  The $k \cdot p$ is a versatile technique that describes the semiconductor
band structure in the vicinity of the bandgap. The technique can be extended to
full Brillouin zone by including more coupled bands into consideration. For
completeness, a detailed formulation is provided where the associated $k \cdot
p$ parameters are extracted from the local empirical pseudopotential method in
the form of band edge energies and generalized momentum matrix elements. We
demonstrate the systematic improvement of the technique with the proper choice
of the band edge states for the group-IV indirect bandgap semiconductors: Si,
Ge, diamond and SiC of the 3C cubic phase. The full zone agreement is observed
to span an energy window of more than 20 eV for Si, and 40 eV for the diamond
with the 15-band pseudopotential-based $k \cdot p$ approach.
