The Investigation of Representation Symmetry of Free Atoms and their Atomic Energy Level Splittings in the ZnO Crystalline Field

Using group theoretical techniques we have investigated the representation symmetry of free dopants (Al, Ga and In) of wurtzite ZnO structure. We have also studied the symmetry of wurtzite ZnO doped with Al, Ga and In. The method allows classification of the state of dopants in the crystalline field. We show that the symmetry of free atoms is the full rotation group (FRG) and that of operators OR (, ,), where, and are the Euler angles. The FRG is reduced to the symmetry operators of the point group of ZnO (C6v) when atoms are doped into the ZnO crystalline field. Our theoretical results confirm the available experimental data.