SIMS2015 Session DP1-ThM: Data Processing and Interpretation

While the sputter processes induced by atomic and cluster ion impacts are increasingly well understood due to both experimental data and molecular dynamics simulations, the ionization process remains somewhat mysterious. This paper proposes a model for molecular and fragment ion formation beginning with a mechanism not very different from that understood for atomic ion formation. This cascade charge transfer model proposes that the primary ion beam and the resulting cascade first litters the sample with charges and causes secondary electrons to be created. This model proposes that the majority of organic positive ions seen in the SIMS spectrum are created after an electron transfers from a neutral molecule or fragment to a nearby ionized piece of the sample. Negative ions are the result of electron attachment by the electrons. Because the time scale of electronic transitions and the sputter process are so different, late ionization events will be more likely to produce surviving ions than early events, and this means that the proximity of these late ionization events to molecules and fragments just leaving the surface will be an important factor influencing ion yields. Since charge transfer involves only single electrons, this hypothesis explains the rarity of multiply charged organic ions, something other hypotheses involving ionization due to direct interaction between the primary ion or the resulting cascade and the leaving molecule / fragment fail to do. The evidence of static SIMS spectra themselves show that ion formation involves much more than protonation and cationization, and even in cases where protons and cations are involved, these ions typically do not exist prior to the primary ion’s impact. The supporting evidence that can be gleaned from SIMS spectra and experiments performed to date for this model, and the implications of this hypothesis for the understanding of static SIMS spectra will be discussed.

The results of a VAMAS (Versailles Project on Advanced Materials and Standards) interlaboratory study on the measurement of composition in organic depth profiling will be reported. Layered samples were manufactured with known binary compositions of Irganox 1010 and either Irganox 1098 or Fmoc-pentafluoro-L-phenylalanine in each layer. The two types of sample were each produced in a single batch and distributed to more than 20 participating laboratories.

The samples were analyzed using argon cluster ion sputtering and either X-ray Photoelectron Spectroscopy (XPS) or Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) to generate depth profiles. Participants were asked to estimate the volume fractions in two of the layers, each having a volume fraction of 0.2 of one of the components. The participants were provided with the compositions of all other layers, which included the two components on their own and a mixed layer with volume fraction 0.5. Participants using ToF-SIMS either made no attempt at compositional measurement, or used various methods that returned compositions ranging in error from 0.02 to over 0.10 in volume fraction, the latter representing a 50% relative error for a nominal volume fraction of 0.2. Error was predominantly caused by inadequacy in the ability to compensate for primary ion intensity variations and the matrix effect in SIMS.

The participants’ data demonstrates that organic SIMS matrix effects are generally consistent for these materials, although there is some indication that these effects are more significant as the number of atoms in both the primary analytical ion and the secondary ion increase. A method that can compensate for these effects is described, which shows that all participants could have obtained accurate compositions from their data using molecular secondary ions or relatively unique fragments.

The participants are gratefully acknowledged for their time and effort in contributing to this study.

We present a new strategy for analyzing imaging TOF~SIMS data sets affected by detector saturation. Rather than attempt to correct the measured data to remove saturation, we incorporate the detector behavior into the statistical basis of the analysis. This is performed within the framework of maximum a posteriori reconstruction, justified on Bayesian grounds. The proposed approach has several advantages over previous techniques. No approximations are involved other than the assumed model of the detector. The method performs well even when applied to highly saturated and/or single-scan data sets. It is statistically rigorous, correctly treating the underlying statistical distribution of the data.It is also compatible with Bayesian methods for incorporating prior knowledge about sample properties. An efficient iterative scheme for solving the proposed equations is presented for the case of the bilinear model commonly used in analyses of SIMS data. The correctness of the approach and its efficacy are demonstrated on synthetic data sets, and then applied to selected experimental results. The method is found to perform better than a widely-used data correction method used in combination with common multivariate analyses.

