36 PHILlPS TECHNICAL REVIEW VOLUME 30

The polyt~.pism of silicon carbide

A. H. Gomes de Mesquita

Silicon carbide is a substance with many interesting applications, some of which imposesome strict requirements on material control. One of the greatest problems here is thephenomenon of polytypism, that is, the existence of innumerable different ways of stack-ing the double layers of carbon and silicon atoms forming the crystal lattice. This givesrise to as many variations again in some of the physical properties.

Silicon carbide is found only very sporadically asa naturally occurring mineral, and then only in un-exploitable quantities. Very nearly all of the materialused today is therefore made in laboratories or in in-dustrial processes. The first synthesis dates from thelast century. Since that time, interest in the substancehas steadily increased, because of its interesting com-bination of chemical and physical properties. Siliconcarbide is exceptionally hard and rigid and possessesgreat tensile strength. It is resistant to chemical actionup to high temperatures, it is an excellent heat conduc-tor which will withstand high temperatures, and it isalso a semiconductor. Such a material clearly has in-teresting potential applications in various fields.

Its hardness was the first property to be used: pow-dered silicon carbide is well known as an abrasive andpolishing agent. Next came applications as an electricheating element, as a voltage-dependent resistor, andas a resistor with a negative temperature coefficientprimarily for use at high temperatures. In the last fewyears several types of diode have been made of siliconcarbide, although not as yet on a large scale. The latestdevelopment is the work now in progress on thestrengthening of plastics and metals by thin "whisk-ers" (thread-like crystals) of SiC.

This brief summary of properties and applications,which is far from complete, explains why Philips Re-search Laboratories have been carrying out investi-gations on silicon carbide for the last twenty years orso. This work has contributed to technical develop-ment and has led to many publications [11.

The chronological sequence of the principal appli-cations: abrasive - heating element - diode, clearly

Dr. A. H ..Gomes de Mesquita is withPhilips Research Laboratories,Eindhoven.

indicates that the controlover the material has im-proved with time. A little impurity in an abrasive doesnot usually do much harm, but in semiconductor mat-erials it is essential to be able to keep the degree ofimpurity under accurate control. This applies bothto chemical impurities and to physical imperfections,the latter category including stacking faults and dis-locations that disturb the crystallattice of the substance.In fact, there has been considerable progress in the

preparation of silicon carbide. While the Acheson in-dustrial process - which uses a mixture of sand, coke,common salt and sawdust as starting materials - isstill widely used, a pure laboratory synthesis is nowavailable which gives a product whose total content ofchemical impurities has been reduced to less than oneforeign atom in 107 silicon and carbon atoms.Control of the physical imperfeètions has not yet

progressed so far. This is directly related with the phe-nomenon of polytypism, which is found. in its most pro-nounced form in silicon carbide. This implies that, un-like nearly all other known substances, silicon carbideis known to occur in a very large number of crystallinemodifications (types) which, although closely related,differ from one another quite distinctly. Up to nowabout 140 have been counted, and others are stillbeing discovered.The crystal structures of all these modifications can .

be described in the hexagonal system with an a-axis ofapproximately 3A (0.3 nm); the length of the c-axis,however, varies from 5 A to 1000 A (0.5-100 nm).This latter distance is 100 times greater than the rangeof all known ordering forces in crystals - a strangefeature indeed. . .Polytypism, that is to say the occurrence of a large

number of types of one substance with crystal structuresdiffering only in one dimension, is observed not only

1969, No. 2 POLYTYPISM OF SiC 37

in silicon carbide but also in zinc sulphide, cadmiumsulphide and cadmium iodide, to quote a few ex-amples. There is also quasi-polytypism, which is foundin substances in which slight differences in chemicalcomposition affect the stacking of the atomic planes inonly one direction. The members of the large groupof ferrites that includes materials like BaFels027 andBa2Zn2Fe12022are probably the best-known examples.Here too the crystal structure can be described in thehexagonal system, and the a-axis of the unit cell isfixed, in this case at 6 Á, while the c-axis varies from15 to 1500 Á.The physical aspects of polytypism are particularly

interesting. The energy difference between the electronsin the highest levels of the valence band and the lowestlevels of the conduction band is found to vary with thelength of the c-axis, though the relation is not a simplelinear one. In silicon carbide this "indirect" bandgap can assume values between 2.4 and 3.3 eV, a varia-tion of as much as 30 to 40 %. The mobilities and theeffectivemasses ofthe electrons are intimatelyconnectedwith the crystal structure. The electroluminescencegenerated in silicon carbide may have almost any col-our ofthe rainbow, depending on the crystal modifica-tion. The colour of material doped with nitrogen (orother donors) is strongly dependent on the type ofstructure.In spite of a great deal of research, it is not yet com-

pletely understood why there are so many structuretypes. The crystal structure of a substance like silveriodide seems to be determined by slight deviations fromthe stoichiometrie composition; in silicon carbide thishas not been shown to be the case. In zinc sulphide,structures with large repeat distances occur during thecooling of crystals already formed; however, there isevery indication that in silicon carbide the variousstructure types occur during growth.In this situation it is not as yet really possible to

treat the phenomenon of polytypism in a truly generalway. The facts and arguments about silicon carbidewhich are presented in this article are therefore notalways necessarily applicable to other substances inwhich polytypism occurs.

