The Maximum Positive Curvature Recognition Method to Determine Etch Profiles in Wet Etching of Quartz on AT and BT Cuts

This paper presents a method to quickly determine the transient and stable profiles of trenches, cavities, and mesas formed by anisotropic wet chemical etching on AT and BT cut quartz wafers. Since most quartz orientations have low etch rates and both AT and BT cuts have no trigonal symmetry (unlike the Z cut), it is typically difficult to explain which sidewalls will appear on a given trench for a particular mask alignment on these cuts. By considering the complete etch rate distribution obtained from an etched quartz hemisphere we show that a maximum positive curvature recognition method can be used in order to determine a small number of key orientations, which will directly appear as the transient and stable sidewalls in the experimental trench profiles on both the AT and BT cuts. Similarly, the proposed method accurately explains the formation of complex facets on square cavities as well as on the top, middle and bottom regions of micro-needle arrays etched on the AT and BT cuts. This indicates that the etch profiles of any cut of the trigonal crystal can be determined by using the location of the proposed key orientations.