Analysis of large areas of biological samples using SIMS generates data that can be prohibitively large to load into memory. The quest for ever increasing higher spatial and mass resolution amplifies the challenge of data handling, analysis and interpretation. To combat this, dimensionality reduction, most commonly through PCA, can be employed to project the data onto a lower dimensional subspace. However, this is computationally expensive for high dimensional data, as is the case in mass spectrometry imaging (MSI). Random projection (RP) has been shown to be an alternative, computationally efficient, dimensionality reduction technique for compressing SIMS data with minimal loss of information in memory constrained situations [1]. In RP, a set of projection vectors are generated from a given distribution with zero mean and normalised to unit length. In a high dimensional space these vectors have a high probability of being orthogonal, and projecting onto this lower dimensional space approximately retains the distances between points.

In this work we demonstrate up to a 100 to 10,000 times reduction in data size (depending on the level of compression desired), making the previously impossible, possible. To avoid the need to have the entire data within memory prior to the compression, we implement a streaming algorithm, which has the potential to compress data in real time as it is acquired. Performing subsequent multivariate analysis, such as PCA, on the compressed data results in significantly reduced computational time and memory overhead. For example, performing PCA on a 19 GB dataset used approximately 85 GB RAM and took over 6 hours to compute, whereas performing streaming random projection and then PCA required only 250 MB (78x less memory) and took just over 36 seconds to complete (620x speed increase). This provides a means of reducing the data sufficiently so that image segmentation can be performed rapidly on a GPU.

Previously described implementations of this method have a potentially significant limitation when used as a precursor to multivariate analysis techniques such as PCA, as the resulting loading plots from PCA are unintelligible, despite the scores being comparable and the distance between data points being retained. To overcome this, we provide a means to convert the loadings back into the m/z domain, through the use of a basis that is generated from the data using randomised methods [2].

[1] K. Varmuza et al. Analytica Chimica Acta. 705, Issues 1–2 (2011) pp. 48–55.

[2] A. D. Palmer et al. Analytical Chemistry. 85(10) (2013) pp. 5078-86.

Continual improvements in ToF-SIMS instrumentation have resulted in a corresponding increase in the number of pixels as well as the number of mass peaks present within acquired datasets, while the task of the analyst – namely determining the chemical makeup of these samples – has remained unchanged. Although ToF-SIMS has traditionally been predominantly used in a laboratory setting, recent years have seen an increase in the technique’s usage in process control during manufacturing. In both scenarios it is desirable to reduce the time and effort needed to analyze measured data.

MVSA techniques, such as PCA and MCR, have been shown to help interpret ToF-SIMS data. Typically these techniques classify a set of replicate measurements (in this case: mass spectra) as contributing to one or more MVSA factors. There are two approaches commonly used when analyzing ToF-SIMS data. One option is to consider the mass spectrum of each voxel of a dataset as a replicate measurement, in this case the factor scores reflect the spatial distribution of each factor within the dataset. Alternatively, if the aim of the analysis is to compare several datasets, the total spectrum of each dataset is used, and the resulting scores reflect how strongly each dataset contributes to each resulting factor. In the latter approach the reduction of each dataset to a single spectrum discards the spatial information inherit to the dataset, which may increase the difficulty of interpreting the resulting MVSA factors.

We demonstrate the simultaneous analysis of several similar 3D datasets, while retaining each dataset’s spatial information, thus combining both approaches. This results in a set of factors which describe the entire content of all analyzed datasets. In addition to the traditional loadings (characteristic spectra of the factor) and scores (spatial distribution of the factor within each dataset), we can determine each dataset’s effective contribution to each factor. This effective contribution allows a quick discrimination between factors common to all datasets and those which are unique to a subset of the datasets.

