We study the stability and electronic structure of previously unexplored two-dimensional (2D) ternary compounds BNP$_2$ and C$_2$SiS. Using $ab$ $initio$ density functional theory, we have identified four stable allotropes of each ternary compound and confirmed their stability by calculated phonon spectra and molecular dynamics simulations. Whereas all BNP$_2$ allotropes are semiconducting, we find C$_2$SiS, depending on the allotrope, to be semiconducting or semimetallic. The fundamental band gaps of the semiconducting allotropes we study range from $1.4$ eV to $2.2$ eV at the HSE06 level $0.5$ eV to $1.4$ eV at the PBE level and display carrier mobilities as high as $1.5{times}10^5$ cm$^2$V$^{-1}$s$^{-1}$. Such high mobilities are quite uncommon in semiconductors with so wide band gaps. Structural ridges in the geometry of all allotropes cause a high anisotropy in their mechanical and transport properties, promising a wide range of applications in electronics and optoelectronics.
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