presentation of the electrical molten zone (emz) technique
TRANSCRIPT
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1Presentation of the Electrical Molten Zone (EMZ) Technique
Joo C. C. Henriques
Faculty of Sciences of the University of Lisbon - Physics Department
Abstract
This article presents a new zone melting crystallization technique for photovoltaic silicon ribbon
production. It starts by showing some background research on related methods concerning, in
particular, to ways of achieving and moving electrical molten zones (EMZ). It presents the
fundamental mechanism responsible for the electric current concentration, which allows zone
formation. Demonstrates the possibility of zone melting recrystallization (ZMR) through this
technique and shows growth rates and energy consumptions that can be expected of it. It exposes
ideas and results of the first attempts to obtain silicon ribbons using commercial (granular)
feedstock. The electrical characteristics and control methods of the system are shown as well as the
related temperature distributions in the ribbons. It reveals the existence of interfacial instability
phenomena, which is thought to be of magnetohydrodynamic (MHD) origin, thus (tentative)
explanations for those are illustrated by analogy with typical occurrences observed (in other
contexts) in tubes of electrically conducting fluids.
Keywords: Magnetic fields; Morphological stability; Recrystallization; Electrical molten zone
technique; Ribbon growth; Semiconducting silicon.
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21. Review of EMZ Concepts
The work presented here shows the state of the art of a project aiming an experimental
demonstration of principle of a new zone melting crystallization technique, for silicon ribbon
production to photovoltaic applications, following the example of others in the industry like EFG
[1], String-Ribbon [2] and Dendritic-Web [3]. This growth method allows, in principle, an
increment of purity and structural perfection of the base materials, while offering a significant cost
reduction by: a) avoiding the use of expensive consumables like crucibles; b) lowering the process
energy consumption and c) suppressing the ingot slicing operation to obtain silicon wafers.
The concept of zone melting (re)crystallization of silicon materials through direct application
of electric current, eitherlongitudinal (i.e. in the growth direction) or transversal, is an old and
relatively straightforward idea, without any special equipment requirements. Worth mentioning,
however, is the precursor work of W. G. Pfann [4] with electrical molten zones and feedstock
supplyingpools, as he was probably the first one to realize them, having even registered several
patents on the process (e.g. [5]).
Pfann suggested several possibilities for moving the molten zones and thus recrystallize the
base materials. This is usually made by creating an asymmetry in the temperature distribution, with
adequate thermal gradients in the material, imposed by the current injecting electrodes themselves,
by using thermal shields or insulation and by modulating the meniscus shape (variation of the
current passage cross-section). The last possibility can be implemented through:
a) The gravity effect, making the meniscus thinner in the upper part in relation to the lower,
thus originating higher Joule dissipation near the former solid-liquid interface, which induces a
upwards zone movement;
b) The meniscus mechanical constriction (with an insulating piece) in order to increase the
resistance locally and cause higher dissipation, the translation of the piece induces zone movement.
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3It is also possible to move the zone even in the absence of any thermal gradient, which
constitutes a very interesting alternative from the point of view of reducing the internal stresses of
the crystals, an especially important problem in ribbon growth techniques due to the limitation that
imposes to their growth rate. This can be done by:
a) The Peltier effect between the material and its own melt (with longitudinal current). The
Peltier heat is absorbed in one of the solid-liquid interfaces and released on the other, depending on
the current direction. It may be seen as if it would inject the heat of fusion in an interface and
extract it in the opposite one with both at the same temperature. For example, in silicon with a
current density of 500 Acm-2 (cf. sec. 5) the interface advance speed may be about 7 mmmin-1.
b) Electrodiffusion of impurities with high ionic mobility. Transfer of these from one
interface to another (segregation) originates the solidification of the first one and the fusion of the
second one (according to thesolidus curve in the phase diagram).
The application of an external magnetic field, perpendicularly to the current direction in the
material, may not only generate a temperature distribution capable of moving the zone, but also
suspend it by magnetic levitation. An interesting way of accomplish this is through the interaction
between the current in the zone and the one that passes in an external electrical conductor
positioned parallel to the zone, that is by the Amperes force action. For example, with currents in
the order of 50 A and a conductor placed at 1 mm from a silicon molten zone, with characteristics
similar to the ones in the present study, the Amperes force is some 70 times the weight of the melt.
Some of the aforementioned concepts were rediscovered and used in this work, however if
high growth rates are desirable, without compromising material purity and system simplicity, only
external radiative pre-heating seems interesting, that is why it was the chosen solution in the present
study. On the other hand in the EMZ technique the current passes transversally in the ribbon (i.e. in
a direction perpendicular to that of the growth, but in the plane of the ribbon), which is a more
efficient direct heating method, since it results in a much more localized temperature distribution in
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4the material. There are several alternatives to do this, for example using an electric arc between an
electrode, of a suitable shape and material, which sweeps the recrystallizing charge. Depending on
the specific configuration, the current may or may not disperse throughout the charge (i.e. the
counter-electrode may or may not be the growing crystal), thus allowing a supplementary degree of
freedom in the temperature distribution of the material.
