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Ultramicroscopy 38 (1991) 47-73

North-Holland

Electron energy-loss spectrum-imaging

J.A. Hunt and D.B. Williams Department of Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015-319.5, USA

Received 4 February 1991; in final form 27 March 1991

Electron energy-loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM) is a powerful method

for analyzing elemental, chemical, dielectric, and other information. The technique can be extended to produce quantitative

images useful for interpreting the spatial distribution of this information. This paper describes an implementation of a new

method of quantitative mapping termed “spectrum-imaging”. The resultant “spectrum-images” consist of complete spectra

stored at each pixel in a scanned image. This allows not only the data in each spectrum to be analyzed a posteriori using

time-consuming methods, but also permits the spatial statistics of the collective spectra to be exploited. Spectrum-image

processing is fundamentally different from previous quantitative image processing that has been performed “on-the-fly”. The

methods used to acquire and process EELS spectrum-images are here described, along with a range of applications and

examples of the technique.

1. Introduction

Several laboratories have combined the acquisition of EELS and X-ray spectra with computer control of the electron beam in a STEM to produce compositional maps [l-6]. The technique of on-the-fly processing is used to process and then discard the raw data collected at a pixel before or during the collection of data for the next pixel. Only the processed data are stored. An important limitation of this method is that only simple processing can be performed without greatly extending the image acquisition time.

This disadvantage is alleviated using spectrum-

imaging. A spectrum-image in its most common form is similar to a normal image, but it contains an entire spectrum at each pixel whereas an image plane has only a single value (e.g. intensity or concentration) at each pixel. This paper is con-

cerned with spectrum-images acquired using a STEM equipped with an electron energy-loss spectrometer, although the techniques are applicable to other instrumentation, particularly X-ray spectrometers.

Spectrum-imaging is a term first published by

Jeanguillaume and Colliex [7], but the technique has been practiced for somewhat longer. Astro- nomers have been collecting X-ray and radio spectrum-images of the heavens for many years [8]. We believe this work represents the first generalized

spectrum-imaging implementation in electron microscopy.

The work described in this paper concerns stor- ing, and later processing, entire 1024-channel parallel EELS spectra and the associated dark-field and probe current signals at each pixel in a spectrum-image. The resulting data can amount to several hundred megabytes. Spectrum-imaging dif- fers fundamentally from previous work which only saved a few pre-chosen channels or a few processed pieces of data at each pixel. The current approach offers significant experimental advantages over these earlier methods.

Saving all the data from an imaging experiment

means that less needs to be known about the nature of the data prior to collection. It is not necessary to know ahead of time what elements are to be imaged (or even what elements are present) or what parameters are to be used for processing. When all the data are saved, complex

03043991/91/$03.50 0 1991 - Elsevier Science Publishers B.V. All rights reserved

48 J.A. Hunt, D.B. Williams / Electron energy-loss spectrum-imaging

and time-consuming processing can be performed off line without extending data acquisition times. Data can be processed multiple times and the effectiveness of applying different techniques to the same data can be compared. Problems and artifacts unanticipated prior to data collection can be corrected. Because processing time and acquisition time are not related, the electron dosage to the specimen can be tailored solely according to the desired statistics and limitations of the electron microscope and the spectrometer. We term this approach batch processing and discuss its advantages compared with earlier methods which process the data on-the-fly.

Collection of spectrum-images and subsequent batch processing was not performed previously because of limitations in computer technology [7,9]. Only recently have storage devices become large enough and inexpensive enough for routine collection of even moderate-sized spectrum-images of 32 megabytes. Recent improvements in processing speed are also important. Parallel-collection EELS spectrometers are essential for spectrum-imaging because serial EELS spectrometers have intrinsically poor collection efficiencies

[lO,ll]. Even with the availability of the necessary

hardware, spectrum-imaging requires the development of sophisticated processing software. This paper describes our implementation of the hardware and software constructed to acquire and process spectrum-images. Also discussed is the processing of spectrum-images containing EELS spectra to produce quantitative maps such as: elemental maps, chemical maps, thickness maps, dielectric maps, plasmon-shift maps, inelastic images, and mass-loss experiments. Superficial details of the acquisition system and processing

software are described and will be published in detail elsewhere. [12]

2. Spectrum-images

The term image plane used herein refers to a multidimensional representation of data with zero or more independent dimensions and a single dependent dimension. An image is composed of one

or more equidimensional image planes. The di- mensionality, D, of an image or image plane refers to the number of independent dimensions. A typical example of both an image and also an image plane is a black-and-white photograph - this is a 2D image possessing three total dimensions, two independent spatial dimensions and one dependent intensity dimension. A color photograph is composed of three such image planes with the dependent dimensions represented by the amounts of cyan, magenta, and yellow (the complements of, and thus reflected intensities of red, green, and blue).

Images in electron microscopy can become more complicated, such as in the case of a spectrum-

image [7]. A typical spectrum-image consists of a spectrum collected for each pixel in two spatial dimensions. Thus there are three independent dimensions, two spatial and one energy, and one dependent dimension of counts.

Spectrum-images can become still more complicated. An example would be a 4D spectrum- image with two independent spatial dimensions, one independent energy-loss dimension, one independent scattering angle dimension, and a dependent counts dimension.

Two spatial dimension spectrum-images are usually processed into 2D images for viewing. In the case of an EELS spectrum-image there may be N core-loss edges per pixel that can be processed yielding N image planes. Additional image planes

can be produced from other quantities such as the entire inelastic signal, plasmon energy shifts, specimen thickness, etc.

The term quantitative imaging is adopted here to describe images that directly relate quantities such as mass, concentration, bond lengths, dielectric response, etc. These are different from quafita-

tive imaging where the dependent axis does not directly correspond to the quantity of interest, but there is some relationship to that quantity. An EELS or X-ray spectrum-image can be processed to generate a quantitative image of elemental concentrations as a function of spatial coordinates. A bright-field or an energy-filtered (not background subtracted) image would be considered a qualitative image because its intensity is not directly related to such quantities.

J.A. Hunt, D.B. Williams / Electron energy-loss spectrum-imaging 49

Data collection for quantitative images can be divided into two types which are discussed below. The first is on-the-fly processing where the data for a pixel are acquired and processed, then the col-

lected data are discarded, and only the processed data are stored. The stored data are generally a set

of processed 2D image planes. The second type is batch collection where generally a 3D (or larger) spectrum-image is collected and stored for later processing into 2D image planes.

2.1. On-the-fly processing techniques

Until recently, compositional image data were only collected using “on-the-fly” techniques to minimize data storage [l-4]. In EELS, a typical image processed this way would involve collecting a spectrum for a single pixel, processing that spectrum to obtain and record the counts under one or more core-loss edges, then discarding the collected spectrum. Typically calculations for pixel N would be performed while a spectrum for pixel N + 1 was being acquired [3]. The process would be continued for each pixel in the image and the stored data would be one plane of data for each element analyzed. The amount of storage required for this was substantial until only a few years ago. See table 1.

Limitations with on-the-fly processing occur because processing times and acquisition times are related. For simple processing there need not be a problem but complicated processing may cause unreasonably long acquisition times. Most implementations of EELS imaging collect only two channels before an edge and one after [l]. The

Table 1

Storage requirements for “on-the-fly” processed image-planes

and unprocessed spectrum-images (the spectrum-image consid-

ered has 1024 channels (words) stored at each pixel)

Image size On-the-fly processed Spectrum-image (pixels) image-plane (words)

(words)

64X64 4K 4M 128x128 16 K 16 M 256 x 256 64 K 64 M 512 x 512 256 K 256 M

1024 x 1024 1M 1G

importance of collecting and processing more than three channels has been noted previously [13]. Because of the limitations of on-the-fly-processing we developed the more versatile batch methods described below.

