Atomistic modeling of the electrostatic and transport properties of a simplified nanoscale field effect transistor

A first-principle model is proposed to study the electrostatic properties of a double-gated silicon slab of nano scale in the framework of density functional theory. The applied gate voltage is approximated as a variation of the electrostatic potential on the boundary of the supercell enclosing the system. With the electron density estimated by the real space Green's functions, efficient multigrid and fast Fourier-Poisson solvers are employed to calculate the electrostatic potential from the charge density. In the representation of localized SIESTA linear combination of atomic orbitals, the Kohn-Sham equation is established and solved self-consistently for the wavefunction of the system in the local density approximation. The transmission for ballistic transport across the atomic silicon slab at small bias is calculated. The charge distribution and electrostatic potential profile in the silicon slab versus the gate voltage are then analyzed with the help of the equivalent capacitive model. Quantum confinement and short gate effects are observed and discussed.