Analysis of three-dimensional SIMS images using image cross-correlation spectroscopy

SURFACE AND INTERFACE ANALYSIS, VOL. 26, 188È194 (1998)

Analysis of Three-dimensional SIMS Images usingImage Cross-correlation Spectroscopy

M. Srivastava,1 N. O. Petersen,1 G. R. Mount,2 D. M. Kingston2 and N. S. McIntyre1,21 Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada2 Surface Science Western Faculty of Science, The University of Western Ontario, London, Ontario N6A 5B7, Canada

Three-dimensional (3D) SIMS images of secondary ion distributions in a solid volume can be produced from astack of individual images acquired sequentially at di†erent depths during depth proÐling of the solid. While it isoften possible to obtain visual correlations of large-scale features that occur in several images in the stack, thecorrelation of less-obvious features requires a more mathematical approach. We present here two cases whereimage cross-correlation spectroscopy (ICCS) can be used to clarify the presence or absence of organized structurein a 3D depth proÐle. In one example, the images of deuterium distribution in a zirconium oxide thin Ðlm wereconÐrmed to exhibit order over a series of images, thereby suggesting the existence of continuous pores in thematerial. In a second example, the apparent clustering of gold distributions in a 3D proÐle of an arsenopyritemineral was shown to be uncorrelated and likely an artefact of data collection. 1998 John Wiley & Sons, Ltd.(

Surf. Interface Anal. 26, 188È194 (1998)

KEYWORDS: SIMS; secondary ion mass spectrometry ; imaging ; 3D

INTRODUCTION

The high selectivity of secondary ion mass spectrometry(SIMS) has been employed increasingly in resolving thespatial distribution of elements in solids. Information inboth the in-depth (z) direction and lateral (x and y)directions is available from SIMS analysis obtainedusing a Cameca ion microprobe. Several researchers1h3have combined the information into volumetric (three-dimensional or 3D) representations that provide aunique view of the spatial distributions even for low-concentration elements.

In the x- and y-directions of the volume, the spatialresolution is determined by the instrumental resolutionand the resolving power of the digital system used tostore the image. For images collected in the microscopemode, the ultimate dark-space image resolution isseldom better than 1lm. By contrast, in the z-directionthe resolution is much better, and is limited only bysputter-related e†ects and the frequency of image collec-tion. (In some cases, z-direction resolutions as low as 2nm have been possible based on intensity changes oftwo standard deviations.)

If an intense feature is mapped whose dimensions aresigniÐcantly larger than the resolution limits describedabove, there is no difficulty in mapping its coordinatesin 3D volume. However, if the feature dimensionsapproach those of the resolutions or if the net intensitydeÐning the feature above background is low, then sta-tistical tests are required to analyse the signiÐcance ofthe feature. This paper describes the use of image corre-

* Correspondence to : M. Srivastava, Department of Chemistry,Faculty of Science, The University of Western Ontario, London,Ontario N6A 5B7, Canada.

lation spectroscopy (ICS)4 and image cross-correlationspectroscopy (ICCS)5 to identify the statistical signiÐ-cance of features acquired in 3D SIMS proÐles. The useof these methods is demonstrated for image volumeswhere a positive identiÐcation of signiÐcance could bemade and where no statistically signiÐcant feature couldbe identiÐed.

Image correlation spectroscopy (ICS) and imagecross-correlation spectroscopy (ICCS) belong to agroup of techniques described as Ñuctuation spectros-copy. Fluctuation spectroscopy refers to those tech-niques that study the spontaneous random Ñuctuationsin a system variable to provide valuable information onvarious parameters of the system.6,7 Correlation func-tions provide a mathematical means of expressing howclosely two variables are related over a certain interval(in this case, depth). The technique of ICCS is based onthe coincidence of a measured signal at identical spatialcoordinates when comparing pairs of images taken atdi†erent depths in the volume. The amplitude of thecross-correlation function will reveal the average depthpersistence of Ñuctuations at particular positions in theimage. Analysis of the rate and shape of decay of theamplitude of the cross-correlation function with depthcan conÐrm the existence of a structure that extends toa depth equivalent to the distance sputtered by the ionbeam between image accumulations. In addition, ICCScan provide statistical conÐrmation of the coincidenceof two di†erent elements within the same volume.

