In this paper, we study local etching of the GaAs(001) surface by Ga droplets at various technological conditions. Effects of the deposition temperature and thickness, interruption time, annealing temperature and arsenic background pressure are discussed. A minimum deposition thickness of 1.5 monolayer of Ga is found to be sufficient to etch the GaAs surface. We demonstrate that an increase in the annealing temperature leads to a decrease in the hole depth and an increase in their diameter. For the first time, we obtain symmetrical nanoholes of pyramidal shape on the GaAs(001) surface with a low surface density (~ 1·108 cm‒2 and below) allowing subsequent formation of single quantum dots for high-efficiency quantum photonic devices.