Electron Holography Surmounts Resolution Limit of Electron Microscopy

Abstract

In high resolution electron off-axis holography, the complete information about amplitude and phase of the complex electron image wave is captured in a single hologram, fed to a computer, numerically reconstructed, and analyzed using methods of wave optical image processing. Specifically, the blurring effect due to the aberration of the objective lens of the electron microscope is corrected under reconstruction.The presented first results, achieved with a Philips CM30FEG electron microscope specially developed for the needs of high resolution electron holography, reveal that the point resolution of modern electron microscopes is significantly improved.PACS numbers: 42.30.Rx, In contrast to the light optical case, in electron microscopy the lateral resolution is not limited by the diffraction error, i.e. , by the wavelength of the electrons, but instead is governed by the spherical aberration of the objective lens. As shown by Scherzer [1] already in 1936, this error cannot be avoided as long as common rotational symmetric lens designs are used. For example, in the case of the Philips CM30FEG high resolution electron microscope applied in this work, the best point resolution is 0.198 nm, about 2 orders of magnitude worse than the diffraction limit of the A = 1.98 pm wavelength, 300 keV electrons.In electron microscopy we deal with a complex electron wave o(r) = a(r) exp[i'(r)] modulated in both amplitude and phase due to the interaction with the object. During the imaging process from this object wave to the recordable image wave, the aberrations of the objective lens lead to a blurring of the available information.The backpropagation from the aberration-corrupted image wave b(r) = A(r) exp[i@(r)] to the level of the object is possible following the wave laws given by the Kirchhoff diffraction integral. Prerequisites are the registration of the image wave amplitude and phase as well as a sufhcient knowledge of the lens aberrations. This approachcalled holography -was proposed by Gabor already in 1948 [2] but it took nearly 50 years until electron holography finally achieved this goal. From the various forms of electron holography [3] under investigation, the off-axis technique has proven to be most promising [4]. Using a Moellenstedt biprism, the image wave is coherently superimposed with a plane reference wave, and the resulting interference pattern -the hologram -reveals a cosinusoidal intensity distribution, I(r) = 1 + A(r) + 2A(r) cos(2rrq, . r + &b(r)). (1)

Electron Ptychography. I. Experimental Demonstration Beyond the Conventional Resolution Limits

“…Beyond this limit, the information is corrupted and contrast reversals occur. Various techniques have been suggested in order to solve for the phase of the image-plane wave function, such as off-axis holography (Lichte, 1991;Orchowski, Rau & Lichte, 1995) and focal-series reconstruction (Van Dyck, Op de Beeck & Coene, 1993). Knowledge of the image phase informa-tion allows the lens aberrations to be deconvolved, thus extending the resolution.…”

Imaging columns of the light elements carbon, nitrogen and oxygen with sub Ångstrom resolution

“…those that operate in the mid-voltage range around 300 kV and use coherently scattered electrons, an information limit of 0.10 nm was reported already in 1993 8 . Electron holography exploited this information limit down to 0.104 nm 9 . Alternatively, it was reported that a direct reconstruction of the phase and the amplitude of the scattered electron wave from a focal series of HRTEM images is suitable to extend the interpretable resolution of a field emission microscope down to its information limit 10 .…”

Collaborative Research and Development. Delivery Order 0006: Transmission Electron Microscope Image Modeling and Semiconductor Heterointerface Characterization

“…Furthermore, the resolution of these techniques is limited to the pointresolution of the microscope, which typically ranges from 1.7 Å to 2.5Å for midvoltage TEMs. More recently, significant experimental and computational advancements have been made in HRTEM-based techniques designed to retrieve the electron wave function at the exit surface of the specimen [15][16][17]. The use of exit-plane wave function (EPWF) images offers important advantages over existing methods.…”