A significant gap in our understanding of polytypism exists, caused partly by the lack of experimental data on the spatial distribution of polytype coalescence and knowledge of the regions between adjoining polytypes. Few observations, Takei & Francombe (1967) apart, of the relative location of different polytypes have been reported. A phenomenological description of the boundaries, exact position of one-dimensional disorder (1DD) and long period polytypes (LPP’s) has been made possible by synchrotron X-ray diffraction topography (XRDT)

Baumhauer H.

Berzelius J. J.

Fisher G. R.

G. R. Fisher

Heine V.

J. F. Kelly

Lely J. A.

P. Barnes

Price G. D.

Takei W. J.

English

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Long period polytype boundaries in silicon carbide

Kelly JF

Barnes P

Fisher GR

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Ferroelectrics

Long period boundaries in silicon carbide

Kelly, Jim

Barnes, Paul

Fisher, G.R.

Name not available

  Birkbeck ePrints: an open access repository of the research output of Birkbeck College  http://eprints.bbk.ac.uk   Kelly, J.F.; Barnes, P.; Fisher, G.R. (2001) Long period polytype boundaries in silicon carbide. Ferroelectrics 250: 187-190.   This is an author-produced version of a paper published in Ferroelectrics (ISSN 0015-0193). This version has been peer-reviewed, but does not include the final publisher proof corrections, published layout, or pagination.    All articles available through Birkbeck ePrints are protected by intellectual property law, including copyright law. Any use made of the contents should comply with the relevant law.    Citation for this version: Kelly, J.F.; Barnes, P.; Fisher, G.R. (2001) Long period polytype boundaries in silicon carbide. London: Birkbeck ePrints. Available at: http://eprints.bbk.ac.uk/archive/00000400   Citation for the publisher’s version: Kelly, J.F.; Barnes, P.; Fisher, G.R. (2001) Long period polytype boundaries in silicon carbide. Ferroelectrics 250: 187-190.    http://eprints.bbk.ac.uk Contact Birkbeck ePrints at lib-eprints@bbk.ac.uk  Long Period Polytype Boundaries in Silicon Carbide J.F. KELLY 1, P. BARNES 1 and G.R. FISHER 2 1 Industrial Materials Group, School of Crystallography, Birkbeck College, University of London, Malet Street, WC1E 7HX, UK. 2 Electronic Materials Inc. Mailzone 6, 501 Pearl Drive, P.O. Box 8, St. Peter’s, MO63376, U.S.A.  Abstract A significant gap in our understanding of polytypism exists, caused partly by the lack of experimental data on the spatial distribution of polytype coalescence and knowledge of the regions between adjoining polytypes. Few observations, Takei & Francombe (1967)1 apart, of the relative location of different polytypes have been reported. A phenomenological description of the boundaries, exact position of one-dimensional disorder (1DD) and long period polytypes (LPP’s) has been made possible by synchrotron X-ray diffraction topography (XRDT).    1. On the origins of silicon carbide Silicon carbide may be older than our solar system, having wandered through the Milky Way for billions of years as stardust generated in the atmospheres of carbon rich red giant stars. The gravitational coalescence of our solar system trapped these micron-sized SiC grains in meteorites. Recent analysis of carbonaceous chondrites has revealed that these starry messengers contain anomalous isotopic ratios of carbon and silicon, indicating an origin from outside the solar system2. The idea that a silicon-carbon bond might exist in nature had been proposed as early as 18243; carborundum dates from 1892. 2. Unique behaviour – polytypism, semiconductor and gemstone The word polytypie entered the literature in 1912 when Baumhauer4 attempted to describe materials that crystallise into modifications that differ unidirectionally. However polytypism did not attract widespread attention until studies in the 1940/50’s revealed new polytypes. An improvement in the sublimation growth of SiC by Lely5 enabled its wide bandgap (Eg~3eV) semiconductor potential to be further explored. Manufacturing advances by GEC Hirst Research Centre U.K. in the 1960’s led directly to the availability of the crystals used in the present survey. Despite this potential the poor material quality, has handicapped device development. One stumbling block appears to be lack of a complete theoretical description6 of the prolific tendency for SiC to form so many polytypic modifications, including long period polytypes (LPP’s).  