Ultramicroscopy 111 (2011) 1375–1380

Contents lists available at ScienceDirect

Ultramicroscopy

0304-39

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ultramic

Effect of sample thickness, energy filtering, and probe coherenceon fluctuation electron microscopy experiments

Feng Yi, P.M. Voyles n

Materials Science and Engineering Department, University of Wisconsin, 1509 University Ave., Madison, WI 53706, USA

a r t i c l e i n f o

Article history:

Received 24 March 2011

Received in revised form

6 May 2011

Accepted 8 May 2011Available online 13 May 2011

Keywords:

Fluctuation electron microscopy

Nanodiffraction

Thickness

Coherence

Energy filter

Shot noise

91/$ - see front matter & 2011 Elsevier B.V. A

016/j.ultramic.2011.05.004

esponding author.

ail address: voyles@engr.wisc.edu (P.M. Voyle

a b s t r a c t

We have explored experimentally the effects of the TEM sample thickness, zero-loss energy filtering,

and probe coherence on fluctuation electron microscopy (FEM) experiments implemented using

nanodiffraction. FEM measures the variance V of spatial fluctuations in nanodiffraction. We find that

V is inversely proportional to the sample thickness, as predicted by earlier models. Energy filtering

increases V at all thicknesses we measured. V increases as the coherence of the probe increases. All of

these factors must be carefully controlled to obtain quantitatively reliable FEM data.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

Fluctuation electron microscopy (FEM) is a technique to uncovermedium range order (MRO) in amorphous materials. It can beimplemented using nanodiffraction in a STEM or dark-field imagingin a TEM. The fundamental data set is the diffracted intensity I as afunction of diffraction vector k (or vector magnitude k¼9k9), spatialresolution R, and position on the sample r. FEM measures spatialfluctuations in I(k, R, r) using the normalized variance

Vðk,RÞ ¼/Iðk,R,rÞ2Sr

/Iðk,R,rÞS2r

�1, ð1Þ

where /Sr indicates averaging over position r. Since it was invented[1], FEM has been applied to amorphous semiconductors [2,3],chalcogenide alloys [4], and metallic glasses [5–8]. The details offundamental theory behind FEM can be found in [9], and Treacy hasrecently reviewed the technique and its applications [10].

FEM performed in STEM nanodiffraction mode has severaladvantages compared with FEM performed in dark-field TEM mode[11], and as a result has largely replaced dark-field TEM FEM. STEMFEM makes more efficient use of diffracted electrons and thereforedose to the sample, and it acquires significantly more data points ink. STEM nanodiffraction also uses a virtual aperture to control theprobe size and thus the resolution, R, so we can continuously varythe resolution by adjusting the condenser lens current [12]. Thiscreates the flexibility to do variable resolution FEM [11,13,14]. FEM

ll rights reserved.

s).

in a FEG STEM offers improved coherence compared to FEM on aLaB6 TEM. Stratton and Voyles [15] compared the FEM experimentalresults performed on the Al88Y7Fe5 using TEM mode and STEMmode and found the variance in STEM mode is almost an order ofmagnitude higher. They attributed this difference to higher coher-ence in STEM mode, and argued that this is inherent to the opticalconfiguration, not simply a result of the difference in emitters.

STEM FEM also offers unexpected opportunities to removeartifacts from the FEM data, and therefore improve its quality.Bogle et al. [16] demonstrated that in mixed phase crystal/amorphous samples STEM FEM makes it easier to identify regionsin which large crystals dominate the variance. These data pointscan be removed by post-processing so that the variance datareflect only MRO in the sample. Bogle et al. [13] did variableresolution FEM experiments on amorphous Si film, using fourdifferent probe sizes to detect MRO in amorphous Si, compared tothe two different probe sizes used by Voyles and Muller [11].Therefore, their data are a more robust test of the pair persistencetheory [17] used to extract MRO size based on variable resolutionFEM. They discovered that MRO are similar in the amorphous Sigrown by dc magnetron sputtering and plasma enhanced chemi-cal vapor deposition.

