Calculate the threshold voltage of a MOS system using an aluminum gate. Consider a p-type silicon substrate at T=300 \mathrm{~K} doped to N_{a}=10^{15} \mathrm{~cm}^{-3} . Let Q_{s s}^{\prime}= 10^{10} \mathrm{~cm}^{-2}, t_{o x}=12 \mathrm{~nm}=120 \mathring{A}, and assume the oxide is silicon dioxide.