The continued evolution of electronic devices relies on the development of new semiconductor memory technology. Given the high compatibility of the Hf0.5Zr0.5O2 thin films with the CMOS technology, we investigate the charge transport mechanisms that occur in a relative thick Hf0.5Zr0.5O2 thin film (4 to 6 nm-thick) when subjected to electrical stresses. To that end we fabricate Hf0.5Zr0.5O2 heterostructures with a Pt tip as the top electrode and TiN and Pt as bottom electrode by radio-frequency magnetron sputtering. After analyzing the surface morphology of the as-received and as-deposited films by atomic force microscopy, the transfer of the desired chemical stoichiometry from the sputtering target to the substrate surface is studied by Raman spectroscopy. The ferroelectricity of the Hf0.5Zr0.5O2 thin films is confirmed by piezoresponse force microscopy measurements, and a retention of 22 h is obtained, attesting to the non-volatility of the samples. Nanoscale electrical measurements reveal the presence of resistive switching, where the low resistance state (ON state) in both Pt-tip/Hf0.5Zr0.5O2/TiN and Pt-tip/Hf0.5Zr0.5O2/Pt heterostructures can be created by the formation of a conductive filament based on oxygen vacancies.