GATE 2024 EC – Question 61
A MOS capacitor made with p-type silicon. It has an oxide thickness of 100 nm, a fixed positive oxide charge of $10^{-8}$ C/cm$^2$ at the oxide-silicon interface, and a metal work function of 4.6 eV. Assume that the relative permittivity of the oxide is 4 and the absolute permittivity of free space is $8.85\times10^{-14}$ F/cm. If the flatband voltage is 0 V, the work function of the p-type silicon (in eV, rounded off to two decimal places) is ______.
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Correct answer: 4.30 to 4.34
Explanation
$V_{FB}=\phi_M-\phi_S-\dfrac{Q_{ox}}{C_{ox}}=0$. $C_{ox}=\dfrac{4\times8.85\times10^{-14}}{100\times10^{-7}\text{ cm}}=3.54\times10^{-8}$ F/cm$^2$, so $Q_{ox}/C_{ox}=10^{-8}/3.54\times10^{-8}=0.2825$ V. Therefore $\phi_S=4.6-0.2825=4.32$ eV.