Consider an Al-n-Si Schottky barrier at \( \mathrm{T}=300 \mathrm{~K} \) with \( \mathrm{N}_{\mathrm{d}}=10^{16} \mathrm{~cm}^{-3} \). (work function of \( \mathrm{Al} \) is \( 4.28 \mathrm{eV} \) and Si electron affinity is \( 4.01 \mathrm{eV} \) ). (a) Find \( V_{b i} \) and \( E_{\max } \). (b) Using the value of Emax from part (a) determine \( \Delta \phi \) and \( \mathrm{xm} \) for the Schottky barrier lowering. (c) Repeat part (b) for the case when a reverse bias of \( \mathrm{V}=4 \mathrm{~V} \) is applied (d) If the reverse saturation \( \mathrm{J}_{\mathrm{ST}} \) is \( 7 \times 10^{-5} \mathrm{~A} / \mathrm{cm}^{2} \) find the value of Richardson constant (e) Schottky diode current for \( \mathrm{V}=0.4 \mathrm{~V} \) (forward biased voltage) (f) Calculate forward biased ( \( \mathrm{V} \) or \( \mathrm{Va} \) ) required to generate a forward bias current density of \( 15 \mathrm{~A} / \mathrm{cm}^{2} \)