Large piezoelectric response of quarternary wurtzite nitride alloys and its physical origin from first principles

The potential of quarternary wurtzite TMx/2Mx/2Al1-xN (TM = Ti, Zr, Hf; M = Mg, Ca, Zn) alloys for piezoelectric applications is investigated using first-principles calculations. All considered alloys show increased piezoelectric response compared to pure AlN, and competing with the best ternary system proven to date: ScAlN. (Zr, Hf)(x/2)(Mg, Ca)(x/2)Al1-xN alloys are particularly promising. Calculations reveal positive mixing enthalpies indicative for phase separating systems; their values are smaller compared to related nitride alloys, which still can be grown as metastable thin films. The wurtzite phase of the alloys is lowest in energy at least up to x = 0.5 and for Tix/2Znx/2Al1-xN in the full composition range. Moreover, calculations reveal that wurtzite TM0.5Zn0.5N (TM = Ti, Zr, Hf) are piezoelectric alloys with d(33,f) = 19.95, 29.89, and 24.65 pC/N respectively, up to six times that of AlN. Finally, we discuss the physical origin behind the increased piezoelectric response and show that the energy difference between tetrahedrally coordinated zinc-blende (B3) and the layered hexagonal (B-k) phases of the TM0.5M0.5N alloy can be used as a descriptor in a high-throughput search for complex wurtzite alloys with high piezoelectric response.