  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.