Crystal structure

Since the turn of the century there has been a greatdeal of crystallographic research on silicon carbide.Studies of the external crystal faces brought out at anearly stage the existence of a number of different modi-fications with trigonal, hexagonal, rhombohedral andcubic symmetry and with widely different lattice con-stants. With the aid of X-ray analysis methods verymany more modifications have been discovered, and ina large number of them the crystal structure has also

been determined on an atomic scale [2].We shall nowdiscuss some of these modifications in greater detail,at the same time explaining the nomenclatures used toindicate the different types of structure.To picture the crystal structure of silicon carbide,

think first of a flat layer consisting exclusively of siliconatoms which are at a distance apart of 3.08 Á and arearranged in a close-packed structure of equal spheres(jig. 1). The (two-dimensional) periodic pattern is arhombic unit cell with sides of 3.08 Á. Vertically abovethis layer, and at a distance of 1.89 Á, we now place acongruent layer of. carbon atoms. In the resultant

Fig. 1. Close-packed arrangement of atoms in a plane. The two-dimensional repetition pattern is a rhombic figure with atoms atthe position A (the corner points) arid interstices-at Band C. Inan isolated layer the last two positions are equivalent, but thisis not true any more when the stack contains more than onelayer.

double layer we can distinguish two sets of interstices atthe sites marked Band C. Above one of these two setswe now place the next double layer, in which there areagain two sets of interstices, and so on. Note that thereare two possible ways of placing each double layer; thisis the essential characteristic of polytypism.

With this method of stacking, all the atoms come tolie on axes of the type A, Band C, which are perpendic-ular to the plane of the drawing of fig. 1.Each crystallo-graphic unit cell contains one axis of each of these threetypes. Since they lie in one plane, the whole crystalstructure can be represented two-dimensionally by across-section in the plane ABC at right angles to fig. 1.

(1] See W. F. Knippenberg, Growth phenomena in silicon car-bide, Philips Res. Repts. 18, 161-274, 1963; W. F. Knippen-berg and G. Verspui, Influence ofimpurities on the growth ofsilicon carbide, to be published in Mat. Res. Bull.

(2] Until recently this appeared to be a hopeless task, but nowa fairly simple standard method exists that can be used in alarge number of cases. On this subject see: M. Farkas-Jahnke,Acta cryst. 21, A173, 1966; A. H. Gomes de Mésquita, Actacryst. B24, 1461, 1968 (No. ,11).

38 PHILlPS TECHNICAL REVIEW

If successive double layers occupy' the consecutivepositions ABCABC ... (fig. 2a) the result is a structurewhich closer examination shows to be cubic (sphal-erite structure), which means that by the transfor-mation of coordinates we can describe the structure inthe cubic system. Stacking in the opposite directionCBACBA ... also corresponds to the cubic structure.We shall not go any further into this subject here, butsimply note that cubic p-SiC is the end product of many

b

VOLUME 30

chemical reactions in which silicon carbide is formed.If, during the crystal growth of p-SiC, a stacking

fault is made in which the sequence of the layers isreversed, changing for example from ABC ...to CBA ... , the result is a twinned crystal (fig. 2b):ABCABCBACBA. The repeated occurrence of astacking fault is referred to as multiple twinning.Where the frequency of their occurrence is great, andthe distance between the faults irregular, the structure

c

lJ( ;,ti iJI_')~ V AI ;,'t-t-V ij ;,V ;,t-l4V ;,V ;,~l4V ;,V I /, ~t-(V ;,/ ;,V ;,_l4V ;,V ;,r[IsV /,V ;'~f-J ;,V ;,V ;,_l4V ;,V ;,~.iV /,/ ;'~t-V'--l........l..;, / il ;,,_l4r? /,V l(_,4Vl ij i(__cVT /~Vl ;,V /8ABCABCABCA ABCABCABCA ABCABCABCA

ABCABCABCA ABCABCABCA ABCABCABCA

~ 1 ~

ABC ABC ABC A

Fig. 2. Two-dimensional re-presentation of some com-mon silicon-carbide struc-tures. The vertical direction(perpendicular to the planeof fig. 1) is that of the crys-tallographic c-axis. Thewhitecircles represent silicon at-oms, the black dots car-bon atoms. For clarity, simi-lar atoms in successive layersare connected by lines; theselines have no physical sig-nificance.a) The structure of cubic or

(3-SiC.b) Twinned (3-SiC.c)-g) Five different structure

types for ex-SiC.

1969, No. 2 POL YTYPISM OF SiC 39

is said to be disordered, which is here one-dimensionaldisorder. In some structures the stacking may even becompletely random. Experiments havè shown that allthese modes of stacking occur in silicon carbide.It is also possible, however, for the stacking order to

change direction frequently and periodically. The manymodifications of silicon carbide in which this occursare generally referred to as a-SiC. The individualdesignation indicates that a-SiC is regarded as a formof silicon carbide that is clearly distinct from the cubicphase. In particular, it should not be seen as a kind ofmisgrowth of IJ-SiC.

Some of the most frequently encountered structuresof a-SiC are shown in figs. 2c-g. The stacking ABAB ...(fig. 2c) corresponds to the well-known wurtzite struc-ture. Along the crystallographic c-axis, i.e. the verticaldirection in fig. 2, the repetition pattern consists of twodouble layers. Closer examination shows that the unitcell is hexagonal. This modification is therefore oftengiven the designation 2H.

