Festk6rperprobleme 27 (1987)

Structure and Reactivity of Solid Surfaces

Gerhard Ertl

Fritz-Haber-lnstitut der Max-Planck-Gesellschaft, D-1000 Berlin (West) 33, Germany

Summary: The geometric configuration of the atoms in the surface of a solid is correlated withtheir valence electronic properties and thereby also with their chemical reactivity towards mole-cules interacting from the gas phase. Several aspects of these interactions are briefly reviewed:The atomic structure of clean single crystal surfaces and their changes by bond formation(chemisorption), the formation of chemisorbed phases with long-range order and associatedphase transitions, the dynamics of the gas-surface interaction processes, as well as temporaloscillations in a catalytic reaction coupled to periodic structural transformations of a surface.

1 Introduction

The ideal crystal with infinite three-dimensional periodicity will never be realized.Apart from bulk defects a crystal will always exhibit a strong distortion of thisperiodicity at its termination: the surface. The ratio of atoms in the surface t othose in the bulk increases with decreasing particle size or film thickness. Theoverall properties of such systems may then be essentially determined by those ofthe surface.

The surface atoms are missing part of their nearest neighbors which causes variationsof the valence electronic properties as well as of the equilibrium positions of thenuclei. The former effect is reflected in the chemical reactivity of the surface bywhich 'dangling bonds' may become saturated, while the latter manifests itself instructural parameters deviating from those of the bulk. The present contributionintents to illustrate by means of a few selected examples our present knowledge ofthese phenomena and their mutual interplay.

2 T h e Structure o f Clean Surfaces

The geometric location of the atoms in the outermost layer may differ from thoseof a corresponding bulk plane in two respects, namely, alterations of the interlayerspacings (relaxation) and lateral displacements connected with changes of the unitcell within the surface layer (reconstruction) [ 1].

As a first example Fig. 1 shows the structure of the clean Ni (110) surface whichexhibits the same lateral periodicity as the bulk, but where the spacing betweenthe first and second layer is contracted by 8.5 %, while that between the secondand third is expanded by 3.5 % [2]. These findings are quite general and have now

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Fig. 1 Structure model of the (110) surfaceof fcc metals without reconstruction,suchas Ni(110).

Fig. 2 'Missing row' structure of thePt(110) surface.

been established for a large series of metal surfaces [1]. The effects are more pro-nounced with the more open planes for which Adx2 of up 15 % were reported,while the atoms in the most densely packed planes exhibit usually only very minordeviations from their regular bulk positions.The surface atoms will generally have the tendency to minimize their free energyby surrounding themselves by as many nearest neighbors as possible, i.e. by forminga most densely packed plane. This tendency is counterbalanced by the resultingmismatch between surface and bulk planes. This qualitative argument indicates whysurfaces may undergo reconstruction: While the Ni (110) surface is unreconstructed,the P t ( l l 0 ) surface is reconstructed (Fig. 2) [3]: Every second row in [1]-0]-direction is missing (leading to a 1 × 2 superstructure), and the surface may nowbe considered as existing of microfacets of the most densely packed (111) plane.Similarly, the (I00) planes of Ir, Pt, and Au are reconstructed in a way as illustratedby Fig. 3 [3]. The atoms of the topmost layer exhibit a quasi-hexagonal ('hex') con-figuration similar to that of the (111) plane placed on the square lattice of the(100) plane forming the second and deeper layer. The mismatch between first andsecond layer is in this case reflected by the fact that the topmost atoms do notform a perfectly flat plane, but are slightly 'buckled'. This buckling may be nicelymade visible by the scanning tunneling microscope (STM). The STM image in Fig. 4from a clean Pt (100) surface shows two domain orientations of the 'hex ' surfacewith its corrugation periodicity of 13.5 A, whereby the step in the center serves asdomain boundary [4].While most of the clean metal surfaces are not reconstructed, the situation isopposite with semiconductor surfaces where reconstruction is the rule. The 7 X 7-

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Fig. 3Reconstructed Ir (100) surface where the atoms ofthe topmost layer form a hexagonal configurationyielding a 5 × 1-superstructure. Similar structures arefound with clean P t (100) and Au (100) surfaces.

Fig. 4Scanning tunneling microscope(STM) image of a clean P t (100) sur-face with a step 14I.

s t r u c t u r e o f the a n n e a l e d S i ( l l l ) s u r f a c e is p r o b a b l y the most f a m o u s e x a m p l ew h i c h is n o w - a f t e r many y e a r s o f intense research - c o n s i d e r e d to be s o l v e d [5].

3 S t r u c t u r e o f A d s o r b a t e C o v e r e d S u r f a c e s

The e n e r g y o f s u r f a c e s m a y be l o w e r e d by the formation o f chemical b o n d s w i t hs u i t a b l e particles arriving from the gas p h a s e (chemisorption). W e will r e s t r i c t ou rd i s c u s s i o n to c a s e s in w h i c h this reactivity d o e s not e x t e n d into d e e p e r l a y e r s ,eventually l e a d i n g to the f o r m a t i o n o f n e w bulk c o m p o u n d s s u c h a s o x i d e s etc.However, also t h o s e p r o c e s s e s are i n i t i a t e d by chemisorption s t e p s a t t h e o u t e r -most a t o m i c layer.

