High-resolution transmission electron microscopy

High-resolution transmission electron microscopy (HRTEM) (or HREM) is an imaging mode of specialized transmission electron microscopes (TEMs) that allows for direct imaging of the atomic structure of the sample. HRTEM is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp2-bonded carbon (e.g., graphene, C nanotubes). While HRTEM is often also used to refer to high resolution scanning TEM (STEM, mostly in high angle annular dark field mode), this article describes mainly the imaging of an object by recording the 2D spatial wave amplitude distribution in the image plane, in analogy to a 'classic' light microscope. For disambiguation, the technique is also often referred to as phase contrast TEM. At present, the highest point resolution realised in phase contrast TEM is around 0.5 ångströms (0.050 nm). At these small scales, individual atoms of a crystal and its defects can be resolved. For 3-dimensional crystals, it may be necessary to combine several views, taken from different angles, into a 3D map. This technique is called electron crystallography. High-resolution transmission electron microscopy (HRTEM) (or HREM) is an imaging mode of specialized transmission electron microscopes (TEMs) that allows for direct imaging of the atomic structure of the sample. HRTEM is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp2-bonded carbon (e.g., graphene, C nanotubes). While HRTEM is often also used to refer to high resolution scanning TEM (STEM, mostly in high angle annular dark field mode), this article describes mainly the imaging of an object by recording the 2D spatial wave amplitude distribution in the image plane, in analogy to a 'classic' light microscope. For disambiguation, the technique is also often referred to as phase contrast TEM. At present, the highest point resolution realised in phase contrast TEM is around 0.5 ångströms (0.050 nm). At these small scales, individual atoms of a crystal and its defects can be resolved. For 3-dimensional crystals, it may be necessary to combine several views, taken from different angles, into a 3D map. This technique is called electron crystallography. One of the difficulties with HRTEM is that image formation relies on phase contrast. In phase-contrast imaging, contrast is not necessarily intuitively interpretable, as the image is influenced by aberrations of the imaging lenses in the microscope. The largest contributions for uncorrected instruments typically come from defocus and astigmatism. The latter can be estimated from the so-called Thon ring pattern appearing in the Fourier transform modulus of an image of a thin amorphous film. The contrast of a HRTEM image arises from the interference in the image plane of the electron wave with itself. Due to our inability to record the phase of an electron wave, only the amplitude in the image plane is recorded. However, a large part of the structure information of the sample is contained in the phase of the electron wave. In order to detect it, the aberrations of the microscope (like defocus) have to be tuned in a way that converts the phase of the wave at the specimen exit plane into amplitudes in the image plane. The interaction of the electron wave with the crystallographic structure of the sample is complex, but a qualitative idea of the interaction can readily be obtained. Each imaging electron interacts independently with the sample. Above the sample, the wave of an electron can be approximated as a plane wave incident on the sample surface. As it penetrates the sample, it is attracted by the positive atomic potentials of the atom cores, and channels along the atom columns of the crystallographic lattice (s-state model). At the same time, the interaction between the electron wave in different atom columns leads to Bragg diffraction. The exact description of dynamical scattering of electrons in a sample not satisfying the weak phase object approximation (WPOA), which is almost all real samples, still remains the holy grail of electron microscopy. However, the physics of electron scattering and electron microscope image formation are sufficiently well known to allow accurate simulation of electron microscope images. As a result of the interaction with a crystalline sample, the electron exit wave right below the sample φe(x,u) as a function of the spatial coordinate x is a superposition of a plane wave and a multitude of diffracted beams with different in plane spatial frequencies u (spatial frequencies correspond to scattering angles, or distances of rays from the optical axis in a diffraction plane). The phase change φe(x,u) relative to the incident wave peaks at the location of the atom columns. The exit wave now passes through the imaging system of the microscope where it undergoes further phase change and interferes as the image wave in the imaging plane (mostly a digital pixel detector like a CCD camera). It is important to realize, that the recorded image is NOT a direct representation of the samples crystallographic structure. For instance, high intensity might or might not indicate the presence of an atom column in that precise location (see simulation). The relationship between the exit wave and the image wave is a highly nonlinear one and is a function of the aberrations of the microscope. It is described by the contrast transfer function. The phase contrast transfer function (CTF) is a function of limiting apertures and aberrations in the imaging lenses of a microscope. It describes their effect on the phase of the exit wave φe(x,u) and propagates it to the image wave. Following Williams and Carter, if we assume the WPOA holds (thin sample) the CTF becomes where A(u) is the aperture function, E(u) describes the attenuation of the wave for higher spatial frequency u, also called envelope function. χ(u) is a function of the aberrations of the electron optical system. The last, sinusoidal term of the CTF will determine the sign with which components of frequency u will enter contrast in the final image. If one takes into account only spherical aberration to third order and defocus, χ is rotationally symmetric about the optical axis of the microscope and thus only depends on the modulus u = |u|, given by where Cs is the spherical aberration coefficient, λ is the electron wavelength, and Δf is the defocus. In TEM, defocus can easily be controlled and measured to high precision. Thus one can easily alter the shape of the CTF by defocusing the sample. Contrary to optical applications, defocusing can actually increase the precision and interpretability of the micrographs.