Somewhat more complicated is the stackingABCBABCBA . .. which is also hexagonal (fig. 2d).The atomic stacking is repeated after every four layers,giving what is called a 4H structure. Since the environ-ment of the layers in which the atoms are situated onthe B-axis is the same as in the cubic structure, they areknown as "c" layers, unlike the layers with atoms on Aand C whose immediate environment corresponds tothe 2H structure and are therefore referred to as "h"layers. In the nomenclature system based on this the4H structure is described as hchc .... Another systemof nomenclature, introduced in 1945 by Zhdanov [3J,counts the number of layers situated between the re-versal points in the atomic stacking. In the 4H struc-ture this number is always two, and the structure canthus be described as (22). Similarly 2H may be de-scribed as (11), while IJ-SiC is given the symbol 00 (forinfinity).Figs. 2f and 2g now present no further difficulties.

The modifications shown there are 6H and 8H res-pectively, which mayalso be described as hcchcc andhccchccc or (33) and (44).The structure shown in fig. 2e is rather more difficult.

Cubic and hexagonal layers alternate in the patternwith hcchc and this atomic stacking is repeated afterevery five layers. Seen along the crystallographic c-axis,however, these five layers do not form a repeat dis-tance. Ifthe atoms ofthe first layer lie on the axisA, thenthose of the sixth layer do not lie on A but on B. Nowthe structure can be described in a cell containingonly five layers, but this crystallographic cell is nothexagonal but rhombohedral. If, for the sake of clarity,we also wish to describe the rhombohedral structures ina hexagonal system, we take the unit cell three tirnes

larger, so that it contains - in this case - 15 layers.The structure illustrated in fig. 2e is therefore called15R or (32)3 [4J.The a-SiC structures we have discussed so far are

among the simplest encountered; 6H, 15R and 4H, inthat order, are also the most common. We shall notgive a description of all the other silicon-carbidestructures. To illustrate the possible degree of com-plexity however, we can quote the following [5J.

174R = [333333633333333334]3;120R = [322222222222322233]3;33T = [3333353334];

168R = [2323232323232323232333]3.

Polymorphism and polytypism

The occurrence of more than one crystalline modi-fication of a substance is not in itself particularly un-usual. The phenomenon is known as polymorphismwhen it occurs in a compound, and allotropy when itoccurs in an element. Standard examples are white andgrey tin, graphite and diamond, and white and violetphosphorus, where the same solid has two forms ofdifferent appearance.In the case of tin there is a phase transition at 13°C.

At atmospheric pressure the grey tin is stable belowthat temperature, and above it the white. The trans-formation. takes place so very slowly, however, thatobjects made of pure tin do not usually decompose as aresult of ambient temperature fluctuations. Neverthe-less, this does sometimes happen and it is knoV;n as"tin plague".Diamond and graphite can be reversibly transforrned

into one another at very high pressures. Under at-mospheric conditions graphite is the stable form; thetransformation of diamond into graphite, however,does not take place at a speed that can be measured.Investigations have shown that in these cases there

is a specific region of existence.("homogeneity region")for each modification, i.e. a certain range of pressuresand ternperatures within which it is stable. This is notthe case for violet and white phosphorus; the whitevariety is metastable under all conditions. The directconversion of violet to white phosphorus is thereforenot possible. The reverse transformation from whiteto violet phosphorus does of course take place, too

(3] G. S. Zhdanov, C. R. Acad. Sci. U.R.S.S. 48, 43, 1945.(4] In an analogousway the structure of IJ-SiC is also designated

as 3C. The figure "3" again indicates the repeat distance alongthe crystallographic e-axis, and the letter "C" indicates cubicsymmetry.

(5] There is only one cubic modification. All the others are rhom-bohedral (R), hexagonal (H) or trigonal. In the literature thetrigonal modifications are usually also denoted by H, butsometimes however by T, thus here we have 33T.

40 PHILlPS TECHNICAL REVIEW VOLUME 30

slowly to be measured at room temperature, but at ameasurable speed at, higher temperature.

Returning now to our subject proper, we can atonce see the connection with what has just been dis-cussed. Clearly, the question of what causes polytyp-ism leads at the same time to a question about thestability of the different structure types. Are regionsof existence to be indicated for a few or for all the modi-fications, and if so, why is it that under certain con-ditions one structure is more stable than all the others?As we saw in the above examples, transformations in

the solid state are often very slow. The fact, that asingle furnace charge usually yields many differenttypes of silicon-carbide crystals at the same time, andthat different types of structure may even frequently befound in the same fragment of silicon carbide there-fore proves very little about their stability. It chieflyillustrates that phase transitions in silicon carbide arealso very slow processes, certainly at room tempera-ture, so that we do not reach the equilibrium situation,in which a single stable structure occurs. At higher tem-peratures one might expect the transition effects to beaccelerated, but even here, strange to say, transitionsin situ have never been observed. This approach thusdoes not yield direct evidence showing whether anytype of structure is stable or not.'In principle, information about the stability of cer-