3. The synchrotron topography story so far By 1990 the potential of a synchrotron radiation source for imaging polytypic materials had been well demonstrated by Fisher & Barnes7, showing that it was possible to locate polytype positions along the c-axis using the method of edge topography. Further with the improved resolution that became available at second-generation machines Barnes et al. (1991)8 were able to observe fine one-dimensionally disordered (1DD) layers at polytype boundaries. This enabled the construction of complete spatial models of complex patterns of polytypism occurring in practice. A unique database has now been compiled from the results of a survey, to date, of 132 such edge profiles distinguishing the common 6H, 4H, 15R polytypes and LPP’s from regions of 1DD. With the broad classification scheme developed by Kelly et al.9 the authors have been able to describe polytype coalescence in terms of a non-degenerate sandwich model. Complex features such as LPP’s and thin 1DD layers appear to be found as essential ingredients of polytype coalescence in these models (e.g. Fig1). Altogether 23 of the 135 crystals in this survey contain a measurable LPP repeat as distinct from a 1DD layer; these are listed in Table 1.            a(i)                                                                                       b(i) Figure 1: The current status of polytype model building from SiC synchrotron topographs illustrated with two examples a and b. a(i) A rare example of two LPP’s in the same crystal (J113) assigned as 40H/120R (arrowed reflections) and 64H/192R. a(ii) A model of J113 termed an American Club Sandwich (ACS)9: 6H+1DD(5μm)+6H+64H/192R+1DD(40μm)+40H. b(i) Over-exposed indexed region from J108 showing the LPP reflections. b(ii) A model of J108 (with magnifying lens x50): 15R+6H+LPP+6H+1DD(30μm)+6H ACS.  4. Long period polytype boundaries and nearest neighbours  While searching for a scheme to classify polytype nearest neighbour relationships in SiC it became apparent that it was possible to identify LPP repeats and measure their widths (μm) on the topographs. Table 1 constitutes the only known database on experimentally determined SiC long period polytype neighbours. From the survey of 135 crystals, which has yielded 25 LPP’s, only two cases could be found where more than one LPP is present (Figure 1 a). It is interesting to note that the shorter of the LPP’s in both cases is on the outside face of the crystal, in keeping with the general sandwich rule9 (LPP’s are always sandwiched between the shorter polytypes). In all other cases only a single LPP is found to coalesce with the common 6H,15R,4H polytypes. No obvious pattern of preference for polytype coalescence emerges and no correlation between LPP width and crystallographic repeat could be found.   Table 1: All long period polytypes found in a survey of SiC edges. The LPP’s are shown relative to their immediate adjacent neighbours/next nearest ordered    Polytype            Reflection                                              _ 6H                                    3144 15R                                  3148Long PeriodPolytype80H/240R                                              _  6H                                  3142                                              _15R                                  31426H6H15RLPP6H40H64H/192R6H6H LPPb(ii)a(ii)                                   6H       64H/192R40H        6Hpolytype; – indicates the crystal edge. The sandwich model acronyms9 are: OS =open, DFS=doubly filled, ACS= American club, SS=simple, AS =asymmetric. Crystal number Polytype neighbour  Long period polytype repeat Polytype neighbour (other side)  LPP (μm) Model J1 6H 1DD (270μm) 78H/234R  *24H/72R 1DD (270μm)/LPP* - 20 200 ACS J26 6H 152H/456R(8) 6H 12.5 ACS J31 4H 24H/72R 1DD (1225μm)/6H 260 DFS J33 15R  78H/234R(9) 1DD (70μm)/6H 50 DFS J34 6H 201H/603R 6H 20 AS J40 4H 106H/318R 1DD (145μm)/15R 15 DFS J43 6H 24H/72R 6H 300 SS J48 6H 342H/1026R - 20 ACS J59 6H 146H/438R(9) 1DD (300μm) 10 OS J64 6H 42H/126R(8) 1DD (15μm)/6H 15 DFS J101 6H 24H/72R 6H 70 ACS J105 4H 201H/603R 1DD (270μm)/15R 20 ACS J108/G31 6H 80H/240R 6H 20 ACS J110/G158 6H 130H/390R 1DD (30μm)/8H 5 ACS J113/G104 6H 1DD (40μm) 64H/192R *40H/120R 1DD (40μm)/LPP* - 20 150 ACS J115/G185 6H 474H/1422R 1DD (270μm) 7.5 OS J123/G111 6H 66H/198R 15R 50 ACS J126/G39 6H 24H/72R 1DD (20μm) 90 OS J128/G122 6H/1DD (110μm) 106H/318R - 25 OS J129/G159 6H 27H/81R 1DD (280μm) 70 OS J131/G117 6H 72H/216R 8H 20 ACS J133/G88 15R 289H/867R 1DD (320μm)/15R 30 ACS J135/G163 6H 106H/318R 1DD (1380μm) 20 OS The general trend of polytypism in SiC that is observed from Table 2 is in broad agreement with the theoretical predictions, of short period stability, as predicted by the ANNNI model which is discussed further in the next section. Table 2: Statistical frequency of the common polytypes in the survey.  