A mathematical model of surface erosion in a course of a trench formation by translationally moving ion beam of a Gaussian shape is considered. The solutions obtained in self-similar variables describe the states of equilibrium of the boundary value problem and their dependence on the sputtering parameters. It is shown that there are three parameter areas in which only smooth, smooth and discontinuous and only discontinuous solutions exist. The plots of the surface profiles corresponding to three possible types of solutions are given. Formulas for calculating the profile of etching trenches and examples of calculating profiles corresponding to smooth and discontinuous solutions are given.

考虑通过平移移动高斯形状的离子束形成沟槽的过程中的表面侵蚀的数学模型。在自相似变量中获得的解描述了边界值问题的平衡状态及其对溅射参数的依赖性。结果表明，存在仅光滑、光滑和不连续和仅存在不连续解的三个参数区域。给出了对应于三种可能类型的解决方案的表面轮廓图。给出了计算蚀刻沟槽轮廓的公式和计算光滑和不连续解对应的轮廓的例子。