Quantitative analysis of electron spectroscopic imaging series

Pergamon Plh S0968-4328(97)00037-1

Micron Vol. 28. No. 5. pp. 361 370, 1997 (" 1997 Elsevier Science Ltd

All rights reserved. Printed in Great Britain 0968M328/97 $17.00+0.00

Quantitative Analysis of Imaging

Electron Series

Spectroscopic

J. M A Y E R , * U. E I G E N T H A L E R , J. M. P L I T Z K O and F. D E T T E N W A N G E R

Max-Planck-lnstitut fiir MetallJbrschung, Seestr. 92, D-70174, Stuttgart, Germany

(Received 5 March 1997; accepted 21 April 1997)

Abstract We have developed new methods to quantify the data acquired by electron spectroscopic imaging (ES1) which are based on recording series of energy filtered images across inner shell loss edges or in the low loss region. From the series of ES] images, electron energy loss (EEL) spectra can be extracted for any given image area, i.e. each individual pixel or an array of pixels over which the signal is integrated. The EEL spectra can subsequently be analysed using standard EELS quantification techniques. This makes it possible to obtain a measure of the absolute amount (area density) of an element in the given sample area 0r of the concentration ratios of one element with respect to other elements. From a series of ESI images in the low-loss region, accurate values of the specimen thickness can be obtained, provided the mean free path for inelastic scattering is known. As ~xamples, results obtained on Si2N20 ceramics and thin A1203 films, which were grown by anodical oxidation, will be shown. The number densities of the atoms and concentration ratios can be measured with an accuracy of 10 15°/,, using calculated inelastic .Scattering cross-sections. Similar accuracies can be obtained for the measurements of the specimen thickness, as will be shown for the thin A1203 films and for a wedge shaped silicon crystal. In the case of Si, convergent beam electron diffraction was employed to determine the mean free path for inelastic scattering. For the same sample, the thickness of the carbon contamination I~yers and the amorphous surface oxide layers were measured. The results of the latter measurements may provide important information for the quantitative evaluation of high resolution images or CBED patterns.~7~ 1997 Elsevier Science Ltd. All rights reserved

Key words: electron spectroscopic imaging, energy filtering transmission electron microscopy, quantitative analysis, concentration ratios, specimen thickness measurement, contamination layer thickness.

I N T R O D U C T I O N The increasing number o f energy filtering transmis-

sion electron microscopes (EFTEMs) has given many microscopists the ability to apply the fast and very efficient tool o f electron spectroscopic imaging (ESI) for analytical characterization, rather than to record elec- t ron energy loss (EEL) spectra. Mos t commonly , ESI analysis is based on identifying the presence o f a char- acteristic inner shell loss edge o f the element under investigation (for an overview see Reimer, 1995). This can be accomplished by recording two or three ESI images at energy losses in the background region before and the signal region just above the edge. The two methods mainly used are the three-window technique, which was first proposed by Jeanguil laume et al. (1978), and the ratio map technique which was introduced by Krivanek et al. (1993). After background subtraction, the resulting maps show the distribution o f the element in the specimen area. The signal in the maps is related to the concentra t ion o f the corresponding element, however, it also depends on a number o f other factors like crystal orientation, mass thickness and collection angle (Hofer et al., 1995; Jfiger and Mayer, 1995; Schenner et al., 1996). Thus, elemental maps produced by ESI are an efficient tool for qualitative characterization, but are not readily amenable to quanti tat ive analysis.

Strategies to extract more quanti tat ive informat ion f rom elemental maps have first been discussed by

*Corresponding author.

Shuman et al. (1986). These authors and a number o f other groups have applied a division by a reference image acquired in the zero loss and/or low loss region to the elemental maps (Crozier, 1995; Bentley et al., 1995). While this is a suitable way to remove mass thickness effects, it fails to remove strong diffraction effects, e.g. in the vicinity o f bend contours. A more s t raightforward analysis is possible if only concentra t ion ratios between two different elements are sought. Shumani et al. (1986); Crozier (1995); Bentley et al. (1995) a n d Hofer et al. (1997) have applied a simple division o f the two elemental maps acquired with the three window technique with subsequent normal izat ion by the ratios o f the core loss scattering cross-sections to produce maps o f concentra t ion ratios.

In the present paper we will present results obtained with a new method for quanti tat ive anal~csis which is based on a mult i -window approach. Rather than acquir- ing only two or three ESI images, we acquire a series o f ESI images a round an inner-shell loss edge and, if required for quantification, in the low loss region. The advantages o f this method are: (1) infOrmation on the energy loss spectrum is obtained for eaCh pixel in the image and the s tandard quantification methods developed for EEL spectra can be used for th~ analysis; (2) the background extrapolat ion and the signal integration regions can be extended over a large energy loss range o f up to 80-100 eV below and above the edge~ respectively; and (3) the s tandard EELS methods for single scattering deconvolut ion and least squares fitting for overlapping

361

362 J. Mayer et al.

edges can be used. In biological, medical and polymer applications it has been shown by K6rtje (1994); Lavergne et al. (1994); Martin et al. (1995); Martin et al. (1996), and Yase et al. (1996) that accurate information on the EEL spectrum can be obtained from ESI series. Beckers et al. (1994, 1996) have also discussed the feasibility of a quantitative evaluation of ESI series and have given first examples for the application.