Kuhlmann-Schfer [6] patented in 1976 an electrical molten zone process, which presents
remarkable similarities of principle with the one proposed here. In that, two or more electrodes of
the same material as the charge are disposed laterally in contact with the crystallizing material (fig.
1). These electrodes or the inferior part of the charge may serve as feedstock source to the zone. In
the second case, the electrodes must be at a lower temperature in order to avoid being consumed in
the process, allowing only for movement in relation to the charge, which may have a cylindrical or
plane shape. The cross sections of the electrodes in contact with the charge should be small in order
to achieve the necessary current concentration and, therefore, the desired temperature. However,
they should have higher thickness than the zone width in order to provide the necessary
confinement to it.
Figure 1 Kuhlmann-Schfer method for generation of cylindrical (a) or ribbon (b) shaped crystals
by electrical molten zone. Electrodes 2 are fixed to supports 4 around charge 1 delimitating the
molten zone 3 (the lower drawings represent top views).
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5A more recent (1993) German patent also shows a similar electrical molten zone process
(initiated by radiative heating fig. 2) [7]. The method allows the production of ribbons (up to 10
cm in width) or thin walled tubes and is destined specifically to the photovoltaic market.
Figure 2 T. Wolfgang method for ribbon generation by electrical molten zone. The silicon
electrodes 2 delimitate the molten zone 3 and the silicon piece 4 molds the meniscus for the
extracting ribbon 1. Underneath the zone is the feeding material 5. The zone is initiated by (laser)
radiation 6.
2. Electrical Molten Zone
The positive dependence of the electrical conductivity with temperature, characteristic of
semiconductor materials (in contrast to what happens in metals), allows the current concentration
phenomenon which is fundamental in the EMZ technique. It should be noted that in silicon the
electrical conductivity rises exponentially from about 410-4 Sm-1 at room temperature to nearly
5104 Sm-1 (1.25106 Sm-1 in the liquid) at fusion temperature, 1687 K [8, 9]. On the other hand, in
the same temperature interval, the thermal conductivity falls from 156 Wm-1
K-1
to 22 Wm-1
K-1
[10].
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6Comparatively in a metal like copper the electric conductivity decreases slightly from 6.5107 Sm-1
at ambient temperature to 5.5106 Sm-1 at fusion temperature, 1385 K, and the thermal conductivity
decreases linearly only from 400 Wm-1
K-1
to 325 Wm-1
K-1
[11].
Consider, then, the consequences of the abovementioned characteristics in the behavior of a
system comprising a certain material volume of arbitrary shape in which 2 electrodes were placed
and through which electric current was injected. In these conditions, the current density and
temperature distribution functions are naturally variable from one point to another in the volume
and dependent of, besides the intrinsic material properties, the volume geometry and its losses to the
environment. In the case of the metal, the current density will be lower in the hotter regions of the
material and these have large thermal conduction losses. This causes a dispersion of energy, thus
the volume temperature tends to become homogeneous, with smooth thermal gradients, determined
mainly by losses to the surroundings. In the case of the semiconductor, the situation is symmetric,
the current density will be higher in the hotter regions of the material and these have smaller
thermal conduction losses. This originates a concentration of energy and generates very steep
thermal gradients, being the losses to the surroundings relatively unimportant.
The mentioned energy concentration mechanism eventually results in the phase transition of
the material and the formation of a molten zone (fig. 3). For an isotropic material, with heat transfer
losses approximately symmetric in relation to the straight line that passes through the electrodes, the
molten zone will form itself along that line, as that is the shortest electrical resistance path. The
zone is at every instant in an equilibrium position, although this might not be a stable one. The zone
displays some mobility and may have non-rectilinear trajectories. The causes for this behavior
should be sought mainly in environmental conditions disturbances, like convective turbulence or
alterations in radiative transfers (e.g. oxide deposits). In addition, certain material geometries are
more stable than others.
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7
Figure 3 Closing of a linear electrical molten zone in a silicon plate with 100 20 0.45 mm3
(inter-electrode distance of ~90 mm). The process starts at the electrodes with 20 A and ends at
centre with 40 A having, in this case, a duration of 55 s. Notice the alteration on the temperature
distribution of the plate as the extremities of the zone advance to the centre.
The possibility of obtaining very thin linear electrical molten zones and their inherent stability
problems were also observed by Pfann (in longitudinal current configurations). He noticed that in
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8materials for which the ratio of the electrical resistivities of the solid by that of the liquid is s/l > 1
(s/l 25 for silicon), the electrical zones are unstable unless there is a sufficiently large
temperature gradient in the adjacent solid. The reason for this is that any protuberance in the liquid
zone is amplified by the tendency of current lines to concentrate on it, thus propagating the zone.
Through this effect Pfann was probably the first researcher to attain electrical molten zones inside
10 cm long germanium crystals (s/l 17) [12].