2.2. Batch collection and processing techniques

Storage of all the collected EELS data is costly in terms of storage space. Parallel EELS spectra collected for spectrum-imaging will typically contain a large number of contiguous channels (e.g. 1024 channels for a single readout of the Gatan PEELS) and it is often desirable to store all of them for later processing. Thus substantially larger storage capacity is required for spectrum-imaging compared with on-the-fly processing techniques. However, the necessary storage capacity is now routinely available and this paper is primarily concerned with batch collection and processing of

spectrum-images. Processing individual EELS spectra in an image

“on-the-fly” is often insufficient for quantitative imaging. Saving the entire spectrum-image and batch processing allows processing the data multiple times. Erroneous fitting and unexpected acquisition problems that frequently cause on-the- fly-processing errors can often be overcome through modifications of the processing parameters or software without reacquiring the image. Edges whose existence were not predicted prior to acquisition can be detected and processed. Processing time need not be limited to acquisition time, and thus complicated and robust analysis routines may be used. Multiple least-squares (MLS) fitting routines in place of linear least- squares (LLS) and area ratio background modeling techniques can greatly improve accuracy and detectability [14,15]. Other time-consuming analyses such as isolating chemical effects and dielectric response information can be employed. The processing time for such routines most likely far exceeds the desired acquisition time, particularly when specimen drift, beam sensitivity, and microscope operating costs are of concern.

On a multitasking system, it is possible for batch processing to begin while data are being collected. This is useful for providing feedback to


the user during the experiment. It is concluded that the only reason to do on-the-fly processing is when batch processing cannot be performed because of equipment and storage limitations. Con- servation of storage space is the only significant advantage of on-the-fly processing over batch collection and processing.

2.3. Flavors

EELS spectrum-images typically have two spatial dimensions but we have generalized the term to include several variants. This generalization is useful in practice because the same software can be used to process the different spectrum-image flavors listed in table 2. A common variant is a line scan that suffices when data are needed from only a single spatial dimension. Another is a zero spatial dimension time-series that would typically be used to measure beam-damage or mass-loss. There can also be time-series of line scans, etc. Processed examples of several variants appear later in this paper. Spectrum-images with three spatial dimensions may soon be realized.

Spectrum-image pixels could theoretically contain any amount or type of data. Most spectrum- images collected in this investigation have been single EELS spectra per pixel, but a few have contained two EELS spectra or an EELS spectrum and an X-ray spectrum. All other available data that are potentially relevant should also be stored. Examples include the beam-current which is used for the correction of beam-current fluctuations, and the dark-field signal which can be used for quantitative analysis.

Typically our two spatial dimension (xyE)

Table 2 The following notation was adopted to abbreviate and eluci-

date the variations of spectrum-images

Abbreviation Spectrum-image type

E

tE

xE

XYE

Spectral data from a single point

Time-resolved spectral data from a point

Spectral data from a line scan Spectral data from each point in a 2D image

xtE

xyzE

Time-resolved spectral data from line scans

Spectral data from each point in a 3D image

spectrum-images have been 128 X 128 pixels with a 1024 channel energy-loss spectrum at each pixel (x: 128, y: 128, E: 1024). However, spectrum-

images as large as (x: 256, y: 256, E: 2048) (256 MB) have been collected, and spectrum-images as small as (x: 10, y: 10, E: 100) have proven useful. The ultimate size of the spectrum-images is limited by both storage space and collection time. The latter is constrained by specimen drift, beam sensitivity, microscope costs, and patience.

2.4. Other spectrum-image uses

Many applications of spectrum-images are listed in refs. [7,16]. One of the more useful techniques is to collect a spectrum-image around a feature of interest and later sum together spectra corresponding to the feature. This allows spectral information to be obtained from any desired regions of even irregularly shaped features and di- lutes the effects of a stationary STEM probe such as beam damage and contamination. Similarly it is useful to indicate regions-of-interest using a bright-field or dark-field image using image processing software. The data acquisition software is fed this information and only collects spectrum-image data from these regions thus reducing data collection times.

A spectrum-image is a useful substitute in situations where a single measurement is suspect of not being representative. For instance, the thickness of a foil or film determined at a few hundred pixels in a spectrum-image is more infor- mative than a single measurement. Such a spectrum-image can be collected and processed to produce a relative-thickness (sample thickness divided by mean-free-path of the incident electron) map in about a minute with the implementation

described in this paper.

3. Equipment

EELS spectrum-imaging was first implemented on a Hitachi H700H fitted with a Gatan 666 parallel detection EELS spectrometer (PEELS) at the National Institutes of Health (NIH) in August 1988. Development efforts concentrated on


streamlining data collection and developing methods for correcting spectrum artifacts and spatial- and energy-coordinate shifts. A year later enough was learned about spectrum-imaging to begin a more general and user-friendly implementation of the spectrum-imaging system. The features of this software are described later. The system has since been installed on a VG HB501 STEM at NIH and a Philips EM430 TEM/STEM at Lehigh Univer- sity (see fig. 1).

3. I. Gatan PEELS

The capabilities of the Gatan PEELS spectrometer are discussed fully elsewhere [lO,ll], but relevant details are summarized here. The energy- loss spectrum is read from a 1D photodiode array as a series of one or more detector integrations.

The minimum integration time for the standard 1024 channel array is normally 24.6 ms which is equal to the minimum time needed to read each cell in the array. This can be reduced to 12.3 ms at the expense of introducing higher readout noise in the spectra. Longer integration times are possible by inserting a wait time before reading the array. Shorter collection times may be obtained by using an attenuator which exposes the detector array for only a small fraction of an integration time. Por- tions of the spectrum not falling on the detector array are measured as a shield current, although some energy losses of importance may pass

Comouter I Goton PEELS spwtrometer

I J

Tape backup

Dark-field detector

External timers

Fig. 1. Spectrum-imaging equipment connectivity.

through the gap between the shield and the detector array.

The collection of a spectrum is done in parallel but the channels are read one at a time. When a channel is read it is cleared and begins collecting again. The time to read each channel multiplied by the number of channels is the same as the minimum integration time. An important ramifi- cation for spectrum-imaging is that the portion of the spectrum read from the last array element is approximately one array readout time older than of the first array element. This complicates the interpretation of spectrum-images obtained with short integration times. To prevent the “blurring” of information between time-adjacent pixels the spectrometer should be cleared of “old data” after scanning to each new pixel. This introduces a dead-time of one array readout time per pixel. The spectrometer must also be cleared in between each component spectrum in a difference spectrum. This generates large dead-times (typically 30% to 50% for spectrum-images).

Concurrent or successive acquisition of core-loss and low-loss spectra is difficult. A one nA zero-loss peak that is one electron-volt (ev) wide (full-width at half-maximum (FWHM)) and is dispersed to 0.5 eV per channel upon the photodiode array will saturate the channels under the zero-loss in less than 250 ps. This is approximately one-hundredth of the minimum integration time. If the intensity of the core-loss signal is optimized so that it uses a significant fraction of the array’s dynamic range then the accompanying low-loss spectrum (even if taken with the smallest integration time) will most likely saturate the array. The attenuator can be used to minimize array exposure to about 500 ~LS but introduces large dead-times.

A pre-specimen beam blanker can be used to prevent sample irradiation during collection dead-time. It can also provide a more flexible alternative to the Gatan PEELS attenuator for attaining spectrum collection times less than an integration time.

3.2. Computer hardware

The system was created around an IBM per- sonal computer (PC) AT clone, although any rea-


sonably sized computer system could be used. The availability, flexibility, quality, and low cost of PC

hardware and software allowed rapid system development [9]. A large storage device is necessary. Previously hard drives (320 MB at Lehigh, 220 MB at NIH) were used for data collection and processing, and a 60 MB tape backup unit was used for archival purposes. However, the speed and flexibility of 4 mm DAT (digital audio tape) backup units now permit the direct storage of spectrum-images onto 1.3 gigabyte tapes. Because spectrum-image data is usually processed sequen- tially (in the order that the data are stored) there is little or no time penalty incurred during data collection and processing. Optical disks would also be useful but at present are more expensive and offer little advantage over DAT for current spectrum-image processing techniques.

