Silicon carbide (SiC) is regarded as an important semiconductor for a variety of applications including high-temperature, high-power and high-frequency devices. The most common polytypes of SiC are hexagonal (4H-or 6H-SiC) and cubic silicon carbide (3C-SiC), which differ from each other by the ordering of the Si-C bilayers along the c-axis crystal direction. Among different polytypes of SiC, 3C-SiC has attracted specific interest due to its prominent properties such as high electron mobility and low interface trap density in MOSFET devices. Moreover, with a relatively small bandgap of 2.36 eV and suitable conduction and valence band positions, 3C-SiC has also been considered as a promising material for solar water splitting application, which provides a completely renewable approach to convert solar energy into storable hydrogen fuel. However, the growth of high-quality 3C-SiC remains a great challenge for decades. Graphene, a single layer of sp 2-bonded carbon atoms, has shown outstanding electronic properties and becomes the most promising candidate for next-generation electronic and optoelectronic devices. Epitaxial growth of graphene on SiC substrates by sublimation of Si from SiC provides a feasible route to fabricate wafer-scale device-quality graphene. The most advantage of this method is that a variety of devices can be processed directly on graphene/SiC without any transfer process, which is needed in the case of graphene produced by exfoliation or CVD on metals. During past years, the growth of monolayer (ML) graphene on hexagonal SiC (6H-SiC, 4H-SiC) substrates has been extensively studied. However, it is challenging to grow large-area and uniform multilayer graphene on hexagonal SiC substrates due to the stepbunching issue during the sublimation growth. Multilayer graphene has recently attracted great interest due to its tunable electronic properties for various electronic and optoelectronic applications. It has been shown that the electronic properties of multilayer graphene are strongly influenced by its stacking sequence. In particular, the rhombohedral stacking sequence (ABC stacking) has shown its potential to introduce a flat band energy dispersion at the K points of the Brillouin zone, which would result in many exotic phases of matter such as superconductivity. Among various SiC polytypes, 3C-SiC is predicted to be the most suitable substrate for the epitaxial growth of rhombohedral multilayer graphene. This thesis work mainly covers the sublimation growth of high-quality Si-face and C-face 3C-SiC on off-oriented 4H-SiC, exploring the proper parameter window for the growth of