On the modeling of Coulomb scattering in p-MOSFETs with hafnium based metal gate stacks

The hole mobility degradation due to remote dipole scattering in p-MOSFETs with TiN/HfO₂/SiO₂ gate stacks is studied based on the self-consistent solution of 6×6 k · p Schrödinger equation, multi-subband Boltzmann transport equations and Poisson equation using a deterministic (non Monte Carlo) solver. The dipole density assumed at the HfO₂/SiO₂ interface is consistent to the measured flat-band voltage shift of about 0.3 V observed after introduction of the HfO2 layer. Static screening by the 2D dielectric function is considered and the polarization factor is calculated based on the full 6×6 k · p band structure. To the authors best knowledge 2D screening for Coulomb scattering has not been considered before for p-MOSFETs on this detailed physical level in a semiclassical transport model.