  Zincblende copper iodide has attracted significant interest as a potential
material for transparent electronics, thanks to its exceptional light
transmission capabilities in the visible range and remarkable hole
conductivity. However, remaining challenges hinder the utilization of copper
iodide's unique properties in real-world applications. To address this,
chalcogen doping has emerged as a viable approach to enhance the hole
concentration in copper iodide. In search of further strategies to improve and
tune the electronic properties of this transparent semiconductor, we
investigate the ternary phase diagram of copper and iodine with sulphur or
selenium by performing structure prediction calculations using the minima
hopping method. As a result, we find 11 structures located on or near the
convex hull, 9 of which are unreported. Based on our band structure
calculations, it appears that sulphur and selenium are promising candidates for
achieving ternary semiconductors suitable as $p$-type transparent conducting
materials. Additionally, our study reveals the presence of unreported phases
that exhibit intriguing topological properties. These findings broaden the
scope of potential applications for these ternary systems, highlighting the
possibility of harnessing their unique electronic characteristics in diverse
electronic devices and systems.
