Novel approaches for the characterization of electromagnetic fields using electronholography

Takeshi Kasama1,2, Yanna Antypas2, Ryan K.K. Chong2 and Rafal E. Dunin-Borkowski2,1

1RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan2Department of Materials Science and Metallurgy, Pembroke Street, Cambridge CB2 3QZ, U.K.

ABSTRACT

Two recent developments related to the application of off-axis electron holography to thecharacterization of magnetic and electrostatic fields in nanoscale materials and devices aredescribed. The first is based on the design and implementation of a three-contact electricalbiasing specimen holder that allows electron holograms to be recorded from samples as they aretilted to angles of up to ±70° with voltages applied to them in situ in the electron microscope.The second relates to the prospect of characterizing magnetic vector fields in materials in threedimensions using electron holography.

INTRODUCTION

Off-axis electron holography is increasingly used to characterize magnetic and electrostaticfields in materials in the transmission electron microscope (TEM) at a spatial resolution that canapproach the nanometer scale. The technique [1] involves applying a positive voltage to anelectron biprism in order to overlap a coherent electron wave that has passed through a samplewith a part of the same electron wave that has passed only through vacuum. Analysis of theresulting interference pattern allows the phase shift of the specimen wave

€

φ(x) = CE V(x,z)∫ dz −eh

B⊥∫∫ (x,z) dxdz (1)

to be recovered quantitatively and non-invasively. In Eq. 1, x is a direction in the plane of thesample, z is the electron beam direction, CE takes a value of 6.53×106 rad V-1m-1 at 300 kV, V isthe electrostatic potential and B⊥ is the component of magnetic induction perpendicular to x andz. Here, we illustrate the use of an ultra-high-tilt cartridge-based TEM specimen holder designedby E.A. Fischione Instruments, Inc. to acquire electron holograms from samples that have up tothree electrical contacts applied to them. We also describe recent developments in the acquisitionand analysis of electron holograms that may lead to the use of the technique to characterizemagnetic vector fields inside materials in three dimensions, rather than simply in projection.

EXPERIMENTAL DETAILS

The off-axis electron holograms that are presented below were all acquired at anaccelerating voltage of 300 kV using a Philips CM300ST field emission gun TEM equipped witha 'Lorentz' lens, an electron biprism, a GatanTM imaging filter and a 2048 pixel charge-coupled-device camera. The holograms were acquired with the conventional microscope objective lensswitched off and the sample located in magnetic-field-free conditions. Reference holograms wereused to remove distortions associated with the imaging and recording system of the microscope.

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EXPERIMENTAL RESULTS

Ultra-high-tilt three-contact electrical biasing specimen holder

The concept of a 'laboratory in an electron microscope', which allows several high spatialresolution analytical techniques to be combined with experiments that are traditionally carriedout ex situ, is highly attractive for tackling a wide range of problems in nanoscience andnanotechnology. We have recently taken delivery of a TEM specimen holder that allows samplesto be examined under an applied bias using both electron holography and electron tomography,as well as allowing each sample to be transferred between the TEM specimen holder and ascanning electron microscope (SEM), a focused ion beam (FIB) workstation, a plasma cleanerand an Ar ion miller in a universal cartridge assembly. Figure 1 shows the design of thespecimen holder. The end of the holder is shown in the inset to Fig. 1, while the removeablespecimen cartridge, in which two independent electrical contacts can be made to the specimensurface, is shown in Fig. 2a. A third electrical contact can be moved towards the specimen usingmicrometers and piezoelectric drives. Sample tilts of up to ±70˚ can be achieved before thecentral 500 µm of the sample begins to be shadowed by the edges of the holder, and samples thatare at different stages of examination or preparation can be stored in separate cartridges.

Figure 1. Design drawing of an ultra-high-tilt three-contact cartridge-based electrical biasingnanopositioning TEM specimen holder, with coarse and fine three-axis movement of the probeprovided by micrometers and piezoelectric crystals, respectively. The inset illustrates thelocation of the cartridge (see also Fig. 2a) and the position and motion of the third contact.

