Question

In the three dimensional view of a silicon n channel MOS transistor shown below, $\delta =20nm$. The transistor is of width $1\mu m$. The depletion width formed at every p-n junction is $10nm$. The relative permittivities of Si and $Si{O}_2$, respectively , are $11.7$ and $3.9$ and ${ϵ}_0=8.9\times {10}^{-12}F/m$.

The gate-source overlap capacitance is approximately

Answer 1

Ans : (a)

Gate source capacitance $C_g$ is
$C_g=\frac{{ϵ}_1{A}_1}{d_1}=\frac{{ϵ}_0{ϵ}_{r1}{A}_1}{d_1}$
${ϵ}_{r1}=3.9$ as between gate and source there is $Si{O}_2$
$A_1=1\mu m\times \delta =1\times {10}^{-6}\times 20\times {10}^{-9}$
$=2\times {10}^{-14}{m}^2$
$d_1=1nm={10}^{-9}m$
So, $C_g=\frac{8.9\times {10}^{-12}\times 3.9\times 2\times {10}^{-14}}{{10}^{-9}}$
$C_g=69.42\times {10}^{-17}F$
$C_g=0.69\times {10}^{-15}$
$C_g=0.7fF$