Multicrystalline Silicon for Solar Cells: Process Development by ...

Multicrystalline Silicon for Solar Cells:
Process Development by Numerical
Simulation
By Christian Häûler,* Gunther Stollwerck,
Wolfgang Koch, Wolfgang Krumbe, Armin Müller,
Dieter Franke, and Thomas Rettelbach
Continuously improving crystallization conditions and solar cell processes have lead
to steadily increasing efficiencies of solar cells based on multicrystalline silicon.
There is, however, still an efficiency gap between mono- and multicrystalline silicon
amounting to 1±2 % (absolute) depending on the cell process used. Topographies of
the local solar cell performance clearly reveal that the main contribution to this efficiency
gap is due to recombination-active dislocations present in multicrystalline silicon. A further improvement
of the efficiencies attainable with multicrystalline solar cells therefore is achievable by a reduction of the dislocation
density. Dislocations originate from thermal stress that originates from temperature gradients inside a multicrystalline
ingot during crystallization and cooling. In order to reduce this thermal stress and consequently the
dislocation density we employ a numerical simulation routine, the so-called virtual crystallization furnace, for
perfect control of the temperature distribution during the entire ingot fabrication process.
1. Introduction
The major challenge of today's photovoltaic technology,
which is still mainly based on crystalline silicon wafer technology,
is the increase of solar cell efficiencies while still using
cost-effective, high-throughput, and large-scale processes.
Employing multicrystalline silicon (mc-Si) wafers, solar cell
conversion efficiencies up to the 15 % range are presently
achieved even with industrial production scenarios for crystallization
and solar cell manufacturing. Solar cell efficiencies,
generally, are governed by the concentration and type of impurity
atoms and the density and electrical activity of extended
defects such as grain boundaries and dislocations. The
requirement of both the increase of process speed and material
quality necessitates nearly perfectly controlled temperature
±
[*] Dr. C. Häûler, Dr. G. Stollwerck, Dr. W. Koch, Dr. W. Krumbe
Bayer AG
Rheinuferstraûe 7±9, D-47829 Krefeld (Germany)
E-mail: christian.haessler.ch@bayer-ag.de
Dr. A. Müller
Deutsche Solar GmbH
Postcode 1711, D-09587 Freiberg (Germany)
Dr. D. Franke, Dr. T. Rettelbach
ACCESS e.V.
Intzestraûe 5, D-52072 Aachen (Germany)
profiles. For the fabrication of large mc-Si ingots this perfect
control is achieved by means of a so-called virtual crystallization
furnace (VCF) that represents a detailed computer model
of the actual crystallization chamber and is the basis of an accurate
numerical simulation of the temperature distribution
during crystal growth. The unique advantage of the VCF
model isÐin addition to the ability of calculating macroscopic
parameters such as temperatures, process times, etc.Ðthe possibility
of predicting the distribution of even microscopically
small crystal defects such as dislocations. Dislocations generated
by thermal stress during crystal growth have been identified
to crucially determine solar cell efficiencies and, therefore,
have to be effectively suppressed in high-efficient solar
cells. In this work it is shown that the optimization of the crystallization
process within the VCF model may result in a
reduction of the dislocation density by approx. 50 % that in
turn is estimated to lead to an efficiency increase of 0.5±1 %
absolute.
2. Silicon-Based Solar Cells
The current strong growth in the photovoltaic market is still
mainly based on the crystalline silicon wafer technology. Both,
monocrystalline silicon and multicrystalline (mc) Si is em-
Adv. Mater. 2001, 13, No. 23, December 3 Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2001 0935-9648/01/2312-1815 $ 17.50+.50/0 1815
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ployed for the fabrication of solar cells. [1] Specifically mc-Si,
however, is able to meet the requirements of actual photovoltaics,
which are a cost-effective large-scale production technique
and high solar cell efficiencies. Consequently, Deutsche
Solar GmbH in Freiberg, Saxony, established a high-throughput
block-casting production facility for Baysix mc-Si. [2,3] The
capacity of this plant amounts to an annual production of
approx. 16 million wafers (in the year 2000) and will be
tripled by 2003. State of the art are the multicrystalline ingots
solidified in a Si3N4-coated quartz crucible with a height of
approx. 30 cm and weights of more than 200 kg. After crystallization
these ingots are divided into several columns, which
subsequently are sliced into mc-Si wafers with areas between
10 ” 10 cm 2 and 15 ” 15 cm 2 , and a typical thickness of
300 lm.
