Perfect Cooper pair splitting is proposed, based on crossed Andreev reflection (CAR) in a p-type semiconductor-superconductor-n-type semiconductor (pSn) junction. The ideal splitting is caused by the energy filtering that is enforced by the band structure of the electrodes. The pSn junction is modeled by the Bogoliubov–de Gennes equations and an extension of the Blonder-Tinkham-Klapwijk theory beyond the Andreev approximation. Despite a large momentum mismatch, the CAR current is predicted to be large. The proposed straightforward experimental design and the 100% degree of pureness of the nonlocal current open the way to pSn structures as high quality sources of entanglement.