Particle Incorporation in Crystalline Silicon

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Particle Incorporation in Crystalline Silicon INAUGURALDISSERTATION zur Erlangung des Doktorgrades der Fakultät für Chemie und Pharmazie der Albert-Ludwigs-Universität Freiburg im Breisgau vorgelegt von Thomas Jauß aus Leonberg 2016

Transcript of Particle Incorporation in Crystalline Silicon

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Particle Incorporation in Crystalline Silicon

INAUGURALDISSERTATION

zur Erlangung des Doktorgrades

der Fakultät für Chemie und Pharmazie

der Albert-Ludwigs-Universität Freiburg im Breisgau

vorgelegt von

Thomas Jauß

aus Leonberg

2016

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Vorsitzender des Promotionsausschusses: Prof. Dr. Stefan Weber

Referent: Prof. Dr. Harald Hillebrecht

Korreferent: Prof. Dr. Arne Cröll

Datum der mündlichen Prüfung: 20.12.2016

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„Zwei Dinge sind zu unserer Arbeit nötig: Unermüdliche Ausdauer und die Bereitschaft etwas, in das man viel Zeit und Arbeit gesteckt hat, wieder weg zu werfen.“

Albert Einstein

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Acknowledgements

Prof. A. Cröll for providing me with the opportunity of working on this thesis. I enjoyed a tremendous

amount of knowledge personally and professionaly, guidance and generous hospitality on my vistit to

Hunstville Alabama, his home by choice.

Prof H. Hillebrecht for the spontaneous willingness to supervise this thesis.

Dr Tina Sorgenfrei, kicking me constantly forwards, never accepting my grumpy doubts of my work,

and forcing me over and over to find the good sides in my results.

Dr A. Danilewsky, who albeit not being directly involved in this work, always found ways to

encourage and guide me in the hard times unavoidable in PhD studies. His competence and

invaluable connections to many great names in our scientific community is deeply appreciated.

Dr. Jan Zähringer, who provided the simulations presented in this work, for always having an open

ear for struggles, proof reading, giving advice and support.

Dr. Katharina Gimbel for endless encouragements, proof reading and help with formatting. Design

isn’t my forte …

Dr. Christian Reimann of Fraunhofer IISB in Erlangen for helpful discussions and providing different

points of view whenever more conventional approaches did not help.

Dr. Michael Fiederle for his supervision and guidance.

Zhiyan Liu, Mohammad Yasseri and Nadine Pfändler, who accepted my style of teaching and

supervision during their Master Thesis, doing tremendous work, and from whose findings I greatly

profited.

The team at NASA MSFC in Huntsville, Alabama for their great support during the opportunity to use

their superconducting magnet in 2013.

Financial support through DLR within the projects „Bestimmung der kritischen

Einfanggeschwindigkeit von Partikeln bei der gerichteten Erstarrung von Silizium im Weltall", FKZ

50WM1146 and „Bestimmung des Einfangverhaltens von Si3N4-Partikeln bei der gerichteten

Erstarrung von Solarsilizium im Weltall“, FKZ 50WM1446, and for providing the two launch tickets for

the sounding rockets, is greatfully acknowledged.

To all the staff of the institute for crystallography, especially Luitgart Rees-Isele, and Manfred Kranz-

Probst, I owe sincerest thanks for technical and general support.

Thanks to all my friends not explicitly mentioned, who supported me through their friendship.

Finally, my parents and family, for their patience and love throughout my seemingly endless studies.

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Table of Contents I

Table of Contents

1 Introduction ..................................................................................................................................... 1

2 Theoretical Aspects ......................................................................................................................... 3

2.1 Silicon Material Properties ...................................................................................................... 3

2.2 Silicon Material Properties ...................................................................................................... 6

2.2.1 Single Crystalline Growth after Czochralski ..................................................................... 6

2.2.2 Single Crystalline Growth by the Floating Zone Technique ............................................. 7

2.2.3 Multi-Crystalline Growth by the Heat Exchange/Vertical Gradient Freeze Method ...... 8

2.3 Segregation .............................................................................................................................. 9

2.3.1 Macrosegregation ........................................................................................................... 9

2.3.2 Microsegregation .......................................................................................................... 11

2.3.3 Impurities in Silicon ....................................................................................................... 13

2.3.4 Particles in Solar Silicon ................................................................................................. 14

2.4 Interaction of Particles with the Solid/Liquid Interface ........................................................ 15

2.5 Research Gaps ....................................................................................................................... 20

3 Research Aim ................................................................................................................................. 21

4 Materials and Methods ................................................................................................................. 22

4.1 Description of Furnaces and External fields .......................................................................... 22

4.2 Growth Experiments.............................................................................................................. 28

4.2.1 Powders for the Growth Experiments ........................................................................... 28

4.2.2 Sample and ampoule manufacturing ............................................................................ 29

4.2.3 Sample Preparation ....................................................................................................... 34

4.2.4 Timer Plan and Power Profile Extrapolated from TEXUS 12, 22, and 27 ...................... 35

4.3 Characterization .................................................................................................................... 38

4.3.1 Circular Polarized Differential Interference Contrast Microscopy - CDIC ..................... 38

4.3.2 Infrared Transmission Microscopy - IRTM ..................................................................... 39

4.3.3 Video Analysis ................................................................................................................ 39

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II Table of Contents

4.3.4 Synchrotron X-ray topography - SXRT ........................................................................... 40

5 Results ........................................................................................................................................... 41

5.1 Growth Experiments.............................................................................................................. 41

5.1.1 Terrestrial Experiments ................................................................................................. 41

5.1.2 µg Experiments .............................................................................................................. 53

5.2 Additional results .................................................................................................................. 62

5.2.1 Distribution Experiments ............................................................................................... 62

5.2.2 Infiltration and Wetting Behaviour Experiments .......................................................... 64

5.2.3 Experiments With a Model Melt System ....................................................................... 70

5.2.4 Simulations of Melt Movement in Various Zone Heights ............................................. 73

6 Discussion ...................................................................................................................................... 75

6.1 Growth Experiments.............................................................................................................. 75

6.1.1 Terrestrial Experiments ................................................................................................. 75

6.1.2 µg Experiments .............................................................................................................. 78

7 Conclusions and Outlook ............................................................................................................... 79

8 References ..................................................................................................................................... 80

9 List of Figures ................................................................................................................................. 86

10 Appendix .................................................................................................................................... 94

10.1 Abbreviations ........................................................................................................................ 94

10.2 Sample IDs ............................................................................................................................. 97

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1. Introduction 1

1 Introduction

After the incident of Fukushima in 2011, already present demands for alternative, clean, renewable

energy grew stronger. The decision to decommission nuclear power plants, and with the

environmental impact of fossil fuel power plants in mind, leaves technologies like wind turbines,

hydroelectric power generation, bio mass power plant and harvesting the suns energy. While

generating heat with sun power, the direct conversion of light to electrical energy is more

favourable. In the last years, photovoltaic (PV) technology has experienced truly astonishing leaps

forwards to achieve competitiveness with conventional energy sources. Taking a look at the solar

report of 2016, provided by the Fraunhofer ISE [1], the advances in this technological field come

quite apparent. In the past fifteen years between 2000 and 2015, the compound annual growth rate

of the PV-market was 41 %. China has taken over the top production rank, with 71 % of modules

produced in 2015. On the technological side, silicon module rules the market, with 93 % of all

modules produced being silicon wafer based. Silicon based PV-modules, are further distinguished in

monocrystalline, polycrystalline and amorphous silicon, with mono- and multi-crystalline (MC) wafers

as the more important varieties. In quantity, MC-silicon dominates this group with 69 % of market

share. In Germany, 33 % of the electrical power needed was generated by renewable energy sources,

7 % was provided by PV installations. The roughly 1.5 million PV systems installed delivered 38.4 TWh

and with this saved 24-27 million tons of carbon dioxide (CO2). To achieve this, some necessary

technological advances were for example, the increase in efficiency of MC-cells, the current lab

record cell sporting an efficiency of 20.8 %. Another important step was the reduction of silicon

material needed for the individual cells. In the ten years from 2004 to 2014, the wafer thickness was

reduced from 400 µm down to 135 µm. With this, the amount of Si needed per Watt peak (Wp) went

down from 16 g/Wp to just 6 g/Wp.

For the most common MC-silicon production technology, the vertical gradient freeze (VGF) or heat

exchange method (HEM), this reduction of wafer thickness has unfortunate downsides. Inherent to

this technology, which provides large amounts of silicon very rapidly, is its high concentration of

impurities. These impurities can lead to foreign phase precipitates during growth, and when

exceeding a certain size, they reach the thickness of the final wafer. This leads to problems during

the wafering of the silicon ingots, which is carried out with large multi-wire saws, wafering the whole

ingot in one process step. Foreign phases with a hardness higher than that of silicon lead to a

deviation of the cutting wire during that step [2]. The result is a wavy surface of the produced wafer,

if the particles are small enough. With particles larger than the distance between the individual

cutting wires, the risk of wire breakage rises. In the case of wire breakage during the wafering, the

whole ingot has to be discarded [3], for the process cannot be continued with a new wire installed.

The sources of such particles are the original feedstock, the crucible, the crucible coating, and the

gases in the furnace atmosphere. While particles can be breaking of from the crucible surface, the

majority of foreign phases is a result of supersaturation of chemical species in the melt, leading to

precipitation during the crystallization of the silicon ingot [4–6]. Besides the complications during the

wire sawing process, foreign phases can create shunts in the solar cells [7], short circuiting, and

created heat by the current flowing through [7, 8]. Particles also act as sources for dislocations,

leading to a small grained grit structure of the growing ingot [9]. For these reasons, the incorporation

of foreign phase needs to be avoided.

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2 1. Introduction

To predict the behaviour of particles in front of the moving solid liquid interface, a number of models

are being developed since the mid-sixties. Many models define a critical growth velocity (Vc), above

which a particle is incorporated and below which, transport is observed. The first model to introduce

this Vc is model of Uhlmann, Chalmers and Jackson [10]. The models vary in their mathematic

complexity, the chemical species involved, and in their degree of simplification. For example, most

models neglect gravity, so no gravitational sedimentation takes place, no melt movement due to

density gradients is present. Also, the chemical interactions between the phases is often neglected,

as well as the particle shape, which is commonly assumed to be spherical. Such simplifications lead to

a discrepancy of the predicted particle size and its projected incorporation velocity. The prediction

can be off by orders of magnitude, predicting particles with sizes of up to 2 mm being pushed at

typical growth rates during industrial crystallization. In reality, particles with much lower sizes are

found in the bulk of the ingots. To investigate, where the models need to be improved, experiments

are required, that are close to the conditions used in the simulations. Growth experiments with truly

diffusive conditions cannot be achieved on earth and so, they demand microgravity conditions. While

buoyancy is immediately eliminated in space, any free melt surface has to be avoided or else,

Marangoni convection leads to melt movement, even stronger than buoyancy. An experimental

setup as used in the TEXUS 12 mission in 1986, carried out by A. Cröll et al. [11], where the silicon

sample is covered by a several µm thick SiO2 skin, can provide diffusive conditions as required.

This thesis is structured as follows:

In the second chapter the theoretical background to this thesis will be addressed. Material

parameters of silicon and its growth methods are presented. Particle inclusions common in silicon,

their origin and interaction with the phase boundary are shown.

The third chapter will introduce the aim of this work, the fourth chapter deals with the materials and

methods applied. The growth experiments and the necessary preparations are illustrated and the

characterization technique introduced.

The results of the growth experiments under terrestrial and microgravity conditions is shown in the

fifth chapter of this work. Additional results to specific thematic aspects are presented as well.

After discussing the results in chapter six, the thesis will be concluded and an outlook on possible

further research given in chapter seven.

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2. Theoretical Aspects 3

2 Theoretical Aspects

In this chapter the material properties of silicon, silicon crystal growth, impurities and their

behaviour in silicon will be presented. An introduction to some existing models for the prediction of

particle incorporation will be given.

2.1 Silicon Material Properties

Silicon is the 14th element of the periodic table, and an element of the fourth main group, below

carbon and above germanium. It crystallizes in the diamond cubic lattice, and all the bonds between

the silicon atoms are of covalent type. The unit cell consists of two cubic face centred cells

shifted 1 4⁄ 14⁄ 1

4⁄ along the body diagonal of the first cell. The space group is 𝐹𝑑3𝑚, and all Si

atoms are tetrahedral coordinated. For highly pure Si at room temperature, the lattice constant is

5.43102018(34) Å [12] and the band gap 1.1692 eV [13]. Rhim and Ohsaka [14] reported the

temperature dependent values for density, surface tension, and viscosity as follows:

Density:

𝜌(𝑇) = 2.58 − 1.59 ∗ 10−4(𝑇 − 𝑇𝑚) − 1.15 ∗ 10−7(𝑇 − 𝑇𝑚)2 𝑔

𝑐𝑚3⁄ (1)

Surface tension:

𝜎(𝑇) = 765 − 0.016(𝑇 − 𝑇𝑚) 𝑚𝑁𝑚⁄ (2)

Viscosity:

𝜂(𝑇) = 0.75 − 1.22 ∗ 10−3(𝑇 − 𝑇𝑚) 𝑚𝑃𝑎 ∗ 𝑠 (3)

All three with a melt temperature as reported by Desai et al. [15] of 1687 K. At room temperature

the density is 2.329002 g/cm³ [16]. The density of the silicon melt is reported by Rhim et al. 1997 [17]

as 2.56 g/cm³. In the same publication, Rhim et al. present the surface tension of silicon as 875-

0.22(T-Tm) mN/m, a discrepancy which is argued by Shinshin and Basin 2004 [18] as well as Niu et al

1997 [19] as a function of impurity content.

Silicon in its unit cell is tetrahedrally coordinated by four other Si atoms (Figure 1 a), the lattice type

is that of diamond. If every other atom is substituted by another chemical species, the zinc blende

lattice is formed (Figure 1 b), this is the most common lattice type for compound semiconductors as

for example gallium arsenide. It can be deducted from these two unit cells, that in different

crystallographic directions, the packing density of the atoms, the number of free bonds, and in case

of GaAs, the chemical species varies. This explains, that even for elemental cubic semiconductors,

crystal properties and crystal structure is anisotropic.

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4 2. Theoretical Aspects

Figure 1: Presented are the two most important unit cell types for semiconductors. Elemental

semiconductors like silicon crystallize in the diamond cubic lattice (a), compound semiconductors like GaAs

crystallize in the zinc blende structure (b) [20].

Silicon, is an elemental semiconductor and an indirect semiconductor. In an indirect semiconductor’s

band structure the conduction band minimum is not directly accessible from the valence and

maximum. To get an electron from the conduction band into the valence band, the electron not only

changes its energy state, but it has also to change its momentum. A direct recombination is therefore

impossible. In contrast to that, the electron can transfer from the conduction band into the valence

band in a direct semiconductor as for example GaAs. For this reason, GaAs has a far higher switching

frequency capability as silicon. The band structures for silicon and GaAs are presented in Figure 2,

taken from Sze 2007 [21].

Figure 2: The figure shows the band structure of Si (a) and GaAs (b). The electrons in the conduction band are

shown as black dots, while the corresponding holes in the valence band are shown as circles. [21]

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2. Theoretical Aspects 5

Impurities and dopants create levels between conduction and valence band, reducing the band gap.

These levels when ionized, are located below the conduction band edge for donators and above the

valence band edge for acceptors. Dopants create shallow ionization levels, while impurities for

example metals like gold and copper in silicon, create deep level traps, that act as recombination

centres. As the name implies, at recombination centres, electron hole pairs can recombine, and the

function of the semiconductor is disturbed. Some dopants and metal impurities common in silicon,

and their function as dopants or deep level traps is shown in Figure 3. Common dopants for silicon

and their segregation coefficient after Trumbore [22] are listed in Table 1.

Figure 3: Shown are the measured ionization energies in eV in silicon for several impurities and dopants from

Sze 2002 [20]

Table 1: This table shows common donator and acceptor dopants for silicon with their respective segregation

coefficient k0 after Trumbore 1960 [22]

Acceptor k0 Donor k0

B 0.8 P 0.35

Al 0.002 As 0.3

Ga 0.008 Sb 0.023

In 0.0004 Bi 0.0007

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6 2. Theoretical Aspects

2.2 Silicon Material Properties

As the major contributor of electricity from photovoltaic installations, the production technologies

for solid, crystalline silicon are presented in this chapter. Growth technologies for single and

multicrystalline silicon are discussed, thin film technologies, as well as amorphous silicon applications

are neglected.

2.2.1 Single Crystalline Growth after Czochralski

Now already a hundred years old, the single crystal growth method after Jan Czochralsi [23] is the

most important growth technique for silicon single crystals. The method, constantly improved, can

be used to produce crystals with a diameter of up to 450mm. The technology, although it can be

automated to a certain degree to produce large diameter single crystals of high purity, is comparably

expensive. It utilizes complex technological apparatuses, like after heaters and strong magnetic fields

for interface shape control and melt mixing, as well as expensive consumables like the single use

crucible made of high purity fused silica. This crucible is also a source of oxygen in the crystal, since

the melt is slowly dissolving it during the growth. A basic setup is shown in Figure 4. Key in this

growth technique is the use of a seed crystal, that provides the crystallographic orientation. To

eliminate the dislocations that are created by the thermal shock when the seed is dipped into the

melt, dash necking is performed, where the crystal is pulled fast from the melt, growing a thin neck.

In this neck, the dislocations which are present and multiplying, are literally outgrown by the silicon.

After a certain grown length, the dislocations are pinned at the neck surface and the temperature

gradient is too low for them to climb and multiply anymore. From this point on, the crystal can be

grown dislocation free. The diameter is then widened in the shoulder region of the crystal, and after

reaching the desired diameter, the crystal is grown cylindrical. At the end of the growth process, it is

necessary to grow an end conus. This conus prevents the crystal from experiencing another thermal

shock when it is separate from the melt. Without this last step, the thermal shock would create a

vast amount of dislocations, multiplying and creeping back into the crystal as far as two times its

diameter. One limitation of silicon crystals grown by the Czochralski method is the fact, that the

dissolved oxygen is incorporated. By diffusion the oxygen can agglomerate and form precipitates.

Another limitation for solar cell application presents itself, when boron doped p-type silicon is used

for cells. When exposed to sun light the dissolved oxygen forms a complex with boron atoms, leading

to a reduced number of carriers, reducing cell and module efficiency [24].

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2. Theoretical Aspects 7

Figure 4: Setup for silicon growth by the Czochralski technique after Sze 2002 [20].

2.2.2 Single Crystalline Growth by the Floating Zone Technique

Although originally developed as a technique for purification [25]and doping of semiconductor

materials by Pfann 1952 [25], it was also developed and presented as a growth technology for silicon

single crystals by Theurer 1952 [26], Keck and Golay 1953 [27], and Emeis 1954 [28]. When used for

purification, a small volume of liquid is created in a larger volume of material usually in a tube or

boat. The molten zone is then moved through the rod or boat, melting on one end and solidifying on

the other. Impurities acting according to their segregation coefficient, will accumulate at the end or

beginning of the material. By repeating this process or by applying several zones per run, a purified

an increasingly pure part of material is created. At some point, where back diffusion of an impurity

into the purified material limits further purification, the corresponding impure part has to be cut off.

With the zone refining technique, high purity material can be obtained from impure feedstock. When

refining silicon by this approach, a major limitation presents itself. Molten silicon will react with

almost any other material, which is why Theuer developed the floating zone refinement in 1952 [26].

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8 2. Theoretical Aspects

In his approach a silicon rod is mechanically held vertical and the liquid zone passes vertically through

the silicon without contact to a crucible. The zone keeps itself between the two solid pieces of silicon

by surface tension. Independently, this approach was developed by Keck and Golay 1953 [27], and

Emeis 1954 [28] at Siemens in Germany. With this, the Float zone technique for crucible free growth

of silicon crystals was born.

A distinct advantage of the float zone technique over the Czochralski method is, as described before,

that the crystal is not in contact with any form of crucible. The melt is suspended between the seed

crystal and the feed material by surface tension. As feed material, polycrystalline material or a

pressed powder is possible. Ideally, the feed should be round and a made of and free from gaseous

inclusions or voids. In cases where pressed powder serves as feed material, the porosity of the

material has to be considered. The melt can seep back into the feed, reducing the melt volume in the

zone. Also, if the feed is porous, the mass flow into the zone might not be homogenous, and the melt

volume of the zone can vary accordingly. To some degree, this can be corrected by the operator, but

it presents serious limitations to automation. The procedure of a float zone growth is as follows: seed

and feed crystal are positioned close to the thermal focus of the furnace, and two droplets at the tips

are created. When those droplets are connected, a melt bridge, is created between seed and feed

crystal, held by surface tension. The seed and feed crystals are then moved relatively to the thermal

focus, leading to the zone travelling through the crystal, melting the feed and crystallizing at the seed

crystal. By adapting the translation rates of seed and feed accordingly, diameter control, and necking

for dislocation elimination is possible. Necking can also provide seed selecting and single crystal

growth from polycrystalline seed material.

