The etching of HfO2 and ZrO2 high-k dielectrics is studied using plasma enhanced atomic layer etching. The etching method relies on a continuous argon inductively coupled plasma discharge in which reactive gases are pulsed, followed by substrate biasing; both steps are separated by purge periods. It is found that pure BCl3 is too chemically active while a Cl2–BCl3 allows a high process synergy; in addition, the latter gives a high selectivity to SiO2. The optimal etch conditions are applied to high-k layers deposited on top of WS2 transition metal dichalcogenide. Postetch analysis shows negligible tungsten and sulfur depletion as well as negligible change in optical (Raman) response of the 2D layer, indicating that atomic layer etching concepts allows us to prevent WS2 material loss or damage.