Could anyone explain the bonding character of wurtzite ZnO? I think it possesses both covalent and ionic characters. Is there a relationship between bond type and forbidden band gap?
Yes indeed, as many compounds with transition metals do. Also, there is a close relationship between the bond type and band gap as much as it influences the band structure by the repulsive-attractive interactions between nuclei and electrons. I attach a reference where the bonding type in doped Cu2O is studied with inference on the electronic structure of the final material. Also references about ab initio calculations on ZnO band structure can be of help for you. Also try solid state books such as Kittel
wurtzite structure are more familiar for ionic charecters but there can be a mixture of inoic as well as covalent depends on the material. bond type definitely have an influence on their electronic states which in turn on their band gap.
if we compare the electronegativity values of oxygen and zinc (according to Pauling's scale, for example), their difference is 1.79 (=3.44-1.65). It is rather close to the arbitary boundary between covalent ( 2) bond type.