Complex band structure and the band alignment problem at the Si–high- k dielectric interface

We investigate the use of the complex band structure of high-$k$ gate dielectrics to estimate their charge neutrality levels, and compute band offsets to Si. A comparison is made with the available results obtained with direct electronic structure methods and experiment. It appears that charge neutrality levels thus obtained indeed provide a consistent picture for simple interfaces. However, the uncertainty in the conduction band position inherent in the local density approximation may render the theory inadequate for engineering support. Despite this limitation, linear rescaling of the charge neutrality levels based on the experimental band gaps for six oxides (${\mathrm{SiO}}_{2}$, ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$, $c\text{\ensuremath{-}}{\mathrm{HfO}}_{2}$, $m\text{\ensuremath{-}}{\mathrm{HfO}}_{2}$, ${\mathrm{La}}_{2}{\mathrm{O}}_{3}$, and ${\mathrm{SrTiO}}_{3}$) has shown excellent agreement with experimental data.