High resolution transmission electron microscopy

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High resolution transmission electron microscopy ( English high resolution transmission electron microscopy , HRTEM ) is a TEM -Abbildungsmodus that allows, the crystallographic structure of a sample with an atomic map resolution. Because of its high resolution, HRTEM is a widely used tool for studying nanostructures in crystalline materials such as semiconductors and metals . A standard resolution of 0.8 Å (0.08 nm ) can currently be  achieved. In order to be able to use this resolution directly with the TEM, correctors for the spherical aberration are used. Due to the development of new types of correctors, which in addition to the spherical aberration also reduce the chromatic aberration , a resolution of up to 0.5 Å will soon be usable.

In the HRTEM, objects with a thickness of a few nanometers are examined. The contrast in HRTEM images is therefore generated mainly on the basis of phase and not amplitude differences. Phase contrast images often cannot be interpreted directly in HRTEM because aberrations also modulate the phase of the electron wave function and thus smear the structural details in the image.

Contrast formation and interpretation

Simulation of the exit wave and recorded images for GaN [0001] .

In contrast to conventional microscopy, HRTEM does not use amplitude changes such as B. Absorption, for illustration. The contrast is generated here by the interference of the electron wave in the image plane . As a result of the interference, a phase contrast in the electron wave, which carries the information about the object structure, can be converted into amplitude contrast. The amplitude contrast of the generated interference pattern can now be measured with a detector. Although amplitude contrasts are recorded, the cause of the image contrast is based on phase differences, which is why HRTEM is also described as phase-contrast imaging . From a statistical point of view, there is always only one imaging electron in the sample, so the image arises from the interference of this electron with itself.

The interaction of the electron wave with the lattice atoms of the sample is here simplified and described qualitatively. Before entering the object to be imaged, the electron can be viewed as a plane wave. Within the sample, the positive atomic nuclei attract the electron and thus change its path. Often, in HRTEM, crystalline objects are imaged along so-called zone axes, in which the crystal structure has a high degree of symmetry. In such orientations the atoms form pillars along the direction of incidence of the electron beam. The electron begins to oscillate along these columns. In the image of the electron as a wave , this pendulum solution is described by a phase shift. Depending on the thickness of the object, i. H. depending on the number of atoms per column, and depending on the type of atoms, the electron wave has experienced a position-dependent overall phase shift in the exit surface. The periodicity of the projected crystal structure allows a description of the interaction between electron and object structure as a diffraction phenomenon .

The result of this interaction, the exit wave ( english electron exit wave ) φ e ( x , k ), as a function of the location x is a superposition of a plane wave, and many other waves having diffraction vector k . The phase difference between φ e ( x , k ) and the incident wave is maximal at the locations of the atomic columns. The exit wave is now passed through the imaging system of the microscope and interferes in the image plane (photo plate or CCD sensor ). This image is not a direct representation of the crystallographic structure of the sample. For example, high intensity may or may not be an indication of an atomic column at this location (see simulation ).

In order to draw conclusions about the structure of the sample, the phase shifts caused by the microscope itself must be described.

The phase contrast transfer function (CTF)

CTF of a CM300 microscope with FEG from FEI

The CTF is a function of the aberrations in the imaging optics of an electron microscope and describes the propagation of the exit wave φ e ( x , k ) to the image plane. If all third order aberrations have been corrected (such as astigmatism and coma ) and higher orders and chromatic aberrations are neglected, then:

,

here C s is the coefficient of the spherical aberration, ʎ the electron wavelength, k the spatial frequency and Δ f the defocus.

If the defocus is set to zero (Gaussian focus), the CTF becomes an oscillating function in C s k 4 . This means that the contrast contribution to the image of certain diffracted rays with diffraction vector k is inverted.

To some extent, the oscillation of the CTF can be influenced by the second, in k parabolic term, i.e. that is, the defocus Δ f can be used to shape the CTF. The influence of the CTF makes a direct interpretation of HRTEM images impossible and further image processing is necessary.

There are two ways to bring HRTEM images into an interpretable form:

  1. Contributions with spatial frequencies that are higher than the point resolution can be filtered from the image with a corresponding aperture. The point resolution is defined here as the point at which the CTF has its first zero crossing. In this way there is no contrast inversion in the rays that contribute to the image. The focus at which the point resolution is maximal is called the Scherzer defocus (it is at Δ f = - (λ C s ) 1/2 ). This simple method has the disadvantage that it does not fully utilize the microscope's resolution.
  2. exit wave reconstruction reconstructs the exit wave as it left the sample by subtracting the CTF from the image wave.

Reconstruction of the exit shaft

Exit wave reconstructed through a series with focus variation

In order to obtain the exit wave φ e ( x , k ), the wave in the image plane must be numerically propagated back to the sample. If the image wave and all properties of the microscope are known, the original exit wave can be reconstructed with high precision.

For this, however, the phase and amplitude of the image wave must be measured. Since TEMs can only record amplitudes, an alternative method must be used to preserve the phase. There are two methods to choose from:

  1. Holography , first developed by Dennis Gábor for TEM, uses a prism (more precisely a Möllenstedt biprism , named after Gottfried Möllenstedt ) to split the electron wave into a reference beam and a sample beam. Phase differences between the two beams are then expressed in small shifts in the interference fringes in the image plane. This maps both the phase and the amplitude of the sample beam.
  2. Image series with focus variation ( through focus series ) uses the dependence of the CTF on the focus. A series of 20 images is shot under the same imaging conditions, in which only the focus is gradually changed. If the CTF is known, it can be calculated back to φ e ( x , k ) (see figure).

Both methods serve to expand the point resolution. The ideal defocus for this type of image is the light defocus named after Hannes Lichte and is normally several hundred nanometers negative (under focus).

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