Breaking the spherical and chromatic aberration barrier in

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Ultramicroscopy 102 (2005) 209–214 www.elsevier.com/locate/ultramic

Breaking the spherical and chromatic aberration barrier in transmission electron microscopy B. Freitag, S. Kujawa, P.M. Mul, J. Ringnalda, P.C. Tiemeijer FEI Electron Optics, PO Box 80066, 5600 KA Eindhoven, The Netherlands Received 24 April 2004; received in revised form 24 September 2004; accepted 28 September 2004

Abstract Since the invention of transmission electron microscopy (TEM) in 1932 (Z. Physik 78 (1932) 318) engineering improvements have advanced system resolutions to levels that are now limited only by the two fundamental aberrations of electron lenses; spherical and chromatic aberration (Z. Phys. 101 (1936) 593). Since both aberrations scale with the dimensions of the lens, research resolution requirements are pushing the designs to lenses with only a few mm space in the pole-piece gap for the specimen. This is in conflict with the demand for more and more space at the specimen, necessary in order to enable novel techniques in TEM, such as He-cooled cryo electron microscopy, 3D-reconstruction through tomography (Science 302 (2003) 1396) TEM in gaseous environments, or in situ experiments (Nature 427 (2004) 426). All these techniques will only be able to achieve A˚ngstrom resolution when the aberration barriers have been overcome. The spherical aberration barrier has recently been broken by introducing spherical aberration correctors (Nature 392 (1998) 392, 418 (2002) 617), but the correction of the remaining chromatic aberrations have proved to be too difficult for the present state of technology (Optik 57 (1980) 73). Here we present an alternative and successful method to eliminate the chromatic blur, which consists of monochromating the TEM beam (Inst. Phys. Conf. Ser. 161 (1999) 191). We show directly interpretable resolutions well below 1 A˚ for the first time, which is significantly better than any TEM operating at 200 KV has reached before. r 2004 Published by Elsevier B.V. Keywords: Aberration correction; Monochromator; High resolution TEM

Scherzer showed that round electron lenses inherently suffer from spherical and chromatic aberration, which cannot be made zero or negative [1]. Both their magnitudes scale with the size of Corresponding author.

E-mail address: [email protected] (J. Ringnalda). 0304-3991/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.ultramic.2004.09.013

the electron lens, thus pushing lenses to smaller designs causing magnetic saturation and reducing the available specimen space. These ‘‘high-resolution’’ optimized lenses therefore reduce the tilt capability, and remove the ability to do cryo or straining type of experiments. The spherical aberration (Cs) causes the information in

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the image to be blurred. In order to reduce this problem, during the last decade, post-processing methods have been developed to retrieve the true information from recorded images, such as through-focus series reconstruction [2] or holography [3]. A technical breakthrough was achieved by the recent introduction of Cs correctors in the TEM [4,5]. Cs correctors consist of a series of nonround lenses, which are not subject to Scherzer’s law of positive spherical aberration. The now remaining barrier is the chromatic aberration (Cc). The chromatic blur leads to increasing loss of image contrast at decreasing detail size, up to a point where the signal gets lost in the noise. Cc correctors have been proposed [6], but extreme demands on their electrical stability and mechanical accuracy have prevented resolution improvements so far [7]. Chromatic aberration causes electrons of different energies to be focused with different strengths. This spread of focal strengths Df depends on the energy spread of the electron source DEE0.3 eV (RMS value) and the instabilities of the electron beam potential DV/VE0.5 106 (RMS). Instabilities of the objective lens current DI/IE1.0 106 (RMS) also

contribute to the focal spread, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 DE DV 2DI 2 : þ þ Df ¼ C c eV V I The focal spread reduces the image contrast at high spatial frequencies G as described by the temporal coherence-damping envelope ðplDf Þ2 G 4 E D ðGÞ ¼ exp ; 2 which is near one for low spatial frequencies G, and decreases to zero for high G. Fig. 1 shows ED(G) for a typical standard 200 kV microscope. Here the electron wavelength l is 2.51 pm, the chromatic aberration Cc is 1.2 mm, and the focal spread Df is 3.0 nm. The temporal coherencedamping envelope drops below the noise level at the information limit around 1/GmaxE0.11 nm. Proposed future Cc correctors will compensate the focal spread introduced by the variations DE and DV of electron energies, but naturally they cannot compensate for the focal spread introduced by the instabilities of the objective lens. Our present alternative is to use a beam E_D(G) conventional E_D(G) corrected E_D(G) corrected monochromated CTF conventional CTF corrected CTF corrected monochromated

Contrast Trasnfer Function

1.0

0.5

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-1.0 spatial frequency G [1/nm]