The spectrum-imaging technique, which has been described by Hunt and Williams (1991), and Botton and L'Esp6rance (1994), represents a complementary approach, in which spectra are acquired for a two- dimensional array of probe positions. The data obtained by this technique and the data obtained by ESI series in both cases determine the intensities in a three- dimensional data space, in which two coordinates are given by the positions x and y on the specimen, and the third coordinate is given by the energy loss AE (Krivanek et al., 1991). In the present work we focus on the quantitative ~Cnalysis of the ESI series, but the differences and advantages of both techniques will be discussed. It will be shown that the quantification of the ESI series can not only result in values for concentration ratios, but also in accurate values for the number density of a specific element in a given sample area, the specimen thickness and contamination layer thicknesses. These results may also be an important basis for the quantitative analysis of high-resolution images and electron diffraction patterns.

• ~ . . , . . ~ ~ ~ ~ ~ ~ ~

Image mode: I = I(x,y,AE) AE EELS

Fig. 1. The three-dimensional data space which represents the intensity distribution at the bottom surface of the specimen. It is assumed that the scattered intensity is integrated up to a maximum scattering angle which is defined by the collection

aperture.

Table 1. Typical parameters used for the acquisition of the series of ESI images

Window width OE Energy step Exposure time Number of images in series Width of background fitting region

Width of integration region

Acceptance semi-angle

10-20 eV 10-20 eV (9E or 3E/2) 5 20 s/image

10-30 50-80 eV (ends 10 eV before edge) 50-80 eV (starts at edge onset or 10-20 eV above edge) 12.5 mrad

EXPERIMENTAL TECHNIQUES

E S I data acquisition

The ESI investigations were performed on a Zeiss EM 912 Omega operated at 120 kV. ESI image series were recorded on a Gatan 1024x 1024 slow scan charge coupled device (CCD) camera using Gatan's Digital Micrograph software. The ESI images were recorded in the binning mode, in which 2 x 2 pixels or even 4 x 4 pixels are summed up into one effective pixel during the read-out process, so that 512 x 512 or 256 x 256 pixel images result. Image processing and analysis routines were written in the script language within Digital Micro- graph and the quantitative analysis of the resulting spectra was performed using the Gatan 'ELP' program package.

The three-dimensional data space which has to be evaluated in a spatially resolved quantitative analysis is depicted in Fig. 1. The graphical representation imme- diately suggests that the intensity distribution I ( x , y ,AE) can equally well be evaluated by applying the standard EELS techniques or the new ESI technique (Krivanek et al., 1991). In the former case only a small spot on the specimen is illuminated and EEL spectra are recorded, whereas in the latter case a large specimen area is illuminated and filtered images are recorded with an energy selecting window of finite width DE. How- ever, any quantitative analysis of the resulting intensity

distribution I ( x , y ,AE) should be independent of the sequential way in which the data are acquired. The aim of the present work is to apply standard EELS programs, which are in common use and well tested, for the analysis of our ESI series. The main advantages of the ESI technique are that a large number of pixels (typically 1024x 1024 or 512x512) is recorded in parallel during each image acquisition, and that the total number of ESI images and the energy window width can easily be adapted to any given situation. The information on the EEL spectrum can subsequently be extracted from the series for the individual pixels or, by integrating over the corresponding pixels, for a given area.

The typical parameters which we use for the acquisition of ESI series are listed in Table 1. In the experiments, ESI series are recorded across the inner shell loss edges of one or several different elements and, if required, in the low loss region from AE=0 to typically 200 eV. In most of the cases, the slit width is adjusted to be equal to the step width, i.e. the energy loss increment between two subsequent images. Using a narrow slit and a small step width one can even obtain detailed information on the energy loss near edge fine structure (ELNES) at the edge onset (Mayer and Plitzko, 1996; Martin et al., 1996). The slit width can be adjusted and calibrated by projecting an EEL spectrum with inserted slit onto the CCD camera. The slit adjustment is most critical for series acquired in the low loss region, where, owing to the discreteness of the zero loss peak, the slit

Quantitative Analysis of Electron Spectroscopic Imaging Series 363

8E

AE

Fig. 2. Schematical EEL spectrum extracted from a series of ESI images. The data can be visualized as individual data points at the centre position of the energy windows, in a data bar representation, or as a curve obtained by linear interpolation of

the data points.

width has to be known accurately. In the case of a deviation of the slit width from the chosen step width, a correction factor given by the ratio of the step width and the slit width 0E can be applied. This correction factor drops out completely if only concentration ratios are calculated.

