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

The hole mobility reduction 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 at the HfO2/SiO2 interface assumed in the simulations is consistent to the measured flat-band voltage shift of about 300 mV which is observed after introducing 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. Comparing simulated and measured effective mobilities it is shown that in p-MOSFETs the mobility degradation caused by the HfO2 layer cannot be totally explained by remote dipole scattering and a dipole density which is consistent to the flat-band voltage shift. To the authors best knowledge the effect of 2D screening on Coulomb scattering and hole mobility including the influence of dipole layer position and charge separation as well as temperature dependence has not been considered before for p-MOSFETs on this detailed physical level in a semiclassical transport model.