If one of the dimensions of the aforementioned material volume is much smaller than the
others, the molten zone may have free surfaces. This makes its profile determined by the solid-
liquid-gas interface equilibrium (surfaces free energies), situation which results in an increase of
complexity of the system, originating very relevant surface tension phenomena.
Figure 4 One of the first linear electrical molten zones made in the present study (silicon plate with
100 15 0.45 mm3).
In the present study the material used consisted in thin solar-grade silicon plates (fig. 4) with
typical dimensions of 100 30 0.35 mm3 and a resistivity of 0.5-5 cm. The choice of an
adequate size for the silicon plates allows for a passive form of zone stabilization. In plates with
more than 30 mm width (in a direction transversal to that of the zone), any perturbation capable of
driving the zone towards one side of it tends to increase the temperature of that side which is
compensated by higher thermal dissipation of that side. Experience shows that this asymmetry in
the temperature profile is unstable, hence the zones remain very straight and immobile at the centre
of the plate. On the other hand in narrow plates that deviation is susceptible to be amplified, as the
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9side towards which the zone drifted becoming more conductive increases its current density, thus
heating even more (the opposite happens on the other side, which cools down strongly). This may
be the driving force for zone drifting to the edge, where it usually collapses (fig. 5; see also sec. 7).
Figure 5 Image series showing the rupture of a zone (closing at 41.3 A) through drift to the edge of
the plate. Time from closing to rupture: 220 s.
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10Another passive approach for zone stabilization consists in the use of optical feedback from
the zone itself, with the plate positioned in a reflective cylindrical cavity. An active approach to the
problem may consist in the imposition of external thermal gradients, for example by optical
concentration in the centre of the plate and / or cooling of its edges. In either case, if the plate is to
survive its internal strains, excessively steep thermal gradients should be avoided. It was also
observed that it is possible to define the trajectory and even extinguish locally the zone (e.g. near
the graphite contacts, in order to avoid contamination of the melt) by placing shield plates over the
main one (which is equivalent to a local thickness increment). These tend to homogenize the
temperature throughout the width of the plate, forcing a current redistribution and consequently
preventing its concentration.
3. Zone Melting Recrystallization
As a preliminary step towards a full crystallization process from feedstock, and in order to
gain some insight into the involved stability and control matters, some recrystallizations of silicon
ribbons were carried through by sweeping the electrical molten zone through the base plate. The
first attempts in this direction faced some difficulties, particularly in the electrodes interfaces, for
that reason a substantial number of different configurations for those were tried (fig. 6). It was
found that graphite electrodes were very wettedby silicon (contact angle of 12 [13]) which
originated mass extraction from the zone and accumulation of it in the extremities of those. This
generates strong solid bridges between the electrodes and the ribbon, which makes the movement of
the zone impossible. It was sought to alleviate the problem without success using rotating
electrodes on the edges of the ribbon (fig. 6d). Finally, a demonstration of the process viability was
achieved by edge stabilization with small graphite or silicon plates frames (fig. 6e) and with
electrodes of identical material. In this configuration, the electrodes slide smoothly over the frame
and there is no relative movement between this and the ribbon. The graphite frames are easily
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11removable at the end of the process. The silicon frames, however, become heavily welded to the
edges of the ribbon, which is an important disadvantage of its use, given that it is unfeasible to
remove them without fracturing the ribbon.
Figure 6 Evolution of the electrode configuration.
The graphite frames generate the thermal gradient necessary to recrystallization, but only in
narrow ribbons and at low speeds. High recrystallization rates may originate zone curvature,
delaying it in the central portion of the plate in relation to the electrical contact position on the edge.
The silicon frames do not generate the gradient necessary to a purely electrical recrystallization;
hence, this is only possible with optical assistance (fig. 7). However, this also facilitates
considerably the beginning of the process and makes irrelevant the electrode geometry, given that
the zones are sharply localized at the optical centre of the furnace. It was also observed that, in
some operating regimes, it is possible to have just surface recrystallization of the ribbon.
In this configuration the maximum growth rate depends strongly on the optical component,
falling from 12.5 mmmin-1 with the internal lamps at 1200 W to 3-5 mmmin-1 without optical
component (for a plate with 100 30 0.35 mm3). The energy consumption per unit of
recrystallized area, for an optical furnace with a global efficiency of about 28% and with an
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12adequate power supply, is around 38 kWhm-2, which is about 50% higher than what can be attained
with optical recrystallization solely.
Figure 7 Electrical molten zone recrystallization with auxiliary optical concentration (current
injection perpendicular to the plane of the figure, on the optical centre of the furnace).
4. Silicon Ribbon Pulling
Despite the relative success of the recrystallization processes, the objective of the study was
the crystallization of silicon ribbons from commercial feedstock (in granular form). This can be
implemented through a smallpoolof molten silicon made at one of the extremities of the zone in
which the silicon granules are introduced. Interesting enough it was also Pfann who suggested the
use of these pools, confined in support plates of the same material in order to avoid melt
contamination by foreign matter [14]. The pools made in the present work are just liquid silicon
films with a diameter up to 10 mm and a thickness up to 1 mm, suspended by the plate (i.e. held
only by their own surface tension) or confined in a crucible in the plate itself (when this one does
not melt throughout its thickness). The silicon granules transport is made via a vibratory system. At
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13any given instant the total melted mass in the system is very small, 100-200 mg for the pool and 10-
20 mg for a 30 mm long zone.
