以第一原理研究 GaAsBi 的結構特性與不互溶性

Abstract

本研究以密度泛函理論（DFT）為核心，計算 GaAsBi之結構性質與相圖。模擬採用特殊準隨機結構（special quasi-random structures, SQS）以近似隨機合金之局部配位統計，系統性評估不同交換關聯泛函、色散修正與自旋軌道耦合（SOC）對計算結果的影響。 研究中以二元材料GaAs進行基準測試，並在一致的計算框架下比較 PBEsol 與 rSCAN+D4 等方法對晶格常數與彈性性質的再現能力；結果顯示，引入 D4 色散修正可改善 GaAs 端點的結構與彈性常數偏差。隨後，本研究建立不同尺寸之 SQS 超胞（supercell），針對Bi之組成比例進行結構優化並計算總能與能帶結構，得到GaAsBi能隙對Bi含量的下降率約為-69.7meV/%Bi。 而由 0 K 混合焓可擬合取得有效交互作用參數，並推導混合自由能與擬二元相圖。計算結果指出，混合焓在整個成分範圍皆呈正值且於中間成分附近形成單峰，對應到明顯的相分離驅動力；此外，相圖預測對計算設定具有顯著敏感度，其中 rSCAN+D4 相較 PBEsol 會給出更寬的 miscibility gap 與更高的臨界溫度，而較小超胞亦傾向高估不相容性強度與臨界溫度；相較之下，SOC 對臨界行為的改變幅度較小，但仍會使 miscibility gap 與臨界溫度上移。 對比實驗，由於未考慮晶格振動自由能與非諧效應，會系統性高估混合不利的程度，導致臨界溫度T_c變高。此外，實驗觀察到的分解起始溫度常受擴散與缺陷等動力學限制，並不等同於平衡spinodal邊界，因此也會呈現比理論更低的可觀測分解溫度。 綜合而言，本研究計算了GaAsBi晶格常數、彈性係數與能帶結構，探討提高Bi含量之影響，並定量評估 GaAsBi 合金的混溶性與相分離趨勢，凸顯交換關聯泛函選擇與有限超胞尺寸效應在高失配合金物性與相圖建模中的關鍵性，提供後續理論預測與材料設計之方法學依據。

This study employs density functional theory (DFT) to investigate the structural properties and phase diagram of GaAsBi alloys. Special quasi-random structures (SQS) are adopted to approximate the local coordination statistics of random alloys, and the effects of the exchange–correlation functional, dispersion correction, and the treatment of spin–orbit coupling (SOC) on the predicted results are systematically assessed. Benchmark calculations are first performed for the binary compound GaAs within a consistent computational framework to compare the performance of representative approaches, including PBEsol and rSCAN+D4, in reproducing lattice constants and elastic properties. The results indicate that incorporating the D4 dispersion correction improves the structural description of the GaAs endpoint and reduces the deviation in elastic constants. Subsequently, SQS supercells of different sizes are constructed for various Bi compositions, followed by full structural relaxation and calculations of total energies and band structures, yielding a band-gap reduction rate of approximately −69.7 meV/%Bi with increasing Bi content. In addition, effective interaction parameters are extracted by fitting the 0 K mixing enthalpies, from which the mixing free energies and pseudo-binary phase diagrams are derived. The calculated mixing enthalpies remain positive over the entire composition range and exhibit a single maximum near intermediate compositions, indicating a pronounced thermodynamic driving force for phase separation. The phase-diagram predictions show strong sensitivity to computational settings: compared with PBEsol, rSCAN+D4 yields a wider miscibility gap and a higher critical temperature, while smaller supercells tend to overestimate the immiscibility strength and the critical behavior. In contrast, SOC has a relatively modest impact on the critical behavior, yet it still shifts both the miscibility gap and the critical temperature upward. When compared with experiments, the present framework is expected to overestimate the mixing penalty and thus predict a higher critical temperature T_c, primarily because lattice vibrational free energies and anharmonic effects are not included. Moreover, the experimentally observed onset temperature of decomposition is often kinetically limited by atomic diffusion and defects, and therefore does not necessarily coincide with the equilibrium spinodal boundary, leading to a lower observable decomposition temperature than theoretical predictions. Overall, this work computes the lattice constants, elastic constants, and band structures of GaAsBi, clarifies the impact of increasing Bi content on these properties, and quantitatively evaluates its miscibility and phase-separation tendencies. The results further highlight the critical roles of exchange–correlation choices and finite supercell-size effects in property prediction and phase-diagram modeling of highly mismatched alloys, providing a methodological basis for subsequent theoretical studies and materials design.