F i g . 5 s h o w s the configuration o f H a t o m s f o r m e d o n a N i ( 1 1 1 ) s u r f a c e a t T < 2 0 0 Ka n d a t a coverage 0 = 0.5 *) [6]. The H a t o m s p r e f e r three-fold c o o r d i n a t e d s i t e s

*) The coverage 0 is defined as the ratio of the density of adsorbed particles over that of thesubstrate atoms in the topmost layer.

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Fig. SStructure of the ordered 2 X 2-overlayer of H atomsadsorbed on a Ni (111) surface at T < 200 Kwith acoverage O= 0.5.

Fig. 6 Phasediagram of the 2 x 2-structure of the H/Ni(111) system.

(i.e. as many nearest neighbors as possible) t o which they are attached by an energyof about 2.5 eV. The mutual configuration is under these conditions characterizedby pronounced long-range order, giving rise to 'extra' beams in low energy electrondiffraction (LEED). This long-range order is obviously due t o the operation ofinteractions between the adsorbed particles, which in the present case are of theorder < 0.1 eV and are of the 'indirect' type, i.e. mediated through the valenceelectrons of the substrate metal. Increasing the temperature leads t o continuousorder-disorder transitions as can be followed through the variation of the respectiveLEED intensities. Determination of the transition temperatures at varying coveragesenables t o establish a phase diagram as reproduced in Fig. 6. Such two-dimensionalphase diagrams have now been determined for different systems for which in turntheoretical simulation yielded good agreement if the interaction parameters wereproperly adjusted [7].

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Fig. 2Schematic diagram ofa modern Czochralskicrystal growth system. A. pulling rodwith seedholder, B. seed crystal, C. crystal neck, D. crystal,E. interface, F. melt,G. crucible, H. RF-coil,J. thermoeouple.

is preferred. The problems introduced by the rotation of the crystal and o f thecrucible for achieving rotational temperature symmetry will be discussed below.The seed is fixed at the lower end o f the pulling rod. In the sketched stage o f thepulling process, the crystal neck, a region with a strongly decreased diameter, isalready pulled, followed by the shoulder region: the transition to the final diameter.Pulling o f a crystal neck, as invented by Dash [4], is a very important part o f theprocess. In this thin region the dislocation density, grown in from the seed orgenerated by the immersion o f the seed in the melt , may be reduced to zero.The growing crystal is connected with the pool o f melt by the meniscus. Opaquematerials allow observation of the triple-phase-line crystal/melt/gas only. Its distancedown to the melt surface for nearly flat interfaces is equal to the interface heighth.In general growth occurs below the upper edge o f the crucible. One has to watchthe growing crystal with a steep viewing angle (Fig. 3a). The adhering meniscusappears as a bright ring due to light reflections o f the free crubicle part and theupper meniscus part, both reflected from the lower part o f the meniscus. Pullingfrom a filled crucible (Fig. 3b) is ideal for measuring growth determining para-meters.The actual crystal diameter, that means the shaping process, is controlled by theshape o f the adhering meniscus and the height o fthe triple-phase-line.The mechanismcan be described quantitatively for the growth o f fee metal crystals. Here thegrowth conditions are rather simple: 1) the crystal is wetted totally by the melt and

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a) b}Fig. 3 Growingcopper crystals (10 mm q~). TV-monitor photographs. The whiteline indicatesthe position of electronical diameter measurement.a) The diameter of the bright ring is used for diamter control.b) Real diameter measurement is performed at the triple-phase-line.

Fig. 4Meniscus shapes of differentgrowth stages.

wettingis isotropic [5], 2) as already mentioned, the interface hight is approximatelyequal t o the height of the triple-phase-line, 3) the interface height is proportionalto the bulk melt-temperature [6, 7]. For these conditions radial growth occurs inthe direction of the meniscus angle amen determined by the tangent in the triple-phaseqine at the meniscus and the vertical direction. Since the height of the triple-phase-line can be shifted by the bulk melt-temperature, amen, and thus the geo-metry of the shape-building menisci [8] can be adjusted (Fig. 4), and the importantstages of crystal growth as shown in Fig. 5 can be obtained.The crystals of other materials are not wetted totally: the contact angle Otton isnot zero. For example for silicon aeon is ca. 11 °. Singular faces (facets) of NaC1are only wetted under an angle of ~on ~ 30°. In these general cases one has t o

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a) b)

c) d)Fig, 5 Growth of a copper crystal. Except from the stage "'Diameter increase" the correspondingmeniscus shapes are shown in Fig. 4 . a) Diameter decrease (necking process), b) diameterincrease ("shoulder"), c) stationary growth (wanted diameter is reached), d) melting-off ("theend").

d i s t inguish b e t w e e n the meniscus angle amen as defined a b o v e and the c o n t a c tangle aco n . Crystal g r o w t h o c c u r s in the direct ion o f the growth angle agr:

ag r = amen - acort . (1)