For small particles or thin layers, the information on the spectra has to be extracted from areas with dimen- sions of 10 nm or less in one or two directions. In this case, drift between the individual images may be a severe problem and lead to artefacts. We have developed a drift correction algorithm based on cross-correlation of the first image of a series with the subsequent images. The determined drift values are then applied to the integration mask over which the signal is integrated for the corresponding images.

Data analysis

The energy loss spectra extracted from an ESI series with n images can graphically be visualised in several different ways (Fig. 2). The data are obtained as intensities I(AE) integrated over the energy window 0E defined by the slit aperture. A simple plot would consist of a series of n data points which give the integrated intensities at the centre positions AE i (i=1 ... n) of the corresponding energy windows (Fig. 2). Most analysis programs use a bar representation showing the intensities in steps with a width which corresponds to the energy increment. In the following, we will use this type of representation for the low loss spectra. For the spectra in the core loss region we use linear interpolation between the individual data points (Fig. 2). The resulting spectra resemble very closely the spectra which would be obtained with a parallel energy loss (PEELS) detector with much higher sampling frequency. At the present stage we also use data produced by this linear interpolation for the quantitative analysis. The simple reason for this is that the programs for quantification, which are presently available, require a large number of data points in order to produce an accurate b '~V~ound fit.

In a pixel notation, the linear interpolation yields N segments and thus ( N - 1) new data points between two neighbouring experimental data points. Mathematically, the intensities in the new data points are given by:

for

I( AEj)=I [ N[_ Ii+J(//+'N - li) ]

AEj=AEi+ J(AEi+t - AEi)

(1)

(2)

and j=0, 1 ... N - 1, with N normally being in the range of 20 30, yielding a separation of 0.5 to i eV between the newly created data points. I~ and I~+1 are the intensities, and AE; and AE~+ l are the corresponding energy losses of the original experimental data points, respectively. In modification of the standard linear interpolation a factor 1/N has been introduced in Order to keep the integrated intensities constant. The procedure given by equation (1) and (2~ is repeated for the intervals between all original data points i= 1 ... n. It ican easily be shown that summing (or integrating) over all data points produced by linear interpolation exactly reproduces the original intensities, as long as the integration extends from one original data point to any other. Graphically, this can also be seen from the equality of the two hatched triangles in Fig. 2.

The background extrapolation and subtraction is performed via a power-law background fit. We have found that, using the spectra obtained by linear interpolation, very accurate background fits can be obtained. However, it should be kept in mind that the linear interpolation is only an approximation. To become more accurate, a modelling of the exact functional dependence of the intensity variation for windows with a finite width 3E is required. For example, for a curved background, the original data points (cf. Fig. 2) represent the intensity accumulated within windows with a finite width DE and are found to lie slightly above the real background curve• A power-law fit through the experimental data points would thus als0 be only an approximation and finding the exact posit!on of a fit to the original curved background would be a numerically demanding problem. A quantitative measure for the additional error introduced by the background extrapolation is the h-parameter introduced by Egerton (1982). Small values of h correspond to a large signal-to-noise ratio of the integrated core-loss intensities. According to Egerton (1982), typical values for EELS investigations lie in the range of h=5 ... 20. For the interpolated spectra, we have obtained values of h in the range of 8 to 15 for extrapolation and integration intervals with 80 to 100 eV width, respectively. This shows that the spectra obtained by linear interpolation from ESI'series can be quantified with the same accuracy as conventional EEL spectra.

The integrated intensities under the inner shell loss edges after background subtraction are also calculated

364 J. Mayer et al.

from the interpolated spectra. Again, the interpolation leaves the total signal intensities unaffected as long as the integration starts at one original data point and ends at another original data point, as shown in Fig. 2. This means that the integration region does not start at the onset energy of the edge, but at the energy corresponding to the centre of the first ESI window below or above the edge. We use integration regions with a width A between 50 and 80 eV which are standard in quantitative EELS analysis (Egerton, 1996). The integrated intensity is given by:

Ik(zX)=N.ak(A)I~(6) (3)

where N a is the number of atoms of the element 'a' per unit area, ak(A) the inelastic scattering cross-section for the K-edge of element 'a' in an integration region of width A and I1(A) the intensity in the low loss region integrated up to the energy loss A (Egerton, 1996). Choosing the starting point of the integration window 10-20 eV above the edge onset has the advantage that the first strong oscillations of the near edge structure are omitted. The theoretically calculated inelastic scattering cross-sections ~k(A) are thus more accurate. From equation (3) the area density Na (atoms/nm 2) can be calculated. N a is related to the specimen thickness t by:

tl 0 0

NN e Fig. 3. Schematical drawing of the~experimental set-up used to grow the thin Al203 films. Aluminium films which were evapo- rated on a glass slide are suspended in a solution of 3% (NH4)2C4H406 in water and anodically oxidized. Under these

conditions a very uniform oxide layer grows.

where/tot is the total intensity integrated up to A and 10 is the intensity in the zero-loss peak only.

