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Surface Analysis Spotlight Part 1: How Does Angle-Resolved X-Ray Photoelectron Spectroscopy Capture the Depth Distribution of Multi-Layered Thin Films?

Surface Analysis Spotlight Series: Angle-Resolved X-Ray Photoelectron Spectroscopy

by Norb Biderman    XPS Scientist

StrataPHI analysis of angle-resolved X-ray photoelectron spectroscopic (ARXPS) data is a non-destructive method to reconstruct relative depth information for various chemical species in multi-layered thin films by considering the inelastic mean free path (IMFP) of photoelectrons below the sample surface generated by X-ray beam irradiation. As the photoelectrons in the sample travel through the sample toward the surface, they encounter a series of inelastic collisions that result in the loss of photoelectron kinetic energy.

For generated photoelectrons of a given kinetic energy representing a specific chemical species, the likelihood of such inelastic losses increases with depth below the sample surface, thus fewer photoelectrons with the same initial kinetic energy reach the vacuum from greater depths below the sample surface. The photoelectron kinetic energy is related to the IMFP – the distance traveled in the material by a photoelectron on average before it undergoes an inelastic collision with other electrons in the sample.

IMFP is a property of the chemical matrix through which the photoelectron travels, especially in a multi-layered thin film. Thus, to study the thicknesses of individual layers and their location below the sample surface, the XPS scientist can modify the distance that photoelectrons travel through each layer by physically tilting the sample with respect to the analyzer.

For example, tilting the sample to a take-off angle of 90° coincides the sample’s surface normal to the axis of the input lens of the hemispherical analyzer, resulting in the shortest path length possible through the individual layers that photoelectrons travel toward the analyzer as illustrated in Figure 1. Conversely, decreasing the take-off angle increases the path length, making it more difficult for photoelectrons to reach the vacuum due to inelastic collisions. Due to the geometry of the analyzer, the take-off angle in any ARXPS experiment can be varied between 90° and nearly 0° where the lower bound is limited by the significantly decreased photoelectron signal as the sample’s surface normal is tilted away from the analyzer.

Figure 1. Geometry of a sample with a thin overlayer with respect to the hemispherical analyzer. The blue arrow points to the analyzer, and the angle between the arrow and the sample surface plane is the take-off angle θ.  The length d represents the sampling depth of the ARXPS analysis.

It can be imagined that the XPS intensities from a very thin surface layer (e.g. a layer of adventitious hydrocarbon) should not be as sensitive to the change in take-off angle compared to those coming from deeper in the sample (e.g. the Si substrate under a SiO2 layer). The effect is illustrated in Figure 2 which shows experimentally measured XPS peak intensities of a sample consisting of a 7.6 nm-thick SiO2 film on a silicon substrate. The C 1s signal is from a thin (0.13 nm) surface contamination layer, and the Si 2p (Si-Si) signal is from the Si wafer substrate. The C 1s signal changes very little as the take-off angle increases while the Si 2p (Si-Si) signal increases substantially as the photoelectron path length to the surface decreases.

Figure 2. ARXPS measurement on a SiO2/Si sample showing the difference in intensity vs. take-off angle for a surface (C 1s) and a bulk (Si 2p Si-Si) sample chemical species.

Mathematically from Figure 1, the generalized probability P_obs that a photoelectron with IMFP λ generated at depth z below the surface escapes to be observed by the analyzer at take-off angle θ is:

XPS spectra from the multi-layered thin film sample as a function of take-off angle serve as the basis for non-destructive reconstruction of the sample depth profile via StrataPHI data analysis. However, the seemingly simple Equation 1 becomes computationally unwieldly when considering the intensity of photoelectrons from all depths below the sample surface. In the second part of the PHI Angle-Resolved X-Ray Photoelectron Spectroscopy (ARXPS) Surface Analysis Spotlight Series, we will discuss the challenge with extracting a depth profile from Equation 1 even with the full knowledge of all instrumental and materials parameters such as the photoelectron ionization cross-section and inelastic mean free path. We also will present the StrataPHI approach to this technical challenge.