With the shrink of critical dimensions of semiconductor devices to a few nanometers, atomic layer etching (ALE) has become an important technique to achieve single-atom resolution. The ALE can divide plasma etching into two self-limiting reaction processes: passivation process and etching process, allowing for the sequential removal of material atomic layer by layer. Therefore, it encounters the problem of low etch rate. In this work, the variation in surface substance coverage during the passivation process and the etching process are investigated numerically to optimize both the passivation duration and the etching duration. A coupled model integrating a two-dimensional inductively coupled plasma discharge chamber model, a one-dimensional sheath model, and a three-dimensional etching trench model is developed and used to investigate the optimal time for one single cycle ALE of silicon through the use of Ar/Cl₂ gases under the condition of Ar inductively coupled plasma discharge. The results indicate that during the passivation stage, the surface coverage of SiCl and SiCl₂ initially increase with time going by and then decrease, while the surface coverage of SiCl₃ continuously increases, and eventually, the surface coverage of these three species stabilize. When the surface is predominantly covered by SiCl₂, it is the optimal time to trigger the etching process, which induces a relatively favorable surface state and a relatively short etching time. Comparing with typical ALE etching techniques, the time of our optimal ALE single cycle is shortened by about 33.89%. The ALE cycle time (etching rate) exhibits a linear relationship with the aspect ratio. Additionally, the duration of the passivation process and etching process increase linearly with the aspect ratio or etch depth increasing. Moreover, as the etch depth increases, the effect of the passivation process on the ALE rate becomes more significant than that of the etching process.