G r o w t h and crystal s h a p e are determined by the vertical and the radial g r o w t hveloci ty:

i = V - h , (2)

= (V - h ) • tgasr. (3)

The g r o w t h veloci ty i s only e q u a l to the pul l ing s p e e d V for I~ = 0 .The meniscus-shape is a so lu t ion o f the non-linear Gaul,-Laplace-equation and i sd e p e n d e n t on the b o u n d a r y condi t ions at the crystal but also at the crucible wal l .T h e r e f o r e , vibrat ions o f the crucible and also a hysteresis o f the c o n t a c t a n g l e atthe crucible wall mus t be avoided. When pul l ing crystals of dissocia t ing m e l t s asGaAs one has to avoid decomposi t ion e i t h e r by a l a y e r o f a non-active f l u i d as

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B203 above the melt or by pulling in an appropriate gas atmosphere. In the case ofGaAs this requires the use of a hot crystal puller for avoiding precipitation of Ason the wails. The pullingspeed of the Czochralski process is in the range of somecm/h (pure materials) down to 2 mm/h (alloys).If one can use a completely f'tlled crucible, one can watch the growth processduring all stages with a horizontal view direction. With this arrangement we havemeasured growth parameters and compared them with a model calculation in realtime. For this purpose we have developed a Czochralski system suitable for routinemeasurements of growth values and for special investigations: surface pyrometryof the crystal or of the melt (accuracy: - 4 K, resolution: -+ 0.5 K), temperaturefluctuations in the melt (4096 values, sample rate: 0.08 s) combined with Fourieranalysis, temperature-step response of the growing crystal to study the controlbehaviour of the Czochralski process. The Czochralski system with periphery isshown in Fig. 6. An automaticdiameter control is necessary for obtaining a constantdiameter: The energy dissipated from the crystal increases in the course of thegrowth; temperature deviations have to be controlled. The control accuracy ofour system is -+0.150 ~tm.For comparison in Fig. 7 temperature measurements in a copper melt and in anickel melt are plotted.

Position

TV-Meosuring S

" ' P D P ~'I145

one t ! ! 1 1 :F 'P Is,-[, Control-System ~ 1 ,I I Termina!

Process Computer OperatorConsole

Fig. 6 Czoehralski system with periphery. Directly measured quantities: Pulling rod position(± 10 ~m), by thermoeouple bulk melt-temperature(± 0.1 K), by television picture processing:diameter (± 20 u.m, range: 2.5 cm ¢), interface position (± 0.15 tam), local signal amplitude(pyrometry). CPU-intensive computations (for example Fourier analysis) ate performed on theIBM usingthe fast JOKER-connection.

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I•

l i .l ii:, ~;"~ ,

P I : . " '

iI

a) b)

Fig. 7Temperature measurementsa) In a coppermelt (accuracyofcontroh ± 0.15 K);b) in anickel melt. Due to the largertemperature fluctuations(higher meltingpoint causeshigher temperaturegradients)control accuracy of themelt temperatureis worse.

MENISCUSS H A P ESTAB ILITY

P R O C E S SHEATBALANCE

MENISCUS iHEATFLOW"

PROCESSIDENTI-FICATION

PREDICTIONOF T(r.z)

/ _AGR°~___

\ -1 GRO~Va

\l ROC .Ss] TRANSFER1FUNCTION

Fig. 8 Model of macroscopic Czochralski growth. At the left hand side the problems whichhad to be solved,at the right hand side the possibilities offered by such a model.

A model describing the shape generation during growth ("Macroscopic Growth")was developed by studying the single problems as shown in Fig. 8. We had to solvethe Gaufi-Laplace-equation in respect of shape and stability of the relevant Czoch-ralski menisci [8]. Originally, the temperature of the bulk melt was assumed to beconstant in respect to location and time. The temperature distribution in thecrystal during all steps of the process was computed assuming high thermal con-ductivity and a limited diameter. Therefore we were able to apply a slice model[9 ]. Shape of the crystal neck and additional heat dissipation of a present atmospherewere taken into account quantitatively. The heat flow in the meniscus part issomewhat more complicated as assumed in the beginning [6]. But the recentlymeasured temperature distribution in the meniscus [I0] can be introduced in thismodel.

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This results were brought together to a closed model. It allows according to Fig. 8:a) to compute the crystal shape as a function o f the melt temperature, b) to com-pute some parameters in real t ime,c) to simulate the Czochralski growth includingthe thermal stresses acting in different stages o f the growth, d) to determine thetransfere function describing the behaviour o f the Czochralski process in respectto control theory.In Fig. 9 the most important growth parameters are plotted. The quantity "position"approximately corresponds to the crystal length. The picture clearly shows thenecking process: the decrease o f the diameter is a consequence o f the melt-tem-perature increase. Values o f the temperature gradient and the heat flow should bemultiplied with a factor o f 1/4 according to the already mentioned recent meas-urements.The viewing conditions are in general worse than in our case. Therefore othermethods for diameter control have been developed in the past. Their principlefeatures are shown in Fig. 10. The following methods are used nowadays [ 11]:1) the horizontal TV-method, as described, 2)TV-method for measuring an hori-zontally generated X-ray shadow, very expensiv method, possibility o f the de-termination o f the interface shape, 3)light-beam reflexion method, 4)bright ringmeasurement, 5) the weight method either o f the crystal or of the crucible, com-plicated because the weigth signal is the sum o f the crystal weight W1 plus theweight o f the liquid in the column inside the meniscus W2 and the weight o f the

Fig, 9 Online plotted growth parameters ofa copper crystal.