2.2.3 Multi-Crystalline Growth by the Heat Exchange/Vertical Gradient

Freeze Method

The most common industrial method to grow silicon for solar cell applications is by the heat

exchange or vertical gradient freeze method. This method is popular, since it requires less manpower

to operate and oversee, contains no moving parts to be serviced, and it can produce large amounts

of silicon in a single run. As of 2011, the mass of a silicon ingot grown industrially by this method was

up to 640 kg. From these ingots 25 columns 156 mm x 156 mm x 350 mm are cut. The square

columns obtained by this way are then wafered by multi-wire saws and further processed for solar

cell application. A growth cycle for such an ingot works as follows, at first the silicon feed material,

chunks or pellets of silicon of the necessary purity are placed into the crucible. This crucible consists

of a carbon support crucible, which is dimensionally stable at the temperatures necessary for silicon

growth. The support crucible holds an SiO2 ceramics crucible, which is chemically more resistant to

the silicon melt, as the carbon crucible. If not further treated, the silicon ingot may stick to the SiO2

crucible due to its wettability. To avoid this sticking, which may lead to breaking of the ingot during

the cooling process, the crucible is slurry coated by silicon nitride powder, which is then sintered

onto the SiO2 under oxygen atmosphere. During this sintering, the silicon nitride gains mechanical

stability and further, silicon oxide nitride is created. This nitride species, shows even better non-

wetting and non-sticking properties than pure silicon nitride.

The silicon feedstock mentioned before is filled in by hand to ensure the coating stays as undamaged

as possible. After the crucible is filled, it is transferred into the furnace, evacuated, and under purge

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2. Theoretical Aspects 9

gas flow, the material gets molten. After the melt is homogenised, the silicon is crystallized from the

crucible bottom to the top. This is achieved either by reducing the bottom heater power, and or

actively cooling the crucible bottom. Despite the fact, that the furnace atmosphere it purged with gas

during the whole process, large amounts of carbon monoxide are present. The sources of the carbon

monoxide are mainly the furnace parts themselves, such as the heater elements and the support

crucible.

Figure 5: Schematic representation of the vertical gradient freeze process, the main industrial scale

production technique for growing multicrystalline silicon for PV applications. Shown are the graphite heater

elements, carbon support crucible, fused silica crucible, silicon nitride coating, and silicon in solid and liquid

form. A: silicon chunks are filled into the Si3N4 coated crucible B: All silicon is molten C: By extracting heat

from the bottom of the crucible, either by reducing heater power or active water cooling, Silicon is solidifying

from the bottom up. D: Completely solidified Silicon ingot

2.3 Segregation

Segregation describes the phenomenon of how dissolved chemical species are incorporated into a

growing crystal. Chemicals possess a distribution coefficient, that describes their incorporation

behaviour of whether they are enriched in the liquid or in the solidifying solid. It can be distinguished

between macro- and micro segregation. Macro segregation describes the distribution of an impurity

r dopant over the whole solid, either as a constant distribution or as an increasing or decreasing

gradient. The scales are in the range of centimetres to metres. Micro segregation describes the

distribution of impurities or dopants in the scale of nanometres or micrometres. The mechanisms are

described in the following two subsections.

2.3.1 Macrosegregation

In silicon for solar cells grown by the VGF method, several foreign phase particle species are

common. Their origin varies, but most of them are generated by dissolved impurities in the silicon

melt. Metals and carbon originate for example from the initial feedstock, where solar grade silicon,

or upgraded metallurgical silicon with varying purity already contains impurities [6]. Carbon also

originates from graphite furnace parts, such as graphite support crucibles, or heating elements. At

high temperature, graphite and residual oxygen in the furnace atmosphere form carbon monoxide

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[29], which is dissolved into the melt upon contact. The melt itself is contained in a crucible of

ceramic silicon oxide or fused silica. As soon as the melt is in contact with the crucible, it starts to

dissolve it and oxygen is introduced into the melt. Since silicon oxide and silicon possess different

thermal expansion coefficients and silicon also sticks to silicon oxide, the crucibles crack during

cooling. This leads to the destruction of the crucible, and also to possible material loss, since the

ingot can take damage if the crucible breaks. To reduce this sticking behaviour, a coating of silicon

nitride/silicon oxynitride is applied to the crucible. While silicon shows non-wetting behaviour

towards silicon oxynitride, the wetting behaviour on silicon nitride is depending on the oxygen partial

pressure of the surrounding atmosphere [30]. In the presence of silicon melt, the coating also slowly

dissolves, introducing nitrogen and oxygen. Once dissolved into the melt, and supersaturation is not

yet reached, carbon, nitrogen, oxygen as well as other dissolved impurity species follow the laws of

segregation. After Müller G. 1986 [31] an equilibrium state, which can only be reached if

1. an infinite supply of melt is present

2. Cs = Cl

3. in a finite volume of melt, the amount of impurity that gets incorporated, is constantly resupplied

to the melt meaning that Cl stays constant.

The segregation coefficient is then described as

𝑘0 =𝐶𝑠

𝐶𝑙 (4)

If any melt movement is present, the model of Burton, Prim and Slichter 1953 [32] has to be applied.

The model states that a steady state only exists in a thin boundary layer in front of the solid/liquid

interface, moving with a constant velocity in one direction, with constant thickness. In this diffusion

boundary layer, mass transport is controlled by diffusion. From this follows, that in this boundary

layer, no melt movement is present. Outside of this layer, complete mixing of the melt is assumed,

impurities are present with concentration Cl, inf. An effective segregation coefficient is describable as

𝑘𝑒𝑓𝑓 =𝐶𝑠

𝐶𝑙,∞= 𝑘0 ∗

𝐶𝑙

𝐶𝑙,∞ (5)

Burton, Prim and Slichter assume an exponential distribution of impurities in the diffusion boundary

layer. If the growth velocity Vgr is known, keff can be calculated as

𝑘𝑒𝑓𝑓 =𝑘0

(𝑘0 + (1 − 𝑘0)−Δ𝐵𝑃𝑆) (6)

With

Δ𝐵𝑃𝑆 = 𝛿 ∗𝑉𝐺𝑟

𝐷 (7)

The symbols stand for , the diffusion boundary layer thickness, D is the Diffusion coefficient of the

impurity in the melt and VGr is the growth velocity of the crystal. Convection is only considered, if

BPS is adapted. With a higher degree of, mixing BPS gets smaller, and vice versa. For the two

extreme cases, complete mixing and diffusive mixing following statements are true:

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2. Theoretical Aspects 11

For complete mixing, BPS approximates 0, 𝑘𝑒𝑓𝑓 → 𝑘0

For diffusive mixing, BPS approximates ∞, 𝑘𝑒𝑓𝑓 → 1

2.3.2 Microsegregation

Microsegregation is the driving mechanism of chemical distribution on a micro scale in front of the

solid liquid phase boundary. It describes the creating of minute chemical variations in for example

silicon. Microsegregation is caused by variations in growth parameters such as temperature

fluctuations, melt movement or changes in growth kinetic where keff is changed. Changes in the

microscopic growth rate and changes in the thickness of the diffusion boundary layer cause Type-I

striations. Changes in the growth kinetics create inhomogeneities called Type-II striations. Both types

can be observed for example by lateral photovoltage scanning [33], and/or defect selective etching

after Dash [34], Sirtl [35], Secco [36] or Wright-Jenkins [37].

First Order Striations

In contrast to macrosegregation, where the concentration of an impurity, or dopant changes

gradually over the length of the grown crystal, microsegregation describes concentration changes in

the order of micrometres or millimetres. As described by Burton, Prim and Slichter, keff is a function

of growth velocity, and so every change in growth rate is followed by a change in incorporation

behaviour of dopants and impurities. Another influencing factor is BPS, which is a measure of the

mixing of the melt in the vicinity of the phase boundary. Since no thermal field is microscopically

symmetrical under any growth conditions, a rotation of the crystal during the growth process leads

to a variation of the growth rate, in extreme cases even a partial remelting of the already grown

crystal is possible. In Figure 6 A, the red arrows indicate striations created by rotation during the

growth. This remelting can be recognized by the striations cutting previous striations at an angle. In

Part B of the figure, microstriations are shown by the red arrows. As the name implies, these

striations are created at an even lower scale. In this case, they are just a few micrometres apart. It is

also apparent that they envelope a SiC crystal, indicated with green arrows, that was precipitated

during the fast crystallization of the last zone. The carbon necessary for this precipitation is

transported there by macrosegregation. At this point, SiC must form, since the last zone is solidifying

and by this, gets supersaturated with respect to carbon. Further, a few small crystallites of silicon due

to poly crystalline growth, are also indicated by blue arrows. Rotational striations and microstriations

from melt movement, are reproductions of the phase boundary at their time of creation, they can

therefore deliver information about the growth rate, if the rotational frequency is known and they

give an indication of how the temperature distribution in the zone looked like, as they show the

silicon melting isotherm.

Page 20: Particle Incorporation in Crystalline Silicon

12 2. Theoretical Aspects

Figure 6: Part A: First order striations caused by variations in growth velocity are indicated by the red arrows.

The variation in growth rate is caused by sample rotation during the growth. The weaker, more random

micro striations between the rotational striations are caused by melt movement due to the rotation. Part B:

Micro striations (red arrows) created in the last rapidly solidifying melt zone of a float zone growth

experiment. The micro striations envelope SiC-crystallites, shown by green arrows, precipitated and grown in

the melt zone. The blue arrows point at micro crystallites, silicon grains formed during the fast solidification,

where the growth conditions are not controlled anymore.

Second Order Striations

Second order striations have their origin not in the mechanical setup of the growth, but in its

kinetics. A common growth scenario, where second order striations occur, is liquid phase epitaxy.

Woking intensively with this growth technique, E. Bauser characterized the appearance and

formation of this type of striations in detail [38–43]. On an atomistic scale, the phase boundary,

where the crystal is growing, is flat. On this flat plane, the crystal grows laterally, the layers that are

stacked on top of each other lead to the macroscopic growth of the crystal. New atoms or molecular

blocks are preferably added at kink positions, which are energetically favourable. If the growth plane

is inclined less than 0.1° towards a lattice plane of a low Miller index, facetted growth may occur. A

facet is atomically flat, so that if one layer is completed, there are no favourable kink positions

available. In this case, two-dimensional nucleation is necessary, to adhere a new atom or molecule.

This is the most energy intensive way to add building blocks to the growing crystal, so the energy for

this nucleation must be drawn from undercooling the melt in front of the phase boundary. Once 2D

nucleation took place, a new step and then kink position is available, leading to a fast lateral growth

further supported by the now undercooled facet. If the misalignment is between 0.1° and 2° the

monoatomic layers can agglomerate to macrosteps, leading to a growth front that is terrace shaped.

On the top, the terrace growth is similar to that of a facet, but at the riser part, the growth

morphology, the growth mode, and growth rate is different for the terrace step. The differences in

growth rates of these growth modes, facetted, terrace, step and riser leads to a different dopant

incorporation. While facets lead to a core with different properties from the off-facet grown crystal,

the risers leave a trace of different dopant distribution. In the extreme case of a concave phase

Page 21: Particle Incorporation in Crystalline Silicon

2. Theoretical Aspects 13

boundary, risers may move towards each other, annihilate or leave a trace of a valley Figure 7. In

contrast to Type-I striations, that follow the growth front, Type-II striations don’t necessarily.

Figure 7: Formation principle of Type-II striations. Terraces and valleys leave a dopant concentration trace,

that is different from the surrounding crystal, leading to Type-II striations when the crystal is etched.

redrawn after Cröll & Müller-Sebert 1988 [44].

Type-II striations should not occur in [100] grown silicon with a convex phase boundary, they may

however occur in the rapidly solidifying last zone. For the experiments on incorporation behaviour of

particles in silicon presented in this work, they are not relevant.

2.3.3 Impurities in Silicon

Metals mainly originate from the original feedstock, but also get introduced into the ingot by

diffusion from the ceramic oxide crucible during the cooling process, where the whole melt is already

crystallized, but the temperature is still high enough for solid state diffusion. Here the metals follow

the temperature gradient, diffuse into the material and contribute to a low lifetime zone, where the

minority carrier lifetime is limited by recombination at deep level traps, caused by the in diffused

metal impurities [45].

Segregation dictates, whether an element gets incorporated into the growing crystal, or gets

enriched in the melt. The segregation coefficient describes this behaviour. In the case an element

gets enriched, and its solubility limit in the melt is reached, precipitates start to form. The solubilities

and segregation coefficients for carbon, nitrogen and oxygen are listed in Table 2.

Table 2: Solubilities of carbon, nitrogen, and oxygen in silicon melt and silicon crystals and their equilibrium

segregation coefficients

Impurity C N O

Solubility in liquid Si [at/cm³] 3.5*1018 [46] 6.0*1018 [47] 2.2*1018 [47]

Solubility in solid Si [at/cm³] 3.5*1017 [46] 4.5*1015 [47] 2.75*1018 [47]

Equilibrium segregation

coefficient k0 0.1 [46] 0.0007 [47] 0.13 – 1.25 [22, 48–50]

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14 2. Theoretical Aspects

2.3.4 Particles in Solar Silicon

When the solubility limits listed in Table 2 are reached, precipitated can start to form in the melt. The

most common precipitates are discussed in the following paragraphs.

Silicon Carbide

Carbon originating from the original feedstock and carbon monoxide in the furnace atmosphere gets

enriched in the melt due to its segregation coefficient of 0.1 [46]. Once saturation is reached or the

stable growth velocity exceeded, silicon carbide is formed in the melt. Under standard process

conditions, 3C-SiC is stable in the melt [51]. These precipitates can be present as isometric,

dodecahedral monocrystallites or filaments. The crystallites can occur in silicon grains, at the crucible

walls or at other precipitates, namely Si3N4 needles, which serve as nucleation points for the SiC

crystallites [51]. Further, SiC can precipitate as filaments in grains of silicon and at the boundaries

between silicon grains. The cubic crystallites, as well as dislocations, also can act as nucleation points

for the filaments. Besides the high hardness of SiC, it can cause ohmic shunts [52].

Silicon Nitride

Silicon nitride with a grain size of several µm is mixed with water or poly ethylene glycol before being

applied to the SiO2 crucibles by means of spray coating or simply spreading on. It serves as an anti-

sticking coating and it prevents the silicon ingot from adhering to the crucible and thus from cracking

itself and the crucible during the cooling step of the growth process. During the solidification of

silicon, the melt convection can rip of particles from the coating and dissolve them, until saturation is

reached. The dissolved nitrogen also possesses a segregation coefficient of 0.0007 [47], much lower

than one, and therefore gets enriched in the melt during crystallization of the ingot. The precipitates

forming upon supersaturation, present themselves as needles, filaments and clusters of beta-

Si3N4.[51, 53, 54] These can occur in combination with SiC particles, which nucleate at the nitride

filaments. Needles of Si3N4 can reach diameters of several tens of µm and a few mm in length [51,

53]. Needles and filaments occur in the silicon matrix oriented parallel or slightly inclined with

respect to the growth direction [53].

Silicon Oxide

If the melt gets into contact with the SiO2 crucible, the dissolution of it introduces oxygen into the

system. Oxygen, in contrast to carbon and nitrogen, instantaneously gets incorporated into the

growing crystal, with a reported range of k0 from 0.13 to 1.25, with most experimental analysis

indicating a k0 of almost 1 [48]. Since it is incorporated as an interstitial atom into the silicon lattice, it

does not form precipitates during the growth process of directionally solidified solar silicon. SiO2

particles are not known to occur as a particle species in solar silicon.

The most important species of particles in solar silicon as mentioned above, are silicon carbide and

silicon nitride. Some key material properties for both are given in Table 3. The density of the particles

is higher than that of liquid silicon, therefore under gravity conditions they are expected to sink down

in the melt.

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2. Theoretical Aspects 15

Table 3: Material properties of SiC and Si3N4

Property SiC Si3N4

Density at 1673K [g/cm³] 3.16 [55] 3.16 [56]

Therm. conductivity [W/mK] 10-70 [57] 10-40 [58, 59]

Wetting angle [°] <40 [60, 61]

wetting

110-150 [62]

non-wetting

Interfacial Energy 0 [J/m²] 0.1-0.5 [60] 0.5-2.0 [61, 63]

The effect of the wetting angle is shown in Figure 8. Presented are three case, the non-wetting case,

with a wetting angel larger than 90°, the special case of a wetting angle of 90° and the wetting case,

where the angle is lower than 90°.

Figure 8: Wetting angles for non-wetting behaviour ( > 90°) on the left, the special case of a =90°

in the middle and case of complete wetting ( < 90°)

More detailed information on O, N, and C related particle species can be found in [53].

2.4 Interaction of Particles with the Solid/Liquid Interface

Studies of particle interaction with the solidification from of crystals and metals can be found in the

literature. They differ for example in the mode of incorporation, the incorporated particle species

and the shape of the solid liquid interface. The incorporation of ceramic particles in metal alloy

casting was studied by Pötschke and Hohenstein 1982 [64] or Pötschke and Rogge 1989 [65] even

under microgravity conditions. Due to the high amount of undercooling in metal casting, the

solid/liquid interface in not planar in these cases, but dendritic. Figure 9 show the possible

interactions of particles with a dendritic S/L interface after Wilde et al. 2000 [66]

Page 24: Particle Incorporation in Crystalline Silicon

16 2. Theoretical Aspects

Figure 9: The three modes of interaction of particles with a dendritic interface is shown. the particles can be

pushed by the interface and by this enrich in front of it. If dendrites start to branch, particles can be trapped

between the branched columns. In the third case, the particles are incorporated into the propagating solid

without being pushed or trapped after Wilde et al 2000 [66].

Models that deal with a planar solid liquid interface are necessary for the general crystal growth

case. These models can be categorized by the effect they focus on, for the prediction of the

incorporation. Models which focus on the kinetics, defining a critical velocity Vc that separates

incorporation and pushing are for example published by Bolling & Cisse 1971 [67], Pötschke & Rogge

1989 [65], Stefanescu et al. 1988 [68] and Sen et al. 1997 [69]. A second group of models focus on

thermodynamic properties as for example Omenyi et al. 1976 [70], Chernov and Temkin1977 [71],

and Uhlmann et al. 1964 [10]. As a simplification, melt convection and gravity are neglected in for

example Pötschke & Hohenstein 1982 [64], Agliotis et al. 2008 [72], and Bellmann et al. 2010 [73].

Graphically represented in Figure 10, is the model of Soiland 2004 [54], where gravity is also

neglected, but a prediction is made for the pushing engulfing transition for particles in silicon. Drawn

as a dashed line is the typical crystallization velocity for silicon during the directional solidification of

solar silicon with 5.5 µm/min. The model predicts the critical particle radius for this system to

Page 25: Particle Incorporation in Crystalline Silicon

2. Theoretical Aspects 17

1.3 mm, above which engulfment is observed and below which pushing should take place.

Figure 10: Model for particle behaviour calculated by Soiland [54]. The solid line marks the transition for a

particle of being pushed or being engulfed for a given combination of particle radius and velocity of the

moving S/L interface. The dashed line represents a typical solidification velocity during the industrial

production of solar silicon (5.5 µm/s). After this model, particles with a diameter lower than 1.3 mm should

be pushed.

In more complex models than in the one proposed by Soiland, a particle in the melt experiences

several forces acting on it. Figure 11 shows the particle in front of a S/L interface, that is moving with

the growth velocity VGr. The particle is characterized by its diameter and is moving with VP.

Depending on the physical properties of the system, the forces and their direction acting on the

particle are: the drag force FD, the buoyant force FG, Magnus force FM, lift force FL, and interface force

FI. Drag is created, when the particle moves through the melt, it acts towards the interface and

promotes incorporation. The buoyant force is created by the density difference of particle and melt

under terrestrial conditions with gravity present. If the density of the melt (L) is lower than the

density of the particle (P), the particle sinks down towards the S/L interface, promoting

incorporation. The interface force is created by the surface energy difference of the growing crystal

and the particle in the melt, the difference creates a repulsive or attractive force between the two.

The Magnus force FM and the lift force FL are depending on the melt movement. The melt flow

parallel to the interface creates a lift force keeping the particle afloat, promoting particle pushing.

