As the feature size of the metal-oxide-semiconductor field effect transistors (MOSFETs) decreases to the nanoscale, various quantum mechanical phenomena, such as geometrical confinement and tunneling, become dominant in determining the performances of the MOSFETs. In addition to these quantum effects, the phonon scattering effect is one of the dominant factors governing the device performance. Hence, it is important to perform the device simulation considering these effects. In this thesis, the tools that facilitate the full quantum transport simulation including phonon scattering with affordable computational cost have been developed. We focus on the practical device simulation with realistic device size. The kp method is applied to calculate the Hamiltonian using the finite element method. The mode space method is used to reduce the computational burden related to the phonon scattering. Using the tools, the phonon scattering effects on the circular nanowire MOSFETs have been investigated. The geometry effects of the cross section have been studied. We suggest the best design configuration that minimizes the variation of the device performances by the imperfection of the fabrication process. In addition, the design guidelines to improve the device performances are suggested.