# Spatial Resolutions of On-Axis and Off-Axis Transmission Kikuchi Diffraction Methods
## 3 Results and Discussion
### Effects of the Accelerating Voltage and Specim Thickness on the On-Axis and Off-Axis TKDs  
As shown in Figure 3, the spatial resolutions of both configurations were improved, from tens of nanometers to below 10 nm, with the increase in accelerating voltage or decrease in sample thickness. At the voltage of 30 kV and sample thickness of 74 nm, the on-axis and off-axis TKD methods achieved the lowest resolutions of 6.2 and 9.7 nm, respectively. With the increase in thickness, the Kikuchi bands became less sharp and higher noises were observed at the boundaries of the patterns. For the on-axis TKD, the size of the direct beam decreased with the increase in thickness, which indicates a larger energy loss before the electrons emerge from the sample (Figure 4). The results also demonstrate that a thinner sample leads to a better spatial resolution. If the thickness is reduced by only tens of nanometers, the spatial resolution would be significantly improved. This can be explained by the scattering events of diffracted electrons along the crystal plane [19; 21; 23; 24]. For the same material at the same accelerating voltage, the electron penetration depth is the same. If the sample is thicker, the electron point source would be further from the emergence surface. This increases the likelihood of incoherent scattering along the emergence  
Figure 3: Spatial resolution of the on-axis and off-axis TKD methods as functions of the accelerating voltage at thicknesses of 91 and 74 nm. path, which leads to a larger energy loss and reduced pattern contrast [8,25]. On the other hand, less scattering events lead to a smaller electron beam broadening, and thus to a lower spatial resolution. Usually, the thickness of the TKD sample should be 1.5 times the grain size. If the specimen thickness is more than two times the grain size, the Kikuchi patterns of the top and bottom layers would overlap. This would lead to a significantly reduced pattern quality. The minimum thickness for TKD is a quarter of the extinction distance, according to [PERSON] et al. [24], because the total number of scattering events will be rapidly reduced and the scattering angle will be very small, below the threshold. With the increase in accelerating voltage, the width of the Kikuchi band decreases and the boundary becomes clearer. For the on-axis TKD, the transmitted-beam diameter and diffraction spot brightness are increased (Figure 5). The spatial resolution can be improved by increasing the accelerating voltage; however, the influence of the voltage on the spatial resolution is reduced above 25 kV. In other words, if the accelerating voltage is sufficiently high so that most electrons reach the detector, the spatial resolution will be minimally affected by the voltage. When the acceleration voltage is 30 kV, the spatial resolution is optimal, which can also be explained by scattering events. According to a Monte Carlo simulation, the electron penetration depth increases with the accelerating voltage [20]. Therefore, for a material with the same thickness, the point source will be closer to the emergence surface. This indicates fewer scattering events will happen before the electrons leave the sample because of the shorter path, which leads to better spatial resolution. However, in both configurations, the accelerating voltage has a minor role in the spatial resolution compared to that of the specimen thickness. Figure 4: Kikuchi patterns at the accelerating voltage of 30 kV and thicknesses of (**A**,**C**) 91 and (**B**,**D**) 169 nm for the on-axis and off-axis TKDs, respectively. These two samples are presented because the difference in their thickness is larger. Figure 5: Kikuchi patterns of the 91-nm-thick sample at the voltages of (**A**,**C**) 20 and (**B**,**D**) 30 kV for the on-axis and off-axis TKDs, respectively. The results are in agreement with our previous study on the spatial resolutions of the off-axis TKD method for 41-, 69-, and 91-nm-thick austenitic steel samples [19].