced by the European
Social Found within the Sectorial Operational Program Human Resources
Development 2007 – 2013
 K.Dadzis andV.Bojarevics for the fruitful discussions concerning scaling and
EVF flow analysis

Published articles
THANK YOU FOR YOUR ATTENTION !
1. V. Pupazan, R. Negrila, O. Bunoiu, I. Nicoara, D. Vizman - Effects of
crucible coating on the quality of multicrystalline silicon grown by a
Bridgman technique, Journal of Crystal Growth 401 (2014), 720-726. (IF:
1.698, AIS: 0.401)
2. R. A. Negrila, A. Popescu, D. Vizman - Numerical and experimental
modeling of melt flow in a directional solidification configuration under the
combined influence of electrical current and magnetic field, European
Journal of Mechanics B/Fluids 52 (2015), 147-159. (IF: 1.656, AIS: 0.701)
3. R. A. Negrila, A. Popescu, B. Barvinschi, M. Paulescu and D. Vizman,
GaInSn melt flow structure variation with crucible size in an isothermal
electromagnetic stirring configuration, în curs de publicare în AIP
Conference Proceedings
4. R. A. Negrila, A. Popescu, M. Paulescu, D. Vizman - Control of convective
flows in a rectangular crucible by a special type of electromagnetical stirring,
Procedings of the 9th PAMIR International Conference on "Fundamental
and Applied MHD, Thermo acoustic and Space technologies", Riga, 2014,
Volume 2, 205-208

Role of damping force
 “Vortex”: and
 Transition: and
 “Poloidal”: and

MHD damping of vortical flow
-the convergent poloidal part
0.5 A, 20 mT2 A, 5 mT 0.1 A, 20 mT

Vorticity Azimuthal and
Poloidal Governing Equations
•Governing equation for Poloidal vorticity (azimuthal velocity)
•Governing equation for Azimuthal vorticity (poloidal velocity)
Axial gradients in azimuthal velocity generate a poloidal flow !
Inertial forces balance the accelerating Lorentz force in the core flow
P. A. Davidson, J. C. R. Hunt - Journal of Fluid Mechanics 185 (1987), 67-106

Centrifugal pumping for vortex case
for streamlines in the middle
(a) 0.1 A 30 mT; (b) 45A 30 mT

Keeping impurity concentrations below
solubility limit through melt mixing
•Diffusion boundary layer thickness reduced by forced mixing prevents
precipitation formation and morphological destabilization of growth interface.
•Controlling the convection structure in DS is an important issue for Si crystal
quality improvement

Purification through segregation – the UMG
route cheaper than Electronic Grade silicon
•Controlling the convection structure in DS is important for a better
purification through axial segregation and Si crystal quality improvement

Melt Flow Study EMF

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