Article
Surface Analysis Spotlight Part 2: The StrataPHI Approach to Reconstructing the Depth Distribution of Multi-Layered Thin Films Non-Destructively
Surface Analysis Spotlight Series: Angle-Resolved X-Ray Photoelectron Spectroscopy
by Norb Biderman XPS Scientist |
As mentioned in the first part of the PHI Angle-Resolved X-Ray Photoelectron Spectroscopy (ARXPS) Surface Analysis Spotlight Series, extracting a non-destructive depth profile of a multi-layered thin film is challenging, even with the full knowledge of all instrumental and materials parameters such as the photoelectron ionization cross-section and inelastic mean free path (IMFP). We now discuss in detail two parts to this problem, and the solution offered by StrataPHI.
Photoelectron intensity I expected from a species of interest at depth z is proportional to its concentration at that depth c(z) and the photoelectron escape probability P_{obs} which is represented by the exponential term containing IMFP λ and take-off angle θ:
To estimate the total spectral peak intensity from all depths of a layer under the surface as observed with the detector in a XPS instrument, Equation (2) is integrated:
where t is the layer thickness. Note that important parameters like the photoelectron ionization cross-section and analyzer transmission are ignored in this simplified version of Equation (3).
The equation shows the first part of the problem determining the depth distributions of chemical species from standard XPS spectra collected at a single take-off angle (without yet considering ARXPS): the integral over the layer thickness t reduces the c(z) distribution to a single number. Information on the variation of the species concentration with respect to depth is lost.
Collecting XPS spectra at various take-off angles in ARXPS is the first step in attempting to recover such lost information. As introduced in the first part of the Surface Analysis Spotlight Series, the detected spectral peak intensity varies with take-off angle. The set of ARXPS measurements can then be expressed in the form of a matrix equation:
where b is the peak intensities at various take-off angles, A is a matrix of attenuation functions P_{obs}(z,θ), and x is the species concentration with respect to depth.
The second part of the problem with extracting depth profiles from ARXPS becomes evident here. The analyst may be tempted to simply invert the matrix equation to obtain species concentration as a function of depth below the surface, x = A^{-1}b. However, as commonly encountered in physics and chemistry problems described by similar matrix equations, ARXPS is ill-posed, meaning the result of the inversion calculation is highly sensitive to small changes to inputs in the b matrix. Such a small change manifests in ARXPS as spectral noise, even in high-quality spectra with barely perceptible noise as depicted in Figure 3, showing Si 2p spectra from an ARXPS experiment of a 7.6 nm SiO_{2} overlayer on a silicon substrate. Consequently, the variation in spectral noise in repeated measurements of the same sample may give wildly different results using the matrix inversion method. |
Figure 3. ARXPS measurement on a SiO_{2}/Si sample illustrating the Si 2p signal as a function of take-off angle as well as the associated spectral noise; extracted from the same data as Figure 2. |
Instead of attempting to invert the matrix to calculate the unknown input values in an ARXPS experiment (i.e. x discussed above), the "forward calculation" approach in StrataPHI uses the prior knowledge of the layered sample to predict spectral peak intensities as a function of take-off angle (Figure 4). The analyst proposes a model, specifying the composition and thickness of each layer in the sample. StrataPHI then simulates photoelectron emission and transport processes as well as effects of the instrumental factors on the intensities. In the last step, the peak intensities calculated from the model are compared with the measured values, and the model is automatically adjusted iteratively until the best match between calculated and measured intensities is obtained. In this fashion, ARXPS and StrataPHI reconstruct the depth profile of a multi-layered thin film non-destructively.
Figure 4. StrataPHI’s “forward calculation” approach in non-destructively reconstructing the depth profile of a multi-layered thin film structure via ARXPS.
StrataPHI relies on two key assumptions in its calculations: each layer under the sample surface 1) is compositionally homogeneous (material density, etc.) and 2) has a uniform thickness throughout the area sampled by the X-ray beam in XPS. StrataPHI reports the results in terms of film thicknesses as illustrated by the 2.3 nm HfO_{2}/1.1 nm SiO_{2}/Si substrate example in Figure 5.
Figure 5. Representative StrataPHI reconstruction result output from ARXPS data of a HfO_{2}/SiO_{2}/Si sample collected from multiple take-off angles. “HC” (hydrocarbon) represents the adventitious (adv) contamination on the sample surface typically observed in an XPS experiment.
In the next part of the PHI Angle-Resolved X-Ray Photoelectron Spectroscopy (ARXPS) Surface Analysis Spotlight Series, we will discuss typical film thicknesses that StrataPHI can calculate from XPS and hard X-ray photoelectron spectroscopy (HAXPES) data as well as strategies to collect the best ARXPS data efficiently.
To learn more about non-destructive depth-profiling of multi-layered thin films as well as fractional coverage analysis with StrataPHI, attend Dr. Norb Biderman’s AVS 69 International Symposium talk: “Fractional Coverage Analysis of Monolayers with XPS and Non-Destructive Depth-Profiling with Combined Soft and Hard X-Rays” on Wednesday, November 8^{th} at 5:00 PM.