  Empirical tight binding(ETB) methods are widely used in atomistic device
simulations. Traditional ways of generating the ETB parameters rely on direct
fitting to bulk experiments or theoretical electronic bands. However, ETB
calculations based on existing parameters lead to unphysical results in ultra
small structures like the As terminated GaAs ultra thin bodies(UTBs). In this
work, it is shown that more reliable parameterizations can be obtained by a
process of mapping ab-initio bands and wave functions to tight binding models.
This process enables the calibration of not only the ETB energy bands but also
the ETB wave functions with corresponding ab-initio calculations. Based on the
mapping process, ETB model of Si and GaAs are parameterized with respect to
hybrid functional calculations. Highly localized ETB basis functions are
obtained. Both the ETB energy bands and wave functions with subatomic
resolution of UTBs show good agreement with the corresponding hybrid functional
calculations. The ETB methods can then be used to explain realistically
extended devices in non-equilibrium that can not be tackled with ab-initio
methods.
