Any defects like oxygen vacancies, reduced oxidation states present in metal oxide (ZnO, TiO2 etc) will effect by enhancing the absorption properties by extending in visible region. This can be confirmed from UV-Vis spectroscopy analysis. A band gap reduction due to defects is attributed to such visible light absorption.
Although, it is always better to analyse the PL spectra for understanding the defect states, still you may get some idea about the defect states in ZnO nano rods from UV-Vis-NIR spectral analysis from the following articles.
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If you wish to know about the oxygen vacancy related defect states in TiO2 and H2Ti3O7 nanostructures then I'll request you read the following articles.