Fig. 1. Typical temporal coherence-damping envelopes ED(G) and contrast transfer functions (CTF) for a conventional microscope, for a Cs corrected microscope, and for a Cs corrected and monochromated microscope. A large defocus of 500 nm has been used for the conventional CTF in order to boost the CTF at 8 nm1. The Cs corrected CTFs have been calculated for a defocus of only 3 nm. The CTFs without monochromation have half convergence angles of 0.2 mrad. The CTF with monochromation has a half convergence angle 2 mrad. The Cs corrected CTFs hardly depend on the half convergence angle.


monochromator [8] to reduce the energy spread DE of the electron source to negligible values. This reduces the focal spread to Df ¼ 1:4 nm and improves the information limit Gmax by about 25% and the resolution to well below 0.1 nm. This improvement is almost as good as obtainable, not proven yet, with proposed Cc correctors, since the effect of DE dominates the effect of the beam potential instabilities DV by an order of magnitude. Fig. 1 includes plots of the temporal coherence damping envelope ED(G) for the Cs corrected microscope without monochromation and for the Cs corrected microscope with monochromation. In the Cs corrected microscope, we have used an improved objective lens supply with DI/IE0.5 106 (RMS). This improves the focal spread and information limit, even though the Cs corrector increases the total chromatic aberration from 1.2 mm to approximately 1.4 mm. It is important to note that the monochromator reduces the beam current. Therefore, the illuminating beam must be made less parallel in order to keep the same amount of beam current on the sample. Without a Cs corrector, less parallelism would lead to resolution loss. However, in combination with a Cs corrector, this does not happen.

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These theoretical considerations were tested on a 200 kV TEM (FEI Tecnai F20ST) equipped with an FEI monochromator [8] and a CEOS image Cs corrector [4]. The Cs corrector reduces the spherical aberration from 1.2 mm to typically 3 mm. The monochromator reduces the energy spread DE in the beam from 0.55 eV (FWHM) to well below 0.15 eV (FWHM). The magnification of the system was calibrated on a standard gold sample. The information limit is measured by summing two images of amorphous tungsten, which have been slightly shifted with respect to each other. The shift creates interference bands in the Fourier transform of this summed image (known as Young’s fringes), which help to show the information limit. The left-hand side of Fig. 2 was obtained with Cs correction but without monochromation. The right-hand side of Fig. 2 was obtained with Cs correction and with monochromation. Fig. 2 shows that, when the monochromator is off, the information limit is a somewhat above 0.1 nm (typically 0.11 nm). When the monochromator is on, the information limit is well below 0.1 nm (its precise value depends on the signal-to-noise ratio that will be used to define the information limit). This is the first time that an

Fig. 2. Two Young fringe images of an amorphous tungsten film, showing the improvement of information limit obtained by the monochromator: (a) monochromator off (DE=0.55 eV) and Cs corrector on (Cs=3 mm), (b) monochromator on (DEo0.15 eV) and Cs corrector on (Cs=3 mm). The dots in the right image are lattice reflections from small gold particles in the tungsten film used for calibration. The light blue circle shows the 0.10 nm frequency. The dark blue circle shows the 0.14 nm frequency. The Young fringes show that, without monochromator, the information limit is a little worse than 0.1 nm. With monochromator, the information limit is well below 0.1 nm. The images were taken with 0.3 nA beam current on the CCD, 1 s exposure time, and 0.2 mrad half convergence angle (a) or 2 mrad half convergence angle (b).

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information limit better than 0.1 nm on a 200 kV TEM has been obtained, and it is the first experimental proof that the combination of Cs correction and monochromator gives spatial

Fig. 3. TEM image of a cross section of a MOSFET transistor showing the amorphous gate oxide layer between crystalline silicon and polycrystalline silicon, recorded with monochromator on and Cs corrector on. The image was taken with 0.1 nA beam current on the CCD, 1 s exposure time, and 2 mrad half convergence angle.

resolution beyond what is achievable on a standard TEM and beyond what is achievable with only Cs correction. A direct benefit of this technology for highresolution TEM applications is exemplified in Fig. 3. It shows a gate of a MOSFET transistor and has been recorded with the monochromated and Cs corrected TEM, at 1 s exposure time. The gate consists of a 2 nm thick amorphous silicon oxide layer sandwiched between crystalline silicon and polycrystalline silicon. Fig. 4 compares part of the gate oxide with a TEM image obtained without Cs correction and without monochromator. Two differences are striking: the first difference is that, without Cs correction, all atomic columns look identical in the crystalline area. The spherical aberration has redistributed the information of each atomic column over many of its neighbouring columns, thus effectively averaging out variations between columns. The uncorrected image cannot give insight into the precise location of the interface between crystalline silicon and amorphous silicon oxide, or on how the crystal structure is affected near this interface. This difference was already demonstrated in earlier work on Cs corrected (but not monochromated) TEM [9–11]. The second difference is that the monochromator has increased the contrast in the smaller details, especially in the 0.136 nm spaced