Hwang and Voyles reported VR FEM measurements on a Cu-Zrmetallic glass covering an even wider range of probe diameter witheven more data points. They showed that V goes nearly to zero withan 11 nm diameter coherent probe, which indicates that this is amaximum useful probe size for this material. They also implemen-ted a correction to V(k) developed by Fan et al. [18] that accounts forvariance arising from shot noise in the number of diffractedelectrons. This is a particularly pernicious artifact: the shot noise V

F. Yi, P.M. Voyles / Ultramicroscopy 111 (2011) 1375–13801376

is inversely proportional to the average diffracted intensity /I(k, R,r)Sr [11], so it has structure in k just like the signal from the sample.

Daulton et al. [19] have done a series of experiments on whatfactors influence FEM data, including instrumental factors andanalysis methodology. They also did a type of variable resolutionFEM by varying the probe defocus instead of the convergenceangle to extract MRO size from FEM experiment performed onAl88Y7Fe5 based on the amorphous/nanocrystal composite modelby Stratton and Voyles [15,20]. They concluded that both con-denser lens current and sample thickness affect the variancesubstantially. They calculated four different variance functions,including the type defined by Eq. (1).

In this paper, we explore experimentally the effect of thesample thickness, zero-loss energy filtering of the nanodiffractionpatterns, and probe coherence on the STEM FEM V(k) from ametallic glass sample. Small sample thickness, zero-loss energyfiltering, and high probe coherence increase V, and are useful forcomparing to FEM theories. Control over all of these parameters isnecessary to ensure reproducible FEM data sets that can bequantitatively compared to one another.

1.1. Sample thickness

Current theories of FEM are based on kinematic scattering [9,10].To achieve kinematic scattering, the sample must be quite thin.Dynamical diffraction is not present in amorphous materials, so theissue is to avoid plural elastic scattering. In amorphous materials,elastic scattering is an isolated, rare event, so the scattering prob-ability as a function of thickness t can be reasonably modeled by aPoisson distribution. The requirement for single scattering is thenthat t must be smaller than one elastic mean free path, le. In someprevious FEM experiments, the authors either did not report thesample thickness explicitly [7] (we have also been guilty of this [5]),or used a sample more than one Le thick [19]. Not only does thismake experiments hard to reproduce, it also complicates the theoryexplanation of FEM results. Stratton and Voyles [15,20] developed aphenomenological model of how the variance depends on thesample structure, which predicts that the variance is proportionalto 1/t. As discussed below, Daulton et al. [19] did not find this 1/tdependence. There is also a limit to the minimum usable samplethickness, set by the increasing exposure time to obtain the needednumber of scattered electrons within the time over which themicroscope and sample are stable.

Since thickness affects V, sample roughness must also have aneffect. Bogle et al. [13] described how to remove thickness non-uniformity from STEM FEM data using the intensity at high k inthe nanodiffraction pattern as a measure of the local thickness.Hwang and Voyles [14] developed a similar method using thehigh-angle annular dark field (HAADF) image intensity acquiredsimultaneously with nanodiffraction pattern as a reference to dothickness filtering. These methods remove the effects of rough-ness and sample thickness gradient effects from V.

1.2. Energy filter

Current theories of FEM do not account for inelastic scattering.Hence, it is helpful to only use elastically scattered electron toform the nanodiffraction patterns. The angular distribution ofinelastically scattered electrons is not strongly related to thestructure of the sample, and especially not to MRO. Zero-lossenergy filtering of the diffraction patterns can remove plasmonand ionization loss electrons, but not phonon losses. However,phonon scattering has a relatively flat angular distribution, so asignificant fraction of it falls outside the scattering angles used forFEM, which are typically o20 mrad at 200 kV. Plasmon losses aremore stongly peaked near the zero beam of the diffraction pattern

and pose more of a problem. Hwang and Voyles [14] used zero-loss energy filtering in their FEM experiment but did not system-atically explore the effects.

