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The band diagram of a $p$-type semiconductor with a band-gap of $1$ eV is shown. Using this semiconductor, a $\text{MOS}$ 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


  1. $1.70\times 10^{-8}$
  2. $0.52\times 10^{-8}$
  3. $1.41\times 10^{-8}$
  4. $0.93\times 10^{-8}$
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