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

TL;DR

The paper develops a valence force field for wurtzite semiconductors by exploiting the close elastic-tensor analogy with [111]-oriented zinc blende systems, extending the analytic Tanner et al. framework to WZ without adding new parameters. The authors present a three-step parameterization workflow that links ZB elastic constants to WZ force constants and bond asymmetry, and validate the model against DFT data for binary III-N materials and boron-containing HMAs such as (B,Ga)N and (B,In,Ga)N. The VFF accurately reproduces elastic constants, bond lengths, internal parameters $u$, and lattice ratios $c_0/a_0$, and, when combined with DFT, also captures band gaps and crystal-field effects with high fidelity. Importantly, the model reliably describes highly mismatched alloys, enabling large-scale structure relaxations and predictive electronic-structure calculations, which is valuable for designing WZ-based heterostructures and BN-containing III-N devices.

Abstract

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.

Figures (5)

• Figure 1: (a) Zinc blende and (b) wurtzite crystal structures, with crystal axis directions in Miller indice notation. (c) Zinc blende and (d) wurtzite nearest neighbor tetrahedrons, respectively. The equilibrium nearest neighbor bond lengths are denoted by $r^{0}_{01}$ (dashed line), $r^0_{02}$, $r^0_{03}$ and $r^0_{04}$ (solid lines) following notation in the main text.
• Figure 2: Schematic illustration of the workflow to establish a valence force field (VFF) model for wurtzite semiconductor materials building on the analytic model by Tanner et al.TaCa2019 for zinc blende materials. More details on the different steps are given in the main text. The last step is introduced specifically for materials where the band gap is a key property for, e.g., device applications.
• Figure 3: Comparison of bond length distributions from density functional theory (DFT) and valence force field model (VFF) for (B,Ga)N alloys, with a histogram bin value of 0.01 Å. Inset: a quantile-quantile plot comparing the distributions, where the solid line indicates perfect agreement between VFF and DFT. For the B$_{3}$Ga$_{51}$N$_{54}$ ($\approx$ 5% BN) we have plotted results from the random alloy configuration labeled as RA II in the main text.
• Figure 4: Comparison of bond length distributions from density functional theory (DFT) and and valence force field (VFF) model for (B,In,Ga)N 108 atom supercells. The histogram bin values are 0.01 Å. Subplot: a quantile-quantile plot comparing the distributions, where the solid line indicates perfect agreement between VFF and DFT.
• Figure 5: Comparison of bond length distributions from density functional theory (DFT) and valence force field model (VFF) for the the additional B$_{3}$Ga$_{51}$N$_{54}$ random alloy configurations (a) RA I and (b) RA III. As in the main text the histogram bin value is 0.01Å. Inset: quantile-quantile plots comparing the distributions, where the solid line indicates perfect agreement between VFF and DFT.