Question

A MOS capacitor is fabricated on p-type Si (Silicon) where the metal work function is $4.1eV$ and electron affinity of Si is $4.0eV.$ $E_C-E_F=0.9eV$ , where $E_C$ and $E_F$ are the conduction band minimum and the Fermi energy levels of Si respectively. Oxide ${\epsilon }_r=3.9,{\epsilon }_o=8.85\times {10}^{-14}F/cm$ ,oxide thickness $t_{ox}=0.1\mu m$ and electronic charge $q=1.6\times {10}^{-19}$ C. If the measured flat band voltage of this capacitor is$-1V$ then the magnitude of the fixed charge at the oxide- semiconductor interface, in $nC/c{m}^2$ is

• A. 6.903

Answer 1

The correct option is A 6.903

$e{\varphi }_m=4.1eV$, electron affinity = 4~ eV\)
$E_C-E_{F_P}=0.9eV$
$e{\varphi }_s=electronaffinity+0.9=4.9eV$
$e{\varphi }_m=4.1V,{\varphi }_s=4.9V$
$e{\varphi }_{ms}=e{\varphi }_m-e{\varphi }_s=4.1-4.9=-0.8V$
$C_{ox}=\frac{{ϵ}_{ox}}{t_{ox}}=\frac{3.9\times 8.85\times {10}^{-14}}{0.1\times {10}^{-4}}$
$=34.515\times {10}^{-9}F/c{m}^2$
$V_{FB}={\varphi }_{ms}-\frac{{\varphi }_{ox}^{\prime }}{C_{ox}}$
$\frac{{\varphi }_{ox}^{\prime }}{C_{ox}}=-0.8+1=0.2V$

$=0.2\times 34.515\times {10}^{-9}C/c{m}^2$
$=6.903nC/c{m}^2$