Being one of the most sensitive methods for optical thin film metrology ellipsometry is widely used for the characterization of zinc oxide(ZnO), a key material for optoelectronics, photovoltaics, printable electronics and in a range of critical applications. The dielectric function of ZnO has a special feature around the band gap dominated by a relatively sharp absorption feature and an excitonic peak. In this work we summarize and compare direct (point-bypoint) and parametric approaches for the description of the dielectric function. We also investigate how the choice of the wavelength range influences the result, the fit quality and the sensitivity. Results on ZnO layers prepared by sputtering are presented.