The magnus force FM is created, when the particle is rotating in the melt flow, creating a lift

Page 26: Particle Incorporation in Crystalline Silicon

18 2. Theoretical Aspects

perpendicular to the particle surface, that is moving towards the melt flow. This lift can be compared

to the lift, an airplane air foil creates, due to the velocity difference of the medium streaming along

the surfaces. Depending on the rotational direction, the Magnus force can create lift or downforce.

The particle’s behaviour can be predicted by the balance of all these different forces.

Figure 11: Shown is the force balance on a particle that is in front of the solid liquid interface. The interface is

moving with velocity VGr, the particle with velocity VP. Forces driving the particle towards the interface are

the drag force FD of the melt and the buoyant force FG (with l < P). Helping the particle staying afloat are:

the interface force FI, the lift force FL, and the Magnus force FM. FL and FM are depending on the melt flow

moving with Vref parallel to the S/L interface. The minimum distance between the particle and the solid is

referenced as dmin. describes the momentum boundary layer thickness. Redrawn after [74]

Detailed expressions for the force equations can be found for in [55, 60, 68, 70, 71, 75–80]. Possible

expressions for the calculation of the forces shown in figure are given in Friedrich et al. 2016 [74]:

The interface force after Chernov 1977 [71]:

𝐹𝐼 = 2𝜋𝑅𝑃∆𝛾0 (𝑎0

𝑎0 + 𝑑𝑚𝑖𝑛)

2 𝜅𝑃

𝜅𝐿 (8)

The drag force after Stefanescu et al. 1998 [75]

𝐹𝐷 = 6𝜋𝜇𝑉𝑃

𝑅𝑃2

𝑑𝑚𝑖𝑛(

𝜅𝑃

𝜅𝐿)

2

(9)

The buoyant force, assuming a spherical particle:

Page 27: Particle Incorporation in Crystalline Silicon

2. Theoretical Aspects 19

𝐹𝐺 =4

3𝜋𝑅𝑃

3𝑔(𝜌𝑃 − 𝜌𝐿) (10)

The Saffman force or lift force after Mukherjee et al. 2004 [79]:

𝐹𝐿 = 6.46𝜇𝑅𝑉𝑟𝑒𝑙𝑅𝑃2

√𝜌𝐿

𝜇(

𝑑𝑉𝐿𝑥

𝑑𝑦)

𝑎𝑣𝑔

(11)

With

𝑉𝑟𝑒𝑙 =𝑉𝑟𝑒𝑓

6𝛿2𝑅𝑝((𝛿 − 𝑑)3 + (2𝑅𝑃 − (𝛿 − 𝑑))

3) (12)

And

(𝑑𝑉𝐿𝑥

𝑑𝑦)

𝑎𝑣𝑔

=𝑉𝑟𝑒𝑓

2𝛿2𝑅𝑝((𝛿 − 𝑑)2 − (2𝑅𝑃 − (𝛿 − 𝑑))

2) (13)

The Magnus force can be approximated after Mukherjee at al. 2004 [79] and Chernov 1977 [71] as:

𝐹𝑀 =1

2𝜌𝐿𝜋𝑅𝑃

3𝑉𝑟𝑒𝑙 (𝑑𝑉𝐿𝑥

𝑑𝑦)

𝑎𝑣𝑔

(14)

Where 0 describes the surface energies, is the momentum boundary layer thickness, and µ the

dynamic viscosity of the liquid.

Steady state, as is often assumed in literature [60, 68, 75–77, 79, 80], is achieved by setting VP=Vc,

where Vc is the velocity at which a particle has equilibrium separation from the S/L interface at the

distance dmin:

𝐹𝐼 + 𝐹𝐿 + 𝐹𝑀 − 𝐹𝐷 − 𝐹𝐺 = 0 (15)

If

𝐹𝐼 + 𝐹𝐿 + 𝐹𝑀 − 𝐹𝐷 − 𝐹𝐺 > 0 (16)

The particle gets pushed.

If

𝐹𝐼 + 𝐹𝐿 + 𝐹𝑀 − 𝐹𝐷 − 𝐹𝐺 < 0 (17)

The particle gets incorporated.

Under microgravity conditions and without melt flow, the force balance is simplified to:

𝐹𝐼 − 𝐹𝐷 = 0 (18)

Using the expression above for interface force and drag force, Vc can be calculated after Stefanescu

et al. 1998 [75]

Page 28: Particle Incorporation in Crystalline Silicon

20 2. Theoretical Aspects

𝑉𝑐 =1

3

∆𝛾0

𝜇

𝜅𝑝

𝜅𝐿

(𝑎0

𝑎0 + 𝑑𝑚𝑖𝑛

)2

(𝑅𝑝

𝑑𝑚𝑖𝑛

)−1

(19)

If convection is present in a system, the momentum boundary layer thickness, Vrel and (𝑑𝑉𝐿𝑥

𝑑𝑦)

𝑎𝑣𝑔

must be determined or estimated, and with them FL and FM can be calculated.

2.5 Research Gaps

Present models of particle incorporation do not predict the incorporation of particles correctly. It

is not understood, where the limitations of the models do come from. In industrial processes,

particle incorporation can be avoided, but neither without technical challenges nor with a

scientific explanation. There is still little understanding, of how foreign phase particles behave in

the melt before and during incorporation into the advancing solid liquid interface.

Page 29: Particle Incorporation in Crystalline Silicon

3. Research Aim 21

3 Research Aim

The aim of the work presented here, is to study the incorporation behaviour of foreign phase

particles into growing silicon crystals. For the improvement of existing models it is crucial to

determine the critical growth velocity, at which a particle of given size is incorporated into the

growing crystal under given experimental conditions.

Parts of the experiments have to provide diffusive growth conditions, without gravity, since many of

the existing models, neglect melt movement and gravitational sedimentation of the particles. To

achieve microgravity conditions, the furnace Silicon carbide and silicon nitride particles of various

size were investigated at various growth rates. This includes a comparison between cases with

convection present in the system and cases with reduced or without convection.

As a base for the experiment of this work, light radiation heated mono-ellipsoid furnaces are used as

a small-scale model system for directional solidification of silicon. The use of a mirror furnace is

crucial, since the microgravity experiments related to this work, only provide about six minutes of

microgravity. During this limited time, directional solidification with a planar solid liquid interface is

impossible, due to the limited extraction of latent heat in this process.

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22 4. Materials and Methods

4 Materials and Methods

This chapter deals with the growth equipment, the preparations and the methods of

characterization. The furnaces for the growth in the laboratory and for the µg experiment will be

explained. The necessary preparations for the experiments and steps for the characterization is

briefly mentioned.

4.1 Description of Furnaces and External fields

The following paragraphs are dedicated to the furnace equipment used for the preparation of the

powders and the samples themselves. The furnaces for the growth experiments will also be briefly

introduced. For the preparation of the samples a double ellipsoid mirror furnace is used, the lab

experiments were carried out in a monoellipsoid furnace (ELLI). The third radiation furnace, the

TEXUS ELLI, is used for the µg experiments. A resistance heated tube furnace is used for powder

treatment and sessile drop experiments.

Mirror Heater Facility (MHF)

The mirror heater facility, or MHF for short, is a double ellipsoid mirror furnace with separate

translation and rotation axes for seed rod and feed rod (Figure 12). Powered by two 450 W

lightbulbs, it is capable of floating-zone growth of silicon crystals with diameters up to 12 mm. It has

been successfully used for the preparation and execution of former µg missions in the past [81, 82].

In this work, it served for closing in of the powder depots, wetting experiments, and float zone

growth of several samples.

During sample preparation, a desired amount of particle powder has to be introduced into the

sample rods. This is accomplished be filling it into a drilled hole and since a closed surface is needed,

melting the drill hole shut again. For closing the depot drill holes an asymmetric heat flux has to be

created by powering the two lightbulbs at different output levels. The lightbulb facing the drill hole

has to be driven at max. design power, the second one at variable but lower output levels, to support

the superficial melting of the drill hole, without actually melting the side of the sample vice versa of

the drill hole.

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4. Materials and Methods 23

Figure 12: MHF furnace on the right side for closing the powder filled drill hole under vacuum conditions. On

the left side, the control rack is shown, in the foreground an additional power supply is placed, for applying

an asymmetric heat influx on the sample inside the furnace.

ELLI

The ELLI furnace was main furnace for the experiments in the laboratory at the chair of

crystallography in Freiburg and the furnace for the experiments under strong static magnetic fields at

NASA, Marshall Space Flight Center, Huntsville, Alabama, USA. The ELLI furnace is an upright mono

ellipsoid mirror furnace, half axes 90 mm / 80 mm, powered by a single FEL 1000 W lightbulb in the

upper focus of the ellipsoid, and a translation/rotation axis holding an ampoule with the sample in

the lower focus (Figure 13). Since the light bulb and therefore the heat source is on the

translation/rotation axis of the sample, this furnace cannot be operated without an ampoule or

metal cage holding the sample due to its lack of “feed holder”. Without an ampoule/cage the upper

part of the sample will simply fall down after achieving melt through. In this work, the only setup

used was with fused silica ampoules as sample containers, so that the results are comparable to the

experiments in the TEXUS ELLI. Although not necessary for sample protection, the furnace always

was purged with argon flow during experiments, mainly to protect the furnace parts. Also in contrast

to the flight furnace, the lab ELLI is water cooled at the mirror half shells and more importantly at the

lamp housing. The water cooling enables long term experiments over several hours or days without

damage to the furnace and keeping its surface temperatures at a safe level.

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24 4. Materials and Methods

Figure 13: Monoellipsoid mirror furnace (FR-ELLI) with two-stage rotary vane pump, translation and rotation

motors and camera system. On the right part of the figure a graphical representation is shown [83]

TEXUS ELLI

The furnace used on the TEXUS 51 mission is geometrically identical to the laboratory ELLI. It is

powered by the same type of lightbulb and capable of comparable translation and rotation rates

(Figure 14). Additionally, it provides a rotating magnetic field with 5 mT induction, rotating at 50 Hz.

The rotating field stirs the melt and thereby improves the heat influx providing faster melt trough.

According to simulations carried out by the Fraunhofer IISB [84], the magnetic field, when used with

alternating rotation direction should be able to distribute the particle slug into a disc or cloud of

single particles before starting the growth experiment. It was therefore decided to apply the

magnetic stirring to the melt for 30s with alternating direction every 8 s. To give the melt enough

time to settle down again and ensure diffusive conditions during the µg-phase, the magnetic field

was switched off 30s before the translation was started. For the two campaigns, parameters

changeable by tele command were lamp power and start of the translation. All other parameters

were coded into the timer plan and ran automatically.

Page 33: Particle Incorporation in Crystalline Silicon

4. Materials and Methods 25

Figure 14: Part A: Airbus TEM02-3 ELLI furnace for the µg-experiments aboard the TEXUS 51 & 53 sounding

rocket missions. The furnace inside is geometrically identical to the Freiburg laboratory one and uses the

same OSRAM FEL1000 1 kW lightbulbs. Part B Technical drawing of the TEM02-3 module, inside the

aluminium outer shell of the payload structure. The drawing is kindly provided by Airbus Defence and Space

[85].

Sessile drop furnace

A Nabertherm resistance heating furnace was used for powder treatment and sessile drop

experiments. Pure silicon nitride is not wettable [30, 62] by silicon in the presence of oxygen in

furnace atmosphere. The material develops even stronger non-wetting behaviour if silicon oxinitride

is present. For this reason, the Si3N4 powders had to be heat treated to remove the oxinitride content

[86]. The furnace, shown in Figure 15 can deliver up to 1600°C homogeneously over appr. 20 cm

length of the tube. This is important for the wetting angle measurements, since temperature

gradients over the sample could deliver false results in the measurements. For the superheating of

the powders, the temperature profile in Figure 16 was applied. To limit the reoxidation of the

powder and to further purify the purge gas, metallic getters manufactured by SAES were introduced

to the furnace tube. These getters have a high capability to absorb O2, H2O, CO, CO2 and N2 by

chemical reaction under vacuum and low pressure at high temperatures [87].

Page 34: Particle Incorporation in Crystalline Silicon

26 4. Materials and Methods

Figure 15: Tube furnace used for removing the oxygen containing species in the silicon nitride powders for

improved wetting behaviour.

Figure 16: Temperature profiles used for wetting experiments (red graph) and for powder preparation (black

graph).

Page 35: Particle Incorporation in Crystalline Silicon

4. Materials and Methods 27

External field:

Strong static magnetic fields are known to have a dampening influence on melt convection [88–90].

Since there is no magnet available in Freiburg, the solenoid magnet situated there only provides half

a Tesla or 0.5 T and as mentioned in the publications before, stronger fields are needed. For this

reason and as a collaboration with NASA, the ELLI furnace was taken to NASA Marshall Space Flight

Center in Huntsville, Alabama. In their labs, a superconducting FeTi magnet is available, providing a

magnetic induction of up to 5 T. At such strong inductions, the stray field is considerable, therefore

the translation and rotation system of Freiburg could not be used. The substitute system provided by

NASA, sitting as far from the magnetic maximum as possible, could deliver comparable translation

rates to the TEXUS and Freiburg lab system. The rotation was limited to 8 rpm versus the standard

12 rpm used in the TEXUS and Freiburg ground experiments. Also in contrast to the TEXUS campaigns

and experiments in Freiburg, the lamp is not powered by DC current, but with high frequency AC

current. The reason is that DC current creates such a strong Lorentz force in these high magnetic

inductions, that the lamp filament would bend and move by the electrons moving in it. For the same

reason, the observation camera has to be also as far away from the centre of the magnetic field as

well. This is accomplished by a 1.2 m long borescope with 90° angle of view, attached to which is the

camera head, while the camera’s electronic box is attached via a 10 m long cable. A view on the

magnet and into its inner bore with the furnace inside is presented in Figure 17. For these

experiments, the furnace cannot contain any magnetic parts, why only brass, aluminium and silver

steel are used. The tools for mechanical works have to be made of beryllium bronze.

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28 4. Materials and Methods

Figure 17: In part A, the magnet is shown, the furnace is inserted from below on the black platform, here in

the „up“-position. Also below the magnet, the translation/rotation motors are mounted. Protruding from

the top, the borescope is visible. This 1.2 m long borescope with 90° sight angle is necessary to keep the

camera head as far away as possible from the magnetic field maximum. Image B shows the view from the

top down along the borescope into the inner bore of the magnet with the ELLI furnace inside.

4.2 Growth Experiments

4.2.1 Powders for the Growth Experiments

To study the behaviour of specific foreign phases in growth experiments, it is necessary to know the

type of phases, SiC or Si3N4, as well as the grainsize. The powders used in this work were provided by

the Fraunhofer IISB in Erlangen. The SiC particles were provided in grainsizes with mean values of

7 µm, 60 µm, 150 µm, and 300 µm. to ensure the chemical purity with respect to impurities, the

particles were obtained from Chemical Vapour Deposition reactors, used in the epitaxial growth of

SiC thin films for device application. They were characterized, sorted, and sized before they were

shipped to Freiburg for the growth experiments. The Si3N4 powder used in this work was also

supplied by Fraunhofer IISB, but this time it is a commercial product. Requirements for this powder

are chemical purity and most important low oxygen content. Denka corporation ltd. Provides a

powder called SN7, which is produced by direct nitridation of silicon and therefore sold as free from

oxygen [91]. The grainsize bought is 4 µm, but the powder is again sorted and sized to a grainsize

distribution which is sharper and more suited to the experimental needs. In this work, Si3N4 particles

with a d50 value of 9.6 µm are used.

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4. Materials and Methods 29

4.2.2 Sample and ampoule manufacturing

The experiments in this work were carried out with Silicon rods of 8 mm diameter and 90 mm length.

All samples were doped; one part of the samples with Boron, leading to p-type material with a

resistivity of 1 Ωcm, the other part of the samples were n-type material, doped with phosphorous to

a resistivity of 0.04 Ωcm. The p-type material is similar to silicon grown by the VGF or HEM process in

the solar industry, the n-type material on the other hand delivers would be the preferred type of

material when considering the limitations of Si:P in some areas of solar cell applications. One

limitation for example is the Boron-Oxygen complex which is formed [24] during the illumination of

the solar cell, reducing the number of free charge carriers and therefore cells/module performance.

N-type material, like Si:P does not show a efficiency diminishing complex forming process, but is

more difficult to produce. For instance, the segregation coefficient of phosphorous in Si according to

Trumbore is 0.35 [22], which will lead to an inhomogeneous distribution of dopant and therefore

resistivity over the height of the grown silicon ingot. This behaviour, while complicating the industrial

application of n-type material, will give much stronger striations in the floating-zone grown crystals

on the laboratory scale, therefore characterization is much easier. The electronic grade silicon

material used in this work was bought from Andrea Holm Silizium Bearbeitung (84367 Tann) and

machined to the specified sample geometry mentioned above. These rods were prepared by

introducing the desired amount of foreign phase particles into a central hole, closing the particles in

by covering the hole with silicon melt and crystallizing it in the MHF, where the temperature can be

delivered asymmetrically. For sample fixation, small holes at both ends of the crystal are necessary,

providing fixture points to hold the crystal in place. Depending on the experimental parameters, an

oxide skin was applied to the crystal surface, to supress Marangoni convection. The cleaning and

etching agents are summarized in Table 4 The steps for sample manufacture, including cleaning

steps, are summarized in Table 5.

Page 38: Particle Incorporation in Crystalline Silicon

30 4. Materials and Methods

Table 4: Cleaning and etching agents used in this work.

Application Composition Time & condition Reference

Cleaning solution

RCA1

7 parts H2O 18 MΩ

2 parts H2O2 30%

1 part NH4OH 25%

10 min @ 80°C [92]

Cleaning solution

RCA2

7 parts H2O 18 MΩ

2 parts H2O2 30%

1 part HCl 37%

10 min @ 80°C [92]

Polishing etch

3 parts HF 48%

5 parts HNO3 65%

3 parts CH3COOH 99%

Max. 60s, manual

agitation [93]

Wright-Jenkins etch

2 parts HF 48%

1 part HNO3 65%

1 part 5M CrO3 solution

2 parts CH3COOH 99%

2 parts 0.007M Cu(NO3)2 solution

10-20min, continuous

stirring [37]

Page 39: Particle Incorporation in Crystalline Silicon

4. Materials and Methods 31

Table 5: Description of steps for sample manufacture

Step Comment

1. Drill holes 2 mm diameter for particle depot, 1.2 mm for holding pins

2. Cleaning Cleaning in RCA1 and RCA2 for 10 minutes at 80°C respectively

3. Filling with powder

Insert chosen amount of powder in centred, 2 mm diameter

drill hole, choose suitable piece of silicon as “plug” to

compensate material loss during drilling

4. Closing in MHF Created melt cap over drill hole at approximately 10-6 mbar

5. For oxidation

5.1. Remove melt tip

5.2. Clean in RCA1&2

5.3. Polish etching to remove upmost surface layer

5.4. Create 5-6 µm thick oxide skin

6. Ampoule manufacturing Enclose in ampoule

Page 40: Particle Incorporation in Crystalline Silicon

32 4. Materials and Methods

To use this type of sample in the ELLI mono-ellipsoid furnace an ampoule of fused silica is necessary.

The ampoule serves two purposes, one is to hold the rod in the furnace, since the type of furnace

does not have separate holders for seed and feed crystal for technical reasons. The second purpose

of the ampoules is to provide the desired gas atmosphere around the crystal. It is possible to use

gases like oxygen, without destroying the furnace during the experiments. Furthermore, this closed

atmosphere prevents the crystal from being contaminated by furnace parts releasing vaporized

contaminants. In the case of sample material which was originally grown by the Czochralski-

technique, the gas atmosphere also prevents the solved oxygen content in the sample from

evaporating in large quantities. For this purpose, argon gas at 1.5 bar at room temperature is

enclosed in ampoule with samples with a free melt surface, and oxygen for ampoule containing

samples with an oxide skin on the surface. Over time the oxide skin would be dissolved by the silicon

melt and/or evaporate. A behaviour that can be sufficiently supressed by an oxygen gas pressure of

1.5 bar at room temperature. With an oxygen gas atmosphere, the oxide skin stays intact for the

time of the experiments, which for the longest tests was almost four hours. To achieve this gas

atmosphere in a fused silica ampoule, which have to be closed below ambient pressure, the amount

of gas for the desired pressure in the finished ampoule has to be frozen out at liquid nitrogen

temperature. This means that the ampoule is partially submerged in LN2 while being molten shut by

an oxyhydrogen gas flame (Figure 18).