Principal Component Analysis (PCA), Factor Analysis (FA) and other multivariate analysis methods have been used increasingly to analyse and understand depth profiles in XPS, AES and SIMS. These methods have proved as useful in fundamental studies as in applied work where speed of interpretation is very valuable. Until now these methods have been difficult to apply to very large datasets such as spectra associated with 2D images or 3D depth-profiles. Existing algorithms for computing PCA matrices have been either too slow or demanded more memory than is available on desktop PCs or even High Performance Computers. This often forces analysts to “bin” spectra on much more coarse a grid than they would like, or select only part of an image for PCA analysis, even though PCA of the full data would be preferred.

We apply a new method of PCA to ToFSIMS images and 3D ToFSIMS data for the first time[1]. This increases the speed of calculation by a factor of several hundred, making PCA of these datasets practical on desktop PCs for the first time. For large images or 3D depth profiles we have implemented a version of this algorithm which minimises memory needs, so that even datasets too large to store in memory can be processed into PCA results on an ordinary PC with a few gigabytes of memory in a few hours. We add to this a third new improvement useful for PCA of the very largest images and 3D depth profiles, by implementing a sampling method based on low discrepancy series (e.g. Sobol series) which we show improves convergence significantly compared to, for example, random sampling. We show PCA results for very large images, for example 512x512 pixels, with each pixel containing a mass spectrum of 67000 values. This single dataset takes up 134GB of disc space when uncompressed - we perform PCA successfully on an ordinary personal computer even though it is impossible even to load it all into memory.

[1] P J Cumpson, N Sano, I W Fletcher, J F Portoles and A J Barlow, Multivariate Analysis of Extremely Large ToFSIMS Imaging Datasets by a Rapid PCA Method, Submitted to Surface and Interface Analysis

Multivariate statistical methods are finding extensive application in spectral and image deconvolution due to their utility in variable reduction and advances in routine computing power [1, 2]. Among these methods, Principal Component Analysis (PCA) is particularly attractive due its ability to preserve maximum variance following dimensional reduction, and the absence of any domain-specific assumptions regarding covariance. In chemometrics, PCA provides a statistical means for extracting meaningful associations between chemical variables which are not obvious during routine data examination. As a result, unprecedented, quantitative relationships between traditionally unrelated variables may be extracted following the proper handling of input data.

Proper data normalization is mathematically required for the implementation of PCA; however, the manner by which variables are normalized is profoundly consequential to the significance of the resultant principal components [3]. Traditional mean and median-centered loading, while easily programmed and widely available in commercial statistical packages, fails to account for the widely varying physical and chemical properties contributing to the collected signal. The use of PCA in chemometric analysis necessitates a normalization process which is able to account for such subtle disparities in variable behavior.

In this work, alternative methods for scaling chemical tracers are examined and compared to traditional median-centered normalization. Signals from common polycyclic aromatic hydrocarbons (PAHs) obtained by Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) analysis are utilized as a case study in exploring the use of different normalization techniques. Certified reference standards are additionally normalized using median-centered normalization, reference sample scaling, and normalization to sublimation energy (ΔH°_sub) to generate principal components to determine which is appropriate for ToF-SIMS spectra generated from environmental samples.

[1] Fletcher, J. S., et al., Rapid Communications in Mass Spectrometry. 25(7), 2011, 925-932.

[2] Amstalden van Hove, E. R., et al. Journal of Chromatography A, 1217, 2010, 3946-3954.

[3] Abdi, H., Williams, L. J. Wiley Interdisciplinary Reviews: Computational Statistics, 2010.

Time of Flight Secondary Ion Mass Spectrometry (ToF-SIMS) has developed into a "workhorse" screening technique for samples of completely unknown composition. This is due to the fact that inorganic and organic molecules can be measured simultaneously and with high sensitivity. Modern ToF-SIMS instruments are highly automated and routinely offer the possibility of three-dimensional (3D) analyses. This promises quick and comprehensive analysis of complex samples. However, the interpretation of such data is often time consuming and complex. For example, a 3D analysis with 256 x 256 pixels running for 1000 scans (data points) results in 6.4 x 10⁷ individual mass spectra.

