The effective attenuation length (EAL) is a useful parameter in quantitative applications of x-ray photoelectron spectroscopy (XPS). This parameter is used in place of the inelastic mean free path (IMFP) in expressions for different XPS applications to correct those expressions for elastic scattering of the photoelectrons. We consider expressions used to determine (i) the thickness of an overlayer film on a planar substrate, (ii) the surface composition, (iii) the depth of a thin marker or delta layer, and (iv) the shell thickness of a core–shell nanoparticle. An EAL can be used for each of these applications. In general, the EAL depends on the particular defining equation as well as on the XPS configuration. Many attempts were made in the 1970s and 1980s to measure EALs for the determination of overlayer-film thicknesses, but there were often wide scatters in the reported results due to the difficulty in preparing uniform films with known thicknesses. We have therefore been motivated to calculate EALs for each application. The SRD 82 database from the National Institute of Standards and Technology (NIST) provides EALs for the measurement of overlayer-film thicknesses and of marker-layer depths. These EALs can be determined for photoelectron energies between 50 eV and 2 keV and for user-specified XPS configurations. We review EAL predictive equations for the determination of overlayer-film thicknesses on a planar substrate for XPS with unpolarized x rays and with linearly polarized x rays as well as an EAL predictive equation for quantitative analysis by XPS. These equations are simple analytical expressions that are valid for well-defined ranges of experimental conditions and for useful ranges of electron energies. We also point out that EALs for the determination of overlayer-film thicknesses can be derived from the simulated photoelectron intensities obtained from the NIST Database for the Simulation of Electron Spectra for Surface Analysis (SRD 100). Where possible, we make comparisons of the calculated EALs with illustrative experimental results. A key parameter in the EAL predictive equations is the so-called albedo, a useful measure of the strength of elastic-scattering effects in a material. The albedo is a simple function of the IMFP and the transport mean free path (TRMFP). We provide a tabulation of albedo and TRMFP values in the supplementary material for 41 elemental solids and 42 inorganic compounds for photoelectron energies between 50 eV and 30 keV. For other materials, albedo values can be determined from IMFP and TRMFP data available in the NIST SRD 82 and SRD 100 databases.

中文翻译：

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X 射线光电子能谱不同定量应用的有效衰减长度

有效衰减长度 (EAL) 是 X 射线光电子能谱 (XPS) 定量应用中的一个有用参数。该参数用于代替不同 XPS 应用表达式中的非弹性平均自由程 (IMFP)，以校正光电子弹性散射的那些表达式。我们考虑用于确定 (i) 平面基材上覆膜厚度、(ii) 表面成分、(iii) 薄标记或 delta 层的深度以及 (iv) 核壳厚度的表达式-壳纳米颗粒。EAL 可用于这些应用程序中的每一个。通常，EAL 取决于特定的定义方程以及 XPS 配置。在 1970 年代和 1980 年代进行了许多尝试来测量 EAL，以确定覆盖层膜的厚度，但由于难以制备已知厚度的均匀薄膜，报告的结果往往存在很大差异。因此，我们有动力为每个应用程序计算 EAL。来自美国国家标准与技术研究院 (NIST) 的 SRD 82 数据库提供了用于测量覆盖层薄膜厚度和标记层深度的 EAL。这些 EAL 可以针对 50 eV 和 2 keV 之间的光电子能量以及用户指定的 XPS 配置确定。我们回顾了 EAL 预测方程，用于确定平面基板上的 XPS 与非偏振 x 射线和线性偏振 x 射线以及用于通过 XPS 进行定量分析的 EAL 预测方程。这些方程是简单的解析表达式，适用于明确定义的实验条件范围和有用的电子能量范围。我们还指出，用于确定覆盖层膜厚度的 EAL 可以从 NIST 表面分析电子光谱模拟数据库 (SRD 100) 获得的模拟光电子强度中推导出来。在可能的情况下，我们将计算出的 EAL 与说明性实验结果进行比较。EAL 预测方程中的一个关键参数是所谓的反照率，这是材料中弹性散射效应强度的有用度量。反照率是 IMFP 和传输平均自由程 (TRMFP) 的简单函数。我们提供了补充材料中 41 种元素固体和 42 种无机化合物的反照率和 TRMFP 值的表格，用于光电子能量在 50 eV 和 30 keV 之间。对于其他材料，可以从 NIST SRD 82 和 SRD 100 数据库中提供的 IMFP 和 TRMFP 数据确定反照率值。