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GATE 2020 EC – Question 42

Electronic Devices · P-N Junction and Semiconductor Devices · 2 marks · Multiple choice

The band diagram of a $p$-type semiconductor with a band-gap of 1 eV is shown. Using this semiconductor, a MOS capacitor having $V_{TH}$ of $-0.16$ V, $C'_{ox}$ of 100 nF/cm$^2$ and a metal work function of 3.87 eV is fabricated. There is no charge within the oxide. If the voltage across the capacitor is $V_{TH}$, the magnitude of depletion charge per unit area (in C/cm$^2$) is

Diagram for GATE 2020 EC question 42
  1. $1.70\times10^{-8}$
  2. $0.52\times10^{-8}$
  3. $1.41\times10^{-8}$
  4. $0.93\times10^{-8}$

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Correct answer: (A) $1.70\times10^{-8}$

Explanation

The vacuum level is 4 eV above $E_C$, and the Fermi level is 0.2 eV above $E_V$ (0.8 eV below $E_C$), so the semiconductor work function is $4+0.8=4.8$ eV. Then $\phi_{ms}=3.87-4.8=-0.93$ V. The Fermi potential is $\phi_F=E_i-E_{Fs}=0.5-0.2=0.3$ V, so $2\phi_F=0.6$ V. From $V_T=\phi_{ms}+2\phi_F+\frac{|Q_d|}{C_{ox}}$: $|Q_d|=100\text{ nF/cm}^2\times(-0.16+0.93-0.6)=1.70\times10^{-8}$ C/cm$^2$.