Maybe difficult to handle with E-beam to get a stoihciometric ZnO film.
Sputter deposition can probably yield.
Must know the deposition rate correctly.
Need to establish a stable plasma, set an appropriate (Ar+O2) gas mixture, and an appropriate sputtering pressure. Then have a shuttering action to stop the deposition will be in time. Make a few samples and study their thickness.
alternately atomic layer deposition (ALD) will be a better suitable technique.