This paper presents two examples of 3D imageanalysis where cross-correlation is used to conÐrm orrefute the existence of extended structure in the z-direction of a 3D volume. In one of these examples, therelationship between elemental distributions in thevolume was also analysed.

The Ðrst example involves analysis of the 3D depthproÐle of hydrogen (as deuterium) that is distributed

CCC 0142È2421/98/030188È07 $17.50 Received 21 July 1997( 1998 John Wiley & Sons, Ltd. Accepted 17 October 1997

3D SIMS IMAGES USING IMAGE CROSS-CORRELATION SPECTROSCOPY 189

within a layer of zirconium oxide on the surface of aZrÈNb alloy8 following its high-temperature corrosionin vapour. In Fig. 1 the intensity cross-sections ofD2OZrO~ and D~ are shown for one such reaction. Thethermal-scale ZrO~ intensity is quite even within theoxide and decreases sharply at the interface with theunderlying alloy. The D~ intensity, representing D2Odistribution in the oxide, shows that has pen-D2Oetrated the oxide to within 1 lm of the oxide-metalinterface. Even within this intervening oxide layer, it isnot clear if some is penetrating portions of theD2Ooxide. The signal roll-o† in this region could result from

penetration of some pores and Ðssures in theD2Ooxide ; alternately, the signal roll-o† could be the resultof ion beam knock-in processes. Thus, the macroscopicdepth proÐle provides little information on the existenceof possible “breakthroughÏ of through the oxideD2OÐlm adjacent to the interface.

A plan-view image of the D~ distribution in this par-ticular oxide region is shown in Fig. 2. Within this 25lm Ðeld image, D~ appears to be concentrated inpockets of 2È4 lm in diameter. No evidence of obviouslateral interconnecting porosity is observed. A 3Dvolume rendering of a stack of D~ images taken in thisregion of the oxide9 is shown in Fig. 3. Such rendering

would be expected to allow an easier visual correlationof image features in adjacent slices. In fact, some evi-dence of one or two continuous connections of D~ canbe discerned in the oxide region adjacent to the inter-face (see arrows). However, such evidence can hardly beconsidered as statistical proof of local porosities in theoxide. A more quantititative analysis of structural corre-lations can be made by ICCS analysis of the imagesacquired at di†erent depths in this oxide.

The second example where ICCS is used in theanalysis of elemental distributions involves the measure-ment of the size of “invisibleÏ gold particles in the 3DSIMS depth proÐle of an arsenopyrite mineral grain.Invisible gold is so called because it has been impossibleto distinguish individual particles of native gold or thegold-containing compound using conventional micro-scopic methods.10,11 In Fig. 4(a), SIMS image distribu-tions of Au~ intensities are displayed for a mineralsample known to contain invisible gold, on the basis ofprevious mineralogical examination. The image per-spectives shown are a 2D display that encompasses aplan-view image of the topmost slice of the image stack,along with edges of all images taken further into thesample (a “pseudo-3DÏ image). In addition, another planview of the Ðfth image into the sequence is shown

Figure 3. Volume-rendered 3D SIMS image of the DÉ distribution within a thin-film oxide on zirconium alloy. The outside of the oxide andthe oxide/metal interface are outlined in white lines. The oxide region immediately adjacent to the metal interface is characterized by a lowdensity of D-containing regions, some of which appear to be connected (see dark arrows). The D-containing structure below the interface isa solid deuteride contained within the metal.

