TEM Microstructural Analysis

TEM observation along with diffraction analysis was used to identify the presence of a single crystalline structure after electroplating as well as examine the pre- and post-deformation dislocation structure of nanopillars. Both of which were determined through diffraction techniques.

2.3.3.2.1 Diffraction – Microstructure Determination

In TEM, the incident electrons either pass through the sample or are diffracted by lattice planes satisfying the Bragg condition [72]. In the case of a single crystal at a high-symmetry orientation, these diffracted electrons have a highly symmetric pattern corresponding to the available diffracting planes [72]. The angle and relative distance of these spots can be used to accurately determine the crystal structure and the lattice constant. An example of a single crystalline pattern is found in Figure 2.8b,c, the diffuse rings around the spots are from the protective layer. In the case where multiple crystals are present, other, asymmetric spots are also observed in the diffraction pattern. The presence of these additional diffraction spots demonstrates that multiple crystals exist; however, this information is insufficient to describe the relative extent and size of the other grains. An individual grains size can be determined through a combination of selected area diffraction, SAD, and dark field. Both of these techniques use apertures in the imaging and diffraction planes respectively to show only selected regions. SAD uses an aperture to limit incident electrons to a small region of the pillar such that only these electrons are collected at detector. SAD provides more diffraction contrast by removing unwanted scattered electrons. Dark-field, DF, uses apertures in the diffracting plane to select individual diffraction spots, the resulting pillar image is dark except for the diffracting grain, which is strongly illuminated. An example of SAD patterns and their corresponding dark-field images are shown in Figure 2.2b-e. Through a systematic analysis of the diffraction spots in SAD and DF, the extent of the crystal structure can be determined. The pillars examined in this work had a range of microstructures from pure single crystals to, nanocrystalline; however, only pillars with nominally single crystalline microstructures were tested. An example of a nominally single crystalline pillar ~250nm diameter copper pillar is shown in Figure 2.8. This pillar has one major grain with a very small twin near the base of the pillar.

Figure 2.8 a) 250nm diameter single crystal copper pillar. b) and c) SAD patterns of the top and bottom of the pillar respectively. Dark-field images of the spots D1 and D2 in d) and e) respectively

2.3.3.2.2 Pillar Loading Axis Determination

When the crystal is tilted in a high-symmetry orientation, the diffracting beams can be accurately indexed and compared with the image revealing the crystallographic orientation of the specimen. The most important direction to determine is the loading axis or the direction parallel to the pillar’s height as this will control the resolved shear stress through the Schmid factor. The procedure is as follows: first the pillar is tilted into several high-symmetry zone axes and the resulting diffraction patterns are indexed. The diffraction pattern is then rotated to correct for the rotation difference between the image and the diffraction pattern. In the FEI Technai TF20 used in this work, this rotation corresponds to ~28 degrees counterclockwise as determined by MoO3 standards. The high symmetry

directions are compared with the resulting image in order to obtain the orientation of the pillar. Furthermore, as the TEM image is a two-dimensional projection, the tilt of the pillar needs to be considered when identifying the loading axis. The resulting single crystalline copper pillars have a loading direction that is found to be within 10 degrees of a <111> orientation.

a) b) c)

2.3.3.2.3 Dislocation Structure and Character Determination

Both the dislocation lines and their character, Burgers vector, can be determined through TEM techniques that take advantage of the atomic level displacements around a dislocation. Dislocation lines are visible in TEM because the atomic disregistry at the dislocation core is an efficient electron scatterer. The dislocation character, Burgers vector, can be observed through dark-field or two-beam techniques that selectively image the crystal with only one diffraction vector. A dislocation will only be visible under these conditions if the dislocation’s displacement field distorts the selected diffracting planes. If the displacement field does not distort the selected diffracting planes, the dislocation will be invisible. A dislocation’s Burgers vector can be determined by selecting multiple different independent diffraction vectors and recording under which diffraction vectors a dislocation is visible and invisible.

2.3.3.2.4 Bright-Field/Zero-Loss Filtered

The most basic method to measure dislocations is through bright-field imaging. In bright field, the central, transmitted beam of electrons, those that do not diffract, are selected for imaging through insertion of a diffraction aperture. Any feature that results in a diffraction or scattering event, for example, the highly strained lattice near a dislocation core, will appear dark in contrast to the much brighter background. Under these conditions, the width of the dislocations can be much broader than otherwise expected for a line defect due to the additional inelastic scattering near the dislocation core

The apparent width of the dislocation core can be narrowed by using an electron energy loss spectroscopy (EELS) technique known as zero-loss filtering. EELS provides extra information over conventional TEM by passing after-sample electrons through a magnetic prism and separating the electrons by their energy. Furthermore, this technique can be used to acquire specimen images or diffraction patterns with narrow energy ranges. By selecting only the electrons that retain their initial incident energy, or have zero energy loss, the inelastic scatter that thickens the dislocation lines can be removed revealing higher dislocation line contrast and in the case of entangled dislocations, more information about the dislocation network. An example of this type of image can be found in Figure 3.4.

2.3.3.2.5 Weak-Beam Dark Field (WBDF)

Another method to provide fine dislocation resolution is weak-beam dark-field. In this technique, the crystal is tilted into a diffraction condition with one weak diffracted beam. When the weak beam is selected through a diffraction aperture, the resulting image is dark as the crystal is far from this

diffraction condition. However, if the image is averaged over long times, 60s or more, dislocation lines appear as thin white lines as dislocation cores are the only regions in the crystal in which the diffraction condition is met due to the high local strain; therefore, the dislocation cores now appear as bright white on a dark background.

2.3.3.2.6 Burgers Vector Analysis (g dot b)

The previous techniques take advantage of the break in lattice periodicity at the dislocation core to image dislocations. These techniques show the dislocation line; however, they provide no information about the dislocation character or Burgers vector. In order to gain insight into the dislocation Burgers vectors present in these crystals, we employ “g dot b” analysis. Burgers vectors can be identified by selectively choosing specific diffraction vectors and when 𝑔∙𝑏= 0 the dislocation will be invisible. When a dislocation’s Burgers vector is perpendicular to the selected diffraction vector, the dislocation will be invisible in the image as the Burgers vector shift is in-plane with the diffraction condition. By selecting a series of diffraction vectors, the Burgers vector for an individual dislocation can be determined. This process is especially important in WBDF or more generally two-beam techniques, as imaging with only one diffraction vector may not reveal all the dislocations. A WBDF of a post- compression copper pillar is shown in Figure 3.4.

2.3.3.2.7 Dislocation Density Estimates

The dislocation density in TEM samples is estimated by measuring the apparent dislocation line length through ImageJ (free software) and then dividing that line length by the pillar volume. As TEM produces a two-dimensional projection of a three-dimensional pillar, the depth of the pillar is estimated from the thickness of the lamella after thinning. This dislocation density estimate will always an underestimate of the total dislocation density as this technique cannot resolve dislocation line length that runs parallel to the beam direction.