| In this work, we studied the atomic and electronic structures of the (3×3) and (2(31/2)×(2(31/2))R30° reconstructions on the 3C-SiC(111) and 6H-SiC(0001) surfaces usingthe first-principles calculations within the density-functional theory. For the (3×3) reconstruction, we proposed a fluctuant-trimer model which is in best fit with the Patterson map from the x-ray diffraction, direct and inverse photoemission spectroscopy, high-resolution electron energy loss spectroscopy and scanning tunneling microscopy (STM) experiments. Moreover, we also proposed two structural models (double-trimermodel and single-trimer model) with different Si-coverage for the (2(31/2)× 2(31/2))R30°reconstructions which were recently observed on the 3C-SiC(111) island and 6H-SiC(0001) surface in the experiments, respectively. The simulated STM images of these two models are in good agreement with the STM experiments, and they are energetically more favorable than previous DV model and Tri-Ad model.In the first chapter, the mechanical, chemical and electronic properties of the SiC and its relevant applications and preparation methods are extensively introduced. And then the atomic and electronic properties of the bulk SiC are briefly reviewed. Finally theatomic and electronic structures of various reconstructions including the((31/2) ×(31/2))R30°,(3x3) and (2(31/2)× 2(31/2))R30° on the Si-SiC(111) and Si-SiC(0001) surfaces, the (2×2) onthe C-SiC(001) surface, and (2x1), c(4x2) and c(3x2) on the Si-SiC(001) surface are systematically reviewed.Chapter 2 gives a brief description of the calculation methods which include the Born-Oppenheimer approximation, density-functional theory, Bloch theorem, local density approximation and generalized gradient approximation of the exchange-correlation energy, pseudo-potential methods, the relaxation procedures of electrons and ions, and supercell method.In chapter 3, we proposed a new structural model (fluctuant-trimer model) for the (3×3) reconstruction on the 3C-SiC(111) and 6H-SiC(0001) surfaces. This model is constructedby the vacancy-free Si adlayer on Si-terminated SiC substrate and three trimer-Si atoms with height differences of 0.4 and 0.5 A in each (3×3) cell. The calculated Patterson of the new model is in best fit with the Patterson map obtained from the x-ray diffraction experiments. The calculated energy band structure in which four surface-state levels exist in the energy gap of the SiC bulk is in good agreement with the direct and inverse photoemission spectroscopy and high-resolution electron energy loss spectroscopy experiments. And the simulated STM images of the new model basically agree with the previous STM experiments. At present, in various structural models of the (3×3) reconstruction the fluctuant-trimer model proposed by us is in best fit with all previous experimnts.In chapter 4, we proposed two structural models (double-trimer model andsingle-trimer model) with different Si-coverage for the (2(3(1/2)) × 2(3(1/2)))R30°reconstructions on the 3C-SiC(111) island and 6H-SiC(0001) surface, respectively. The double-trimer model is constructed by the vacancy-free Si adlayer on Si-terminated SiCsubstrate and two Si-trimers with different heights in each (2^3 × 2^3) cell. And everytwo neighboring Si atoms belonging to two different trimers form a buckled Si-dimer. The double-trimer model has Si-adatom coverage of 18/12, which is higher than that ofthe (3×3). This is in agreement with the experiment in which the (2(3(1/2)) ×2(3(1/2))) phasecoexists with the (3×3) phase on the 3C-SiC(111) islands and annealing at lower temperature could vanish the (3×3) phase. The simulated STM images of double-trimer model are in good agreement with the observations in the STM experiments. Calculated energy band structure shows that the dangling bonds of the buckled dimer-Si atoms form a π bond which results in a semiconducting surface. The single-trimer model is constructed by the vacancy-free Si adlayer on Si-terminated SiC substrate and oneSi-trimer in each (2(3(1/2)) × 2(3(1/2))) cell. The Si-adatom coverage of the single-trimer model is 18/12, which is slightly lower than that of the (3×3). This is also in agreement with the experiment in which (2(3(1/2))×2(3(1/2))) phase coexists with the (3×3) phase on the 6H-SiC(0001) surface and long time annealing could decrease the area of the (3×3) phase.The simulated STM images of the coexistence of the single-trimer model of the (2(3(1/2)) ×2(3(1/2))) reconstruction and the fluctuant-trimer model of the (3×3) reconstructionon the 6H-SiC(0001) surface are also in good agreement with the STM experiments. Calculated energy band structures show that the single-trimer model has a semiconducting surface and Tri-Ad model has a metallic one. This is a very convenient criterion to distinguish the single-trimer model and Tri-Ad model by measuring the energy band structure in future experiments. Finally, the calculations of the formation energies show that the double-trimer model and single-trimer model are energetically more favorable than previous DV model and Tri-Ad model.
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