Frontiers of analytical electron microscopy with special reference to cluster and interface problems

Ultramicroscopy 29 (1989) 31-43 North-Holland, Amsterdam

31

FRONTIERS OF ANALYTICAL ELECTRON M I C R O S C O P Y W I T H SPECIAL REFERENCE TO CLUSTER AND INTERFACE P R O B L E M S C. COLLIEX Laboratoire de Physique des Solides, Associ$ au CNRS, Batiment 510, Universit$ Paris-Sud, F-91405 Orsay, France

J.L. M A U R I C E Laboratoire de Physique des Mat~riaux, CNRS, 1 Place Aristide Briana~ F-92195 Meudon, France

and

D. U G A R T E Laboratoire de Physique des Solides, Associ~ au CNRS, Batiment 510, Unioersit~ Paris-Sud, F-91405 Orsay, France Received at Editorial Office October-November 1988; presented at Conference May 1988

This paper discusses two main aspects of high spatial resolution analytical electron microscopy (AEM): (i) the relationship between the macroscopic properties of the material and its local chemistry as determined from X-ray or EELS spectroscopies, connected with the sampling procedure; (ii) the accessible detection limits, i.e. the frontiers of the technique which are determined by different considerations involving the physics of the interaction, the specimen and the instrument. A graphical representation of the important factors defining the domain of accessible performance, using a chart (Concentration, Resolution), is introduced. Its range of application covers many practical situations encountered in materials science: two representative ones, relative to small metal clusters and to segregation on an interface, are discussed extensively in order to demonstrate the usefulness of the present description.

1. Introduction

Analytical electron microscopy (AEM) uses spectroscopic signals which originate from a welldefined volume of material and carry a specific chemical or electron signature. This spatially resolved chemical information constitutes a unique tool for local investigations in all domains of materials science, at a resolution level which may be in the nanometer range with dedicated STEMs equipped with field emission sources. Consequently, it can be fruitfully used for the characterization of systems exhibiting inhomogeneities at this scale, such as interfaces or small particles. The purpose of this paper is to comment on several aspects of high spatial resolution AEM: (i) the relationship between the macroscopic properties of the material and its local chemical composi-

tion, as determined from the X-ray or EELS signals under the primary probe of electrons - this refers to the sampling process; (ii) the accessible detection limits, i.e. the definition of the frontiers of the technique, which must be satisfactorily known in order to decide whether there exists a non-negligible probability of solving the problem. Such a goal requires a basic knowledge of some important factors. The first one concerns the physics of signal generation for both X-ray emission (EDX) and characteristic electron energy loss spectroscopy (EELS) considered in this paper. This information (ionization cross-section, probability of emission) can be found in standard references [1-4]. On the other hand, one must know the main parameters involved in the microscope operation, such as the detailed characteristics of the incident beam. The experimental part of the present study

0304-3991/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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C. Colliex et al. / Frontiers of A E M - cluster and interface problems

has been performed with a VG-HB501 STEM, the working conditions of which have already been described [5-7]. For instance, a probe with I 0 --- 0.2 nA (primary beam current), d o --- 0.5 um (support of 70% of the incident current) and a 0 = 7.5 × 10 -3 rad (illumination semi-angle) is optimum for high resolution imaging. However, for X-ray emission, a more intense primary beam with about 2 nA can be obtained within a minimum diameter of --- 1.5 nm. Finally, the specimen has to be taken into account and, most important, the way it is sampled and observed at various magnifications to reconcile the world of macroscopic measurements and that of nanoanalysis.

2. From the materials science problem to the AEM diagnosis 2.1. General considerations The elementary volume of matter analyzed in an AEM measurement is made, in a first approximation, of a cylinder of section d 2 and length t (specimen local thickness). It contains N = ntd 2 atoms (with n = number of a t o m s / u n i t volume). It is generally a matrix with different impurities ( j ) in concentrations Cj (i.e. Nj = number of impurity atoms j = CjN). The useful signals Sj delivered by these impurities, or minority components of interest, are governed by cross-sections oj (or probabilities of excitation Pj.). The task of a microanalytical investigation is to relate through a quantification procedure the measured signals Sj to the numbers of atoms Nj. It is then important to optimize the geometry of the analysis with respect to the problem under investigation. It will be illustrated in the following exampies ~or common situations encountered in interface or small particles studies.