tain modifications can also be obtained from the re-sults of accurate measurements of thermodynamicquantities, such as the heat of combustion and the spe-cific heat as a function oftemperature. For silicon car-bide these quantities have been determined in onlytwo cases: for p-SiC and for (X-SiCof the type 6H. Thevalues of the heat of combustion found were identicalwithin the accuracy of the measurements, and moreexact experiments are therefore needed in order to dem-onstrate any possible differences. Nor is this so verysurprising, since the disposition of the nearest andnext-nearest neighbours of the atoms is the same inall structures. Related to this is the fact that the densi-ties of the different structure types differ by no morethan about 0.1%. In tin, carbon and phosphorus thecorresponding differences are very much greater. Wesaw in the introduetion that the conspicuous features ofpolytypism are the large number of modifications andthe peculiarly large repeat distances in the crystallattice. In view of what we have just said we ought toadd that polytypism mayalso be distinguished fromnormal polymorphism by the subtlety of the differencesthat determine the stability of the crystalline phases.Because of this it has still not been found possible togive any clear demarcation of the possible existenceregions, even for the most common structure types ofsilicon carbide.

Some theories on polytypism

In the last twenty-five years many special theorieshave been put forward to account for the occurrenceof polytypism. This again shows that polytypism is re-garded as something which is clearly distinct from nor-mal polymorphism and requires distinct treatment. Insome theories each modification is considered to be astable phase. Most of them, however, assume that for-tuitous causes such as impurities or lattice defects giverise to the growth of long-period structures. In some ofthe theories the two types of argument - thermody-namic and growth-kinetic - are combined. .The first attempt at an explanation was made by

Lundqvist [6l, who attributed polytypism to the effectof chemical impurities. He based this viewon differenceswhich he had observed in the aluminium content ofindustrially prepared 4H, 15R and 6H crystals (fig. 3).

Fig. 3. The relation between the aluminium content and the rel-ative number of crystals (in %) of the three most common typesof IX-SiC(after D. Lundqvist [61).

Some initial experiments carried out by Knippenbergof these Laboratories with aluminium-doped siliconcarbide crystals gave no confirmation on this point,for with crystals grown under otherwise identical con-ditions it was not possible to show any relation betweenaluminium content and crystal structure.Recently, however, it has been shown that the growth

of a few simple structure types can be stimulated by theaddition of certain impurities - discovered quite bychance. With complicated structures this has never yetsucceeded; for that matter, it would be difficult to seehow the presence of impurities could cause the forma-tion' of these structures. This, and the fact that highlycomplicated structures, like 387H, have also been foundin crystals of the highest purity, indicate that we mustlook elsewhere, at least for the origins of the more com-plicated structures.A later theory attributes the growth of all except a

few of the simplest structures to the effect of screw dis-locations. The idea underlying this theory, originallyput forward by Frank [7], can be understood by pictur-

1969, No. 2 POLYTYPISM OF SiC 41

ing a growing crystal, for example of the type 6H, inwhich for one reason or another a screw dislocationoccurs during growth, and is propagated along a growthspiral. A very clear diagrammatic illustration of such acrystal-growth mechanism has been given by Read [8];

this is shown in jig. 4. When the Burgers vector of the

Fig. 4. Schematic representation of crystal growth by means of ascrew dislocation mechanism (after W. T. Read [Sl). The height ofa block is equal to the Burgers vector. In Frank's theory [71, thisis at the same time the repeat distance ofthe structure type under-going growth.

dislocation, i.e. the height of one block in the figure, isa whole multiple of six layers, then according to thistheory the 6H structure will grow without further mod-ification. If the length of the Burgers vector is equalto five layer-spacings, however, then we find the l5Rstructure (32)3, while seven layer-spacings gives(331)3 = (34)3 = 21R, eight layer-spacings gives(332)3 = (35)3 = 24R, eleven layer-spacings gives(3332)3 = 33R, and so on. This theory can thus explainmany structures that have been found, and indeed caneven predict new structures, many of which have sincebeen found. This theory is also supported by the factthat structures with large repeat distances are usuallyfound in parallel intergrowth (syntactic coalescence)with simple types such as 4H, l5R or 6H; it thereforeseems quite possible that the simple structures serveas a basis for the more complicated ones. Sometimes,too, beautiful growth spirals are found on the basalplanes of silicon-carbide crystals as visible evidence ofthe presence of a screw dislocation inside the crystal(fig. 5); the pitch of the spiral has in some cases beenfound to be equal to the length of the crystallographicc-axis (repeat distance) of the type that has been grown,demonstrating the relation between the crystal structureand the length of the Burgers vector.

Fig. 5. Growth spirals on the surface of a silicon-carbide crystal.This photograph and figs. 8b and 10 were supplied by courtesyof Dr. W. F. Knippenberg.

However, there are a large number of cases in whichthis relation can not be shown at all, either because ofthe complete absence of any growth spiral where onewould be expected, or because the pitch does not cor-respond to the periodicity of the structure. Vand andHanoka [9] have pointed out that this does not invali-date the theory, because there is always a reasonablechance that the crystal surface has grown differentlyfrom the interior from which, with the aid of X-raydiffraction methods, the structure has been determined.

