ECE $370$ Homework #$7$

The charge distribution for four ideal MOS capacitors are shown below. For each MOS capacitor,

a$.$ Is the sample N$-$type or p$-$type?

b$.$ What region of operation is the device in$?$

c$.$ Draw the energy band diagram for this device and region

Determine the metal$-$semiconductor work function difference ${}_{ms}$ in MOS with n$-$type Si with $N_a=5**{10}^{15}c{m}^{-3}$ for the case when the gate is:

a$.$ AL

b$.n^{-}$poly $-Si$

c$.P^{+}$poly Si

Consider a MOS device with n$-$type Si substrate with $N_a={10}^{16}c{m}^{-3}.$ The oxide thickness is $20$ nm and equivalent oxide charge is $8**{10}^{10}c{m}^{-2}.$ Calculate the threshold voltage for

a$.$ A $p^{+}$poly Si gate

b$.$ an $n^{-}$poly Si gate

c$.$ An Al gate

$A{n}^{+}$polySi gate has oxide thickness of $28$ nm and $N_a=3**{10}^{16}c{m}^{-3}.$ The oxide charge density is $Q_{ss}^{\text{'}}=7\mathrm{.}5**{10}^{10}c{m}^{-2}.$ Calculate

a$.V_{FB}$

b$.V_{TH}$