For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity \( \left( \frac{\partial V_T}{\partial |V_{BS}|} \right) \) is found to be 50 mV/V at a substrate voltage
\[
|V_{BS}| = 2 \, \text{V}, \text{ where } V_T \text{ is the threshold voltage of the MOSFET. Assume that } |V_{BS}| \gg 2 \Phi_B, \text{ where } q \Phi_B \text{ is the separation between the Fermi energy level } E_F \text{ and the intrinsic level } E_i \text{ in the bulk. Parameters given are:}
\]
\[
\text{Electron charge } (q) = 1.6 \times 10^{-19} \, \text{C}, \quad \text{Vacuum permittivity } (\varepsilon_0) = 8.85 \times 10^{-12} \, \text{F/m},
\]
\[
\text{Relative permittivity of silicon } (\varepsilon_{si}) = 12, \quad \text{Relative permittivity of oxide } (\varepsilon_{ox}) = 4.
\]
\text{The doping concentration of the substrate is:}