The programming and erase performance of atomic layer deposited HfO2/Al2O3 memory stacks is investigated depending on the thickness of the tunnel oxide and the annealing of the structures. The as-grown stacks require applying of voltage pulses with duration of about 10-3 s for a measurable electron trapping (programming). The time dependence of the electron trapping process is quite sharp initially - the increase of the charging time from 4×10-4 s to 4×10-3 s provides more than 80% of the saturation value of the trapped charge obtained at durations above 1 s. The annealing increases the time needed for the onset of the electron trapping. For the chosen voltage amplitudes the programming characteristics does not depend on the tunnel oxide thickness. The electron detrapping (erase) is observed even at durations of ~10-7 s, but with a low efficiency. The erase characteristics is more gradual then the program one, and shows some dependence on tunnel oxide and annealing. The complete erase is achieved for times comparable to those for programming the cell. Erase pulses with duration > 10-2 s results to accumulation of positive charge in the capacitors.