Fig. 4. Comparison of part of the gate oxide image of Fig. 3 with an image measured on a 200 kV TEM. (a) Corrected (Cs=3 mm) and monochromated. Each silicon column can have its own contrast and its own orientation. Details can be clearly seen because of the increased image contrast. (b) Uncorrected (Cs=1.2 mm) and no monochromator. Silicon columns all look identical due to the redistribution of image information by the spherical aberration. Image b was taken with 0.2 nA beam current on the CCD, 1 s exposure time, and 0.2 mrad half convergence angle.


‘dumbbells’ in the crystalline silicon. It reveals that some of the dumbbells slightly rotate their orientation, and that the intensity of the dumbbells can vary from column to column, both effects especially near the interface. The variation of intensity is not an optical artefact but indicates that some atomic columns are distorted or perhaps filled differently, and others are not. Figs. 5 and 6 show a Cs corrected set of images taken of a gold bicrystal sample. In these images, the reduction of delocalization effects and removal of Fresnel fringing can be seen just by the change in clarity of the edge, as in Figs. 5a and b, and the crispness of the twin boundary, as in Fig. 6. In the coming years, we expect that the monochromated and Cs corrected TEM will perform part of the imaging that is now done through high-resolution scanning transmission electron microscopy. It offers about the same information content as HR-STEM, however, at much shorter acquisition times and without the noise and the distortions that can be typical for STEM images, unless great care is taken for both system and site optimization.

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Fig. 6. Image of gold bicrystal recorded with monochromator on and Cs corrector on. The edge is clearly imaged, and the twin boundaries is imaged with significantly improved resolution and crispness, removing delocalization effects and producing a directly interpretable image. Images were taken with 0.3 nA beam current on the CCD, 1 s exposure time, and 0.2 mrad half convergence angle.

A more important development will be the introduction of the monochromator and Cs corrector technologies in combination with new lens designs, which offer A˚ngstrom resolution with ample distance between the sample and the imaging lens, in order to allow next era advanced electron microscopy [12]. The additional space enables studies with atomic resolution in various applications like experiments on beam sensitive material using helium cooling, or 3D reconstruction with tomography using high tilt angles [13], scanning probes applications, or time resolved in situ observation of specimen responses to variations in temperature, stress, or chemical environment [14].

Fig. 5. Images of gold crystal recorded with monochromator on and Cs corrector on, with insets illustrating the difference between Cs corrector on and Cs corrector off: (a) The edge is clearly imaged, without fresnel fringes or delocalization effects. (b) The image without Cs correction, illustrating the difficulty of directly interpreting an image from a conventional field emission gun system.

Acknowledgements The Cs corrected TEM-FEG used for this experiment has been funded by the CNRS and the ‘‘Re´gion Midi-Pyreńeés’’. FEI Company acknowledges the CEMES-CNRS laboratory for

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making their instrument available for this study. We thank CEOS GmbH for their support in getting the Cs corrector operational at our factory. Special thanks to Felix van Uden for technical support. Furthermore, special thanks to Dr. Christian Kisielowski from the National Center of Electron Microscopy in Berkeley, CA (NCEM) for providing the gold high-resolution sample. References [1] O. Scherzer, Z. Phys. 101 (1936) 593. [2] W. Coene, G. Janssen, M. Op de Beeck, D. Van Dyck, Phys. Rev. Lett. 69 (1992) 3743.

[3] Q. Fu, H. Lichte, J. Microsc. 179 (1995) 112. [4] M. Haider, et al., Nature 392 (1998) 768. [5] P.E. Batson, N. Dellby, O.L. Krivanek, Nature 418 (2002) 617. [6] H. Rose, Optik 33 (1971) 1. [7] W. Bernhard, Optik 57 (1980) 73. [8] P.C. Tiemeijer, Inst. Phys. Conf. Ser. 161 (1999) 191. [9] K. Urban, B. Kabius, M. Haider, J. Electron Microsc. 48 (1999) 821. [10] C.L. Jia, M. Lentzen, K. Urban, Science 299 (2003) 870. [11] M. Lentzen, et al., Ultramicroscopy 92 (2002) 233. [12] Transmission Electron Achromat Microscope Project, http://www.science.doe.gov/Sub/Facilities_for_future/20Year-Outlook-screen.pdf 2003. [13] K. Gruenewald, et al., Science 302 (2003) 1396. [14] S. Helveg, et al., Nature 427 (2004) 426.