HfO2 and ZrO2 are two high-k materials that are important in the downscaling of semiconductor devices. Atomic-level control of material processing is required for the fabrication of thin films of these materials at nanoscale device sizes. Thermal atomic layer etching (ALE) of metal oxides, in which up to one monolayer of the material can be removed, can be achieved by sequential self-limiting (SL) fluorination and ligand-exchange reactions at elevated temperatures. However, to date, a detailed atomistic understanding of the mechanism of thermal ALE of these technologically important oxides is lacking. In this paper, we investigate the hydrogen fluoride (HF) pulse in the first step in the thermal ALE process of HfO2 and ZrO2 using first-principles simulations. We introduce Natarajan–Elliott analysis, a thermodynamic methodology, to compare reaction models representing the self-limiting (SL) and continuous spontaneous etching (SE) processes taking place during an ALE pulse. Applying this method to the first HF pulse on HfO2 and ZrO2, we found that thermodynamic barriers impeding continuous etching are present at ALE-relevant temperatures. We performed explicit HF adsorption calculations on the oxide surfaces to understand the mechanistic details of the HF pulse. A HF molecule adsorbs dissociatively on both oxides by forming metal–F and O–H bonds. HF coverages ranging from 1.0 ± 0.3 to 17.0 ± 0.3 HF/nm2 are investigated, and a mixture of molecularly and dissociatively adsorbed HF molecules is present at higher coverages. Theoretical etch rates of −0.61 ± 0.02 Å/cycle for HfO2 and −0.57 ± 0.02 Å/cycle for ZrO2 were calculated using maximum coverages of 7.0 ± 0.3 and 6.5 ± 0.3 M–F bonds/nm2, respectively (M = Hf, Zr).