2.2. A typical problem involving an interface." origin of the electrical activity in silicon grain boundaries In order to obtain a rather complete evaluation of the origin of electrical activity in large-grained silicon, a model system (a bicrystal with F.--25

coincidence index) has been characterized, after different annealing treatments, with various techniques investigating as well global and local behavior [8]. Deep level transient spectroscopy (DLTS), using transients of the grain boundary capacitance, provides a curve of the density of states, in the band gap, which act as traps for majority carriers and estimates their total number at about ( 3 - 4 ) X 1015 m -2 [9]. Electron beam induced current (EBIC) is measured in a SEM to evaluate the role of the grain boundary as a reservoir of recombination traps for the minority carriers [10]. Finally, samples containing the unique grain boundary are selected and thinned to electron transparency by mechanical polishing and ion milling. This process is successful when relatively thin sections containing the boundary oriented with its plane roughly parallel to the beam direction can be observed in a TEM. Two groups of specimens have been distinguished because they exhibit different contaminations depending on the preparation sequence. They are characterized by distinct types of precipitations. Fig. 1 shows, for each category, a typical micrograph and associated EDX spectra recorded when the probe is focused either on the matrix or on one of the colonies of precipitates seen end-on. The results gathered from T E M and AEM studies are summarized in table 1. The origin of Cu a n d / o r Ni contamination in these specimens is not clearly understood. It is, however, not quite surprising because different morphologies of Ni and Cu precipitates have already been observed in silicon wafers [11]. These elements (Cu and Ni) are actually known to be very fast diffusers [12]. Further identification, in terms of silicide phases, of the precipitate colonies observed after annealing, can be made by diffraction techniques. It seems to rule out the presence of oxide or silicate phases though some oxygen could be detected by EELS, but not conclusively as most of the signal comes from surface native oxide. This work is representative of what type of information can (or cannot) be obtained in a common materials science problem. In this case, the limits of the analysis are more imposed by the specimen itself than by the instrument. Concerning the sampling scheme, there is very little alter-

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Fig. 1. TEM images of the annealed Si bicrystal with the grain boundary parallel to the beam. They slow clearly the colonies of precipitates mentioned in table 1, for the two groups of specimens. Inserts are typical EDX spectra with the characteristic Cu, and Ni and Cu lines.

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C. Colliex et al. / Frontiers of AEM - clusterand interfaceproblems

Table 1 Summary of the characteristics of the precipitation in silicon bicrystals Colonies of precipitates Disk Disk diameter concentration (/~m) (m -z) Group I 0.1 -1 -- 5 X.101° Group II 0.05-0.2 1 × 10l°

Size of individuals (nm) 5-30 2-10

Nature of precipitates Cu Cu, Ni

native for the choice of the analysis volume, because there exists only one grain boundary per disk of 3 mm. Moreover, areas where the precipitates can be distinguished are generally rather thick (typically 100-200 nm). It is also difficult to avoid completely the growth of contamination spikes during the spectral acquisition, as evidenced by an a-posteriori observation of the analysed area. Consequently, beam broadening effects generally lie in the 10-30 nm range, introducing a degradation of spatial resolution in X-ray microanalysis which has been previously assessed by several authors [13-16]. 2.3. A typical problem involving small particles: cobalt on lanthanide oxide supports

