Is Cu$_{3-x}$P a semiconductor, a metal, or a semimetal?

Despite the recent surge in interest in Cu$_{3-x}$P for catalysis, batteries, and plasmonics, the electronic nature of Cu$_{3-x}$P remains unclear. Some studies have shown evidence of semiconducting behavior, whereas others have argued that Cu$_{3-x}$P is a metallic compound. Here, we attempt to resolve this dilemma on the basis of combinatorial thin-film experiments, electronic structure calculations, and semiclassical Boltzmann transport theory. We find strong evidence that stoichiometric, defect-free Cu$_3$P is an intrinsic semimetal, i.e., a material with a small overlap between the valence and the conduction band. On the other hand, experimentally realizable Cu$_{3-x}$P films are always p-type semimetals natively doped by copper vacancies regardless of $x$. It is not implausible that Cu$_{3-x}$P samples with very small characteristic sizes (such as small nanoparticles) are semiconductors due to quantum confinement effects that result in opening of a band gap. We observe high hole mobilities (276 cm$^2$/Vs) in Cu$_{3-x}$P films at low temperatures, pointing to low ionized impurity scattering rates in spite of a high doping density. We report an optical effect equivalent to the Burstein-Moss shift, and we assign an infrared absorption peak to bulk interband transitions rather than to a surface plasmon resonance. From a materials processing perspective, this study demonstrates the suitability of reactive sputter deposition for detailed high-throughput studies of emerging metal phosphides.