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Lab course Crystal Growth I, Master of Science Crystalline Materials
Experiment: Float-Zone Growth of Silicon
Relevant Literature:
Attached scripts
J. Bohm, A. Ldge and W. Schrder: Crystal growth by floating zone melting. In: Handbook
of Crystal Growth 2a, Ed. D.T.J. Hurle (Elsevier/North-Holland, Amsterdam 1994), 213
K.Th. Wilke and J. Bohm: Kristallzchtung. (VEB Deutscher Verlag der Wissenschaften,
Berlin 1988, and under license, Harri Deutsch, Thun 1988).
W. Keller and A. Mhlbauer: Floating-zone silicon. Vol. 5 of: Preparations and properties ofsolid-state materials, Ed. W.R. Wilcox (Marcel Dekker, NewYork 1981)
W. G. Pfann: Zone melting. 2nd Ed.(J. Wiley, New York 1966)
Task:
FZ growth of an 8-10mm diameter silicon crystal in a double ellipsoid mirror furnace
(MHF).
Step 1: Introduction to the furnace and equipment. Observation of an FZ experiment done by
the advisor (1st day)
Step 2: Setup of seed and feed rod in the furnace, FZ growth of the crystal (2nd day)
Experiment protocol: the protocol should contain a brief introduction to the process as well as
relevant data (material used, power used, growth rate etc.) and a short discussion of the
results.
Material used: doped (P or As or Sb) silicon, orientation (111) or (100).
Dangers involved: The process involves high-voltage electricity, vacuum and pressurized
process chambers and high temperatures. No changes to the equipment are allowed without
consent of the advisor.
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MHF description (in
German)
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2. The floating-zone process
The general setup of the floating-zone process is shown in fig. 2-1: A
small free melt (or solution) volume,
held only by surface tension and
adhesion, is suspended between the
growing single crystal and a
polycrystalline feed rod. Under earth
conditions, hydrostatic pressure due
to gravity causes the characteristic
bottle shape of the zone. Crystal
growth is achieved by a relative
movement of the crystal and feed rod
versus the melt zone, i.e. the heater.
2.1 History and practical considerations
The FZ process can be regarded as a special variant of the zone
melting process invented by Kapitza [Kap28] for the crystal growth of
bismuth, and later developed by Pfann [Pfa52, Pfa66] with respect to the
purification (zone refining) and doping (e.g. zone leveling) of semicon-
ductor material. Zone melting employs a container for the material to be
processed, usually a long tube, boat or ampoule, and is used in horizontal
and vertical configurations. A small portion of the material is kept
molten by a suitable heater which is then moved relative to the material.
For impurities or dopants with segregation coefficients k=cs/cl 1
(where cs and cl are the concentrations in the solid and liquid,
2. The floating-zone process 5
Fig. 2-1: Schematic drawing ofthe floating-zone process.
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respectively) a redistribution profile characteristic for the process is
obtained (fig. 2-2, see chapter 3 for details) with a concentration reduc-
tion in the first part of the material and a corresponding increase in thelast zone for segregation coefficients k < 1 and vice versa for coefficients
k > 1. The impurity reduction can be further improved by several zone
passes (fig. 2-2), including using several heaters at a time. In addition to
the purification effect, advantage can be taken of the plateau region of
the initial profile to achieve doping profiles of constant concentration.
For the same reason, incongruently melting materials can be grown from
the melt by this process, because after the initial transient the zone has
the peritectic composition in equilibrium with the solid.
6 2. The floating-zone process
Fig. 2-2: Calculated (eqs. 3-Iand 3-II) axial dopant segregation curvesor a Si:P crystal (co= 61017cm-3, ko= 0.35) grown by zone melting with a
zone length of 12mm, for 1 zone pass and 3 zone passes, respectively.
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In the floating-zone process, the container is omitted and the melt
zone is suspended between the growing crystal and the feed material as
shown in figs. 2-1, 2-3 and 2-4. The floating-zone process was firstdescribed and introduced in the fifties, by Theuerer [The52], Keck and
Golay [Kec53], and Emeis [Eme54]. Its first application was the crystal
growth of silicon [Kec53] and this remains the dominant industrial appli-
cation of the process to this day [Zuh89, Boh94]. Nevertheless, within
the last 40 years a large variety of materials has been grown by this
method, ranging from semiconductors (fig. 2-3) to refractory metals,
oxides (fig. 2-4), halides and others (see [Boh94], pages 244, 245,
247-249 for a comprehensive listing).
2. The floating-zone process 7
Fig. 2-3: Silicon (mp: 1410oC)floating zone of 10mm in adouble ellipsoid mirror furnace(see section 2.1.1.1b).
Fig. 2-4: Gadolinium GalliumGarnet (Gd3Ga5O12, GGG, mp:1767oC) floating zone of 4mm in a double ellipsoid mirrorfurnace, from [Ger84]
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Variations of the process are: a) the standing pedestal method, where
the feed rod, located at the bottom, is much larger than the crystal above
it, and the crystal is pulled from a pool of melt at the top of the large rod.This method, introduced by Dash [Das58, Das60] and Poplawsky and
Thomas [Pop60], can be regarded as a cross between the CZ and the FZ
technique and is often used for the production of crystalline optical fibers
(see e.g. [Fei86, Ima95]); a hanging pedestal method, with the positions
of feed rod and crystal reversed, is also possible. b) the ribbon to ribbon
technique (RTR) invented by Lesk [Les76] and Gurtler [Gur78] for the
recrystallization of silicon sheets for photovoltaic applications, uses a
very asymmetric zone, where the height and the thickness of the zone are
orders of magnitude smaller than the width. This geometry poses some
specific problems with regard to dimensional control, interface shape and
heat transfer [Yec95]. In addition to ribbons, the production of crystal
tubes by the FZ technique has also been studied [Pfa66, Gle89, Lan94a,
Lan94b, Hsi96].In principle, it is also possible to substitute the floating melt zone of
the FZ process by a floating solution zone, resulting in the FSZ (or
traveling solvent floating zone, TSFZ) method. It can be regarded as a
derivation of the traveling heater method (THM, see e.g. [Ben79,
Ben80]) invented by Broder and Wolff [Bro63], similar to the way the
FZ process was derived from zone melting. The process appears advan-
tageous with respect to crystal quality, because the lower growth
temperature leads to a defect reduction, and due to the absence of the
ampoule wall the stress in the peripheral parts of the crystal is reduced.
That this effect is indeed possible has been shown by growth experi-
ments with GaSb crystals from free Ga solutions [Ben80, Ben82].
A free zone of near peritectic composition may be used for growing
incongruently melting materials with aggressive fluxes, such as YFe2O4,
8 2. The floating-zone process
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Y3Fe5O12 (YIG) [Kim77, Kim78, Kit79, Shi79, Fei88], or high Tc super-
conductors [Fei88, Gaz88, Gaz89]. Other materials grown from
(partially) free solvent zones are CaCO3 from a Li2CO3 flux [Bri71,Bel72, Bel76], Ba0.65Sr0.35TiO3 from a TiO2 flux [Hen74], and LaB6 from
La or B fluxes [Ota92, Ota93]. Due to the usually slow growth rates of
solution growth compared to melt growth (mm/day vs. mm/h - mm/min),
the FSZ process has been used rather seldom.
Due to the action of gravity on the liquid, the majority of experiments
is done in a vertical configuration, although horizontal systems employ-
ing electromagnetic levitation to counteract gravity have been used
[Pfa56, Pfa66]. For the same reason, the pulling direction of the crystal is
usually parallel to the gravity vector under earth conditions (compare
also section 2.2). Exceptions are the standing pedestal method and
processes with very small zones (e.g. RTR) where the influence of
gravity on the zone shape is not as important.
The actual growth equipment differs widely depending on the heaterconcepts (section 2.1.1) and the materials used. For zone translation, it is
possible to move either the heater or the crystal and feed rod. The first
solution is preferable in terms of disturbances and mechanical vibrations,
but the latter allows two independent translation and rotation mecha-
nisms to achieve a much better control of the zone and interface shapes.
Especially important is the fact that with two translation drives it is
possible to employ the necking process first introduced by Dash [Das59]
and Ziegler [Zie61] for the growth of dislocation-free silicon and germa-
nium. In this technology, also used in Si-CZ growth, a thin "neck" of
material is produced by employing a larger translation rate of the crystal
compared to the feed rod. Dislocations introduced by the seed or the
thermal shock upon melting propagate to the surface of the crystal and
2. The floating-zone process 9
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disappeara; after achieving dislocation-free growth, the crystal diameter
is increased to its final value. As the critical resolved shear stress neces-
sary to form new dislocations is much larger than the stress necessary tomultiply existing ones, the crystal remains free of dislocations. This
process is mainly possible for elemental semiconductors (Si and Ge),
because their critical resolved shear stress for the formation of new dislo-
cations is much higher than that of most compound semiconductors. For
heavy crystals such as in the industrial FZ-Si production, the thin neck
makes the attachment of an additional supporting mechanism above the
neck necessary [Boh94].