In the field of catalysis, it is very important to determine the relation between the activity and selectivity of the chemical reaction and the detailed structural and chemical nature of the system at different stages of the process. The present example deals with the syngas reaction: (CO, H2) ~ (CH4, C, H2n; CnH2n+2 ) on C o / L a 2 0 3 and C o / C e O 2 catalytic systems, i.e. using a distribution of small cobalt clusters supported on rare-earth oxides. Various physical techniques, such as ESCA, X-ray diffraction, X-ray absorption, can be used to characterize, with a high degree of structural accuracy, macroscopic volumes of material; this is particularly true with EXAFS and XANES types of analysis performed on the fine structures recorded on Co-K edges at the Lure synchrotron facility [17]: These methods have pointed out the influence of the supporting layers on the cobalt environment, but have failed

in assessing its exact nature. This is due to the fact that these techniques average the information over a large number of Co atoms which are not all involved in the same type of environment. With a combination of AEM and H R E M , it has been possible to show that, after the chemical reaction, Co particles are covered with catalytic carbon layers in the case of a LaEO 3 support while they are in direct contact with the CeO 2 support [18]. Moreover, they are rather substantially oxidized. In such a situation, EELS is a powerful tool because it can be used [19]: (a) for elemental qualitative and semi-quantitative identification of individual nanometer-sized volumes, through the occurrence of characteristic K edge for O, M23 and L23 edges for Co, N45 and M45 edges for Ce; (b) for edge fine structures studies, equivalent to XANES ones, but relevant to individual small grains of = 10 nm which can also be characterized by lattice imaging or diffraction patterns (clear changes on the O-K edge have been found when one moves the probe from the CeO 2 support to the oxidized Co particle); (c) for chemical mapping with characteristic signals such as the Co-M23 at = 60 eV and the Ce-N45 at = 135 eV. This is very useful to investigate the complex spatial arrangement of the different components. It is illustrated in fig. 2 which gathers STEM bright field and annular dark field micrographs (and their morphological and diffraction contrasts) and characteristic cobalt and cerium maps. Details of the method have been published elsewhere [20]: it requires recording a sequence of energy-filtered images at energy losses respectively below and above the edges of interest, together with satisfactory a posteriori processing in order to discriminate for each image pixel the true elemental contribution from the non-characteristic background. In this case, there is no real sampling constraint because the specimen is made of a huge number of particles. Consequently, one has to acquire many maps and to apply stereological methods to obtain a quantitative knowledge (i.e. number, size, nature of the different components) of the particle-support system. In the above elemental maps, a spatial resolution of a few nm is routinely accessible. The

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Fig. 2. EELS elemental mapping of the spatial distribution of Co particles on CeO2 support. The characteristic signals for Co-M23 and Ce-N45 have been used. Sequences of energy-filteredimages are handled following the method described by Bonnet et al. [20]. pertinent question is: " w h a t is the minimum particle size which can be identified?" An experimental investigation requires suitable test specimens. An ideal one would consist of a r a n d o m distribution of N-atoms clusters (with N ranging from 1 upwards) of different nature, scattered over an infinitely thin support. Small metal clusters of heavy atoms, such as U and Tb used as staining agents for biomolecules, constitute a satisfactory approximation, on which Mory and Colliex have recently evaluated detection limits close to the single atom identification [21]. They use advanced image processing techniques, which require simultaneous A D F and inelastic images, sequences of energy-filtered images at increased energy losses, duplication of all measurements, and which involve background subtraction and cross-correlation. Their results will be considered later within

the frame of a more extensive discussion of the ultimate performance accessible with an analytical technique.

3. Detection limits in EELS (or EDX) on thin foils 3.1. Definition o f detection fimits

In order to evaluate, on a c o m m o n quantitative basis, the performance attainable on thin foils with microanalytical techniques such as EELS (or EDX), it is necessary to define several criteria [221: (i) The spatial resolution ( d ) in the specimen plane; similarly to standard optics, it corresponds to the distance between two features which can be

