Static and dynamic aspects of black silicon formation.

We present a combination of experimental data and modeling that explains some of the important characteristics of black silicon (BSi) developed in cryogenic reactive ion etching (RIE) processes, including static properties (dependence of resulting topography on process parameters) and dynamic aspects (evolution of topography with process time). We generate a phase diagram predicting the RIE parameter combinations giving rise to different BSi geometries and show that the topographic details of BSi explain the metamaterial characteristics that are responsible for its low reflectivity. In particular, the unique combination of needle and hole features of various heights and depths, which is captured by our model and confirmed by focused ion beam nanotomography, creates a uniquely smooth transition in refractive index. The model also correctly describes dynamical characteristics, such as the dependence of aspect ratio on process time, and the prediction of new etching fronts appearing at topographical saddle points during the incipient stages of BSi development--a phenomenon reported here for the first time.