  We develop a first-principles theory for Schottky barrier physics. The
Poisson equation is solved completely self-consistently with the electrostatic
charge density and outside the normal density functional theory (DFT)
electronic structure iteration loop, allowing computation of a Schottky barrier
entirely from DFT involving thousands of atomic layers in the semiconductor.
The induced charge in the bulk consists of conduction and valence band charges
from doping and band bending, as well as charge from the evanescent states in
the gap of the semiconductor. The Schottky barrier height is determined when
the induced charge density and the induced electrostatic potential reach
self-consistency.