There are however other objections to the screw-dislocation theory. The energy of such a dislocation isto a first approximation proportional to the square ofthe length of the Burgers vector. For a length of theorder of 1000 A this energy becomes very large, and itis therefore not clear why the crystal should be able toprovide this energy and not that for a large number ofedge dislocations and stacking faults, which wouldrequire much less energy. Moreover, since these faultscan pass through the screw dislocation, they woulddestroy the periodicity of the screw and hence of thestructure. Nor is it to be understood why - except inthe 2H structure - two successive hexagonal doublelayers (corresponding to the figure" I" in the Zhdanovsymbol) have never yet been found in any known typeof SiC. If this were already an energetically unfavour-able configuration, the energy effect would still be in-significant compared with the energy required for somescrew dislocations.

(6] D. Lundqvist, Acta chem. scand. 2, 177, 1948.[7] F. C. Frank, Phi!. Mag. 42,1014,1951.(8] W. T. Read, Jr., Dislocations in crystals, McGraw-Hill, New

York 1953, p. 144.(9] V. Vand and J. I. Hanoka, Mat. Res. Bull. 2, 241, 1967.

42 PHILlPS TECHNICAL REVIEW VOLUME 30

Partly because of some of the above-mentioned ob-jections, Jagodzinski [lOl put forward a theory aboutfifteen years ago, the "vibration:-entropy" theory,which is based on quite different assumptions. Thebasic assumption of this theory is that p-SiC is reallythe stable modification. The cubic crystals would havethe outer form, however, of an octahedron, a closedfigurefor which in this case growth is slow-an assump-tion which can be justified. The growth process canbe greatly accelerated by the introduetion of stack-ing faults, and larger crystals are then formed. If weselect these crystals for our investigations, then we areapplying a, negative selection. To explain why thestacking faults are built into the cubic structure period-ically, the following reasoning is used. The differencesin lattice energy between the structure types must bevery slight, because the disposition of the nearest andnext-nearest neighbours -of the atoms is the same in allstructures. If we neglect these differences, all that reallyremains for us is to consider the probability of the for-mation of each of the structures. At first sight onemight be inclined to say that any disordered stacking ofdouble layers is more probable than any ordered suc-cession, but upon closer consideration this is not soevident. In fact, at the high temperatures at which SiCcrystals are formed the vibrations of the atoms in thecrystallattice (lattice vibrations) represent a significantpart of the energy content. Now these vibrations areseriously impeded by irregularities in the lattice. Hencea periodic stacking would after all be preferred. Thelattice vibrations play such an important part in thiscase because their (three-dimensional) effect is set offagainst the effect of the one-dimensional sequence ofthe stacking of the atomic layers. This theory is there-fore based entirely on probabilities. The probability ofan ordered lattice is high. However, as the stacking ofthe double layers becomes more complicated and thedifference compared with a completely disorderedstructure becomes smaller, the probability of disorderincreases. The theory thus predicts a certain proba-bility of stacking faults, which increases with the lengthof the stacking period.These predictions were tested experimentally by

Jagodzinski and at first found to be correct. Disorderis found in many crystals of simple structure types,and in the majority of crystals with structures withlarge repeat distances. Crystals of the type 6H and15R are found to be either well-ordered, or the degrèeof disorder (the relative number of disordereddouble layers) fluctuates around 12%, a value whichthe theory suggests is likely (jig. 6).There is however some doubt about the stability

of p~SiC which Jagodzinski has postulated, and thistends to undermine his theory. An even greater diffi-

culty with this theory is that no evidence has everbeen found of any statistical distribution of the dis-order, which would be expected with a probabilitytheory. On the contrary, such investigations as havebeen made have always shown that the disorder waslocalized in the crystals. Moreover, various exampleshave meanwhile been found of structures that havelarge repeat distances but no demonstrable disorder,the occurrence ofwhich would be extremelyimprobableaccording to the theory. Finally Jagodzinski's experi-mental results themselves give indications that it isnot the structures with large repeat distances that have

. most disorder but the simple structures. .

_d_r-,00 10 20 30 40%

_Cl'

Fig. 6. The frequency distribution of the degree of disorder exin an arbitrary sample of N crystals (N = 150), practically all ofthe sample being ofthe types 6H and l5R; LlNis the number ofcrystals with a degree of disorder between ex and ex+ Llex.(After H. Jagodzinski [lOl.)

In spite of their differences, the three theories notedabove are in agreement that the formation of the var-ious types is to some extent a matter of chance. Thethermodynamic stability of the higher structures playsno part in these theories [111. It seems improbable,therefore, that these theories are applicable to thesimple SiC structures, where there are sound reasonsfor accepting the existence of real differences in freeenergy. Knippenberg [11, for example, has found thatthe frequency of occurrence of types 4H, 15R, 6H andSH is a function not only of the degree of impurity, asmentioned earlier, but also of the growth temperature(jig. 7). Furthermore, the energy difference betweenthe highest level of the valence band and the lowestlevel of the conduction band appears to differ consider-ably in these and various other simple types. It there-fore seems not unreasonable to assume that the con-tribution of the electron energy to the totallattice ener-gy is dependent on the structure. The lattice constantsand the average "thickness" of the double layers vary,though only very slightly, with the type of structure,as has bèen shown for types 2H, 6H and 3C. RefinedX-ray-analytical determinations have shown that "h"layers are somewhat thicker than "c" layers. Presum-

1969, No. 2 POLYTYPISM OF SiC 43

ably, this again will involve small variations of the latticeenergy.