Figure 2. a) Design drawing of the removable cartridge used to apply two electrical contacts tothe specimen. b) Photograph of the end of the holder with the cartridge (but no specimen) inplace, and with an etched tungsten needle used to form the moveable contact.

a b

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A conceptually straightforward application of the nanopositioning specimen holder involvesthe measurement of electrostatic fields at the ends of nanowires and nanotubes, with the aim ofunderstanding the details of field emission on a nanometer scale. Figures 3-5 show preliminaryresults obtained from a sample containing bundles of single-walled carbon nanotubes, which wasplaced in the cartridge shown in Fig. 2. A gold needle was used to form an electrode that couldbe brought towards a chosen region of the sample. The application of a voltage between the goldelectrode and the sample resulted in strong attraction of the nanotubes towards the gold wire.Figure 3a shows a bright-field image that illustrates this behavior. This image was acquired outof focus in order to show the deflection of the incident electrons by the electric field at the end ofeach nanotube bundle that has a voltage applied to it. Figure 3b shows a higher magnificationdefocused bright-field image of the end of a nanotube bundle. An interference pattern is visible,similar to that formed by an electron biprism when recording an electron hologram.

Unexpectedly, above a critical applied voltage the nanotube bundles shown in Fig. 2 beganto grow additional branches at their ends, as shown in the form of defocused bright-field imagesin Figs. 4a and b. These branches were subsequently identified to consist primarily of amorphouscarbon. Their growth did not depend on the presence of the electron beam, and was most rapidwhen the microscope vacuum was poor. Their formation is therefore likely to result fromelectric-field-induced migration of carbon-based species within the microscope. Electronholographic amplitude and contoured phase images of a nanotube bundle, recorded before anybranches have grown, are shown in Figs. 5a and b, respectively. In Fig. 5b, the electric field isstrongest where the contours are most closely spaced, close to the end of the bundle.Corresponding images are shown in Figs. 5c and d after the formation of branches.

Figure 3. a) Defocused bright-field image of a sample of bundles of single-walled carbonnanotubes placed in the cartridge shown in Fig. 2, with a voltage applied between the tubes and agold needle that was brought to within 1-2 µm of them in the nanopositioning holder. b) Highermagnification defocused bright-field image of the end of an individual nanotube bundle.

a b

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Figure 4. a) Defocused bright-field image showing bundles of single-walled carbon nanotubesthat have grown branches at their ends after the application of a strong electric field between thetubes and a gold electrode in situ in the TEM. The gold electrode was 1-2 µm from the tubes.The critical applied voltage was typically between 400 and 500 V, but depended on themicroscope vacuum. b) A similar image obtained from a hairpin-shaped carbon nanotube bundle.

Figure 5. a) Amplitude and b) contoured phase images, respectively, obtained from an off-axiselectron hologram of a carbon nanotube bundle that has a voltage applied to it in situ in theTEM. c) and d) show similar images obtained from a carbon nanotube bundle that has grownbranches of amorphous carbon above a critical applied voltage in the microscope.

A wide variety of nanowires or needle-shaped specimens can be used to form the moveablecontact in the nanopositioning holder in order to probe the mechanical, electrical or magneticproperties of a specimen placed in the cartridge. For example, Fig. 6 shows an Fe needle that hasbeen micromachined from a steel sample using FIB milling. Such needles can be used to applylocalized in-plane magnetic fields to samples in the electron microscope in order to examine theirmagnetic properties. Figure 7 shows contoured electron holographic phase images of the ends offour Fe needles. In contrast to the biased carbon nanotubes, outside which the electric fielddepends on the curvature of their tips, the magnetic induction surrounding the end of an Feneedle depends largely on the amount of magnetic material present rather than on tip curvature.

a b

a cb d

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Figure 6. A focused ion beam milled Fe needle.

Figure 7. Contoured electron holographic phase images showing the in-plane component of themagnetic induction, projected in the electron beam direction, surrounding the ends of four Feneedles that are similar to the needle shown in Fig. 6 but have slightly different end shapes.