Preparation of Al203 thin films

Na t= - -

n a

where n a is the number of atoms per unit volume (atoms/nm 3) of element 'a'. The atomic density na of element 'a' in a compound axby(cz...) is related to the mass density r of the compound by:

and

na=x*n

pUn n = m

A

where n is the number of formula units per unit volume, A the molar weight in g and NA the Avogadro number (NA=6.023 x 1023).

If only concentration ratios between two different elements 'a' and 'b' have to be determined then the low loss intensity Ii(A ) does not have to be measured and the result is determined by the ratio of the intensities under the core-loss edges:

Thin A1203 films with well defined thickness can be (4) grown by electrochemical (anodic) oxidation of pure

aluminium (Fig. 3). In a first step, 300-nm-thick A1 films were produced by evaporation of pure A1 onto glass slides under high vacuum conditions. Subsequently, these films were suspended in a solution of 3% (NH4)2C4H406 in water and anodically oxidized. Under these conditions a very uniform oxide layer grows. The

(5) final thickness is determined by the thickness at which the A1203 films become insulating under the applied voltage. For the given experimental conditions a growth constant of 1.5 nm/V resulted (which is the inverse of

(6) the electrical field strength at breakthrough). Films with nominal thicknesses of 10 nm and 30 nm were grown by applying voltages of 6.7 V and 20 V. During growth the electrical current was limited to 0.1 mA/cm 2 which resulted in homogeneous films with uniform thickness. The A1203 films were extracted by dissolving the residual A1 with an HgC1 solution and by picking up the floating oxide films with a TEM copper grid.

RESULTS AND DISCUSSION

Na O'bk(A)rk(A)

N b ¢Tak(A)Ibk(A) (7)

The total specimen thickness t can also be computed from the inelastic mean free path 2 for inelastic scattering processes with energy losses smaller than an integration limit A (Egerton, 1996):

t=2 ln(Itot/Io) (8)

Determination of concentration ratios

As an example for the study of concentration ratios between light elements, we used Si2N20 ceramics which were produced from polymer precursors by Riedel et al. (1995). In these composite materials Si2N20 grains coexist with Si3N 4 grains and an amorphous oxide, the latter being formed by the sintering additives. In elemental distribution images, the Si2N2 O grains show intensity


m ~

100 n m

a) b)

25

~ 20

o o i0

5

31

e)

%' I ' I ' I ' I ' I ' I ' I •

'~ . - - S i 2 N 2 0 ~ ,, . . . . . . S i3N 4

~ \ "" ~ '~ - - am. oxide

i I i i i i i I i ) 4oo 4go sdo ego 7do E n e r g y L o s s (eV)

Fig. 4. (a) Elemental map for nitrogen (red) and oxygen (green) of a Si2N20 composite ceramic. The amorphous oxide formed by the sintering additives (AI203 and Y203) appears in green, Si3N 4 inclusions in red, and the Si2N20 grains in a mixed colorer between red and green. EEL spectra for three different regions in the same specimen area are shown in the bottom. (b) Bright field image of the area under investigation together with the regions over which the signal was integrated and the resulting concentration ratios for the Si2N20 grains. 'Oxygen' and 'nitrogen' denote areas in which, according to the spectra, pure amorphous oxide or pure SigN 4 grains are found. (c) Examples for the spectra which were extracted from the series of 30 ESI images with 3E=10 IV and an

increment of 10 eV by integrating over the rectangular areas indicated in (b).

for both light elements, nitrogen and oxygen, though no direct information on the concentration ratios can be inferred from the grey values or the colours in the combined elemental map shown in Fig. 4(a) Mayer et al., 1995. In the present studies we have acquired a series of 30 ESI images from 350 eV to 640 eV with a ~E=10 eV and an energy increment of 10 eV. Spectra were extracted from several grains and from the areas containing the amorphous phase by integrating the signal in the ESI images over rectangular areas [Fig. 4(b)]. The resulting spectra for three different areas are shown in Fig. 4(c). It can be seen that the three different phases can easily be distinguished by the presence of the nitrogen and/or oxygen K-edges, respectively. The results of a quantitative analysis of the N/O ratios for several different Si2N20 grains are depicted in Fig. 4(c) together with the areas over which the signal was integrated. Hartree-Slater cross-sections were used to compute the concentration ratios following equation (4).

The results for the concentration ratiqs depicted in Fig. 4(b) are smaller than the expected value of 2, i.e. more oxygen is found. Since Si2N20 is known to be a chemically sharp compound, it is unlikely that the deviation from 2 reflects actual changes in the stoi- chiometry of the crystalline phase. Rather, we believe that the oxygen surplus is caused by surface oxidation of the individual grains. This is in agreement with the experimental finding that thicker grains show lower oxygen concentration. Furthermore, the spectrum from the Si3N 4 grain also shows a small oxygen edge, which is indicative of surface oxidation. The formation of an oxide layer is probably promoted by the formation of an amorphous surface layer during ion beam thinning, which can easily be oxidized. Taking this into account, it can be seen that concentration ratios can be measured with an error of less than 10% from E$I series. It is expected that the accuracy could be further improved if k-factors obtained from standards rather than computed inelastic scattering cross-sections are usedl.

