AlN and Al oxy-nitride dielectric layers are proposed instead of Al$2$O$3$ as a component of the gate dielectric stacks on higher mobility channels in metal oxide field effect transistors to improve their positive bias stress instability reliability. It is calculated that the gap states of nitrogen vacancies in AlN lie further away in energy from the semiconductor band gap than those of oxygen vacancies in Al$2$O$3$, and thus AlN might be less susceptible to charge trapping and have a better reliability performance. The unfavourable defect energy level distribution in amorphous Al$2$O$3$ is attributed to its larger coordination disorder compared to the more symmetrically bonded AlN. Al oxy-nitride is also predicted to have less tendency for charge trapping.