The following figure is taken from the paper by D. L. Kendal, “Vertical Etching of silicon at very high aspect ratios”, Annual Review of Material Sciences, 1979, Vol. 9, pp. 373-403. It shows the planes that will emerge when a (110) oriented silicon wafer is etched through a rectangular opening. The (11-1) and the (111) are marked in the figure and they form the slanting faces of the etched groove at either end. Find the angle made by the surface normals to these planes (sketched in the figure as slanting faces) with the top (110) plane.
The stress-strain relationship, represented in the matrix form, for silicon by considering the [100], [010] and [001] directions (shown as red in the figure above) as the base axes is given by:
Write the matrix components with respect to [110], [-110] and [001] (shown in black in the figure above). This new set is obtained by rotating the previous set of axes through 45 degrees about the [001] direction. Use this matrix to find the Young's modulus in the [110] direction.