Figure 18: An ampoule is closed by an oxyhydrogen gas flame, while the gas atmosphere inside the ampoule

is liquefied by partially submerging the ampoule in LN2.

Two types of ampoule designs were utilized in this work. The first type, a simple design for the

laboratory furnace, consists of an outer hull, in which the crystal is held in place by fused silica spacer

rings, fixed with aluminium oxide pins and a cup-shaped foot with a shaft (Figure 19). By this shaft,

the ampoule can be fixed to the furnace translation and rotation shaft via an adapter. This adapter

allows the centring of the ampoule, so that the crystal’s longitudinal axis runs parallel to the

translation and rotation axis of the furnace.

Page 41: Particle Incorporation in Crystalline Silicon

4. Materials and Methods 33

Figure 19: Photograph of an in-house ampoule for the lab experiments in Freiburg. The silver-grey sample is

held in place by the two fused silica rings at its ends, which in turn are fixed to the sample rod by Al2O3 pins.

In the middle of the sample rod, the recrystallized spot over the drill hole containing the introduced particles

is visible.

The second type of ampoule was used during the TEXUS 51 & 53 sounding rocket missions and their

1g reference experiments. This design, although more complex than the in-house type, is more

rugged and mounted to the furnace by a different adapter. This adapter is a stainless-steel holder,

which allows the centring of the ampoule’s foot by means of centring screws, working in a similar

way as the in-house adapter. After the ampoule is centred in the holder, it is glued in by a ceramic

cement. When this cement is hardened, the centring screws are removed. These steps are necessary,

because during the start of the rocket the ampoule experiences acceleration forces of up to 13g. If

the ampoule would only be held by the centring screws, their small contact surfaces would induce

enough force to break the foot, releasing the ampoule atmosphere and or, in a worst case scenario,

loss of the ampoule due to breakage. To manufacture these ampoules, more steps are necessary

than for the in-house type. The longer and heavier foot of this design has to be fused to the hull tube

without losing the axial symmetry of the ampoule, leading to an interleaved intermediate step. After

fusing the foot to the outer hull, and subsequently sawing off the remaining outer hull, the ampoule

is reconnected to the vacuum system, flushed with purge gas and the desired atmosphere is frozen

out. The finished ampoule is then ready to be inserted and cemented into the stainless steel adapter.

The process steps are shown in Figure 20, the flight ready ampoule with holder in Figure 21.

Page 42: Particle Incorporation in Crystalline Silicon

34 4. Materials and Methods

Figure 20: Necessary construction steps for ampoules used on TEXUS missions. A: the Ampoules outer hull is

filled wit the sample crystal and the ampoule’s later foot with fused silica hull attached, which is necessary

for coupling to the vacuum system. B: The outer hull was molten on the ampoule foot and the excess tube

cut away. This part is then attched to the vacuum system and after evacuation to roughly 10-5mbar, and

purged with gaseous oxygen. After evacuating the purge gas, the ampoule is filled with an oxygen amount,

that is frozen out by LN2 andclosed in by melting the ampoule shut. C: The finished ampoule, with an oxygen

pressure of 1.5 bar at room temperature. The photograph below shows the real ampoules at stage A.

Figure 21: Photograph of an ampoule for TEXUS sounding rocket experiment. The ampoules manufactured in

Freiburg are glued into stainless steel holders for fixing them into the ELLI furnace.

4.2.3 Sample Preparation

After the growth experiments, the ampoules were opened, and the crystals cut into slides parallel to

the growth direction. After this, the slides were polished. One slide was polished on both sides for

infrared transmission microscopy, the second slide was polished for defect etching by Wright-Jenkins

etch. This etch reveals the crystals defect structure, such as grain boundaries, facets, etch pits from

dislocations and striations from uneven dopant [37].

The mechanical preparations necessary to prepare the samples for analysis are shortening the seed

and feed rod parts either by inner diameter saw (ID-saw, Capco model Q-35) or diamond coated

circular saw, the same saw that is also used to open the fused silica ampoules. The shortened

Page 43: Particle Incorporation in Crystalline Silicon

4. Materials and Methods 35

samples are mounted via hot wax (Deiberit 502) to a ceramic holder with a V-shaped groove. With

three parallel cuts with the ID-saw, the samples are dissected into four longitudinal slices. The two

inner slices with 2 mm-2.5 mm thickness are the most important ones, the two outer slices, being

more half-cylinder shaped are only analysed in case when the particle slug was not found in the main

slices. The two main slices are then visually inspected to locate the particle slug part(s). Based on the

slug’s location, the slug majority containing slice is double sided polished, the other slice one is

polished for etching and striation analysis.

The polishing is carried out using a Bühler Vector Powerhead polishing and grinding machine, the

polishing head and the polishing disc having the same rotation direction. The head is rotating with

30 rpm, the disc with 100 rpm. After each step, the samples are cleaned twice for 15 min in an

ultrasonic bath. The saw grooves are removed by grinding the samples on a MD-Piano 500 disc, for

up to 2 min. Fine grinding is done by 9 µm diamond paste suspended in water on the hard, textured

polishing cloth DP-Pan, both by Struers, for up to 10 min. Pre-polish and fine polish is achieved by

polishing with 3 µm and 1 µm DP-paste on DP-Mol cloth for 15 min each. For the double-sided polish

of one slice, this process is now repeated for the second surface, the slice intended for striation

analysis is further polished by a mechanochemical step using Struers OP-U suspension mixed with

deionised and filtered water and sodium hypochloride solution with a mixture of 25:23:2 parts each.

Struers OP-Chem is the used cloth for this step, a neoprene like cloth with no structured surface. The

slightly alkaline solution oxidizes the sample surface, and the oxide created is removed by the

0.25 nm small silica colloidal spheres of the OP-U suspension. This etch polish removes the upmost

lattice planes, damaged by the diamond polish process, ideally leaving a scratch free perfectly

smooth surface. In this work, a scratch free surface, although desired, was not strictly necessary and

could not be achieved in most cases, since the introduced particles with their grain sizes between

2 µm and 300 µm and extreme hardness of 9 on the Mohs hardness scale for silicon nitride and 9.5

for silicon carbide. If a particle gets loosened by the polishing, it leaves a scratch on the sample.

Depending on the polishing step, at which the particle is loosened, it is much larger than the diamond

particles used, and therefore the scratch left by it is also much larger. This means that the scratch

won’t be completely removed by the subsequent polishing procedure and it remains on the surface.

After the polishing process, the samples are cleaned from the Deiberit by a xylene bath. The xylene is

rinsed away by methanol and afterwards by isopropyl alcohol. Before the residual oxide from the last

polishing step is removed by diluted HF, the samples are cleaned once again in RCA1. Diluted HF and

RCA1 are not necessary for the samples that are double sided polished, since they do not receive the

final polishing step, and the Deiberit is sufficiently removed by the organic solvents.

4.2.4 Timer Plan and Power Profile Extrapolated from TEXUS 12, 22,

and 27

Ground experiments and microgravity experiments, in contrast to the experiments in the laboratory

are very limited in their duration. The time for these experiments is dictated by the actual µg phase,

which in case of TEXUS missions is roughly 6 minutes. The actual time can only be calculated to a

certain degree, because several parameters like payload weight, rocket motor performance, winds

etc. determine the flight of the rocket and its payload. For this reason, an experiment profile is

defined, that ensures the most use of µg – phase for the actual growth experiment. Every possible

parameter is included in the missions’ timer plan, so that everything happens precisely at the right

Page 44: Particle Incorporation in Crystalline Silicon

36 4. Materials and Methods

moment. Some of the parameters, like lamp power output can be overridden by tele command from

the ground facilities, others like rotation rate cannot, and are hardcoded into the timer. For TEXUS 51

and 53, lamp power and start of translation were the only parameters that could be influenced by

the ground crew. The power profile, for example consists of a 4 min preheat phase with no melting

of the sample, before the lift-off, for which the light bulb it turned off again since it would not survive

the start, melt through phase where power is applied in excess for a fast establishment of a stable

zone, followed by a ramp, reducing power to a stable amount, where the zone is kept at constant

height and a plateau phase where the power is held constant until the end of the experiment. A

more comprehensive list of the parameters according to the timer plan is given in Table 6.

To carry out the sounding rocket experiments, an automated experiment procedure is established

during preparation and ground reference experiments. This experiment profile serves two purposes.

On the one hand, it assures the comparability between the experiments, and on the other hand it

provides a set of growth parameters by which the experiment can be successful even if the payload

loses radio contact with the ground station. If the contact to the payload is lost, there is no possibility

for tele commands by the scientists, and therefore automation is crucial. During ground experiments,

the power usually is kept constant until the end of the experiment after a certain point. The

experiment, in this case the zone height stays stable with this constant influx of heat. Under

microgravity, where cooling by convection of the furnace atmosphere and the gas atmosphere inside

the ampoule is missing, the zone gets steadily higher with a constant power output from the lamp.

The lamp itself also burns brighter, and therefore hotter under microgravity, since its halogen circle,

also driven by convection and temperature gradients, is weaker. By analysing the TEXUS 12, 22, and

27 µg experiment power profiles, where the power was reduced by tele command, a second ramp is

defined to prevent the excess heat build-up in the zone and hereby keeping the experiment more

stable. The power curves including the preheating phase for 1g and µg experiments is shown in

Figure 22.

Page 45: Particle Incorporation in Crystalline Silicon

4. Materials and Methods 37

Table 6: Events per timer plan for the TEXUS53 ground and µg-experiments.

1g reference experiment µg experiment

Time [s] Power/event Translation/Rotation Power/event Translation/Rotation

-260 500W 0/0 500W 0/0

-10 0W 0/0 0W 0/0

0 Lift – off

(software) Lift – off (software) Lift – off (VSB-30) Lift – off (VSB-30)

65 830W 0/12 830W 0/12

110 Magn. stirring

on Magn. stirring on Magn. stirring on Magn. stirring on

120 Reducing

2.1W/s 0/12 Reducing 2.4W/s 0/12

140 Magn. stirring

off Magn. stirring off Magn. stirring off Magn. stirring off

160 746 2/12 734 2/12

230 Power const.

600W 2/12

600W Reducing

0.2W/s 2/12

280 600W 5/12 590W 5/12

400 600W 10/12 566W 10/12

440 0W 0/12 0W 0/12

490 0W 0/0 0W 0/0

500 Experiment off

Page 46: Particle Incorporation in Crystalline Silicon

38 4. Materials and Methods

Figure 22: Timelines for TEXUS 51 and 53. For clarity every parameter except lamp power output was

removed.

For both campaigns the furnace setup, ampoule design, and growth parameters were the same, with

the only difference in lamp power. The lamp power of TEXUS 53 differs in absolute numbers from

TEXUS 51, since a new lightbulb has to be inserted for each campaign, and they suffer from a batch-

to-batch variation, each power profile has to be adjusted accordingly.

4.3 Characterization

4.3.1 Circular Polarized Differential Interference Contrast Microscopy

- CDIC

The main means of characterization in this work is the optical light microscopy with circular polarized

differential interference contrast (CDIC). Due to this contrast mechanism, sub-micron height

differences of the polished and etched sample surface become visible [94]. CDIC reveals the

striations created by the uneven temperature field of the furnace, imprinted into the sample by

rotating during translation. From the rotation frequency and the distance between two adjacent

striations, the growth rate between the two striations can be calculated:

𝑉𝑔𝑟 = ∆𝑑/∆𝑡 (20)

With the distance d between the striations and t the duration of one full rotation

Errors will ensue due to misreading the striations and therefore an error in measuring the distance

between them. This error is estimated to be around 5 %. Another source of error is created by

uncertainties in the rotation rate. If the rotation rate varies or is off the set pace, then the time

between the striations varies also, leading to mistakes in the calculation of Vgr. Assuming an error of

5 % on the time constant, the error on the calculated Vgr, according to Gaussian error propagation

calculates as follows

∆𝑉

𝑉= √(

∆𝑠

𝑠)

2

+ (∆𝑡

𝑡)

2

(21)

Page 47: Particle Incorporation in Crystalline Silicon

4. Materials and Methods 39

With the uncertainties mentioned before, the error on the calculated Vgr is 7.1 %.

4.3.2 Infrared Transmission Microscopy - IRTM

On double sided polished samples, infrared transmission microscopy was carried out by Fraunhofer

IISB. Since silicon is transmitting IR light, the incorporated particles, precipitations and inclusions can

be localized, since those defects do not transmit IR and therefore appear as dark/black contrasts in

the micrograph. This method is successfully used for this purpose by several research groups and on

industrial scale [5, 95].

Once a particle or particle slug is located, its position can be transferred to the CDIC image and the

incorporation velocity for its size can be determined. For the positions, the centre of gravity (COG) is

estimated and used.

4.3.3 Video Analysis

To conduct the experiments and, for example, control the height of the zone, the sample is observed

by an optical system with an attached video camera, providing a life image and the possibility to

record the growth experiment. Afterwards, the zone height during the experiment and the growth

rate can be determined from these video frames. One caveat remaining, is the limited spatial

resolution of the videos systems, since all cameras used only provide PAL signals with 720*576 pixels

and low magnifications (Figure 23). To determine the growth rate of the crystal from the video file,

the stream is divided into frames with a known time interval, ideally in sync with the crystal’s

rotation rate, delivering a standing image concerning surface features. By measuring the distance of

a feature on the crystal surface and the lower phase boundary in two consecutive frames, a X is

obtained, which divided by the time between the frames provides the average growth velocity

between those frames. The microscopic growth velocity cannot be determined this way. It is also

worth mentioning that the margin of error is also higher for the growth rate calculated from the

video files, due to the lack of spatial resolution and uncertainties in the time constant. Also,

geometrical distortion by the optical system are possible and lead to a measurement error of the

distance grown between frames. This method is only chosen to evaluate the growth velocity, when

the striations are too weak to interpret or absent all together.

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40 4. Materials and Methods

Figure 23: Video frame taken during a growth experiment. The live images are necessary to adjust the power

output accordingly to the growing crystal's behaviour. After the experiment, the images from the video file

provide a way to evaluate the zone height and growth rate where striations are too weak for evaluation or

absent altogether. The time constant is obtained by the videos frame rate and number of frames between

two frames taken for evaluation. The red arrows indicate the upper and lower phase boundary, the bright

space between them is the oxide skin covered zone.

4.3.4 Synchrotron X-ray topography - SXRT

To investigate the influence of a foreign phase in front of the phase boundary, backscatter

synchrotron X-ray topographs were made of specific samples. The method reveals defects in the

crystal lattice by the strain field they produce resulting in brighter or darker contrasts on an X-ray

sensitive film or CCD-Camera. The topographs were taken at the ANKA lightsource at KIT Karlsruhe.

For background on the technique it is referred to the literature. [96–98].

Page 49: Particle Incorporation in Crystalline Silicon

5. Results 41

5 Results

5.1 Growth Experiments

5.1.1 Terrestrial Experiments

SiC:

Multiple experiments were carried out under 1g conditions with variations in pulling rate, particle

size, and net weight of particles introduced to the crystal. The experiments are summarized in Table

7, where also the grown length of crystal and the position at which the slug was finally incorporated

is listed.

Table 7: Overview of the SiC experiments under 1g conditions. Parameters varied are pulling rate, particle

size, and slug mass. Also listed are the transported distance of the slug and the total length of grown crystal.

The values for the transported distances listed in red are taken from the DIC image. This was necessary in

cases where no slug or part thereof was found in the IR-image.

Sample-ID Pos. (IR-COG)

[mm]

Grown length

[mm]

Pulling rate

[mm/min]

Slug mass

[mg]

Particle

size [µm] External field

1

41,0 29,0 2 4 7 none

2

25,3 27,1 0,2 4 7 none

3

15,2/13,5 15,4 2, 5, 10 6 7 & 60 None/0T

4

12,4 18,6 2, 5, 10 6 7 & 60 1T, axial, static

5

12,9 16,0 2, 5, 10 6 7 & 60 3T, axial, static

6

8,5 17,9 2, 5, 10 6 7 & 60 4.5T, axial,

static

7

19,6 19,9 2, 5, 10 6 7 & 60 5T, axial, static

8

34,6 26,9 6 4 7 none

9

18,5 17,5 6 4 7 none

10

15,8 19,3 8 4 7 none

11

25,3 19,8 7 4 7 none

12

0 15,2 2, 5, 10 4 7 none

13

0 15,5 2, 5, 10 4 60 none

14

0 15,6 2, 5, 10 2 60 none

15

0 8,9 2, 5 2 150 none

16

0 9,1 2 2 300 none

Page 50: Particle Incorporation in Crystalline Silicon

42 5. Results

As the table shows, the samples can be grouped as follows:

Slow pulling rates, large slug mass, (1, 2, 15, 16)

Fast pulling rates, large slug mass (8, 9, 10, 11)

Transition from slow to fast pulling rates, very large slug mass, increasing dampening

external magnetic field (3, 4, 5, 6, 7)

Transition from slow to fast pulling rates, low slug mass (12, 13, 14)

Slow pulling rates, large slug mass, large particle diameters (15, 16)

In Figure 24, samples 1-16 are shown by their respective IR-map. In these maps, the particle slugs can

be located by their black contrast. The mappings of samples 2, 4, 5, 6, and 7 also show dark contrasts

from precipitations. Samples 3 and 8 are also presented with their DIC-mapping, the reason is that

the IR-map of sample 3 shows an additional slug part, which is also much larger than the part of the

IR-map. As for sample 8, the slug does not appear in the IR map at all, it is found in the polished and

etched slice. The observation for the incorporation behaviour shows that in samples 1, 7, 8, 9, and 11

the slug is travelled further or equally far than the lower phase boundary of the sample. This is

indicating, that the slug was not in contact with the phase boundary during the growth and was only

incorporated, when the last melt zone was solidified. In the samples 2, 3, 4, 5, 6, and 10 the particle

slug was clearly transported for a certain distance before being incorporated, but in the samples 3, 6,

and 7 there are one (in sample 3) or two (samples 6 and 7) parts of the slug, which were

incorporated at an earlier point of the growth. It is apparent that if there are one or two parts of the

slug that were separated and incorporated differently, the parts are always much smaller than the

part that was transported furthest. For samples 3 through 7, a static axial magnetic field was applied

with increasing induction values up to 5T. This type of external magnetic field creates an increasing

dampening effect on the melt movement and albeit not completely suppressing melt movement,

severely slowing it. The only melt fraction still moving, is located at the very outer rim of the sample,

but only due to Marangoni convection if a free melt surface is present [99], which does not apply in

the experiments presented here. A clear influence of reduced melt convection on the incorporation

behaviour cannot be observed.

A difference in incorporation behaviour is observed in samples 12 through 16. In all of these samples,

the slug is located at the first lower phase boundary. In contrast to samples 1 – 11, the slugs of 12,

13, and 14 contained only 2mg of particles and for sample 13 the powder was introduced by three

small 1.2 mm diameter holes, instead of one 2 mm diameter hole. Samples 15 and 16 contained 4 mg

of particles, but the mean particle diameter was 150 µm and 300 µm, respectively.

Page 51: Particle Incorporation in Crystalline Silicon

5. Results 43

Figure 24: This figure shows a comparative array of the IR-mappings of samples 1-16, with the slug

recognizable as black contrasts, as well as dark shadows of precipitations of SiC. Samples 3, 7 and 8 are also

shown with their respective DIC- mappings.

In those cases, where the particle slug was sliced open during the sawing of the sample or was lying

close enough to the sample surface that it was exposed by the grinding and polishing process, an

enlarged overview of the slug is presented in Figure 25. The slug is exposed in this way in samples 3,

8, 11, and 12. The overviews show the shape and the size of the slugs at their point of incorporation.

In sample 3, the slug was incorporated shortly before the end of the experiment at the very outer

skin of the crystal, whereas the slugs in samples 8 and 11 are found at the last upper phase

boundary, in the uppermost parts of the last melt zone. In contrast to the three other samples, the

slug of sample 12 is located directly at the first lower phase boundary, being instantly incorporated

when the translation was started and the crystal began to grow. When comparing the four slugs, it is

recognizable that the transported ones (sample 3, 8, and 11) are hardly infiltrated with silicon and

that they contain voids. For samples 3 and 11 the voids are large and a loss of powder during the

sawing and or polishing and etching process must be assumed. While sample 3 maintained a more

stable ridge in the centre of the slug, which is partially infiltrated by silicon, samples 8 and 11

apparently possess a mechanically more stable ring of powder, also non-uniformly infiltrated by

silicon, visible by the variation in brightness and colour in the ring. As for sample 12, the powder

appears generally in a darker shade compared to the other three slugs and no voids or ring structures

Page 52: Particle Incorporation in Crystalline Silicon

44 5. Results

are observable. Furthermore, sample 12 is composed by smaller, more distributed patches of

particles.

