Differential quantitative analysis of background structure in energy-filtered convergent-beam electron diffraction patterns

Abstract

Measurements of electronic structure in solids by quantitative convergent‐beam electron diffraction (QCBED) will not reach their ultimate accuracy or precision until the contribution of the background to the reflections in energy‐filtered CBED patterns is fully accounted for. Apart from the well known diffuse background that arises from thermal diffuse scattering of electrons, there is a component that has a much higher angular frequency. The present work reports experimental evidence that this component mimics the angular distribution of the elastically scattered electrons within each reflection. A differential approach to QCBED is suggested as a means of quantitatively accounting for the background in energy‐filtered CBED data.

Differential convergent beam electron diffraction: Experiment and theory

“…͑1͒ and ͑2͔͒. Previous work with both energy-filtered and unfiltered CBED patterns 28,29 suggests that this is valid beyond the range of the image shifts that are typically required to obtain angulardifference CBED patterns. Figure 2 examines a small area of I inel ͑͒ that can be considered planar.…”

“…+ ␥. This expression is equivalent to the model for the total intensity given in a related paper, 28 where ␤ is the local gradient of the low-frequency component of the background and ␥ the offset. The high-frequency term, I͑U g , H , ͒, is dominantly composed of the elastically scattered electrons, I el ͑U g , H , ͒, and a much smaller inelastic component, I inel ͑U g , H , ͒.…”

“…The intensity distribution from plasmon scattering is known to mimic the elastic distribution, albeit in a slightly more diffuse manner 26,29,30 and an example was recently given showing that the high-frequency component of the background remaining in energy-filtered CBED patterns ͑in the absence of the plasmon signal but including TDS and scattering from surface defect layers͒ also mimics the elastic signal from the crystal. 28 Based on this recent work and the intensity model that it verified, an expression for the total intensity distribution in an unfiltered CBED pattern can be obtained as follows:…”

“…28 That work 28 lays the foundation for an approach to QCBED that allows an unprecedented level of matching between experimental and theoretical CBED patterns, without recourse to complex calculations of the TDS background. TDS calculations will be required in future to verify the nature of the contribution made by TDS to the total background intensity; however, at present, this is beyond the scope of this work.…”

“…Most recently, the potential for developing an angular-difference approach to QCBED was revealed, 28 based on the large difference in sensitivity to scattering angle exhibited by the elastic and the inelastic components of energy-filtered CBED patterns. Considering all experimentally practicable derivatives that could be used to discriminate between the elastic and the inelastic signals in a CBED pattern, it is concluded that the derivative with respect to scattering angle is the most practical.…”