Today\u27s development of new electronic devices requires materials that can operate under harsh conditions. One such material is Silicon Carbide (SiC) which exhibits superior properties such as chemical inertness, high durability, high thermal stability, high thermal conductivity, and extreme hardness. Today SiC is recognized as a the most promising wide band-gap semiconductor. It is because of its characteristics. It is well known that the surfaces of SiC can produce well-ordered graphite overlayers at temperatures over 1400∘. The excellent quality of the resulting overlayer opens up exciting opportunities for growth and study of metallic nanostructures, and benefits studies of graphitic systems including alkali metal--graphite intercalation compounds. Other aspects that make SiC an interesting material is that it exists in more that 200 different forms, so--called polytypes. Thus the SiC materialrepresents a whole class of semiconductors.This thesis presents a broad theoretical study, which includes, among other things, studies and comparisonsof structure, cohesive/formation energies, and elastic response of the hard SiC and of the soft graphitic materials, which are characterized by sparseness in the electron-density distribution. It also contains studiesof the nature of bonding between SiC surfaces and graphene (a single layer of graphite). All studies use a recently developed density functional that includes van der Waals (vdW) forces (vdW-DF), as the main tool of the study, traditional density functional theory (DFT), lacks an account for van der Waals interactions significant in sparse materials. The nature of the bonds in the SiC/graphene system is revealed by analysis of the electronic structure. Size effect on the transport properties in nanostructured SiC and some related materials are investigated and calculated on the basis of the Boltzmann transport equation (BTE) approach. The phonon transport is found to be significantly reduced below the bulk transport value bythe phonon Knudsen effect that arise from boundary scattering of interface defects and/or interface modes