Figure 25: The figure shows enlarged views on the slugs at their point of incorporation for samples 3, 8, 11,

and 12. While samples 3, 8, and 11 contained a large quantity of powder (6mg powder in sample 3 and 4mg

powder in 8 and 11) and were transported during the growth, sample 12 with only 2 mg of powder was

incorporated at the first lower phase boundary. The slugs of samples 3, 8, and 11 appear to have large voids,

where powder was removed during etching or polishing. Also, especially visible for 8 and 11, the slug

appears to consist of a mechanically more stable rim of powder outlining the shape of the slug and lose

powder in the centre. The silicon melt infiltrates the powder only partially, which can be seen by the central

ridge in the slug of sample 3, and by the brighter area in the rim of the slug in sample 11. For the slug of

sample 12, judged by its colour, it appears more infiltrated by the silicon melt than the other three slugs and

it also appeasr to have less voids than the other three slugs.

A visual comparison of the transported distance versus the grown length of the crystal is presented in

Figure 26. For samples 1, 8, 9, and 11 it is clearly visible that the slug is transported further than the

crystal is grown, indicated by the distance between the slug and the last lower phase boundary.

Sample 7 presents an extreme case, where the difference between the grown length and the

incorporation position is less than half a millimetre. The position of the slug is defined by the centre

of gravity of the contrast in IR-mapping and for this slug, the height of the contrast is approximately

4mm. From the DIC image in Figure 24 the last lower phase boundary in the slug’s vicinity is not

visible, since the slug is incorporated in the fine grained polycrystalline part of the image.

Furthermore, the phase boundary, while generally concave, bends upwards into the dark lamellae of

the polycrystalline growth in the centre of the slice. Due to this bending, the phase boundary is not

observable at the slug’s side of the DIC-image. The slug position is taken from the IR-image, which

leads to the uncertainty in this case.

If only the behaviour of the slug is concerned, three groups of behaviour are observed:

1. Transported and incorporated after a certain grown length

2. Transported, but not incorporated in the grown part of the crystal, but somewhere in the

rapidly solidified last melt zone

3. Not transported at all

Samples 2 through 6 and sample 10 fall into group one. In group two, the samples 1, 7, 8, 9, and 11

are sorted and the samples 12 through 16 are assigned to group three. Generally, any sort of

transport is observed, for slow, fast or multiple pulling rates in samples that contain a large or very

Page 53: Particle Incorporation in Crystalline Silicon

5. Results 45

large amount of powder. Further the grainsize of the powder must be either 7 µm or a mixture of

7 µm and 60 µm SiC crystals, but in any case representing small sizes. For small amounts of powder,

in these cases 2 mg or less, no transport and a higher amount of silicon infiltrated into the slug is

observed (Figure 25 sample 12). Also, no transport can be observed, if the grain size is 150 µm or 300

µm independent of the slug’s net weight. From sample 16’s IR mapping in Figure 24, it is also

apparent that the slug is collapsing more into single particles compared to the other samples.

Figure 26: The figure shows the transport behaviour of the slugs compared to the grown length of crystal. If

the capture position of the slug (red bar) is above the length of grown crystal (black bar), the slug is captured

in the last rapidly solidified zone, rather than being incorporated by the moving solid liquid interface. This is

the case for samples 1, 8, 9, 11, and arguably for sample 7. Samples, where the slug was transported and

then captured by the solid liquid interface are 2 through 6 and 10, whereas in samples 12 through 16 no

transport is observed at all. In addition to the red and black bars, a blue bar is shown, indicating the mass of

the slug in question. The figure shows that transport is only observed for slug masses of 4 mg and 6 mg

regardless of the pulling rates and that for small net weights of 2 mg no transport takes place. Also, no

transport can be observed if the grain size used is 150 µm or 300 µm despite the mass being 4 mg, where

transport was observed for lower grain sizes.

The findings can be summarized as follows:

Particle slugs do not distribute for sizes below 150 µm

Some slugs were not infiltrated by the melt

Parts of the slugs are separated and incorporated at different positions and at different

growth velocities, but no clear dependence on either was found

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46 5. Results

Si3N4:

Under 1g conditions, multiple experiments were carried out with a variety of parameters. The

studied parameters were pulling velocity, particle slug size, and particle size. For the experiments,

the power output of the light bulb and the rotations per minute were kept fixed to not disturb the

growth velocity of the crystal. The findings and the experimental parameters are summarized in

Table 8.

Table 8: Overview of samples and exp. Parameters. The position of incorporation is acquired by finding the

centre of gravity in the IR transmission image, the capture velocity from the striations analysis at the

obtained position. The values in red had to be taken from the DIC micrograph since there was no slug found

in the IR-map.

Sample-ID Pos. (IR-COG) [mm] Pulling rate [mm/min] Slug mass [mg] Capture velocity

[mm/min]

17

11.6 3 2 3.0

18

8.8 3 2 2.9

19

7.5 3 2 2.9

20

8.0 5 2 4.7

21

7.1 5 2 4.5

22

14.5 5 2 5.1

23

5.2 7 2 5.8

24

6.8 7 2 6.3

25

7.2 7 2 6.3

26

11.1 3 2 3.4

27

8.3 3 2 2.9

28

9.3 3 2 3.0

29

1.2 3 4 2.4

30

7.4 3 4 3.0

31

7.1 3 4 2.9

32

9.1 3 6 3.0

33

9.7 3 6 3.0

34

7.1 3 6 2.9

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5. Results 47

For all the samples mentioned in Table 8 the evaluation is carried out in the same way. Since these

experiments were carried out in series of threes with the same set of parameters, Figure 27shows

representatively the samples 17 (A), 18 (B), and 19 (C) as a comparison. All three samples show a

similar and homogeneous striations pattern, from which the growth velocity of the respective crystal

is evaluated. The first lower phase boundaries started in a pronounced convex shape and the

striations grow wider apart as the crystals grow, while at the same time the growth front flattens to a

less convex shape. The last lower phase boundaries, almost flat, is located at roughly the same length

of grown crystal. Also, the height of the last zone is comparable, with the limitation that for 17 the

upper half of the last zone was separated when the crystal was cooling down after the growth

experiment. In part A, the slug introduced in 17 is recognizable as a black contrast at which the V-

shaped twin grains, characteristic for samples with incorporated particles, emerge. Although in part B

and C the slugs are not sliced as in part A, the same twinning behaviour is observed and the slugs’

location can clearly be correlated by comparing the tips of the twins to the black contrast in the IR-

transmission micrographs in Figure 28. From the twinning and the slice slug at the surface, it is

apparent that the position of incorporation varies in the three samples from the same series.

Figure 27: DIC micrographs of samples 17 (A), 18 (B), and 19 (C) grown with the same experimental

conditions. All three samples exhibit a very similar striation pattern, indicating comparable growth velocities,

length of grown crystal, and height of the remaining zone at the end of the experiment, not visible for 17,

since the upper half of the zone broke off while the crystal was cooling down in the furnace. Although only

sliced and lying at the surface of sample 17, the slugs can be located for all samples by the characteristic

twinning, confirmed by the black contrasts in the IR-transmission micrographs.

From the IR transmission micrographs, the capture position of the particle slug is taken. Figure 28

shows the IR-maps of the same series of samples (IDs 17, 18, and 19) as presented in the figure

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48 5. Results

above. In all three IR-maps the seed crystal can be recognized at the very left side by its slightly

darker grey value with a convex transition to the grown crystal. The particle slugs appear as black

shades in the map, the black contrast on the right part of the crystal in part B is caused by cracks in

the bulk of the crystal. The crack planes provide surfaces at which total reflection and refraction

processes of the passing light result in light being lost for the camera. Despite the fact that the net

weight of the powder introduced into the crystal was roughly the same, the area of the shadow

created by the slug is very unequal. Further apparent from the distribution of dark contrasts is the

fact that precipitations only occur in the last liquid zone, upon solidification at the end of the

experiment.

Figure 28: IR-map comparison of three experiments with roughly the same amount of the same type of

powder grown at the same pulling rate. The images shown are from samples 17 (A), 18 (B) and 19 (C). From

centre of gravity of the shadow created by the particle slug the position of incorporation is determined. It is

apparent that despite of the growth parameters being the same for each sample shown, the incorporation

position varies strongly. Also apparent is that the slug of sample 18 in part B is much more intact than the

parts of the slug found in sample 17 and 19. The black shadow in the upper half of the last zone in 18 is

created by cracks in the sample, leading to total reflection and refraction of the light passing through the

sample. This light then never reaches the camera and the black contrast is created. The ringed artefacts in A

and B are newton interference rings from a silicon wafer used placed on top of the sample to reduce

overexposure at the sample edges.

The following diagram (Figure 29) shows the growth velocity at a given point of the crystal length,

measured from the striation pattern versus the grown length of the crystal. In this figure, samples are

plotted from Table 8, of which the net weight of introduced powder is the same, namely about 2 mg,

processed at different pulling velocities. The points where the particle slugs were engulfed is marked

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5. Results 49

by arrows in the diagram, so that the position along the grown crystal body can be read out. The

green box marks the combined initial positions of the particle slugs at the beginning of the growth.

Slugs being incorporated outside this green box is thus being transported before its incorporation

into the growing crystal.

Figure 29: The diagram shows the growth velocity of the crystals over the length of grown crystal. The

positions at which the particle slugs were captured by the moving solid liquid interface are marked by arrows

in the respective colours. The growth velocities for each pulling speed, 3 mm/min, 5 mm/min and 7 mm/min

are comparable between experiments at given pulling rate. The position of the slug strongly varies over the

grown crystal length, despite the growth velocity roughly being the same within each series of experiments.

For a clearer view of the dataset, the capture positions and their respective incorporation velocities

are plotted against the average growth rates of each series of experiments (Figure 30). The slug

positions are plotted in black, the average position and incorporation velocities are potted in red. The

one black value on the outmost right position of the 5 mm/min series is treated as an outlier for the

calculation of the averaged data points. Considering the averaged data points a trend of further

transported slugs with lower growth rates emerges.

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50 5. Results

Figure 30: Shown are the averaged and smoothened growth rates from evaluating the striations of the grown

crystals in dashed lines. The black squares show the capture velocity and travelled distance for each slug in

the respective experiment. Plotted in red squares are the averaged capture velocities and travelled

distances, while the black square on the outmost right position of the 5 mm/min growth experiment is

treated as an outlier. The red squares show a trend in decreasing travelled distance with increased growth

velocity.

The experimental findings of the series to study the influence of particle slug mass on the

incorporation behaviour is presented in Figure 31. The type of powder, namely SN7 with a d50 value

of 9.6 µm grain size, was the same for each set of three experiments. The parameter changed was

the net weight of the particles. Slug masses of 2 mg, 4 mg, and 6 mg of silicon nitride powder were

introduced in a set of three experiments each with the exception that six experiments were carried

out for 2 mg net weight. For the pulling rate 3 mm/min was chosen, the rotation rate was kept at

12 rotations per minute. The individual values for capture velocity and transported distance is

plotted in standing square symbols, the averaged values are plotted as open circles in the respective

colour. Apparent from the distribution of the averaged data points is that the ranking of transport

distance from lowest to highest is: 4 mg slug mass, 6 mg slug mass and 2 mg slug mass with the

furthest transport.

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5. Results 51

Figure 31: The figure shows how slugs of particles with the same grain size of powder, but different net

weights, behave under the same experimental parameters. The standing square symbols mark the individual

data points, indicating a wide spread of capture positions at roughly the same capture velocity. The open

circle symbols mark the positions of the averaged capture positions and capture velocities. It is apparent that

the 2 mg slug are transported furthest, the 4 mg slugs the shortest and the 6 mg slugs occupy an

intermediate positon, however the capture velocity remains roughly the same.

For the series of experiments listed in Table 8 the process parameters, especially the lamp power,

were kept constant. The parameter varied, from the process point of view, is only the pulling rate.

The intension behind this was to avoid sharp transitions in the growth velocity which could prevent

or promote the incorporation of the particle slugs. For comparison, the power profile was the same

for all the experiments, which is a compromise. The profile was chosen to enable the fastest pulling

rates, without the lower and upper phase boundaries to come in contact with each other. Since

faster pulling rates require more heater power for faster melting of the feed material at higher

pulling rates, this higher output is in excess for lower pulling rates resulting in higher zone heights as

shown in Figure 32. The figure shows the development of the zone height over time. Shown are the

graphs beginning with 20 s remaining of the preheating phase, followed by the three-minute-long

phase when the melt zone is established. At 200 s the translation is started with the respective

pulling rates and the power kept constant throughout the entire process. The average zone height at

the start of the translation is 13.8 mm, increasing to its maximum values at the end of the growth

process. For 7 mm/min pulling rate, the zone reaches a maximum value of 17.4 mm, for 5 mm/min

the maximum is 18.3 mm, and for the slowest pulling rate of 3 mm/min the zone reaches the highest

value of 20.5 mm. As a result of the translation pulling for a total length of 20 mm in each

experiment, the experiments have different durations. The drop to zero mm zone height occurs

therefore at different times in the Figure 32. It is apparent that not only the duration of the

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52 5. Results

experiments varies, but also the final zone height even for experiments with the same

duration/pulling speed. There is a 3 mm spread in the final zone heights for the series with

3 mm/min pulling speed.

Figure 32: Plotted in this figure are the developments of the zone height for the individual experiments.

Indicated by the black arrows are the highest zone heights at the start of the experiment and the highest

zone heights at the end of the experiments. Except of the pulling rates of 3 mm/min, 5 mm/min, and

7 mm/min, all other experimental parameters were the same for each experiment. The zone height at the

start of the translation was between 12.5 mm and 14.2 mm (indicated in the graphic). The highest zone

heights were reached at the end of each experiment. In order, the final zone heights were 17.4 mm (pulling

rate 7 mm/min), 18.3 mm (pulling rate 5 mm/min), and 20.5 mm (pulling rate 3 mm/min). Indicated in the

figure are the highest zones heights for each series. Since the translation was active until a distance of 20 mm

was reached, the three pulling rates result in different experiment durations.

Summary of the findings from the silicon nitride experiment series:

For slugs with the same net weight, a trend towards further transport is found, the lower the

pulling and growth rates are chosen

With higher pulling/growth velocities, incorporation is observed earlier

For the three net weights of 2 mg, 4 mg, and 6 mg, the ranking of transported distance is

4 mg, 6 mg, then 2 mg with the furthest transport

Infiltration of silicon into the bulk of the slug was not observed

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5. Results 53

5.1.2 µg Experiments

This part will show the results from the two sounding rocket campaigns, TEXUS 51 and TEXUS 53. In

both campaigns the growth parameters were chosen so that comparability between campaigns is as

high as possible.

TEXUS 51:

For the TEXUS 51 campaign, samples with a mixture of 7 µm and 60 µm SiC particles were prepared

as described in chapter 4.2.2 and processed as described in chapter 4.2.4. While the 1g reference

sample was processed with the automated profile, the power was increased manually at T = +280 s

by 10 W during the µg experiment. By analysing the zone height under µg conditions from the video

recorded during the flight it can be found, that the height at the start of the translation was 12.0mm

and it fluctuated during the growth to a minimum of 10.5 mm and to a maximum at the very end of

the experiment of 12.9 mm (Figure 33). This tells that the phase boundaries during the experiment

were not in contact, since the zone height never went below the diameter of the growing crystal.

Figure 33: Development of the zone height during the TEXUS 51 mission. The mission was carried out with

only one interference of the ground crew and otherwise ran by the preprogrammed flight pofie shown

chapter 4.2.4. The zone height fluctuates between 10.5 mm at the lowest and 12.9 mm at the highest point.

The zone height indicates that during the experiment the upper and lower phase boundary were not in

contact.

The 1g reference sample is shown in Figure 34. Shown are the DIC micrograph of the polished and

etched sample (A), the polished, but not etched backside of the same sample (B) and the IR

transmission micrograph (C). The growth direction of the crystal is from left to right. The DIC

micrograph shows symmetric upper and lower phase boundaries and strong striations on the edge of

the sample, but weaker striations in the centre. In the grown section of the crystal the characteristic

twin grain boundaries associated with particle incorporation are visible. The slightly concave last

lower phase boundary is located roughly 4 mm above the tip of the twin on the upper half of the

crystal. Recognizable as a bright, wavy, U-shaped line is the contact line, where the last upper and

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54 5. Results

lower phase boundaries grew together after the experiment was finished. The last upper phase

boundary is strongly convex. The polished but not etched backside of the sample is shown in part B,

since the particle slug was not present in either image of part A or part C. The transported distance in

this case is obtained by measuring the distance of the slug’s centre of gravity to the first lower phase

boundary in this part of the sample instead of the IR-map. Part C of the figure shows the IR-

transmission micrograph. Clearly visible is the seed part of the crystal by its darker grey shade,

compared to the rest of the crystal, the dark rectangular area is a higher resolution overlay of the

sample at there. This area was suspected to contain parts of the slug or parts thereof, but nothing

can be located here. The contact between the last lower and upper phase boundaries is recognizable

by its darker shade in U-shape. In this case the contrast appears broad, since in this kind of image, a

3D structure in the sample is projected in 2D. In both images the slug is not localized.

Figure 34: TEXUS 51 1g reference. Part A shows the DIC image of the sample, with a clear striation pattern

and V-shaped traces of twin grain boundaries. The last lower phase boundary is found to be concave, while

the last upper phase boundary is strongly convex shaped. The particle slug is found in part B, the polished,

not etched backside of the sample shown in part A. The IR-transmission micrograph (part C) shows the seed

area as a darker contrast with a convex interface towards the grown crystal. The darker rectangular shape is

a higher resolution map of the area where the particle slug or parts thereof were suspected, but not found.

No precipitations or single particles are found either.

The prepared sample from the µg-experiment is presented in Figure 35 A and B, again with growth

direction from left to right. Clearly visible are the strong striations following the shape of the first

convex phase boundary at the interface of seed and grown crystal. In the centre, the striations are

less pronounced than at the crystal edges, they flatten to a less convex shape during the growth and

the distance between them increases as the growth velocity increases. The slug of particles is

recognizable as a round shape with dark grey patches in the centre of the sample. Starting from the

slug, the formation of twins is visible by the V-shaped lines originating at bottom of the slug. Above

Page 63: Particle Incorporation in Crystalline Silicon

5. Results 55

the slug, the crystal grew polycrystalline. As also seen in the 1g reference sample, the last lower

phase boundary is concave. It almost touches the bright line where the last upper and lower phase

boundaries met when the zone solidified at the end of the experiment. From the IR-transmission

micrograph

The findings of the DIC micrograph are confirmed. The particle slug is found as a round black contrast

in the centre of the sample. The seed is visible by its darker shade of grey. Also recognized by a dark

shade of grey is the contact layer where the last upper and lower phase boundary met upon

solidification. No precipitations can be located; neither are parts of the slug or single particles visible

in the mapping.

Figure 35: This figure shows the DIC image (part A) and the IR-transmission micrograph (part B) of the

TEXUS 51 µg sample. The DIC image shows the striations created by the rotation of the sample during the

experiment, the particle slug in the middle of the rod, and V-shaped grain boundaries originating at the slug.

In the IR-transmission micrograph the seed is clearly distinguishable from the grown crystal as well as the

strongly curved contact line where the last upper and lower phase boundary met after the experiment was

switched of. In both micrographs, the slug is recognizable as a circular shadow and intact. It appears as if it

was cut perpendicular to its longitudinal axis.

By analysing the striation patterns from the 1g reference and the µg sample, the actual growth rate

can be determined. The growth rate is determined at the edges of the crystals and are plotted in

Figure 36. The green arrow notes the initial position of the slug; the red arrow show the positions at

which the slug or parts of it were located and the capture velocity can be read out at the given point.

The point of origin for the slug in the 1g reference is at 4.4 mm and the end position is determined as

10.5 mm with a capture velocity of 3.5 mm/min. Under microgravity, the slug was transported from

its original position at 3.2 mm for 1.4 mm, and was incorporated at 4.6mm with a growth velocity of

2.2 mm/min.

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56 5. Results

Figure 36: In this figure, the growth velocities from the striations evaluation of the TEXUS 51 1g reference

sample (A) and the µg sample (B) are shown. The green arrows mark the starting position of the slugs and

the red arrow(s) mark the position where the slug was incorporated. The slug parts were incorporated in the

1g reference at 10.5 mm @ 3.5 mm/min. In the µg sample the slug was moved for 1.4 mm and incorporated

at 4.6 mm @ 2.2 mm/min).

