GATE EC 2016 Set 2 Q35 — Electronic Devices

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 $V_{G}=1.8$ $V$?