Several alternatives were considered for making the silicon pool, among which the possibility
of doing it electrically, in the same way as the zone itself, with an array of electrodes disposed along
a circumference and coupled to a current switching device. There were also made some experiments
with electric arcs and electromagnetic induction, but the final choice rested upon the method of
optical concentration due to its relative simplicity, ease of coupling to the existing apparatus and
previous experience with this solution. For this purpose it was used a 2 kW xenon arc lamp with an
ellipsoidal reflector, which is however, a low efficiency choice and requires the use of an auxiliary
nonimaging concentrator[15, 16] (conical internal mirror) in order to attain the necessary radiation
density on the pool.
The first idea for pulling ribbon from the system, consisted in the configuration of figure 8a,
that is with direct extraction from a zone made in a horizontal silicon plate, with the edges stabilized
by fibers (quartz, carbon, etc.), similarly to the String-Ribbon technique. This idea was abandoned
very early due to the problems that presents, namely of surface flatness (dependent on the zone
trajectory) and of possibility of solid bridge formation (between the ribbon and the horizontal plate)
along the entire perimeter of the zone. A few experiments performed in this configuration showed
that the zone tends to rupture near the fibers or to deviate from them. The alternative configuration
of figure 8b, has a similar topology but with edge stabilization by small intermediate silicon plates.
This geometry offers better guaranties of flatness though without solving the problems of solid
bridge formation at the intermediate plates, and of mass transfer from the pool to the growing
ribbon through those.
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14
Figure 8 Ideas for ribbon pulling by EMZ: (a) Ribbon R is fed by the adjacent pool L and
stabilized laterally by fibers F. The horizontal plate P with electrodes E supports the assembly; (b)
the fibers were replaced by two intermediate plates I and the zone is now supported by the fixed
lower plate S.
The outstanding difficulties found in the demonstration of effective mass transfer in this
configuration instable conditions , manifested themselves in a great number of experiments through
the rupture of the zone due to thickness reduction of the ribbons until critical values. These troubles
even cast some doubt over the existence of a hydraulic link, between the pool and the zone in the
ribbon. The confirmation of this was obtained, nevertheless, through the observation of surface
oscillations in the zone with the fall of granules in the pool, and bypool draining(reduction of its
convexity) when ribbon was drawn without adding feedstock. In unstable conditions, which precede
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15several rupture modes, mass transfers from the zone to the pool and vice-versa are frequently
observed. It was noticed, for example, that when the completion of the zone precedes that of the
pool, this one does not have a circular contour rather it shows itself only as a local widening of the
zone, which is an extremely unstable situation, susceptible to rupture byzone draining(fig. 9).
These rupture modes are common with high currents ( 40 A) and are consistent with the effects of
magnetohydrodynamic (MHD) forces (v. sec. 7) and / or surface tension present in the system. To
avoid them the optical pre-heating should be augmented and the pool approached to the growing
ribbon as much as feasible.
Figure 9 Zone draining to the pool at about 40 A, with rupture of this one typical well-preserved
rupture mode. The pool has roughly 12 mm in diameter and the minimum zone width is 0.35-0.5
mm. It can also be observed a characteristic delta at the pool exit and plate edge.
The severe restrictions that this technique imposes to melt flow, which limit the maximum
growth rate that can be expected of it, specially in thin and wide ribbons, is due primarily to the
small melt flow cross section, given that all mass is injected through one of the edges (or eventually
both). In order to solve this problem a number of options were considered (but not implemented
yet):
a) Create a hydrostatic gradient between the pool and the zone in the ribbon.
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16b) Pressurize the region of the furnace that contains the pool relatively to the one that contains
the zone (particularly difficult to implement).
c) Apply a magnetic field perpendicularly to the plane of the ribbon, along with longitudinal
current (i.e. in the direction of growth), thus implementing a MHD pump. The longitudinal current
could be applied by means of a switching device, alternating with the transversal current.
It should be mentioned still that the process has an important disadvantage, the impossibility
of impurity segregation during growth, due to the small dimensions of the zone and the
unidirectional character of the melt flow. Unless, of course, some form of melt extraction is
implemented in the plate on the opposite side to that of the pool which, nonetheless, results in a
further decrease in the maximum possible growth rate.