TEXUS 53

For the TEXUS 53 campaign, samples with Si3N4 particles were prepared as described chapter 4.2.2,

and processed as described in chapter 4.2.4. In contrast to the TEXUS 51 experiment, only one

particle size was introduced into the samples, in this case the d50 value of the powder is 9.6 µm. Both

samples, the 1g reference and the µg-sample were grown by the automated profile shown in chapter

4.2.4, no interference from the experimenters was necessary. By analysing the zone height under µg

conditions from the video recorded during the flight it can be found that the height at the start of the

translation was 10.5 mm and it fluctuated during the growth between a minimum of 10.5 mm and a

maximum at the end of the experiment of 11.1 mm (Figure 37). Since the zone height never went

below the diameter of the growing crystal, the phase boundaries during the experiment were not in

contact.

Page 65: Particle Incorporation in Crystalline Silicon

5. Results 57

Figure 37: Development of the zone height during the TEXUS 53 mission. The mission was carried out without

interference of the ground crew, and ran by the preprogrammed flight pofile shown chapter 4.2.4. The zone

height fluctuates between 10.5 mm at the lowest and 11.1 mm at the highest point. The zone height

indicates that during the experiment the upper and lower phase boundary were not in contact.

The prepared 1g reference sample is shown in Figure 38 A and B, the growth direction is from left to

right. The DIC micrograph in part A of the figure shows the seed on the left with a convex first lower

phase boundary. The seed appears bright because of its surface roughness; the grown part of the

crystal is visible in a darker grey. The striation pattern is weak but visible at the edge of the crystal. At

the lower edge of the sample, halfway through the grown part, the slug is located as a dark half-

moon shaped contrast. From this contrast, parallel lines indicate polycrystalline growth. The last

lower phase boundary is visible as a concave line approximately 6 mm above the incorporated slug.

Above the last lower phase boundary, polycrystalline structures appear where the zone solidified

rapidly at the end of the experiment. In part B, the IR- transmission micrograph shows the particle

slug as a black contrast located very close to the edge of the sample, its original cylindrical shape is

still recognizable. 3 mm above the slug precipitations appear from the edge of the crystal at the

oxide skin covering the sample, also at this point, the pulling velocity was increased from 5 mm/min

to 10 mm/min. The density of the precipitations oscillates six times, visible by the brighter horizons in

the otherwise homogeneous area. The last brighter horizon coincides with the last lower phase

boundary and upon the rapid solidification of the last melt, the lower half of the zone is veined with

precipitations.

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58 5. Results

Figure 38: This figure shows the DIC image (part A) and the IR-transmission micrograph (part B) of the

TEXUS 53 1g sample. The DIC image shows the striation created by the rotation of the sample during the

experiment, the particle slug in the middle of the rod, and V-shaped grain boundaries originating at the slug.

In both micrographs the slug is recognizable as dark contrast at the lower edge of the crystal. Although the

slug appears block like, it is no more cylinder shaped. In the IR-transmission micrograph there are also dark

curtain shaped contrasts, which relate to precipitations of Si3N4.

The crystal grown under microgravity is presented in Figure 39. Part A shows the DIC image of the

sample, part B shows the IR-transmission micrograph. From the DIC image it is apparent that the µg

sample exhibits more pronounced striations than its 1g reference. The slug of particles is located in

the centre of the rod 5.8 mm above the first lower phase boundary. In this case the slug appears ring

shaped and is filled with silicon. From the location where the slug is incorporated, V-shaped twinning

is evident. Once twin growth started, the crystal grew polycrystalline from there on. 7.4 mm above

the upper edge of the particle slug, the last lower phase boundary can be found, it appears as a

concave transition from medium grey to a brighter shade. By looking at the IR-transmission

micrograph, it is also apparent that the slug is incorporated in the centre of the sample. The next

apparent feature in the image are the grey contrasts from the precipitations, starting approximately

2 mm to the right of the captured slug. The density of these precipitates is oscillating as it was in the

1g reference sample. These oscillations also match the striation pattern in frequency and distance.

This oscillatory behaviour stops, where the last lower phase boundary is. The last zone solidified

much faster, than the grown crystal but less controlled. In both cases, the 1g reference and the µg-

sample, most of the precipitations in the last zone appear in the lower half, and just a few ore none

are observed above the contact line where the last lower and last upper phase boundaries met.

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5. Results 59

Figure 39: This figure shows DIC image (part A) and the IR-transmission micrograph (part B) of the TEXUS 53

µg sample. The DIC image shows the striations created by the rotation of the sample during the experiment,

the particle slug in the middle of the rod, and V-shaped grain boundaries originating at the slug. In the IR-

transmission, micrograph the seed is clearly distinguishable from the grown crystal by its darker grey shade.

On the right side of the incorporated slug, curtain shaped contrasts created by precipitations are visible. In

both micrographs, the slug is recognizable as a dark shadow.

By analysing the striation patterns from the 1g reference and the µg sample, the actual growth rate

can be determined. The growth rate is determined at the edges of the crystals and is plotted in

Figure 40 A and B. The green arrow notes the initial position of the slug as obtained from the video

frames; the red arrow shows the positions at which the slug is located in the micrographs. The

capture velocity can be read out at that given point. The point of origin for the slug in the 1g

reference is at 4.3 mm and the end position is determined at 7 mm with a capture velocity of

3.9 mm/min. Under microgravity the slug was transported from its original position at 3.4 mm for

3.0 mm, and was incorporated at 6.4 mm with a growth velocity of 4.3 mm/min.

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60 5. Results

Figure 40: In this figure, the growth velocities from the striations evaluation of the TEXUS 53 1g reference

sample (A) and the µg sample (B) are shown. The green arrows mark the starting position of the slugs and

the red arrow marks the position where the slug was incorporated. The slugs were incorporated in the 1g

reference at 7.0 mm grown length at a VGr of 3.9 mm/min. In the µg-sample the slug was moved for 3.0 mm

and incorporated at 6.4 mm grown length at a VGr of 4.3 mm/min.

The findings from the TEXUS campaigns is summarised in Table 9. It is found that SiC is incorporated

earlier and with lower growth rates under microgravity than it is under normal gravity conditions.

Silicon nitride on the other hand is transported equally far and incorporated at roughly the same

growth velocity.

Table 9: Summary of the results obtained from the two TEXUS campaigns

Particle species 1g [X & VGr] µg [X & VGr]

SiC 6.1 mm & 3.5 mm/min 1.2 mm & 2.2 mm/min

Si3N4 2.7 mm & 3.9 mm/min 3.0 mm & 4.3 mm/min

SXRT:

The two µg samples of TEXUS 51 & 53 were taken to the ANKA light source at KIT in Karlsruhe for X-

ray topographic investigations. Series of topographs were taken on Slavic VRPM holographic film,

mapping the crystals from the seed to the part where the particle slug was incorporated. From those

films, the 008 reflection was digitized and stitched as a composite in Figure 41 A and B.

In part A, showing the TEXUS 51 µg sample, the seed crystal is visible as the brightest contrast at the

lower part of the image. The seed shows a dense network of dislocations causing the bright

appearance. The grown part of the crystal above the seed appears less bright with fewer dislocations,

until the slug was incorporated. Related to this incorporation, twins are formed, that appear as a

darker V-shape. The darkest part of the topography is created by the slug itself, and a columnar

shape in growth direction above the slug. This column appears dark, since the silicon grown inside it

is rotated with regard to the rest of the crystal, indicated by the bright triangular shade appearing on

the outside of the main reflection topograph. In the topography of the TEXUS 53 µg sample (part B),

the brightest contrast is again the seed crystal with its dense network of dislocations. During this

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5. Results 61

experiment, the dislocation density decreased drastically until the crystal is virtually dislocation free.

At the point where the slug was incorporated, the contrast created by the slug coincides very well

with the slug’s appearance in the DIC-micrograph. Both are superimposable, the contrasts inside the

slug also match the pattern in the DIC-image. From the slug, whose outline is very pronounced by a

bright rim, V-shaped twins are recognizable by their darker than average grey shade. These twins are,

like those in the TEXUS 51 µg-crystal, lamellated themselves. Neither topograph provides any

evidence, of an interaction between the transported slug and the phase boundary pushing the slug in

front of it.

Figure 41: This figure shows the 008 reflection topographs of the TEXUS 51 µg sample (A) and the

TEXUS 53 µg sample (B). In both topographs the seed (green arrow) appears bright due to its high density of

dislocations, with a convex phase boundary to the grown crystal above. The grown crystal appears less

bright, since its dislocation density is lower than that of the seed, single dislocations lines are visible (orange

arrows). Also in both cases, the slug is recognizable as a dark contrast, appearing it the same shape, as in the

DIC micrographs (red arrows). From the incorporated slug, twins are formed. Inside the twined areas

lamellae structures are recognizable (yellow arrows). The TEXUS 51 sample in part A shows a column of

almost no diffracted intensity above the slug. From these areas, parts of the topograph are scattered away

from the main reflection. The bright triangular shape (blue arrow) is scattered there from its original position

(blue dashed arrow) due to a higher rotation of the crystallite. The TEXUS 53 sample shows a lower degree of

dislocation density than the TEXUS 51 sample, there are regions below the slug that are almost dislocation

free (black arrows). Neither topograph provides any evidence that an interaction between the transported

slug and the pushing phase boundary occurred.

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62 5. Results

5.2 Additional results

5.2.1 Distribution Experiments

In these experiments the time dependency of the slug decomposition was studied. The aim was to

find a way to get the particle slug to distribute into the melt zone. For this reason, silicon powder was

mixed with the SiC-particles, to promote easier infiltration of the powder, by reducing the capillary

path length. The silicon used was in one case powder from a powder-XRD standard and in the other

case it was freshly pestled solar silicon material. Both mixtures were then used in experiments,

where there was no translation or rotation applied. In these experiments, a stable melt zone was

established and held for up to 150 min. During the experiment, the zone was naturally mixed by

Marangoni and natural buoyancy convection. The resulting crystal was then cut, polished, and

inspected by IR-transmission microscopy and DIC microscopy. Figure 42 shows the result of

experiment ZL1. The XRD silicon powders grain size is several tens of microns. In part A of the figure,

the black contrast of the slug is found at the lower phase boundary at the bottom of the zone,

looking circular/cylindrical, like the original drill hole in which it was introduced. Part B presents the

DIC micrograph of the slug at the sample surface. The shape in both images coincides, and the DIC

image shows also that the SiC powder was indeed infiltrated by the silicon melt, but no distribution is

observed. A similar situation can be observed in sample ZL2 in Figure 43. The experimental setup

used here is the same as for ZL1, except for the silicon used for mixing the powder originated form

solar silicon, and the powder was freshly pestled under argon flow before it was immediately

enclosed in the sample under vacuum conditions. After the experiment and sample preparation it

can be observed that the slug stayed in its original shape. In Figure 42 A, the slug can be located as a

black circular contrast at the lower phase boundary, the DIC image of the slug is presented in Figure

43 B. Like in sample ZL1, the slug in ZL2 stayed cylinder shaped and as in ZL1 the original shape of the

silicon powder introduced to the mixture is still visible. These silicon pieces are sharp edged, block

like structures and it is clearly visible, that the SiC powder did not drift into the melt created by them.

The SiC powder can be located around these blocks and although the shape of the former silicon

chunks appears unchanged, the powder is infiltrated by silicon melt and no cavities of gas inclusions

or dry powder can be recognized. In both cases, ZL1 & 2, the slug is located to at the lowest part of

the lower phase boundary, and no indications of floating behaviour or distribution are observed.

Additional information can be found in [100]

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5. Results 63

Figure 42: Presented here is sample ZL1 7 µm SiC mixed with XRD standard silicon powder after 150 min of

melting time. Neither the IR transmission micrograph (A) nor the DIC mapping of the slug area (B) shows a

tendency of the powder to distribute into the melt. The slug, being infiltrated with silicon, sunk down to the

lower phase boundary, despite the mixing of the zone driven by Marangoni and buoyancy convection.

Figure 43: Shown is sample ZL2 7 µm SiC mixed with freshly pestled solar silicon powder after 150 min

melting time. The IR-transmission micrographs (A) show the slug at the bottom of the zone at the lower

phase boundary. Part B shows the DIC micrograph of the slug itself, the powder though infiltrated with

silicon melt, shows no indication of particle distribution into the melt. The former chunks of silicon are still

visible without any particles indicating movement into the former chunks’ space. The slug is completely

infiltrated with silicon and it is located at the lower phase boundary at the bottom of the zone.

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64 5. Results

5.2.2 Infiltration and Wetting Behaviour Experiments

Due to the non-wetting behaviour of Si3N4 in the presence of oxygen, technical approaches to

improve wetting behaviour were researched. The nitride powder used is a commercially available

Si3N4 powder manufactured by DENKA, its product name is SN7. The powder is created by direct

nitridation of silicon and should therefore be free of oxygen species. The original d50 value of the

grainsize is 4 µm [91], but the powders are further sized by the Fraunhofer IISB to a d50 value of

9.6 µm. A typical grain is shown in Figure 44.

Figure 44: This figure shows a SEM picture of the habitus of the SN7 particles. [91]

A powder diffractogram of Denka SN7 silicon nitride powder is presented in Figure 45. The standard

powder is composed of 80.4 Vol% alpha silicon nitride, 19.1 Vol% beta silicon nitride, and 0.4 Vol% of

elemental silicon.

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5. Results 65

Figure 45: Diffractogram of standard SN7 Powder. The sample consists of the alpha- and beta-silicon nitride

phase (red and green, as well as a third, elemental silicon phase (orange).

In a silicon sessile drop experiment with standard SN7 powder as substrate material non-wetting

behaviour is observed. During the heat-up phase, where the silicon is molten, a droplet with contact

angels of around 100° is formed as shown in Figure 46. The given temperature range is the heater

temperature from 1450°C to 1500°C, which is linearly increased over a duration of 40 minutes.

Extended details on the temperature ranges and the sample preparation can be found in [101] After

32 minutes, a stable droplet is achieved, showing that silicon melt is not wetting the SN7 powder.

Over the duration of 60 minutes at 1500°C heater temperature, the droplet slowly decreases its

contact angles until it shows wetting behaviour. After 49 minutes of melt in contact with the powder,

the melt starts to infiltrate and seep into the substrate (Figure 47). The development of the left and

right contact angle over time is presented in Figure 48. The figure shows the wetting behaviour of the

melt at a heater temperature of 1500°C, which translates to a sample temperature of 1456°C [45].

The system behaves stable over 12 minutes, before the contact angels start to decrease rapidly. The

spiking increase of contact angle at minute 13 is caused by the separation of the droplet into two

individuals, before both droplets infiltrate the powder. At the end of the experiment the contact

angle is only 6 degrees, showing complete wetting of the remaining melt on SN7 infiltrated with

silicon.

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66 5. Results

Figure 46: Wetting behaviour of a piece of silicon of slightly compacted SN7 powder. The images shown are

taken during the heating phase in the sessile drop furnace. The target temperature for these experiments is

1500°C, measured at the furnace heaters. At a heater temperature of 1454°C the silicon starts to form melt.

As more and more melt is created, a droplet of Si is formed (minute 32, at 1489°C heater temperature),

showing non-wetting behaviour with contact angles of around 102°.

Page 75: Particle Incorporation in Crystalline Silicon

5. Results 67

Figure 47: Sessile drop behaviour of standard SN7 powder. The piece of silicon forms a stable droplet during

heat-up and during the holding time of 60 min at 1500°C, it shows a transition of non-wetting to wetting

behaviour. At minute 52, after 49 minutes of melt present in the system, the wetting angles decrease this

time point, it starts to seep into the substrate until all melt is starting to infiltrated the substrate indicated by

the rapid shrinking of the droplet. Over the course of an hour, almost all melt is seeped into the powder.

Page 76: Particle Incorporation in Crystalline Silicon

68 5. Results

Figure 48: Development of contact angles of standard SN7 powder over time. The spiking increase at mintue

13 is caused by the droplet forming two smaller individual droplets before beeing seeped into the powder.

Superheated SN7 powder:

To change the non-wetting behaviour of SN7 powder to wetting behaviour, the powder was

superheated in the presence of getters. The getters were used to capture any free or created oxygen

during the experiment. After the superheating process the powder was investigated by powder-XRD

again and the obtained diffractogram is presented in Figure 49. It can be observed that the volume

fraction of alpha silicon nitride is reduced from 80.5 Vol% to 45.3 Vol%, the beta phase increased its

volume fraction from 19.1 Vol% to 32.2 Vol% and the fraction of elemental silicon was increased

from 0.4 Vol% to 22.5 Vol%.

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5. Results 69

Figure 49: Powder diffractogram of SN7 powder after superheating treatment. Compared with the original

powder, the same phases are detected, but the volume fraction of each species has changed. Alpha silicon

nitride is present with 45.3 Vol%, beta silicon nitride with 32.2 Vol% and elemental silicon amounts

22.5 Vol% of the powder. This shows a decrease in alpha phase and an increase in beta phase and free silicon

compared to the original powder. Furthermore, there is no indication of an oxide bearing species in the

diffractogram.

Because of the heat treatment in reducing conditions, the wetting behaviour of the powder has

changed as can be seen in Figure 50. The images capture during the melting phase of the sessile drop

experiment show that the edgy shape of the silicon piece just gets smoothed during melting and the

melt formed is directly absorbed by the porous substrate. The surrounding substrate doesn’t change

visually, while it is infiltrated by the silicon melt.

Page 78: Particle Incorporation in Crystalline Silicon

70 5. Results

Figure 50: Sessile drop behaviour of silicon on superheated SN7 powder. As soon as melt is present, it

infiltrates the substrate without forming a droplet at all, indicating wetting behaviour.

5.2.3 Experiments With a Model Melt System

Works carried out in the scope of the master thesis of Nadine Pfändler.

For a better understanding of particle interactions with a solid liquid interface, a model system using

a transparent melt was used. Using a double ellispoid mirror furnace with an optical camera system

for in situ observation of particle movement in the melt, the crystallization front moving, and

observing the melt flow by following particle tracers suspended in the melt. As a model substance for

the silicon melt sodium nitrate was chosen. Both substances are comparable in density. The density

of silicon is 2.33 g/cm³ [16], the density of NaNO3 2.26 g/cm³ [102]. The low melting point of sodium

nitrate of 308°C [102] makes it easy to handle, and although the melt is transparent and heated by

light, it is possible to couple in enough heat to melt the substance, keep it molten, and influence the

phase boundary by varying the power output.

To ensure the comparability, wetting experiments using a lightly pressed slab of SN7 powder was

used as a substrate in a wetting experiment using the Nabertherm sessile drop furnace. During the

experiment, the created portion of melt on the surface of the sodium nitrate chunk is directly seeped

into the substrate slab Figure 51). This behaviour is further observed, when a chunk of particles is

placed on the sodium nitrate in the crucible before melting. When the melt is formed, the particles

start to distribute in the liquid (Figure 52), although if not immediately wetted, after a few seconds to

minutes, the melt infiltrates a chunk of particles on its surface, leading to a spontaneous entry of the

powder into the melt. Further details can be found in [103]

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5. Results 71

Figure 51: Starting (left) and end image (right) of sodium nitrate during wetting behaviour investigation. It is

visible that no droplet is formed upon melting of the sodium nitrate chunk, showing immediate wetting and

infiltration behaviour.

Figure 52: A larger chunk of silicon nitride powder on the surface of the melt is spontaneously wetted and

enters the melt in a shower of single particles.

Once the system is in a stable equilibrium state, the particles start to act as tracers for the melt

convection roles (Figure 53). In contrast to silicon melt, which is not transparent for light, and

therefore heated on the surface in a mirror furnace, sodium nitrate is heated in the centre of the

crucible. The consequence is that in this case buoyancy convection roles travel upwards in the centre

and downwards at the crucible walls. In silicon it is the other way around. In this system, there is also

a strong convection role system present driven by Marangoni convection. Normally, one would

assume that the Marangoni driven roles, with the thermal maximum in the centre of the crucible,

would run in the opposite direction of the buoyancy roles. This is not the case here since the upper

edges of the crucible walls are indeed hotter than the centre of the melt at the surface. The reason

being a carbon absorber lid on the crucible, which is necessary to flatten the phase boundary the

spreading heat to the wall of the crucible. Without this lid, the thermal focus in the middle of the

melt would lead to a severe concave phase boundary. Once stable convective conditions are

established, four prominent features are distinguishable:

1 mm

Page 80: Particle Incorporation in Crystalline Silicon

72 5. Results

1.) One main buoyancy driven torus in the centre of the crucible

2.) Four surface near Marangoni convection roles, each occupying one quadrant of the melt surface

region

3.) A very weak torus in the tip of the crucible, also moving upwards in the centre and downwards at

the walls

4.) A layer of stagnant melt without apparent movement separating the tip and central buoyancy

tori.

