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.