Utilizing space group theoretical methods we have derived so called "Lattice Modes Representation" (LMR) for the ZnO with the space group C(6v-4). The reduction of the LMR leads to the total number of independent (first order) vibrational modes (species) and their symmetries (irreducible representations (irrps)) originating from the centre as well as from the high symmetry points and lines of the Brillouin zone for ZnO. Considering only long-wavelength modes (k=0) we have derived Raman selection rules for: 1-rst order Raman active modes (1RAMs) meaning all possible overtones and combinations, 2-nd order Raman active modes (2RAMs) (all combinations and overtones) and for the third order Raman active processes (3RAMs) in ZnO as well. We have performed the Raman inelastic light scattering experiment in the frequency regions of 1-rst, 2-nd and the third order Raman active modes. Several multi-phonon processes in ZnO are observed. In addition, the low temperature photoluminescence spectra exhibit some phonon replicas these confirm the presence of multi-phonon processes in ZnO. An external perturbation on the ZnO such as ion-implantation, alpha particle irradiation, thermal annealing, high pressure, and so on, frequently generate, treatment induced, new vibrational modes. These phonons can only be distinguished from the multi-phonon Raman active modes by means of our selection rules.
The derived RAMs can also be useful in the determination of the dynamical matrix for a crystal from which the particular frequencies of modes can be calculated and therefore the phonon density of states can be obtained.

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2. Multi-Phonon process in C6v4 (P63mc) hexagonal semiconductors: GaN, ZnO, 2H - SiC, 6H - SiC, ZnS, CdS