Depth Resolution Dependence on Sample Thickness and Incident Energy in On-Axis Transmission Kikuchi Diffraction in Scanning Electron Microscope (SEM)

Abstract

Transmission Kikuchi diffraction is an emerging technique aimed at producing orientation maps of the structure of materials with a nanometric lateral resolution. This study investigates experimentally the depth resolution of the on-axis configuration, via a twinned silicon bi-crystal sample specifically designed and fabricated. The measured depth resolution varies from 30 to 65 nm in the range 10-30 keV, with a close to linear dependence with incident energy and no dependence with the total sample thickness. The depth resolution is explained in terms of two mechanisms acting concomitantly: generation of Kikuchi diffraction all along the thickness of the sample, associated with continuous absorption on the way out. A model based on the electron mean free path is used to account for the dependence with incident energy of the depth resolution. In addition, based on the results in silicon, the use of the mean absorption coefficient is proposed to predict the depth resolution for any atomic number and incident energy.

On the depth resolution of transmission Kikuchi diffraction (TKD) analysis

“…The predicted correlation between λTDS and physical depth resolution is also in agreement with Monte-Carlo simulations carried by van Bremen et al [5] in which they calculated the depth at which the final incoherent electron scattering events occurred, and reported a physical depth resolution of ~12 nm in Au samples (Z=79, ρ=19.3 g.cm -3 , λIMFP= 21.3 nm and λMFP= 3.5 nm) exposed to 30 keV electrons, a material in which we would expect there to be a similar depth resolution as experimentally determined in Pt, 13 nm [15]. A similar relationship has been reported by Brodu et al [14] for Si samples exposed to 30 keV electrons, dphy ≈0.026E/µ0 (where E is the beam energy and µ0 is the absorption coefficient for 100 keV electrons in Si). If we consider the relationship between λTDS and absorption coefficient to be λTDS ≈1/µ0 [42], the Brodu relationship is then similar to the value of dphy proposed above.…”

“…By comparison, in a TKD map only the particles that are distributed close to the bottom surface and have a size larger than the effective depth resolution can be detected. The existing surface-sensitive nature of TKD [14,31] thus needs to be taken into consideration, especially when analysing nano-crystalline materials with grain size of the order of the sample thickness. An example of a nanocrystalline sample of zirconium oxides scanned by TKD over the same region but from opposite directions is shown in Fig.…”

“…However, the authors did not take the influence of the thickness of the upper grain in their bi-crystal sample into consideration, which can affect the intensity of Kikuchi bands associated with this crystal. At the critical thickness of the bottom crystal, ~60 nm [14], which they regard as the physical resolution, the thickness of the top crystal is only ~40 nm, smaller than λTDS, and could limit the intensity of Kikuchi bands generated. It is thus reasonable to infer the physical depth resolution for Si exposed to 30 keV electrons could be larger than 60 nm.…”

“…The physical depth resolution (dphy) is the maximum depth from which diffraction information is collected and the effective depth resolution (deff) is a measure of how accurately the predominant orientation can be extracted from overlapping patterns from through thickness variations in phase or orientation. By using bi-crystal samples, Brodu et al [14] and Sneddon et al [15] have experimentally measured the physical depth resolution of Al, Si, Cu and Pt layers exposed to 30 keV electrons based on the visibility of Kikuchi bands originated from the materials closest to the incident electron beam. The physical depth resolution is seen to be both highly materials-and energy-dependent, but rather independent of sample thickness.…”

“…The physical depth resolution is seen to be both highly materials-and energy-dependent, but rather independent of sample thickness. Based on their results, Brodu et al [14] proposed the function describing the physical depth resolution to be dphy=0.026E/µ0, where E is the primary beam energy and µ0 (nm -1 ) is the absorption coefficient for the thermally diffuse scattered electrons for samples exposed to 100 keV electrons. The practical application of this relationship may be limited due to the availability of data on µ0 values in a wider range of engineering materials.…”