Advanced Techniques for Spectral Mapping
By Paul Thomas, Gatan Inc.

The spectrum-imaging technique (or SI) is a powerful and convenient tool for advanced materials characterization. Using one or a combination of spectral signals (e.g. EELS, CL and/or EDS), large multi-dimensional data sets to be captured in a rapid manner. Data capture using spectrum-imaging offers the major advantage over simple point spectroscopy in that the spatial information is acquired in addition to the spectral data. Once acquired, spectral processing and fitting algorithms can be used to extract physical properties not as single values, but as a 2 dimensional distribution maps. Further, subtle information, not apparent from a few images or spectra alone, can often be found. Accordingly, powerful data-analysis and visualization tools are required to enable the optimal extraction and interpretation of results in a fast, convenient and accurate manner.

Gatan’s DigitalMicrograph software provides a wide range of spectral analysis tools, enabling both generic and signal-specific analysis of, for example, EELS, EDS and CL spectral data all within the same data analysis environment. While some of these data analysis methods are used widely (for example, elemental mapping using background removal in EELS), there are some less well known but nonetheless powerful tools for spectral analysis which can yield information not easily accessible by any other means. This article aims to give a brief overview of a selection of these techniques with some practical examples.

Chemical Phase Fingerprinting

The multiple linear least squares (MLLS) fitting routine provides a very useful means for mapping difference spectral phases or features by reference to their spectral signature. Specifically, the MLLS algorithm fits reference spectra as specified by the user to the dataset of interest. Once the MLLS fit is complete, the algorithm returns the fit coefficients corresponding to the optimal linear combination of the specified reference spectra to the input data. In other words, the routine will fit reference spectra to a dataset and tell you exactly how much of each is present. When applied to a spectrum-image, the technique becomes all the more useful since not only how much of each reference is given but also where. Hence if MLLS is applied correctly to a spectrum-image dataset it provides the ability to map the spatial distributions of the input reference spectra.

A simple use for MLLS fitting is in chemical phase mapping using a technique called MLLS fingerprinting. By specifying reference spectra that represent the main phases present, the analysis returns fit-coefficient maps showing the spatial distribution of the reference spectra. These maps, in turn, may be interpreted as chemical phase distribution maps. For spectrum-image analysis this can be especially convenient since often the reference spectra can be extracted from the SI dataset itself.

This is illustrated below for an EDS spectrum-image acquired from a semi-conductor device. By exploring the SI dataset using the spectrum-picker tool, it is apparent that there are only four discrete spectral signatures present within the entire dataset. Once identified, these spectral types can be extracted using the picker tool for use as references for the MLLS routine and analyzed independently (shown center below). Performing MLLS fitting on the SI dataset, specifying the four extracted spectra as the references, yields four co-efficient maps. Providing no other spectral signatures are present other than the reference spectra specified, then the intensity distribution in each co-efficient map is directly proportional to the amount of that phase present. These can be color-indexed and combined to give a single color image showing the distribution of each phase mapped over the analysis region (below right). This is a simple example of MLLS fingerprinting – a more advanced use for the technique is for the mapping of chemical state or even orientation for a single core-loss edge using the electron loss near-edge structure in the EELS spectrum.

Chemical phase mapping using MLLS fingerprinting. The EDS spectrum-image was acquired in STEM mode from an electronic device (left). Spectra extracted from the SI show the four spectral signatures present (center). Performing MLLS fitting yields the distribution maps for each spectral signature (right).

Spectral Peak Characterization

It is often the case that a user wishes to accurately measure some simple properties of a spectral-peak – for example, its full width maximum (FWHM), central dispersion and/ or its amplitude. For a spectrum-image data set, this requirement extends to actually mapping that value to show how it changes with spatial position. A technique called Non-Linear Least Squares Fitting (NLLS) provides a convenient means for doing this. The NLLS routine in DigitalMicrograph facilitates the fitting of single or multiple Gaussian models to spectra over a specified fitting range. Once fitted, the individual fit parameters can be output.

