  Accurate theoretical prediction of the band offsets at interfaces of
semiconductor heterostructures can often be quite challenging. Although density
functional theory has been reasonably successful to carry out such calculations
and efficient and accurate semilocal functionals are desirable to reduce the
computational cost. In general, the semilocal functionals based on the
generalized gradient approximation (GGA) significantly underestimate the bulk
band gaps. This, in turn, results in inaccurate estimates of the band offsets
at the heterointerfaces. In this paper, we investigate the performance of
several advanced meta-GGA functionals in the computational prediction of band
offsets at semiconductor heterojunctions. In particular, we investigate the
performance of r2SCAN (revised strongly-constrained and appropriately-normed
functional), rMGGAC (revised semilocal functional based on cuspless hydrogen
model and Pauli kinetic energy density functional), mTASK (modified Aschebrock
and K\"ummel meta-GGA functional), and LMBJ (local modified Becke-Johnson)
exchange-correlation functionals. Our results strongly suggest that these
meta-GGA functionals for supercell calculations perform quite well, especially,
when compared to computationally more demanding GW calculations. We also
present band offsets calculated using ionization potentials and electron
affinities, as well as band alignment via the branch point energies. Overall,
our study shows that the aforementioned meta-GGA functionals can be used within
the DFT framework to estimate the band offsets in semiconductor
heterostructures with predictive accuracy.