1.3. Probe coherence

The enhanced V in FEG STEM FEM versus LaB6 TEM FEM suggeststhat coherence is important to the FEM signal [15]. The FEM theoriesassume perfect coherence, so assuring that the coherence is at leastconstant from one set of measurements to another is important.Voyles and Muller [11] mentioned that ringing in the TEM image ofthe probe indicates good coherence, and Gibson et al. [21] alsodescribed the probe coherence in their measurements as ‘‘good’’. Werecently developed a method to measure probe coherence quantita-tively for probes in the 1–10 nm diameter range useful for FEM [12],based on work by Dwyer et al. [22]. For probes that are largecompared to the TEM resolution of the microscope so that aberra-tions in the imaging system can be neglected

IiðX,YÞ ¼ ½9c92� 9A92

�ð�Mx,�MyÞ, ð2Þ

where I is the TEM image of the probe, X and Y are coordinates in theimage plane, c is the intensity distribution of the incoherenceextended source, A is the coherent probe wave function, M is themagnification, and x and y are the coordinates in the source plane.For small convergence angles, so that aberrations of the probeforming lens can be neglected, A is an Airy function, andwe assumed, following Dwyer, that c is a Gaussian. By fitting theI(X, Y) to Eq. (2), we can extract the size of the source function at thesample, which determines the coherence of the probe.

We applied this method to determine the probe coherence onour Titan STEM as a function of the C1 lens excitation (spotnumber in FEI parlance) at constant convergence angle using twodifferent condenser apertures [12]. The C2 and C3 lenses wereadjusted to create the same convergence angle with a 10 mm anda 30 mm diameter condenser aperture. The source diameterdecreases as a square root of the spot number, and is system-atically lower for the larger aperture. All the data for bothapertures falls on the same line showing that the source diametersquared is proportional to the probe current. This provides aneasy method of maintaining constant coherence by maintainingconstant probe current [14]. It also shows that the minimumusable probe current, subject to microscope instability andsample drift, sets the maximum achievable coherence at fixedsource brightness.

2. Experiment

The samples for this study were Al87Y7Fe5Cu1 metallic glassribbons fabricated by melting spinning. We are studying howMRO in these samples influences their nanocrystallization [5]. Tominimize the contaminants on the sample surface, we firstultrasonicated the sample in Formula 409 degreaser, then in thedistilled water. Then we used electropolishing in 75% methanol/25% nitric acid electrolyte at �4375 1C to prepare the TEMsamples. After polishing, we used methanol to remove the acidresidue on the sample, then cleaned the samples again intrichloroethylene (TCE) for 40 s, acetone for 30 s, and methanolfor 40 s. FEM experiments were done within 48 h of electropol-ishing. When the samples are not in use, we stored them in afreezer.

STEM experiments were performed in an FEI Titan STEM withCEOS aberration corrector operated at 200 kV. The Schottky emis-sion gun was operated at 4500 V extraction voltage and gun lenssetting 8, the same conditions used for our previous coherencemeasurements [12] and previous FEM experiments [14]. Before we

Fig. 1. V(k) for Al87Y7Fe5Cu1 samples of different thickness with zero-loss filtering

of the diffraction patterns and spot number 8.

Fig. 2. The magnitude of the 1st peak in V(k) at k¼0.40 A�1 as a function of

sample thickness with and without zero-loss filtering. Spot number is 8.