To handle such complex data sets different Multivariate Data Analysis Techniques (MVA) were applied to various sample systems.^1,2,3 MVA methods help to find structures in the data and thereby reduce the complexity of the data set and the time of data analysis. The application of MVA requires a preprocessing of the data. This usually comprises a manual selection of peaks, which is time consuming and includes the possibility to overlook essential peaks with low intensity. Also, appropriate scaling, normalization, and centering is important. Depending on the scaling chosen, it is possible to enhance peaks of low or high intensity. Clearly, preprocessing affects the results of multivariate data analysis and is of crucial importance.

The aim of this study is to develop a suitable preprocessing approach, which enables the application of MVA to various sample systems with a completely unknown surface composition. Among other sample systems, aged Li-ion battery electrodes containing unknown degradation products are analyzed. The application of multivariate data analysis to these sample systems facilitates a classification of the degradation products in the ToF-SIMS spectra and thereby simplifies their identification. Additionally, MVA is used to find characteristic differences between electrodes with different additives to determine their influence on degradation products.

(1) Wagner, M. S.; Graham, D. J.; Ratner, B. D.; Castner, D. G. Surf. Sci.2004, 570, 78–97.

(2) Graham, D. J.; Castner, D. G. Biointerphases2012, 7, 1-12.

(3) Lee, J. L. S.; Gilmore, I. S.; Seah, M. P. Surf. Interface Anal.2008, 40, 1–14.

When surface-to-volume ratios are large, heterogeneity among nano-particles, NPs, becomes a major concern and may not be duly reflected in results from ensemble averaging. For accuracy, assays should thus be on individual NPs, yet extracting detailed chemical information from one vanishingly small object is virtually impossible. Our approach is to probe a large number of individual NPs one-by-one each time with a single projectile and to record the secondary ions from each NP separately. The overall data set will contain mass spectra from subsets of like-NPs which can be summed for statistics. We demonstrate here on a mixture of like-NPs their identification based on different functionalization.

The methodology requires that the nano-objects be dispersed on a flat surface (e.g. silicon wafer, graphene). As noted bombardment is in the shot-by-shot mode, for a total of 10⁶-10⁷ projectiles, the analysis of the large data set generated, 10⁶ – 10⁷ individual mass spectra, is accomplished with the SAMPI software solution, Surface Analysis and Mapping of Projectile Impacts. Using SAMPI, coincidence tests can be applied to the set of mass spectra. A coincidence test, will examine the set of mass spectra for an ion of interest and identify all ions which were co-emitted with the ion of interest. Testing one or more coincidence conditions on the set of mass spectra allows to select an ensemble of impacts, from this selected ensemble, the mass spectrum of like-NPs can be obtained. When measuring secondary ion, SI, yields of dispersed NPs, the SI yields may be underestimated by a factor proportional to their fractional coverage. Using SAMPI, the SI yields can be calculated using only impacts on the NPs.

The methodology described above was applied to obtain specimen specific mass spectra from a 50/50 mixture of 5nm dodecanethiol coated Au NPs with 5nm 1-mercaptoundec-11-yl tetraethyleneglycol coated Au NPs dispersed on a silicon wafer. The mass spectra were obtained using Au₄₀₀⁺⁴ at 520keV. The impacts on each NP are selected by a coincidence test on a specific SI: SH(CH₂)₁₁OC₂H₄O^- and S(CH₂)₁₁CH₃^-. Selecting the impacts on the NPs, we can calculate the number of effective impacts on each NP and evaluate the SI yields from these impacts. Thus we can identify NPs of identical core makeup and size differing only by the respective self-assembled monolayers, a task unattainable with SEM or TEM.

The application of SAMPI will be illustrated with several other test cases. The methodology is not limited to this custom instrumentation it can be applied to commercial instruments using pulsed primary ions.

Work Supported by NSF grant CHE-1308312.