GATE ECE 2021 | Question: 30

Question

For an $n$-channel silicon $\text{MOSFET}$ with $10\:nm$ gate oxide thickness, the substrate sensitivity $\left ( \partial V_{T}/\partial \left | V_{BS} \right | \right )$ is found to be $50\:mV/V$ at a substrate voltage $\left | V_{BS} \right |=2V$, where $V_{T}$ is the threshold voltage of the $\text{MOSFET}$. Assume that, $\left | V_{BS} \right | \gg 2\Phi _{B}$, where $q\Phi _{B}$ is the separation between the Fermi energy level $E_{F}$ and the intrinsic level $E_{i}$ in the bulk. Parameters given are

• Electron charge $(q)$ = $1.6 \times 101^{-19}\:C$
• Vacuum permittivity ($\varepsilon _{0}$) = $8.85 \times 10^{-12}\: F/m$
• Relative permittivity of silicon ($\varepsilon _{Si}$) = $12$
• Relative permittivity of oxide ($\varepsilon _{ox}$) = $4$

The doping concentration of the substrate is

• A. $7.37\times 10^{15}\:cm^{-3}$
• B. $4.37\times 10^{15}\:cm^{-3}$
• C. $2.37\times 10^{15}\:cm^{-3}$
• D. $9.37\times 10^{15}\:cm^{-3}$