Supplementary material: Comment on Infrared dielectric function of GaAs1-xPx semiconductor alloys near the reststrahlen bands [Appl. Phys. Lett. 123, 172102 (2023)]

In the main text, we outline an updated version of the PM for GaAs(1-x)P(x) that explains, beyond existing CM and PM approaches, its phonon mode behavior, as apparent in the novel IR-ellipsometry Im{εr (ω,x)} data of Zollner et al. (Fig. S1, symbols). Sec. I reports on the main features of the cluster model (CM) and of the percolation model (PM). A common terminology is introduced to facilitate the discussion. Both the TO-frequency and the TO-intensity aspects are covered. In Sec. II, an updated version of the PM for GaAs(1-x)P(x) is presented (Fig. S2), supported by existing (Fig. S3) and novel (Fig. S4) ab initio phonon calculations at minimum (x~0,1 - TO-frequency aspect) and maximum (x~0.5 - TO-intensity aspect) alloy disorder. This updated PM scheme for GaAs(1-x)P(x) is directly confronted with Zollner's Im{εr (ω,x)} experimental data (Fig. S1, curves). An overview of the so far tested CM and PM approaches on GaAs(1-x)P(x), including the current PM one, helps to evaluate their relative bias and merits. The overview focuses on the sensitive Ga-P phonon signal at the critical GaAs0.725P0.275 composition (Fig. S5), used as a case study. Last, for the sake of completeness, we show how the latter signal is impacted within the PM by deviating from the ideal random As↔P substitution (Fig. S6).

在正文中，我们阐述了针对GaAs(1-x)P(x)的更新版渗流模型（Percolation Model, PM），该模型在现有团簇模型（Cluster Model, CM）与渗流模型方法的基础上，可解释Zollner等人的新型红外椭偏测量（IR-ellipsometry）数据Im{εᵣ(ω,x)}中呈现的声子模式行为，该数据对应图S1中的符号点。第I节介绍了团簇模型与渗流模型的核心特征，并引入统一术语体系以方便后续讨论，同时覆盖横向光学（Transverse Optical, TO）频率与横向光学强度两个维度。第II节给出了针对GaAs(1-x)P(x)的更新版渗流模型（对应图S2），该模型得到了最低合金无序条件（x≈0，对应横向光学频率维度）与最高合金无序条件（x≈0.5，对应横向光学强度维度）下的已有从头算声子计算（ab initio phonon calculations，对应图S3）与新型从头算声子计算（对应图S4）的支撑。上述针对GaAs(1-x)P(x)的更新版渗流模型方案，直接与Zollner等人的Im{εᵣ(ω,x)}实验数据（对应图S1中的曲线）开展比对验证。对目前已在GaAs(1-x)P(x)体系中测试过的团簇模型与渗流模型方法（包括当前的更新版渗流模型）进行综述，有助于评估各类方法的相对偏差与优劣。该综述聚焦于临界组分GaAs₀.₇₂₅P₀.₂₇₅处的灵敏Ga-P声子信号（对应图S5），并将其作为案例研究展开分析。最后，为保证内容完整性，我们展示了当偏离理想的随机As↔P取代时，上述声子信号在渗流模型框架下会受到何种影响（对应图S6）。