Analytical formalism for calculations of parameters needed for quantitative analysis by X-ray photoelectron spectroscopy

Quantitative analysis by X-ray photoelectron spectroscopy (XPS) requires knowledge of a theoretical model relating different features of recorded spectra with needed characteristics of a studied sample. An advanced theoretical approach describing an electron transport in condensed matter typically involved Monte Carlo (MC) simulations of electron trajectories since signal electrons undergo multiple interactions in a solid. The relevant algorithms are relatively slow and are burdened with statistical errors; thus they may be inconvenient in certain applications. However, much effort in the past was devoted to create models that describe electron transport by an analytical formalism with similar accuracy as Monte Carlo simulations. There are two major advantages of analytical approaches: (i) the computing time can be much shorter as compared with MC algorithms, and (ii) the relevant software can be easily included in external programs when large number of calculated parameters is needed. In the present work, the analytical formalism derived within the so-called transport approximation (TA) is described in detail, and implemented in the enclosed software TRANS_APPROX (Fortran 90). The formalism of quantitative XPS is based on an expression that provides a probability that a photoelectron emitted at a given depth reaches an analyzer without energy loss (emission depth distribution function – EMDDF). Consequently, the analytical expression for the EMDDF derived from the TA is discussed here. Stress is also put on parameters descending from the EMDDF: (i) the photoelectron signal intensity, (ii) the information depth, (iii) the mean escape depth, and (iv) the attenuation length for overlayer thickness measurements. The input parameters needed for calculations are briefly overviewed, followed by recommendations for use in the proposed program. Finally, it is indicated that the TA formalism requires calculations of numerous integrals with integrable singularities. It was proven here that these singularities do not need to be removed if the quadrature used is based on the so-called double exponential (DE) rule. This approach ensures high accuracy and fast convergence.

X射线光电子能谱（X-ray photoelectron spectroscopy, XPS）定量分析需构建理论模型，以将采集谱图的不同特征与待测样品的目标特性相关联。用于描述凝聚态物质中电子输运的先进理论方法，通常需借助蒙特卡洛（Monte Carlo, MC）模拟电子轨迹——这是因为信号电子在固体内部会经历多次相互作用。此类相关算法普遍运算速度较慢，且受统计误差困扰，因此在部分应用场景中并不便捷。不过，过往已有大量研究致力于构建基于解析形式论的电子输运模型，其精度可与蒙特卡洛模拟相媲美。解析形式论方法具备两大核心优势：（i）相较于蒙特卡洛算法，其计算耗时可大幅缩短；（ii）当需处理大量计算参数时，相关软件可便捷地集成至外部程序中。本研究详细阐述了基于输运近似（transport approximation, TA）的解析形式论，并将其实现于随附的TRANS_APPROX软件（Fortran 90编写）中。X射线光电子能谱定量分析的形式论基于一项表达式，该表达式可给出在特定深度逸出的光电子在无能量损耗的情况下抵达分析仪的概率，即逸出深度分布函数（emission depth distribution function, EMDDF）。因此，本文将讨论基于输运近似推导得到的逸出深度分布函数解析表达式，并着重阐述由该函数衍生出的四类参数：（i）光电子信号强度；（ii）信息深度；（iii）平均逸出深度；（iv）用于覆层厚度测量的衰减长度。本文简要概述了计算所需的输入参数，并给出了该程序的使用建议。最后，本文指出输运近似形式论需处理大量含可积奇点的积分计算。本文证实，若采用基于双指数（double exponential, DE）规则的求积方法，则无需对这些奇点进行移除处理。该方法可兼顾高精度与快速收敛性。

搜集汇总

背景与挑战

背景概述

该数据集提供了一个基于传输近似（TA）的解析形式主义，用于计算X射线光电子能谱（XPS）定量分析所需的关键参数，如发射深度分布函数（EMDDF）、光电子信号强度和信息深度等。它包含一个Fortran 90软件TRANS_APPROX，相比蒙特卡罗模拟，具有计算速度快、易于集成到外部程序的优点，适用于凝聚态物理和计算物理领域的研究。