At this stage it is difficult to establish which struc-tures are to beconsidered as true equilibrium phases;this is still the subject of much debate. From the avail-able experimental material one might be inclined to drawa distinction between structures with large and smallrepeat distances, and attribute an existence region tothe latter structures only. In this connection we shouldmention the work of Van Vucht and Buschow [12] ofthese Laboratories on compounds of rare earths (R)with aluminium of the type RAI3. These have struc-tures, related to SiC, ofthe types 2H, 9R, 4H, 15R, 6Hand 3C. Which type is formed depends on the atomicradius of R and on the growth temperature. For in-stance, the structure of ErAla corresponds to 3C, Ho Alncorresponds to 15R, while DyAla takes the 15R or 4Hstructure, depending on the temperature. There canbe no doubt about the thermodynamic stability ofthese structures. Zinc sulphide has the same structureas silicon carbide; below 1000°C the cubic phase isstable, above 1200 "C the 2H structure. Studies of thetransition region have yielded evidence in support ofthe stability of the 4H and 6H types of zinc sulphidegrown in that region.

No such evidence exists for the complicated types,whether of SiC or of ZnS. Rather than attempting toexplain their existence and origin in terms of unknownlong-distance interactions between atoms, we are in-clined, like Frank and Jagodzinski, to attribute themto special circumstances during growth. To determinewhether this is justified or not, we shall have to look atwhat is known about the inter-relationships betweengrowth conditions, crystal habit and structure types.The investigations of these subjects have nearly all beencarried out since the theories we have mentioned were

f

i

BH

15R....*' ..

4H_._ ..,.::.···· .• ~. .-............. .'O. BH

»: '-. .:. -------.. ,. -.....c:: .

1600 2000 2400 2800 32000C-T

Fig. 7. Relation between the crystallization temperature and therelative quantities f of resultant crystals of a number of simplestructure types. (After W. F. Knippenberg [1), as are also figs. 8a,9 and 11.)

put forward. Conversely, these theories are largelybased on data applicable to industrial-quality siliconcarbide and not to material prepared under well-de-fined conditions. It is therefore not surprising that thelater crystal-growth experiments have led to thepostulation of a new and alternative explanation forthe polytypism of silicon carbide. This will be dealt withat the end of this article.

The growth of silicon-carbide crystals

As we mentioned earlier, the raw materials for theindustrial preparation of silicon carbide by the Ache-son process are sand, coke, common salt and sawdust.The reaction 3C + Si02 = SiC + 2CO takes placein a furnace whose centre is first heated to 1900 °C,then slowly to 2700 °C, and is finally maintained forsome time at a temperature of 2000 °C. The chemi-cal reaction in fact starts to take place at 1800 °C;the higher temperatures are needed to effect the recrys-tallization, which results in an end product that canbe used as a grinding and polishing agent.

In laboratory syntheses this process' is divided intotwo stages:a) the preparation of SiC,b) the recrystallization.

The initial materials used for the formation of ex-tremely pure SiC are of course quite different fromthose mentioned above. One such material is methyl-trichlorosilane, CH3SiCla, which is decomposed on apure graphite rod at 1300-1800°C in a hydrogen at-mosphere, resulting in the formation of SiC. With thisprocess, known as the Van Arkel process, crystals ofhigh chemical purity can be prepared. Crystallographi-·cally, however, the products are very impure; the crys-tals are of very irregular shape and are built up from askeleton of a-SiC of indeterminate structure, betweenwhich large amounts of {J-SiC have grown, constitutingthe bulk of the crystals.The recrystallization takes place at higher tempera-

tures, normally at 2300-2700 °C. For this next oper-ation the SiC obtained is made into hollow cylinders(fig. Ba) which are heated in a graphite crucible in anargon or helium atmosphere (Lely's method [13]). Onthe outside surface of the cylinders there is partialdecomposition of SiC, while at the same time there istransport of material to the inside surface of the cylin-der, where large crystals are formed, usually in the

(10) H. Jagodzinski, Neues Jahrb. Mineral. Monatsh. 3, 49, .1954.

(11) A theory that attempts to explain the phenomenon of poly-typism on thermodynamic grounds, but which has foundlittle or no experimental support, has been put forward in:C. J. Schneer, Acta cryst. 8, 279, 1955.

(12) J. H. N. van Vucht and K. H. J. Buschow, J. less-commonMet. 10, 98, 1966. .

(13) J. A. Lely, Ber. Dtsch. Keram. Ges. 32, 229, 1955.

44 PHlLIPS TECHNiCAL REVIEW VOLUME 30

a

shape of platelets (fig. 8b). Very occasionally polyhedralcrystals are found among them (jig. 9). Among thecrystal platelets the types 6H, ISR and 4H are by farthe most strongly represented; the relative quantitiesdepend to some extent on the recrystallization tempera-ture. If the cylinder is rapidly cooled, f)-SiC is depositedfrom the supersaturated vapour upon the hexagonalplatelets (jig. JO). The higher structure types are foundonly occasionally, as a rule intergrown with one of thesimpler structures mentioned above. Most crystals,moreover, exhibit non-periodic stacking faults.

The crystal structure of these platelets closely re-sembles that of industrially prepared SiC. The differ-ence is that their chemical purity is very much higher.

b

Fig. 8. Hollow cylinders of silicon carbide, a) before and b) after recrystallization in a graphite crucible.

