First-principles prediction of structure, energetics, formation enthalpy, elastic constants, polarization, and piezoelectric constants of AlN, GaN, and InN: Comparison of local and gradient-corrected density-functional theory

A number of diverse bulk properties of the zinc-blende and wurtzite III-V nitrides AlN, GaN, and InN, are predicted from first principles within density-functional theory using the plane-wave ultrasoft pseudopotential method, within both the local density approximation (LDA) and generalized gradient approximation (GGA) to the exchange-correlation functional. Besides structure and cohesion, we study formation enthalpies (a key ingredient in predicting defect solubilities and surface stability), spontaneous polarizations and piezoelectric constants (central parameters for nanostructure modeling), and elastic constants. Our study bears out the relative merits of the two density-functional approaches in describing diverse properties of the III-V nitrides (and of the parent species ${\mathrm{N}}_2,$ Al, Ga, and In). None of the two schemes gives entirely successful results. However, the GGA associated with the multiprojector ultrasoft pseudopotential method slightly outperforms the LDA overall as to lattice parameters, cohesive energies, and formation enthalpies of wurtzite nitrides. This is relevant to the study of properties such as polarization, vibrational frequencies, elastic constants, nonstochiometric substitution, and absorption. A major exception is the formation enthalpy of InN, which is underestimated by the GGA (∼0 vs -0.2 eV).