X-ray diffraction using focused-ion-beam-prepared single crystals

Abstract

High-quality single-crystal X-ray diffraction measurements are a prerequisite for obtaining precise and reliable structure data and electron densities. The single crystal should therefore fulfill several conditions, of which a regular defined shape is of particularly high importance for compounds consisting of heavy elements with high X-ray absorption coefficients. The absorption of X-rays passing through a 50 µm-thick LiNbO₃ crystal can reduce the transmission of Mo Kα radiation by several tens of percent, which makes an absorption correction of the reflection intensities necessary. In order to reduce ambiguities concerning the shape of a crystal, used for the necessary absorption correction, a method for preparation of regularly shaped single crystals out of large samples is presented and evaluated. This method utilizes a focused ion beam to cut crystals with defined size and shape reproducibly and carefully without splintering. For evaluation, a single-crystal X-ray diffraction study using a laboratory diffractometer is presented, comparing differently prepared LiNbO₃ crystals originating from the same macroscopic crystal plate. Results of the data reduction, structure refinement and electron density reconstruction indicate qualitatively similar values for all prepared crystals. Thus, the different preparation techniques have a smaller impact than expected. However, the atomic coordinates, electron densities and atomic charges are supposed to be more reliable since the focused-ion-beam-prepared crystal exhibits the smallest extinction influences. This preparation technique is especially recommended for susceptible samples, for cases where a minimal invasive preparation procedure is needed, and for the preparation of crystals from specific areas, complex material architectures and materials that cannot be prepared with common methods (breaking or grinding).

Keywords: X-ray diffraction; focused ion beams; sample preparation.

Figure 1

Crystal preparation using a FIB. The prospective crystal for SC-XRD is marked in blue. (a) outlines the cube-shaped crystal which will be cut out from the wafer edge. In the first preparation step (b) two trenches (1) perpendicular to the edge at a distance of 50 µm were cut, and then a staircase-like cross section parallel to the edge (2). For the final cutting step on the opposite side, the crystal was rotated by 180° around the electron-beam axis (c) and tilted as far as possible (−10°) in the reverse direction (d). In this position another trench (3) was cut. (e) shows the final crystal fixed on an easily transferable tungsten tip of the micro-manipulator (marked in orange). The platinum patch on the crystal surface (marked in red) links the crystal and tip so that the crystal can now be removed from the bulk in situ under microscope control (f).

Figure 2

Scheme demonstrating the two different stage positions, i.e. the orientations and rotations of the crystal with respect to the electron and ion beams used for cutting (a) trenches (1) and (2) and (b) trench (3). For a stage tilt of 52° (rotation of 0°) the large crystal surface is perpendicular to the ion beam, while a stage tilt of −10° followed by a rotation of 180° results in an angle of 62° between the edge surface and the ion beam.

Figure 3

The three differently prepared crystals. (a) FIB-prepared cube-shaped crystal (LN1) mounted on a MicroGripper as crystal holder (olive), (b) FIB-prepared cube-shaped crystal (LN2) mounted on a tungsten micro-manipulator tip and (c) randomly shaped as-cut crystal (LN3) manually prepared from the same bulk material, also mounted on a MicroGripper. The inset in (c) shows a detailed view of the surface and shape of crystal LN3.

Figure 4

Near-surface distribution of implanted gallium ions induced by FIB milling into an LiNbO₃ crystal calculated with SRIM (Ziegler et al., 2010 ▸) (acceleration voltage: 30 kV). (a) shows the lateral and depth gallium distribution with maximum penetration levels of <250 Å and <500 Å, respectively, according to an alignment of the ion beam perpendicular to the crystal surface. (b) represents the number of gallium ions distributed along the crystal depth. The red triangles mark the positions of the highest density of gallium ions.

Figure 5

Crystal structure of LiNbO₃ with space-group symmetry R3c (161).

Figure 6

Sections of difference EDs (; aspherical contributions) perpendicular to the [100] direction for crystals LN1, LN2 and LN3. A schematic view of the section is provided on the left, while the difference EDs of the different crystals are shown in the center. The experimental ED is most blurred for the LN2 crystal. For comparison purposes, a theoretical difference ED calculated from a spherical IAM-ED and an aspherical DFT-ED is shown on the far right. The theoretical ED does not include thermal smearing.