Fig. 9. Columnar crystal of SiC grown among platelet crystalsat 2550 -c in an argon atmosphere.

The polyhedra, which we will presently deal with atgreater length, usually consist of pure 6H, in whichstacking faults or other types of structure do not occur.

Apart from the above, there are many other methodsof preparing silicon-carbide crystals. The reaction be-tween carbon and Si02, the first stage of the Achesonprocess, has been investigated in detail by Knippen-

...-1

Fig. ID. Hexagonal crystal platelet on which a circular piece ofcubic silicon carbide has formed during rapid cooling of the fur-nace.

berg [11. When the reaction takes place between 1000 °Cand 1800 °C by means of gas transport or surface diffu-sion, whiskers of various shapes are formed, as de-scribed earlier in this journal [141. These whiskers areusually of cubic structure. The 2H structure is onlyformed as a result of the presence of certain impurities.If monocrystalline (X-SiC is used as a substrate, the

1969, No. 2 POL YTYPISM OF SiC

whiskers growing at right angles to the c-axis of thesubstrate assume the same structure. However, thewhiskers growing along the c-axis are usually of cubicstructure. In other words, the hexagonal stacking inthe substrate continues in a parallel direction in thewhiskers. If, however, new layers are formed in thewhiskers, then in this situation cubic stacking takesprecedence. Above 1900°C reactions in the gas phasegive platelet crystals of the types 6H and ISR.

Silicon-carbide crystals can also be prepared frommelts of different composition. Microcrystalline ti-SiChas been prepared from silicon melts and crystals ofthe type 6H have been prepared from various metalmelts. A related but more refined method is the travel-ling-solvent method, known as TSM [151, in which achromium zone is introduced between a single-crystalseed and a polycrystalline rod. Using a kind of zone-refining process, where the chromium is drawn throughthe rod by means of a heat treatment, the seed can bemade to grow at the expense of the rod. With thismethod, under identical conditions, it has been foundpossible to grow the types 4H, ISR and 6H withno change of structure type, in the direction of thec-axis. It is therefore evident that crystals of thisstructure growing under these conditions need nospecific outside influence to enable growth to con-tinue; they seem to have a kind of internal memorywhich regulates the stacking of the atomic layers. Un-fortunately it is not yet known whether this is also thecase for the more complicated structures, since growthexperiments of this kind have not yet been performedwith such structures.

Attempting now to survey the whole field of crystal-growth experiments, we arrive at the following broadsummary.

The simple types of structure can be formed underwidely different conditions, the 6H structure being byfar the most frequently encountered.

The complicated structures, on the other hand, areonly obtained (as far as is known at present) at highertemperatures in crystals grown from the gas phase orby surface diffusion during reactions or recrystallization(Lely's method). The great majority of these crystalsare in the shape of platelets.

The growth mechanism of these crystals, preparedby the Lely method, has been investigated by Kroko [16J

and by Knippenberg [IJ using an ingenious method.

[14J W. F. Knippenberg, H. B. Haanstra and J. R. M. Dekkers,Philips tech. Rev. 24, 181, 1962/63; H. B. Haanstra andW. F. Knippenberg. Philips tech. Rev. 26,187,1965; W. F.Knippenberg and G. Verspui. Philips tech. Rev. 29, 252,1968 (No. 8/9).

[15J W. F. Knippenberg and G. Verspui, Philips Res. Repts. 21,113, 1966.

[16J L. J. Kroko, J. Electrochem. Soc. 113, 801, 1966.

These investigators found that the crystals, which inthemselves are virtually colourless, can be coloured bythe addition of a small quantity of nitrogen duringgrowth. This makes 6H crystals green, ISR yellow, 4Hbrownish, and so on. If nitrogen is then suddenly ad-mitted into the furnace during recrystallization, crystalsare obtained with sharp colour transitions, so that twostages of growth can be distinguished one from theother. Fig. 11 gives an example which shows that thecrystals in the form of platelets, or sometimes wedges,grow in a lamellar form on the polycrystalline cylinderwall. A fact entirely in accordance with this mechanismis that when different structure types are present inone crystal, they also tend to occur in the form of

Fig. 11. Wedge-shaped crystals of IX-SiC to which nitrogen hasbeen added at an advanced stage of growth. This has made thestages in the growth clearly visible.a) Plan view of the basal plane. bl Cross section parallel to thehexagonal axis, i.e. perpendicular to the plane of (a).

45

a

b

46 PHlLlPS TECHNlCAL REViEW VOLUME 30

stacked lamellae. This can be demonstrated by grind-ing away layers from the crystal and making an X-rayexposure at each stage. It can then be seen that thestructure types disappear successively from the X-raydiagram. We have carried out an experiment of thiskind on a crystal which contained, in addition to azone with random stacking faults, zones with 6H, 8Hand 24R (fig. 12). An analogous case, reported byKuo Chang-lin [17), relates to the structure types 6H,15R and 69R.

a

b

Fig. 12. Two crystal platelets of (X-SiC intergrown. a) Side view;b) plan view of the larger crystal. The structures indicated in (a)were determined by taking X-ray diffraction pictures after repeat-ed grinding away of layers of the crystal (W represents the dis-order).

