In a micromanufacturing process a 50 nm thick silicon nitride layer is employed as a hard mask for a silicon layer. The etchant is potassium hydroxide (KOH). The etch rate of silicon is 1 μm/min using KOH. The selectivity ratio (defined as the ratio of the etching rate of silicon to the etching rate of another material using the same etchant) is 10^4 for silicon nitride.
a) How long will it take for all the silicon nitride mask layer to be etched away (removed) using KOH?
b) How much silicon will be removed in this time?