Hardware control is performed through ma- chine-language drivers called from high-level lan- guages (HLL) such as C and C++. The software drivers and hardware were designed to minimize processor involvement in the data collection process, resulting in the capability to collect data while processing continues within the parent HLL.

This design simplifies the HLL program structure and minimizes data collection dead time.

Precise timing on PC’s is difficult because asynchronous events (specifically interrupts) can take hundreds of microseconds of processing time from the microprocessor per event. These inter- ruptions can cause delays or errors with the high data transfer rates characteristic of spectrum- imaging. A solution is to use direct-memory access (DMA) to transfer large amounts of data. Exter- nal timers are used to accurately signal the end of data collection from the X-ray spectrometer and the bright-field and dark-field detectors. Once programmed, the Gatan PEELS handles its own timing.

DMA is fast because it does not rely on the microprocessor to store data from a device into memory. It can store information while the processor is working on something else. DMA is used to transfer bright-field and dark-field data, X-ray data, and EELS spectra. An important design philosophy for this project was to use DMA whenever more than 1000 bytes of information per

second were likely to be transferred. This minimizes processor involvement in data collection, allowing the processor to do other tasks. Gener-

ally no more than 95 000 bytes per second are acquired from the spectrometers, although theoretically about 184000 bytes per second are possible.

During drift correction data transfer from the bright-field and dark-field detectors can take place at one megabyte per second.

4. EELS spectrum-image processing complications

The processing of .spectrum-images is complicated by the presence of spectrum artifacts and by the drift of the spatial and energy coordinates of the spectrum-image. The handling of artifacts is basically the same for EELS spectrum-images and for normal EELS spectra. The correction of coordinate drift is less straightforward. Both types of complications and the solutions we implemented to correct them are discussed below.

4.1. Artifacts

Three detector artifacts should be considered when collecting spectra and spectrum-images using the Gatan PEELS. These artifacts are common to

virtually all parallel-recording detectors. Dark-current is the signal that is read from the

detector array even when there is no incident illumination. The shape and magnitude of the dark-current profile is strongly dependent on the array temperature and integration time. This artifact is particularly important when working with small signals of only a few hundred counts per channel.

Gain variations between cells in the detector array can vary by more than several percent from the mean detection efficiency. This is caused by small variations in the collection area and efficiency of each cell of the array.

Detector persistence is when a portion of a signal persists after that signal was read and cleared from the detector. The persistent signal is measured in subsequent readouts.

The most obvious method to artifact-correct a raw PEELS spectrum is to first subtract the dark


current and then divide out the gain variations. In practice this is not trivial because the size of these artifacts may not be accurately known. Methods such as the collection of difference spectra effec-

tively suppress the dark current and gain variation artifacts [17] without this knowledge, but standard EELS processing methods cannot be directly used.

4.1.1. Dark-current When a dark-current spectrum, DS, is acquired

it contains a repeatable term, DC (counts due to charge leakage and analog-to-digital conversion offsets), and dark-current noise DN. The sub- scripts below indicate a time dependence, i.e. DN, and DN, are different because they are acquired at different times. This treatment assumes the

spectra are single integrations, but it is easily extended for multiple integration spectra:

RS=S.G+DS,,

DS, = DC + DN,,

where RS is the acquired raw spectrum, S the actual spectrum and G the gain function.

The dark-current spectrum can be subtracted directly from the spectrum signal if they were both acquired using identical integration times. This operation removes the dark-current signal but not

the dark-current noise:

RS-DS,=S.G+DS,-DS,

=S.G+DN,-DN,.

Let DN, _ z = DN, - DN,,

IDN,_J2= IDN,l’+ lDN,l’.

Although the dark-current noise terms in the processed spectrum are doubled, if Poisson statistics are assumed then the magnitude of the dark- current noise is only increased by a factor of 0. This factor can be reduced asymptotically to 1 by

increasing the number of integrations, n, in the dark-current spectrum and scaling appropriately:

DS=DC+f i DN(J’), j=l

n

lim c DN(J’) = 0, n+w j=l

lim (RS-DS)=S.G+DN,. n+oo

Normally it is best to collect the spectrum such that the features of interest are very much larger than the DN. When spectrum-imaging this is not always possible due to collection time limitations and thus it is useful to minimize the DN contribu-

tion by collecting many DS integrations so that DS is effectively DC. Reducing the noise present

on small edges increases the likelihood that their thresholds can be accurately and repeatably found. Smoothing during processing reduces the noise but can also mask small features.

Usually the DC component is assumed in- variant over the duration of the spectrum-image collection time. When this is a reasonable assump- tion then a DS collected at the beginning or the end of the spectrum-image is sufficient. Otherwise a DS could be collected at the end of each scan line in the image while the beam is blanked or scanned off the array. The latter has not yet been necessary.

The dark-current read from the Gatan photodiode array is higher immediately after a pause in array readout. Thus it is important to throw away the first spectrum acquired after even short inter- ruptions in spectrometer operation such as during drift-correction calculations. For longer delays the

first several spectra should be discarded - the latter usually being necessary only for the first pixel in the spectrum-image.

4. I .2. Gain variations The channel-to-channel gain function, G, for a

particular set of spectrometer and microscope operating conditions can be known accurately. How- ever, this is not necessarily useful particularly for a 1D detector array (such as in the Gatan PEELS) because small changes in the operating conditions

54 J.A. Hunt, D.B. Williams / Electron energv-loss spectrum-imaging

can change the effective gain of a single channel by several percent. This effect occurs because the energy-loss dispersion is not focused over the entire height of the detector array. Small changes in the spectrometer or microscope conditions change the position of the dispersion on the array in the height direction. Inhomogeneities or contamination in the detector or scintillator material can change the efficiency of a portion of a detector cell. Thus movement of the dispersion over such defects will alter the channel-to-channel gain function.

This condition is restrictive. Changing operating conditions such as beam voltage, collection angle of the spectrometer, focusing conditions of the microscope, and any of the lens settings within the spectrometer will cause the dispersion to move along the array. Therefore G can not be considered accurate if it was obtained using different microscope or spectrometer focusing conditions from those used for the spectrum being analyzed. Techniques for calculating G such as flat-fielding (where the array is evenly exposed) are not accurate because they require changing the spectrometer lens settings from normal operating conditions. The G calculated is not the same G that affects

subsequently acquired spectra. If the spectrometer incorporates a two-dimen-

sional array where the dispersion is focused over elements in both directions along the array, then this problem can be minimized. The gain function for each detector cell can be determined and it is then assumed that the cell dimensions are vanish- ingly small and thus the dispersion will never only partially illuminate a cell.

The gain function of the active portion of the

array on the Gatan 666 PEELS can be determined assuming that offsetting the spectrum electrostatically does not change the active portion of the array. A spectrum feature is stepped across the array one channel per integration using the elec- trostatic offset. At each step the feature is summed into an array that becomes an unnormalized gain function that is unique and useful for the correction of subsequent spectra acquired at that particular set of spectrometer operating conditions. For some dispersions (eV/ch 2 1) the PEELS voltage scan unit does not have enough offset

range to permit gain function determination of the entire array.

4.1.3. Detector persistence

This artifact becomes important when the signal intensity of a recently examined feature greatly exceeds the currently monitored signal. Complica- tions can arise when acquiring both a core-loss

spectrum and a low-loss spectrum for each pixel in a spectrum-image. For example, the persistence remaining from a previously acquired zero-loss

peak may appear as a core-loss feature in subsequent spectra. This problem can be avoided by insuring that intense portions of the low-loss spectrum are not placed on channels that will be used in the core-loss spectrum. Generally it is possible to collect spectra such that persistence is not a serious problem. An exception to this is collection of low-loss difference spectra where false difference peaks may appear. The problem can be minimized by not cooling the detector array (which reduces persistence but increases dark current) and clearing the array multiple times between acquisition of the difference component spectra (which increases collection dead time).

