AI 中文总结
研究GaN(0001)表面重构稳定性，将搜索转化为离散平铺问题，通过列举所有构型及平铺分解多重性预测稳定性，减少候选集，确定局部机制，提供覆盖保证和稳定结构预测途径。
AI 中文摘要
传统上，通过密度泛函理论（DFT）能量引导启发式或贝叶斯搜索来寻找半导体表面的稳定吸附原子构型，但构型空间过大难以覆盖。本文表明，对于电子计数（EC）规则下的GaN(0001)-(6×6)表面，可将搜索转化为离散平铺问题并彻底解决。列举表面晶格的所有菱形平铺以及基于它们的所有EC兼容吸附原子排列，得到固定化学计量比（3个Ga吸附原子和18个H原子）下416,683种构型的完整目录，按对称性分为14个Ga放置类。与给定构型兼容的平铺数量，即其平铺分解多重性$n_{til}$，可预测稳定性。在每个类中，使$n_{til}$最大化的构型最稳定。该规则在14个类中的13个严格成立；在其余类中，最小值本身就在最高多重性构型之中，$n_{til}$最大的构型仅比其高8.5 meV；这种排序由独立的DFT计算重现，在生长温度下差异可忽略不计。稳定性筛选使用针对710个DFT计算结构验证的机器学习原子间势。该规则将第一性原理评估的候选集从416,683个减少到24个构型，所有这些都已用DFT评估。对该规则的分析确定了局部机制，即避免相邻的裸表面位点，而存在兼容平铺仍是一个单独的要求，且有自身的能量成本。因此，列举提供了采样无法提供的东西：覆盖保证，以及一种稳定结构预测途径，其中第一性原理输入仅在最终排序步骤进入。
英文摘要
The stable adatom configurations of a semiconductor surface have traditionally been sought by sampling: density functional theory (DFT) energies steer a heuristic or Bayesian search through a configuration space far too large to cover. Here we show that, for the GaN(0001)-$(6\times6)$ surface under the electron counting (EC) rule, the search can instead be posed as a discrete tiling problem and solved exhaustively. Enumerating all rhombus tilings of the surface lattice, together with all EC-compatible adatom arrangements built on them, yields the complete catalog of 416,683 configurations at fixed stoichiometry (3 Ga adatoms and 18 H atoms), organized by symmetry into 14 Ga placement classes. The number of tilings compatible with a given configuration, its tiling decomposition multiplicity $n_\mathrm{til}$, predicts stability. Within each class, the configuration maximizing $n_\mathrm{til}$ is the most stable. The rule holds strictly in 13 of the 14 classes; in the remaining class the minimum is itself among the highest-multiplicity configurations, with the $n_\mathrm{til}$-max configuration only 8.5 meV above it; this ordering is reproduced by independent DFT calculations, and the difference is negligible at growth temperature. Stability screening uses a machine-learning interatomic potential validated against 710 DFT-computed structures. The rule reduces the candidate set for first-principles evaluation from 416,683 to 24 configurations, all of which have been evaluated with DFT. Analysis of the rule identifies the local mechanism, the avoidance of adjacent bare surface sites, while the existence of a compatible tiling remains a separate requirement with an energy cost of its own. Enumeration thus provides what sampling cannot: a coverage guarantee, and a route to stable-structure prediction in which first-principles input enters only at the final ranking step.
Comments16 pages, 11 figures, 3 tables
