“…However, due to a lack of knowledge of their concentration dependence and due to the fact the measured concentration profile fits the expression of (13), described below, reasonably well [13], our assumption is justified. For a rectangular initial exchange region (depth = h, width = w ) with a width dependent uniform proton concentration C,",(w), the solution to (12) is given by [20] (See Eq. (13) below) where dy = 2(D,yt,)1/2 is the diffusion distance in the width direction after annealing and t, is the annealing time.…”