4.1.4. Difference spectra

The use of difference spectra can greatly en- hance the visibility of very small edges without curve fitting [14,15]. Edge shapes and areas are not preserved so quantitative analysis is performed by fitting differentiated reference spectra of standards to the unknown difference spectrum. A properly selected energy window for differentiation will remove the background beneath the edge without the inaccuracies associated with curve fit-

ting. Very small elemental concentrations can be detected and quantified in this manner [18].

Difference spectra can be used to effectively suppress dark current and the channel-to-channel gain fluctuations to negligible levels. A second difference technique can be used for this purpose by acquiring three spectra: A, B, and C. After acquiring A the energy-scale of the spectrometer is electrostatically offset by an energy-window and B is collected. The energy-scale is again offset by the energy-window and C is collected. These spectra are combined according to the equation D =


2B - A - C to form the second difference, D. In many cases a first difference spectrum, D = B - A,

is sufficient although its background is not as flat as that of the second difference.

A major disadvantage of the difference spectra approach is that multiple spectra must be acquired for a difference spectrum. The resultant increase in collection time may be important when performed at each point in an image. For second difference spectra it is practical to combine the component spectra before storage to conserve space. Saving the combined spectra as both a normal spectrum and a difference spectrum is a flexible alternative to saving all three component

spectra.

4.2. Drift corrections

When acquiring an image it is possible for any of the independent coordinates to drift from their presumed positions. For the spatial dimension this can be due to random specimen drift induced by vibration or by localized specimen heating. The energy-loss dimension can drift because of slow changes in the beam accelerating voltage or instabilities within the spectrometer. In some microscopes the energy-loss dimension drifts because scanning the probe causes the beam to enter the EELS spectrometer at varying angles. The probe current can also change during the time required to collect an image. This can be considered a change in the scaling factor of the dependent dimensions of the spectrum-image.

Energy drift in a high-quality STEM using de- scanning coils should be negligible. Spatial drift will be a problem in any microscope at high magnifications over long periods of time. Probe current changes may not be important for ther- mionic sources but are significant with field emission sources. Many STEM’s exhibit large energy, current, and spatial drift problems. Thus it was necessary to develop means of correcting for these faults in order to obtain reasonable images.

4.2.1. Energy-drift correction Energy-drift correction is best done after

acquisition because it can become relatively complex and it is often done incorrectly on the first

attempt. The drift of the energy scale of the spectrum-image spectra happens for several reasons. Unpredictable drifts occur from changes in the energy of the beam electrons and from spectrometer instabilities. In microscopes without double- deflection coils the entrance angle of the electrons into the EELS spectrometer changes appreciably as the STEM probe scans at low to medium magnifications. This causes a predictable shift of the energy scale that can be easily corrected. (The collection angle is also changed when limited by the spectrometer collection aperture.)

Determining how the energy scale shifts as a function of position in the scan is done by collecting a zero-loss spectrum-image at a low magnification (e.g. 5-20000 x ). The spectrum-image is processed to produce an image plane of energy shift as the dependent axis (see fig. 2). The Gatan 666 spectrometer mounted on a VG HB501 ex- hibits a shift that can be parameterized as a linear function of relative shifts of the X and Y positions of the probe. The parameters can be used to calculate energy shifts for any magnification. The spectrum-image used for calibration purposes is usually small (e.g. x: 10, y: 10, E: 100) and can be collected in a few seconds. STEM’s with double-deflection coils, such as the Philips EM430, do not exhibit this energy-scale shift.

All electron microscopes exhibit unpredictable probe energy-shifts. The basis behind their correction is to find a feature set of fixed energy-loss

features such that at least one member of this set is found in each pixel of the spectrum-image. The energy scale of the spectrum in each pixel of the spectrum-image is calibrated by matching a feature of known energy-loss to a feature in the spectrum. If no feature can be found then no probe energy shift is assumed.

The first step is to find an element in the feature set that occurs in the spectrum with sufficient signal quality. Next, some characteristic of the feature must be exploited - for instance the

maximum value in an edge or the slope of the edge threshold. A region in the spectrum is chosen to search for the feature selected, and the characteristic chosen is used as a search criterion. Other useful criteria are the total counts in the feature and the height of the feature above the


Fig. 2. Processed image plane of a spectrum-image indicating the apparent energy-shift of the zero-loss as a function of scanning

position. This image plane is used to parameterize the apparent energy-shift to correct subsequently obtained spectrum-images. Note

the small fluctuations in energy due to minor beam-energy instabilities.

background. More details on feature characteris- tics are given later in the snap-to function discus- sion.

Errors in energy-drift correction can occur for several reasons. Unanticipated edges can arise within the search region of another feature which can confuse simple search criteria. Large amounts of noise can also obfuscate the thresholds of small search features. Often many pixels are processed without a successful match to the search criteria during which significant energy drift may have occurred and yet was not corrected. It is useful to generate an image showing the energy-shifts as a function of position. Rapid changes in the energy scale are often only artifacts of incorrect processing. The energy-shift image can also be compared to elemental image planes to check for correlations that would indicate a chemical shift of a feature and not an actual energy drift of the spectrum being measured.

4.2.2. Current-drift correction

Probe current change is often the most serious drift in spectrum-imaging. When using a field-

emission source the intensity of the probe can drop by as much as 50% during the collection of an image. (Sometimes the intensity will disappear altogether for fractions of a second.) In such situations the probe current or an analogous signal can be recorded and used to scale the spectrum. The scaling is computationally trivial but is performed after acquisition along with the correction of the artifacts and the energy-drift. Implementations of spectrum-imaging on systems with a field-emission gun should provide the ability to stop acquisition so the user may modify gun parameters during long acquisition times.

Correction for current drift is not necessary when an analysis is current independent. This is the case when mapping elemental concentrations. However, in most instances it is more straightfor-


ward to map an absolute quantity than a con- We prefer to use on-the-fly spatial-drift correction centration. In these cases the current entering the because it is computationally more straightfor- spectrometer (I,) is needed, not the current in the ward. The test for drift should be performed fre- incident probe (I,). These signals change propor- quently enough that the image drifts no more than tionally to the measured signals i, and i, respec- one or two pixels per test. Generally it is sufficient tively. to test at the end of each scan line.

The current striking a pre-specimen aperture is the optimum signal to use for i,, but this requires an aperture that is electrically isolated from the column. The first condenser aperture may not fully indicate the changes in probe current as it collects electrons emitted over a much wider angu- lar distribution.

When a low-loss spectrum is collected at each pixel there is no need for an external i, reference. (Although an i, reference can be used to remove probe current variations between component seg- ments of multiple-segment-per-pixel spectra.) When it is not practical to collect the low-loss region it is sometimes a valid approximation to use the shield current as an i, reference. In some situations i, may be estimated using the background before a low-energy major edge or the entire recorded spectrum.

With the current instrumentation a typical (x: 256, y: 256, E: 2048) spectrum-image with a low-loss spectrum (dwell time 25 ms) and a core- loss spectrum (dwell time 80 ms) taken at each pixel amounts to a 2.8 hour image (this includes a dead time of 50 ms per pixel). During this time it would not be uncommon for a specimen to drift 20 nm or more in the NIH VG HB501 STEM.

5. Processing implementation

The dark-field signal (idl) collected simulta- neously with the spectrum-image can be used directly for estimating i, and i, when there is negligible elastic contrast. A more general approach is to collect a reference dark-field image (i,, r(x, y)) without probe current variations. Another dark-field image (i,,(x, y)) is collected during the spectrum-image acquisition. The spectrum-image probe-current image (i,(x, y)) is obtained by dividing i,,(x, y) by idf,r(x, y).