As starting material for FZ growth a compact (and preferably cylindri-
cal) rod is necessary; this can either be obtained from solid (poly)crystal-
line material prepared by other melt growth processes, deposited from
the gas phase, or be pressed and/or sintered from powder. In the latter
case the remaining porosity of the rod has to be taken into account in the
mass balance, i.e. the pulling speeds of crystal and feed rod. Additionalproblems can arise through the formation of bubbles released from a
porous feed rod [Ger90] or an absorption of zone material through capil-
lary action by a feed rod with open porosity. An additional run for
compacting the material is helpful in these cases, see e.g. [Pfa66, Hig95].
Employing an oriented seed crystal to achieve single crystal growth is
the most common method, but it is possible to make a seed selection by
necking if no single crystal is available.
For the translation/rotation mechanisms, avoiding mechanical vibra-
tions is of paramount importance; floating zones are very effective vibra-
tion sensors. Likewise, the resonance frequencies of the growth
equipment should be far from those of the zone (the latter are usually in
10 2. The floating-zone process
a an exception are orientations where the directions of growth and dislocation
movement coincide, such as [110] in the diamond lattice.
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the range of 0.1 to 10 Hz, depending on the size and material) and the
crystal. Otherwise, resonance in the system can lead to a disruption of a
zone near its stability limit, or even break the crystal in the neckingregion [Boh94].
Control signals used for automation include image analysis of video
pictures, scanning of the zone and crystal shapes by lasers, absorption of
radiation from a radioactive source [ Aut75, Lub86], or analysis of the
torque when employing differential rotation [Que75, Lub86]. Weighing
the crystal and/or the feed rod, as in some Czochralski systems, is not
very common. Manual control and observation of the zone, especially in
the critical phases of seeding, necking, and increasing the diameter is
still widely employed.
2. The floating-zone process 11
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2.1.1 Heater concepts
The fact that only a small volume of the material to be processed isheated to temperatures above melting point (mp), and that usually no
other material must be heated, allows for a much larger than usual
variety of furnace types for the FZ process. A rough classification leads
to the main groups of radiation heating (fig. 2-5), high frequency heating
(fig. 2-21), electron beam and plasma heating (fig. 2-24), and direct
heating (figs. 2-26, 2-27).
12 2. The floating-zone process
Fig. 2-5: Radiation heating methods: (a) electrical resistance heating,(b) heating by focused light, employing either an ellipsoidal mirror(top) or two parabolic mirrors (bottom), (c) laser heating (adaptedfrom [Car91]); E is a conventional beam expander and A an axicon-based ring beam expander.
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2.1.1.1 Radiation heating
Radiation heating includes the classic resistance heater concept,heating by focused light (image/mirror furnaces), and laser heating. Fig.
2-5 illustrates the principles of these methods.
2.1.1.1a Resistance heating
Resistance heating furnaces for floating-zone processes can be
anything from a simple ringwire as in fig. 2-5a to elaborate versions withseveral central heaters, cooling rings, isothermal heaters and after heaters
as in the so-called zone melting facility (ZMF) shown in fig. 2-6. The
more elaborate furnaces allow the individual tailoring of the temperature
profile for a given material system, e.g. an optimization of the axial
temperature gradient with respect to growth conditions at the interface
and with respect to thermal stress in the grown crystal region. Most resis-
tance heating elements are made either from Kanthal (operating tempera-
tures up to 1200oC) or from PtRh alloys (usual operating temperatures up
to 1400oC). For higher temperatures, resistance heating is more difficult,
possible heating elements being made from Pt/Ir, MoSi2 (Super Kanthal),
SiC, or carbon (graphite, CFC, or carbon on BN), the latter requiring an
inert gas atmosphere or vacuum for operation.
A major drawback of most resistance heaters with operating tempera-tures above approximately 800oC is that visual control of the melt zone,
either directly or via some optical and/or electronic system, is nearly
impossible or leads to a significant disturbance of the thermal field. This
problem complicates crystal growth considerably, as the knowledge of
the zone shape is vital for the control of the process (see section 2.2).
Under such circumstances, one has to rely on temperature information
2. The floating-zone process 13
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from the heating elements, experience and/or numerical simulations of
the heat transfer in the system for optimizing control parameters. Heater
control itself is easily achieved with thermocouples and the usual PID
controllers; for high precision requirements (relative accuracies of
14 2. The floating-zone process
Fig. 2-6: Concept of the zone melting furnace ZMF developed by theaerospace company Dornier, after [Beh89, Len90, Sch92].
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0.01K), optical fiber thermometry of the heating elements can be used
[Dol95].
2.1.1.1b Imaging furnaces
Imaging furnaces using focused light are a rather special type of heater
with a distinct set of advantages and limitations. They can be very
energy efficient, there is no principal limit to processing temperatures,
and the visual control of the zone and the crystal growth process is excel-
lent. On the other hand, temperature measurements during growth are
practically impossible. The temperature in the heating elements (i.e. the
lamps) is only indirectly related to the sample temperature, and contact-
less measurement of the sample temperature by pyrometry is also nearly
impossible due to the much higher level of light reflected versus radia-
tion emitted from the sample [Eye77, Eye81]. Information on the
temperature field can only be obtained from special measuring samples
with incorporated temperature sensors, and from numerical simulations.
Starting in the fifties and sixties [Wei56, Bau59, Koo61], different
imaging furnaces have been developed over the years for floating-zone
applications, e.g. [Fie68, Aka69, Tri70, Sau71, Cox72, Ars73a, Ars73b,
Miz74, Kit77, Eye77, Eye79, Eye81, Bal81, Bed84, Car84, Car86a,
Len90, Mat92, Bal93], some of them for microgravity experiments on
manned and unmanned space flights (compare figs. 2-7, 2-8, 2-10 and
2-16). The original rationale for preferring image furnaces for that appli-
cation was the absence of electromagnetic interference in comparison to
radio frequency heating (section 2.1.1.2) and, in comparison to resistance
heating, the small weight and volume in relation to the maximum
temperature obtainable. At the moment, commercial systems specifically
designed for floating-zone growth are available from three different
2. The floating-zone process 15
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16 2. The floating-zone process
Fig. 2-7: Monoellipsoid mirror furnace ELLI developed at the Crystal-lographic Institute in Freiburg [Eye81, Eye84], with half-axes 80mmand 90mm. Furnaces with the same internal geometry have been flownon several sounding rocket campaigns (TEXUS, module TEM02-ELLI) and the Spacelab mission D1 (MEDEA-ELLI, old version).Compare fig. 2-8. Also shown is an ampoule for the FZ growth of Si.
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companies, NEC and Tsukuba Asgal in Japan, and the Moscow Power
Engineering Institute in Russia. Practically all mirror furnaces employ
catoptric, not refractive or catadioptric elements because the geometric
efficiency of lenses is quite limited [Eye77] and the heat exposure of the
optical elements excludes most refractive materials except fused quartzor sapphire.
Either ellipsoidal or parabolic mirrors (or a combination of both) are
used to focus the light from one or several lamps as shown in fig. 2-5b.
Monoellipsoidal mirrors as in figs. 2-7/2-8 have a better efficiency
because nearly all of the light is focused onto the sample; parabolic
mirrors do not use the radiation not reflected by the first mirror shell, but
2. The floating-zone process 17
Fig. 2-8: The monoellipsoid mirror furnace ELLI, half-axes 80/90mm.Left: Laboratory version plus an additional mirror shell at the bottom.
Right: Module TEM02 for experiments on sounding rockets (TEXUSprogram), built by the aerospace company ERNO.
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have the advantage that the distance between the foci is variable. A
somewhat better efficiency of parabolic mirrors or of ellipsoidal reflec-
tors using only partial ellipsoids [Ars73a, Ray88] is possible by theintroduction of an additional hemispherical mirror as shown in fig. 2-9.
Another division can be made between furnaces where the sample axis
and the main axis of the furnace coincide, and furnaces where the main
axis is at 90o to the sample axis. The former concept as shown in figs.
2-5b, 2-7 and 2-9 allows a very good rotational symmetry of the radia-
tion field (i.e. the thermal field), but the accommodation of different
translation mechanisms for the feed rod and the crystal is quite difficult
(e.g. see the construction in [Bed84]) and the maximum processing
length is usually limited to a value smaller than the distance of the two
foci. In this type of furnace, ampoules are necessary to fix the feed rod
and the growing crystal (fig. 2-7). With the second type of construction,
the processing length is only limited by the translation mechanisms, but
the thermal symmetry is degraded considerably, making crystal rotationa necessity. Often several mirrors are combined to alleviate the thermal
asymmetry as in the double-ellipsoid mirror furnace in figs. 2-10 and
18 2. The floating-zone process
Fig. 2-9: Image furnace with twoparabolic mirrors and ahemispherical additional mirror,1/4 the diameter of the mainmirrors, to increase the solidangle from W=5.9sr to 11.2sr.The additional mirror, if activelycooled, also shields the top of thesample from direct radiation,thus improving the axialtemperature gradient.
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2. The floating-zone process 19
Fig. 2-10: Double ellipsoid mirror furnace MHF [Eye77, Eye79],developed at the Crystallographic Institute in Freiburg, with half-axes80mm and 90mm. A furnace with the same internal geometry has beenflown on the Spacelab missions FSLP (MSDR-MHF) and D1(WL-MHF). Compare also fig. 2-11.
