Developing a valence force field model for wurtzite semiconductors by exploiting similarities with [111]-oriented zinc blende systems: The case of wurtzite boron nitride, III-N materials and (B,In,Ga)N alloys

Controlling the crystal phase and lattice mismatch of semiconductors offers a powerful route to engineer electronic and optical properties of heterostructures. As a consequence, semiconductors in the wurtzite phase are increasingly sought after, superseding the thermodynamically favored cubic zinc blende phase. Empirical atomistic modeling, required for large scale simulations of heterostructures and their properties, relies heavily on valence force field (VFF) methods to find the equilibrium atomic positions in an alloy. For zinc blende crystals, VFF models are well-established. In the case of wurtzite, such parameters are frequently adopted without rigorous analysis, despite subtle but consequential differences from the zinc blende structure. Such an approach can compromise accuracy in describing material properties, since the structural differences between zinc blende and wurtzite directly influence electronic and optical characteristics. Based on the analytical VFF model by Tanner et al., and using structural similarities between wurtzite and [111]-oriented zinc blende, we construct a wurtzite VFF without introducing additional parameters. Our framework relies on analytic expressions and minimization routines to project zinc blende models onto wurtzite systems. Beyond elastic tensors, we train the model to reproduce bond length asymmetries and band gaps by using output of the VFF model in density functional theory calculations. Applied to wurtzite III-N compounds and BN, the model accurately reproduces targeted observables but also properties it has not been trained on, including the internal parameter u. We further validate the model on highly mismatched alloys such as (B,Ga)N and (B,In,Ga)N, exhibiting good agreement between VFF and density functional theory results when using identical supercells in these calculations.