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Fig. 10 Diameter control methods.

meniscus part W3 itself. The determination o f diameter changes, therefore, has totake into account possible changes of these quantities.

5 Di scon t inuous Face t t ing Control led Growth

Quite an other mechanism of radial growth is exhibited from materials whichdeveloped singular faces (facets). For example, by lowering the bulk melt-tem-perature, radial growth occurs in macroscopic steps. This is demonstrated in Fig. I 1for the case of {100} -facets o f sodium chloride [45]. The pulled crystal has devel-oped these vertical facets but is rounded at the < 1 iO>-directed corners o f theotherwise square cross-section. Radial growth consists a) in filling the [ 100} -facetsby lateral growth, b) a subsequent fast non-crystallographic oriented growth belowthe solid/liquid interface. Therefore the contours o f the [010]-shadowgraphare unsteady (Fig. l la) whereas the contours o f the [0if]edge shows a smoothradial increase (Fig.1 lb) o f the crystal. Local temperature measurements showedthat the fast radial growth occurred only after a supercooling o f 2 K was gained infront of the faces. This mechanism o f discontinuous growth is controlled by asurface nucleation mechanism. The Fig. 12 demonstrates that also an impurityparticle can start radial growth. Stranski [ 12] was the first who described this kindof discontinuous growth. He named the resulting morphology "Vergr6berungen".

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Fig. 11 Shoulder region of a NaCI crystal.[1001-growth direct ion (vertical). Height of thepictures corresponds ca. 1.0 cm crystal length . Shadowgraphs of; a) the [010l-view direction;the picture shows the step-like, unsteady growth, b) 1011 ]-view direction; steady growth.

T h e s e singular f a c e s , but (I l l )-oriented, may also develop in materials wi th ad i a m o n d lat t ice structure as in s i l i con . The nomlal ly c u r v e d interface in th i s case isp a r t l y singular and p a r t l y r o u g h . This very unfavourable g r o w t h condi t ion leads tocrystals wi th "cores 'J : the radial concentration dis t r ibut ion of a s e c o n d c o m p o n e n t( d o p a n t ) is s t rongly d e p e n d e n t on the structure o f the interface (different segrega-t ion). Facet t ing o f the interface is avoided by achieving an interface g e o m e t r yw h i c h i s s l igh t ly c u r v e d t o w a r d s the g r o w i n g crystal .

Fig. 12

An impur i ty par t ic le on an (100)-facet s tar tslateral layer growth. Picture heightcorresponds ca. 0.2 era.

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6 Non-Rotational S y m m e t r i c H e a t i n g

A continuous growth of the crystal can only be obtained if the isotherms in themelt are symmetric in respect to the geometrical axis. This condition is neverexactly fulfdled. We have to distinguish three origins of asymmetric heating:

1. At the beginning of t~e one turn coil, energy input into the graphite is higherthan at the opposite site. In order to obtain an averaged symmetric temperaturefield, the cruciblehas to be rotated.

2. A slight non-symmetric energy input was observed in the meniscus region. InFig. 13 a non-rotating crystal is sketched. The crucible is rotated. Neverthelessthe interface is shifted slightly upwards in the region where the coil is beginning.Therefore, during growth the crystal at the right grows thinner than on the lefthand side. By measuring the melt temperature and the inclination of the inter-face, we estimated an input of additional energy of 4.5% directly induced inthe region of the meniscus. Thus only the rotation o f the crystal can generatea circular cross-section by a periodical local remeltingand regrowth.

3. Due t o the orientation dependent properties, especially of the electrical resisti-vity and of the radiation absorption-coefficient of the graphite used as sus-ceptor or crucible material, the reception of energy even of a rotated crucibleis not rotationally symmetrical. By a slow rotation of the crucible this kind ofasymmetry can be determined using a thermocouple for temperature meas-urement. The result of such a measurement is shown in Fig. 14. The asymmetrictemperature field rotates with the angular velocity of the crucible.

Growth of a crystal for these reasons normally occurs periodically with a faster anda lower speed (changing of 1"1). In worst cases the lower speed may even convert toa periodic back melting of the crystal. These effects are not very important for

Fig. 13 Inclined solid/liquid interface ofa non-rotating crystal.The left interfaceheight h 5° correspondsagrowth angleof - 5~ whereas the right height ha. leadsto stationary growth.

Fig. 14 Radial temperature field in arotating crucible (without crystal).Isotherms constructed. Estimatedhorizontal temperaturegradients oncircle R5: gradT/,max = 0.70 deg/cm, onR3: grad T/,max = 0.93 deg/cm.

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one-component crystal-growth but extremely important for the growth o f multi-components systems. It will be shown in the following that in these cases thechemical composition in general is influenced strongly by these growth-rate fluc-tuations.

