Relativistic band structure calculation of cubic and hexagonal SiC polytypes

Abstract

A full-potential band structure calculation, within the local density approximation to the density functional theory, has been performed for the polytypes 3C, 2H, 4H, and 6H of SiC. The calculated effective electron masses are found to be in very good agreement with experimental values. The electron-optical phonon coupling has been estimated and the polaron masses are calculated to be 3%–13% larger than the corresponding bare masses. The effective electron masses of the second lowest conduction band minima are also presented and the calculated energy difference between the two lowest minima in 4H–SiC is only 0.12 eV. The lowest conduction band in 6H–SiC is found to be very flat and to have a double-well-like minimum along the ML line. The top of the valence bands has been parametrized according to the k⋅p approximation, whereupon the effective hole masses have been determined. The spin-orbit interaction was found to have a strong influence on the value of the effective hole masses. Furthermore, total and partial densities of states are presented.

Opto-Electronic Study of SiC Polytypes: Simulation with Semi-Empirical Tight-Binding Approach

“…For the hole effective masses there are few theoretical reports of the polytypes and even fewer are the experimental values. The effective electron masses of 3C-and 4H-SiC have been measured experimentally and reported by several groups, and they agree quite well with the theoretically calculated values (19), (26), (83). For 6H-SiC, only the longitudinal effective mass along the c-axis has been measured (82), but due to the peculiar band shape along the direction there is still a large inconsistency between the measured value and the calculated ones, even among the values calculated theoretically by different groups (19), (26), (83).…”

“…According to the calculation done by Persson et al (26), (38), the second CBM of 3C-SiC is at the same symmetry point (X) as the first one with 2.92 eV higher in energy and this was confirmed experimentally from optical absorption measurements with slightly larger energy difference ( 3.1 eV) between the two minima (13). Persson et al calculations also show that the three hexagonal polytypes (2H, 4H, 6H) have their second CBMs located at the M point and the energy difference between the first and second CBMs is 0.60 eV for 2H, 0.122 eV for 4H, and 1.16 eV for 6H respectively.…”

Valence band structure and band offset of 3C- and 4H-SiC studied by ballistic hole emission microscopy

“…We believe that the second threshold observed in the BHEM spectra on the 4H sample represents this crystal-field split band because ͑1͒ the measured splitting is consistent with theoretically calculated values and ͑2͒ we do not observe a second threshold on p-type 3C-SiC. We note that another type of valence band splitting due to the spin-orbit interaction has been calculated to exist 7 for both 3C-and 4H-SiC, but is expected to be very small ͑Ͻ10 meV͒. This would be very difficult to observe in room-temperature BHEM measurements because it is less than the ϳ25 meV thermal smearing of the metal Fermi energy.…”

“…12 This should produce a small ͑Ͻ200 meV͒ crystal-field splitting in the valance band of the hexagonal polytypes that is absent in 3C-SiC. 3,6,7 It has been found [13][14][15] that differences in the n-type Schottky barrier heights ͑SBHs͒ measured using ballistic electron emission microscopy 16 ͑BEEM͒ on n-type 4H-, 6H-, and 15R-SiC closely track the corresponding difference in band gap. This suggests that measured differences in SBH can be used to track the corresponding bulk conduction band offsets.…”

“…Of particular interest is the large ͑up to ϳ1 eV͒ variation of SiC band gap with polytype, [3][4][5][6][7][8][9] which offers the possibility of making unique quantum-well heterostructures and twodimensional electron gas devices that are based only on the stacking sequence of pure SiC. 10,11 A number of firstprinciple calculations [3][4][5][6][7] have indicated that most of the band gap variation between polytypes is in the energy of the conduction band minimum ͑CBM͒, with only ϳ0 -130 meV offset in the valence band maximum ͑VBM͒ between different polytypes. Calculations also indicate that spontaneous polarization exists in hexagonal SiC polytypes, but not in the ͑cu-bic͒ 3C-SiC polytype.…”