The processing of spectrum-images is complicated. During the early developmental stages of this work, processing involved slightly rewriting pieces of code to tailor the analysis and acquisition software to each spectrum-image. The code has now been generalized to allow routine processing of quantitative images using LLS and MLS methods, thickness determination, peak shifts, and others. The complex nature of gener- alizing this diverse process was aided by using object-oriented software engineering techniques [19,20] and thus the majority of the currently used software was written in C-t+, the remaining parts in C and assembler.

4.2.3. Spatial-drift correction In contrast to the other drift correction proce-

dures, performing spatial-drift correction “on-the- fly” is not inferior to correcting after acquisition. Batch spatial-drift correction requires large amounts of data to be stored each time a test for drift is made, but this is typically a small fraction of the size of the spectrum-image. On-the-fly correction requires no additional storage space. Diffi- culties arise using batch correction because the dimensions of the processed image may be different from the unprocessed image and some pixels will have longer equivalent dwell times than others.

Processing a spectrum-image is usually done in several steps. After acquisition a spectrum-image viewer @IV) is used to inspect individual spectra within the image. The spectrum-image processor (SIP) can perform artifact-removal and drift-corrections throughout the image. Although this last step can be deferred until actual quantitative processing, doing so first and recording the results permits the user to verify the correctness of the artifact-removal and drift-corrections. This also allows the use of tools that require a corrected spectrum-image such as the spectrum-image calculator (SIC) and the spectra-combining tool. A feature-search tool can be used to determine what features exist within the spectrum-image and where. Further processing to create quantitative

58 J.A. Hunt, D. B. Williams / Electron energy-loss spectrum-imaging

images is done using the SIP. Examination of the SIP log files is used to inspect the quality of processing operations performed using the SIP.

Most spectrum-images are processed to obtain floating-point compositional image planes. These images are then analyzed using an image processor or further manipulated using the SIC. The large dynamic range typical of these images requires that image processing be performed in floating- point or, as a compromise, high-precision integer arithmetic. Important image detail can be lost due to precision limitations in processing on the most common image processors that use only eight bits per pixel. We have developed a floating-point image processor tailored to the needs of spectrum-imaging.

5. I. Spectrum-image processor

The function of the SIP is to process the desired spectra within the spectrum-image by invok- ing a series of processing units (PU). Typically it selects all the pixels individually and in the order acquired, although it is possible and often useful to process only portions of the spectrum-image.

A PU performs an analysis on data provided to it by the SIP. Current units include those listed in table 3. The output generated by a PU is stored to disk as a log file that contains an entry for each pixel. Many PUS maintain log files that contain information useful for debugging such as fit vari- ances or points where processing failed com- pletely. These “debugging” log files can be viewed as image planes and thus can be overlaid upon processed image planes in an image processor to flag points of erroneous processing.

Information is traded between PUS through the use of user-defined variables within the PU’s. A variable is a single value or an array of either integers or floating-point values. The initialization file for the SIP contains the list of PUS to be called and the names of the PU initialization files. The PUS are executed for each pixel in the order listed. A PU may be specified more than once; each time it is listed a PU object is created. A PU object has access to all the SIP variables. Each PU object has four functions that are invoked with the

appropriate message: initialize, process, skip pixel,

and terminate. When the SIP is started it loads the SIP initiali-

zation file. With this information it allocates memory for the variables and creates the PU objects. The SIP sends each PU object the message to initialize itself. Each PU object then loads its initialization file which contains information on what parameters and variables to use during processing, and what log files to create. The SIP begins processing by loading the data for the first pixel into the appropriate variables. The PU objects are then called in order to process the data. The SIP then loads the data for the next pixel and the procedure is repeated for all the specified pixels. If the SIP is not processing all the pixels in the image then a skip pixel message is sent to each of the PU objects for each of the pixels that will not be processed. This message simply causes a specified placeholder to be stored in each log file ensuring that the log files have the appropriate dimensions to be displayed as image-planes. When the processing is finished the SIP sends each PU

object a terminate message that allows the PU objects to close their files and store a summary of the processing in the SIP’s log file.

The PU process function returns a value that the SIP can test and base decisions upon using IF-THEN-ELSE and IF-THEN-GOT0 clauses within a SIP initialization file. If a test causes control to bypass a PU object then that PU object will be sent a skip pixel message instead of a process message. Many program control structures are possible and will be discussed elsewhere [12].

5.1.1. Snap-to function Often it is desirable to specify energies or chan-

nel numbers relative to a spectrum feature. The feature is located using the snap-to function and the desired channel or energy is calculated accord- ingly. The feature can be selected by searching a specified range for: the minimum or maximum, the maximum slope after a minimum, the maximum slope before a maximum, or the minimum slope after a maximum. A smoothing window can be used prior to the search. The centroid of Gaus- sian-like features can be located by a simplex fit of an ideal Gaussian.

J.A. Hunt, D. B. Williams / Eleciron energy-loss spectrum-imaging 59

Searching for maximum or minimum value within a region is the most simple algorithm and can work quite well if that region is smoothed first. However, in a noisy spectrum shot noise can seriously corrupt this method. A more robust and slightly more involved technique is to search for the abrupt change of slope from a core-loss threshold. The latter method works best for K- and L-shell edges, less well for higher-order shells. Perhaps the best method is the fitting of an element in the feature set to the spectrum using a method which varies both the energy-loss and feature height during the fit. If the feature includes only the first few electronvolts of the core- edge then the correlation between the reference feature and the spectrum feature will be high, even with significant plural scattering.

5.2. Spectrum-image viewer

The SIV allows inspection of the individual spectra contained within the spectrum-image. It allows the user to quickly examine spectral changes between pixels and determine what features need to be analyzed.

The spectrum displayed by the SIV can be manipulated in ways similar to that of an MCA. The horizontal and vertical scaling can be changed and energies of features can be determined. Thus the SIV is useful for determining processing parameters such as window energies and widths.

The SIV also allows convenient movement of the spatial-coordinate cursor around the spectrum-image. It is often useful to choose a line of the spectrum-image and examine the spectra from beginning to end in rapid succession. At several spectra per second a great deal of the spectrum- image can be inspected allowing fuller understand- ing of the processing demands and potential complications.

5.3. Spectrum-image calculator

The function of the SIC is to manipulate data structures that relate to spectrum-imaging in an interactive manner. The data structures that can be operands for the SIC are constants, spectra, image planes, and spectrum-images. Simple

mathematical operations can be performed such as those listed in table 4.

5.4. Feature-search tool

Often the analyst does not know a priori all of the spectrum-image features that can be imaged. Using the SIV to examine each spectrum in the spectrum-image is time-consuming and laborious. The feature-search tool rapidly searches through the spectrum-image and reports the energies of features found that pass a set of user-defined criteria. The search engine twice differentiates the logarithm of a smoothed spectrum. The user specifies the size of the differentiation window, the amount of smoothing to use, and the minimum peak size to consider. When a peak of sufficient size is found, its energy and location are recorded. The user is provided with a summary of this data, and can then use the SIV to inspect the located features.

5.5. Spectra-combining tool

Portions of the spectrum-image can be combined to create a single spectrum. This is done by loading a processed image plane or a dark-field or bright-field image into an image-processing package. Typically a thresholding or edge-en- hancement tool is used to highlight pixels of interest. An image plane is stored indicating from which pixels spectra are to be combined and this is sent to a program that performs the combina- tion. Additionally, individual files within the spectrum-image can be extracted for printing or loaded into a spreadsheet program or spectrum analysis package.

5.6. Processing times

It is difficult to quote meaningful statistics on processing times because of the variety of determining factors. The execution speed of the routines are generally very dependent on the size of integration or fitting windows and the amount of energy shift to be corrected. The processing power of the computer is also important. The times quoted in table 5 are for execution of the

60

Table 3

J.A. Hunt, D.B. Williams / Electron energy-loss spectrum-imaging

A list of currently implemented processing units (noteworthy SIP variables used by the PU object are denoted between angle bracken

and given descriptive names; the log files that can be created by the processing unit are also listed)

Processing unit Description Log files

Load Fills a variable from an image-plane or a spectrum-image.