5. Electrical Characteristics
Consider again the hypothetical system mentioned in section 2, consisting of a certain volume
of material of arbitrary shape in which two electrodes were placed and through which electrical
current was injected. Observe now the behavior of this system in transient conditions, when
controlled in voltage as in the present work. If in instant t0 a potential difference were applied
between the electrodes, the material reaches equilibrium distributions for current density J and
temperature T at the end of a certain thermal relaxation time t, during which the current varies. At
instant t0+t, in the case of a metal, the current would be inferior to the initial one, since the
electrical conductivity decreases with temperature, in the case of a semiconductor it would be
superior to the initial one since the electric conductivity increases with temperature. Thus, during
the transient, one has dT/dJ < 0 for the metal and dT/dJ > 0 for the semiconductor. This means that
in the case of the metal the system exhibits negative feedback, which makes it particularly stable
and easily controlled. In the case of the semiconductor, the intrinsic positive feedback makes the
system evolution towards equilibrium, from about 700 K in heating or cooling, being abrupt. If
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17sufficient power is available, temperature transients in the order of 1400 Ks
-1are possible during
heating, which leads to the systematic fracture of the silicon plates.
The high initial plate resistance forces high starting voltages, however once a critical value is
reached designated in this work as ignition voltage the control system should reduce the applied
voltage smoothly in order to avoid sudden temperature variations, thus implementing metastable
equilibrium conditions. It should be noticed that at this stage the system presents a negative
dynamic (or differential) resistance, Rd = dV/dI < 0. The transient response time is very short, for
this reason a control in current, with a programmable power supply, besides being much more
efficient, greatly facilitates the work and, by avoiding the operator manual control, makes the
results more reproducible. Nevertheless, in the absence of such power supply the control problems
may be solved in alternative ways:
a) By placing ohmic resistances in series with the silicon plate, adapted to the internal load,
like plates dimensions and contact resistances, in order to guarantee stability during ignition (high
voltage) without penalizing the operation regime (high current).
b) By optical pre-heating, making it possible to have a positive Rd during startup, which
makes the system very stable and easy to control, although with higher energy consumption. Notice
that even so, for higher currents (with molten zone), the dynamical resistance becomes again
slightly negative, thus persists the tendency towards the elevation of the current by itself, for the
applied voltage. This approach has the additional advantage of attenuating the thermal gradients in
the material and consequently its internal stresses.
c) By a hybrid solution, coupling the electrical to the optical circuit, thus making the
resistance increase of the internal lamps compensate the resistance decrease of the silicon plate with
the current. This configuration behaves similarly to option a) until zone formation and is much more
energy efficient than option b).
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18The V(I) curves (and particularly P(I) fig. 10) show a characteristic step at the point of
effective zone closing due to the significant alteration of the plate temperature distribution (cf. fig.
3) and, therefore, of its resistance. A curious aspect of the V(I) characteristics is, apparently, the
appearance of hysteresis phenomena whenever there are fast temperature transients, as in the
instance of zone closing. This is probably due to heat of fusion absorption and release from the
material, which seems to be corroborated by the observation that the areas of the cycles vary from
3.5-4 W in the situation of low optical heating to about 0.5 W in the situation of high optical
heating.
Figure 10 Variation of electrical power with current for various optical powers Pl in a silicon plate
with 100 30 0.35 mm3 (inter-electrode distance: 30 mm). Pl = Variable refers the hybrid
configuration (v. text).
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19The electrical functionsFE(L,e) of current, voltage and power vary, in first approximation,
linearly with width (L) and thickness (e) of the silicon plates, but in a strongly non-linear way with
the optical powerPO(L,e), and may be well adjusted by the relation
1=+
Oo
O
n
Eo
E
P
P
F
F(1)
in whichFEo(L,e) is the electrical function forPO = 0 andPOo (L,e) is the optical power forFE= 0,
the exponent n is 6 for current, 3 for voltage and 2 for power. Figure 11 shows a family of curves
for various plate widths (with average thickness of 0.336 mm), obtained in the configuration of
figure 6b and in typical conditions of zone closing. The measurements include all losses in both the
optical and electrical circuits.
Figure 11 Variation of electrical power with optical power for various plate widths (L).
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20The zone width is a function of current and, in stable conditions for a plate 0.35 mm thick, has
values below 1 mm (fig. 12), being able to reach close to 2 mm near the electric contact in
conditions approaching rupture. A typical zone current density is in the order of 125 Amm-2 and the
power dissipated per unit of length is 1.4 Wmm-1
. This means that, due to the low resistivity of
liquid silicon, less than half the power in the plate is being dissipated in the zone.
Figure 12 Zone width (at the centre of the plate) as a function of current for a plate with cross-
section of 30 0.35 mm2.
6. Temperature Distribution
The temperature profiles in the plate on the configuration of figure 6b and the conditions of
table 1 may be seen in figure 13. In the absence of optical component (Pl = 0 W) the profile is
reasonably well approximated by a simple function like
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21
kx
TTTxT
af
a +
+=
1)( (2)
with Ta the ambient temperature (300 K), Tf the temperature at the edges of the zone (1687 K) and
ksuggests the profile curvature, with values of 125 and -140 m-1 for the upper and lower parts of the
plate respectively. All curves show some asymmetry between the upper and the lower halves of the
plate, especially in conditions of high optical power, attributable to (argon) convection currents
inside the furnace.
