We present a theoretical study of electron mobility in cylindrical gated silicon nanowires at 300 K based on the Kubo-Greenwood formula and the self-consistent solution of the Schrödinger and Poisson equations. A rigorous surface roughness scattering model is derived, which takes into account the roughness-induced fluctuation of the subband wave function, of the electron charge, and of the interface polarization charge. Dielectric screening of the scattering potential is modeled within the random phase approximation, wherein a generalized dielectric function for a multi-subband quasi-one-dimensional electron gas system is derived accounting for the presence of the gate electrode and the mismatch of the dielectric constant between the semiconductor and gate insulator. A nonparabolic correction method is also presented, which is applied to the calculation of the density of states, the matrix element of the scattering potential, and the generalized Lindhard function. The Coulomb scattering due to the fixed interface charge and the intra- and intervalley phonon scattering are included in the mobility calculation in addition to the surface roughness scattering. Using these models, we study the low-field electron mobility and its dependence on the silicon body diameter, effective field, dielectric constant, and gate insulator thickness.

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Based on the nonequilibrium Green’s function formalism, we have developed a three-dimensional (3D) simulation framework capable of handling electronic transport in nanoscale silicon devices within the effective mass and Hartree approximations. Using the deformation potential theory and the self-consistent Born approximation, we obtain the spatially local self-energy functions for the intravalley and intervalley phonon scattering mechanisms. To make the 3D simulation practicable, we reduce the computational complexity by using the mode space approach suitable for the device whose cross section is relatively uniform along the transport direction. We also obtain the expression for the phonon-limited low field mobility in the long channel limit from the linear response theory. As an application, we study the quantum transport of the silicon nanowire transistor whose channel length is 15nm in the ballistic limit and in the presence of the electron-phonon interactions. We can observe various effects of the electron-phonon interactions such as the reduction of the drain current, broadening of the local density of states, and the energy relaxation of the electrons injected from the source.