366 J. Mayer e t al.

Fig. 5. (a) Zero-loss filtered bright field image and (b) ESI image obtained at AE=555 eV, i.e. above the oxygen K-edge of a 10-nm-thick A1203 film. The film is ruptured and the pieces fold together so that areas with double and triple film thickness are also

present. The zero loss image shows the areas from which the spectra were extracted.

Measurement o f the number o f atoms per unit area Q

The absolute number N of atoms per unit area, or in other words, the area density of a given chemical element, can be measured if the core loss intensities are related to the total beam current according to equation (3). Hence, the low loss intensities up to an energy loss A also have to be measured. Compared to the measurement of concentration ratios, this leads to severe experimental complications because, depending on the inner shell loss edge, the intensity typically drops by a factor of 1000 to 10,000 from the zero loss to the core loss region. In the commonly used PEELS technique, the large dynamical range which has to be covered leads to two major problems: (1) the zero loss peak is focused into one or only a few pixels of the linear detector array which requires that, while recording the low loss region, the current density must be strongly reduced in order not to oversaturate the detector; and (2) for the measurement of the inner shell losses the intensity has to be increased by a well calibrated factor, which has to be of the order of the numbers given above.

In ESI measurements the intensity problems can more easily be overcome, mainly because the total intensity, e.g. of the zero loss, is recorded in images and thus spread over the whole 1024 x 1024 pixels of the CCD array, rather than being focused into just a few pixels, as is the case on the linear photodiode array of a PEELS. The gain change required when proceeding from the low loss to the inner-shell loss region can be achieved by combining three different experimental factors: (1) The exposure time can be increased by a factor of up to 100 (which is common practice for PEELS measurements as well); (2) We use binning of the CCD pixels, which effectively increases the intensities by a well defined factor, e.g. 4 x 4 binning increases the intensities in the resulting pixels by a factor of 16; (3) On the Zeiss EM 912 Omega the illumination intensity can be increased in calibrated, digitally controlled steps. This is an advantage which the Koehler illumination (Benner and Probst,

1994) offers compared to the more common illumination systems, in which the beam is spread and condensed in the object plane in order to reduce or increase the illumination intensity. We have measured the total beam current per unit area for the individual illumination steps by means of a Faraday cup and making use of this we possess an additional means to influence the intensity in well calibrated steps by up to a factor of 100 and more.

As an example for the measurement of the number of atoms per unit area we have chosen the A1203 films produced by electrochemical deposition because of their uniform and well known thickness. Moreover, in each of the TEM specimens used, there are frequently areas where the film is ruptured and folded together so that areas with multiples of the film thickness lie next to each other. For a film with a nominal thickness of 10 nm, Fig. 5(a) shows a zero loss filtered bright field image and Fig. 5(b) an ESI image above the O - K edge of an area with single, double and triple film thickness. It can clearly be seen that the intensity in the zero loss decreases with increasing film thickness, whereas the element specific signal in the core loss region increases.

For the quantitative analysis we have acquired two series of ESI images, one in the low loss region from 0 to 200 eV and one around the oxygen K-edge from 435 to 635 eV energy loss. Both series were recorded with a slit width of 20 eV and an energy loss increment of 20 eV. Between both series the exposure time was increased by a factor of 10, the illumination current was increased by a factor of 4 and the CCD camera was switched to 4 x 4 binning, which results in a total gain change by a factor of 640. From the two series of images, spectra were extracted for the three areas shown in Fig. 5(a), which correspond to the three different specimen thicknesses produced by superimposing individual films. The resulting spectra are shown in Fig. 6(a) [not interpolated] for the low loss and Fig. 6(b) [with linear interpolation] for the core loss region. The spectra were evaluated on the basis of equation (3) which yields the number of oxygen


(a) i

3O O 3

2~

'~ 2o

o

~°1o L~ L~ 5

• i , i , i •

-bo 'o loo 2bo' Energy Loss (eV)

(b) 1,0 i , i • i , i • i

~ 25 0,8

"-,,// t 'st "'-._,k . . . . . . . . . i'-I 1

°2r . . . . . . . . I t 0 , 450 500 550 600 650

Energy Loss (eV)

Fig. 6. (a) Low loss spectra and (b) core loss spectra extracted from the three different areas indicated in Fig. 5 (a).

100

texp/nm

8O j,," j ,

60 /i/s., / ' 1Onto -E. -30 nm

• /

• /

• /

40 s/

20 j" /

/

, i r i , i L , i ,

0 ' 20 4'0 60 80 100 tnom/nm

Fig. 7. Experimentally measured thicknesses versus nominal thicknesses plotted for the 10- and 30-nm-thick A1203 films

with single, double and triple film thickness.

