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Polymorphs of silicon carbide

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Many compound materials exhibit polymorphism, that is they can exist in different structures called polymorphs. Silicon carbide (SiC) is unique in this regard as more than 250 polymorphs of silicon carbide had been identified by 2006,[1] with some of them having a lattice constant as long as 301.5 nm, about one thousand times the usual SiC lattice spacings.[2]

The polymorphs of SiC include various amorphous phases observed in thin films and fibers,[3] as well as a large family of similar crystalline structures called polytypes. They are variations of the same chemical compound that are identical in two dimensions and differ in the third. Thus, they can be viewed as layers stacked in a certain sequence. The atoms of those layers can be arranged in three configurations, A, B or C, to achieve closest packing. The stacking sequence of those configurations defines the crystal structure, where the unit cell is the shortest periodically repeated sequence of the stacking sequence. This description is not unique to SiC, but also applies to other binary tetrahedral materials, such as zinc oxide and cadmium sulfide.

Categorizing the polytypes

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A shorthand has been developed to catalogue the vast number of possible polytype crystal structures: Let us define three SiC bilayer structures (that is 3 atoms with two bonds in between in the illustrations below) and label them as A, B and C. Elements A and B do not change the orientation of the bilayer (except for possible rotation by 120°, which does not change the lattice and is ignored hereafter); the only difference between A and B is shift of the lattice. Element C, however, twists the lattice by 60°.

  • Structure of major SiC polytypes.
  •  
    2H-SiC
  •  
    4H-SiC
  •  
    6H-SiC
 
3C structure

Using those A,B,C elements, we can construct any SiC polytype. Shown above are examples of the hexagonal polytypes 2H, 4H and 6H as they would be written in the Ramsdell notation where the number indicates the layer and the letter indicates the Bravais lattice.[4] The 2H-SiC structure is equivalent to that of wurtzite and is composed of only elements A and B stacked as ABABAB. The 4H-SiC unit cell is two times longer, and the second half is twisted compared to 2H-SiC, resulting in ABCB stacking. The 6H-SiC cell is three times longer than that of 2H, and the stacking sequence is ABCACB. The cubic 3C-SiC, also called β-SiC, has ABC stacking.[5]

Physical properties

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Main article: silicon carbide

The different polytypes have widely ranging physical properties. 3C-SiC has the highest electron mobility and saturation velocity because of reduced phonon scattering resulting from the higher symmetry. The band gaps differ widely among the polytypes ranging from 2.3 eV for 3C-SiC to 3 eV in 6H SiC to 3.3 eV for 2H-SiC. In general, the greater the wurtzite component, the larger the band gap. Among the SiC polytypes, 6H is most easily prepared and best studied, while the 3C and 4H polytypes are attracting more attention for their superior electronic properties. The polytypism of SiC makes it nontrivial to grow single-phase material, but it also offers some potential advantages - if crystal growth methods can be developed sufficiently then heterojunctions of different SiC polytypes can be prepared and applied in electronic devices.[5]

Summary of polytypes

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All symbols in the SiC structures have a specific meaning: The number 3 in 3C-SiC refers to the three-bilayer periodicity of the stacking (ABC) and the letter C denotes the cubic symmetry of the crystal. 3C-SiC is the only possible cubic polytype. The wurtzite ABAB... stacking sequence is denoted as 2H-SiC, indicating its two-bilayer stacking periodicity and hexagonal symmetry. This periodicity doubles and triples in 4H- and 6H-SiC polytypes. The family of rhombohedral polytypes is labeled R, for example, 15R-SiC.