F. Yi, P.M. Voyles / Ultramicroscopy 111 (2011) 1375–1380 1377

put the sample into the STEM column, we plasma cleaned thesample at least 4 min to remove carbon-related contaminants. Weused a convergence half-angle of 0.82 mrad, and a camera length of512 mm using the Titan ‘‘EFSTEM’’ lens program during our FEMexperiments. For study of thickness and energy filter effect,0.82 mrad was achieved with a 10 mm diameter condenser (C2)aperture, for study of probe coherence effect; the same convergenceangle was achieved with a 5 mm diameter condenser (C2) aperture.We used a Gatan US1000 CCD camera at binning 4 in a GIF 865 ER tocollect the diffraction patterns. The 512 mm camera length and4 pixel binning corresponds to 0.00536 A�1/pixel on the CCD and amaximum k of 1.065 A�1 inside the 2.5 mm diameter GIF entranceaperture. In this paper, we use k¼y/l as the wave vector magnitude.Some nanodiffraction patterns were zero-loss energy filtered with aslit width of 10 eV. The zero beam in the diffraction patterns wasblocked with a beam stop mounted in the STEM viewing chamber.The FEI standard beam stop was reduced at the end to a40�40�200 mm3 needle using a FIB to make it compatible withthe GIF post-column magnification.

Sample thickness was measured using the log-ratio method[23], but applied to elastic scattering, not inelastic scattering [24].In STEM, this involves measuring the diffraction pattern zerobeam intensity off the sample, I0, then in the region of interest, I.Then, ln(I0/I)pt/le. Schewiss et al. [25] measured le¼8171 nmfor Al87Y7Fe5Cu1 from samples with known thickness prepared byFIB. For each region of interest on a TEM sample, we simulta-neously acquired a 10�10 grid of nanodiffraction patterns andthe HAADF intensity. We calculate V(k) from each area, thenreport the mean from typically 10 areas, quoted with onestandard deviation of the mean error bars. For each set ofexperimental conditions, we adjusted the exposure time so thatthe first ring in the nanodiffraction patterns had �700 counts,which corresponds to 148 beam electrons, given the CCD gain of4.72. This ensures that the shot noise contribution to V wassimilar for every data set. We also applied the Fan et al. [18] shotnoise correction to V. Before calculating V, the set of nanodiffrac-tion patterns were thickness filtered by the HAADF intensity asdescribed in [14] so that each FEM data set comes from regions ofthe sample that have a spread in thickness of 0.039le. We allowedvariations in the mean thickness of 1.5% from area to area.

3. Results and discussion

3.1. Sample thickness and thickness filtering dependence of variance

Fig. 1 shows V(k) of the same sample at regions of differentthickness using the energy filter. The magnitude of the large firstpeak in V(k) decreases as the sample grows thicker and only at thelargest thicknesses does the shape of the peak change. Fig. 2shows V(k¼0.40 A�1), the position of the first major peak in V(k),as a function of inverse of sample thickness in units of le.V(k¼0.40 A�1) is inversely proportional to the sample thicknessfor all but the thickest sample, as predicted [20], but with non-zero intercept. In the kinematic theory, V goes to zero at largethickness because as the volume sampled at each probe positionbecomes large, every volume comes to reflect the average samplestructure and fluctuations from position to position becomesmall. The real non-zero intercept may be due to sample rough-ness or other imperfections in the experiment, or it may arisefrom plural scattering or phonon scattering not captured in thekinematic theory. The total thickness range in Fig. 1 is 24–57 nm,so tight experimental thickness control is required for FEMexperiments.

V(k¼0.40 A�1) for the thickest sample, 0.70le is off the linear fit.We believe this is due to plural elastic scattering. Fig. 3(a) shows P0,

the probability that an electron from the samples in Fig. 1 will passthrough the sample unscattered, based on the Poisson distribution.When the sample thickness is below 0.7le, the majority of electronspass through the sample without being scattered. However, it isthe scattered electrons that give rise to the diffraction pattern.Fig. 3(b) shows the ratio of probability that the electron is scatteredonce, P1, to the probability that the electron is scattered anynumber of times PN. P1/PN is a measure of plural scattering. Whenthe thickness reaches 0.7le, about 32% electrons are scattered atleast twice, so plural scattering may explain the deviation fromthe 1/t trend.

