  The LDA-1/2 method for self-energy correction is a powerful tool for
calculating accurate band structures of semiconductors, while keeping the
computational load as low as standard LDA. Nevertheless, controversies remain
regarding the arbitrariness of choice between (1/2)e and (1/4)e charge
stripping from the atoms in group IV semiconductors, the incorrect direct band
gap predicted for Ge, and inaccurate band structures for III-V semiconductors.
Here we propose an improved method named shell-LDA-1/2 (shLDA-1/2 for short),
which is based on a shell-like trimming function for the self-energy potential.
With the new approach, we obtained accurate band structures for group IV, and
for III-V and II-VI compound semiconductors. In particular, we reproduced the
complete band structure of Ge in good agreement with experimental data.
Moreover, we have defined clear rules for choosing when (1/2)e or (1/4)e charge
ought to be stripped in covalent semiconductors, and for identifying materials
for which shLDA-1/2 is expected to fail.