Under certain circumstances, it may be advantageous to apply a voltage to a sample toseparate a parameter of interest from other, unwanted contributions to the contrast. A simpleexample of how this separation may be achieved is shown in Fig. 8. Figure 8a shows aholographic amplitude image of two needles, one of Fe and the other of W, which have beenbrought to a separation of 560 nm using the nanopositioning holder. The acquisition of phaseimages with different voltages applied between the two needles allows the contribution to thephase shift from the electric field applied between the needles to be separated from magnetic andmean inner potential contributions to the contrast, as well as from any diffraction contrast thatmay be present. Figure 8b shows magnetic phase contours originating from the Fe needle, beforea voltage is applied between the needles. Figure 8c shows electrostatic phase contours alone,obtained by recording a hologram with the W needle at +5 V with respect to the Fe needle, andby using the 0 V hologram as a reference hologram to remove the magnetic and mean innerpotential contributions to the signal. A similar result is shown in Fig. 8d for a voltage of -5 V.

a cb d

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Figure 8. a) Holographic amplitude image of the ends of two Fe and W needles, which havebeen positioned with respect to each other with a separation of 560 nm using the nanopositioningholder. b) Phase contours measured using electron holography showing the in-plane componentof the magnetic induction alone integrated in the electron beam direction (contour separation 2"radians). c) Phase contours showing the applied electrostatic potential alone, integrated in theelectron beam direction, with the W needle at +5 V with respect to the Fe needle (contourseparation 6" radians). d) As for c) but with the W needle at –5 V. The slight asymmetry aboutthe horizontal axis in the contours in c) and d) arises because of the long-range electrostatic field,which perturbs the wave that is overlapped onto the sample to form the hologram.

An interesting and unexpected note of caution relates to the fact that the magnetic field at theend of an Fe needle may be affected by the presence of non-magnetic particles such as carbideswithin it. An example of this situation is shown in Fig. 9. Figure 9a shows an experimental phaseimage of the magnetic induction outside an FIB-milled Fe needle that contains a non-magneticCr carbide particle close to its end. Superficially, the phase contours are similar to those recordedfrom needles of pure Fe in Fig. 7. However, the magnetic induction is modified in the region ofthe carbide particle. Simulations in which both the base and the tip of the particle are magnetizeduniformly either parallel or antiparallel to the axis of the needle were performed using theFourier space approach of Beleggia and Zhu [2], and are shown in Figs. 9b and c. A comparisonof the simulated and experimental phase contours in the region of the carbide particle suggeststhat the end of the needle is magnetized antiparallel, rather than parallel, to its base. This curioussituation has almost certainly arisen because this needle is adjacent to a larger needle, whosedemagnetizing field may influence its end differently from its base. The needle shown in Fig. 9has a length of 10 µm, and is approximately 800 nm laterally from a larger needle of diameter5 µm. Two further important points are apparent from Fig. 9. First, the measured induction isapproximately four times weaker than that of the simulations, suggesting that the preparation ofFe needles using FIB milling affects their magnetic properties. Second, it is important to notethat simple calculations rather than full micromagnetic simulations can be used to provide usefulsemi-quantitative information about the magnetic properties of nanoscale materials.

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Figure 9. a) Experimental electron holographic phase contours showing the magnetic inductionoutside an Fe needle that contains a non-magnetic Cr carbide particle close to its end (contourspacing "/2 radians). b) and c) show simulations of phase contours for a needle whose end ismagnetized parallel and antiparallel to its base, respectively (contour spacing 2" radians).

Progress towards magnetic vector field electron tomography

We now examine the prospect of characterizing magnetic vector fields inside nanocrystals inthree dimensions by combining electron holography with electron tomography. Theseexperiments can be carried out either on working devices using the nanopositioning holderdescribed above, or on more conventional unbiased samples using a standard electrontomography sample holder. The motivation for developing this capability is illustrated in Fig. 10.Figure 10a shows magnetic phase contours measured from a chain of five closely-spaced FeNinanocrystals, whose diameters range from 22 to 79 nm. Although the smaller crystals in thechain appear to contain single magnetic domains, the largest crystals are in fact observed to havea more complicated domain structure when similar phase images are recorded with the sampletilted to other orientations. These domain structures often take the form of magnetic vortices,whose core lies parallel or perpendicular to the chain axis, and which can have a helical pitch. Insuch samples, it is not possible to identify the details of the three-dimensional magnetic vectorfield within each crystal unambiguously from conventional holographic phase images recordedwith the sample in a single orientation. Conventionally, electron tomography is used in thephysical sciences to record the three-dimensional shapes or compositions of materials fromultra-high tilt series of, typically, high-angle annular dark-field images recorded about a singletilt axis [3]. Such a reconstruction showing the morphologies of the particles in the FeNi chain isshown in Fig. 10b. Our aim is to develop electron tomography so that it can be used to recoverthe magnetic induction in such crystals, rather than their shapes, in three dimensions.

