Characterization of Inversion-Layer Capacitance of Electrons in High- $k$/Metal Gate Stacks

The inversion-layer capacitance
C
_inv
of electrons in high-
k
/metal gate stacks (HKMGs) is studied theoretically and experimentally from the viewpoint of the penetration of electrons into the dielectrics. The numerical calculation of
C
_inv
in the dielectric/substrate bilayer structure has clarified the influence of penetration on
C
_inv
.
C
_inv
in an HKMG is evaluated experimentally and is compared with the computational predictions in terms of the dependence on the dielectric boundary and the silicon crystal orientation. The consistency of the experiment and the calculation is the first evidence for the considerable modulation of
C
_inv
due to penetration in the actual HKMG. Moreover, the dependence of
C
_inv
on substrate biasing is investigated. The detailed analysis of
C
_inv
in the system where the confinement of the inversion layer is intentionally changed has led to a further understanding of
C
_inv
determined by penetration.