7 Transpor t Processes, Mul t i -Component Mel ts

The usual aim o f crystal growth o f multi-component materials is a crystal withconstant macroscopic and microscopic concentrations o f the components. Ideally,two conditions should be fulfilled for this purpose. We need a concentrationdistribution in the melt which is either homogeneous or at least independent ontime. One can try to understand the flow phenomena and to achieve rules for theoptimization o f the rotation rates by numerical simulation. For this purpose onehas to solve simultaneously the differential equations describing the followingquantities:

in the melt: momentum (Navier-Stokes-equation), mass (diffusion and convec-tion), concentrations,heat;at the interface: boundary layer o f momentum, heat and concentrations;in the crystal: heat (dissipation by conduction and radiation).

A simulation of the whole Czochralski process at present seems to be impossible.However, simulation, also a three-dimensional one, of separated regions (crystal,melt) is performed in some laboratories (see for example [13, 9]).The behaviour of the melt flow is determined by the ratio momentum transfer/heat transfer which may be characterized by the ratio kinematic viscosity/heatdiffusivity. This value increases from metals, semiconductors to oxides. The follow-ing flow phenomena are important for crystal growth: the free gravity drivenconvection and the forced convection generated by rotation which is important fora mixing o f the melt .Finally, the thermocapillary convection (Marangoni-convection) driven by atemperature dependent surface tension d(r/dT or a concentration field dc/dT maybe generated at free liquid surfaces.The quality on the crystal extremely depends on the kind o f convection in the meltduring growth.

8 The G r o w t h o f Solid Solu t ions

Now the problems that may arise during growth o f solutions may be understoodeasily. The additional problems are the following:1) Corresponding to the phase diagram for a givenconcentration CLiq o f a secondcomponent in the liquid, the concentration Csol in the solid at the interface islower in our example (Fig. 15a). The ratio CsJCLiq is called the equilibrium

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Fi8. 15 Two-component melt.a) Phase diagram, b)concentration distribution close to the interface, c)constitutionalsupercooling, TI: temperature gradient high enough to avoid supercooling, T2: gradient so lowto generate supercooling.

Fig. 16 Striations in agallium dopedgermanium crystal. Longitudinal section.Crystal diameter ca. 1.5 era. From [141.

Fig. 17 As Fig. 16 but radial section.From [14I.

distribution coefficient K. 2) Backward diffusion of the material is influenced byconvection: a boundary layer with the thickness ~¢ is generated in front of theinterface (Fig. 15b). 3) So the second component is incorporated during growthwith an effective distribution coefficient K~. 4) Ken is a function of K and of8 e. This quantity is dependent on the flow conditions, expressed by the rotationrate w and the microscopic growth rate v, strongly dependent on the local melttemperature. 5e should be kept constant. The growth is purely diffusion controUedif 8e is larger than the characteristic diffusion layer thickness D/v. If growth iscontrolled by diffusion and rotation generated convection, gc is approximatelyx/-D-~. 5) Since Ketr on facets is different from that for rough interfaces, mixture

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o f rough and facetted growth should be avoided.8c is disturbed by rotation o f thecrystal in a non-axisymmetric heated melt or by temperature fluctuations causedby gravity convection. In this case concentration striations are generated. Fig. 16shows a longitudinalsectionwith striations o fa Ge-crystalcontaining 10:° atoms/cm~o f gallium (Lang-topography). Fig. 17 is the corresponding cross-section with asingle spiral-like striation [14] according to the origin (rotation in a non-axisym-metric heated melt).The same concentration distribution would arise if the solubility in the melt islower than in the solid. In this case the distribution coefficient is higher than 1.Second kind striations of quite another origin may arise according to Bauser [ 15]by the lateral growth of facets. They can be distinguished by their intersectionwith the first kind striations discussed above. Artificial striations can be generatedand may be used to study the interface geometry by applying o f short and regularcurrent pulses [16, 17].

9 Cons t i tu t iona l Supercool ing

According to the concentration layer in front of the interface the correspondingequilibrium freezing temperature TEa may be higher than the experimental tem-perature T2. In this case the dashed region o f Fig. 15c is constitutionally super-cooled. Mullins and Sekerka [18] showed by perturbation analysis that in the caseo f a low temperature gradient and/or a high growth velocity the interface in thebeginning becomes sinusoidal and finally breaks down. This constitutional super.cooling can be avoided if the growth rate v at the interface meets the followingrelationship (for convection-free melts):

G m Cs (1 --K)- - > ( 4 )v K D '

where G is the temperature gradient in the melt , m is the slope o f the liquidus andCs is the solute concentration.Romero [19] in 1981 found out that the single crystal after break-down splits upinto new grains by nucleation in front o f the general interface. Fig. 18 demonstratesthe transition to polycrystalline growth of Cu3Au [20]. According to the increasingpulling speed the T-ray reflection peaks are measured out over a large range o fangles. As a consequence we may state following rules: a) for growing concentratedalloys the danger of constitutional supercooling is very high, b) pull slowly, c)avoid uncontrolled fast growth during seeding and necking, by vibrations, and bytemperature oscillations.

