Transmission electron microscopy

Transmission electron microscopy (TEM) is a transmission imaging technique. A focused beam of electrons is directed through a thin (~100 nm) sample. The electrons that pass through the sample irradiate a phosphor screen, converting the electron image into a visible image. To capture the image the phosphor screen is substituted for a CCD. TEM provides information on the crystal quality, layer thickness, defect density, composition and topography of materials.

Prior to imaging, samples must be thinned until they are electron transparent. This is achieved through mechanical grinding using abrasive SiC paper, followed by ion milling and polishing within a precision ion polishing system. This equipment uses a low energy (2 - 4 keV) argon beam to slowly erode the surface. Reference [54] provides an extensive description of the TEM sample preparation process used within this work.

Contrast in TEM images represent the variation in electron absorption over the sample. A TEM image is a conversion of electron absorbance into greyscale, providing an optical method to observe density variation within solid materials.

The resolution of conventional optical microscopes is limited by the wavelength of light. This is not the case with TEM, with wavelengths of 0.0025 nm commonly used, the limiting factor to TEM resolution (~ 0.1 nm) is imperfections in the focusing lens. Calculating the wavelength of the electron beam represents an exercise commonly conducted in undergraduate physics courses. It was Louis de Broglie who initially explained that matter could propagate as

a wave, with the wavelength of a particle given by: 𝜆 = ℎ 𝑚𝑣⁄ where 𝜆 is the wavelength of a

particle, ℎ planks constant, 𝑚 the particle mass and 𝑣 the particle velocity. For the electrons the velocity is determined by the accelerating voltage given by: 𝑣 = √2𝑒𝑉 𝑚⁄ where 𝑣 is the electron velocity and 𝑉 the accelerating voltage. Therefore, the formula for calculating the

classical wavelength of an electron beam is: 𝜆 = ℎ √2𝑚𝑒𝑉⁄ . However, electrons within a TEM

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a relativistic correction will have a notable impact on the true wavelength value. When including a relativistic correction, the wavelength of the electron beam is given by:

𝜆 = ℎ

√2𝑚𝑒𝑉×

1 √1 +_2𝑚𝑐𝑒𝑉₂

( 2.1 )

Where 𝑐 is the speed of light. Inputting values for electrons accelerated at 200 KeV returns a wavelength of 0.0025 nm, which is where the value quoted above for resolution comparison originates from.

2.1.1. Alligning the TEM in diffraction mode

The samples imaged in this work are crystalline. Therefore, when the electron beam passes through the sample some beam paths are diffracted and some are transmitted. The TEM can then be placed into two different conditions, bright field (BF) and dark field (DF). BF is when an aperture is added that only allows transmitted (un-diffracted) electrons to pass. Whereas, DF is when the added aperture only permits some diffracted electrons to pass (which diffracted beams are selected should be specified). The image in either BF or DF displays the variation in diffraction contrast over the samples surface, highlighting features that may not be previously visible. When there is a large intensity in the diffracted beam there is a corresponding reduction in intensity from the transmitted beam. This explains why feature contrast is extensively improved when using an aperture.

When the TEM is switched into diffraction mode it involves an internal adjustment of the projector lens. Lenses in a TEM use electromagnetic fields to focus the electron beam, behaving similarly to conventional optical lenses. On selecting diffraction mode, the projector lens transfers the image from the back focal plane (converging of rays before the image plane) onto the phosphorus viewing screen. At the back focal plane parallel rays intersected, hence in diffraction mode an array of spots is observed. Each spot corresponds to a specific reflection from a plane within the sample crystal. In standard imaging mode what is observed are reflections from all planes, superimposed on top of each other. Diffraction mode separates these reflections into spots, the spots are located based on their position relative to the incident beam angle. By selecting electrons reflecting from a specific plane, while rejecting others, contrast of specific features is achieved.

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Dislocations are only visible when the planes displaced by the dislocations cause diffraction of the electron beam. When a dislocation causes a disturbance in a crystal lattice it is quantified by the Burgers vector, b. When the diffraction condition g is perpendicular to the Burgers vector, 𝑔 ∙ 𝑏 = 0, the dislocation is not visible in the TEM image. This is called the invisibility criterion [55].

2.1.2. Origin of kikuchi lines in TEM spectra

To align the TEM to obtain a specific diffraction condition, Kikuchi lines are used. When the electron beam is diffracted a grid pattern of spots is observed. The diffraction spots will either fade or become brighter as the crystal orientation is altered, however their location remains fixed. This displays which spots correspond to a plane that is fulfilling the Bragg condition. Kikuchi lines display a different behaviour, unlike the diffraction spots the Kikuchi lines will move across the phosphor screen as the crystal orientation is altered. The contrasting behaviour of diffraction spots and Kikuchi lines stems from their separate sources.

The diffraction spots represent electrons from the incident beam that have been elastically scattered. The Kikuchi lines represent electrons that have been in-elastically scattered and subsequently diffracted.

Figure 2.1 Diagram displaying how Kikuchi lines are formed from secondary diffraction of electrons originating from an inelastic scattering event.

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When an inelastic scattering event occurs, electrons are produced that have a different wavevector to the incident beam (as depicted in Figure 2.1). Most of these secondary electrons contribute to the background intensity of the diffraction pattern. However, some secondary electrons will fulfil the Bragg condition, diffracting from the planes within which the inelastic source lies. These paths are labelled A and B within Figure 2.1. The impact of A and B on the background intensity is shown in the graph at the bottom of Figure 2.1. One path is lower in intensity and one is higher. These discontinuities within two dimensions form a pair of Kikuchi lines.