Besides continuously rising production capacities, improving
crystallization conditions and solar cell processing sequences
have led to steadily increasing photovoltaic conversion
efficiencies of mc-Si solar cells. Based on Baysix, mc-Si
efficiencies of 13±15 % and 16±17 % have been attained for
industrial-type fabrication and for solar cell processes on laboratory
scale, respectively. [4±7]
Generally, from a technology point of view, conversion efficiencies
of solar cells based on mc-Si are depending on the
crystallization process, the solar cell processing sequence, and
the mutual adjustment of both process scenarios.
3. Improving Solar Cell Efficiencies
The implementation of optional defect passivation steps,
e.g., hydrogen plasma treatments, and the temperature profiles
of individual process steps, such as phosphorus diffusion
for the fabrication of pn-junctions, play an important role in
solar cell processing.
Deutsche Solar GmbH, as a supplier of silicon wafers,
focuses its research and development efforts on the crystallization
conditions. The crystal defect scenario within the mc-Si
ingots forms a basis for the solar cell performance level that is
achievable in subsequent solar cell fabrication. From the
viewpoint of defect physics the following parameters are of
specific importance:
l the concentration and type of impurity atoms
l the concentration and electrical activity of extended defects,
e.g., dislocations and grain boundaries
l the interaction of impurity atoms either with other impurity
atoms (complex and cluster formation) or with extended
defects.
The dependence of the solar cell efficiencies on the impurity
concentration is trivial, but it nevertheless puts stringent
requirements on the purity of feedstock materials and on the
temperature stability of construction materials. Transition
metals are considered as specifically detrimental to cell efficiencies:
concentrations in the 10 12 cm ±3 range or even lower
should be maintained for high quality solar-grade material in
this case. A key role concerning metal impurity concentra-
C. Häûler et al./Process Development of Solar Cells by Numerical Simulation
tions is played by the segregation process. Elements with low
segregation coefficients (e.g., transition metals) are effectively
segregating in the silicon melt during crystallization. After
completion of the ingot solidification (the crystallization front
is moving from the bottom to the top) these impurities are
efficiently accumulated in the ingot top region and can, therefore,
be removed easily. It is estimated that the purification
effect by segregation, i.e., the impurity concentration ratio
between raw material and the final solar-grade silicon wafers
is equal to 100±1000 or even above for elements with low segregation
coefficients. This purification by solidification, however,
is affected by the crystallization velocity and generally
becomes less effective for higher crystallization speeds.
Extended defects, i.e., grain boundaries and dislocations,
may carry electrical charge and consequently act as highly efficient
recombination centers for minority charge carriers.
The electrical activity of these defect centers is strongly influenced
by their interaction with impurity atoms and usually
tends to increase with increasing impurity concentration.
Nevertheless, it was experimentally verified that the electrical
activity of grain boundaries is depending on the crystallization
conditions, too, and can be considerably reduced if a strictly
planar solidification front is preserved during crystallization. [8]
Therefore, for actual mc-Si with a grain size of several millimeters
up to the centimeter region and a low grain boundary
activity, grain boundaries do not play a significant role concerning
attainable solar cell efficiencies.
In contrast to grain boundaries, crystal dislocations have
been identified to be the most efficiency-relevant defect centers
in mc-Si for photovoltaics. [9] Dislocations are generated
during ingot growth and cooling by mechanical stress that is
caused by temperature gradients inside the solidified ingot.
An example of the importance of crystal dislocation is given
in Figure 1, which depicts a typical topography of the short
circuit current of a mc-Si solar cell. Microscopic optical inves-
Fig. 1. Typical LBIC (light beam induced current) topography of the short
circuit current of a solar cell based on mc-Si. The sample size is 5 ” 5 cm 2 , redcolored
and dark regions indicate high and low current output, respectively.
Reduced current output generally is caused by recombination-active defect
centers. Microscopic investigations reveal the line-shaped structures to be due
to grain boundaries whereas the more extended defect regions originate from
crystal dislocations.
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C. Häûler et al./Process Development of Solar Cells by Numerical Simulation
tigations reveal that the dark regions in the topography, which
correspond to a reduced current output, are perfectly correlated
to high dislocation density regions.
From the above considerations it can be concluded that a
perfect control of the temperature distribution inside the crystallization
furnace is essential for high-throughput production
of mc-Si for high-efficiency solar cells. The most important parameters
that have to be thoroughly adjusted are
l the planarity of the solidification front for a low activity of
extended defects
l the crystallization speed affecting impurity segregation
and process times
l the temperature gradients and thermal stress leading to
dislocation generation.
4. Simulating the Process
In order to optimize temperature control inside our crystallization
chambers, we generally established a numerical simulation
[10] of the temperature distribution as a tool for process
development. The so-called VCF model [11] is employed to
simulate the three-dimensional, time-dependent temperature
distribution within our crystallization chambers. Basically, the
VCF model consists of three major parts, which are a geometry
and thermophysical data set, the software package, and
the user interface.