Figure 13 Temperature profiles for several optical powers P l (the positive abscissa indicates the
upper part of the plate, which has 100 30 0.35 mm3).
Pl / W 0 900 1700
I / A 32.5 0.5 20.0 0.1 -V / v 14.2 0.7 10.9 0.7 -t / mm 0.34 0.74 2.5
Table 1 Current (I) voltage (V) and zone width (t) for the temperature profiles of figure 13.
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22The analysis of these profiles suggests a thermal gradient at the solidification interface of 250-
350 Kmm-1
(Pl = 0 W), thus growth rates up to 100 mmmin-1
seem theoretically possible. This
advantage of the electrical molten zones it is not, however, likely to be utilizable given that the rate
of change of the gradients (2T), which determine internal stresses and plastic strain of the ribbons,
is also very high [17, 18].
Regarding the temperature transients, it was observed that with only 1 A (~90 W) applied the
temperature near the electrical contact at the edge rises to 858 K and at the centre of the plate to 638
K. Thus to prevent its fracture, particularly below 993 K (the silicon brittle-ductile transition
temperature [19]), the heating rate should be low, which is rather difficult in the absence of optical
pre-heating due to the very negative dynamic resistance at this stage. The temperature difference
between the centre and the edge (at contact level) reaches 435 K, immediately before fusion of the
edge (~300 W), generating a transversal gradient in the plate of almost 30 Kmm-1
, which constitutes
the driving force for zone progression.
7. Zone Stability Problems
The passage of high electrical current densities directly through conducting fluids generates
complex magnetohydrodynamic (MHD) stability problems. These have been the object of
numerous studies concerning crystal growth and especially plasma physics (nuclear fusion,
astrophysics, etc.), therefore only some features of those, with importance in the present
experimental work, will be sketched here. Some (tentative) explanations for the instabilities are
sought, by analogy with typical phenomena observed (in other contexts) in tubes of electrically
conducting fluids. It should be remembered that the electrical molten zone is nothing more than a
conducting fluid capillary in equilibrium by the forces of gravity, surface tension and
magnetodynamic. Chandrasekhar [20] made an excellent analysis of these problems, showing the
conditions for development of hydrodynamic instabilities and its settling as stationary convection
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23patterns in fluids, giving various examples for the cases of systems with thermal gradients, rotation
and presence of magnetic fields.
The Lorentz force over a fluid volume due to the presence of a magnetic induction B may be
written in the form
BBF )(
B +
=
1
2
2
(3)
(with the magnetic permeability of the medium) thus being composed by a (1) term of
hydrostatic pressure transverse to the field lines (electromagnetic pinch), and a (2) term of tension
along the field lines, both of magnitudeB2/2. Integrating F in an infinite conducting fluid cylinder
of radiusR and with a constant axial current density (I/R2) one obtains thepinch pressure (directed
radially inwards) [21]
=2
22
2
14
)(R
r
R
Irp
(4)
Figure 14 illustrates two of the most characteristic instabilities in conducting fluid tubes [22].
In thesausage instability type, the magnetic field pressure increases in the constricted region (since
the current density increases v. eq. 4) and decreases in the expanded region, thus generating a tube
of variable cross section without altering its curvature, situation that tends to get worse until its
collapse. In the kinkinstability type, the magnetic field lines compress themselves in the concave
part and expand themselves in the convex part of the tube surface, thus generating a larger curvature
without changing its cross section, which accounts for the tendency of the distortion to propagate in
the direction of the convexity until it collapses. The characteristic surface undulation, mainly of the
first instability, is analogous to the one that occurs in the well known Rayleigh-Taylor
hydrodynamic instability, which in the presence of a magnetic field is also known as the Parker
instability. Characterizes itself through the periodic deformation of the equilibrium surface between
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24two moving fluid layers (of different densities), under the action of inertial forces (gravitational or
centrifugal).
Figure 14 Instabilities in a conductive fluid cylinder: (a) Unstable equilibrium (B0 is the maximum
field at the surface of the conductor); (b) Sausage instability; (c)Kinkinstability.
The susceptibility for both types of instability may be minimized by applying an axial
magnetic field. The field lines tension tends to keep them straight opposing deflections (mainly of
short period), thus stabilizing the tube. However, the presence of an axial fieldBz(in addition to the
azimuthalB) leads to helicoidal instabilities (fig. 15) [23, 24, 25]. When the magnetic flux lines are
sufficiently twisted (but not enough to originate a kink) by analogy with the torsion of an elastic
line the tube spontaneously assumes a helicoidal form, thus relaxing the magnetic energy
accumulated as field line tension. The total magnetic energy decreases converting itself into kinetic
energy and this in turn into internal energy via Joule heat and viscous dissipation. For an
incompressible inviscid fluid the instability occurs when the field lines helical pitch q exceeds a
critical value qcr
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25 cr
z
qrB
Bq (5)
Figure 15 Helicoidal instability for q = 5.