Properties of major SiC polytypes[6][7][8][9][10] "Z" is number of atoms per unit cell, "SgNo" is space group number, a and c are lattice constants
Polytype Space group Z Pearson symbol SgNo a (Å) c (Å) Bandgap
(eV) 		Hexagonality (%)
3C T2d-F43m 2 cF8 216 4.3596 4.3596 2.3 0
2H C46v-P63mc 4 hP4 186 3.0730 5.0480 3.3 100
4H C46v-P63mc 8 hP8 186 3.0730 10.053 3.2 50
6H C46v-P63mc 12 hP12 186 3.0730 15.11 3.0 33.3
8H C46v-P63mc 16 hP16 186 3.0730 20.147 2.86 25
10H P3m1 10 hP20 156 3.0730 25.184 2.8 20
19H P3m1 19 hP38 156 3.0730 47.8495
21H P3m1 21 hP42 156 3.0730 52.87
27H P3m1 27 hP54 156 3.0730 67.996
36H P3m1 36 hP72 156 3.0730 90.65
9R not found 9 hR18 160 3.073 66.6
15R C53v-R3m 15 hR30 160 3.073 37.7 3.0 40
21R C53v-R3m 21 hR42 160 3.073 52.89 2.85 28.5
24R C53v-R3m 24 hR48 160 3.073 60.49 2.73 25
27R C53v-R3m 27 hR54 160 3.073 67.996 2.73 44
33R C53v-R3m 33 hR66 160 3.073 83.11 36.3
45R C53v-R3m 45 hR90 160 3.073 113.33 40
51R C53v-R3m 51 hR102 160 3.073 128.437 35.3
57R C53v-R3m 57 hR114 160 3.073 143.526
66R C53v-R3m 66 hR132 160 3.073 166.188 36.4
75R C53v-R3m 75 hR150 160 3.073 188.88
84R C53v-R3m 84 hR168 160 3.073 211.544
87R C53v-R3m 87 hR174 160 3.073 219.1
93R C53v-R3m 93 hR186 160 3.073 234.17
105R C53v-R3m 105 hR210 160 3.073 264.39
111R C53v-R3m 111 hR222 160 3.073 279.5
120R C53v-R3m 120 hR240 160 3.073 302.4
141R C53v-R3m 141 hR282 160 3.073 355.049
189R C53v-R3m 189 hR378 160 3.073 476.28
393R C53v-R3m 393 hR786 160 3.073 987.60

See also

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References

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  1. ^ Rebecca Cheung (2006). Silicon carbide microelectromechanical systems for harsh environments. Imperial College Press. p. 3. ISBN 1-86094-624-0.
  2. ^ J.F. Kelly; et al. (2005). "Correlation between layer thickness and periodicity of long polytypes in silicon carbide" (PDF). Materials Research Bulletin. 40 (2): 249–255. doi:10.1016/j.materresbull.2004.10.008.
  3. ^ Laine, Richard M. (1993). "Preceramic polymer routes to silicon carbide". Chemistry of Materials. 5 (3): 260–279. doi:10.1021/cm00027a007.
  4. ^ Ramsdell, L.S., Studies on Silicon Carbide, Am. Mineral. 32, (1945), p. 64–82
  5. ^ a b Morkoç, H. (1994). "Large-band-gap SiC, III-V nitride, and II-VI ZnSe-based semiconductor device technologies". Journal of Applied Physics. 76 (3): 1363–1398. Bibcode:1994JAP....76.1363M. doi:10.1063/1.358463.
  6. ^ "Properties of Silicon Carbide (SiC)". Ioffe Institute. Retrieved 2009-06-06.
  7. ^ Yoon-Soo Park, Willardson, Eicke R Weber (1998). SiC materials and devices. Academic Press. pp. 1–18. ISBN 0-12-752160-7.{{cite book}}: CS1 maint: multiple names: authors list (link)
  8. ^ S. Adachi (1999). Optical Constants of Crystalline and Amorphous Semiconductors: Numerical Data and Graphical Information. Springer. ISBN 0-7923-8567-5.
  9. ^ W. J. Choyke; Hiroyuki Matsunami; Gerhard Pensl (2003). Silicon carbide: recent major advances. Springer. p. 430. ISBN 3-540-40458-9.
  10. ^ Nakashima, S (1991). "Raman intensity profiles and the stacking structure in SiC polytypes". Solid State Communications. 80 (1): 21–24. Bibcode:1991SSCom..80...21N. doi:10.1016/0038-1098(91)90590-R.
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