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2-11; this allows also an increase in available heating power. For ellip-
soidal mirrors, however, the good efficiency is reduced because the
radiation directly emitted from one lamp into a different ellipsoid is not
focused and lost. A limitation to two joined ellipsoids has been shown to
be the best compromise [Eye77, Eye79]. A furnace where a part of an
ellipse is not rotated around the major axis but an axis perpendicular to it
(fig. 2-12) can also be regarded as part of this group, or as a cross
between a ring resistance heater and an image furnace. The rotational
symmetry of such a furnace should be quite good, but, probably due to
the manufacturing difficulties of making and supporting the heating
element and the mirrors, only a few constructions have been reported to
date [Dav78, Quo93]. The latter, used for the crystal growth of Ge and
Bi12GeO20, employed a Super Kanthal resistance heating element,
because it does not need as many mechanical supports as a filament.
Mirrors are usually machined from metal, e.g. aluminum alloys (such
as Al with 3% Mg), brass, or steel. The inner surface has to be polished
and can either be used as is (aluminum alloy mirrors) or is electrolyti-
cally coated with gold (reflectances see fig. 2-13). Silver, although
20 2. The floating-zone process
Fig. 2-11:Laboratoryversion of thedouble-ellip- soidmirror furnace(MHF-L).
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having the best reflectance, is avoided due to its unfavorable tarnishing
properties.
If processing in air is not possible, the processing atmosphere can be
provided by the furnace volume itself in the case of closed mirror
furnaces with vacuumtight feedthroughs, or by additional transparentcontainers, e.g. ampoules or fused quartz tubes. Transparent pressurized
vessels for up to 107 Pa have been reported [Bal81].
2. The floating-zone process 21
Fig. 2-12: Schematicview of a float-zonefurnace with ellipti-cal reflector. Such afurnace was devel-oped and built byCANMET for thegrowth of Ge andBi12GeO20 crystals[Quo93]. It employsa MoSi2 (SuperKanthal) heating
element.
Fig. 2-13: Reflectivity ofseveral mirror materialsrom 200 to 4000nm
(after [Nau87]).
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Although some of the first furnaces developed employed carbon arcs
[Koo61], the light sources mostly used today are either tungsten halogen
lamps of the order of 0.5-1.5kW (fig. 2-14) or Xenon arc lamps up to
10kW for high power requirements [Kit77, Bal81]. In the latter case, the
spectral distribution of the radiation has to be taken from the manufac-
turer's data. The spectral intensity I of thermal radiators such as tungsten
filaments is given by :
(2-I)I(,T) = (,T) $ Ib(,T)
where e=spectral and temperature dependent emissivity of the material,
=frequency, T=absolute temperature, and Ib=spectral intensity of a
black body radiator given by Planck's law:
22 2. The floating-zone process
Fig. 2-14: Tungsten halogen lampstypically used in mirror furnaces.Left: Special development (Sylva-nia A 708, 36V, 450W). Right:Commercial type normally usedfor studio lighting, available fromseveral vendors (FEL1000, 120V,1000W).
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(2-II)Ib(,T) =2$hc2
$
eh$
k$T 1
where h=Planck's constant, c=speed of light, k=Boltzmann's constant,
other symbols as above.
In all cases where lamp bulbs made of fused quartz are employed,
wavelengths shorter than 0.2m or longer than 4m are cut off. For
borosilicate glass the transparent region ranges only from 0.35 to 2.5m.
The filaments or arcs should be as small and isometric as possible, as
the focusing properties degrade rapidly for nonfocal/nonparaxial rays
(fig. 2-15) due to the strong coma in parabolic and elliptic mirrors
[Ray88]. Optical aberrations are more pronounced for strongly curved
surfaces, i.e. for ellipsoids with an axes ratio
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Feedback control of image furnaces is uncommon, because no usable
temperature signal can be obtained from the zone without difficulties
[Eye77, Eye81]. Theoretically, pyrometric measurements can be made in
the far infrared where the radiation from the lamp is cut off by the fused
quartz bulbs , but this would exclude any ampoules or fused quartz tubes
around the sample or fused quartz/glass windows in the furnace. A
24 2. The floating-zone process
Fig. 2-15: Focusing properties of differently shaped parabolic andellipsoidal mirrors for focal rays and rays at axial positions 5mmfrom the focus; shown are three rays 15o apart on each side for eachposition. f is the distance from the focal point to the apex of the mirror.The progressive coma for strongly curved geometries is clearly visible.
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chopper in front of the lamps is also not practical [Eye77]. The zone is
usually controlled by visual observation of the zone and manual regula-
tion of the power. If automatic processing must be used as in unmanned
space flights, an optimum parameter set (power/translation/rotation) isfirst established by test runs and then executed automatically. A control
loop regulates either the lamp power (or voltage if the lamp resistance
can be assumed to be time independent) or the light intensity measured
by photodiodes pointing at the filament. Light intensity control takes into
account changes of the light output not only related to voltage fluctua-
tions and filament resistance, but also to the discoloration of the lamp
2. The floating-zone process 25
Fig. 2-16: Paraboloid -ellipsoid mirror furnacedeveloped by theaerospace companyDornier (MEDEA- ELLI,2nd version). The foci ofthe two outer parabo-loids coincide with thefoci of the center ellip-soid. The lower focus isan annulus of 20mm .This furnace was
successfully used on theSpacelab mission D2and, under the nameCFZF, on theSPACEHAB-4 mission.
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bulb, or the higher light intensity under microgravity, caused by the
absence of convective gas cooling of the filament [Eye84]. Due to the
very nature of closed mirror furnaces, however, the photodiode signalcan be quite susceptible to changes of the light reflected back from the
sample towards the lamp, such as changes of the zone shape. Light inten-
sity measurement devices employing diffusers and beamsplitters are
possible in open mirror furnaces and are better suited for control [Bal81].
With modern computing techniques, a control loop using the zone shape
or height determined by image analyzers might be possible, but has not
been reported yet. With reflecting samples, the many reflections and
backreflections in a mirror furnace (fig. 2-3 and frontispiece) make
automatic detection of the interfaces difficult.
The power of incandescent lamps can of course be varied between
zero and full power, but most arc lamps allow changes of the light inten-
sity only in a small power range (usually 3/4 to full power). In this case,
or when a constant color temperature is desired with incandescent lamps,the light flux can be controlled by an aperture in certain geometries (see
[Bal81]).
Temperature gradients are mainly determined by the geometries of the
furnace, the filament, and the sample, as well as the optical and thermal
coefficients of the solid and liquid sample material. The direct radiation
of the lamp onto the sample top in monoellipsoid furnaces and the focus-
ing properties lead to a considerable flattening of the temperature gradi-
ent at the upper interface (fig. 2-17). A small absorber or reflector
mounted between the tips of lamp and sample like the hemispherical
mirror in fig. 2-9 can reduce this effect. It needs to be actively cooled,
though, because otherwise it will heat up and emit radiation itself
[Wat94]. A small (1-5mm) defocusing of the lamp towards the apex of
the ellipsoid also steepens the temperature profile between the focus and
26 2. The floating-zone process
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the center of the ellipsoid (fig. 2-17), because it diminishes the amount
of defocused rays coming from parts of the filament located nearer to the
furnace center (green rays in fig. 2-15) in favor of rays coming from near
the apex (blue rays in fig. 2-15). The latter are better focused, but can
lead to a second focus below the original one for certain defocusing
distances [Dol94]. Paraboloidal mirrors with moderate curvature allow a
steeper axial gradient at the expense of efficiency. Trying to get the best
of both concepts, a mirror furnace using a combination of two parabo-
loids and an ellipsoid (fig. 2-16) has been built by the aerospace
company Dornier [Len90]. It was successfully used on the Spacelab
mission D2 in 1993 for the floating zone growth of GaAs crystals (mp:
2. The floating-zone process 27
Fig. 2-17: Numerical simulations of the axial temperature profiles in theELLI furnace (fig. 2-8) with the A708 lamp at 100W for a graphitesample of 15mm diameter and 140mm length. The conductive andconvective heat transport by the surrounding argon is taken intoaccount, from [Wat94].
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1238oC) with 20mm diameter at 600W lamp power [Cr94b, Her95], and
for several other materials on the SPACEHAB-4 mission in 1996.
Temperature gradients are also determined by the reflectance, trans-mittance and emittance values of the materials in relation to the radiation
spectrum on one hand and by thermal conductivities, dimensions,
convection and the latent heat of melting/solidification on the other hand.
A further description is given in section 2.2.2. It should be noted,
however, that the position of the temperature maximum in mirror
furnaces, sometimes called "thermal focus", is usually not located at the
geometric focus, but a few mm towards the center of the ellipsoid.
