5. (20%) For a conventional planar n-MOSFET, source/drain regions are heavily doped with a concentration of ND=
and the channel has a doping level of
. The oxide is 1-nm HfO2with a dielectric constant of 32 and the gate is aluminum (work function Φm = 4.1 eV). Trapped charges are inside the oxide and adjacent to the oxide/semiconductor interface with a density of
The gate length is 1 μm. The dielectric constant of Si is 11.7.
F/cm
(d) (5 %) If Si substrate is biased under 10 V. Please calculate the △VT.