Q$.$ pts$)$

You are asked to design a $10K$ resistor made of Si with different design parameters specifina :$-$

$($i$)$ and $($ii$)$ below. The resistor operates at $300$ K $.$

i$)(0$ pis$)$ A current density of $\frac{?}{\text{b}\text{a}\text{r}}(z0)Ac{m}^2$ should flow when $V=5V$ is applied across the resistor. Calculate the length L $,$ area A and conductivity $$ of the resistor when intrinsic Si is used. The clectron and hole mobilities are $1400$ and $400c\frac{m^2}{V-sec},$ respectively. Answer:

$($i$)(12$ pts$)$ The same resistor $(R=10k)$ will be realized using n $-$type material with only donor doping. Length and area of the resistor are specified as $L=5{10}^{-2}cm$ and $A=2\mathrm{.}08{10}^{-4}c{m}^2,$ respectively. The jonized donor concentration $N_D^{+}$in the bar is given by the following expression. The energy band diagram is shown on the right.

$N_D^{+}=\frac{N_D}{1+2e^{\frac{E_F-E_D}{\frac{?}{?}}R}}$

Calculate the doping density $N_D$ to satisfy the requirements. You can ignore the effect of holes in conductivity calculations:

Answer:

$10k2$