Electronic Structure of intrinsic and doped Silicon Carbide and Silicon

Abstract: Silicon (Si) is the most exploited material within the semiconductor device technology, mainly due to its relatively good electron and hole mobilities and the simplicity to fabricate and process the material. Silicon carbide (SiC) has, however, a wider band gap, a higher breakdown electric field strength, and a higher thermal conductivity, which makes SiC one of the most promising materials for high-power devices. The high saturation drift velocity in SiC is a quality suitable also for highfrequency applications and, furthermore, the chemical and radiant inertness makes SiC-based devices capable to operate in harsh environments. Although the increasing interest in SiC has resulted in comprehensive investigations of the material, there is still deficient knowledge about the basic electronic properties of SiC.The present thesis comprises a theoretical study on the electronic structure of the cubic polytype 3C and the hexagonal polytypes 2H, 4H, and 6H of SiC. Detailed investigations of the energy bands near the fundamental energy band gap, important for the understanding of the electronic transport properties in these materials, have been performed and special attention has been paid on the non-parabolicities of the energy bands. Throughout the work, comparisons have been made with cubic Si and in some case with the corresponding hexagonal Si polytypes.The electronic band structure of the intrinsic materials have been calculated employing a relativistic and full-potential linearized augmented plane wave (LAPW) method based upon the local density approximation (LDA) to the density functional theory (DFT). Geometric optimizations of the crystals result in lattice constants confirming the experimental values and it is demonstrated that even small variations in the atomic positions have a strong impact on the crystal-field splitting of the uppermost valence bands in the hexagonal polytypes. For the time being there is a lack of experimental information about the electronic band structure in SiC and the values of the effective hole masses have not been experimentally established. The effective hole masses in Si and effective electron masses in both SiC and Si calculated here agree well with available measured values. It is shown that inclusion of the spin-orbit interaction is crucial for accurately calculating the effective hole masses. The uppermost valence bands in all materials considered here have been found to be nonparabolic in the vicinity of the Γ point and, furthermore, the lowest conduction band in 6H-SiC has a very flat and non-parabolic double-well structure. Electron and hole scatterings, caused by the existence of interaction potentials or through optical or thermal excitations, are dependent on the selection rules for the transitions and on the density-of-states of the energy bands. This thesis provides a symmetry classification of the electron states, both for the single and the double space groups. Moreover, the density-of-states have also been determined. Using the calculated density-of-states, the temperature dependent carrier concentration has been worked out for 4H-SiC:Al and 6H-SiC:N.In order to properly design semiconductor devices, the effects on the electronic band structure due to doping or plasma-injection have to be known. In this thesis calculations of the self-energy for the lowest conduction-band states and for the uppermost valence-band states in n-type, p-type, and plasma-induced SiC and Si have been performed, utilizing the zero-temperature Green's function formalism. The correlation interaction was described within the random phase approximation (RPA) with a local-field correction of Hubbard, and the electron-impurity ion interaction was obtained from second-order perturbation theory. The resulting energy shifts of the fundamental band gap and of the optical band gap have been worked out. It is found that the non-parabolicities of the energy bands strongly influence the calculated bandgap narrowing for high dopant concentration. Furthermore, the distortions of the conduction band in n-type SiC and Si have been investigated and the modified effective electron masses are presented. By comparing the calculated total energies of the localized donor electrons in the non-metallic phase and of the electron gas in the metallic phase the critical concentrations for the metal non-metal transition (the Mott transition) have been estimated for n-type SiC and Si.

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