0,2

~. = 102 nm +10 •"

/ ,

t - "/• "/"" - * - - 1 0 nm

/, (" -e - -30 nm

i i i i i i , i i i

20 40 0~0 , i , , , i , , , , , , ,

0 60 80 1 O0 120 tnom/nm

Fig. 8. t/,;~-ratios measured from low loss intensities for the 10- and 30-nm-thick A1203 films with single, double mad triple film

thickness.

atoms per unit area. Based on a value of (3 .2~0.1)g/ cm 3 for the density of amorphous A1203, an atomic density for oxygen of 57 atoms/nm 3 is obtained from equation (5) and (6). Applying equation (4) the thicknesses plotted in Fig. 7 versus the nominal thicknesses were obtained. It can be seen that the measured values agree well with the nominal thickness values and that the deviations are smaller than the estimated total error of 15%. Furthermore, the data for the different film thicknesses lie almost perfectly on a straight line, which suggests that the major contribution to the total error stems from a systematic deviation in either the nominal film thickness or the inelastic scattering cross-sections.

The same experiments were subsequently repeated for the 30-nm-thick film. We also choose areas with single, double and triple film thickness, which means that the maximum film thickness which we studied in our experiments was 90 nm. Figure 7 shows that even for the thick- est areas the experimental data are in excellent agreement with the nominal values of the total film thicknesses.

Measurement of the specimen thickness from low loss' in tensities

The specimen thickness can also be measured from the low loss intensities alone, provided that the mean free

Fig. 9. Bright-field image of a wedge shaped Si crystal showing two-beam thickness contours. Boxes indicate tile areas from which the thickness data were extracted. At the point denoted

with 'x' the specimen thickness was measured With CBED.

path for inelastic scattering ~ is known. Since we have to measure the low loss intensities in the experiments discussed in the previous section, equation (8) provides an independent measurement of the specimen thickness. However, in general, values for the mean free path 2 are not available. Consequently, we have plotted t/2=ln(Itot/ Io) as a function of the nominal film thickness and the results are shown in Fig. 8. Based on the known film thickness, we have determined an effective mean free path 2 from the data depicted in Fig. 8. A fit to all the data points results in a value of 2=(102± 10)nm. The final thickness values which can be obtained from this 2 for the two films and their multiple thicknesses agree within better than 10% with the results obtained by the analysis of the core loss intensities. The tendency that

368

2 , 0 . . . . . . . . . . . . . . . . . . . t/X

1 , 5 -

1,0

0,5 50

0,00 '200' ' '400' ' '600' ' '800 '1000 distance from edge / nm

Fig. 10. Plot of the t/2-values as a function of the distance from the edge for the area shown.

J. Mayer et al.

250 t/nm

200

150

100

the 10 nm film seems to be somewhat thinner than the nominal value, whereas the 30 nm film appears to be slightly thicker, can be seen reproducibly in the two independent measurements.

As a final example, a thickness measurement for a wedge shaped Si crystal is shown. The bright field image (Fig. 9) shows thickness fringes with a regular spacing, indicating that the sample area is almost perfectly wedge shaped. From this area a series of 16 ESI images from 0 to 150 eV with a window width of 10 eV was recorded. In the regions indicated in Fig. 9 the low loss spectra have been extracted and the resulting t /2 ratios are plotted in Fig. 10 as a function of the distance from the edge. A smooth and almost straight curve results, which reflects the almost linear increase in specimen thickness in the wedge shaped area shown. In order to calibrate the mean free path 2, we have acquired one convergent beam electron diffraction (CBED) pattern (Fig. 11). The

~0 . B ¢..

,4 3000- o3

.~->'2000. 03 C

~ 1000.

0 t 1 5 0 2 0 0 2 5 0 ' 0

pixel Fig. 11. (a) Zero-loss filtered CBED pattern used for an accurate measurement of the specimen thickness at the position marked

with x in Fig. 9. (b) Line profile across the pattern showing the Pendell6sung oscillations in the 220 reflection.


200

15O

O

100

70

o 60

50 e"

o = 4(1 u

30 U U

20

(a)

20(1 250 300 350 400

Energy loss (eV)

(b} 91)

8O

x5 10

0 I [ 450 500 550 600

Energy loss (eV)

Fig. 12. (a) The C K-edge used to determine the carbon contaminat ion layer thickness and (b) the O K-edge showing the thickness of the amorphous surface oxide on an ion-milled

Si specimen.

pattern has been acquired with zero loss filtering in a two beam orientation with a ~ strongly excited 220 reflection at the position indicated in Fig. 9. A quantitative analysis of the Pendell6sung oscillations shown in Fig. 1 l(b) by means of dynamical calculations gave a value of t=(199 ± 4) nm. The measured value of t/2= 1.55 4- 0.08 at the same specimen position results in 2=-(128 4- 8) nm.