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Figure 10. a) Magnetic phase contours of spacing 0.049 radians measured using electronholography from a chain of five closely-spaced FeNi crystals, whose diameters in nm are markedon the image. b) High-angle annular dark-field tomographic reconstruction of the shapes of thecrystals in the same chain of FeNi nanoparticles, recorded at 200 kV using a Tecnai F20 TEM.

The application of electron tomography to characterize the magnetic vector field both insideand outside the chain of five FeNi nanoparticles shown in Fig. 10 in three dimensions is nowsignificantly more complicated than the approach used to acquire either Fig. 10a or Fig. 10balone. Magnetic fringing fields outside a material can be characterized in three dimensions byacquiring two ultra-high-tilt series of electron holograms of a sample about orthogonal axes [4].If each phase image is differentiated in a direction perpendicular to the tilt axis, then standardtomographic reconstruction algorithms can be used to calculate the three-dimensionaldistribution of the component of B that lies parallel to the tilt axis, based on the relations

€

ddyφ x, y( ) = −

eh

Bx x, y,z( )dz

z=−∞

z=+∞∫ (2)

and

€

ddxφ x, y( ) = +

eh

By x, y,z( )dz

z=−∞

z=+∞∫ (3)

In this way, two tilt series can be used to provide the three-dimensional distribution of two of thethree components of the magnetic induction, Bx and By, where x and y are directionsperpendicular to the incident electron beam direction z. After determining Bx and By in threedimensions in this way, Bz can be inferred by making use of the criterion that ∇.B = 0. Theapplication of this approach to the characterization of magnetic fields inside nanostructuredmaterials is complicated by the fact that the (often dominant) mean inner potential contributionto the measured phase shift must be removed at each sample tilt angle. This requirement can beachieved if each tilt series is recorded both before and after reversing the direction of

a b

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magnetization in the specimen (e.g., using the microscope objective lens). Subsequently, half ofthe difference between pairs of reversed images acquired at each tilt angle can be used to providethe magnetic contribution to the phase shift. Four tilt series of holograms are therefore required.

The fact that Equations 2 and 3 are expected to hold can be illustrated by considering thecase of a single uniformly magnetized sphere, for which each term in these equations can beevaluated analytically. If the sphere has magnetization M, radius a, and is magnetized along y,then analytical expressions for the induction B and the magnetic contribution to the phase shift φinside and outside the sphere are given by the expressions

€

Bx

By

Bz

inside

=

023

µ0 M

0

(4)

€

Bx

By

Bz

outside

= µ0 Ma3 −1

3 x2 + y2 + z2( )32

0

1

0

+y

x2 + y2 + z2( )52

x

y

z

(5)

€

φ x, y( )outside =

eh

23 µ0 Ma3 x

x2 + y2

(6)

€

φ x, y( )inside =

eh

23 µ0 Ma3 x

x2 + y2

1− 1−

x2 + y2

a2

32

(7)

[5]. Both sides of Equation 2 can be shown to equal

€

−eh

23 µ0 Ma3 2xy

x2 + y2( )2

for

€

x2 + y2( ) > a2, and

€

−eh

23 µ0 M

xy

x2 + y2( )2

2a3 − 2a2 + x2 + y2( ) a2 − x2 − y2

for

€

x2 + y2( ) ≤ a2. Similarly.

