Silicon carbide (SiC) is one of the most promising materials for high temperature, radiation-hardened, power and high-speed electronics due to its unique physical and electronic properties. Silicon carbide exists in the form of different polytypes. Today the number of described structures of silicon carbide polytypes is about 200. Authentic causes of polytypism are unknown. In accordance with an accepted dislocation theory of polytypism [1], screw dislocations with Burgers vectors not multiple to the lattice parameters of basic polytypes (6H, 4H or 15R) may create new polytypes.

Model example: polytype 27R. In the dislocation theory the polytype 27R (2,2,2,3) is considered as a derivative structure based on 4H (2,2) polytype. Structure and polytype composition of 27R-samples grown by non-seeded Lely technique [2] have been investigated by X-ray Berg-Barrett topography, Laue pattern technique, X-ray diffractometry as well as by micro Raman spectroscopy.  Extended 6H – polytype inclusions have been detected in about a half of samples. Polytypes form sintaxial joints (numerous sandwich structures) with the same arrangement of crystal axes. One sample had small misorientation (about 3 degrees) between C-axes of 6H- and 27R-polytypes. We have found no statistical disorder of 27R-polytype within the limits of resolution of used techniques. Also, we have not revealed any presence of presumed parent phase 4H within the representative set of 8 samples.

One-dimensional matrix assembly of basic polytypes. Ramsdell and Kohn proposed [3] so-called polymeric concept of polytypism assumed an existence of 7 various hypothetic polymeric group in gas phase having the following Zhdanov indexes (3,3), (3,2), (2,3), (2,2), (3,4), (4,3), (4,4). At the same time, taking into account the great difference in occurrence rate for various polytypes, it seems to be the most authentic to modify and to use this concept only for relatively small set of basic polytypes (6H, 4H, 3C, 15R).

The main molecular forms in a gas phase during the growth of silicon carbide crystals are Si(g), Si₂C(g) and SiC₂(g). Due to the first principles an interaction of these species could lead to occurrence of two intermediate stoichiometric forms, namely, so-called dimer Si₂C₂ and trimer Si₃C₃. Actual spatial configuration of activated clusters which forms a polytypic sequence is unknown. Therefore below we simply consider all possible results of one-dimensional cluster assembly from dimers and trimers (see table).

As known, at rather low temperatures (T<2200^oC) gaseous silicon prevails and, according to this approach, leads to formation of 3C or 4H polytypes from dimers, in conformity with an experiment. Moreover, because of the concurrent creation of 4H and 3C polytypes being unlikely one polytype should replace another at elevating the temperature. Polytype chains of 2H, 3C, 6H or 9R should be formed from trimers. As known, polytype 2H-SiC is not grown in high-temperature Lely process while 3C and 6H polytypes meet most frequently. As for 9R version of silicon carbide this rare polytype is also known for a long time. Note that assembly of the chain of monomers (for example, during CVD growth of SiC) should lead to the occurrence of only two polytypes, i.e. 2H or 3C.

15R polytype. Co-polymer analogy. 15R polytype structure can not be described as the chain composed of the same elementary cluster but – similarly to a copolymer – of two alternating those. Considering the concurrent growth of 4H and 6H polytypes, in the framework of polymer analogy and kinetic approximation we obtain:

P_4H = K₂₂[M₂]/(K₂₂[M₂]+K₂₃[M₃]), P_6H = K₃₃[M₃]/(K₃₂[M₂]+K₃₃[M₃]),

where P_4H, P_6H are probabilities of growth of 4H and 6H polytypes, correspondingly, K_AB is a chain propagation reaction constant for an addition of A-mer to B chain, [M₂], [M₃] are the concentrations of dimers and trimers, accordingly.

Then, probabilities of failure of polytype sequence can be written down:

P_4H→6H = 1 – P_4H , P_6H→4H = 1 – P_6H.

Assuming second-order reaction in the gas we have for concentrations:

[M₂] = K₂[Si][SiC₂], [M₃] = K₃[Si₂C][SiC₂],

where K2, K₃ corresponding reaction constants for dimer and trimer formation.

Using all expressions above we carried out qualitative simulation of concurrent growth in a wide range of parameters. All possible scripts of chain assembling are presented below:

(i) -222222333332222- growth of 4H-polytype containing bulk inclusions of 6H-polytype;

(ii) -23322232323223- growth of 15R polytype, with a great fraction of statistically disordered 15R-polytype (improbable variant);

(iii)   -2323232323- ideal 15R-structure;

(iv) -222222232222223222222- prevailed growth of 4H, with small inclusions of trimers.

Note that ideal 15R structure could be composed when the growth of one polytype is suppressed by kinetic limitations, another – by an absence of “building material”, i.e. by negligible concentration of dimers or trimers, accordingly. Also, presence of two polytypes (4H and 6H) in syntaxial joint could lead to an occurrence of elementary steps with motive of 15R-polytype. Results of HRTEM-analysis of 15R-inclusions in 4H-ingots grown by modified Lely technique [4] have been presented and interpreted. Possible restrictions of proposed approach are considered.  

References

[1] Franc F.C. Phil.Mag.42, 1014(1951).

[2] Lely J.A. Ber.Deut.Keram.Ges. 32, 229(1955).

[3] Ramsdell L.S., Kohn J.A. Acta Cryst. 5, 215(1952).

[4] Tairov Yu., Tsvetkov V.F. J.Crystal Growth 43, 209(1978).

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1. Growth of 4H-SiC single crystals on the prismatic seeds