One important peculiarity of radiation heating, especially image
furnaces and laser heating systems, is the feedback between the heating
power absorbed and the change of absorption and reflection coefficients
28 2. The floating-zone process
[Nas90]20.083-
0.111
0.090.07-
0.08
Y3Al5O12/YAG(633nm)
[Nas90]0.50.01-0.1
0.060.04Al2O3 /Sapphire(633nm)
[CRC81]0.220.140.780.86Au(650nm)
[CRC81]0.370.350.630.65Fe(650nm)
[Cro82]0.180.650.820.35Ge(VIS)
[Cel85]0.280.600.720.38Si(VIS)
Ref.l[mm-1]
s[mm-1]
elesrlrsMaterial
(Wavelength)
Table 2-a: Optical material parameters in the solid (index s) and liquid(index l ) state for several materials. r: reflectivity, e: emissivity, a:
absorption coefficient. The s and s values are for smooth surfaces.Value ranges indicate temperature dependent measurements. Note thatthe absorption coefficient is used here, not the absorptance equivalent tothe emittance (=emissivity for opaque materials with smooth surfaces).VIS: visible range of the spectrum.
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upon melting. For some materials, these coefficients change considerably
at the melting point (table 2-a). In figs. 2-3 and 2-4 one can easily see the
substantial increase of the reflectivity of silicon and of the absorptioncoefficient (color change) of GGG upon melting, respectively.
The first case, i.e. the increase in reflectivity of an opaque substance
upon melting, leads to the formation of a pattern of crystallographically
oriented droplets and solid material (fig. 2-18) on the surface at melting
temperature [Cel84, Cel85, Jac85]. By this, the system adjusts the
macroscopic average reflectivity in such a way that the melting tempera-
ture is maintained despite the changes in absorption coefficient at the
phase transition. In other words, between the point where the surface
starts melting and the point where the whole surface is molten, a substan-
tial increase in heating power is necessary to allow for the reduction of
the absorptivity, in addition to the latent heat required. The droplets at
the interface are not stable, but move and coalesce in the temperature
2. The floating-zone process 29
Fig. 2-18: Droplet formation on melting silicon rods (8mm ) in amirror furnace. Left: free surface, right: covered by SiO2 , showing
triangular melt areas following crystallographic directions.
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gradient due to surface tension effects, and due to gravity. This often
gives the impression, especially with high translation rates at the feed
rod interface, that the material is "boiling", and can introduce someirregular vibrations of the zone. These effects are enhanced for materials
where superheating of the solid is possible, such as many semiconduc-
tors [Wen78]. Apart from the movements, this change of reflectivity is
advantageous in general in that it leads to a self-stabilization of the
system; it damps the effect of a perturbation or an asymmetry of the
radiative flux, unavoidable in real systems, on the energy flux into the
sample (i.e. on the zone height and shape, the temperature distribution).
Materials with a higher absorption coefficient of the melt than of the
solid such as many oxides show the opposite effect. Upon the formation
of the melt zone, the power must be decreased, and asymmetries in the
30 2. The floating-zone process
Fig. 2-19: Axial incident power distribution at the surface of a GaSbsample of 10mm in the TEM-02 ELLI furnace at 90W total power,
calculated with and without secondary radiation. From [Wat94].
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external radiation/temperature field can be amplified considerably.
Constant attention is necessary for the control of these melt zones.
The complex interplay between the different material parameters,
temperatures, convective flows and the geometry as listed in table 2-b
leads to difficulties in determining the temperature fields in mirror
furnaces. Due to the recent progress in computing, numerical simulations
by finite element methods are able to predict reasonably well some
aspects of the processb; with some simplifications (i.e. only one
2. The floating-zone process 31
b The results in [Kai93, Dol94, Wat94] were obtained by combining a program
(ELLI, see [Dol94]) calculating the radiation field of the mirror furnace (includingsecondary radiation, multiple reflections, diffuse reflections, wavelength as a
function of the reflectivity) with the commercial finite element program FIDAP fora global numerical simulation of the temperature field in the furnace, including the
heat conductivity of the furnace atmosphere.
xLatent heat
xxxConvectiveheat transport
xxxxxxThermalconductivity
xxxxTransmittance
xxxxxReflectance
xxxxxEmittance/Absorptance
xxxxxGeometry
Lamp(filament/bulb/gas
filling)
Furnaceatmosphere
FurnaceAmpouleor
structural
parts
Crystal/feed rod
MeltZone
Table 2-b: Parameters influencing the temperature field in a mirrorheating system; except for the geometry and the latent heat, the parame-
ters themselves may be temperature dependent.
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reflection at the mirror) analytical methods are also a possibility [Riv92,
Hay96). For example, numerical simulations have shown that the secon-
dary radiation, i.e. the radiation emitted by the sample, cannot beneglected in calculating the temperature field in mirror furnaces, as
shown in fig. 2-19 [Kra85, Dol94, Wat94]. A similar result was obtained
by a recent analytical study [Hay96]. Numerical simulations as well as
analytical calculations depend, however, on the availability of reliable
thermophysical data. For a lot of systems, even well-known materials
such as silicon, these are not available with the necessary accuracy
(compare section 3.1.2). Therefore, a check against experimental results
is nearly always necessary.
32 2. The floating-zone process
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2.1.1.1c Laser heating
Laser heating shares many aspects with the image furnaces described
above. This includes the good visual control, the in principle unlimited
temperature range, no general limitations for the processing atmosphere,
and the effects associated with the change of reflectivity and absorption
coefficient at the melting point. Due to their monochromatic nature, and
in contrast to mirror furnaces, laser heaters allow straightforward
pyrometric temperature measurements. Secon- dary radiation does not
influence the temperature profile considerably unless radiation shields
are used. Automatic diameter control, e.g. with a second laser at a differ-
ent wavelength [Fej84], is also easier than in mirror furnaces. The energy
efficiency of laser furnaces, however, is not very good compared to
mirror furnaces, starting with a low electrooptical conversion efficiency,
e.g. 10% for a CO2 laser [Car91]. The available optical power is then
further reduced in the optical system (beam expander, mirrors) by
2. The floating-zone process 33
Fig. 2-20: Axiconbased laser heatingsystem for pedestalgrowth, employingonly catoptricelements to producea ringfocus. A:axicon mirror, P:parabolic mirror.After [Fej84] and[Fei86].
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reflection and absorption losses. Typically, 4-10 optical surfaces are
necessary in advanced systems. Additional pre- and afterheaters are
sometimes used to reduce the necessary laser power. Although all typesof lasers providing the power at an appropriate wavelength might be
used, the cw CO2 laser with a wavelength of 10.6 m is the predominant
type. This is due to the fact that oxides, the material group where laser
heating furnaces are most often applied, are opaque at this wavelength.
The same reason precludes the use of this laser for standard ampoule or
tube materials (SiO2, Al2O3) as sample containment if processing in an
oxidi- zing atmosphere is not possible. Therefore lasers with wavelength
in the VIS or near IR, such as YAG-Nd3+ lasers with =1.06m, are also
utilized.
The use of lasers for floating-zone growth was started in 1969 by
Eickhoff and Grs [Eic69] with the growth of ruby crystals and has
continued over the years, see e.g. [Gas70, Tak77, Bur77, Gur78, Kim79,
Dre80, Elw85, Car91, Che95, Che96]. The main application in recentyears has been for pulling optical single crystal fibers by the pedestal
method, e.g. [Fej84, Fei86, Fei88, Tan88, Nas90, Til91, Yan91, Ima95].
Early designs employed a single laser or several lasers directed at the
zone (sometimes with beamsplitter and mirrors, see e.g. [Gas70]), result-
ing in strongly asymmetric temperature profiles. For a good rotational
symmetry, axicon optics as shown in fig. 2-5 or fig. 2-20 are employed
[Fei86, Car91]. A catoptric focusing system as in fig. 2-20 does not pose
any difficulties for cooling the optical elements and, at the CO2 laser
wavelength, more materials than the ones listed in fig. 2-13 are available
as mirrors (e.g., molybdenum has a reflectivity of 98% at this
wavelength). Another possibility is the use of a catadioptric system as
shown in fig. 2-5. The refractive elements can be made of GaAs, ZnSe
(Irtran4) for =10.6m; Si or Ge are not suitable for high power CO2
34 2. The floating-zone process
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lasers due to absorption bands (Si) or thermal runaway (Ge) [Kar93].
The high refractive index of these materials (n=2.43 for ZnSe, n=3.28 for
GaAs at 10.6m) leads to a considerable loss of power by reflection(17% for ZnSe) and makes antireflection coatings a necessity. An analy-
sis by Carlberg [Car91] showed that only 50% of the power leaving the
laser is absorbed by the sample (Al2O3), and 900W of electrical power
(equivalent to 58W laser power reaching the sample) was needed to form
a floating zone in 10mm LiNbO3 (mp: 1260oC) rods. Tilting of optical
elements might be used for moving the zone without sample translation
[Bag86].
The axial temperature gradient in laser heated floating zones is
normally rather high (up to 1000K/cm [Fei88]) if the profile of the laser
beam is maintained or focused by the optical system. This can be advan-
tageous with respect to high possible growth rates [Fei86, Fei88], but
also introduces higher thermal stress in the crystal and strong, time-
dependent thermocapillary convection in the zone (chapter 3). If thesedisadvantages outweigh the benefits of a high pulling rate, the axial
gradient (as well as the interface curvature) can be changed by additional
pre- and afterheaters, thermal shields around the sample, defocusing of
the beam profile by the optical system, the use of several laser/axicon
systems for producing concentric ring beams [Car91], or a combination
of these approaches.