( 1998 John Wiley & Sons, Ltd. SURFACE AND INTERFACE ANALYSIS, VOL. 26, 188È194 (1998)

190 M. SRIVASTAVA ET AL .

(depth 100 nm). All images, as displayed, show evidenceof Au~-containing regions that are 1È2 lm in diameter.This could suggest the presence of gold-bearing par-ticles of this size ; alternately images of this size could becaused by “bloomingÏ of the channel plate detector atthis location, as the result of a relatively high intensitysignal. Even a relatively weak submicron source of sec-ondary ions would generate an image with a pixel sizeequivalent to the instrument lateral resolution (D1 lm).

One method to determine a limiting size to themicroscope source of intensity is to take advantage ofthe depth resolution, which is much higher in the z-direction than in the lateral plane. Thus, ICCS could beused to measure whether a signal at a particular loca-tion can be traced into the next image acquired, therebyproviding an estimate of the maximum possible particlesize.

EXPERIMENTAL

Three-dimensional SIMS depth proÐles were takenusing a modiÐed Cameca IMS 3f whose performanceand imaging system have been described previously.3 A600È1000 nA caesium primary ion beam was used inboth studies, with a net energy of 14 keV. In the arseno-pyrite specimens, a total of 48 images were accumulatedfor each of four di†erent secondary ions. Using pro-Ðlometry, it was determined that the depth sputtered foreach cycle of four elemental images was 20^ 5 nm. Inthe case of the depth proÐle study in the oxide on zir-conium, the distance between each cycle of two elemen-tal images (D~ and ZrO~) was determined to be 10 nm.

The zirconium oxide thin-Ðlm specimen was takenfrom a corrosion study of surfaces of ZrÈ2.5% Nb alloypressure tube supplied by Ontario Hydro Technologies.The specimen had been in Pickering NGS for a periodof several years in contact with vapour at 300 ¡C.D2OThe arsenopyrite specimen containing invisible goldwas supplied by American Barrick Resources.

The ICCS calculations were done on a massivelyparallel processor (MasPar MP-2) at the UWO Com-puter Centre.

THEORY OF IMAGE CROSS-CORRELATIONSPECTROSCOPY (ICCS)

Image cross-correlation spectroscopy entails calculationof the normalized cross-correlation function, g, f),g

ij(m,

which is deÐned by

gij(m, g, f) \ Sdi(x ] m, y ] g, z] f)dj(x, y, z)T (1)

where

di(x ] m, y ] g, z] f)

\ i(x ] m, y ] g, z] f) [ Si(x, y, z] f)TSi(x, y, z] f)T

(2)

and

dj(x, y, z) \ j(x, y, z) [ S j(x, y, z)TS j(x, y, z)T

(3)

where j(x, y, z) \ intensity at a particular location in aSIMS image collected at depth z and I(x, y,z] f) \ intensity at the same location in the sameSIMS image collected at a di†erent depth z] f. Theangular brackets in the equations indicate an integra-tion over all space.

Computationally, the calculation of a cross-correlation function is done by using the Fourier trans-form method.12 This is done by calculating the inverseFourier transform (F~1) of the product of the Fouriertransform of one image F[I(x, y, z] f)] by thecomplex conjugate of the Fourier transform of the otherimage F*[ j(x, y, z)]. In order to get the normalizedcorrelation function g, f), the result from above isg

ij(m,

divided by the product of the average intensities fromeach original image and subtracting the number 1, asgiven by Eqn. (4)

gij(m, g, f)

\F~1[F[i(x, y, z] f)]]F*[ j(x, y, z)]][Si(x, y, z] f)TS j(x, y, z)T]

[ 1 (4)

If I and j represent the same function (same image), thecross-correlation function will contain the same infor-mation that is inherent in the autocorrelation functiong(f, g), and we get the maximum cross-correlation pos-sible (because we are comparing an image with itself).Recently, image correlation spectroscopy4 has beendeveloped, which involves autocorrelation analysis of a2D spatial record of intensity. In this case, the 2D inten-sity records are the SIMS images. Image correlationspectroscopy involves calculation of an autocorrelationfunction g(m, g) from the intensity data j(x, y), stored aspixels comprising the image. The 2D autocorrelationfunction is deÐned as

g(m, g) \ Sdj(x ] m, y ] g)dj(x, y)T (5)