Daulton et al. also studied the effects of sample thickness on V

from an Al-based metallic glass. They report the ratio of the twopeaks in V(k) data like Fig. 1 at k¼0.40 and 0.70 A�1. If Vp1/t for allk, as predicted, the ratio should be constant as a function ofthickness. Instead, Daulton et al. report non-monotonic behavior inV(k¼0.44 A�1)/V(k¼0.76 A�1) (Fig. 4(b) in [19]). There are twodifficulties with this result. First, the samples thickness range was0.3–2 inelastic mean free paths, li, which is 40.5–270 nm, accordingto our measurement of li¼13574 nm [25]. So only the twothinnest specimens are thin enough to avoid significant pluralelastic scattering. Second, the experiments were performed atconstant exposure time and not corrected for shot noise [26]. Thismeans that as the sample thickness increased, so did the averagenumber of counts in the nanodiffraction patterns, and the shot noisecontribution to V decreased. The V(k) curves in Fig. 4(a) in [19] show

Fig. 3. (a) P0, the probability that the electron is not scattered and (b) the

probability that an electron is scattered one and only one time, P1, divided by

the probability of scattering any number of times, PN, calculated from the Poisson

distribution for the sample thicknesses in Fig. 2.

F. Yi, P.M. Voyles / Ultramicroscopy 111 (2011) 1375–13801378

an upwards slope in V(k) at high k which is characteristic of FEMdata with a large, uncorrected shot noise contribution to the data.We therefore do not believe that these data show a meaningfuldisagreement with our previous prediction of Vp1/t.

Fig. 4. Nanodiffraction patterns acquired (a) with zero-loss energy filtering and

(b) without zero-loss energy filtering (The two nanodiffraction patterns were

taken from different regions in the same sample).

3.2. Comparison between the variance with and without energy filter

Fig. 4(a) and (b) compares two nanodiffraction patterns acquiredfrom a sample region 0.43le thick with and without zero-loss energyfiltering, respectively. The pattern in Fig. 4(b) shows significantlyhigher intensity near the zero beam, which is presumably due toplasmon scattering at small angles. The inelastic background persiststo higher scattering angles, reducing the intensity to background ratioof the speckles in the first diffraction ring. The inelastic backgroundincreases /IS in the dominator of Eq. (1), which decreases V(k). Fig. 5shows that even for the thinnest sample (0.29le) V(k) withenergy filtering is about 17% higher than without energy filtering.More complete results are shown in Fig. 2, which shows thatV(k¼0.40 A�1) is consistently higher with filtering than without overthe entire thickness range. The absolute difference between V withand without energy filtering is almost constant from 0.29le to 0.43le,then decreases a little bit at 0.57le and increases at 0.7le. Withoutenergy filtering, Vp1/t only up to 0.43le. Energy filtering is thereforeimportant at all sample thicknesses we have measured and extendsthe usable thickness range to somewhat larger thicknesses.

3.3. Variance comparison of different spot size

Fig. 6(a) shows V(k) at constant convergence angle, andconstant sample thickness (0.43le) with energy filtering, as afunction of the C1 lens excitation (FEI spot number). As we haveshown previously, increasing spot number by one decreases thesource diameter at the sample by 1=

ffiffiffi

2p

, increases the probecoherence, and reduces the probe current by half [12]. Weincreased the exposure time for the diffraction patterns by 2 witheach step in spot number to keep the number of electronscollected by the CCD camera constant from 0.5 s for spot 3–8 sfor spot 7. The Titan offers spot numbers up to 11, but the sampledrift became prohibitive at the exposures times required forhigher spot numbers. In this data set, spot 3 corresponds to a

Fig. 5. V(k) with and without zero-loss energy filtering, from a sample 0.29le thick

acquired with spot number 8.