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discriminated in terms of analytical signal. It may simply be a point-to-point, or an edge resolution, but one can use more elaborate criteria such as deduced from a transfer function or a cross-correlation [23]. (ii) The depth resolution (t) which is confined to the specimen thickness for EELS (and EDX); information is then averaged along the electron trajectory through the foil. Contrarily, the escape depth would be the relevant factor for surfacesensitive techniques such as Auger electron spectroscopy. (iii) The sensitivity or minimum detectable concentration (Cmin) for a minority element contained within a given matrix. (iv) The minimum detectable number of atoms ( N ~ ) of this element contained within the total analyzed volume (d2t). The mass equivalents for these two last factors were introduced by Isaacson and Johnson [24] as M M F (minimum mass fraction) and M D M (minimum detectable mass). For anyone who has to call upon a microanalyrical experiment in all fields of materials science, it is therefore of primary importance to be aware of the present frontiers of the technique and to know the influence of various parameters which might extend these limits in one or another specific direction. Theoretical predictions have been made by a number of authors; they generally combine basic equations with scattering probabilities or cross-sections and statistical analysis for the evaluation of errors and consequently of the detection limits [1,24-29]. In the following discussion, our intent is pragmatic. The used mathematical expressions do not pretend to be exact as to quantification. They only constitute a support for discussing the performance of microanalytical methods and classifying different effects which govern the detection limits. We have chosen to present them on a graph with a coordinate axis system (d, C) or (resolution, concentration), such as previously used by Castaing [30] for the comparisons of EELS and SIMS techniques. In a rather similar work concerning the lateral resolution in Auger electron spectroscopy, Cazaux [31] has introduced a set of axis (Craig, Dose) which obviously constitutes a suitable alternative.

a (rim) 10 -t i

I '

"\'"','%,

10

t O -~

to

-'.

I0 z

..................

i

\, I'

\\% °e

Fig. 3. Definition on a (Concentration, Resolution) graph of the important parameters involved in detection limits: spatial resolution (d), minimum concentration ( Cmin), minimum number of atoms (Nmin), dose ( D ) and signal-to-noise ratio (SNR). See text for discussion.

In fig. 3, a first family of reference curves corresponds to equal numbers of atoms ( N ) such as:

N = Cnd2t;

(1)

n varies generally little between 5 and 10 times 1022 a t o m s / c m 3, but thickness (t) may range from a few nanometers for very thin specimens required in ultra-high-resolution studies, to a few hundred nanometers for standard metallurgical foils. These curves are made of lines of slope ( - 2 ) on the (C, d ) set of axis with logarithmic coordinates. In order to evaluate the minimum detectable number of atoms (Nmin), eq. (1) can be used in two different ways: (i) either Nmi~ is defined as the smallest analyzed volume dmi~t 2 (elementary volume of signal generation, or lateral spatial resolution) with average concentration C; (ii) or Nmin is due to a minimum detectable concentration Craig, controlled essentially by statistical considerations, in the analyzed volume dEt. Consequently, the range of accessible experiments is determined by two families of curves corresponding to each one of these criteria, the

C. Colliex et al. / Frontiers of A E M - cluster and interface problems

ultimate performance being reached for the minimum detectable concentration Cmi~ with the best spatial resolution dmi~. Before discussing these criteria more extensively, let us point out some of the involved assumptions. The first one is that the concentration Cm~ corresponds to an average over the analyzed volume. This is not the case, in reality, for the equilibrium segregation on boundaries or for the small uranium cluster on a carbon foil. As pointed out by J. Cazaux (private communication), there may exist some confusion between the minimum detectable size and the spatial resolution. Precipitates smaller than the probe size can be detected, but an extra assumption about their shape or density is then necessary to provide an estimate of their dimension. This remark has the interest of raising several possibilities about the improvement of spatial resolution, beyond the volume of signal generation by deconvolution techniques, if one knows, through a different experiment, a point spread function for this type of analysis. This subject, however, remains beyond the scope of the present paper.

3.2. Classification of various factors governing the detection limits [1,32] 3.2.1. Size of the volume of signal generation The first contribution is the probe diameter (do) which may be, in optimum focusing condition, as small as a fraction of nanometer for a field emission gun STEM. The signal itself is issued from a larger volume which encompasses the cylinder of diameter do, but the exact shape and dimension of this volume depend on the physics involved in signal generation and on specimen thickness. Multiple elastic scattering broadens the probe to an extent that the irradiated exit surface may be substantially wider than the entrance one. Various theoretical approaches have been followed for quantitative estimates of this effect [3,4,29,33]: parametrized single scattering model, Monte-Carlo methods and transport equation theory, which all employ a ballistic model for electron collisions, that should be satisfactory for a dense random assembly of atoms. But this description fails to represent diffractive probe spreading in single crystals, which is highly reduced in channeling

