Diffraction contrast TEM

In diffraction contrast TEM, the diffracted electron beams reaching the back focal plane is allowed to be passed straight to the phosphorous screen by adjusting the current and magnetic field strength of the projector lens as seen in figure 3.5(a). The resulting diffraction pattern seen on the phosphorous screen is of the straight through electron 000 beam, Bragg peaks and Kikuchi lines. Kikuchi lines are created by incoherent scattering of electrons from thicker regions of the sample, however if the sample is too thick inelastic scattering will dominate and no discernible Bragg diffraction can be detected [119]. The intersection points of Kikuchi lines form zones as seen in figure 3.5(b).

111

Figure 3.5: Diffraction mode on the TEM. Figure (a) shows the TEM in diffraction mode. This is achieved by adjusting the magnetic field strength of the projector lens which in turn allows the image from the back focal plane to be displayed on the florescent screen. Figure (b) is an image taken of the TEM phosphorous screen in diffraction mode whilst setting up a two beam condition showing the Kikuchi lines on the [001] zone axis, and the straight though beam on the 𝟐̅𝟐̅𝟎 Kikuchi line and the Bragg peak on the 220 Kikuchi line.

The diffraction vector is known as g and each pair of Kikuchi lines represent g and g̅.

the distance between Kikuchi line pairs is |g|. As the sample is tilted using the

goniometer in two axes of movement, the straight through beam is found to remain stationary but the Kikuchi lines start to move. It is clear that the sample orientation affects the Kikchi lines made visible, and that they are in effect fixed to the crystal and connected via different zones axes. For an X-TEM sample that has along the <110> cross sections, the closest zone axis seen is the [110] and for a plan view sample the closest zone axis is the [001]. Kikuchi lines are used as guides to find and identify specific planes on which to set up two beam diffraction conditions. For lattice resolving an image at high resolution, as well as correcting for objective astigmatism at high resolution and ensuring that the voltage centre is corrected, the straight through beam must be placed through the zone axis centre.

Back focal plane Projector lens [001] Zone axis 2̅2̅0 220

112

Figure 3.6: Stereographic [001] Kikuchi line map for FCC diamond and zinc blende crystals [122]. The [001] zone axes is indicated by the red dashed circle.

3.1.3.1.

Two beam diffraction condition

The dark field condition is where only the electrons scattered by the sample and collected by the objective lens are used in imaging, as opposed to bright field where both scattered and unscattered electrons are used to create an image of the sample. A two beam condition can be created when the straight through beam in bright field is isolated along with the diffracted beam from a desired plane in dark field. The technique involves tilting the sample until the straight through beam is brought over the Kikuchi line of a desired plane with a diffraction vector g in bright field. Then in dark field condition, the straight through beam is brought over to the Kikuchi line and Bragg peak of g̅. The objective aperture is placed over the straight through beam in bright field, thereby isolating it, blocking scattered electrons from the other spot, and providing contrast between bright field and dark field images.

113

Thickness measurements of the layer were carried out using the two beam diffraction condition in 004 because in FCC diamond and zinc blende structures the (004) structure factor gives the strongest intensity symmetrical Bragg peak along the crystal growth direction.

For clearly seeing defects in (001) zinc blende and FCC diamond crystals the 220 diffraction condition is used because this diffracted beam has the shortest extinction distance; the distance travelled before the beam is diffracted again. A shorter extinction distance leads to minimal broadening of the Bragg angle around the dislocation strain field, thus providing greater contrast between perfect crystal and the dislocation. A dislocation will only show residual contrast when g ∙ b = 0 as shown in figure 3.6. It

will be completely invisible when g ∙ (b × u) = 0 as well. This is known as the invisibility criterion.

Figure 3.7: (a) represents the condition when 𝐠 ∙ 𝐛 = 𝟎, i.e. the diffraction vector and Burgers vector are orthogonal to each other and only residual contrast is seen. Figure (b) shows the condition where 𝐠 and 𝐛

are parallel, therefore the distortion caused by the dislocation is visible. Taken from Shah [96].

It is not often that both conditions are met simultaneously, hence calculations show that 60° misfit will appear in any combination of b =a

2< 110 > and g and g̅ are

either Kikuchi pairs 220 and 2̅2̅0 or 2̅20 and 22̅0. Stacking faults will be invisible when g. R is an integer, where R is the stacking fault vector and is the Burgers vector

of either of the two partial dislocations.

Finally, the weak beam diffraction condition involves moving the straight through beam not over to the Kikuchi line and Bragg peak of g̅ in dark field, but onto the Bragg

114

peak and Kikuchi line of weakly scattered electrons in the opposite direction with a diffraction vector −g̅. For 220 diffraction condition, this shortens the extinction distance even more and gives much stronger diffraction contrast which is particularly useful in the 220 diffraction condition to clearly see dislocations.

115

3.2.

High Resolution X-Ray Diffraction (HR-