Comprehensive Raman and photoluminescence (PL) results on ZnO nanocrystals are presented in this work. The ZnO nanocrystals were prepared by plasma-assisted electron beam evaporation of metallic Zn films on GaInPAs films, which were previously grown on InP substrates by MOCVD, then a low-temperature annealing process was conducted on the as-deposited Zn films. Raman results show the presence of a surface phonon (SP) mode, which reveals that nanocrystals are embedded in a compound matrix. Seven longitudinal optical-phonons (LOs) accompanied by SPs are observed in the resonant Raman spectrum for our ZnO nanocrystals at 80K, which is probable due to a strong surface enhanced Raman scattering (SERS) effect and quantum confinement effect. Room temperature PL spectra show a single broad UV peak at around 3.45eV with sharp Raman lines superimposed upon it, indicating a large quantum confinement effect in the ZnO nanocrystals due to their small dimensions. PL spectra measured at different temperatures show an anomalous dependence of the PL intensity with variation in temperature, which is analyzed on the basis of John-Singh's model. The total PL intensity is governed by the combination of radiative and non-radiative processes.