2. The floating-zone process 35
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2.1.1.2 High frequency heating
Heating by high frequency (HF) is one of the major methods of
floating-zone growth. HF heating with frequencies between several
100kHz and a few 100Mhz is referred to as radio frequency (RF)
heating, with frequencies from 0.5 to several GHz as microwave heating.
It is based either on induction heating for conductive or ferromagnetic
materials or on capacitive heating for dielectrics such as organic materi-
als, the former being the predominant type of operation. Industrial float-
zone processing is almost exclusively done by RF induction heating.
In induction heating, the charge is surrounded by the HF carrying coil
and the heating effect is due to the resistance heating by the induced
eddy currents in the material. The setup is similar to an electric trans-
former with the sample as a single turn secondary coil. Additional
heating due to magnetic losses (hysteresis losses) occurs only in ferro-
magnetic materials below the Curie point and is usually of no practicalimportance for crystal growth. Typical frequencies range from 400kHz
to 5MHz and the maximum resistivity of the sample should be below
100cm. For materials such as undoped semiconductors or salts, where
the conductivity of the material is sufficiently high only above certain
temperatures, the initial heating must be done by an additional heater,
e.g. by radiation heating. This can also be achieved by introducing
temporarily an additional charge (e.g. a metal or graphite ring) which in
turn heats the sample by radiation and/or heat conduction until the
sample conductivity is high enough to absorb a sufficient amount of the
induced energy.
In principle, processing can be done both under vacuum or with a gas
atmosphere. When using a gaseous atmosphere, e.g. to reduce the evapo-
ration of material, the voltage between the coil turns and/or the coil and
2. The floating-zone process 35
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the - usually grounded - sample should not exceed the breakdown
voltage for the given gas species and pressure to avoid corona discharges
or arcing. Argon and hydrogen, in contrast to helium, have suitably high
breakdown voltages; in the case of Ar, a small addition of N2 is helpful
in this respect [Boh94]. At the cost of efficiency, the inductor coil and
the sample can be separated by a nonconducting container, e.g. to avoid
condensation of evaporated material onto the cooled coil.
Several other boundary conditions must be considered in the heater
construction and choice of frequencies, namely zone dimensions, heating
efficiency, skin depth, and the electrodynamic pressure.
Heating efficiency is determined by the coupling between the sample
and the primary coil; the coil shape should preferably follow the sample
shape as closely as possible. Furthermore, the resonant resistance of the
oscillator should be matched to the impedance of the sample, the former
given by (after [Sha80a]):
(2-III)R=530$Q
C$0
where Q=circuit quality factor=reactance/resistance, C=circuit capaci-
tance and 0=resonance frequency= , L being the circuit1/(2 $ L $C)
inductance.
Due to the self induction effect, the current distribution is not constant
across the sample diameter, but follows
(2-IV)I= I0 $ exsk
36 2. The floating-zone process
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where I0=current at the sample surface, x=depth below the sample
surface, sk=skin depth, the depth at which the current is 1/e of the
surface current.
The skin depth is dependent on the frequency as well as the resistivity
and permeability of the sample and can be calculated by
(2-V)sk=!
$$0$r
where =resistivity, =frequency, r=relative permeability (close to 1
for most melts), 0=absolute permeability=4 10-7 Vs/Am.
For high frequencies (MHz), the heat is thus generated in a very thin
layer and then distributed by heat conduction and convection. For silicon
and a frequency of 2.4MHz, sk is about 292m [Boh94]. Consequently,
the sample resistance is no longer inversely proportional to the cross
section, but to the circumference of the sample. For the same reason,
tubes instead of wires can be used as primary coils without increasing
resistance losses; in addition, they allow very efficient water cooling.
Arcing problems and sufficient cooling of the primary coil must also
be considered in the choice of the operating frequencies [Gup78],
because for a given power the RF voltage goes up with 3/4 and the
current goes down with 1/4 [Kel81]. Fig. 2-21 shows some possibilities
for coil geometries: a) is the basic single turn coil, b) to f) are different
possibilities for multiple turn coils, which allow higher currents in the
sample in proportion to their number of turns. Case 2-21b, sometimes
called a pancake coil, allows a better concentration of energy at the
expense of efficiency, whereas 2-21c gives better coupling, but the
2. The floating-zone process 37
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induced current is spread over a larger area. Case 2-21f is similar to
2-21c, but makes use of an additional watercooled concentrator to focus
the induced currents.
An important aspect of induction heating is the presence of the
Lorentz force (eq. 3-XXXV), which for the case of induction heating can
be written as [Mh83]:
(2-VI)FL =
2H2 +(H)H
with H=magnetic field strength, =0r=permeability.
The resulting electrodynamic pressure, a repulsive force between the
induction coil and the zone, can be used to support larger zones than
usually possible. Fig. 2-21d shows a possible shape for a levitating coil.
The electrodynamic pressure is inversely proportional to the square root
of the frequency (eq. 2-XXXVI, section 2.2.3), so lower frequencies
would allow a larger levitating effect. If, due to other considerations, thepossible frequency range for the heating coil is limited to higher values
[Gup78, Kel81], a setup with two independent coils, one mainly for
heating, one mainly for levitation, can be used (fig. 2-21e).
The electrodynamic pressure is also utilized in a special coil configu-
ration called needle-eye technique (fig. 2-22). Industrial FZ growth of
silicon is almost exclusively done with this setup. The large single turn
"pancake" coil has an inner diameter which is considerably smaller than
the diameters of both the feed rod and the growing crystal. It usually
consists of two parts, electrically separated by a ground connection (gray
section in fig. 2-22), to halve the voltage between the coil and ground,
and thus reduce arcing problems [Kel81]. For the same reason, compara-
tively high currents (above 1000A [Kel81]) are employed, necessitating
very good cooling. For silicon, the electrodynamic pressure of this
38 2. The floating-zone process
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arrangement allows an approximate doubling of the length of a floating
zone to values of about 30mm. In addition, the diameter of the liquid is
considerably reduced at the center by being compressed through the
"needle-eye", thus enabling absorption of energy not only at the circum-
ference of the rods as it would be the case in the arrangements of fig.
2-21, but also close to the solid-melt interfaces. The crystal interface
shape is mostly concave or w-shaped with this arrangement and theaspect ratio external zone height/zone diameter can be much smaller than
usual (compare chapters 2.2.2 and 2.2.3). For FZ-silicon, the maximum
industrially produced diameter is now 150mm (6") [Zuh89].
The coil inner diameter and the coil contours influence the interface
shape (and the radial segregation) to a large extent [Kel81, Mh83,
Rie95, Mh95]. For disk-shaped coils with rectangular cross section,
2. The floating-zone process 39
Fig. 2-21: Different coil configurations for RF heating. a: single-turn
coil b: pancake coil c: multiple turn coil d: levitating coil e: two
separate coils, the upper single-turn coil for heating, the lower three-
turn coil for levitation f: coil with concentrator. After [Sch64, Jon74,
Sha80a, Sha80b]; compare text.
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thinner disks appear to be advantageous [Kel81]. Steps at the coil
bottom, as well as coils with a wedge-shaped cross section (fig. 2-22)
tend to flatten the lower interface due to an afterheater effect [Kel81].
Further optimization leads to coil shapes with rather complicated cross
sections [Rie95]. Another possibility to influence the interface shape -
apart from the introduction of separate afterheaters - is a deviation from
circular symmetry, by moving the crystal axis laterally with respect to
the feed rod and zone axis (eccentric needle-eye float-zone technique
[Kel81]), by moving the coil to an eccentric position with respect to the
crystal and feed rod [Sch89], by using elliptic shapes for the coil
openings [Sch89], or a combination of these.
In addition to the control concepts mentioned in section 2.1, one can
also use the feedback signals from the tuned heater circuit in the case of
induction heating, because any changes in the shape and size of the
40 2. The floating-zone process
Fig. 2-22: Schematic view of a single turn watercooled RF heating
coil for needle-eye floating-zone growth.
