Etching Through a Slit

The problem of etching through a slit-shaped orifice is formulated in mathematical terms. Although a full solution to this problem can be obtained only by the application of numerical methods, it is shown that certain aspects of it can be dealt with by analytical means. Asymptotic solutions that are valid in certain parts of the time domain are derived. Early, intermediate and late asymptotes are considered. These analytical results are compared with numerical ones, and a satisfactory agreement is found, emphasizing the validity of the two approaches.