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conditions [34,35]. Actually, when the scanning spot coincides with the centre of an atom row oriented parallel to the beam axis, the positively charged ions act as microlenses focusing the electrons towards the centre of each row: "the crystal could be considered as a fiber-optic plate for electrons" (Fertig and Rose [36]). In EELS analysis, the spectrometer entrance aperture further sets an upper angular limit (fl) to the divergence of recorded electrons. This "collimating" effect maintains the beam broadening diameter below a typical value 2fit, which is typically much smaller than the expected broadening due to elastic scattering. As for X-ray production, its distribution is obtained by integrating through the specimen the results of the calculation of the spatial electron distribution. The average width of X-ray generation is therefore narrower than the irradiation disk on the exit surface. A good resolution test can then be defined as the diameter within which x % (i.e. 80%) of all X-rays are produced. This definition neglects, of course, all stray emissions which originate from secondary processes at large distances from the primary electron trajectory. A significant remark is made by Garratt-Reed [29]: "the probe size and the specimen broadening should be of equal magnitudes in order to optimize the compromise between signal (associated to larger probe size and thicker specimens) and spatial resolution". As an example, he calculates the optimum values of probe size and specimen thicknesses for a given count rate in an iron specimen (for instance: dopt - 1.8 nlTl and topt = 22 nm at 100 kV and 2000 cps in the characteristic Fe K~ peak with a field emission gun; d o p t = 14 nm and topt = 87 nm with a thermoionic gun). As a consequence, the first family of limiting contours in the (d, C) graph is made of vertical lines corresponding to practical dmm values: dm~ is governed by d o (probe diameter) for EELS analysis of very thin specimens, and by beam broadening effects for EDX analysis of moderately thick foils.

3. 2.2. Statistical signal-to-noise considerations As it is necessary to reduce the total recording time to a reasonable value, the relatively low

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cross-sections for the signal and the strong background are generally responsible for a low signal visibility when compared to random intensity fluctuations. It is true as well when one wants to discriminate one or several channels in a spectrum, or one or several pixels in a filtered image. The generally used criterion for the estimation of the minimum detectable signal is expressed as: Signal Signal uncertainty

S =SNR>_L (=3). AS

(2)

It states that the SNR variable must be large enough to force the risk of false detection below a given level. Improvements can be made which take into account both kinds of risks (false positive and false negative values) [27], but they do not modify the general following arguments. The major problem is to evaluate the uncertainty on the signal. When the measured current is the sum: signal + background or I = S + B, the uncertainty AS has two origins, the random noise on the total number of counts (for a Poisson distribution) and the error in predicting the background as an extrapolation from other channels. It can be written with the notations that Egerton has used in EELS for the rather complex background subtraction:

AS = ( S + hB) 1/2,

(3)

where h = 1 + (var B ) / B can be estimated from the quality of the background fit [27]. If the background were perfectly known, h should be equal to 1. If it followed a Poisson distribution as it can be assumed in EDX measurement, it should be equal to 2. In EELS, common values of h = 2 to 15 have been measured when the signal is integrated over an energy window of 50-100 eV. Using basic definitions of cross-sections, Egerton [37] shows that the detection criterion can be written: Cmin = SNR a-~-- ( /h' ~o ]b 11/2 ' with

,0

(4)

being the total number of electrons contributing to the spectrum, the exponential term making allowance for elastic scattering of electrons outside the spectrometer aperture; SNR is the signal/noise of the experiment, D is the primary dose, ~ / T is the fraction of recording time with respect to irradiation time (i.e. , / T = 1 for parallel acquisition, r / T = 1/200 for present sequential acquisition), o K and o b are the involved cross-sections for signal and background production in the energy loss range of interest. If one neglects the factors h and e x p ( - t / X e ) , this equation is equivalent to the expression: 3

S

r

-

1/2

in Castaing's paper [30], where: ( S / B ) o = signalto-background ratio for the pure element and P = oKnt = t / h K = probability of excitation of the relevant signal for a foil of pure element and thickness t. This description introduces a second family of curves with slope ( - 1 ) in the (d, C) chart: they correspond to the required doses for elemental detection with a given SNR. The involved coefficient depends on the physics of the excitation process through ( S / B ) o and P, and of the experimental conditions through D z/T. The D - 1 / 2 is the important physical constraint because it quantifies the primary dose required for a given measurement.

