$8\mathrm{.}11.$ In the ion implantation process, positively charged ions impact on the semiconductor surface. Normally these ions are neutralized by capturing an electron from the conducting substrate. However, when the mask is an insulator like $Si{O}_2,$ the charge on the ions may not be neutralized as easily. Consider the case where a dose $Q$ is implanted into the surface of an $Si{O}_2$ layer $($assume all the charge resides at the oxide surface$).$ Further assume that the oxide can withstand an electric field of ${10}^{7}Vc{m}^{-1}$ before it breaks down. What implant dose $Q$ is required to cause electrical failure of the mask? That is$,$ what dose will cause a field of ${10}^{7}Vc{m}^{-1}$ across the oxide?