The effect of Al content on the work function engineering at TiAlN/HfO$_{2}$ interface

In high-k/metal gate stacks of metal-oxide-semiconductor field-effect transistors, it is important to control the metal work function such that it should be close to the valence and conduction band edges of Si in p- and n-channel devices. It was reported that depositing TiAl on top of TiN/HfO$_{2}$ stack in gate-last process can effectively induce the n-type shift of work function, while the work function is of p-type at TiN/HfO$_{2}$ stack. In this work, we perform first-principles density functional calculations to investigate the Schottky barrier height at TiAlN/HfO$_{2}$ interface. In bulk TiN, it is found that a substitutional Al is the most stable form of Al impurity. When substitutional Al atoms are introduced at TiN/HfO$_{2}$ interface, the effective work function tends to decrease. At TiAlN/HfO$_{2}$ interface, the n-type shift of the work function increases almost linearly with the Al content. This is attributed to the change of interface bonds by Al incorporation and the dipole field induced at the interface. On the other hand, relative thicknesses of TiAl and TiN at abrupt TiAl/TiN/HfO$_{2}$ interface do not significantly affect the effective work function.