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crystal as well as the zone change the inductance of the system and thus
the position of the resonance curve (fig. 2-23). For a given system,
thermal or mechanical self-stabilization can be achieved by an appropri-
ate choice of the frequency [Kel81]: For materials with a negative
temperature coefficient of the resistivity, a fixed workpoint at a on the
inductive slope of the resonance curve leads to thermal stabilization,
because a temperature increase leads to a higher conductivity and thus to
a smaller inductance, which shifts the resonance frequency 0 to higher
values (black curve -> gray curve in fig. 2-23). By this shift, the coil
voltage (i.e. the power) goes down, moving from a to a'. For materials
with positive temperature coefficients of the resistivity, a workpoint on
the capacitive slope gives thermal stabilization. In both cases, a mechani-
cal stabilization is possible with a fixed workpoint at b on the capacitive
slope; any movement of the melt or crystal towards the coil increases the
power (the voltage goes from b to b') and thus the electrodynamic
pressure at this point .Capacitive heating of insulators by high frequency electromagnetic
radiation utilizes the interaction of the alternating electric field with the
dielectric polarization of the material. Heating is only possible when, due
to relaxation of dipoles, a phase difference between the electric field
vector and the polarization vector is present. The amount of heating is
governed by the loss factor of the dielectric, which is the imaginary
part of the frequency dependent complex dielectric constant :
(2-VII)& = i$
Possible contributions to the polarization of a material are electronic
polarization, atomic polarization, dielectric polarization and, for hetero-
geneous systems, the so-called Maxwell-Wagner polarization due to
2. The floating-zone process 41
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charge build-up at interfaces. The contribution of the first two to the loss
factor are in the VIS and IR; this leaves the dielectric polarization losses
(sometimes called reorientation losses), and conductivity losses for the
heating of a single phase system with high frequency. The useful
frequency range is considerably higher than that of induction heating,
ranging from radio frequencies of 30MHz [Sha80a] to microwaves of
several GHz [Sch64, Met88]. The heating efficiency is given by the total
power loss w in the dielectric, which is given by [Sha80a]:
(2-VIII)w= U2 $C$* $
42 2. The floating-zone process
Fig. 2-23: Schematic voltage (power) - frequency diagram for two
different resonance curves of a tuned RF heater circuit (after [Kel81]).
Workpointa gives thermal stabilization, workpointb mechanical stabili-
zation of the zone. See text for details.
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where U=voltage, C=capacitance, =rotational frequency, =dielectric
loss factor.
For a given frequency, the maximum power for capacitive heating, i.e.
the maximum voltage, is given by the electric breakdown limit of the
material. For frequencies in the microwave range, i.e. above 0.5GHz, a
wired circuit such as a coil cannot be used. The microwave radiation,
usually generated by a klystron or magnetron, is transferred to the
sample by a waveguide. A concentration of the microwave energy is
possible by designing the growth chamber as a resonant cavity [Met88].
It should be mentioned that in magnetic materials a magnetic loss
factor of the complex permeability * might contribute to heating
[Met88]. The effect, not to be mistaken with hysteresis losses, is caused
by domain wall and/or electron spin resonance in the RF and microwave
range of the spectrum.
2. The floating-zone process 43
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2.1.1.3 Electron beam and plasma heating
Both methods use mainly charged particles, i.e. electrons and/or ions
to heat the sample; their principles are illustrated in fig. 2-24. The main
practical difference is that electron beam heating requires vacuum,
whereas an ambient gas is necessary for all plasma heating methods.
2.1.1.3a Electron beam heating
In electron beam heating, the sample is heated by the absorption of
kinetic energy of electrons emitted from a cathode and then accelerated
by the applied voltage to the sample anode (fig. 2-24). Since its intro-
duction in 1956/1957 by Davis and Calverley [Cal57], the main use in
float-zone processing in the last 40 years has been the crystal growth
(and zone refining) of refractory metals and alloys with high melting
points, see e.g. [Neu62, Sel64, Mau68, Hay78, Jur82, Gle89, Jur90a,Jur90b, Sem95, Liu96]. The method is often called EBZM (electron
beam zone melting) and requires operation under a vacuum better than
10-4mbar. For this reason, materials with a considerable vapor pressure at
the melting point are not very suitable, though an additional purification
effect is often achieved by the outgassing of volatile impurities during
processing [Sch64]. In the usual setup, with the sample as anode, the
sample material must be conducting, excluding insulators and most
(undoped) semiconductors. This disadvantage can be overcome by the
use of an additional grid as anode around the sample.
Typical voltages are several kV, the upper limit set by the generation
of X-rays, with currents of the order of 10-2-10-1A. In most cases, the
cathode is on ground potential and the positive voltage is applied to the
44 2. The floating-zone process
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sample [Boh94]. Electron beam heating can be highly efficient, with
over 99% of the cathode current arriving at the sample [Sha81a].
Current-voltage characteristics are similar to those of a vacuum diode:
Up to the saturation current, the current is space charge limited, with the
current density j given by
(2-IX)jl 0 $2$em $
U32
x2
where 0=permittivity of vacuum, e=electron charge, m=electron mass,U=voltage, x=distance between the electrodes.
The saturation current is given by the Richardson equation:
(2-X)jsc= A $K$T2 $ eWek$T
2. The floating-zone process 45
Fig. 2-24: General representation of the principles of electron beam
heating (a) and plasma heating (b) in FZ growth. In electron beam
heating, vacuum is necessary and the zone as anode is heated by the
accelerated electrons. In plasma heating, requiring an ambient gas,
there is no macroscopic charge and the heating is by excited electrons
and ions from the plasma. See text for details.
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where A=area, K=material constant ( 60 Acm-2 for metals), T=filament
temperature, We=emission work function (4.54eV for tungsten),
k=Boltzmann's constant.
The most simple arrangement uses a ringwire as cathode surrounding
the zone (fig. 2-24), often made from tungsten or the same material as
the crystal to avoid contamination. If the latter is not possible, contami-
nation by filament material can be a problem with this setup at higher
temperatures. Similar to vacuum triodes/pentodes or electron micro-
scopes, more sophisticated electron guns (see e.g. fig 2-25) use modula-
tor grids, additional focusing and accessory electrodes, as well as
electron lenses to reduce this problem and to allow better control of the
electron beam. The cross section of the electron beam can be reduced to
an area of m2 to produce very high power densities (up to 105 kWcm-2
[Sha81a]) and high temperature gradients. Control of the power, i.e. of
the emission current is achieved either by controlling the cathode-anodevoltage or the filament temperature (maximum working temperature is
0.9 mp). Control of the emission current can be complicated by a
positive feedback due to the outgassing of material from the sample or
the cathode: The additional ions increase the current, which in turn
increases the sample temperature leading to even stronger outgassing.
This cycle can end in a voltage breakdown by glow or arc discharge.
Temperature measurements by pyrometry are possible and have for
instance been used to determine the temperature gradients in an electron-
beam heated floating zone of refractory metals [Jur82, Jur90a, Jur90b].
2.1.1.3b Plasma heating
Setups requiring or permitting operation in a gas atmosphere allow the
use of a plasma as heat source. In a plasma the atoms or molecules of the
46 2. The floating-zone process
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gas are excited and ionized to a degree allowing good conductivity, but
there is no macroscopic charge. The heating effect is due to the transfer
of kinetic energy of the electrons, ions and sometimes excited neutral
molecules of the plasma to the sample. A plasma can be characterized by
a) the degree of ionization, b) the operating pressure, c) the plasma
temperature, and d) the method of ionization, e.g. glow discharge,
electric arcs, RF and microwave excitation, electron-cyclotron resonance
(ECR), focused laser radiation and flame heating.
A glow discharge plasma is a low pressure (typically 0.1-1mbar), low
temperature and low degree of ionization (a few %) plasma. The depend-
ence of the current density j on the gas pressure p is given by
(2-XI)ji p2
The plasma is generated by a suitable voltage between two electrodes.
Often, but not always, one of the electrodes is the sample. Usually the
glow discharge in the chamber is concentrated in two regions, the
cathode fall region with a high electron density due to ion bombardment
2. The floating-zone process 47
Fig. 2-25: Setup o
an electron gun with
additional electrodes
to focus the electronbeam. The contami-
nation of the sample
by tungsten evapo-
rated from the
cathode wire is
greatly reduced by
the larger distance
lus the shielding o
the upper accessoryelectrode. After
[Sem95].
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of the cathode, and the anode fall region with thermally excited ions and
electrons. Both regions have been used for plasma heating in FZ crystal
growth, see e.g. [Tro62, Cla67, Cla68, Sto70, Bro71]. In addition to this
naturally occurring concentration of the plasma due to space charge
effects, hollow cathodes or anodes allow further focusing of the energy.
According to [Sha81a], typical parameters for a hollow cathode appara-
tus are 1.5-5kV and 0.1-1.5A in the pressure region specified above.
Operational limits of the process are given by the transition to an arc
discharge and sample contamination by sputtering of electrode material
at elevated temperatures.
The electric arc discharge is distinguished from the glow discharge by
the different mechanism of electron emission from the cathode. In the
case of a glow discharge, electrons are emitted mainly due to ion
bombardment, whereas in an arc discharge the higher electrode tempera-
ture leads to thermal emission of electrons. Thus the necessary voltage
for the discharge is reduced and the current density goes up considerably(j 0.1Acm-2 [Sha81a]). In this case, the pressure dependence of the
current density is
(2-XII)ji p43
By using an electric arc, very high temperatures can be attained, but it
is quite difficult to achieve sufficient temperature control. Another
problem is the high degree of contamination by electrode material,
although this can be reduced or overcome by watercooling of the
electrodes [Ger63], or by using electrodes made from the same material
as the crystal [Ver76, Mac88].
A plasma can be generated by RF heating with frequencies above
4MHz at low vapor pressures [Sha81], similar in construction to a RF
48 2. The floating-zone process
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plasma torch used for welding. Focusing of the plasma flame can be
achieved by magnetic and electric fields. To initialize the ionization,
temporary additional heating of the gas is necessary, e.g. by inserting a
conducting rod into the RF field. The method is capable of achieving
very high temperatures in excess of 4200K and there are no problems
from contamination; carbides of tantalum, hafnium, niobium and
vanadium have been grown by this process [Sav78, Kum81a, Kum81b].
