Transmission electron microscopy

In TEM, electrons are transmitted through a thin sample and the interaction of the electrons with the sample is used to form an image and gain analytical information on it. The resolution of a standard TEM/STEM lies in the sub-nanometer regime (see chapter 3.2) and in addition it allows the accomplishment of several analytical measurements. The setup of a TEM/STEM is similar to a SEM (see Figure 3.3) with the main difference that only electrons that are transmitted through the electron transparent sample are detected. The electron beam can be generated by different electron guns as described in chapter 3.2.1. TEMs are operated at an acceleration voltage ranging from 80–300 kV depending on the studied material. Just like in SEM the focusing and deflection of the beam is realized via electromagnetic lenses. Usually a TEM consists of three sets of lenses and corresponding apertures. The condenser lens system focuses the electron beam on the specimen and regulates the intensity and the convergence of the beam. It can be operated such that an illumination with a parallel or a convergent electron beam is possible. The objective lens system forms the first intermediate image or diffraction pattern of the sample and is located in close distance to the specimen. The specimen itself is inserted via a special sample holder and usually has a diameter of 3 mm and a thickness of less than 100 nm. The ED pattern of the specimen is created in the back focal plane of the objective lens. Via the objective aperture inserted in this back focal plane a selected part of the transmitted electrons can be blocked in order to enhance the contrast of the resulting image (explained in more detail later). The following selected area diffraction (SAD) aperture which is placed in the first image plane below the objective lens allows to choose a specific sample area. The intermediate and projection lens system magnifies the intermediate image generated by the objective lens. The resulting image or diffraction pattern can be detected via a fluorescent screen or a charge coupled device camera. One advantage of a TEM is the ability to switch between imaging and diffraction mode. This can be achieved by changing the strength of the intermediate lens so that the back focal plane of the objective lens is projected on the screen. Figure 3.5 shows the beam paths in the lens system below the specimen in the case of diffraction and imaging.

Figure 3.5: Beam paths in a TEM for diffraction (left) and imaging mode (right). Modified from Brandon and Kaplan.[6]

Different lens aberrations like spherical aberration, chromatic aberration and astigmatism together with the diffractions limit the resolution of a TEM. While astigmatism can be corrected in each TEM, additional correctors have to be implemented to eliminate the spherical and chromatic aberrations. By doing so, the resolution of a TEM can be enhanced to < 1 Å. In addition, the implementation of a monochromator can reduce the energy width of the primary beam to ~0.1 eV which is of interest for EELS measurements with high energy resolution.[3,5]

Electron diffraction

Just like in XRD (see chapter 3.1) diffracted electrons can interfere constructively and lead to spots in ED patterns. Since the wavelength of electrons in a TEM is much smaller

than the radiation used in XRD, a much larger Ewald sphere occurs and several reflections can be observed in the pattern. The lattice spacings dhkl of a material can be

calculated for a known camera constant (see equation (3.6)).

= (3.6)

The camera constant λL can be determined by measuring a standard sample like a Si

single crystal. R is the distance between the primary beam and the investigated

diffraction spot and can be measured in the diffraction pattern. A specific area of the specimen can be selected for diffraction by inserting a SAD aperture.[2,3]

Conventional TEM

The most common imaging mode in conventional TEM is the bright-field (BF) imaging. Hereby, the objective aperture is positioned around the primary beam. The electrons that are scattered by the specimen are blocked. Areas exhibiting stronger scattering appear darker. On the contrary only electrons scattered in a preferred direction can be used for imaging in dark-field (DF) mode. Either the aperture is placed at the position of a scattered beam or the beam is tilted in a way that the diffracted beam is oriented parallel to the optical axis. In this mode only the specimen areas that scatter the beam in a certain direction appear bright. Diffraction contrast arises when the sample is oriented such that the Bragg condition is fulfilled, meaning that crystalline specimen regions appear darker in BF images. Besides the diffraction contrast the mass-thickness contrast plays an important role in conventional TEM. Regions of the specimen that are thicker or have a larger atomic number scatter electrons more strongly and also appear darker in BF images.[3]

High resolution TEM

High resolution TEM (HRTEM) is used to study the specimen at the atomic scale. When a crystalline specimen is tilted in zone axis its lattice planes become visible. The objective aperture is removed in this mode, so that all scattered and unscattered electrons contribute to the image. Using aberration-correcting optics and a monochromated high- brightness source resolutions of 0.05 Å _{can be realized in HRTEM.}[9] _{Nevertheless, unlike} in STEM, the interpretation of the obtained HRTEM images is not intuitive and more difficult. Therefore, simulations have to be performed in order to be able to assign the gathered signals to atomic columns. The parallel electron beam which is used in HRTEM

is treated as a plane wave. In general the phase and the amplitude of this plane wave is shifted when it passes through the specimen due to interactions with the Coulomb potential of the atoms. The so-called exit wave which is the electron wave that leaves the sample is influenced by the atomic arrangement, the chemical composition and the thickness of the specimen. For thin samples it is assumed that, the amplitude of the electron wave stays constant and only the phase changes (“weak-phase object”). Due to defocussing and lens aberrations the different wave vectors of the exit wave experience different phase shifts. The simplified contrast transfer function (CTF) (3.7) for a weak phase object describes the influence of defocus and spherical aberration on the phase of the exit wave.

( ) = Δ +1

2 (3.7)

Δf is the defocus, λ is the wavelength, u is the spatial frequency and Cs is the spherical

aberration coefficient. Whenever the function passes zero, the contrast in the resulting image is reversed. The instrumental resolution limit is defined as the first zero-crossing of the CTF at the highest possible spatial frequency. The corresponding defocus value is called Scherzer defocus.[2,3]

Scanning TEM

In STEM mode the specimen is scanned by a convergent electron beam (probe) and the transmitted electrons are detected. The beam is deflected with two pairs of scan coils in such a way that the beam is always parallel to the optical axis when it is scanned across the specimen. For each scanned position the scattered signal is measured and an image is formed point by point. Three different detectors which are placed around the optical axis can be used depending on the scattering angle θ of the transmitted electrons. A BF

detector is applied for electrons that are scattered in forward direction (θ < 10–

25 mrad). For larger scattering angles (25 < θ < 50 mrad) annular dark-field (ADF) and

finally high angle annular dark-field (HAADF) detectors (θ > 75 mrad) are used. The

HAADF signal is proportional to the scattering cross section of the incoherent, elastically scattered electrons. This Rutherford cross section is directly proportional to the atomic number squared. This allows an intuitive interpretation of HAADF STEM images regarding the distinction of heavier and lighter elements in the specimen.

Figure 3.6: Schematic drawing of the available detectors in STEM mode. Modified from Williams and Carter.[3]

Due to the image formation, STEM images are not affected by aberrations of the imaging lenses but depend on the quality of the condenser system. The resolution in a STEM image depends on the size of the formed probe. By implementing a probe corrector in the condenser lens system resolutions of < 0.1 nm can be achieved. A great advantage of STEM is the possibility to obtain analytical signals, like EDS and EELS, with a high spatial resolution while simultaneously acquiring a HAADF image.[3,10]