Time-Dependent Relaxation of Strained Silicon-on-Insulator Lines Using a Partially Coherent X-Ray Nanobeam

We report on the quantitative determination of the strain map in a strained silicon-on-insulator line with a $200\times 70{\mathrm{nm}}^2$ cross section. In order to study a single line as a function of time, we used an x-ray nanobeam with relaxed coherence properties as a compromise between beam size, coherence, and intensity. We demonstrate how it is possible to refine the line deformation map at the nanoscale, and follow its evolution as the line relaxes under the influence of the x-ray nanobeam. We find that the strained line flattens itself under irradiation but maintains the same linear strain (${ϵ}_{zz}$ unchanged).

Figure 1

Nanofocused x-ray beam at the sample position: (heavy black line) sketch of the rectangular cross section of the SSOI line, $225\times 70{\mathrm{nm}}^2$; (black contour levels) normalized intensity distribution at the sample position, calculated using a point source 49 m from the fully illuminated Fresnel zone plate; (red contour levels) normalized intensity distribution taking into account the source size ($64\times 13.8\mu {\mathrm{m}}^2$ r.m.s.) for the id01 beam line. Contour levels are represented at 25%, 50%, and 75% of the maximum intensity. The calculations are made at $150\mu \mathrm{m}$ from the focal point, i.e., the estimated position for the sample. The resulting illumination of the SSOI line is both partially coherent and inhomogeneous.

Figure 2

Diffraction from a SSOI line by a partially coherent x-ray nanobeam [($1\overline{1}3$) reflection], calculated from a simulated deformation of the SSOI line, using either (a) a plane wave illumination or (b) taking into account the partially coherent illumination of the FZP.

Figure 3

(a), (c), (e), (g) Two-dimensional diffraction patterns compared to (b), (d), (f), (h) calculations for the chosen silicon line at different times $T=0$, 800, 1600, and 2900 s. Relevant changes are visible in the experimental intensity distribution and well reproduced by calculations. Intensities are expressed using the same logarithmic color scale, with a total amplitude spanning 3 orders of magnitude. The horizontal stripe near $l=2.996$ is due to the Si substrate, and was masked during the refinement. The slight bending visible in (g) is due to a small ($<0.1°$) rotation of the line [see Fig. 4d] around the irradiation, which results in a twisting along the [$1\overline{1}0$] direction, and cannot be reproduced in a 2D model.

Figure 4

Displacement fields $u_z$ obtained from the time-dependent analysis of radiation damage at $T=0$, 800, 1600, and 2900 s. The $u_z$ profiles is visibly less curved at $T=2900\mathrm{s}$ (d) with respect to the one obtained at (a) $T=0$. Scale units expressed in nanometers are represented by colors.