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Fig. 18 Total break-down of the lattice by constitutional supercooling. ~.-diffractometermeasurements of a Cu3-Au-crystal. The rocking curves become worse with the increasingsupercooling caused by the increasingpulling speed (values at the right of the rocking-curves)and finally vanish totally.

10 Melt G r o w t h in S p a c e

For many years it was believed that purely diffusion controlled growth could beperformed in the absence of gravity. So it was expected to obtain homogeneouslydoped crystals by grawth under microgravity even on an industrial scale. We cannow evaluate these hopes based on the results obtained by the various experimentsfrom skylab t o the D1 mission.Different experimental choices of meniscus controlled growth can be applied undermicrogravity: (a) crucible-free solidifications of a sphere, (b) a Czochralski-kindmethod by shaping the meniscus with a mask, and (c) the crucible-free zone-melting.Only the last method finally was tested [21]. However, silicon specimens remeltedby this method contained striations similar to those observed by ground basedexperiments. The reason is clearly the overwhelming influence of thermocapillaryconvection due t o the high temperature gradient.Free surfaces were avoided in Bridgman-like experiments of Witt et al. [22]. Thoseparts of InSb and gallium doped Ge crystals remelted and resolidified under micro-gravity were free of striations. So indeed in this arrangement only diffusion con-trolled growthoccurred. However, a careful investigation of the dopant distribution

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Fig. 19 Isoconcentration curves of a PbAu liquid diffusion experiment performed in space.Thepicture demonstrates that the diffusion process from the left to the right is slowed down bythe graphitewails of the crucible (1-0 cm ¢).

showed a radial dopant concentration [23]. This effect can be caused by a macro-scopic non-planar interface influencing the lateral diffusion. This problem wasinvestigated in a recent theoretical paper [24]. It was shown that lateral diffusioncan be neglected for fast solidification rates. However, quiteanother principle walleffect sometimes described but not well understood may control the diffusion inliquids. This effect may be the origin of the macroscopic inhomogeneity in Bridg-man crystals grown in space. 'An example gives Fig. 19. The picture shows thedistribution of the diffused gold of a liquid PbAu diffusion experiment performedaboard the Apollo-Soyuz flight in 1975 [25]. The specimen was quenched after thediffusion soak time. The isoconcentration lines, strongly curved, demonstrateconvincingly the wall effect influencing the diffusion, In a recent paper Carlberg[26] again described this phenomena.

b

So one may ask what is the future of crystal growth in space? In addition to thelimited heating power there seem t o exist fundamental problems as the impossibilityt o suppress Marangoni convection but also the influence of the g-jitter [27]. Theyhave t o be overcome before we can expect the growth of highly perfect crystalsin space on an industrial scale.

11 Magnetic Damping of Free Convection

A strong reduction of temperature oscillations caused by free convection can beachieved by magnetic damping.

Since the fundamental work of magneto.hydrodynamics [28] it was well-knownthat a metallic fluid flow in a magnetic field was influenced by the induced eddycurrents: the viscosity of the melt increases in the field when it is directed vertically

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to the flow. Hurle [29] was the first to investigate the damping o f temperatureoscillations in a crystal growth arrangement (horizontal boat filled with gallium).Meanwhile during the last years crystal growth of silicon and GaAs has been per-formed in some institutes by applying magnetic fields. The results show that stria-tions caused by convection are reduced strongly [30, 31, 32]. The development o fcrystal pullers for industry-sized semiconductor crystals, (some 40 cm diameter)equipped with superconduction magnets is in progress (Japan, Germany, UnitedStates). So indeed this method seems very promising. However, striations causedby thermal asymmetry (variable growth speed) cannot be avoided by this improve-ment. An excellent thermal symmetry is necessary.

12 Latt ice Defects and their M u t u a l Origin

The mechanisms of defect generation are sketched in Fig. 20. The upper fields showthe defect structures which may be observed in the grown crystal. The originalmicroscopic defects are vacancies, interstitials, and impurities.A one-component single crystal grown without special care will exhibit a dislocationnetwork with small angle boundaries caused by polygonization. Alternatively, thedislocations may be arranged on slip planes with a density o f l0 s to 106 cm-2. Inthis case slip with multiplication caused by thermal stress is the final defect formingmechanism during cooling the crystals after growth. Twin boundaries may begenerated in the case of low stacking fault energywhich is material dependent [33 ].

Fig. 20 Lattice defects (rectangular fields) and possible mechanisms of their generation (roundedfields). Generation of EL2 defects and antisites in GaAsis still under discussion.

