1" is all you need if, its not a floating design.

There is zero point to using such thick treads with a closed stringer. The end result is likely to be a huge safety hazard, severely out of code, unless all the math is done correctly from the beginning to build them with that in mind. If this isn't a new build, forget it. If it is a new build, only do this with open stringer floating stairs. That is the only time it is successful.

Thanks! This is for a new staircase and open stringers (for the bottom half of the staircase).