Crystal intergrowths as a possible cause of polytypism

It appears that the problem of polytypism in siliconcarbide is of a dual nature, and that a distinction mustbe made between the simple structures and the morecomplicated ones. The reasons have already been men-tioned. The simpler structures grow under widely dif-ferent conditions, their growth is sometimes stimulatedby impurities, there is evidence of differences in ther-modynamic stability, stable analogues are found amongthe intermetallic compounds, and in certain circum-stances they grow in single-crystal form. The more com-

plicated structures, on the other hand, are formedexclusively at higher temperatures from the gas phaseand by surface diffusion, their occurrence is fortuitousand no means of stimulating their growth are known;structurally they resemble the simpler types (174R islike 6H, 168R like 15R, and l20R like 4H), they haveno stable analogues and almost without exception theyoccur intergrown with one or more of the simpletypes.

The explanation for the growth of the simple struc-tures does not yet seem to be within reach; there arerather more promising ideas for the structures withlarge repeat distances, but none of the theories men-tio.ied seem really satisfactory. Now all of these theor-ies assume that the crystal under investigation has itsown internal memory controlling the growth, in theform of a screw dislocation, say, or lattice vibrations,so that the stacking of the atomic layers is continuedin the way it has been started. Zhdanov and Minervina,on the other hand, suggested more than twenty yearsago [18) that the growing structure might well havean external memory instead. Their actual suggestionwas that the structure of a crystal is determined by theway in which it is intergrown with other crystals.

We have recently taken up this suggestion, and wehave noted 119) that the higher structure types occur inplatelet crystals which are always found to grow in theLely furnace with the "memory direction " (the c-axis)roughly parallel with the polycrystalline cylinder wall.An external memory-influence, which may even differconsiderably from one place to another, is thus quiteconceivable; it could perhaps reside in the relativeorientation of wall and growing single crystal (fig. /3).

I,_.----I P

Fig. 13. Illustrating the growth of crystal platelets on a poly-crystalline cylinder wall. The SiC double layers are imagined to beperpendicular to the plane of the drawing, the direction of stack-ing (c-axis) in the plane of the drawing. There are reasons forassuming that the crystal platelet P consists of lamellae whosestructure is partly determined by intergrowth with the grains(A, B, ... ) of the wall (see text).

1969, No. 2 POLYTYPISM OF SiC

a

Fig. 14. a) Top face of a crystal of the type 33 R placed in a beam of light. The crystal clearly consists oftwo parts at a small angle to one another. One part is exactly in the right position to reflect the incidentlight, and thus gives a very strong reAection; the other part is not. b) Diagram of a cross-section of thetype 33R crystal. This cross-section is taken along the dotted line of (a) and at right angles to the crystalface shown there. The hexagonal axes ofthe two halves of the crystal enclose a small angle «, which prob-ably deterrnines the type of structure formed (C( = ale; see text).

This hypothesis is supported by a number of facts.For example, SiC polyhedra, grown in the same fur-nace but with their c-axis practically perpendicular to thewall, contain no higher types. This orientation of thecrystals apparently excludes the memory effect. Only6H is formed and perhaps also ISR. Complicated struc-tures are again found however in polyhedra that areintergrown with one another, as can be seen fromthe occurrence of re-entrant angles. Here one inter-grown part apparently forms the memory of the otherone and vice versa. In one case we have established aquantitative relation [2U] between the structure typeformed (33R) and the angle tx at which two halves of apolyhedron were intergrown (fig. 14a). The ratio of thecrystallographic a- and c-axes was exactly equal to a(expressed in radians), strongly suggesting the existenceof a relation between the manner of intergrowth andthe type of structure (fig. l4b).

[17] Kuo Chang-lin, Scientia sinica 15,604, 1966.[18] G. S. Zhdanov and Z. v. Minervina, J. Phys. USSR 9,244,

1945.[19] W. F. Knippenberg and A. H. Gornes de Mesquita, Z.

Kristallogr. 121, 67, 1965.[20] A. H. Gornes de Mesquita, J. Crystal Growth 3,4, 747,1968.[21] W. Kleber and P. Fricke, Z. phys. Chemie (Leipzig) 224,353,

1963.

Evidence for the existence of such a relation has alsobeen found in investigations with the related Cd ls,which can be prepared in different ways: the methodyielding most crystal intergrowths also leads to the for-mation of the largest number of different structures [21].

It seems to us, therefore, that this is where the key tothe solution of the problem of polytypism is hidden, atany rate for the more complicated structures. However,the whole story will not be known until we have alsounderstood the mechanism underlying their formationon an atomic scale.

Summary. Several theories have been put forward to explain thephenomenon of polytypism as it occurs in silicon carbide. Someof the principal theories are discussed. A view common to all ofthese is that chance factors (lattice defects) present in the crystalitself are responsible for the growth of the often very complicatedtype of structure. None of these theories are entirely satisfactory.Closer consideration shows that a small number of simplestructures can grow under very different conditions. This makesthe mechanism of their growth more difficult to explain than thatof the more complicated structures which, although fortuitousin origin, are nevertheless grown under better defined conditions.Experiments have provided clear evidence in support of thehypothesis that the growth of these more cornplicated structurescan be caused by external influences, in part icular by the way inwhich they are intergrown with other individual crystals.

47

b