A method is provided for depositing a gate dielectric that includes at least two rare earth metal elements in the form of an oxynitride or an aluminum oxynitride. The method includes disposing a substrate in a process chamber and exposing the substrate to a gas pulse containing a first rare earth precursor and to a gas pulse containing a second rare earth precursor. The substrate may also optionally be exposed to a gas pulse containing an aluminum precursor. Sequentially after each precursor gas pulse, the substrate is exposed to a gas pulse of an oxygen-containing gas, nitrogen-containing gas or an oxygen- and nitrogen-containing gas. In alternative embodiments, the first and second rare earth precursors may be pulsed together, and either or both may be pulsed together with the aluminum precursor. The first and second rare earth precursors comprise a different rare earth metal element. The sequential exposing steps may be repeated to deposit a mixed rare earth oxynitride or aluminum oxynitride layer with a desired thickness. Purge or evacuation steps may also be performed after each gas pulse.