Save Stores the value of a user-specified variable. A single-valued variable 1.

creates an image-plane. Array variables cause a spectrum-image to be

created.

Artifact correction

Energy-scale calibration

Current-scale calibration

Fourier-log deconvolution

Removes dark-noise and gain variation artifacts from (spectrum 1) and

stores result in (spectrum 2).

The energy-scale of (spectrum 1) is calibrated using a feature of known 1.

energy found using the snap-to function. A log file is created containing

the channel number of the feature. On failure the calibration for the

previous pixel is used.

Corrects (spectrum 1) for probe current shifts and stores the corrected

spectrum in (spectrum 2).

Removes plural scattering from (spectrum 1). which contains the 1.

low-loss region, and stores the results in (spectrum 2). See refs. [21-231

for details on the Fourier-log method.

Math

Linear least-squares

Fourier-ratio deconvolution Removes plural scattering from (spectrum 2), given (spectrum 1) which 1.

contains the low-loss region, and stores the results in (spectrum 3). See

refs. [21-231 for details on the Fourier-ratio method.

Elastic/inelastic tools Creates a bright-field image plane, an inelastic signal image plane, and a 1.

relative thickness (thickness divided by inelastic mean-free-path) image 2.

plane from (spectrum 1). The zero-loss peak is isolated by one of three 3.

methods: fitting a reference zero-loss to (spectrum l), estimating the 4.

counts in the (spectrum 1) zero-loss by parameterization of areas on

either side of the zero-loss center, or estimation of the counts in the 5.

(spectrum 1) zero-loss by integrating a specified window around the

zero-loss. If one of the former two methods is used and the zero-loss peak

is saturated then the zero-loss peak area can still be accurately de-

termined. The counts beyond the end of the (spectrum 1) can be

estimated using a LLS fit to the background continuing to infinity.

Performs mathematical operations on specified operands. These operands

can be spectra, portions of spectra, or single values depending on the

operation requested. See table 4 for the list of operations. When operands

are arrays (such as spectra), masks can be set restricting operations to a

specified range. Operations are easily added as needed.

The most common method for removing background below an edge is to 1. use a least-squares fit of Y(E) = A*E”( - r) to the background before 2.

the edge, where A, r are fitting constants, E is energy-loss and Y is the

height of the background [21]. The fit is performed on (spectrum 1) and 3. the background subtracted spectrum is placed in (spectrum 2). The edge is integrated over a specified region. Although the fitting windows are 4.

specified in the initialization file, this routine discards portions of the fitting window that seem to be inappropriate. This step corrects problems 5. associated with unexpected peaks occuring in the fitting region and 6.

selecting a window too close to the edge. Any of the window positions

can be specified to be relative to a feature found using the snap-to

function.

User-specified variable

Channel number con-

taining feature

Error: Deconvolution

failure

Error: Deconvolution

failure

Bright-field

Inelastic signal

Relative thickness

Error: Can’t find zero-

loss

Cl&square of LLS fit

Integrated peak area

Normalized cm-square of

fit First fitting window

channel number Last fitting window channel number

Fitting constant A

Fitting constant r

Table 3 (continued)

Processing unit

Multiple least-squares

J.A. Hunt, D. B. Williams / Electron energy-loss spectrum-imaging 61

Description Log files

MLS fitting of reference spectra is useful for separating peak overlaps, - _ and quantifying very small peaks [14,15]. The fitting method imple-

mented here is basically the generalized LLS technique described in ref.

[24]. It is typical to fit many reference spectra at once, for example: one

reference for the major and up to three of that reference convolved with

an additional plasmon (to take into account the effects of plural

scattering) and the first derivative of that major edge. In addition, there

will be the reference spectra of smaller edges. Fitting regions for

(spectrum 1) can be specified to be relative to a feature found using the

snap-to function.

Two logs files can be

created for each reference

spectra to be

Fit coefficient

Variance of fit coeffi-

cient

Feature tracking

Kramers-Kronig analysis

X-ray analysis

The energy of a feature found using the snap-to function is stored in a log

file.

Determines the real and imaginary parts of the dielectric function. Three

log files are created: one normal image-plane indicating the success of the

operation at each pixel, and spectrum-images for the real and imaginary

parts. More details can be found in refs. [21,25,26].

Only simple X-ray processing has been implemented here. Background

subtraction is performed by fitting a straight line between the average

values of two windows of background usually chosen to be on either side

of the X-ray peak.

Array FFT

* Array Reverse FFT

Array

* Value

Value, Value * Value

Table 4

Operations available in the math processing unit

Operands = destination

Array, Array

* Array

Available operations

+, -> *> / exponentiation

= (set equal to)

and, or, xor, not

Array, Value = Array

+, -1*,/ exponentiation

= (set equal to)

>, <, = = (test)

max, min

smooth

differentiate

integrate

integrate

log

+, -> *,/ and, or, xor, not

>, <, = = (test) max, min

exponentiation

log

1. 2.

1.

1.

2.

3.

1.

Energy of feature, or

prespecified default

value on error

Spectrum-image of real

part

Spectrum-image of imag-

inary part Error: Analysis failure

Integrated peak counts

SIP on a 25 MHz 80386 computer (DELL 325) with an 80387 math coprocessor. Generality and robustness have been the most important design criteria for the SIP and PUS. In several instances increased processing speeds would be possible by writing more specialized code for specific cases.

5.7. Data compression

The large amount of redundant information within the spectrum-image makes it an ideal candidate for data compression. There is an important tradeoff between storage space savings and data compression time. Clearly the compression and storage time for a pixel of data should be less than the time needed to collect the data, otherwise one of the major advantages of spectrum-imaging is compromised. Only lossless data compression was considered, i.e. methods that are capable of restoring exactly what was compressed. Lossy compression methods can only restore an approximation of the original data but can have higher compression factors. We believe it is important to use a lossless method.

62 J.A. Hunt, D.B. Williums / Electron energy-loss spectrum-imaging

Table 5

Execution times for the processing of a sample (x: 128, y: 128,

E: 1024) spectrum-image using a 25 MHz 80386/387 computer

Operation Execution time

(mm)

Artifact correction and energy

calibration using up to 2

12

features; corrected spectrum-image

is stored.

Fourier-log deconvolution;

corrected spectrum-image is

stored.

45

LLS (1 edge, 50 channels to fit,

100 channels to integrate)

11

MLS (7 reference spectra,

100 channels to fit)

32

BF/inelastic image/

relative thickness image

6

Plasmon-energy image

Kramers-Kronig analysis; the

complex dielectric-response

function is stored.

4

55

X-ray image (1 peak) 1

The processing times will vary greatly depending on the nature

of the data being processed as well as the parameters chosen

for the individual operations. Many of these times could be

reduced significantly by further specializing the processing

units.

A quick method for compression stores only the differences between adjacent values. For this method to be space efficient the maximum difference in adjacent channels must be significantly smaller than the values in the channels. This is not necessarily the case in EELS or X-ray spectra. Typical compression attained using this method on low-loss spectra were 82% (of the original data size) and 67% for core-loss spectra. (The “typical” spectrum was 0.3 eV/ch, 1024 channels, maximum value in the spectrum - 15 000.)

More significant savings can be realized by modifying the latter method to divide a spectrum into several regions, each compressed separately. The algorithm scans the spectrum for large jumps between channels and creates separate regions around these jumps. Most spectra are divided into five to ten regions and are compressed to 35% of

the original size. On a 25 MHz 386 processor the compression algorithm requires under 6 ms per spectrum. Decompression requires under 2 ms. These time requirements are minimal - no dead time is generated during acquisition and a 128 x

128 pixel spectrum image will require about 30 extra seconds to process. The details of this algorithm will be published elsewhere [12].

