First principles study of size and strain effects on the electronic properties of silicon and silicon carbide nanostructures

In the first part of the thesis, we systematically explore the combined effects of size and strain on the Eg in Si nanoclusters. It has been demonstrated that different types of strain have different effects on the Eg in Si clusters. Hydrostatic strain effects on the Eg display qualitatively novel trends for Si nanoclusters smaller than ∼2 nm. While the bulk indirect band gap decreases linearly with increasing compressive strain, this trend is reversed for small clusters (≤1 nm). In the intermediate 1 ∼ 2 nm size range, strain appears to have almost no effect. These results follow from the fact that the bonding/anti-bonding character of the highest-occupied-molecular-orbital (HOMO) and the lowest-unoccupied-molecular-orbital (LUMO) change non-monotonically with size. Comparing the strain effects between hydrostatic and non-hydrostatic (e.g. biaxial and shear) strains, we found hydrostatic strain has a relatively weak effect on the Eg in the size range 1 ∼ 2 nm, while non-hydrostatic strains result in significant variation in the Eg. The evident modifications of the gap by non-hydrostatic strains, which break the tetrahedral bonding symmetry in Si, result from the splitting of degenerate orbitals in the clusters. Further comparing two non-hydrostatic strains, we find shear strain changes the Eg in Si clusters more evidently than that of biaxial strain since shear strain fully destroys the symmetry of Si atoms. Our results suggest that photoluminescence in Si nanoclusters can be engineered by controlling their size and strain. This offers an exciting avenue for designing new classes of optical devices and chemical sensors.; In the second part, we have investigated the size and strain effects on the electronic properties, such as band structures, energy gaps, and effective masses of the electron and hole, in Si nanowires along the <110> direction with diameters up to 5 nm. From the structures of the nanowires, we find that wires expand along the axial <110> direction compared to bulk Si: the expansion is evident for small wires, and there is almost no apparent expansion for wires larger than 4 nm. From the band structures, we find that the <110> wires display a direct band gap at the Gamma point. Under uniaxial strain, we find the band gap variation with strain is size dependent. For the 1 ∼ 2 nm wire, the band gap is a linear function of strain, while for the 2 ∼ 4 nm wire the gap variation with strain shows nearly parabolic behavior. This size dependence of the gap variation with strain may result from the orbital characters of the band edges. In addition, the effective masses of the electron and hole in <110> nanowires are found to be smaller than those of bulk Si suggesting Si wires could be a super material with high electron and hole mobility. We also find strain affects the effective masses of the electron and hole differently---expansion increases the hole effective mass, while compression increases the electron effective mass. The study of size and strain effects on effective masses shows that effective masses of the electron and hole can be reduced by tuning the diameter of the wire and applying proper strain. This result supports the motivation for using Si nanowires as functional components in future nanoelectronics.; In the third part, we have studied the combined effect of polytype and size on the Eg in SiC nanoclusters deriving from three different parent polytypes, namely 3C, 2H and 4H, in the size range of 0.5 nm ∼ 2.0 nm. We found that for the clusters smaller than 1 nm, regardless of the parent polytype, identical size - Eg dependency is achieved. For clusters larger than 1 nm, different polytypes exhibit distinct Eg values, systematically approaching their bulk band gaps. The critical size of 1 nm is correlated to the number of bilayers and the stacking sequences within the clusters. These studies suggest how the structure, energetics, and electronic properties are evolv...