  The band gap engineering of group IV semiconductors has not been well
explored theoretically and experimentally, except for SiGe. Recently, GeSn has
attracted much attention due to the possibility of obtaining a direct band gap
in this alloy, thereby making it suitable for light emitters. Other group IV
alloys may also potentially exhibit material properties useful for device
applications, expanding the space for band gap engineering in group IV. In this
work the electronic band structure of all group IV semiconductor alloys is
investigated. Twelve possible A:B alloys, where A is a semiconducting host (A =
C, Si, and Ge) and B is an isovalent dopant (B = C, Si, Ge, Sn, and Pb), were
studied in the dilute regime (0.8%) of the isovalent dopant in the entire
Brillouin zone (BZ), and the chemical trends in the evolution of their
electronic band structure were carefully analyzed. Density functional theory
with state-of-the-art methods such as meta-GGA functionals and a spectral
weight approach to band unfolding from large supercells was used to obtain
dopant-related changes in the band structure, in particular the direct band gap
at the {\Gamma} point and indirect band gaps at the L(X) points of the BZ.
Analysis of contributions from geometry distortion and electronic interaction
was also performed. Moreover, the obtained results are discussed in the context
of obtaining a direct fundamental gap in Ge:B (B = C, Sn, and Pb) alloys, and
intermediate band formation in C:B (B = Sn and Pb) and Ge:C. An increase in
localization effects is also observed: a strong hole localization for alloys
diluted with a dopant of a larger covalent radius and a strong electron
localization for alloys with a dopant of smaller radius. Finally, it is shown
that alloying Si and Ge with other elements from group IV is a promising way to
enhance the functionality of group IV semiconductors.