5.8. The future of spectrum-imaging

The system described in this paper collects EELS and X-ray data as fast as the spectrometers can transmit it. However, this system would be inadequate for some ultra-fast readout CCD EELS spectrometers that will eventually reach fruition. Such a system will require a huge amount (16 M or more) of fast memory (perhaps in a frame grabber) to collect (x: 512, y: 512) spectrum- images in less than five seconds. This would be particularly useful for imaging catalysts and bio- logical specimens that are extremely sensitive to electron radiation.

Spectra collected in the aforementioned system could potentially have only 1 or 2 counts per channel. Fortunately the CCD systems can be biased and cooled so they exhibit no significant dark noise. With an image intensifier placed before the CCD array it would be capable of counting single electrons. The spectra would require new methods of quantification. The most obvious method would be to combine spectra from pixels selected from a single-electron counted dark-field image in an image processor. The combined spectra would have better statistics than a single point and could be analyzed using standard techniques.

Further experiments may include surface and interfacial plasmon imaging, EXELFS and ELNES imaging, more complex dielectric response imaging, and three spatial dimension spectrum-images.

Quantitative X-ray maps are routinely acquired in many labs and are less complicated to process than EELS maps. Processing of situations that require peak-overlap separation or atomic number, absorption and fluorescence (ZAF) corrections could be handled more accurately by spectrum-imaging. The techniques described here are directly applicable to such cases even though only

J.A. Hunt, D.B.

rudimentary X-ray spectrum-imaging performed in this study.

6. Results and examples

6.1. xyE spectrum-images

Williams / Electron energy-loss specwtm-imaging 63

has been

The processed images in the following examples include a “ palette” image that shows a linear

progression from black to white. The black value and the white value reported for each image correspond to the image values that are displayed as all black and all white respectively. The palette image is provided so images can retain their quantitative nature despite changes from reproduction processes. For example, the shade of grey half-way between the black side and the white side corre- sponds to 50% of full scale. Pixels with this shade of grey indicate a value of (white value - black value) X 0.50 + black value.

Fig. 3. Processed image planes of a spectrum-image from a beta cell showing correction of current-drift by ratioing the N plane with the low contrast planes of C and 0.


Table 6 Scaling factors for freeze-dried beta cell image planes

Image

A

B

C

D

E

F

G

H

1

Description

C-uncorrected

O-uncorrected

N-uncorrected

C-corrected

O-corrected

N-corrected

Probe current

Image E smoothed

Palette

Black value White value

0 1.006E6

0 4.302E3

0 3.155E3

7.259E5 1.011E6

2.072E3 4.310E3

0 3.281E3

0 100

2.354E3 4.086E3

0 100

Units

cts/pixel

cts/pixel

cts/pixel

cts/pixel

cts/pixel

cts/pixel

%

cts/pixel

%

Fig. 4. Processed image planes of a spectrum-image of myotube cells. See text for details.

J.A. Hunt, D.B. Williams / Electron energy-loss spectrum-imaging

Table I

Scaling factors and errors for myotube image planes

65

Image Description Black White c, c ns.tw 6 “SJni” c ns.max Units

value value

A C 1.46e3 3.52e3 20% 1.60% 1.52% 5.91el atoms/nm2

B Ca 0 2.02e2 20% 2.11% 2.01% 4.69eO atoms/nm2

C N 0 1.41e2 20% 2.53% 2.40% 4.09eO atoms/nm2

D 0 0 6.81e2 20% 1.15% 1.09% 7.90eO atoms/nm2

E Inelastic 69.7% 100% 20%

F Effective Z 6.01 8.23 20%

G e- MFP 104.0 114.0 20% 6.67% nm

H Thickness 18.9 27.2 20% 6.67% nm

I Palette 0 100%

6.1.1. Errors Error estimation for quantitative EELS imaging

is complicated. In general, these errors will be different for each pixel of each image plane. They typically depend on counting statistics, artifact removal, background removal, and cross-sections. The qualitative nature of these images is predomi- nantly affected by nonsystematic error which

manifests itself as a relative error between pixels (precision). Systematic errors, e.g. those that affect all pixels in the same manner (accuracy), tend to be the dominant error source in the EELS spectrum-imaging performed to date. Sources of systematic error include cross-section estimates, thickness parameterization, poor background modeling using LLS, or differences between the reference feature and the unknown feature when using MLS. Major nonsystematic error sources

include signal noise and detector noise. Further relative error between pixels can be introduced by actual changes in an elemental partial cross-section due to bonding changes, thickness variations causing differences in plural scattering, and large amounts of noise in small LLS fitting regions.

If we claim to have quantitative images then estimates of error must be supplied. The most complete method to do this is to provide an error image plane for each quantitative image plane.

Generally, this tends to produce a great number of images with little interesting contrast. Since this is the case for the compositional images in this paper we instead report for each image plane an estimate of systematic error (es), typical non-systematic

error ( e ns,typ ), and maximum and minimum nonsystematic error (en,,,,, and E,, min). The non-systematic errors for the thickness image planes were

Fig. 5. Thickness map of myotube cells.


not calculated. The cross-sections used for the compositional images in this paper were calculated using SIGMAK and SIGMAL [21] and thus cs is + 20% [27]. The thickness images were created using a parameterization method that is assumed to have an error of f20% [28] provided the composition is exactly known. The reported values of z, for these images are higher due to uncertainties in composition.

6.1.2. Freeze-dried beta cells Figs. 3A-3C are processed image planes of an

(x: 128, y: 128, E: 1024) spectrum-image of a beta cell showing carbon, oxygen, and nitrogen without corrected beam current drift. Figs. 3D-3F show this artifact removed by ratioing with the probe current image 3G. The latter image ap- proximates the spectrum current i, and was created by smoothing image 3A only in the horizontal direction. The analysis method was LLS with energy-drift and spatial-drift corrections. Using SIGMAK to determine the appropriate cross-sections, the maximum values in the oxygen and nitrogen planes correspond to approximately 19 k 3.8 at% and 11 f 2.2 at% respectively. Table 6 contains scaling information.

6.1.3. Freeze-dried myotube cells Figs. 4A-4D are processed image planes of an

(x: 128, y: 128, E: 1024) spectrum-image of myotube cells showing carbon, calcium, nitrogen, and oxygen. Table 7 contains scaling information. The compositional analysis method was LLS with energy-drift correction. Fig. 4E is an inelastic image created by summing all the counts in the spectrum and subtracting the zero-loss.

The SIC was used to calculate a thickness map. A relative-thickness image-plane was calculated (not shown) using the inelastic image and the beam current. An effective atomic number at each pixel (image 4F) was calculated and then the inelastic mean-free-path (image 4G) was estimated at each pixel. The latter image plane was multiplied with the relative thickness image-plane yielding a thickness image-plane (figs. 4H and 5).

6.1.4. CuBeCo An (x: 128, y: 128, E: 2048) spectrum-image

was acquired from the edge of an electropolished foil of commercial Cu-1.85wt%Be-0.2wt%Co. Each pixel contained a spectrum from the region

3ooa I

*c&J . . . . . . . . . . . Spectrum-Image Pixel (26,lO) . . . . . . . . .._...............................................................

\

,500. ...................................................................

,m. ................. ................................

500

i i

.

\ geCK’ . . . . . . . . . . . . .._. .__ ___ __ ,.. . ._ / 0 -50 0 50 100 150 2uo

Energy Loss (eV)

Average of pixels (103,20) - (105,20)

%o 500 600 Ensq$ks (&‘I

8cil 900 11 10

Fig. 6. Core-loss edges that are mapped in fig. 7.

J.A. Hunt, D.B. Williams / Eleciron energy-loss spectrum-imaging 61

- 5 eV to 200 eV (0.2 eV/ch), and the region 440 eV to 1464 eV (1 eV/ch). The SIP was used to correct for artifacts, energy-drift, and current-drift.

The spectrum-image was acquired on the NIH VG HB501 at moderate magnification (13000 X ) and thus there was an energy-scale shift across the

Fig. 7. Processed image planes of a CuBeCo spectrum-image. See text for details.


