For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity (∂VT/∂|VBS|) is found to be 50 mV/V at a substance voltage |VBS| = 2 V, where VT is the threshold voltage of the MOSFET. Assume that, |VBS| >> 2ϕB, where qϕB is the separation between the Fermi energy level EF and the intrinsic level Ei 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 (εSi) = 12
Relative permittivity of oxide (εox) = 4
The doping concentration of the substrate is
1
7.37 × 1015 cm-3
2
9.37 × 1015 cm-3
3
2.37 × 1015 cm-3
4
4.37 × 1015 cm-3