Fig. 6. (a) V(k) as a function of spot number/probe coherence for samples with

constant thickness of 0.43le and with zero-loss energy filtering. (b) The 1st peak in

V(k) at k¼0.40 A�1 as a function of spot number/probe coherence. (5 mm diameter

C2 condenser aperture was used in the measurement.)

F. Yi, P.M. Voyles / Ultramicroscopy 111 (2011) 1375–1380 1379

probe current approximately of 6.8 pA, and spot 7 corresponds toa probe current approximately of 0.42 pA.

In Fig. 6(a), the first peak in V(k) systematically decreases withdecreasing probe coherence/spot number (corresponding source sizesmay be found in [12]). There may also be some change in the shape ofthe high-k shoulder, especially at low spot number. Fig. 6(b) showsthat V(k¼0.40 A�1) increases monotonically with probe coherence/spot number. We have shown that V(k) from this material arises fromnanometer-diameter clusters with fcc-Al-like internal atomic struc-ture. The first peak then corresponds to {1 1 1} Bragg diffraction fromthose clusters. The peak intensity of the diffraction maxima increaseswith increasing coherence, so when the probe lands on, then off,a cluster, the excursions in the diffracted intensity are larger, andV(k) increases. This mechanism should work for diffraction from anykind of cluster, even without crystal symmetry, so we believe thisphenomenon is not specific to this material.

The broad second peak in V, near k¼0.7 A�1 is relativelyinsensitive to the spot number. This second peak originates from/2 2 0S Al-like ordered structure, and simulations from perfectlyordered crystals show much higher V than we observe. We suspectthat this is evidence of strain or defects inside the nanometer-sized Alclusters which more strongly effects higher order Bragg diffraction.The strain reduces the diffracted intensity, resulting in a lower V. Italso reduces the effects of probe coherence because there is lessstructural coherence to respond to it.

The results in Fig. 6 indicate that it is necessary to control theprobe coherence to ensure reproducible, comparable measurementsof V(k). This is particularly important for variable-resolution FEM,since changing the physical condenser aperture size changes theprobe coherence, even at the same convergence angle. On our TitanSTEM, changing the C2/C3 lenses to change the convergence angle atconstant physical aperture size also changes the coherence. This isbecause the C2 aperture is below the C2 lens, so changing the C2 lenschanges the wave field incident on the aperture. Fortunately, theprobe current provides an easily-measured proxy for the coherence,so as long as the C1 excitation (spot number) is adjusted to keep theprobe current constant for different apertures and convergenceangles, the probe coherence will be kept constant as well and reliableFEM data can be obtained.

4. Conclusions

We have shown that the TEM sample thickness, zero-lossenergy filtering, and the probe coherence effect on the FEM V(k)signal. Over the range of thickness 0.29–0.57le, V is inversely

proportional to the sample thickness. At larger thicknesses, pluralelastic scattering causes deviations from inverse proportionality.Zero-loss energy filtering increases V at all thicknesses, down to0.29le. It also increases the usable range of sample thicknesses.Increased probe coherence increases V, up to the limit imposed bythe decrease in probe current with increasing coherence.

Theories of FEM assume perfect probe coherence and kine-matic elastic scattering. Samples much less than le thick, thehighest possible probe coherence, and zero-loss energy filteringmake the experiments more like the theories and increase theinformation that can be extracted from the FEM signal. Theseconditions also maximize V, making it easier to detect smallfeatures. Even if optimum conditions cannot be established for agiven sample or microscope, the thickness and probe coherenceshould be kept constant between data sets that are quantitativelycompared to one another.

Acknowledgement

We thank Seth Imhoff and John Perepezko for preparing theAl87Y7Fe5Cu1 metallic glass ribbons used in this study. This workwas supported by the U.S. National Science Foundation (DMR-0905793).

F. Yi, P.M. Voyles / Ultramicroscopy 111 (2011) 1375–13801380

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