6H 15R+6H 4H+6H 15R+4H+6H 8H+6H 21R+6H 21R+15R+6H Total 54 38 23 14 1 1 1 132 5. The Axial Next Nearest Neighbour Ising model and polytype boundaries Elliott (1961)10 introduced the axial next nearest neighbour Ising model (ANNNI) which applied to anisotropic couplings with competing interactions leads to infinitely many commensurate phases and “the devil’s staircase”. Price and Yeomans (1984)11 using the same approach showed that the ANNNI model provides a simple equilibrium mechanism whereby short range couplings lead to the existence of polytypes with very long stacking sequences. After a lengthy computational study into the origin of SiC polytypes Heine et al. (1992)12 have speculated on the nature of the higher order polytypes, noting that this is beyond the limit of calculation. In summary confirmation of the relative absence of odd numbers of bands in the Zhdanov symbol of polytypes and the frequency of regular polytypes with long periods compared with random stacking sequences (which mathematically are infinitely more probable) is the kind of experimental detail that the theoreticians hope can distinguish between mechanisms. 6. LPP boundaries and one-dimensional disorder Theoreticians bemoan the lack of experimental data on SiC polytype coalescence. This paper gives the most extensive and detailed database to date from which we can test theoretical predictions and pose fundamental evidence that the theoreticians need to address. In this spirit we summarise the main conclusions on the spatial extent of long period polytypism in SiC:  • One-dimensional disorder (1DD) is far more common than previously realised, exemplified by the very thin (~5μm) layers reported earlier. In total 106 /135 crystals display a 1DD layer (in some cases more than one).  • This observation confirms the theoreticians’ implication that the existence of random stacking sequences of layers is more likely than regular LPP’s. Here the experimental evidence is overwhelming: 106 crystals contain 1DD layers as compared to 23 crystals containing LPP’s. • The lack of reporting on LPP coalescence is now directly addressed; we can say that the LPP’s are usually associated with 1DD’s and that they do not normally coalesce on both sides directly to the common 15R, 4H polytypes. • Furthermore the sandwich rule7,9 applies even when two arbitrarily long LPP’s are found to coalesce together, the shorter LPP outermost (J1, J113). • Again the predominance of the 6H polytype is emphasised by its frequency and obvious syntactic coalescence to the long period polytypes. Notwithstanding the above points Jagodzinski (1995)13 has indeed pointed to the need to assess the role of disorder in the equilibrium conditions of polytype formation. We look forward to comments from other experimentalists and invite theoreticians to critically evaluate our findings in attempting to reach a consensus on a unified view of polytypism in silicon carbide.  Acknowledgments The authors gratefully acknowledge the facilities of the Daresbury Laboratory, personnel (station 7.6) and the EPSRC for beam time. References 1. Takei W.J., Francombe M.H., J. Appl. Phys., 18, 1589-1592 (1967). 2. Clayton D.D., Astrophysical Journal., 484, L67-L70 (1997). 3. Berzelius J.J., Ann. Phys. Chemie., 1, 169-230 (1824). 4. Baumhauer H., Zeit. Krist., 50, 33-39 (1912). 5. Lely J.A., Ber. Deutsch. Keram. Ges., 32, 229-231 (1955). 6. Trigunayat G. C., Solid State Ionics, 48, 3-70 (1991). 7. Fisher G.R., Barnes P., Phil. Mag., B61, 217-236 (1990). 8. Barnes P., Kelly J.F., Fisher G.R., Phil. Mag. Lett., 64, 7-13 (1991). 9. Kelly J.F., Barnes P., Fisher G.R., Radiat. Phys. Chem., 45, 509-522 (1995). 10. Elliot R.J., Phys. Rev., 124, 346-353 (1961). 11. Price G.D., Yeomans J., Acta. Cryst. B40, 448-454 (1984). 12. Heine V., Cheng C., Needs R.J., Mat. Sci. Eng., B11, 55-60 (1992). 13. Jagodzinski H., Zeit. Krist., 210, 481-488 (1995).  

Long period polytype boundaries in silicon carbide

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