GATE Electronics and Communications (EC) 2021 Solved Paper

For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity (∂V_T/∂|V_BS|) is found to be 50 mV/V at a substance voltage |V_BS| = 2 V, where V_T is the threshold voltage of the MOSFET. Assume that, |V_BS| >> 2ϕ_B, where qϕ_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 × 10^-19 C
Vacuum permittivity (ε₀) = 8.85 × 10^-12 F/m
Relative permittivity of silicon (ε_Si) = 12
Relative permittivity of oxide (ε_ox) = 4
The doping concentration of the substrate is