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Pores may be present in the crystal either by the nucleation o f vacancies or byfreezing-in o f gas bubbles.In binary solid solutions long-range concentration changes caused by segregationand short-range inhomogeneities (temperature oscillation introduced striations) canexist. In addition one may find impurities in the crystal not present in the startingmaterial as oxygen in silicon crystals caused by the decomposition o f the silicacrucibles [34]. The impurities may precipitate, leading to local stress concentrations(volume indentation) followed by prismatic punching o f dislocations [35]. Asurface indentation is also a very effective dislocation source. In the case o f con-stitutional supercoolinggrowth nuclei may be built [ 19] leading to a polycrystallinesample with lineage structure. The release of (constitutional) stresses or even o flong range thermal stresses due to the Tiller mechanism [36] can only generatedislocations if the theoretical shear stress, which is remarkably high (ca. 1/4 x shearmodulus), is overcome. So the present discussion o f stress induced dislocationsin GaAs [37] seems not to be relevant. The dislocations seem to be generatedat the crystal surface following decomposition or at the interface of the III-Vcompounds, perhaps by the contact with the encapsulating liquid B203 due toa still unknown process [38]. There are some hints supporting this assumption:

1) Dislocation glide has occurred only in thicker GaAs crystals (> 2"). This isunderstandable because thermal stresses increase with increasing diameter.

2) Even when dust particles are grown into the surface o f metal crystals o f smallerdiameters (-~ 1 inch)one can obtain crystals with rather small dislocationdensities o f 102 cm-2. This can be understood by assuming that due to thesmall crystal diameter and the high thermal conductivity the thermal stressesare so low that dislocation multiplication is impossible [39].

3) On the other hand the touching o f only one particle at the triple-phase-line o fa growing 10 inch silicon crystal leads to the generation of dislocations and bymultiplication to a very high dislocation density.

The concept o f dislocation generation in III-V compounds as GaAs and InP bythermal stresses larger than the critical resolved shear stress (lower yield point)[37] seems to be unlikely. It should be mentioned that investigations o f plasticityo f III-V compounds show the same behaviour as that o f Si and Ge: The beginningo f plasticity shows an upper yield point combined with the appearance o f analready high dislocation density. Further deformation then leads to a lower yieldpoint [40]. The plastic behaviour of the discussed semiconductors is determinedby the rather weak dependence o f the dislocation velocity on the shear stress(compared to the plasticity o f metals or ionic crystals).Finally we should mention the generation o f twin boundaries. Since the investiga-tions o f Bonner [4] one has learned that twin boundaries often are generated inthe stage between neck and final diameter, when the diameter increase occurs sosteep that (111)-planes either on or in the shouldercan develop.Therefore, applyinga sufficient slow increase rate can remove the danger of twinning.

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13 Results, T r e n d s , and Specia l Efforts

Applying the ingeniousnecking technique o f Dash. [4], we may grow very soft andsensitive fcc metal crystals either dislocation free (Cu) or nearly perfect with adislocation density o f less than 102 cm-2 . These crystals are mainly for research.For obtaining only very small thermal stresses the diameter is limited to 1" [42].For the same reason, ionic crystals such as NaC1 can only be grown up to 3 mm indiameter with a low dislocation density (Sch6nherr [43 ]). Recent attempts to growsuch single crystals with diameters larger than 3 mm were, however, not successful.Quite to the contrary, silicon crystals with 10 fold dimensions(10")can be growndislocation free. One problem is the inhomogeneous distribution of oxygen. Byapplying magnetic damping one tries to avoid striations and to achieve homogeneousdoping. Till now homogeneous doping o f silicon with P is only possible by neutronactivation [34]. With this method a dopant level o f some 10~4 atoms/cm3 o fphosphorus can be obtained. This material is only used for power devices.In the course o f the last five years the effort to grow dislocation free III-V com-pounds such as GaAs and InP has been high. The driving force is the need o f high-quality material for optoelectronic devices and for ICs.The best result, the growthof a 2" GaAs dislocation free crystal, was published recently by a Japanese team[44]. They pulled strongly indium doped crystals (102o Atoms/cm-3). Indium isisoelectric and leads to a solution hardening. The crystal was surrounded by a deeplayer o f encapsulating B203 during the whole growth process, thereby reducingthermal stresses. During growth, convection in the melt was damped by applyinga magnetic field. Another possible way may be, to avoid liquid encapsulation byadjusting the As pressure in a hot crystal puller. Indium doping for blocking thedislocation multiplication in the thermal stress fields may not be necessary in thisc a s e .

Crystal growth research is still necessary. Only one example should be given: thereason for elimination of dislocations by the Dash process is not understood verywell: Climbing out o f dislocations, growing out, or a smaller dislocation velocitythan the applied pulling speed can be the effective mechanism to reduce the dis-locations. Detailed simulations of the Czochralski process would be very instructive.But the results are only relevant if the applied boundary conditions,which in manycases cannot be measured, are realistic. Finally, new crystal-growth methods willonly survive if the quality o f the resulting crystals is high.

AcknowledgementsThe author would like to thank A. Fat tah and G. Hanke for technical assistance, Prof. H. Wenzlfor valuable discussions, and the ,,Zentralinstitut f'fir Elektronik" and the ,,Zentralinstitut fiirMathematik" for the excellent technical suppor t .