3.2.3. Radiation damage considerations The above analysis proves that one can push forward the frontiers of accessible performances, i.e. reach lower values for (Craig,d), with higher primary doses D. However, it is well known that there generally exists a critical dose D c for specimen modifications. This has been long recognized on biological specimens and many values for Dc between typically 102 and 105 e - / n m 2 have been published, depending on the material and on the criterion of detection. In materials science studies, many previous experiments show that noticeable specimen modifications may occur for primary doses several orders of magnitude higher (typically between 107 and 101° e - / n m 2 ) . Observed beam damages are very

C. Colliex et al. / Frontiers of A E M - cluster and interface problems

diversified: changes of local composition such as electron beam mixing or radiation-induced segregation, preferential desorption, creation of artificially induced concentration gradients, electron beam sputtering [38,39]. In situations similar to those described in the previous paragraph, desorption of oxygen from dislocation cores in Ge occurred for doses of = 5 × 108 e - / n m 2 [40]. In the C o / C e O 2 system, surface diffusion effects and beam-induced chemical reactions between the different components have been observed for doses also typically in the range ( 5 - 1 0 ) × 108 e - / n m 2 [19]. Generally it is not possible to make quantitative predictions. As long as there is a lack of experimental data on beam-induced degradation of inorganic materials, many mechanisms can be evoked. Moreover, the dose rate as well as the total dose may constitute an important factor. Many processes, such as the vaporization of metal halides and of some oxides, have a dose rate threshold. Consequently, increasing the dose rate increases the damage, which is useful for lithographic purposes (Isaacson [41]). In order to improve our understanding of such limitations, this author advocates that it is necessary to report in any analytical work all those parameters on which the radiation sensitivity depends: dose, dose rate, incident energy, temperature, ambient conditions. These parameters would be as important to validate the high resolution analytical experiment as focusing and astigmatism for high resolution imaging studies. A practical suggestion would be to record sequences of spectra or of maps over the same area, to cross-correlate them in order to detect beam-induced modifications (such as atom movement in the experiments of Mory and Colliex [21]) and finally to extrapolate backwards the data towards the zero irradiation limit. In the (Cmi~, d ) graph of fig. 3, the practical consequence is that the dose parameter labeling the different curves of slope ( - 1 ) introduced by previous statistical considerations cannot be increased to a great extent without specimen disturbance. One of these curves, with the appropriate Dc, discriminates the domain of experiments with a reasonable probability of success from those in which the required SNR can only be

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reached at the cost of an unmeasurable specimen degradation in the analyzed area. 3.2.4. Delocalization of the inelastic process Delocalization refers to the non-local response of the analytical signal to the incident particle. For secondary emission processes, such as EDX, one easily conceives that the detected photon may be issued at a given distance from the primary probe electron. For EELS, the delocalization, or impact parameter, is governed in a homogeneous medium by the range of Coulomb interaction, but in heterogeneous systems it is also dependent on the type of excitation. Generally, this effect seems to have been initially overestimated and in the recent past years, experimental measurements [20,42,43], as well as theoretical calculations [44], have shown that it concerns only subnanometer distances for a typical 100 eV energy loss and a primary voltage of 100 kV. As a practical consequence, this fundamental limit is of restricted importance and can be merged into a common value with other parameters governing the size of the volume of signal generation. It is responsible for a slight shift in fig. 3 of the spatial resolution limit ( d ) towards higher values. 3.2.5. Miscellaneous parameters The present description neglects several aspects of a practical analysis which can degrade the quality of the results. They differ from the above parameters, because there exist provisional solutions to avoid them. The first problem is to control the position of the probe on the feature of interest during signal acquisition. In a fixed mode, one has to monitor simultaneous information such as a microdiffraction pattern. When it is not possible, and consequently when one is obliged to work blindly, there are some possibilities, such as to interrupt periodically the analysis, acquire an image, calculate the shift of the specimen by cross-correlation and correct the beam position by a feed-back control of the scanning coils. Such a tracking analyzer software has already been developed to track a drifting object and automatically reposition the beam for EDX or EELS microanalysis [45]. In their EDX detection of As segregation

