  The journey of theoretical study on semiconductors is reviewed in a
non-conventional way. We have started with the basic introduction of
Hartree-Fock method and introduce the fundamentals of Density Functional Theory
(DFT). From the oldest Local Density Approximations (LDA) to the most recent
developments of semi-local corrections [Generalised Gradient Approximation
(GGA), Meta-GGAs], hybrid functionals and orbital dependent methodologies are
discussed in detail. To showcase the performance of DFT, results obtained via
different approximations are compared. We indicate the success of semi-local
approximations in structural properties prediction. We also show how less
computationally costly but withstand architecture of some semi-local DFT
methods can solve the long riddle of bandgap underestimation. In semiconductor
physics, the importance of not only the band structure prediction, but also,
the proper calculation of Fermi energy, and, exact finding of band alignment is
argued. The comparison of Fermi energy dependent properties can channelize the
theoretical studies on modern age environment-friendly researches on
semiconductors, like artificial photocatalysis, energy efficient
opto-electronic devices, etc. This prescription on proper choice of DFT method
is potentially competent to complement the experimental findings as well as can
open up a pathway of advanced semiconducting materials discoveries.