261

References

[1] G. Wassermann and P. h~incierz, in: Das Metall-Laboratorium der Metallgesellschaft AG1918-1981. Chronik und Bibliographie (Frankfurt/Main), p . 9 - 2 0

[21 J. CzochralskL Z. Physik Chem. 92 , 219 (1918)131 J. C. Brice, The Growth of Crystals from the Liquids in: Selected Topics in Solid State

Physics, Vol. XII, ed. by E. P. t¢olfarth (North HoUand, Amsterdam 1973), pp . 245I41 I¢. C Dash, J. Appl. Phys. 30,459 (1959)15] H. ICenzl, A. Fattah, and I¢. Uelhoff, J. Crystal Growth 36,319 (1976)[61 D. Geist and P. Grosse, Z. Angew. Phys. 14 , 105 (1962)[7] I¢. Uelhoffand K. Gdrtner, Rost. Kristallow. 12,238 (1972)[81 K. Mika and I¢. Uelhoff J. Crystal Growth 30 , 9 (1975)[9] A . v . d . Hart and I¢. Uelhoff, J. Crystal Growth 51,251 (1981)

[101 E. Quintero, Diplomarbeit, Aachen 1986[11] 14. Uelhoff, in: Dreiliinder-Jahrestagung tiber Kristallwachstum und Kristallztichtung,

Report JOL-Conf-18 (Jtilich 1976)[121 O. Knacke and L N. Stranski, Ergebn. exakt . Naturw. Bd. XXVI, 383 (1952)[ 131 M. Mihelcic, C. Schroeck.Pauli, K. ICingerath, H. ICenzl, I¢. Uelhoff, and A. v. d . Hart, J.

Crystal Growth 5 7 , 3 0 0 (1982)[141 J . A . M . Dikhoff, PhilipsTechn. Rundschau 25,441 (1963, 64)[151 E. Bauser, in: Festk6rperprobleme/Advances in Solid State Physics, Vol. XXII, ed. by

P. Grosse (Vieweg, Braunschweig 1983), p . 141[161 R. Singh A. F. ~¢itt, a n d H . C. Gatos, J. Electrochem. Soc. 115,112 (1968)[171 M. Lichtensteiger, A. F. ICitt, and H. C. Gatos, J. Electrochem. Soc. 118 , 1013 (1971)

[181 ~¢. I¢.MullinsandR. F. Sekerka, J. Appl. Phys. 35,444(1964)[ 191 J. Vidal and R. Romero, Crystal Research and Technology 16,853 (1981)[201 Y . K . Chang A. Fattak and W. Uelhoff, submitted to J. Crystal Growth1211 A. Eyer H. Leiste, and R. Nitsche, J. Crystal Growth 71 , 173 (1985)[221 H. C. Gatos, A. F. ~¢itt, M. Lichtensteiger, and C. J. Herman, in: Apollo-Soyuz Test

Project , Summary Science Report , Vol. I, NASA SP-412, p . 429 (1977)[231 H.C. Gatos, in: Materials Processing in the reduced gravity environment in Space, ed. by

G. E. Rindone, (Elsevier Science, 1982), p . 3551241 S . R . Coriell and R. F. Sekerka, J. Crystal Growth 46,479 (1979)[251 R. E. Reed, I¢. Uelhoff, and H. L. Adair, in: Apollo-Soyuz Test Project , Summary

Science Report , Vol. I, NASA SP-412, p . 367 (1977)[261 T. Carlberg, J. Crystal Growth 79 , 71 (1976)[271 H. Hamacher, R. Jilg, and U. Merbold, in: 6 th European Symposium "Materials Sciences

under Microgravity Conditions" (Bordeaux 1986), p . 1[281 S . Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon Press, Oxford

1961)[291 D. 7". £ Hurle, Phil, Mag. 13,305 (1966)

[301 K. Terashimi and T. Fukuda, J. Crystal Growth 63,423 (1983)[311 D. 7'. 3". Hurle and R. ~¢. Series, J. Crystal Growth 73 , 1 (1985)[321 7". Kimura, T. Katsumata, and T. Fukuda, J. Crystal Growth 79,264 (1986)[331 H. Gottschalk. G. Patzer, and H. Alexander, phys. stat . sol. (a) 45,207 (1987)

262

[34] Iv. Zulehner J. Crystal Growth 65 , 189 (1983)[351 J. Friedel, Dislocations (Pergamon Press, Oxford 1964)[361 IV. A. Tiller, J. Appl. Phys. 29 , 611 (1958)[37] A . S . Jordan, A. R. yon Neida, and R Caruso, J. Crystal Growth 76,243 (1981)[381 P. Haasen, private communication[391 E. Kappler, W. Uelhoff, H. Fehmer, and F. Abbink, in: Herstellung yon Kupfereinkri-

stallen kleiner Versetzungsdichte, Opladen 1971140] H. Siethoff, J. V61kl, D. Gerthsen, and tl. G. Brion, submitted to Appl. Phys. Let t .[411 IV. A. Bonner, J. Crystal Growth 54 , 21 (1981)1421 H. Fehmer and IV. Uelhoff, J. Crystal Growth 13/14,257 (1972)[431 E. SchOnherr, in: International Conference of Crystal Growth, North Holland, Boston

1966144] T. Kobayashi, J. Osaka, and K. Hoshikawa, J. Crystal Growth 71,813 (1985)[451 D. Fehmer. Diplomarbeit, Miinster 1968

263