Those convection roles and their direction of movement is pictured in Figure 54 .

Figure 53: Particles suspended in the melt act as tracers for the convection role system present in the

crucible.

Figure 54: Overview of the present convection roles in the crucible: 1.) Central buoyancy torus; 2.)

Marangoni convection driven tori; 3.) Buoyancy convection roles in conical tip; 4.) A convection stagnancy

layer between 1.) and 3.). The red arrows mark the contact point of the melt surface and the crucible.

1 mm

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5. Results 73

5.2.4 Simulations of Melt Movement in Various Zone Heights

The simulations were carried out by Dr. Jan Zähringer, using the software package Ansys fluent R17.2

academic. The temperature parameters were tweaked so that the resulting zone matches the

experimentally observed zones in height and phase boundary shape. The simulations are steady state

simulations in 2D. Presented in Figure 55, are six calculated zones with their shape in the top row,

the temperature field creating the zone in the middle row and the resulting velocity field in the

bottom row. It is visible that the fastest melt is present in the highest zone, the lowest velocity in the

smallest zone. This is explained by the fact that in these cases the only driving factor of melt

movement is the density gradient created by the temperature field and gravity accelerating the

cooler liquid parts downwards. The velocity field shows that for all zone heights the melt moves in a

torus with the melt moving up at the outer walls and accelerating down in the middle of the zone.

The velocity differences result in the different lengths along which the melt can be accelerated by

gravity, the longer the path, in higher zones, the faster the melt moves. The fastest melt is moving

with 0.345 cm/s in the highest zone and with 0.149 cm/s in the smallest zone.

Figure 55: Shown are 2D simulations of the zones observed in the experiment series using Si3N4 powder, to

understand the development of the melt velocity and its vector field, smaller zones are added for

comparison. The top row shows the shape and height of the zone where red represents liquid silicon, the

middle row shows the temperature field for the respective zone, and the bottom row shows the velocity of

the melt, with red indicating stagnation and blue representing the fastest melt movement. The velocities are

zero at the phase boundaries and at the outer walls of the zones due to the SiO2 skin applied here. Since the

only driving factor for the melt is gravity, higher zones provide a larger acceleration path, resulting in higher

melt velocities, the general shape of the melt movement, stays the same over the series of zones. The melt

always moves as one big torus, with the fastest velocities in the centre of the zone, moving downwards. The

range of velocities is between 0.149 cm/s to a maximum of 0.345 cm/s in the highest zone.

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74 5. Results

.

Page 83: Particle Incorporation in Crystalline Silicon

6. Discussion 75

6 Discussion

6.1 Growth Experiments

6.1.1 Terrestrial Experiments

As presented in the results section, the behaviour of slugs made of SiC particles looks quite erratic.

When looked at in groups instead of individual samples, some trend like behaviour can be found

nevertheless. It is clear that if grouped by their mass and grain size, the results can qualitatively be

linked together. The larger the net weight of fine grained powder in the original slug was, the

stronger the tendency of being transported arises. With and without external field slugs of 4mg or

more move. In contrast, when the same mass of powder of a larger grain size is introduced the slug

sinks to the bottom of the zone and is incorporated immediately without any transport at all. Also, if

the mass of the slug is large enough, its transport cannot be prevented even if convection dampening

external fields are applied. For the strongest external field with the strongest dampening effect on

the melt, the slug was among the one that were transported the furthest. This is a counterintuitive

behaviour, since the density of SiC is around 20 % higher than that of molten silicon. For a slug to be

transported, this either means that the solid liquid interface, the lower phase boundary, pushed it

along until the growth velocity was too high and the slug was captured. If this was the case, a

tendency of slug size and mass versus its capture velocity would arise, but this is not the case.

Furthermore, besides the lack of trend in their behaviour, a coupled mass/size versus growth velocity

behaviour would not explain how slugs can end up at the last upper phase boundary. Reaching the

upper phase boundary, the ceiling, so to speak, would require a floating behaviour. If no other

movement would be present in the zone, a slug less dense than the melt would float. To reach this

state it is sufficient to have a slug with a porosity of 20 % or higher. While the slugs are closed in

under high vacuum conditions at pressures of around 10-5 mbar or less and SiC is wetted by liquid

silicon, the slugs should be infiltrated by silicon, which they not always are. When compared to the

results of chapter 5.2.1, infiltrated slugs do behave as expected and sink to the bottom of the zone.

This is also observed for small slug mass of small grain sizes like sample 12, and for large slug masses

with large grain sizes namely samples 15 and 16. For large masses with small grain sizes infiltration

seems to be hindered, as indicated by samples 3, 8, and 11. A similar behaviour is reported for

example by Yang and Xi 1995 [104], where it is analytically proven that even substances with good

wetting capabilities, cannot infiltrate densely packed spheres or rods, when the wetting angle is

lower than the necessary tangent angle to wet the surface of the sphere or rod package. Besides the

physical capability to infiltrate a slug, the silicon might need time to fully seep into the powder.

Additionally, if there is a layer of natural oxide on the powder, the wetting behaviour changes and

the silicon needs time to dissolve this natural oxide before wetting a particle. To erode this by

dissolution, it also needs to be transported away, which in the capillary space is mainly achieved

through diffusion, which again, needs time. During the short, only several minutes long experiments

of this work, time to infiltrate might not be sufficient. This can be argued in face of the slug of

samples 3, 8, and 11, where it is evident that at least partially silicon infiltrated as either a rim around

the outer perimeter of the slug (sample 11) and maybe along fissures in the bulk of the slug (sample

3). Nevertheless, it appears that in quite a few samples infiltration was not complete enough to

achieve porosities below 20 % where the slug should stop floating. In those cases, where indeed

parts of the slug broke off, those where infiltrated enough to stop them from floating, explaining the

Page 84: Particle Incorporation in Crystalline Silicon

76 6. Discussion

multiple incorporation locations. Slugs made of larger grains should also be easier to infiltrate, since

they possess larger capillaries, the small grained slugs, and therefore the issue with the infiltration

into close packing structures mentioned in Yang and Xi 1995 [104] should be weaker. For the SiC

experiments, it was not possible to find meaningful capture velocities due to this behaviour and the

fact that in many samples striations were too weak to be evaluated. In the cases of slugs being

located at the last upper phase boundary the growth velocity did not influence the slug, since the

phase boundary in contact with the slug did move away from it constantly.

Si3N4:

From the experiment series with slugs of the same net weight of the same silicon nitride powder

processed at different pulling rates, it is observable that the faster the crystal is grown, the earlier

the incorporation of the slugs takes place. This earlier incorporation takes place in terms of

transported distance and in terms of increased capture velocity. It is mentionable that while the

capture velocity increases, the spread in transported distance decreases. Since the power of the

lightbulb was at a constant value to not influence the growth rate and therefore the incorporation

behaviour, the zone height differs for the different pulling rates of the experiment series see Figure

32. The slower the applied pulling rate is, the higher the resulting final zone gets. The reason for this

observation is that the power was chosen to allow a stable growth with well separated phase

boundaries for the fastest pulling rate, where the most power is required for a fast melting of the

feed at the high pulling rates. For this high power, a higher zone results for lower pulling rates. Also,

the experiment takes longer, since the grown length was aimed at around 16-18 mm. The translation

was 20 mm for every experiment.

A possible explanation for the different transported distances in a series of equivalent experiments,

might be for geometric reasons, as to how a slug behaves in the zone. Figure 56 shows the zone

heights for the extreme cases in the 3 mm/min, 5 mm/min, 7 mm/min experiments and TEXUS 53 µg.

From the top, they look the same, as shown by the top row of images, but from the side views, the

different heights are indicated. Drawn is one of the most extreme slugs that was found in the

experiments, with 4.3 mm height and 2 mm diameter. Auxiliary lines are drawn, marking quarter

sections in the zone when viewed from the top and half lines viewed from the side. The figure shows

that with such large slugs, albeit being drawn as a hollow u-shape, it is difficult to have the slug

positioned only in one quarter section of the zone. The only way to achieve this is with the slug

standing upright with only small inclinations with respect to its longitudinal axis and the longitudinal

axis of the zone. Considering the velocity field of the zone as presented in Figure 55, it can be

deducted that a slug of this size will experience a rotational force, since it will reach in the upwards

and in the downwards moving part of the melt torus. Furthermore, since the melt is the slowest

along the phase boundary and along the side wall, the slug will be pressed against the wall or phase

boundary if it comes too close. A similar behaviour is reported by Schmid et al.2015 [105], where

particles in solar silicon growth in a cone shape crucible was investigated. In their case, the particles

were incorporated in the zone of low melt convection in the cone part of the crucible.

Experimentally it was observed that nitride powder slugs tend to stick to the wall if they come in

contact, which is promoted by the velocity field in the zone. If the velocity of the melt is high enough,

the incorporation of particles can be avoided. As shown by Kudla et al. 2013 [106], the strong mixing

induced by a travelling magnetic field, created by the heater magnet module, resulted in flow

velocities high enough to keep the particles precipitating during the growth in suspension. Since this

Page 85: Particle Incorporation in Crystalline Silicon

6. Discussion 77

induced convection is orders of magnitude stronger than Marangoni convection, which is in turn

orders of magnitude stronger than buoyancy convection in the small zones [83] in the experiments

presented here, the larger slugs here cannot be kept afloat in contrast to the observation at

industrial scale.

Figure 56: Schematics of a zone of molten silicon, top row shows view from top on the zone, the bottom row

shows a side view. In the side views, different grey values show the different zone heights of the zone at the

end of experiments with 7 mm/min, 5 mm/min and 3 mm/min in ascending order of zone heights. Marked in

red is the zone height of TEXUS 53 for comparison. The drawings are simplified, showing only the zone itself,

without seed and feed crystal. The phase boundary shape, being convex, is neglected here as well and it is

drawn as flat.

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78 6. Discussion

6.1.2 µg Experiments

From a material point of view, the TEXUS experiments are in partial accordance to the expectations.

It was found that SiC has a lower critical/incorporation velocity under µg conditions than Si3N4, but

SiC was incorporated at a lower growth velocity in space than on earth. When using the equation

(19) published by Stefanescu et al. 1998 [75]

𝑉𝑐 =1

3

∆𝛾0

𝜇

𝜅𝑝

𝜅𝐿

(𝑎0

𝑎0 + 𝑑𝑚𝑖𝑛

)2

(𝑅𝑝

𝑑𝑚𝑖𝑛

)−1

and assuming that the gap width dmin is the same for both species, and the differences are

p SiC ≥ Si3N4 and

SiC < Si3N4

then, without a specific value for Vc, it is evident that Vc for Si3N4 is must be higher than Vc for SiC

under µg conditions. The reason as of why SiC does not behave as expected is unclear, but it can be

argued that if there is any tendency of the particle slug to float upwards, the outcome of the

experiment is misinterpreted. However, this limitation does not exist under µg conditions since

density differences have no effect here. The same is true for the Si3N4 experiment on TEXUS 53.

Under standard conditions under gravity incomplete infiltration provides a serious limitation. As

discussed in the section before, if the porosity of the slug is higher than 20%, the slug could start to

float in the melt, influencing the incorporation experiment. Since the outer rim of the slug is

infiltrated by silicon in both µg experiments, both experiments are still valid. As a data point for the

improvements of the numerical models, the critical particle radius has to be assumed as somewhere

between the diameter of the individual particles and the diameter of the slug. As Sen et al. 1999 [76]

reported, an agglomerate of particles might be transported further under µg conditions, than the a

single particles making up the agglomerate. This makes a definition of an equivalent particle

diameter difficult. It seems, that at least under µg conditions, with reasonable estimates of uncertain

parameters, a model like the one of Stefanescu et al. [75] is capable to give predictions on the

particle incorporation. However, under terrestrial conditions, the model is invaldid, since gravity

effects are neglected. Most recent models like for example [107, 108] and especially [109] where

effects of an oscillating growth rate are considered, it becomes apparent that understanding these

processes prove to be a very complex endeavour.

The fact that no influence of the transported slug on the phase boundary can by observed in the

SXRTs, could be argued as a lack of spatial resolution power of the X-ray film, or the disjoining

pressure of the gap does not lead to enough residual stress in the lattice to cause contrasts on the X-

ray film.

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7. Conclusions and Outlook 79

7 Conclusions and Outlook

In this work, data points for existing models and their improvement have been created. These data

points are in partial agreement with the theoretical predictions of particle behaviour during the

growth of silicon. The most secure data are obtained here from the experiments carried out under

microgravity conditions, since interfering effects of the particles being an agglomerate of particles

and moving or not moving as a slug are reduced.

The experiments carried out under terrestrial conditions in the lab show the complexity of the

presence of foreign phases in crystal growth. For reliable data under lab conditions single particles

are needed, but only agglomerates are found at various incorporation velocities and positions.

Therefore, no single capture velocity can be derived from the experiments, where the slug separated

into smaller chunks.

No fail proof way of ensuring the distribution of particles in the melt was found, neither natural

buoyancy convection, nor Marangoni convection, nor shear forces in the melt due to rotation or

magnetic stirring were found sufficient to separate the initial slug into particles.

The scale of the model system is problematic in itself, since the phase boundary is not infinite for a

slug of several mm in size, as is can be approximated for a particle with just a few µm diameter.

Convection effects, temperature effects and interface curvature differ strongly from an industrial

scale VGF crucible and its growth conditions.

In future, experiments with larger particle diameter and/or different wetting behaviour could be

tested on board of another TEXUS flight. A different wetting behaviour is an expression of different

surface energies, which have an influence on the repulsive forces between a particle and the S/L-

interface. With transparent melts, the transition from pushing to engulfing could be visually

observed. It could also provide insights on the response of the S/l-interface in the presence of a

particle or agglomerates, showing a bending towards or away from the foreign phase. Up to now, no

real prove the influence on the phase boundary is obtained. The limitations of pre-agglomerated, un-

infiltrated particle slugs could be overcome, by the use of silicon material from the VGF process. In

this material precipitated, fully wetted particles are present and distributed. With this approach it

might be possible to get a clearer result on the particle radius dependence of the critical growth

velocity. If a deviation from the Silicon-SiC-Si3N4-system is not possible, then in-situ X-ray tomography

could shed light on the behaviour of the slug or particle in the melt and upon contact with the phase

boundary. This could give insights on the real-time movement of the melt as well since the particles

act as tracers in the melt, as long as they are not incorporated.

Page 88: Particle Incorporation in Crystalline Silicon

80 7. Conclusions and Outlook

8 References

[1] Information on https://www.ise.fraunhofer.de/de/downloads/pdf-files/aktuelles/photovoltaics-

report-in-englischer-sprache.pdf

[2] G. Du, L. Zhou, P. Rossetto, Y. Wan, Hard inclusions and their detrimental effects on the wire

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86 9. List of Figures

9 List of Figures

Figure 1: Presented are the two most important unit cell types for semiconductors. Elemental

semiconductors like silicon crystallize in the diamond cubic lattice (a), compound

semiconductors like GaAs crystallize in the zinc blende structure (b) [20]. .................. 4

Figure 2: The figure shows the band structure of Si (a) and GaAs (b). The electrons in the conduction

band are shown as black dots, while the corresponding holes in the valence band are

shown as circles. [21] ..................................................................................................... 4

Figure 3: Shown are the measured ionization energies in eV in silicon for several impurities and

dopants from Sze 2002 [20]........................................................................................... 5

Figure 4: Setup for silicon growth by the Czochralski technique after Sze 2002 [20]. ............................ 7

Figure 5: Schematic representation of the vertical gradient freeze process, the main industrial scale

production technique for growing multicrystalline silicon for PV applications. Shown

are the graphite heater elements, carbon support crucible, fused silica crucible,

silicon nitride coating, and silicon in solid and liquid form. A: silicon chunks are filled

into the Si3N4 coated crucible B: All silicon is molten C: By extracting heat from the

bottom of the crucible, either by reducing heater power or active water cooling,

Silicon is solidifying from the bottom up. D: Completely solidified Silicon ingot .......... 9

Figure 6: Part A: First order striations caused by variations in growth velocity are indicated by the red

arrows. The variation in growth rate is caused by sample rotation during the growth.

The weaker, more random micro striations between the rotational striations are

caused by melt movement due to the rotation. Part B: Micro striations (red arrows)

created in the last rapidly solidifying melt zone of a float zone growth experiment.

The micro striations envelope SiC-crystallites, shown by green arrows, precipitated

and grown in the melt zone. The blue arrows point at micro crystallites, silicon grains

formed during the fast solidification, where the growth conditions are not controlled

anymore. ...................................................................................................................... 12

Figure 7: Formation principle of Type-II striations. Terraces and valleys leave a dopant concentration

trace, that is different from the surrounding crystal, leading to Type-II striations when

the crystal is etched. redrawn after Cröll & Müller-Sebert 1988 [44]. ........................ 13

Figure 8: Wetting angles for non-wetting behaviour ( > 90°) on the left, the special case of a =90°

in the middle and case of complete wetting ( < 90°) ................................................ 15

Figure 9: The three modes of interaction of particles with a dendritic interface is shown. the particles

can be pushed by the interface and by this enrich in front of it. If dendrites start to

branch, particles can be trapped between the branched columns. In the third case,

the particles are incorporated into the propagating solid without being pushed or

trapped after Wilde et al 2000 [66]. ............................................................................ 16

Figure 10: Model for particle behaviour calculated by Soiland [54]. The solid line marks the transition

for a particle of being pushed or being engulfed for a given combination of particle

radius and velocity of the moving S/L interface. The dashed line represents a typical

solidification velocity during the industrial production of solar silicon (5.5 µm/s).

After this model particles with a diameter lower than 1.3 mm should be pushed. ... 17

Figure 11: Shown is the force balance on a particle that is in front of the solid liquid interface. The

interface is moving with velocity VGr, the particle with velocity VP. Forces driving the

particle towards the interface are the drag force FD of the melt and the buoyant force

FG (with l < P). Helping the particle staying afloat are: the interface force FI, the lift

Page 95: Particle Incorporation in Crystalline Silicon

9. List of Figures 87

force FL, and the Magnus force FM. FL and FM are depending on the melt flow moving

with Vref parallel to the S/L interface. The minimum distance between the particle

and the solid is referenced as dmin. describes the momentum boundary layer

thickness. Redrawn after [74] ...................................................................................... 18

Figure 12: MHF furnace on the right side for closing the powder filled drill hole under vacuum

conditions. On the left side, the control rack is shown, in the foreground an

additional power supply is placed, for applying an asymmetric heat influx on the

sample inside the furnace. .......................................................................................... 23

Figure 13: Monoellipsoid mirror furnace (FR-ELLI) with two-stage rotary vane pump, translation and

rotation motors and camera system. On the right part of the figure a graphical

representation is shown [83] ....................................................................................... 24

Figure 14: Part A: Airbus TEM02-3 ELLI furnace for the µg-experiments aboard the TEXUS 51&53

sounding rocket missions. The furnace inside is geometrically identical to the Freiburg

laboratory one and uses the same OSRAM FEL1000 1kW lightbulbs. Part B Technical

drawing of the TEM02-3 module, inside the aluminium outer shell of the payload

structure. The drawing is kindly provided by Airbus Defence and Space [85]. ........... 25

Figure 15: Tube furnace used for removing the oxygen containing species in the silicon nitride

powders for improved wetting behaviour. ................................................................. 26

Figure 16: Temperature profiles used for wetting experiments (red graph) and for powder

preparation (black graph). ........................................................................................... 26

Figure 17: In part A, the magnet is shown, the furnace is inserted from below on the black platform,

here in the „up“-position. Also below the magnet, the translation/rotation motors

are mounted. Protruding from the top, the borescope is visible. This 1.2 m long

borescope with 90° sight angle is necessary to keep the camera head as far away as

possible from the magnetic field maximum. Image B shows the view from the top

down along the borescope into the inner bore of the magnet with the ELLI furnace

inside. ........................................................................................................................... 28

Figure 18: An ampoule is closed by an oxyhydrogen gas flame, while the gas atmosphere inside the

ampoule is liquefied by partially submerging the ampoule in LN2. ............................. 32

Figure 19: Photograph of an in-house ampoule for the lab experiments in Freiburg. The silver-grey

sample is held in place by the two fused silica rings at its ends, which in turn are fixed

to the sample rod by Al2O3 pins. In the middle of the sample rod, the recrystallized

spot over the drill hole containing the introduced particles is visible. ....................... 33

Figure 20: Necessary construction steps for ampoules used on TEXUS missions. A: the Ampoules

outer hull is filled wit the sample crystal and the ampoule’s later foot with fused silica

hull attached, which is necessary for coupling to the vacuum system. B: The outer

hull was molten on the ampoule foot and the excess tube cut away. This part is then

attched to the vacuum system and after evacuation to roughly 10-5mbar, and purged

with gaseous oxygen. After evacuating the purge gas, the ampoule is filled with an

oxygen amount, that is frozen out by LN2 andclosed in by melting the ampoule shut.