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c. Colliex et al. / Frontiers of A E M - cluster and interface problems

to grain boundaries in Si, Grovenor et al. [46] have used a one-dimensional line cross-correlation along the scan direction, i.e. perpendicular to the interface, which has the effect of maintaining within an acceptable level (one channel width) the specimen drift in this direction. Contamination has finally to be mentioned. Several techniques have been used to reduce it as

much as possible, such as low-temperature work, preirradiation or cleaning of the foil. However, with a small subnanometer probe and recording periods of several minutes, it remains difficult to exclude it completely. Moderate contamination spots offer a small advantage at the end of the analysis because the two marks left on both surfaces of the specimen constitute an a-posteriori

d

~

t

=

N atoms

/ I 200nl/

3.5 nm

a

C

Segregation on grain boundary

Small cluster situation 10

1 0 ~: 1

10 "t

10 ' i

1 i

i

i

i

....

i

10 . . . . . . . .

i

10 a . . . . . . . .

i

10 -~

10

"i

-:

! 10"4-

10 4-

!.,\

\~

I0

-I

I0

:

10 -i

~'~

d ! b Fig. 4. Application of the general chart of fig. 3 to two specific situations: small uranium clusters on a carbon layer, investigated by EELS (a and b); segregationof Cu or Ni on a grain boundary in silicon, analyzedby EDX (c and d).

c. Colliex et al. / Frontiers of AEM - cluster and interfaceproblems

control of the localization and can be used for a rough estimation of the thickness, when observed under a given tilt angle. 3.3. Application to practical situations involving interfaces or small particles

There is an increasing number of papers in the recent literature dealing with high spatial resolution profiles in a range of materials, with special r e f e r e n c e to e q u i l i b r i u m s e g r e g a t i o n on boundaries, planar defects and dislocations [4750]. How can these different experiments be compared with predicted limits of detection? The previous discussion involving the (Craig, d) chart offers an interesting route, as illustrated with the above-described situations involving small particles or grain boundary precipitation. These examples are indeed representative of quite extreme situations for microcharacterization. 3.3.1. Elemental analysis near the single atom detection level on small metallic clusters

We refer here to EELS chemical mapping on subnanometer uranium clusters deposited on a very thin layer of amorphous carbon [21]. The relevant geometry is shown schematically in fig. 4a and the pertinent question is then the minimum detectable number of atoms. The experimental result is a characteristic uranium signal S = 500 superposed above a background B = 600 and detected with a SNR = 12 after background subtraction from a series of 3 filtered images at energy losses below the threshold. These numbers correspond to the central pixel on a small subnanometer cluster. The instrumental conditions are: (i) a probe area of 0.5 nm 2 as measured from cross-correlation in the simultaneous dark field mode; (ii) a primary current 1 = 10 -9 A and a dwell time per pixel z = 2 × 10 -3 s - the pixel increment is 0.2 nm. How can this information be handled in the present context? Fig. 4 provides an answer: (a) The spatial .resolution d (sum of all effects probe size, specimen instabilities, delocalization) is 0.8 nm. (b) The detected concentration C is 0.035 from the ratio of the uranium to the carbon signal. For a

41

thickness t = 3.5 nm, it amounts to a number of uranium atoms Nu = 6. (c) The measured primary dose amounts to D = 1.2 × 1 0 9 e - / n m 2 with z / T = ¼ × ~ ; the first factor of 4 is due to the requirement of recording 4 different images in order to extract the information, the second factor 12 corresponds to the spatial oversampling (ratio of the probe area to the pixel one). (d) The predicted dose using eq. (5) would be 2.8 × 10 e - / n m 3 with reasonable values of ( S / B ) o = 4 and P = 10 -3 for the present situation. The agreement is quite satisfactory for such an evaluation of the order of magnitude of the required dose. (e) This analysis deals with a given measurement. It can be extrapolated to the limit of detection Cmi~ for SNR = 3 and the same dose, along the same vertical line d - - 0 . 8 rim. The result is then Cmm = 0.01 and the number of atoms Nmi" is between 1 and 2. This type of experiment proves that the single atom identification is within the realm of practicability when the adequate specimen with stable isolated atoms is available. 3.3.2. Submonolayer detection on grain boundary segregation

