a) Derive an expression for the potential distribution in an ideal MOS

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a) Derive an expression for the potential distribution in an ideal MOS capacitor in the depletion condition in terms of the surface potential ϕs and the depletion width at the surface xd taking the zero for potential in the silicon bulk. The silicon is doped p type and x = 0 at the oxide silicon interface. b) For Parts(i) through (ii) below, consider the following low-frequency gate capacitance (per unit area) vs. gate voltage characteristic for a metal gate n-channel MOSFET. (5) (i) On the above figure label, the approximate regions or points of Weak inversion Flatband Strong inversion Accumulation Threshold and depletion (ii) What is the oxide capacitance per unit area?

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a) Derive an expression for the potential distribution in an ideal MOS capacitor in the depletion condition in terms of the surface potential

ϕ_{s}

and the depletion width at the surface

x_{d}

taking the zero for potential in the silicon bulk. The silicon is doped

p

type and

x = 0

at the oxide silicon interface. b) For Parts(i) through (ii) below, consider the following low-frequency gate capacitance (per unit area) vs. gate voltage characteristic for a metal gate n-channel MOSFET. (5) (i) On the above figure label, the approximate regions or points of