  We present a new empirical pseudopotential (EPM) calculation approach to
simulate the million atom nanostructured semiconductor devices under potential
bias using the periodic boundary conditions. To treat the non-equilibrium
condition, instead of directly calculating the scattering states from the
source and drain, we calculate the stationary states by the linear combination
of bulk band method and then decompose the stationary wave function into source
and drain injecting scattering states according to an approximated top of the
barrier splitting (TBS) scheme based on physical insight of ballistic and
tunneling transport. The decomposed electronic scattering states are then
occupied according to the source/drain Fermi-Levels to yield the occupied
electron density which is then used to solve the potential, forming a
self-consistent loop. The TBS is tested in an one-dimensional effective mass
model by comparing with the direct scattering state calculation results. It is
also tested in a three-dimensional 22 nm double gate ultra-thin-body
field-effect transistor study, by comparing the TBS-EPM result with the
non-equilibrium Green's function tight-binding result. We expected the TBS
scheme will work whenever the potential in the barrier region is smoother than
the wave function oscillations and if it does not have local minimum, thus
there is no multiple scattering as in a resonant tunneling diode, and when a
three-dimensional problem can be represented as a quasi-one-dimensional
problem, e.g., in a variable separation approximation. Using our approach, a
million atom non-equilibrium nanostructure device can be simulated with EPM on
a single processor computer.