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both sides of Equation 3 equal

€

−eh

23 µ0 Ma3

x2 − y2( )x2 + y2( )

2 for

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x2 + y2( ) > a2, and

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−eh

23 µ0 M

a3 x2 − y2( ) − 2x4 + 3x2 y2 + y4 + a2x2 − a2 y2( ) a2 − x2 − y2

x2 + y2( )2

for

€

x2 + y2( ) ≤ a2. These equations illustrate the fact that for a sphere that is uniformly magnetized

along y Equations 2 and 3 hold when the sample tilt axes are parallel to x and y. A more generalproof of these relations, for arbitrary tilt axes, will be presented elsewhere.

The ability to acquire electron holograms of the chain of FeNi particles shown in Fig. 10 tothe required high tilt angles about orthogonal axes is illustrated in Fig. 11, and the correspondingmagnetic phase contours are shown in Fig. 12. Further processing of the holograms to recoverthe magnetic vector field in the chain is in progress and will not be presented here.

It is important to mention that for this technique to work the region of interest must lie closeto a large enough hole in the specimen support film to allow electron holograms to be acquired athigh sample tilt angles about two axes, without either the region of interest or the hole beingshadowed by other parts of the specimen. The difficulty of finding such a region is illustrated inFigs. 13 and 14, in which a chain of six magnetite crystals is obscured by dirt on the specimen athigh tilt angles even though it is located close to a 20 µm hole in a carbon support film. Ingeneral, the distribution of crystals that is imaged should almost certainly be isolated and small,so that the magnetic signal from the region of interest decreases to close to zero by the edges ofthe field of view. In addition, their diffracting condition must not change between each pair ofreversed images, and the sample must remain unchanged over the time required to record four tiltseries of holograms.

CONCLUSIONS

Two recent developments relating to the application of medium resolution electronholography to the characterization of electromagnetic fields in materials have been described andillustrated. Results have been presented from electrically biased carbon nanotube bundles andmagnetic needles examined using a new cartridge-based ultra-high-tilt TEM specimen holder.Progress towards using electron holography to characterize magnetic vector fields inside, as wellas outside, nanoscale materials has also been discussed, and preliminary experimental data havebeen presented from a short chain of ferromagnetic FeNi nanoparticles.

ACKNOWLEDGMENTS

We thank P.A. Midgley and W.O. Saxton for discussions and assistance, T.J.V. Yates forhelp with electron tomography, S. Hofmann, M.J. Hÿtch, P. Parameswaran, R. Langford andS.B. Newcomb for the provision and preparation of specimens, A.C. Robins, D.W. Smith,J.J. Gronsky, C.M. Thomas and P.E. Fischione of E.A. Fischione Instruments, Inc. for specimenholder design, and RIKEN, the Royal Society and the EPSRC for financial support.

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Figure 11. Selection of off-axis electron holograms taken from two orthogonal ultra-high tiltseries of the chain of FeNi crystals shown in Fig. 10, at the sample tilt angles indicated. Thebiprism voltage is 180 V, and the holographic interference fringe spacing is 3.4 nm.

Figure 12. 0.125 radians magnetic phase contours generated from the images shown in Fig. 11.

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Figure 13. a) Low magnification bright-field image showing the location of a chain of magnetitecrystals adjacent to a hole in a C support film. b) Higher magnification image of the same chain.

Figure 14. Off-axis electron holograms of the crystals in Fig. 13, acquired with the sample inmagnetic-field-free conditions at the tilt angles indicated. The tilt axis is roughly horizontal.

REFERENCES

[1] R. E. Dunin-Borkowski, M. R. McCartney and D. J. Smith. In Volume 3 of theEncyclopaedia of Nanoscience and Nanotechnology, ed. H. S. Nalwa (American ScientificPublishers, 2004) pp. 41-100.

[2] M. Beleggia and Y. Zhu, Philos. Mag. 83, 1045 (2003).[3] P. A. Midgley, M. Weyland, J. M. Thomas and B. F. G. Johnson, Chem. Commun. 10, 907

(2001).[4] G. M. Lai, T. Hirayama, A. Fukuhara, K. Ishizuka, T. Tanji and A. Tonomura, J. Appl.

Phys. 75, 4593 (1994).[5] M. de Graef, N. T. Nuhfer and M. R. McCartney, J. Microsc. 194, 84 (1999).

a) b)

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