The geometry data set contains the crystallization furnace
(including insulation materials, heating and cooling systems,
the quartz crucible, and the silicon material) designed into a
400 000 finite elements system (see Fig. 2). The thermophysical
data of more than 30 different materials given as a function
of temperature is employed for the simulation.
Fig. 2. Numerical simulation results for the time-dependent temperature distribution
during crystallization of a >200 kg mc-Si ingot (cut along the middle
plane). The size of the ingot is approx. 55 ” 55 ” 30 cm 3 . The crystallization furnace
chamber including heaters, insulation materials, the quartz crucible and
the silicon material is designed into a 400 000 finite elements system and the
thermophysical data of approx. 30 different materials are taken into account in
order to simulate the time-dependent temperature profile of the entire silicon
block from basic process parameters (heating power, cooling water temperature).
The light yellow line represents the solidification front, i.e., the interface
between liquid (above light yellow line) and solidified (below) silicon.
The self-written software package CASTS (computer aided
solidification technologies) is specifically designed for the simulation
of technical processes. The starting point is the simulation
of the temperature distribution taking into account heating
power, heat flows, and the release of the latent thermal heat.
The thermal gradients and the dislocation density distribution
inside the silicon material are calculated from the temperature
distribution. The only input parameters of the simulation
are the heating power and the cooling water temperature of
the crystallization chambers of our block casting facility.
The accurate numerical simulation of the planarity and the
speed of the solidification front (see points 1 and 2 above) are
challenging problems, but nevertheless can be solved by adjusting
the parameters of the numerical simulation routines in
accordance with experimental data accessible by, e.g., temperature
monitoring. The prediction of dislocation densities, however,
is still a considerably more complicated case, because
the temperature distribution only represents the starting point
here, whereas the final goal is to calculate the distribution of
microscopic defects in large >200 kg silicon crystals.
Crystal dislocations are taken into account by considering
thermal gradients and the generation of thermal stress, which
is known to be the driving force for dislocation motion. Due
to this motion, dislocation multiplication takes place during
crystallization and cooling of the ingot. The multiplication
process leads to a final, locally varying dislocation density at
room temperature that essentially depends on the thermal
history of the mc-Si material. In order to calculate the dislocation
density generation by thermal stress we employ one of
the basic models of dislocation multiplication that was introduced
by Alexander and Haasen in 1968. [12] The basic
assumptions of this model translate into the following two
equations:
NÇ = KNvs eff
seff = sth ± spl ± A N
p
where, N and N Ç denote the dislocation density and dislocation
multiplication rate, respectively. The parameter v denotes the
velocity of the dislocations moving through the silicon crystal
and s eff stands for the effective stress given as a function of
the thermally induced stress sth, the plastic deformation spl,
and the dislocation density N according to Equation 2
(further parameters K and A are material constants).
In other words, the basic idea of our approach (see Eq. 1)
considers a dislocation multiplication rate N Ç that is proportional
to the dislocation density N and the respective dislocation
velocity v and that is driven by an effective stress s eff. This
effective stress s eff in turn is reduced by the plastic deformation
of the crystal and the dislocation generation itself and,
therefore, is lower than the pure thermal stress sth arising
from the temperature gradients (see Eq. 2).
Generally, each parameter given in Equations 1 and 2 is
dependent on temperature, time, and the position inside the
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(2)
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mc-Si ingots. Thus, finally, a system of several combined differential
equations is numerically solved for calculating the
dislocation density distribution.
Our self-developed numerical simulation routines were verified
by comparing their results to experimental data. Structural
crystal defects such as dislocations are experimentally
accessible by counting micrometer small etch pits with the
help of a microscope after appropriate polishing and chemical
etching steps. A unique measurement system, capable of fast
etch pit density (EPD) mappings even over large areas (up to
10 ” 10 cm 2 wafers), was, therefore, developed for the experimental
verification of the simulation results. It turned out that
the simulated dislocation density distribution even in large
200 kg multicrystalline ingots is in a sufficiently good agreement
with the experimental results (see Fig. 3) in order to be
employed for further process optimization.
Fig. 3. Numerical simulation results for the dislocation density as a function of
the block height in the center position of a mc-Si ingot with a weight of more
than 200 kg. The simulation starts from basic parameters of the crystallization
process (heating power, cooling water temperature) simulating first the timedependent
temperature distribution within the crystallization furnace. By employing
a physical model describing dislocation multiplication by thermal stress
within the solidified silicon the final dislocation density is calculated. The experimental
data was obtained by counting micrometer small etch pits originating
from crystal dislocations with an optical microscope. Due to the inhomogeneous
distribution of the dislocations, the measurements were averaged over
an area of approx. 25 cm 2 using an image analysis system.