Similar to excitation by radiofrequency, a plasma can also be generated
by microwaves in low pressure gas atmospheres. The concentration and
positioning of the microwave plasma is possible by a suitable design of
the waveguide and the cavity.
Float zoning with a gas burner, similar to the heating employed in the
Verneuil method, has been scarcely used. Possible combustible gases are
H2, propane and butane with O2 as oxidizer. It is of course only suitable
for processes without necessity of good temperature control and where
contamination by the burning gas or by air is not important. A fewoxides have been grown by this method [Bro64, Tie72].
2. The floating-zone process 49
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2.1.1.4 Direct heating
The term direct heating is used for two entirely different processes.
The first one, also termed Joule heating, uses the Joule heat of a current
through the sample as heat source (fig. 2-26). The voltage is directly
applied between the upper and lower ends of the sample. A resistance
gradient is then generated either by controlled active cooling of the
sample ends, by active additional heating of a small part of the sample,
or passively by using a small heat reflector around it [Pfa66]. More
power is dissipated in the hotter part than in the colder part, thus forming
a zone by positive feedback. Joule heating is more often used as
additional heating of the whole sample to reduce the required power of
the main power source, or to reduce thermal gradients and influence the
interface shape [Dor64].
In the second process, a heater is immersed into the melt, but has no
contact with the crystal (fig 2-27). The heat is directly transferred fromthe heating element to the melt by conduction. This arrangement is of
course not completely contamination-free and the chemical inertness of
the heater is of utmost importance. It might be argued that for this reason
it is not really a floating-zone process, but it retains the advantage that no
external stress is imposed onto the crystal by an ampoule or crucible.
The first heater of this type was the so-called strip heater (fig. 2-27a),
introduced in 1965 by Gasson for the crystal growth of Nd-doped schee-
lite crystals [Gas65]. A strip (resistance) heater consists of a small
iridium or platinum sheet inserted into the melt zone. Holes in the metal
strip allow the necessary material transport through the heater. This type
of heater has also been used to grow calcite [Bri71, Bel72, Bel76],
Ba0.65Sr0.35TiO3 [Hen74], BaTiO3 [Tur82], and Li2CO3 [Pal82]. In
addition to the strip heater, several other direct heater configurations
50 2. The floating-zone process
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have recently been investigated by Lan and Kou [Lan91a, Lan91b,
Lan91c], namely a step heater (fig. 2-27b) and ring heaters (fig. 2-27c,
d). NaNO3 was used as a model substance for these investigations, with
heaters made from graphite and/or aluminum. The heaters were designed
to act directly as a shaping die, similar to the EFG process. The main
goals were improving diameter control over the standard strip heater
design by reducing the melt creep caused by wetting effects, and a
significant reduction of thermocapillary convection by reducing the free
surface of the zone (see 3.4.3). The step heater (fig. 2-27b) and the
completely immersed ring heater (fig. 2-27c) gave the best shape control
[Lan91a, Lan91c]. The interface shape is of course also influenced by
the heater design and position. For the ring heaters, larger stable zones
than usually possible (see chapters 2.2.1 and 2.2.3) have been reported
and were attributed to the
additional supporting effect of the
ring [Lan91a].
2. The floating-zone process 51
Fig. 2-26: Principle setup of Joule
heating.
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52 2. The floating-zone process
Fig. 2-27: Immersed heater systems: a) strip heater, b) step heater, c)
and d) ring heater. After [Gas65, Lan91a, Lan91b, Lan91c].
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2.2 Floating-zone stability and control
The success of a floating-zone growth experiment depends to a largeextent on the ability to control the zone size and interface curvatures and
to understand their dependence on the growth conditions. An essential
parameter is the hydrostatic stability of the zone (sections 2.2.1, 2.2.1.1),
where exceeding the limits results in immediate termination of the
experiment. In addition to this static stability, the influence of transient
conditions during the crystal growth process must be considered; this
includes the influence of the growth angle and of volume changes on the
crystal size during the process (section 2.2.1.2). The different variables
determining the zone geometry, such as heater profiles and convective
flows, are discussed in section 2.2.2; additional possibilities for control
through external fields are given in section 2.2.3.
2.2.1 Zone and crystal shape
A floating melt or solution zone is held only by surface tension and
adhesion between feed rod and growing crystal. Under the approxima-
tion that the surface tension is not dependent on positiona and neglecting
influences by flows in the melt zone and the surrounding medium, the
shape of a floating zone, as that of any liquid volume with free bounda-
ries, can be described by the Laplace (or Young-Laplace) equation:
2. The floating-zone process 55
a This is of course not true for a real floating zone, but the change in the surfacetension due to temperature or concentration gradients is usually a few % at maximumand thus introduces only a small error in the static calculation of the zone shape. Asthe driving force of thermocapillary convection it has, however, a considerable
impact (compare section 3.1).
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(2-XIII)p= $ 1R1 +1R2
where p=pressure difference at the surface, =surface (interface)
tension, R1 and R2= principal radii (see fig. 2-28).
To put this equation to use one has to take into account the given
geometry, which defines the principal radii (fig. 2-28) by functions and
appropriate surface parameters, as well as any pressures in addition to
the always present capillary pressure, e.g. the hydrostatic pressure undergravity. For most geometries, no analytical solutions are possible and eq.
2-XIII must be solved numerically.
2.2.1.1 Static stability
56 2. The floating-zone process
Fig. 2-28: Principal radii R1
(green arrow) and R2 (red
arrow) from the Laplaceequation (2-XIII) for the floatingzone case. Note that in contrast
to R2, the origin of R1 is not
necessarily located on thez-axis.
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For axisymmetric zones, and taking the hydrostatic pressure due to
gravity into account, eq. 2-XIII can be written as [Cor77a, Cor77b,
Riv79, Teg95]:
(2-XIV)p0
! l$g $ z=
1
r$(1+r2 )12
r
(1+r2 )32
where z=cylindrical axial coordinate, r=r(z): zone radius at axial coordi-
nate z with r' and r'' as the first and second derivative, respectively,
=surface tension, p0=capillary pressure difference between melt andsurrounding gas or liquid at z=0, l=density difference between melt
and surrounding gas or liquid, g=gravitational acceleration.
By introducing dimensionless variables, the zone shape can be
described by four parameters [Cor77a, Cor77b], viz:
(2-XV)rfrc ,
Lrf ,
V
$rf2$L,
! l$g$rf2
= Bos
where rf=feed rod radius at interface, rc=crystal radius at interface,
L=zone length, V=zone volume, Bos=(static) Bond number.
The static Bond number expresses the balance between the destabiliz-
ing effect of gravityversus the stabilizing effect of surface tension. For g
0, as in microgravity conditions, it is close to zero and hydrostatic
pressure can be neglected. Zone (iso)rotation introduces a fifth parameter
similar to the static Bond number to account for the centrifugal force
[Cor77a, Cor77b]:
2. The floating-zone process 57
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(2-XVI)!$*2$rf
3
where =angular velocity, other symbols as above.
Using numerical methods to solve the above equations, one can obtain
the shape for a given set of parameters rf- rc - V - - l, e.g. for paramet-
ric studies. This has been done by a number of authors, e.g. [Cor77a,
Cor77b, Riv79, Bou85, Lan90, Mar95, Tat94, Teg95], for a variety of
configurations.An important special case of float-zone processing is the cylindrical
floating zone (fig. 2-29 top left), i.e. rf/rc=1, V/(r2 L)=1 and Bos0
(either g0 ms-2 as in microgravity conditions, or the zone, i.e. rl, is
very small) where the maximum stable zone lengths Lmax is given by:
(2-XVII)Lmax = 2 $ $ r
This is the famous Rayleigh limit, first observed by Plateau [Pla63]
and theoretically derived by Lord Rayleigh in 1879 [Ray79]. It states that
the length of a cylindrical zone cannot exceed its circumference, because
any sinusoidal perturbation with a wavelength larger than 2 r will
result in a smaller surface and thus a smaller energy than the cylindrical
shape. This relation governs the floating zone process under micrograv-ity conditions. It should be noted, however, that longer zones are possi-
ble with V>r2L, i.e. barrel-shaped zones, and that a zone can break
below the Rayleigh limit if V
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Bos0 the zone stability is independent of the surface tension value or
any other material parameters.
Under gravity, the resulting hydrostatic pressure changes the meniscus
to a "bottle" shape (fig. 2-29, right column, and fig. 2-30). Therefore the
meniscus angle M at the lower interface is increased and the meniscus at
2. The floating-zone process 59
Fig. 2-29: Silicon float-ing zones under micro-gravity (left column),
and 1g conditions (rightcolumn) in a monoellip-soid mirror furnace (seeigs. 2-7 and 2-8). The
g experiment, done ona sounding rocket(TEXUS 29), and the 1gexperiment were madein the same furnace and
with similar parametersettings (less power wasused for the g experi-ment, see section 2.2.2).Shown are the first meltzone (top row) formed
rom a cylindrical rodof 8mm , and the zoneand grown crystal after
about 5mm of growth(bottom row); i marksthe melt-crystal inter-ace. The translation
rate was 5mm/min.