This is illustrated below. On the left is an EELS low-loss spectrum-image acquired in EFTEM mode. Using the spectrum picker tool, a single low-loss spectrum can be extracted from the EFTEM-SI stack. By fitting a Gaussian model to the plasmon peak, an approximate value of the plasmon width and peak energy can be measured (center). By applying these fit parameters to the entire spectrum-image, the plasmon properties can be mapped pixel by pixel over the whole dataset. The color image below is a plasmon energy map measured in this way (below right). Since the various chemical phases present have different plasmon energies, NLLS-mapping provides an approximate but nonetheless convenient way to calculate the spatial distribution of specific phases as a single color-indexed map. Other problems for which the NLLS fitting technique is well suited include mapping changed in the EELS white-line ratio for transition elements, for performing chemical shift measurements and for zero-loss alignment of low-loss EELS spectrum-images.

Plasmon energy mapping using NLLS. The semi-conductor spectrum-image was captured using the EFTEM-SI technique using a GIF Tridiem (left). NLLS fitting of a Gaussian peak to the plasmon peak gives approximate values for the plasmon energy (center). Applying this to the entire SI yields a plasmon energy map, which shows the individual phases clearly in a single image (right).

Separating Overlapping edges using MLLS

MLLS fitting is also a very useful technique in EELS for separating overlapping edges. Overlapping edges present a problem in EELS since it is relatively common to have a core-loss edge that is in close proximity to another. As the conventional approach to EELS edge quantification involves using the pre-edge region to model and subtract the underlying background signal, difficulties can arise where features from a preceding edge renders accurate background extrapolation impractical. Edge separation using MLLS fitting offers a way around this problem. By specifying reference spectra that represent the overlapping signals present in the spectrum, the MLLS routine can then separate the signals to return the relative amount of each component.

This is illustrated in an example below. The dataset (shown below left) was acquired in STEM mode using EELS Spectrum-Imaging with a Tridiem imaging-filter in spectroscopy mode. The problem lies in separating the aluminum K, tungsten M and silicon K edges which are situated at energy losses of 1560eV, 1809eV and 1839eV respectively (below center). Since the signals overlap significantly they cannot be separated for mapping using the conventional background extrapolation technique (particularly the Si and W edges). This common problem can be avoided by using MLLS mapping as follows. Firstly, the EELS background is subtracted over the whole spectrum-image using a fit region just below the lowest energy-loss edge, leaving just the core-loss signals present. Secondly, reference edges corresponding to the overlapping edges must be obtained. The most obvious source for these is the EELS Atlas, which is installed as part of EELS Analysis for DigitalMicrograph. Preferably, if the edges can be found isolated from each other within the dataset itself then these can be used (as in this example). Finally, once reference edges are obtained, the MLLS routine is applied, and the separated signals are output as chemical maps. In this example, the MLLS technique is so versatile that it can also separate the crystalline silicon from the silicon oxide. The resulting color composite map is shown (below right), devoid of any edge overlap artifacts.

Mapping overlapping edges using MLLS fitting. The data was acquired by EELS-SI from an etched semi-conductor device (left). The Al K, Si K and W M edges all overlap, prohibiting conventional background extrapolation (centre). Using MLLS fitting,with reference edges extracted from the data-set itself, the signals can be separated without overlap artefacts (right). The MLLS routine can even provide individual maps for the individual Si phases.

The tools described above are all part of Gatan’s EELS, EDS and CL Analysis suites. For more details on these and other spectral analysis techniques, please refer to the Spectroscopy section in the DigitalMicrograph on-line help (launch DigitalMicrograph and hit F1).

References of interest:
J.A. Hunt and Williams D.B, “Electron energy-loss spectrum-imaging”, Ultramicroscopy, 38, 47-73

R.D. Leapman and C.R. Swyt, “Separation of overlapping core edges in electron energy loss spectra by multiple –least-squares fitting”, Ultramicroscopy 26 (1988) 393-404