Z5 Float Zone

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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).


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,



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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



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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


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.



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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).


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



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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


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



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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


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


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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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


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].


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:


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


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


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



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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:


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


[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


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.


33/113

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


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].


34/113

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


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.


35/113

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.



36/113

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


Fig. 2-20: Axiconbased laser heatingsystem for pedestalgrowth, employingonly catoptricelements to producea ringfocus. A:axicon mirror, P:parabolic mirror.After [Fej84] and[Fei86].


37/113

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



38/113

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.



39/113

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



40/113

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



41/113

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



42/113

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



43/113

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,


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.


44/113

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


Fig. 2-22: Schematic view of a single turn watercooled RF heating

coil for needle-eye floating-zone growth.


45/113

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



46/113

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 $C$* $


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.


47/113

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.



48/113

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



49/113

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


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.


50/113

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



51/113

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


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].


52/113

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



53/113

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].



54/113

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



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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].


Fig. 2-26: Principle setup of Joule

heating.


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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:


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


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]:



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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 rfrc - 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


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)


Fig. 2-30: Basicconfiguration for aloating zone under

gravity. 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,


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


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



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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


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

Z5 Float Zone

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