It concerns EDX analysis on interfaces oriented parallel to the beam in the geometry depicted in fig. 4c. It is possible to use similar arguments to predict reasonable values for detection limits, as shown in fig. 4d: (a) The spatial resolution, superposition of probe diameter and beam broadening through a 200 nm thick silicon foil, is d = 10 nm. (b) The minimum concentration is evaluated from eq. (5) with the following likely values: ( S / B ) o = 102, P = 10 -7, " r / T = 1, 10 = 101° e - / s , T = 100 s. One finds C r ~ = 10 -3, and in the analyzed volume, it amounts to Nma~ --- 103 atoms of impurity (Cu or Ni) segregated on the grain boundary. The required dose is D = l o T / d 2 = 101° e - / n m 2. In order to reduce this value, one can assume that the segregation is homogeneous in the interface plane. Consequently a line analysis with the probe being scanned parallel to the boundary would provide the same results with an average over

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C. Colliex et aL / Frontiers of A E M - cluster and interface problems

102-103 point analysis, i.e. with a primary dose reduced by the equivalent factor. In the above calculations, the value of P is deduced from the complete set of calculations involving the number of K ionizations per second, the number of X-rays created in the K a line and the number of X-rays detected after escape from the specimen and transmission towards the detector. All values refer to our present experimental system o n the VG STEM. (c) It may be interesting to calculate equivalent fractional monolayer coverage of segregant on the boundary, which can be checked by other techniques such as Auger analysis on fractured specimens. In the described situation, Cmin= 10-3 in a slab of 10 nm encompassing the interface is equivalent to about 5% of a monolayer. In his study of phosphorus segregation in a ferritic steel, Titchmarsh [49] quotes the same detection limit of 5% of a monolayer in 100 nm thick foils, but this value remains about one order of magnitude higher than in an optimized EDX experiment, as estimated by Garratt-Reed [29]. The experimental data presented in fig. 1 lie well above this detection limit.

4. Conclusion This paper deals with some aspects of high spatial resolution microanalysis in materials science. Two situations with compositional gradients over typical nanometer scales are described. They concern small supported metallic clusters of catalytic interest and equilibrium segregation of impurities on grain boundaries. Emphasis is first put on a suitable sampling process to connect the analyzed volume and some macroscopic properties of the material. The major topics, however, consist of an extended discussion of the detection limits for given specimen geometry and microchemistry and certain experimental conditions. This is of fundamental importance for anyone involved in microanalytical studies, who has to predict whether a problem, with its topography and nature of involved constituents, has a reasonable chance of being solved. A detailed analysis of all concerned parameters is made on a (d, Craig) graph. It shows

that, for well-adapted specimens, elemental identification close to the single atom level is achievable with EELS techniques. On the other hand, EDX can detect small fractions of monolayer coverage for impurities on grain boundaries. The proposed approach can be extended and applied to many experimental cases.

Acknowledgements This work has been performed with the support of the CNRS unit US 120041: "Microscopie Electronique Analytique et Quantitative". Valuable discussions with N. Bonnet, D. Bouchet, R. Castaing, J. Cazaux, C. Mory and P. Trebbia have helped us greatly in our critical discussion of the detection limits. The permanent assistance of P. BaUongue and M. Tenc6 is acknowledged, and V. Paul-Boncour (Bellevue) and E. Delain (ViUejuif) have provided some of the specimens for the present study. Thanks are also due the organizers of the Gatan workshop on parallel EELS (Pleasanton, April 1988) and of the meeting on Frontiers of Electron Microscopy (Oak Brook, May 1988), who have given to one of the authors (C.C.) the opportunity of clarifying the ideas presented in this text.

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