The signiÐcance of the autocorrelation function is that,by deÐnition, the variance of the random Ñuctuations inthe intensity function is equal to the zero-lag value ofthe correlation function found here in the limit where mand g vanish, i.e. variance dj(x, y)\ g(0, 0). From sta-tistical mechanics, it is known that the variance of con-centration Ñuctuations is inversely proportional to theaverage number of sources of a particular secondary ionin the volume being observed. Hence, the density of thedetected secondary ions can be measured by the magni-tude of g(0, 0), i.e. g(0, 0)\ 1/N, where N is the numberof particles. Thus, an analysis of the zero value of theautocorrelation function of the 2D spatial record ofintensity (bright spots) is a direct measure of the densityof the secondary ions.

RESULTS AND DISCUSSION

Autocorrelation analysis

For the Ðrst example in which distribution in zir-D2Oconium oxide was studied, only the D~ image stack wasanalysed. In the case of the study of invisible gold dis-tribution in arsenopyrite, the intensity stacks for thenegative secondary ions S~, Fe~, As~ and Au~ wereanalysed. Autocorrelation analysis was performed on all

SURFACE AND INTERFACE ANALYSIS, VOL. 26, 188È194 (1998) ( 1998 John Wiley & Sons, Ltd.


image stacks to obtain g(0, 0), average intensity SIT andthe particle density (number of particles per correlationarea) N at all the depth levels. It was found that for thesystems S, Fe, As and Au, the values of g(0, 0), SIT andN were almost independent of depth for an individualsystem. Figure 5 shows an example of an autocorrela-tion function for the element iron (Fe) calculated byEqn. (4). Figure 6 shows an example of the variation ofthe g(0, 0) value as a function of depth for the elementsulphur (S). As can be seen from Fig. 6, the values arefairly constant, indicating that the density of sources ofS~ does not change much as the volume is penetrated.This was also the case for Fe, As and Au. The averageparticle densities calculated per square micrometre forall images are tabulated in Table 1.

As can be seen from Table 1, the g(0, 0) valueincreases with increasing mass number or, in otherwords, the number density of particles (N) decreaseswith increasing mass number (most for S, least for Au).Because no matrix correction of signal intensity hasbeen made, there is no scientiÐc signiÐcance to this par-

Table 1. Correlation values for the arsenopyrite study

Ion detected g(0, 0) N (per lm2)

Sulphur (34SÉ) 0.0226 À4 1.39 À2

Iron (56FeÉ) 0.088 À1 0.357 À5

Arsenic (75AsÉ) 0.106 À1 0.295 À2

Gold (197AuÉ) 1.78 À1 0.0170 À1

Figure 6. Plot of the amplitude of the autocorrelation functiong(0, 0) for the SÉ distribution as a function of depth z.

ticular measurement, but it does illustrate that intensityand density measurements may be made by this pro-cedure.

In the case of the D~ SIMS images obtained for thezirconium oxide thin Ðlm, the amplitude of the autocor-relation function g(0, 0) decreases with depth until theeighth layer and then increases drastically as the ninth

Figure 5. Plot of the raw autocorrelation function data calculated for the FeÉ distribution in the arsenopyrite specimen using Eqn. (4), as afunction of spatial lag in the two independent SIMS image directions.



layer is reached. The decrease in g(0, 0) value indicatesthat the number density of secondary ions increasesuntil the eighth layer is reached and then shows adrastic decrease. The average intensity value SITdirectly represents the number of ions.

Cross-correlation analysis with depth

For each image stack, each particular image was cross-correlated with others in the stack as a function ofdepth. For example, the image at depth 1 was corre-lated with the image at depth 1, i.e. (1] 1) and theimage at depth 1 with the image at depth 2 (1 ] 2), etc.