5. Conclusions
The elaboration of the dislocation density distribution
within multicrystalline ingots led to the conclusion that the
generation of dislocations during the fabrication process of
mc-Si for photovoltaics can be divided into three important
phases [13] (see Fig. 4). First, a relatively strong increase of the
dislocation density is obtained in the vicinity of the solidification
front immediately after the phase change from liquid to
solid. The amount of dislocations generated in this first phase
depends on the solidification velocity because increased solidification
velocities necessitate high thermal gradients within
the solidified silicon. In the second phase of dislocation generation,
dislocation multiplication by thermal gradients is prevailing,
whereas the third lower temperature phase

C. Häûler et al./Process Development of Solar Cells by Numerical Simulation
mc-Si for solar cells. It is expected that the numerical simulation
tool will be specifically valuable for future process developments
addressing even larger ingots and process speeds
aiming at still enhanced solar cell efficiencies.
±
[1] See, e.g., M. A. Green, Solar Cells, Prentice-Hall, Inc., Englewood Cliffs,
NJ 1982.
[2] W. Koch, C. Häûler, H.-U. Höfs, A. Müller, I. A. Schwirtlich, Solid State
Phenom. 1997, 57±58, 401.
[3] C. Häûler, W. Koch, W. Krumbe, S. Thurm, A. Müller, I. A. Schwirtlich,
in Proc. of the 2nd World Conf. and Exhibition on Photovoltaic Solar
Energy Conversion Vienna (Eds: J. Schmid, H. A. Ossenbrink, P. Helm,
H. Ehmann, E. D. Dunlop), European Commission 1998, p. 1886.
[4] H. Lautenschlager, F. Lutz, E. Schäffer, C. Schetter, U. Schubert, R.
Schindler, in Proc. of the 14th European Photovoltaic Solar Energy Conf.
Barcelona (Eds: H. A. Ossenbrink, P. Helm, H. Ehmann), H. S. Stephens
& Associates 1997, p. 1358.
[5] A. El Moussaoui, A. Moehlecke, C. del Caæizo, A. Luque, in Proc. of the
2nd World Conf. and Exhibition on Photovoltaic Solar Energy Conversion
Vienna (Eds: J. Schmid, H. A. Ossenbrink, P. Helm, H. Ehmann, E. D.
Dunlop), European Commission 1998, p. 747.
______________________
[6] R. Lüdemann, A. Hauser, R. Schindler, in Solid State Phenom. Proc. of
the 2nd World Conf. and Exhibition on Photovoltaic Solar Energy Conversion
Vienna (Eds: J. Schmid, H. A. Ossenbrink, P. Helm, H. Ehmann, E. D.
Dunlop), European Commission 1998, p. 1638.
[7] F. Duerinckx, J. Szlufcik, J. Nijs, R. Mertens, C. Gerhards, C. Marckmann,
P. Fath, G. Willeke, in Proc. of the 2nd World Conf. and Exhibition on
Photovoltaic Solar Energy Conversion Vienna (Eds: J. Schmid, H. A. Ossenbrink,
P. Helm, H. Ehmann, E. D. Dunlop), European Commission
1998, p. 1248.
[8] W. Koch, W. Krumbe, I. A. Schwirtlich, in Proc. of the 11th European
Photovoltaic Solar Energy Conf. (Eds: L. Guimaraes, W. Palz, C. de Reyff,
H. Kiess, P. Helm), Harwood Academic Publishers 1992, p.518.
[9] See, e.g., H. El Ghitani, M. Pasquinelli, S. Martinuzzi, J. Phys. III 1993, 3,
1941.
[10] G. Ehlen, A. Ludwig, P. R. Sahm, Giessereiforschung 1999, 51, 56.
[11] I. Steinbach, D. Franke, W. Krumbe, J. Liebermann, in Proc. of the 1st
World Conf. on Photovoltaic Solar Energy Conversion Hawaii, IEEE
Electron Devices Society 1994, p. 1270.
[12] H. Alexander, P. Haasen, Solid State Phys. 1968, 22, 27.
[13] D. Franke, C. Häûler, W. Koch, J. Liebermann, in Proc. of the 2nd World
Conf. and Exhibition on Photovoltaic Solar Energy Conversion Vienna
(Eds: J. Schmid, H. A. Ossenbrink, P. Helm, H. Ehmann, E. D. Dunlop),
European Commission 1998, p. 108.
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