The self-organized in situ drilling of nanoholes into semiconductor surfaces by using liquid metallic droplets during conventional molecular beam epitaxy represents a new degree of freedom for the design of heterostructure devices. A model of this local droplet etching is presented that is based on a core-shell droplet structure. With the model, the evolution of the droplet and substrate morphology is calculated. We demonstrate quantitative agreement between model results and measured morphologies. Furthermore, also the influence of the process temperature is correctly reproduced by the model.