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Surface Analysis Spotlight Part 3: What Range of Film Thickness Can StrataPHI Calculate from Angle-Resolved XPS and HAXPES Spectra?

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

by Norb Biderman    XPS Scientist

StrataPHI can evaluate multi-layered thin-film samples with a total thickness ranging from a monolayer to tens of nanometers with the Al Kα X-ray source traditionally used in X-ray photoelectron spectroscopy (XPS) as well as the recently developed lab-based Cr Kα X-ray source used in hard X-ray photoelectron spectroscopy (HAXPES).

The maximum film thickness for any given film stack layer that can be calculated from angle-resolved X-ray photoelectron spectroscopy (ARXPS) measurements is limited by the inelastic mean free path (IMFP) of the photoelectrons, a measure of how far an electron on average travels through a material before losing kinetic energy. The IMFP is related to photoelectron kinetic energy and the layer density among other variables. The photoelectron kinetic energy in turn depends on the photon energy of the X-ray source.

In the first part of the current Surface Analysis Spotlight Series, it was introduced that the likelihood of a photoelectron escaping into the vacuum without inelastic losses decreases when it originates deeper below the surface. This probability determines the information depth in an ARXPS experiment. Figure 6 illustrates the escape probability for Si 2p photoelectrons generated in silicon (e.g. silicon wafer substrate) using Al Kα and Cr Kα X-rays. In silicon, an Al Kα Si 2p photoelectron has an IMFP λ of 3.1 nm as predicted by the TPP-2M equation, an approach to estimate inelastic mean free path as a function of several parameters including photoelectron kinetic energy.¹

Figure 6. Inelastic escape probabilities of Si 2p photoelectron generated by Al Kα (blue line) and Cr Kα (red line) X-rays as a function of depth below the surface. The dotted line represents an escape probability of 0.05 (5%).

Using Equation 1 introduced in the first part with a take-off angle of 90°, an Al Kα Si 2p photoelectron generated at the depth equal to 3λ (~ 9.3 nm) has a 5% probability (dotted line in the figure) of escaping into the vacuum which roughly corresponds to 5% of an ensemble of many photoelectrons generated at that depth. Because the X-ray beam generates photoelectrons at various depths, the proportion of generated photoelectrons that escape can be summed from the surface to the depth of 3λ. This summation over 3λ results in the oft-cited XPS information depth where approximately 95% of photoelectrons detected by the analyzer originate within the depth of 3λ below the sample surface.

As stated earlier, photoelectron kinetic energy also depends on the photon energy of the X-ray source. Using Cr Kα X-rays instead of Al Kα X-rays increases the kinetic energy of the photoelectron which in turn increases its escape probability due to the larger IMFP. When Cr Kα X-rays are used to generate Si 2p photoelectrons, the TPP-2M-calculated IMFP in the silicon substrate is 9.3 nm, approximately three times larger than Al Kα Si 2p IMFP of 3.1 nm (Figure 6). The increase in IMFP is explained by the larger photon energy of a Cr Kα X-ray (5414.8 eV) versus an Al Kα X-ray (1486.6 eV), resulting in more of the energy converted into kinetic energy after the Si 2p photoelectron absorbs the minimum energy (binding energy) to be ejected from the silicon atom. Consequently, the larger Si 2p IMFP using Cr Kα X-rays increases the 3λ information depth to 27.9 nm.

While comparing the information depths probed by Al Kα X-rays and Cr Kα X-rays, 5-10 nm and 15-30 nm respectively are typically given due to the dispersion in inelastic mean free paths even while using the same X-ray source type.

In a model system comprising an overlayer on top of a thick substrate, the maximum thickness t of the overlayer while being able to detect photoelectrons from the underlying substrate can be estimated as:

where θ is the take-off angle, λ is the photoelectron inelastic mean free path, and I_m is the minimum acceptable signal remaining from the substrate after attenuation by the overlayer.

We now extend the 3λ information depth criterion discussed above (roughly equivalent to 5% minimum acceptable signal) to a multi-layered thin film consisting of HfO₂ and SiO₂ layers on a Si substrate (Figure 7). We may want to estimate the maximum thickness of the HfO₂/SiO₂ stack for the Si substrate to be detected in XPS at a 75° take-off angle. Assuming a Si 1s photoelectron², accessible by Cr Ka X-rays, is liberated from a silicon atom in the substrate just beneath the SiO₂/Si interface, it has an IMFP of 6.7 nm as it travels through the SiO₂ layer toward the HfO₂ layer and the sample surface. The maximum HfO₂/SiO₂ overlayer thickness as implied by Equation 5 is then approximately 19 nm.

Figure 7.  Angle-resolved XPS (Al Kα) and HAXPES (Cr Kα) spectra of a 8.2 nm HfO₂/8.2 nm SiO₂/Si sample at 30°, 45°, and 75° take-off angles.

The estimate is consistent with the detection of Si 1s photoelectrons from the silicon substrate in an actual sample of 8.2 nm HfO₂ and 8.2 nm SiO₂ layers on a Si substrate where the total overlayer thickness is more than 16 nm. Note that a more accurate estimate of the maximum thickness involves incorporating a modified Si 1s IMFP in the HfO₂ layer in the calculation.

Figure 8. (a) StrataPHI reconstruction result output from the same data collected at multiple take-off angles in Figure 7 (8.2 nm HfO₂/8.2 nm SiO₂/Si). Cr Kα Si 1s transition from tens of nanometers below the surface and Al Kα Hf 4f transition closer to the sample surface are combined for structure estimation (b) Integrated intensities of the hafnium transitions from the respective spectra in Figure 7.

StrataPHI 2.0 includes the ability to combine data collected with Al Kα and Cr Kα X-rays from the same sample in a single StrataPHI analysis (Figure 8(a)). For example, with the multi-layered structure of 8.2 nm HfO₂ /8.2 nm SiO₂ on a Si substrate, the Si 1s transition can be collected with Cr Kα X-rays to probe the deep SiO₂ layer and the Si substrate. Al Kα X-rays can be used to collect Hf 4f signal from the relatively shallow HfO₂ layer due to its more intense photoelectron signal compared with the Hf 3d_5/2 and Hf 4f signals detected using Cr Kα X-rays (Figure 8(b)).

To learn more about non-destructive depth-profiling of multi-layered thin films using Al Kα X-rays and Cr Kα X-rays with StrataPHI 2.0, register for Dr. Norb Biderman’s upcoming webinar titled “StrataPHI 2.0 - Updated Software for Multi-Layered Thin-Film Structure Analysis” on January 9, 2024 at 10:00 A.M. CST.

¹M.P. Seah. “Simple universal curve for the energy-dependent electron attenuation length for all materials.” Surface and Interface Analysis, 2012, 44, 1353-1359.

²Cr Kα X-rays generate a lower photoelectron signal compared to Al Kα X-rays at the same X-ray fluence on the sample for a given photoelectron core line transition in the photoelectron spectrum. The intensity of a core line in the spectrum is proportional to its photoionization cross-section, the probability of photoelectron generation upon X-ray irradiation. As the X-ray photon energy increases, the photoionization cross-section for the same photoelectron line generally decreases significantly. This effect is compensated by accessing deep-level photoelectron core lines of the same element with favorable photoionization cross-sections using Cr Kα X-rays (e.g. Si 2p with Al Kα X-rays vs. Si 1s with Cr Kα X-rays).