Contrast of HOLZ lines in energy-filtered convergent-beam electron diffraction patterns from silicon

Abstract

Higher-order Laue-zone (HOLZ) lines were investigated in convergent-beam electron diffraction patterns from silicon near the low-indexed zone axes [100], [110] and [111]. The visibility of these lines depends on the effective structure potentials of the reflections from the first Laue zone depending on their Debye–Waller factor. The contrast of the HOLZ lines is strongly reduced by inelastically scattered electrons. They can be excluded by an imaging Ω filter for energy losses above 2 eV. The diffraction patterns were compared with many-beam calculations. Without absorption, an excellent agreement could be achieved for the [111] and [100] zone axes, while the simulation of the [110] zone-axis pattern needed a calculation with absorption. The reason for this observation is explained in the Bloch-wave picture. Calculations with absorption, however, lead to artefacts in the intensity distribution of the [100] HOLZ pattern. In order to obtain agreement with the experiment, the Debye–Waller factor had to be modified in different ways for the different zone axes. This corresponds to a strong anisotropy of the Debye–Waller factor. To confirm this observation, the temperature dependence of the intensity distributions of the HOLZ patterns was investigated between 50 and 680 K. At room temperature, the parameter D in the Debye–Waller factor exp(−Ds2) was determined as 0.13, 0.26 and 0.55 Å2 for the zone axes [100], [111] and [110], respectively. The reliability of the conclusions is discussed.