For the image stacks of Au~, As~, Fe~ and S~ noevidence of correlation is found. Figure 7 shows anexample of a cross-correlation function calculated forthe element Fe between depth 1 and depth 2. If a corre-lation were present, one would expect a narrow cross-correlation peak at the centre, but only a broad peak isseen representing longer range intensity variations. Forthese elements it is concluded that the particles aresmaller than the layer-to-layer distance. Because, in thiscase, each layer has been determined to be 20^ 5 nm indistance from the subsequent layer for the same mass,the average diameter of the invisible gold particles isinferred to be less than this. Recent studies10 by high-resolution electron microscopy have suggested that Auis randomly distributed in solid solution in the arseno-pyrite lattice. Thus, the appearance of the particles ofÐnite size in Fig. 4(a) is likely to be the result of bloom-ing in the channel plate detector.

The analysis of deuterium distribution with depth inthe zirconium oxide gave a di†erent trend. Correspond-ing cross-correlated images for D~ as a function ofdepth show that the cross-correlation function decreasesas depth increases. This is due to a decrease in the g(0,0) value, as was shown above in the autocorrelationanalysis. Analysis of the rate and shape of decay of thecross-correlation function with depth provides informa-tion on the likelihood of co-existence of the same signalat two di†erent depths. Figure 8 shows a plot of thedecay in amplitude of the cross-correlation functionwith depth for set 1, where the image at depth 1 wascross-correlated consecutively with images from depth 1to depth 8. One observes that the correlation betweenimages at depth 1 and depth 2 is very strong, showingco-localized distributions. Furthermore, a gradual decayof cross-correlation is found for the distribution atdepth 1 which those further down in the layers. Corre-lation is completely lost at layer 19. A similar trend isseen for the other sets of cross-correlations.

Cross-element cross-correlation

In the case of the arsenopyrite image, a cross-correlation was also performed between images for dif-ferent secondary ions at very similar depths, i.e. within5È10 nm (see Fig. 9). No evidence for systematic overlapof any of the sets was found, even though such corre-lation was sought over a stack of 48 image slices. Cer-tainly, on a much larger scale, there are obvious

Figure 7. Plot of the raw cross-correlation function i) calculated for the FeÉ distributions at depths 1 and 2.gi j(y,



Figure 8. Plot of decay of the amplitude of the cross-correlationfunction 0) with depth determined for the distribution of DÉg

i j(0,

in this film of zirconium oxide on the zirconium alloy.

correlations between Au and As distributions, as seen inthe images in Fig. 4. These illustrate the known prefer-ence for siting of invisible Au in arsenopyrite.13However, on a submicron scale there is little evidence of

preferential overlap of any of the four secondary ions.The lack of correlation between distributions of thesame secondary ions in adjacent levels suggests that theinvisible gold particles must be \20 nm in averagediameter.

For the D~ distributions in the zirconium oxide thinÐlm, a clear correlation is found extending over 10image slices. This would represent a depth of 100 nm inthis oxide. This strengthens the evidence that submicronporosities do exist in this part of the oxide Ðlm as sug-gested by Fig. 3.

CONCLUSION

(1) Image cross-correlation has been shown to be e†ec-tive in conÐrming a spatial relationship between fea-tures in images taken at di†erent depths in a 3DSIMS depth proÐle of water in a zirconium oxidethin Ðlm.

(2) In another 3D proÐle of gold distribution in a sul-phide mineral, proof of an extended spatial relation-ship between layers was not observed and it isconcluded that the appearance of agglomerated par-ticles in the image is the result of “bloomingÏ of thechannel plate.

Figure 9. Plot of the raw cross-correlation function i) between arsenic at depth 2 and gold at depth 2, as a function of spatial lag ingi j(y,

the two independent image directions (x and y).



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Analysis of three-dimensional SIMS images using image cross-correlation spectroscopy