All instabilities mentioned here occur between fluids or between a fluid (usually a plasma)
and the vacuum, for this reason its applicability to the phenomena observed in the present work, that
is, between a liquid and a solid boundary in phase transition conditions, is only tentative as this is
clearly a very complex phenomenon.
Solidification interface instabilities capable of originating faceted or cellular structures are
common in crystal growth systems, mainly due to constitution supercooling of the melt. It is also
well known that electromagnetic fields have a strong affect in the distribution coefficient of many
impurities, primarily due to its effect on the liquid convection currents [26, 27, 28]. However, in the
present case, given that the instability manifests itself exclusively in electrical molten zones, even in
stationary conditions, seems to indicate that this is a different phenomenon, one of
magnetohydrodynamic origin. The electrical current in the zone and its inherent magnetic field
seem to originate a convection current pattern that generates periodic temperature fluctuations along
the solid-liquid interface, as those in figures 16 and 17, regardless of plate orientation (e.g.
horizontal or vertical). The sinusoidal undulation of the zone edges has an amplitude and period that
increase, in first approximation, linearly with the zone width (fig. 18). Alongside this, it is possible
to observe zone surface vibrations, through light reflections on it. Not only the interface but also the
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26melt surface itself does not seem flat which, by the way, is confirmed by the appearance of
striations in the areas recrystallized in these conditions.
Figure 16 Image series showing the zone undulation pattern. The instabilities appear around 40 A
and increase their amplitude and period as the zone widens until its rupture (shortly after the last
image of the series) at about 52 A. A liquid protuberance formation generally precedes collapse.
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27
Figure 17 Undulation in a zone with only superficial fusion. Rayleigh-Taylor type of vortices.
Figure 18 Variation of the undulation amplitude and period as a function of zone width (without
optical component) for several plate thicknesses (e). The amplitude should be understood as the
difference between maxima and minima on the same zone edge. Results for e = 0.45 mm
correspond to the zone of figure 16.
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28The applicability of the MHD model for the formation of helicoidal tubes, to the present
results with which presents remarkable resemblances requires the demonstration of the
existence of an axial field in this system. This must certainly be sought in the internal convection
currents, observed by the movement of small oxide particles on the surface of the zone. In very thin
zones stabilized by surface tension, the velocity field is probably dominated by Marangoni
(thermocapillary) currents, which may have speeds up to 100 times the crystals growth rate in the
EFG and FZ techniques [29, 30]. These currents might generate a longitudinal vortex sheet, like a
long solenoid throughout the zone length, susceptible of generating a longitudinal field. Another
possibility worth considering is the fact that convection currents have radial components, which
means that the Lorentz force should have a small axial component, thus driving a helicoidal
movement of the particles.
The apparently discontinuous character of the instability, as evidenced by the fact that it only
manifests itself above a certain current density, seems to find a parallel in the MHD model in the
critical field line torsion parameter (eq. 5) for the helicoidal instability appearance. This limit seems
to occur near (3/2)I0 (I0 is the zone closing current dependent, naturally, of the optical power) and
represents an operational limit to the working current of the system. Rupture occurs generally
around 2I0. In this current interval, the zone doubles its width.
Certain characteristic zone deformation and rupture modes suggest also instabilities of the
kink and sausage types and represent a great source of experimental problems. For example, zones
of variable width are unstable since the pinch generates mass transport from the thinner regions to
the wider, which eventually may originate its collapse. This effect may, however, be compensated
by the zone surface tension, through variation of the liquid surfaces curvature, which adjust
themselves at every instant and in every point, to the electrical current and zone / pool width. Thus,
it is possible in certain conditions, in the previously mentioned current operating interval, the
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29establishment of an equilibrium of null flow, which explains the extraordinary difficulties found in
the ribbon growth process.
Conclusions
It was demonstrated the possibility of silicon ribbon recrystallization by EMZ, with edge
stabilization by graphite or silicon plates. Growth rates up to 12.5 mmmin-1 were achieved, and the
analysis of the solidification temperature gradient suggests the possibility of increments up to 100
mmmin-1. The growth rate and electrical power involved depend strongly on the auxiliary optical
power. Regardless of that, the process energy consumption is in the order of 38 kWhm-2
.
The difficulties of zone stabilization and mass transfer to the growing ribbon have shown to be a
greater challenge than anticipated, which is why, up to the moment, it was not possible to surpass
transient crystallization conditions, being yet to demonstrate the possibility of sustained ribbon
growth. Some ideas for the causes of the instabilities and resolution of the mass transfer problems
were presented, however a deeper analysis of this subjects is out of the scope of the present study.
Still many problems remain to be explained and solved before this technique may be considered a
true alternative in the generation of silicon ribbons for photovoltaic application.
Acknowledgements
The author gratefully acknowledges the helpful discussions and valuable suggestions of Prof. A.
G. Vallra, Prof. J. M. Alves and Dr. R. M. Gamboa from the Semiconductors Laboratory (FCUL),
which greatly contributed for the advancement of the experimental work. Also deeply appreciated
was the support, through grant BD / 11228 / 97, provided by the Foundation for Science and
Technology (MCT) under the PRAXIS XXI program. This work was performed under EU project
THIMOCE (contract JOR-CT98-0287).
