GATE 2017 EC (EC2) – Question 46
A MOS capacitor is fabricated on p-type Si. The metal work function is 4.1 eV, the electron affinity of Si is 4.0 eV, and $E_C-E_F=0.9$ eV. The oxide has $\epsilon_r=3.9$, $\epsilon_0=8.85\times10^{-14}$ F/cm and thickness $t_{ox}=0.1\ \mu$m. Electronic charge is $q=1.6\times10^{-19}$ C. If the measured flat-band voltage is −1 V, the magnitude of fixed charge at the oxide–semiconductor interface (in nC/cm²) is ________.
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Correct answer: 6.85 to 6.95
Explanation
The semiconductor work function is $\phi_s=4.0+0.9=4.9$ eV. Hence the metal–semiconductor work-function difference, expressed as a voltage, is $\phi_{ms}=4.1-4.9=-0.8$ V.
Convert oxide thickness to $10^{-5}$ cm. Capacitance per unit area is $C_{ox}=3.9(8.85\times10^{-14})/10^{-5}=3.4515\times10^{-8}$ F/cm².
The flat-band relation is $V_{FB}=\phi_{ms}-Q_f/C_{ox}$. Therefore $Q_f=C_{ox}[-0.8-(-1)]=6.903\times10^{-9}$ C/cm². Its requested magnitude is **6.903 nC/cm²**.