The accurate calculation of channel electrostatics
parameters, such as charge density and potential, in ultra-thin body (UTB) devices requires self-consistent solution of the
Poisson’s equation and the full band structure, which is channel
material and thickness dependent. For cubic crystals like silicon,
the semi-empirical sp3d5s* tight-binding (TB) model is preferred
in device simulations, over the density functional theory, to
obtain the full band structure because of being computationally
less intensive and equally accurate. However, the computational
time of the TB model scales non-linearly with the channel
thickness and becomes cumbersome for silicon, beyond 5 nm,
primarily because of the increasing size of the TB hamiltonian
that needs to be solved over the entire k-space, in the irreducible
Brillouin zone. In this work, we precisely identify those k-points
corresponding to the energies close to the band minima, where
the Fermi-Dirac probability significantly affects electrostatics
parameters. This enables us to demonstrate a computationally
efficient approach based on solving the hamiltonian only on those
reduced number of k-points. The rigorous benchmarking of the
channel electrostatics parameters obtained from this approach
is performed with results from accurate full band structure
simulations showing excellent agreement over a wide range of
channel thicknesses, oxide thicknesses, device temperatures and
different channel orientations. By showing that the approach
presented in this work is computationally efficient, besides
being accurate, regardless of the number of atomic layers, we
demonstrate its applicability for simulating UTB devices.