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30References
[1] F.V. Wald,Technical Digest of the 5th International Photovoltaic Science and EngineeringConference, International PVSEC-5, Japan, 1990, p. 191.
[2] R.L. Wallace, R.E. Janoch and J.I. Hanoka., Second World Conference on Photovoltaic SolarEnergy Conversion, Report EUR 18656 EN, Office for Official Publications of the European
Communities, Luxembourg, 1998, p. 1818.
[3] B.D. Leigh and T.R. Noel, Method of growing silicon dendritic-web crystals, UnitedKingdom Patent N GB2198966, June 29, 1988.
[4] W.G. Pfann,Zone Melting, 2nd Ed., John Wiley & Sons, USA, 1966.[5] W.G. Pfann, Method of controlling liquid-solid interfaces by Peltier heat, United States
Patent N 3086857, Apr. 23, 1963.
[6] W.H. Kuhlmann-Schfer,Zone melting process, United States Patent N 3960511, June 1,1976.
[7] T. Wolfgang, German Patent N DE4122397, Jan. 7, 1993.[8] D.E. Aspnes, Optical functions of liquid Si, Properties of Crystalline Silicon, Edited by Robert
Hull, INSPEC, The Institution of Electrical Engineers, London, 1999, p. 696.
[9] Landolt-Brnstein,Numerical Data and Functional Relationships in Science and Technology,Edited by K.-H. Hellwege & O. Madelung, Vol.17 - Semiconductors, Springer-Verlag, 1984.
[10] M.N. Wybourne and M.R. Brozel, Thermal conductivity of c-Si, Properties of CrystallineSilicon, Edited by Robert Hull, INSPEC, The Institution of Electrical Engineers, London,
1999, p. 165.
[11] CRC Handbook or Chemistry and Physics, 78th Ed., Edited by D.R. Lide e H.P.R. Frederikse,CRC Press, 1997.
[12] W.G. Pfann,Zone Melting, 2nd Ed., John Wiley & Sons, USA, 1966, p. 101.
-
8/3/2019 Presentation of the Electrical Molten Zone (EMZ) Technique
31/32
31[13] T.F. Ciszek, The growth of silicon ribbons for photovoltaics by edge-supported pulling (ESP),
Silicon Processing for Photovoltaics I, Edited by C.P. Khattak & K.V. Ravi, Elsevier Science
Publishers, 1985.
[14] W.G. Pfann,Zone Melting, 2nd Ed., John Wiley & Sons, USA, 1966, p. 118.[15] A. Goetzberger and T. Goldbach, Ninth E.C. Photovoltaic Solar Energy Conference, Kluwer
Academic Publishers, The Netherlands, 1989, p. 638.
[16] L. Broman, M. Rnnelid, B. Binder and E. Lindberg, Ninth E.C. Photovoltaic Solar EnergyConference, Kluwer Academic Publishers, The Netherlands, 1989, p. 234.
[17] R.W. Gurtler, J. Crystal Growth 50 (1980) 69.[18] B. Chalmers, J. Crystal Growth 70 (1984) 3.[19] S.G. Roberts,Fracture and brittle-ductile transition in Si, Properties of Crystalline Silicon,
Edited by Robert Hull, INSPEC, The Institution of Electrical Engineers, London, 1999, p.
144.
[20] S. Chandrasekhar,Hydrodynamic and Hydromagnetic Stability, Oxford University Press,U.K., 1961.
[21] J.D. Jackson, Classical Electrodynamics, 2nd Ed., John Wiley & Sons, 1975.[22] M.A. Uman,Introduction to Plasma Physics, McGraw-Hill Book Company, 1964.[23] M.G. Linton, R.B. Dahlburg, G.H. Fisher and D.W. Longcope, The Astrophysical Journal 507
(1999) 404.
[24]
M.G. Linton, G.H. Fisher, R.B. Dahlburg and Y. Fan, The Astrophysical Journal 522 (1999)
1190.
[25] Y. Fan, E.G. Zweibel, M.G. Linton and G.H. Fisher, The Astrophysical Journal 505 (1998)L59.
[26] K. Kakimoto, Si melt convection in a crucible, Properties of Crystalline Silicon, Edited byRobert Hull, INSPEC, The Institution of Electrical Engineers, London, 1999, p. 8
-
8/3/2019 Presentation of the Electrical Molten Zone (EMZ) Technique
32/32
32[27] M.G. Williams, J.S. Walker and W.E. Langlois, J. Crystal Growth 100 (1990) 233.[28] A. Wheeler, G. McFadden, S. Coriell and D. Hurle, J. Crystal Growth 100 (1990) 78.[29] H.M. Ettouney and R.A. Brown, J. Crystal Growth 58 (1982) 313.[30] L.M. Witkowski and J.S. Walker,Magnetohydrodynamics 37 (2001), 112