Table 8

Scaling factors and errors for CuBeCo image planes

Image Description Black White CS c ns.typ cns,min ~ns.max Units

value value

A CU 0 3.30e3 20% 5.58% 3.09% 8.22el atoms/nm2

B co 0 1.84e3 20% 6.04% 3.32% 5.OOel atoms/nm2

C Be 0 7.32e3 20% 3.10% 1.66% 1.05e2 atoms/nm2

D 0 0 1.55e3 20% 4.29% 2.30% 3.08e2 atoms/nm2

E Ti 0 3.87e3 20% 10.0% 5.34% 5.57e3 atoms/nm2

F V 0 2.70e2 20% 19.3% 10.0% 2.51el atoms/nm2

G Cr 0 3.30e3 20% 3.10% 1.77% 4.39el atoms/nm2 H Fe 0 1.21e2 20% 9.92% 5.32% 5.57eO atoms/nm2

I Effective Z 0 28.4 20%

J e- MFP 73.3 100.0 20% 6.45% nm

K Thickness 0 44.4 20% 6.45% nm

L Palette 0 100%

image of 1 eV in the x-direction and 4 eV in the y-direction. The current-drift correction was made by normalizing each channel using the estimated total spectrum intensity. The low-loss spectrum

was acquired with the zero-loss intentionally saturated so there were sufficient counts in the core-loss edges to analyze. The zero-loss is recon- strutted by fitting a reference zero-loss to the

Fig. 8. Thickness map from CuBeCo spectrum-image.

J.A. Hunt, D. B, Williams / Electron energy-loss spectrum-imaging

Table 9 Oxygen content for regions in fig. 9

Image Min. 0 content

(atoms/nm *)

Max. 0 content (atoms/nm ‘)

Pixels 1

A 3.03E2 6.07E2 63

B 6.08E2 1 .OOE3 128

C l.OOE3 1.36E3 133

D 1.36E3 1.55E3 72

unsaturated channels of the high-energy side of the saturated zero-loss. The zero-loss exceeded the dynamic range of the array by as much as 20 times in areas of the spectrum-image where there was no specimen. The errors associated with this procedure are typically less than a percent.

I, I I, I I I I I

500 520 540 560 560 Energy loss (eV)

10

The edge-search tool reported the presence of Fe, 0, Cr, and Ti in addition to the expected components of Cu, Be, and Co. So these elements were imaged with the SIP using LLS. Examination of the &i-square log file of the 0 fit revealed

regions with a very poor background fit. These pixels were examined and were shown to contain

Fig. 10. Spectra averaged from regions indicated in fig. 9.

V. The VL,, (513 eV) was not detected by the edge-search tool because of its proximity to the 0 K (532 ev). The SIP was used to map V and 0

Fig. 9. (a-d) Areas of oxidized Be precipitate from increasingly smaller radii selected using an image processor. (e) Detached section

from CuBeCo oxygen plane shows area used in a-d.


1 /y

I I I

20 40 60 I I I

-3.0 nm

Energy loss (ev)

, I I

5 555 5

Energy loss (ev) 5

Fig. 11. Selected spectra from a xE spectrum-image of a ZrOJNiO interface. (A-F) Low-loss region. (A’-F’) Oxygen K edge

Distance from interface for each spectrum is indicated.

J.A. Huni, D. B. Williams / Electron energy-loss spectrum-imaging 71

Electron Dose (e-/A’ “) 0 50 100 150 200 250 300

0.20 ““““““~“““rI,~-I~~,LJI~,,~‘~III,II~I’,~,,~,,~(’~~~,*(~U -.

Oxygen Mass Loss in Formvar due to Electron Radiation

Eo.05 - . . * . . . **.

‘*..,. . ..** .._**

. .-_.*,....*,*.. 04 . . . 0.00 II,,T,r,,,,,,,,,,,,,,,,,,,‘,,,‘,,,,,,,,,,,,,,,,,,,

0.00 2.00 4.00 6.00 8.00 10.00

Duration of Exposure (s)

Fig. 12. (a) tE spectrum-image shows decaying OK edge in Formvar due to radiation-induced mass-loss. (b) Quantitative analysis of the 0 K edge.


by MLS fitting of reference spectra to unravel these edges. Sample spectra from this spectrum- image showing some of the edges mapped are shown in fig. 6. The processed image planes are shown in figs. 7A-7H. Table 8 contains scaling information. The effective atomic number, inelastic mean-free-path, and thickness planes shown in 71-7K and 8 were calculated as described for the

myotube images. Fig. 9E shows the CuBeCo oxygen plane with

an oxygen-rich section detached. An image processor was used to select pixels within this section based on oxygen content. See images 9A- 9D and table 9. The spectra-combining tool was used to combine the spectra associated with pixels in the images 9A-9D. The summed spectra were divided by the number of contributing pixels to produce the spectra in figs. lOA-1OD.

6.2. Spectrum-image variants

6.2.1. xE

An xyE spectrum-image is often not necessary as in the case of an (x: 100, E: 4096) spectrum- image of a ZrO,/NiO interface. Figs. lla and llb show selected spectra from this spectrum-image. The dwell time per pixel was l-2 s for each core-loss spectrum and 25 ms for each low-loss spectrum. The probe was smaller than 1 nm and was stepped at 0.4 nm intervals across the inter-

face.

6.2.2. tE Fig. 12a shows a graph of a (t: 200, E: 1024)

(time-resolved) spectrum-image. Only the region around the 0 edge and 31 time-slices are shown. As Formvar is beam-damaged its concentration of 0 drops rapidly to a steady-state level. This mass- loss is quantified in fig. 12b. The analysis method was LLS. If this experiment was performed with the identical dose rate using serial EELS then the first spectrum with enough counts to analyze would reveal the steady-state concentration of 0, not the original concentration. es is better than +20%, f,, is better than fl%.

7. Summary and conclusions

Quantitative EELS imaging is a powerful method for the spatial interpretation of elemental, chemical, dielectric, and other information. Spec- trum-imaging allows these maps to be created by sophisticated and time-consuming processing techniques. Spectrum-imaging is shown to have

clear advantages over the traditional on-the-fly- processing imaging techniques. Examples are shown in this paper that could not have been processed on-the-fly, such as the CuBeCo spectrum-image. - Processing individual EELS spectra in an image on-the-fly is often insufficient for quantitative imaging. The capability to process the spectrum- image multiple times is gained by saving the entire spectrum-image. - Erroneous fitting and unexpected acquisition problems that would cause on-the-fly-processing errors can often be overcome through modifications to the processing parameters or techniques without reacquiring the image. - Edges whose existence were not predicted prior to acquisition can also be processed. - Processing time need not be limited to acquisition time, and thus complicated and robust analysis routines may be used. MLS routines in place of linear least-squares (LLS) and area ratio techniques can greatly improve accuracy and detectability. Other time-consuming analysis methods such as isolating chemical effects and dielectric information can be employed. Processing time for such routines most likely far exceed the desired acquisition time, particularly when specimen drift, beam sensitivity, and microscope operating costs are concerns.

The algorithms used to generalize the process of EELS spectrum-image analysis are directly applicable to automating standard EELS analysis. For example, in order to perform a quantification routine 65 536 times in a spectrum-image, that routine must be generalized sufficiently to handle the myriad pitfalls that can occur throughout processing the image. Utilization of these routines in an EELS analysis package could assist in mak- ing EELS a “ turn-key” technique approaching the

J.A. Hunt, D. B. Williams / Electron energy-loss spectrum-imaging 13

ease with which X-ray microanalysis is currently performed.

Acknowledgments

The authors wish to thank Dr. Richard Leap- man for frequent and invaluable discussions, Dr. Brian Andrews for providing computer hardware, the National Science Foundation for their support of this work (grant No. DMR 8905459) and Dr. Vinayak Dravid for providing the NiO-ZrO, specimen.

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