Nanoscale tensile strain in perfect silicon crystals studied by high-resolution X-ray diffraction

Abstract

A device was designed, built, and tested to apply small tensile strain to perfect single silicon crystals. It was used on the second axis of a double crystal diffractometer to obtain controllable strain fields. The strain field quality was evaluated by double crystal X-ray diffractometry. The dependence of atomic plane distances on applied stress was determined. Stress-strain curves were obtained from fitted rocking curves in the Bragg-Bragg and Bragg-Laue configurations. These results show that it is possible to obtain a tensile strained lattice with quality suitable for X-ray optics.

Mechanical stretching of a perfect single crystal: a routeway to a d-spacing tunable X-ray monochromator

“…1. The non-dispersive double-crystal setup with the second crystal being the one to be stretched is basically the same as the setup used to explore the tensile strain in perfect Si single crystals (Cusatis, 2019), but with three modifications: (i) Since we are focusing on Bragg case diffraction and are not requiring high tension values, for simplicity, we decided to use a rectangular-shape stretched Si single-crystal blade, taken from a commercially available FZ double-side-polished Si wafer (400 mm thick). (ii) The reference flat and perfect Si 400 single crystal [9 Â 9 mm (H Â V) Â 400 mm thick], also taken from a commercially available FZ double-side-polished Si wafer, was attached in the same angular-rotation axis and on the surface (bottom half) of the stretched crystal with a drop of water.…”

“…The clamps on the traction device are the same as those used in the previous experiment (Cusatis, 2019). The clamp housing was patterned with knurled grooves to 400 mm (depth) Â 18 Â 10 mm (H Â V).…”

“…Gradient crystals, which can be used for interplanar-distance (d-spacing) scanning monochromators (instead of angular scans) for X-ray energy tuning, have been studied for a long time by using ultrasound (Hock et al, 1993;Liss et al, 1997), thermal expansion (Smither et al, 2005;Ru ¨tt et al, 2010) and as-grown gradient crystals (Erko et al, 2001;Barbosa et al, 2003). On the other hand, stress-strain analysis (which includes determination of the elastic constants) on highly perfect single crystals, theoretically and/or experimentally, is an open-challenge issue (Hauch et al, 1999;Kozhushko et al, 2007;Hopcroft et al, 2010;Cusatis, 2019;Fukui et al, 2020).…”

“…This work can be considered an update of a previously published manuscript (Cusatis, 2019). In that work, perfect 200 mm thick Si single crystals were stretched, in both Bragg and Laue cases, with the aim of finding, experimentally, a stress-strain relation (from angular scanning diffraction profiles taken at different applied traction forces) at low tension values (smaller than 260 MPa).…”