C: The finished ampoule, with an oxygen pressure of 1.5 bar at room temperature.

The photograph below shows the real ampoules at stage A. ..................................... 34

Figure 21: Photograph of an ampoule for TEXUS sounding rocket experiment. The ampoules

manufactured in Freiburg are glued into stainless steel holders for fixing them into

the ELLI furnace. It is necessary to glue the ampoules in the holders with a ceramic

cement, since the screws alone which hold and centre the ampoule in the holder,

Page 96: Particle Incorporation in Crystalline Silicon

88 9. List of Figures

have very small contact points on the fused silica foot of the ampoule. These small

contact points create a high pressure on the foot, when the rocket launches, the

ceramic cement distributes this pressure so the ampoule will not break on the

ascent. .......................................................................................................................... 34

Figure 22: Timelines for TEXUS 51 and 53. For clarity every parameter except lamp power output was

removed. ...................................................................................................................... 38

Figure 23: Video frame taken during a growth experiment. The live images are necessary to adjust

the power output accordingly to the growing crystal's behaviour. After the

experiment, the images from the video file provide a way to evaluate the zone height

and growth rate where striations are too weak for evaluation or absent altogether.

The time constant is obtained by the videos frame rate and number of frames

between two frames taken for evaluation. The red arrows indicate the upper and

lower phase boundary, the bright space between them is the oxide skin covered

zone. ............................................................................................................................ 40

Figure 24: This figure shows a comparative array of the IR-mappings of samples 1-16, with the slug

recognizable as black contrasts, as well as dark shadows of precipitations of SiC.

Samples 3, 7 and 8 are also shown with their respective DIC- mappings. .................. 43

Figure 25: The figure shows enlarged views on the slugs at their point of incorporation for samples 3,

8, 11, and 12. While samples 3, 8, and 11 contained a large quantity of powder (6mg

powder in sample 3 and 4mg powder in 8 and 11) and were transported during the

growth, sample 12 with only 2 mg of powder was incorporated at the first lower

phase boundary. The slugs of samples 3, 8, and 11 appear to have large voids, where

powder was removed during etching or polishing. Also, especially visible for 8 and 11,

the slug appears to consist of a mechanically more stable rim of powder outlining the

shape of the slug and lose powder in the centre. The silicon melt infiltrates the

powder only partially, which can be seen by the central ridge in the slug of sample 3,

and by the brighter area in the rim of the slug in sample 11. For the slug of sample

12, judged by its colour, it appears more infiltrated by the silicon melt than the other

three slugs and it also appeasr to have less voids than the other three slugs. ........... 44

Figure 26: The figure shows the transport behaviour of the slugs compared to the grown length of

crystal. If the capture position of the slug (red bar) is above the length of grown

crystal (black bar), the slug is captured in the last rapidly solidified zone, rather than

being incorporated by the moving solid liquid interface. This is the case for samples 1,

8, 9, 11, and arguably for sample 7. Samples, where the slug was transported and

then captured by the solid liquid interface are 2 through 6 and 10, whereas in

samples 12 through 16 no transport is observed at all. In addition to the red and

black bars, a blue bar is shown, indicating the mass of the slug in question. The figure

shows that transport is only observed for slug masses of 4 mg and 6 mg regardless of

the pulling rates and that for small net weights of 2 mg no transport takes place.

Also, no transport can be observed if the grain size used is 150 µm or 300 µm despite

the mass being 4 mg, where transport was observed for lower grain sizes. .............. 45

Figure 27: DIC micrographs of samples 17 (A), 18 (B), and 19 (C) grown with the same experimental

conditions. All three samples exhibit a very similar striation pattern, indicating

comparable growth velocities, length of grown crystal, and height of the remaining

zone at the end of the experiment, not visible for 17, since the upper half of the zone

broke off while the crystal was cooling down in the furnace. Although only sliced and

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9. List of Figures 89

lying at the surface of sample 17, the slugs can be located for all samples by the

characteristic twinning, confirmed by the black contrasts in the IR-transmission

micrographs. ................................................................................................................ 47

Figure 28: IR-map comparison of three experiments with roughly the same amount of the same type

of powder grown at the same pulling rate. The images shown are from samples 17

(A), 18 (B) and 19 (C). From centre of gravity of the shadow created by the particle

slug the position of incorporation is determined. It is apparent that despite of the

growth parameters being the same for each sample shown, the incorporation

position varies strongly. Also apparent is that the slug of sample 18 in part B is much

more intact than the parts of the slug found in sample 17 and 19. The black shadow

in the upper half of the last zone in 18 is created by cracks in the sample, leading to

total reflection and refraction of the light passing through the sample. This light then

never reaches the camera and the black contrast is created. The ringed artefacts in A

and B are newton interference rings from a silicon wafer used placed on top of the

sample to reduce overexposure at the sample edges. ................................................ 48

Figure 29: The diagram shows the growth velocity of the crystals over the length of grown crystal.

The positions at which the particle slugs were captured by the moving solid liquid

interface are marked by arrows in the respective colours. The growth velocities for

each pulling speed, 3 mm/min, 5 mm/min and 7 mm/min are comparable between

experiments at given pulling rate. The position of the slug strongly varies over the

grown crystal length, despite the growth velocity roughly being the same within each

series of experiments. ................................................................................................. 49

Figure 30: Shown are the averaged and smoothened growth rates from evaluating the striations of

the grown crystals in dashed lines. The black squares show the capture velocity and

travelled distance for each slug in the respective experiment. Plotted in red squares

are the averaged capture velocities and travelled distances, while the black square on

the outmost right position of the 5 mm/min growth experiment is treated as an

outlier. The red squares show a trend in decreasing travelled distance with increased

growth velocity. ........................................................................................................... 50

Figure 31: The figure shows how slugs of particles with the same grain size of powder, but different

net weights, behave under the same experimental parameters. The standing square

symbols mark the individual data points, indicating a wide spread of capture

positions at roughly the same capture velocity. The open circle symbols mark the

positions of the averaged capture positions and capture velocities. It is apparent that

the 2 mg slug are transported furthest, the 4 mg slugs the shortest and the 6 mg

slugs occupy an intermediate positon, however the capture velocity remains roughly

the same. ..................................................................................................................... 51

Figure 32: Plotted in this figure are the developments of the zone height for the individual

experiments. Indicated by the black arrows are the highest zone heights at the start

of the experiment and the highest zone heights at the end of the experiments. Except

of the pulling rates of 3 mm/min, 5 mm/min, and 7 mm/min, all other experimental

parameters were the same for each experiment. The zone height at the start of the

translation was between 12.5 mm and 14.2 mm (indicated in the graphic). The

highest zone heights were reached at the end of each experiment. In order, the final

zone heights were 17.4 mm (pulling rate 7 mm/min), 18.3 mm (pulling rate

5 mm/min), and 20.5 mm (pulling rate 3 mm/min). Indicated in the figure are the

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90 9. List of Figures

highest zones heights for each series. Since the translation was active until a distance

of 20 mm was reached, the three pulling rates result in different experiment

durations. ..................................................................................................................... 52

Figure 33: Development of the zone height during the TEXUS 51 mission. The mission was carried out

with only one interference of the ground crew and otherwise ran by the

preprogrammed flight pofie shown chapter 4.2.4. The Zone height fluctuates

between 10.5 mm at the lowest and 12.9 mm at the highest point. The zone height

indicates that during the experiment the upper and lower phase boundary were not

in contact. .................................................................................................................... 53

Figure 34: TEXUS 51 1g reference. Part A shows the DIC image of the sample, with a clear striation

pattern and V-shaped traces of twin grain boundaries. The last lower phase boundary

is found to be concave, while the last upper phase boundary is strongly convex

shaped. The particle slug is found in part B, the polished, not etched backside of the

sample shown in part A. The IR-transmission micrograph (part C) shows the seed area

as a darker contrast with a convex interface towards the grown crystal. The darker

rectangular shape is a higher resolution map of the area where the particle slug or

parts thereof were suspected, but not found. No precipitations or single particles are

found either. ................................................................................................................ 54

Figure 35: This figure shows the DIC image (part A) and the IR-transmission micrograph (part B) of the

TEXUS 51 µg sample. The DIC image shows the striations created by the rotation of

the sample during the experiment, the particle slug in the middle of the rod, and V-

shaped grain boundaries originating at the slug. In the IR-transmission micrograph

the seed is clearly distinguishable from the grown crystal as well as the strongly

curved contact line where the last upper and lower phase boundary met after the

experiment was switched of. In both micrographs, the slug is recognizable as a

circular shadow and intact. It appears as if it was cut perpendicular to its longitudinal

axis. .............................................................................................................................. 55

Figure 36: In this figure, the growth velocities from the striations evaluation of the TEXUS 51 1g

reference sample (A) and the µg sample (B) are shown. The green arrows mark the

starting position of the slugs and the red arrow(s) mark the position where the slug

was incorporated. The slug parts were incorporated in the 1g reference at 10.5 mm

@ 3.5 mm/min. In the µg sample the slug was moved for 1.4 mm and incorporated at

4.6 mm @ 2.2 mm/min). ............................................................................................. 56

Figure 37: Development of the zone height during the TEXUS 53 mission. The mission was carried out

without interference of the ground crew, and ran by the preprogrammed flight pofile

shown chapter 4.2.4. The zone height fluctuates between 10.5 mm at the lowest and

11.1 mm at the highest point. The zone height indicates that during the experiment

the upper and lower phase boundary were not in contact......................................... 57

Figure 38: This figure shows the DIC image (part A) and the IR-transmission micrograph (part B) of the

TEXUS 53 1g sample. The DIC image shows the striation created by the rotation of the

sample during the experiment, the particle slug in the middle of the rod, and V-

shaped grain boundaries originating at the slug. In both micrographs the slug is

recognizable as dark contrast at the lower edge of the crystal. Although the slug

appears block like, it is no more cylinder shaped. In the IR-transmission micrograph

there are also dark curtain shaped contrasts, which relate to precipitations of Si3N4.

..................................................................................................................................... 58

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9. List of Figures 91

Figure 39: This figure shows DIC image (part A) and the IR-transmission micrograph (part B) of the

TEXUS 53 µg sample. The DIC image shows the striations created by the rotation of

the sample during the experiment, the particle slug in the middle of the rod, and V-

shaped grain boundaries originating at the slug. In the IR-transmission, micrograph

the seed is clearly distinguishable from the grown crystal by its darker grey shade. On

the right side of the incorporated slug, curtain shaped contrasts created by

precipitations are visible. In both micrographs, the slug is recognizable as a dark

shadow. ........................................................................................................................ 59

Figure 40: In this figure, the growth velocities from the striations evaluation of the TEXUS 53 1g

reference sample (A) and the µg sample (B) are shown. The green arrows mark the

starting position of the slugs and the red arrow marks the position where the slug

was incorporated. The slugs were incorporated in the 1g reference at 7.0 mm grown

length at a VGr of 3.9 mm/min. In the µg-sample the slug was moved for 3.0 mm and

incorporated at 6.4 mm grown length at a VGr of 4.3 mm/min. .................................. 60

Figure 41: This figure shows the 008 reflection topographs of the TEXUS 51 µg sample (A) and the

TEXUS 53 µg sample (B). In both topographs the seed (green arrow) appears bright

due to its high density of dislocations, with a convex phase boundary to the grown

crystal above. The grown crystal appears less bright, since its dislocation density is

lower than that of the seed, single dislocations lines are visible (orange arrows). Also

in both cases, the slug is recognizable as a dark contrast, appearing it the same

shape, as in the DIC micrographs (red arrows). From the incorporated slug, twins are

formed. Inside the twined areas lamellae structures are recognizable (yellow arrows).

The TEXUS 51 sample in part A shows a column of almost no diffracted intensity

above the slug. From these areas, parts of the topograph are scattered away from

the main reflection. The bright triangular shape (blue arrow) scattered from its

position in real space (blue dashed arrow) due to a higher rotation of the crystallite,

the reflection is scattered further away. The TEXUS 53 sample shows a lower degree

of dislocation density than the TEXUS 51 sample, there are regions below the slug

that are almost dislocation free (black arrows). Neither topograph provides any

evidence that an interaction between the transported slug and the pushing phase

boundary occurred. ..................................................................................................... 61

Figure 42: Presented here is sample ZL1 7 µm SiC mixed with XRD standard silicon powder after

150 min of melting time. Neither the IR transmission micrograph (A) nor the DIC

mapping of the slug area (B) shows a tendency of the powder to distribute into the

melt. The slug, being infiltrated with silicon, sunk down to the lower phase boundary,

despite the mixing of the zone driven by Marangoni and buoyancy convection. ...... 63

Figure 43: Shown is sample ZL2 7 µm SiC mixed with freshly pestled solar silicon powder after

150 min melting time. The IR-transmission micrographs (A) show the slug at the

bottom of the zone at the lower phase boundary. Part B shows the DIC micrograph of

the slug itself, the powder though infiltrated with silicon melt, shows no indication of

particle distribution into the melt. The former chunks of silicon are still visible

without any particles indicating movement into the former chunks’ space. The slug is

completely infiltrated with silicon and it is located at the lower phase boundary at

the bottom of the zone................................................................................................ 63

Figure 44: This figure shows a SEM picture of the habitus of the SN7 particles. [91] .......................... 64

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92 9. List of Figures

Figure 45: Diffractogram of standard SN7 Powder. The sample consists of the alpha- and beta-silicon

nitride phase (red and green, as well as a third, elemental silicon phase (orange). ... 65

Figure 46: Wetting behaviour of a piece of silicon of slightly compacted SN7 powder. The images

shown are taken during the heating phase in the sessile drop furnace. The target

temperature for these experiments is 1500°C, measured at the furnace heaters. At a

heater temperature of 1454°C the silicon starts to form melt. As more and more melt

is created, a droplet of Si is formed (minute 32, at 1489°C heater temperature),

showing non-wetting behaviour with contact angles of around 102°. ....................... 66

Figure 47: Sessile drop behaviour of standard SN7 powder. The piece of silicon forms a stable droplet

during heat-up and during the holding time of 60 min at 1500°C, it shows a transition

of non-wetting to wetting behaviour. At minute 52, after 49 minutes of melt present

in the system, the wetting angles decrease this time point, it starts to seep into the

substrate until all melt is starting to infiltrated the substrate indicated by the rapid

shrinking of the droplet. Over the course of an hour, almost all melt is seeped into

the powder. ................................................................................................................. 67

Figure 48: Development of contact angles of standard SN7 powder over time. The spiking increase at

mintue 13 is caused by the droplet forming two smaller individual droplets before

beeing seeped into the powder. .................................................................................. 68

Figure 49: Powder diffractogram of SN7 powder after superheating treatment. Compared with the

original powder, the same phases are detected, but the volume fraction of each

species has changed. Alpha silicon nitride is present with 45.3 Vol%, beta silicon

nitride with 32.2 Vol% and elemental silicon amounts 22.5 Vol% of the powder. This

shows a decrease in alpha phase and an increase in beta phase and free silicon

compared to the original powder. Furthermore, there is no indication of an oxide

bearing species in the diffractogram. .......................................................................... 69

Figure 50: Sessile drop behaviour of silicon on superheated SN7 powder. As soon as melt is present, it

infiltrates the substrate without forming a droplet at all, indicating wetting

behaviour. .................................................................................................................... 70

Figure 51: Starting (left) and end image (right) of sodium nitrate during wetting behaviour

investigation. It is visible that no droplet is formed upon melting of the sodium

nitrate chunk, showing immediate wetting and infiltration behaviour. ..................... 71

Figure 52: A larger chunk of silicon nitride powder on the surface of the melt is spontaneously wetted

and enters the melt in a shower of single particles. ................................................... 71

Figure 53: Particles suspended in the melt act as tracers for the convection role system present in the

crucible. ....................................................................................................................... 72

Figure 54: Overview of the present convection roles in the crucible: 1.) Central buoyancy torus; 2.)

Marangoni convection driven tori; 3.) Buoyancy convection roles in conical tip; 4.) A

convection stagnancy layer between 1.) and 3.). The red arrows mark the contact

point of the melt surface and the crucible. ................................................................. 72

Figure 55: Shown are 2D simulations of the zones observed in the experiment series using Si3N4

powder, to understand the development of the melt velocity and its vector field,

smaller zones are added for comparison. The top row shows the shape and height of

the zone where red represents liquid silicon, the middle row shows the temperature

field for the respective zone, and the bottom row shows the velocity of the melt,

with red indicating stagnation and blue representing the fastest melt movement. The

velocities are zero at the phase boundaries and at the outer walls of the zones due to

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0. 93

the SiO2 skin applied here. Since the only driving factor for the melt is gravity, higher

zones provide a larger acceleration path, resulting in higher melt velocities, the

general shape of the melt movement, stays the same over the series of zones. The

melt always moves as one big torus, with the fastest velocities in the centre of the

zone, moving downwards. The range of velocities is between 0.149 cm/s to a

maximum of 0.345 cm/s in the highest zone. ............................................................. 73

Figure 56: Schematics of a zone of molten silicon, top row shows view from top on the zone, the

bottom row shows a side view. In the side views, different grey values show the

different zone heights of the zone at the end of experiments with 7 mm/min,

5 mm/min and 3 mm/min in ascending order of zone heights. Marked in red is the

zone height of TEXUS 53 for comparison. The drawings are simplified, showing only

the zone itself, without seed and feed crystal. The phase boundary shape, being

convex, is neglected here as well and it is drawn as flat. ............................................ 77

Page 102: Particle Incorporation in Crystalline Silicon

94 10. Appendix

10 Appendix

10.1 Abbreviations

PV Photovoltaic

MC multicrystalline

TWh Tera Watt hours

Wp Watt peak

VGF vertical gradient freeze

HEM heat exchange method

Vc critical growth velocity at which a particle is incorporated

melt viscosity

surface energy difference

p thermal conductivity of the particle

L thermal conductivity of the melt

a0 atomic diameter

dmin minimum gap width between particle and phase boundary

Rp radius of the particle

Nm nanometre

Å Ångström (1Å = 0.1 nm)

eV electron volt

T temperature

Tm melt temperature

T Tesla

mT milli Tesla

g/cm³ grams per cubic centimetre

mN/m milli Newton per metre

mPa*s milli Pascal seconds

K Kelvin

Page 103: Particle Incorporation in Crystalline Silicon

10. Appendix 95

Kg kilogram

S/L interface solid/liquid interface

k0 equilibrium segregation coefficient

Cs concentration in the solid

Cl concentration in the liquid

Cl, ∞ concentration in the liquid at infinity

diffusion or momentum boundary layer thickness

VGr growth velocity

D diffusion coefficient

0 surface energy difference

a0 atomic distance in the melt

Rp radius of the particle

p thermal diffusivity of the particle

l thermal diffusivity of the liquid

dmin gap width between particle and S/L interface

Vp velocity of the particle

µ dynamic viscosity

FI interface force

FL lift force

FM Magnus force

FD drag force

FG buoyant force

rpm rotations per minutes

COG centre of gravity

s second

min minute

mm millimetre

µm micrometre

Page 104: Particle Incorporation in Crystalline Silicon

96 10. Appendix

mm/s millimetres per second

P Power in Watt

µg microgravity

TEXUS Technologische Experimente unter Schwerelosigkeit

Page 105: Particle Incorporation in Crystalline Silicon

10. Appendix 97

10.2 Sample IDs

Translation from ParSiWal I+II sample IDs to Thesis-IDs

Sample-ID Thesis Sample-ID ParSiWal

1 PT_14

2 PT_22

3 PT_45

4 PT_46

5 PT_45

6 PT_48

7 PT_49

8 PT_65

9 PT_66

10 PT_67

11 PT_68

12 PT_126

13 PT_127

14 PT_128

15 PT_25

16 PT_34

17 PT_165

18 PT_166

19 PT_167

20 PT_162

21 PT_163

22 PT_164

23 PT_173

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98 10. Appendix

24 PT_174

25 PT_175

26 PT_176

27 PT_177

28 PT_178

29 PT_152

30 PT_168

31 PT_169

32 PT_170

33 PT_171

34 PT_172

ZL1 PT_92

ZL2 PZ_93

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