The above analysis, which is based on calibrating ,~. by measuring the thickness of the crystalline silicon, does not take into account the possible presence of an amorphous surface oxide and a carbon contamination layer. In a second step we have measured the thickness of both possible layers with the method discussed above. Experimentally, we have recorded series of ESI images across the carbon K-edge and the oxygen K-edge. Assuming that the total thickness of the two surface layers remains constant with increasing specimen thickness, we have only extracted and quantified the EEL spectra for carbon [Fig. 12(a)] and oxygen [Fig. 12(b)] for very thin areas close to the edge. A quantitative analysis resulted in a total thickness of the amorphous surface oxide of tox=(6.3 ± 1.0) nm and the carbon contamination layer of tc=(1.0±0.5) nm. The measured

values are total values and represent the sum of the two surface layers at the top and bottom of the specimen. A corrected value of ). can now be obtained by adding the amorphous surface layers to the crystalline specimen thickness measured by CBED. This results in a specimen thickness of t=(206 + 5) nm and a new value of the mean free path )~=(133 + 10)nm.

The above discussion of the possible ways to measure specimen thickness and to determine the ]presence and thickness of oxide layers and carbon contamination layers clearly shows that ESI provides information on important specimen parameters which have to be known, e.g. in the analysis of high resolution electron microscopy (HREM) images. An accurate imeasurement of the specimen thickness of HREM specimens is a problem because the specimens are very {hin, typically below 10 nm. At this thickness, CBED measurements cannot be performed because of the lack o f dynamical intensity oscillations. EELS measurements are also problematic because of the large intensity difference between the zero loss and the low loss, and even more the inner shell loss regions at values of t /) ,<O.l. As discussed above, we have found that using ESI it is much easier to deal with these intensit~¢ differences, mainly because the intensity is recorded in images and a number of parameters can be used to increase the image intensity by a known factor. Furthermore, two- dimensional data are obtained which make it possible to compute thickness maps, e.g. of an area imaged by HREM.

The possibility to measure the thickness of oxide layers or carbon layers makes ESI an important tool in systematic attempts to improve the speqimen quality. The fairly large thickness of the amorphous surface oxide can be explained by the formation bf a damaged surface layer during ion beam thinning Which is subsequently oxidized while storing the specimen in air. Our experiments thus show that the thickness of the oxide layer can not only be reduced by storage Under vacuum, but also by lowering the surface damage introduced during ion thinning, e.g. by low angle milling with low energy ions. We have used our new method to measure contamination layer thicknesses as a fuhction of the parameters in low angle ion beam milling from one or both sides of the specimen. The results will be published elsewhere (Strecker et al., 1997). Furthermore. we have determined an optimum thickness of c@rbon coating which is required to make an insulating ~pecimen con- ductive. We obtained a minimum value of (1.5 + 0.5) nm of carbon coating thickness for which no more charging under the electron beam occurred.

CONCLUSIONS

We have demonstrated that series of ESI images can be quantified with very high accuracy. The main advantages of the ESI method are: (1) The data can be acquired in much shorter times than with the complementary scanning techniques: (2) Spectra can be

370 J. Mayer et al.

extracted after the acquisition of the ESI series for any desired image area; and (3) The intensity difference between the zero loss, low loss and inner shell loss regions can be compensated for by a number of different and well calibrated parameters, which makes it possible to measure the absolute number of atoms per unit area with the same accuracy as concentration ratios.

The aim of the present investigations was to apply the new techniques to well characterized examples in order to verify the feasibility in a systematic way. Further- more, for the same reason, we have tried to use standard EELS quantification software to extract the specific information from the experimental ESI data. To accom- plish this we had to modify the spectra in the inner shell loss region by linear interpolation. We have shown that this is a very elegant way to produce continuous spectra and, using certain precautions, does not introduce a significant error in the quantification. However, the aim of future developments should be to set up routines which allow to analyse the three-dimensional data space I(x,y,AE) without the need to extract and quantify individual spectra, and independently of the way the intensity data were acquired, i.e. via PEELS or via ESI.

Acknowledgements--We gratefully acknowledge support by the Stiftung Volkswagenwerk under contract 1/69 931.

REFERENCES

Beckers, A. L. D., De Bruijn, W. C., Gelsema, E. S., Cleton-Soeteman, M. I. and van Eijk, H. G., 1994. Quantitative electron spectroscopic imaging in bio-medicine: methods for image acquisition, correction and analysis. J. Microscopy, 174, 171-182.

Beckers, A. L. D., Gelsema, E. S., De Bruijn, W. C., Cleton-Soeteman, M. I. and van Eijk, H. G., 1996. Quantitative electron spectroscopic imaging in bio-medicine: evaluation and application. J. Microscopy, 183, 78 88.

Benner, G. and Probst, W., 1994. Krhler illumination in the TEM: fundamentals and advantages. 3. Microscopy, 174, 133-142.

Bentley, J., Hall, E. L. and Kenik, E. A., 1995. Quantitative elemental concentrations by energy filtered imaging. Proc. Microscopy and Microanalysis 1995, eds G. W. Bailey, M. H. Ellisman, R. A. Hennigar and N. J. Zaluzec, pp. 268-269. Jones and Begell, New York.

