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A voltage $V_{G}$ is applied across a $MOS$ capacitor with metal gate and $p$-type silicon substrate at $T=300$ $K$. The inversion carrier density (in number of carriers per unit area) for $V_{G}= 0.8$ $V$ is $2\times 10^{11} cm^{-2}.$ For $V_{G}= 1.3$ $V$, the inversion carrier density is $4\times10^{11} cm^{-2}.$ What is the value of the inversion carrier density for $V_{G}=1.8$ $V$?

  1. $4.5\times 10^{11}cm^{-2}$
  2. $6.0\times 10^{11}cm^{-2}$
  3. $7.2\times 10^{11}cm^{-2}$
  4. $8.4\times 10^{11}cm^{-2}$
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