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the upper interface usually bulges inward (for
rc=rf). In this case, the limit for a stable zone
length is given by M = 90o(if+W), where W
is the wetting angle of the melt with its own
solid (e.g., W is 33o for Si, 30o for Ge [Sat80]).
Normally, the maximum possible zone length
under this conditions is considerably smaller
than in the microgravity case.
Assuming flat interfaces and large equal radii
of crystal and feed rod (approximately rf= rc
10mm, depending on ) under gravity, the
above condition leads to the well known
equation [Hey56, Cor77a, Cor77b, Lan90,
Teg95]:
(2-XVIII)Lmax = K('M) $
! l$g
where =surface tension, l=density, g=gravita-
tional acceleration; K(M) is a factor dependent
on the meniscus angle M (fig. 2-30).
The dependence of K on M with M in degrees can be expressed by
[Teg95]:
K('M) = 2.672 + 1.815 $ 102 $ 'M 7.642 $ 105 $ 'M2
(2-XIX)
60 2. The floating-zone process
Fig. 2-30: Basicconfiguration for aloating zone under
gra- vity. M and M
are the lower andupper meniscus
angles, ic andif theangles of the crystaland feed rod inter-aces at the solid-
liquid-gas trijunction,resp.
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For constant diameter growth, the value of the meniscus angle M must
be identical to that of the growth angle Gb (tables 2-d, 2-e).
Eq. 2-XVIII was originally found by Heywang [Hey56] in an approxi-
mate calculation; it is often called the Heywang limit. He only consid-
ered the case M =0o and derived a value of K=2.84. The calculations of
Coriell and Cordes [Cor77a, Cor77b] resulted in K=2.67 for M = 0o; this
value is corroborated by eq. 2-XIX from [Teg95]. Interestingly, using a
value ofM =11o (the growth angle of silicon) in eq. 2-XIX, results in K=
2.86, close to Heywang's value. Table 2-d lists the surface tension,
2. The floating-zone process 61
b Note that the growth angle G itself is not really a material constant, but dependson several other conditions, among them the crystal orientation and the interface
curvature (see the following section, 2.2.1.2).
+4.7[Tay85]5.87[Str77]6.16rtCdTe
-12[Gla69]6.47[Ml84]5.78rtInSb
-3.2[Gla69]5.85[Ml84]5.67rtInAs
-5.9[Gla77]5.07[Ml84]4.79rtInP
-7.4[Gla69]6.03[Ml84]5.61rtGaSb
-7.6[Gla69]5.71[Ml84]5.31rtGaAs
-4.8[Gla69]5.51[Mh84]5.26mpGe
-11.7[Sas95]2.57
-10[Rhi95]2.53
-9.6[Gla69]2.52
[Mh84]2.30mpSi
!s! l!s [%]Ref.l[gcm-3]Ref.s [gcm-3]Material
Table 2-c: Densities in the solid (s) and liquid (l, at mp) state of somesemiconductors and the resulting volume change upon melting (rt: atroom temperature, mp: at melting point). All elementary semiconductorsof the diamond lattice type (space group Fd3m)and most of the binarysemiconductors of the sphalerite or wurtzite lattice type (space groupsF$3mandP63mc, respectively) have a negative volume change.
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density, growth angle and the resulting K and Lmax according to eqs.
2-XVIII and 2-XIX for several materials. It is evident that except for
silicon, having the favorable combination of a high surface tension and a
low density, Lmax is limited to a few mm under gravity for most materials.
Large growth angles like those of InSb or GaSb are not only favorable
because of their higher stability in transient growth situations (seesection 2.2.1.2); they also increase static stability due to the slightly
higher value of K(M). Lmax and the crystal diameter are independent of
each other according to eq. 2-XVIII, which would in theory allow the
growth of large diameter crystals. In practice, this would only be possi-
ble for completely planar or concave interfaces. For thermal reasons
(section 2.2.2), such conditions are usually not possible to attain for large
62 2. The floating-zone process
12.52.96174[Dre80]3.80[Sat80]670[Sat80]Al2O3
6.6290[Nak92]8.13.08251[Sat80]6.47[Gla69]434[Har93]InSb
8.73.1630.72[Teg96]6.03[Gla69]450[Teg95]GaSb
7.82.9315 [Hur63]401[Rup91]
9.92.9617.31.6[Teg95]5.71[Gla69]631[Wan90]GaAs
9.32.8073[Wen78]
9.72.9013[Sur76a]5.49[Gla69]600[Kec53]Ge
15.12.806.1-8.1[Teg95]718[Sas95]
17.12.8611[Sur75]2.52[Gla69]885[Har84]Si
Lmax [mKG[o]l [gcm-3 ] [10-3Nm-1 ]Material
Table 2-d: Surface tension , density l, growth angle G, factor K(G)calculated by eq. 2-XIX, and maximum zone length Lmax for large zonesunder 1g, calculated by eq. 2-XVIII for different materials. For otherdensities of liquid Si see table 2-c. If several material parameter values
were available, both the best and the worst case for Lmax are shown.
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crystals. A good rule of thumb for a lot of growth systems is that the
maximum diameter cannot exceed the zone length without the danger of
forming a solid bridge between crystal and feed rod, i.e. the aspect ratioL/2r should be equal to or larger than 1.
A concave lower interface, often encountered in needle-eye RF
heating, or through the combination of partially transparent materials
(oxides) and radiation heating, actually stabilizes the zone and increases
the maximum zone length by supporting the lower end of the meniscus
[Kel81]. A concave upper interface, however, increases the hydrostatic
pressure at the lower interface due to the larger liquid column height in
the center and hence acts as a destabilizing influence.
For the cases not covered by eq. 2-XVII and eq. 2-XVIII, e.g. with
intermediate values of r or for zones with rc rf, Lmax must be calculated
individually. An interesting result of an analysis of meniscus shapes is
the fact that for certain combinations of r, M and L several solutions
(fig. 2-31) of the Laplace equation - with different volumes- exist[Cor77a, Cor77b, Teg95]. Different meniscus shapes also result if the
crystal pulling direction for a given floating zone process is reversed
with respect to the gravity vector [Wil88]. Depending on the particular
system, stable growth is only possible for a certain range of the ratio
crystal diameter/feed rod diameter; this range is actually larger for
pulling upward than for pulling downward [Tat94]. For the pulling direc-
tion being opposed to the gravity vector, the requirement M=G 0o ,
however, can only be fulfilled for small zones [Dur86], or a substantially
smaller diameter of the growing crystal in comparison to the feed rod as
in the standing pedestal technique. Pulling downward is therefore the
most common case. Stability diagrams for various floating zones (or,
more generally, liquid bridges) can be found in [Cor77a, Cor77b, Riv79,
Lan90, Tat94, Mar95, Teg95]; tables 2 - 4 in [Mar95] give a
2. The floating-zone process 63
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comprehensive list of analyses done on the hydrostatics, stability limits,
and dynamics of liquid columns in general. An example of Lmax as a
function of the crystal radius is shown for silicon in fig. 2-32. As a rever-sal of the usual calculation, one can use the zone shape under gravity to
calculate approximate values of the surface tension for new material
systems [Nak90, Teg95, Teg95a]. Strongly bulging zones increase the
accuracy of this method of surface tension determination, with typical
errors of the order of 5-10%.
In real crystal growth situations, the zone length should be kept well
below the maximum value, because the static stability limit is derived
from the reaction of the surface energy to an infinitesimal small distur-
bance. Any disturbance of finite value, e.g. due to shocks or vibrations,
might easily cause a zone to rupture if its length is close to Lmax. This is
especially true for accelerations perpendicular to the zone axis. Floating
zones are very sensitive to vibrations; GaAs-FZ experiments on the
64 2. The floating-zone process
Fig. 2-31: Two possible meniscus shapes for a silicon floating zone with
the same values of rc=rf, L andM (11o), but different zone volumes and
values. The higher volume mode on the (left) is obviously the morestable one. From [Teg95].
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Spacelab mission D2 showed visible movement with accelerations as
small as 10-3-10-2g if the disturbance frequencies were close to the zone
resonance frequency (typical values are in the range of 0.5- 10Hz).The above considerations on the stability of floating zones can in
principle also be applied to free solution zones. In some cases, however,
an important difference related to the wetting between solid and solution
might complicate the situation. In the floating-zone case, the solid-
liquid-gas trijunctions are assumed to be located at the crystal and feed
rod edges, because the wetting angle is usually
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angle of the liquid can be >90o, in which case a free zone would detach
from the solid, even under microgravityc. If the wetting angle is < 90o,
the solution zone can be anchored at the crystal/feed rod edges, but forsystems with low wetting angles it might also creep over it. It must be
kept in mind that the usual measure (in model systems) to prevent fluid
creep in the case of low wetting angles, sharp edges at the solid end
disks, cannot be employed here. Any prefabricated sharp edge is
energetically unstable in contact with a solvent due to its large surface
and will be dissolved. A solution zone with a solvent showing this
behavior is co