Botton, G. and L'Esprrance, G., 1994. Development, quantitative performance and applications of a parallel electron energy-loss spectrum imaging system. J. Microscopy, 173, 9 25.

Crozier, P. A., 1995. Quantitative elemental mapping of materials by energy-filtered imaging. Ultramicroscopy, 58, 157-174.

Egerton, R. F., 1982. A revised expression for signal/noise ratio in EELS. Ultramicroscopy, 9, 387-390.

Egerton, R. F., 1996. Electron Energy-loss Spectroscopy in the Electron Microscope, 2nd edn. Plenum Press, New York.

Hofer, F., Warbichler, P. and Grogger, W., 1995. Imaging of nanometer-sized precipitates in solids by electron spectroscopic imaging. Ultramicroscopy, 59, 15-31.

Hofer, F., Grogger, W., Kothleitner, G. and Warbichler, P., 1997. Quantitative analysis of EFTEM elemental distribution images. Ultramicroscopy, 67, 83-103.

Hunt, J. A. and Williams, D. B., 1991. Electron energy-loss spectrum- imaging. Ultramicroscopy, 38, 47-73.

J/iger, W. and Mayer, J., 1995. Energy-filtered transmission electron microscopy of SimGen superlattices and SiGe heterostructures. I. Experimental results. Ultramicroscopy, 59, 33-45.

Jeanguillaume, C., Trebbia, P. and Colliex, C., 1978. About the use of electron energy-loss spectroscopy for chemical mapping of thin foils with high spatial resolution. Ultramicroscopy, 3, 237-242.

Krrtje, K.-H., 1994. Image-EELS: simultaneous recording of multiple electron energy-loss spectra from series of electron spectroscopic images. J. Microscopy, 174, 149-159.

Krivanek, O. L., Gubbens, A. J. and Dellby, N., 1991. Developments in EELS instrumentation for spectroscopy and imaging. Microsc. Microanal. Microstr. 2, 315-312.

Krivanek, O. L., Gubbens, A. J., Kundmann, M. K. and Carpenter, G. C., 1993. Elemental mapping with an energy selecting imaging filter. Proc. 5lst Ann. Meeting MSA, eds G. W. Bailey and C.L. Rieder, pp. 58(~587. San Francisco Press, San Francisco.

Lavergne, J.-L., Foa, C., Bongrand, P., Seux, D. and Martin, J.-M., 1994. Application of recording and processing of energy- filtered image sequences for the elemental mapping of biological specimens: Imaging-Spectrum. J. Microscopy, 174, 195 206.

Martin, J.-M., Lavergne, J.-L., Vacher, B. and Inoue, K., 1995. Interactive image-spectrum EELS: Application to elemental mapping of lubricant colloids. Microsc. Microanal. Microstruct., 6, 53-63.

Martin, J.-M., Vacher, B., Ponsonnet, L. and Dupuis, V., 1996. Chemical bond mapping of carbon by image-spectrum EELS in the second-derivative mode. Ultramicroscopy, 65, 229-238.

Mayer, J., Szabo, D. V., Riihle, M., Seher, M. and Riedel, R., 1995. Polymer derived Si-based ceramics, Part II: microstructural characterisation by electron spectroscopic imaging. Z Eur. Cer. Soc., 15, 717-727.

Mayer, J. and Plitzko, J. M., 1996. Mapping of ELNES on a nanometre scale by electron spectroscopic imaging. J. Microscopy, 183, 2-8.

Reimer, L., 1995. Electron spectroscopic imaging. In Energy-Filtering Transmission Electron Microscopy, Springer Ser. in Optical Sciences 71, ed. L. Reimer, pp. 347-400. Springer, Berlin, Heidelberg.

Riedel, R., Seher, M., Mayer, J. and Szabo, D. V., 1995. Polymer derived Si-based ceramics, Part I: preparation, processing and properties. J. Eur. Cer. Soc., 15, 703-716.

Schenner, M., Nelhiebel, M. and Schattschneider, P., 1996. Diffraction effects in electron spectroscopic imaging. Ultramicroscopy, 65, 95-99.

Shuman, H., Chang, C.-F. and Somlyo, A. P., 1986. Elemental imaging and resolution in energy-filtered conventional electron microscopy. Ultramicroscopy, 19, 121 134.

Strecker, A., Mayer, J., Gutekunst, G., Gemming, T., Eigenthaler, U., Baretzki, B. and Riihle, M., 1997. Optimisation of TEM specimen preparation by double sided ion beam thinning under low angles. To be published.

Yase, K., Horiuchi, S., Kyotani, M., Yamamoto, K., Yaguchi, A., Futaesaku, Y., Suwa, T., Kakimoto, M. and Imai, Y., 1996. Observations of cross sections of plasma-polymerized films of Benzene and Naphthalene by electron spectroscopic imaging. Jpn. J. Appl. Phys., 35, L657-L660.

Documents

Quantitative analysis of electron spectroscopic imaging series