GATE 2022 EC – Question 34
An ideal MOS capacitor ($p$-type semiconductor) is shown in the figure. The MOS capacitor is under strong inversion with $V_G=2$ V. The corresponding inversion charge density ($Q_{IN}$) is $2.2\ \mu\text{C/cm}^2$. Assume oxide capacitance per unit area as $C_{ox}=1.7\ \mu\text{F/cm}^2$. For $V_G=4$ V, the value of $Q_{IN}$ is ________ $\mu\text{C/cm}^2$ (rounded off to one decimal place).

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Correct answer: 5.57 to 5.63
Explanation
In strong inversion the extra gate charge is supplied by the inversion layer, so $\Delta Q_{IN}=C_{ox}\Delta V_G$. Raising $V_G$ from 2 V to 4 V adds $1.7\times2=3.4\ \mu\text{C/cm}^2$, so $Q_{IN}=2.2+3.4=5.6\ \mu\text{C/cm}^2$.