Our first-principles calculations are performed using DFT within the projector augmented-wave method (PAW) as implemented in the code VASP. We used a plane-wave energy cut-off of 400 eV, and a Γ-centred 7 × 7 × 4 k-point mesh to describe the Brillouin zone of the primitive cell. The electrons considered as valence for each element are as follows: Ca 3p 6 4s 2 (8 total), Cu 3d 10 4s 1 (11 total), P 3s 2 3p 3 (5 total). We use the PBEsol functional for calculating the vibrational properties and the hybrid PBE0 functional for all other calculations, in accordance with previous simulations on CaCuP. Defect formation energies were calculated according to the Lany-Zunger correction scheme, thermodynamic stability analysis computed with the CPLAP software, charge transport properties calculated using the AMSET code, absorption calculations performed using the independent particle approximation (IPA), the electric dipole approximation and the Williams-Lax theory, and the surface band alignment calculations were performed using the SUR-FAXE code. Further details on the computational methods can be found in the ESI. †