Atomic layer deposition (ALD) is a standard technique employed to grow thin-film oxides for a variety of applications. We describe the technique and demonstrate its use for obtaining memristive devices. The metal/insulator/metal stack is fabricated by means of ALD-grown HfO2, deposited on top of a highly doped Si substrate with an SiO2 film and a Ti electrode. Enhanced device capabilities (forming free, self-limiting current, non-crossing hysteretic current-voltage features) are presented and discussed. Careful analysis of the stack structure by means of X-ray reflectometry, atomic force microscopy, and secondary ion mass spectroscopy revealed a modification of the device stack from the intended sequence, HfO2/Ti/SiO2/Si. Analytical studies unravel an oxidation of the Ti layer which is addressed for the use of the ozone precursor in the HfO2 ALD process. A new deposition process and the model deduced from impedance measurements support our hypothesis: the role played by ozone on the previously deposited Ti layer is found to determine the overall features of the device. Besides, these ALD-tailored multifunctional devices exhibit rectification capability and long enough retention time to deserve their use as memory cells in a crossbar architecture and multibit approach, envisaging other potential applications.