Correlated Three-Dimensional Imaging of Dislocations: Insights into the Onset of Thermal Slip in Semiconductor Wafers

Correlated x-ray diffraction imaging and light microscopy provide a conclusive picture of three-dimensional dislocation arrangements on the micrometer scale. The characterization includes bulk crystallographic properties like Burgers vectors and determines links to structural features at the surface. Based on this approach, we study here the thermally induced slip-band formation at prior mechanical damage in Si wafers. Mobilization and multiplication of preexisting dislocations are identified as dominating mechanisms, and undisturbed long-range emission from regenerative sources is discovered.

Figure 1

(a) XWBT image (220 reflection on film) of the sample region investigated. After annealing, the point of indentation (white triangle) is surrounded by a dislocation network. For later reference, the surface regions $A–D$ are defined [see (c), Fig. 3, and Fig. 4]. (b) Illustration of the four $\{111\}$ slip bands (red, bottom part indicated) containing the 3D paths of all dislocations. The bands mutually intersect nearby the indentation damage and thus leave a pyramidal region directly below dislocation-free (blue). A gray hemisphere depicts the strong deformation surrounding the indentation damage. (c) A 3D rendering based on the combined information from XDL and XWBT, for regions $A$ and $B$ also indicating the relation to the CDIC surface maps in Fig. 3 (see Supplemental Movie [21]). Tubes with a radius of $3\mu \mathrm{m}$ (estimated spatial resolution) represent the 3D dislocation paths, and a color code indicates the associated BV orientations determined.

Figure 2

(a) Top view [compare Fig. 1] on the BV distribution determined, with all screw segments highlighted. Only $⟨110⟩$ orientations are found. White dots mark the surface end points of the dislocations within the $(111)$ and $(\overline{1}\overline{1}1)$ slip bands, illustrating their uncorrelated appearance. (b) The thermally induced RSS ${\tau }_{\{111\}⟨110⟩}^{\mathrm{th}}$ on the 12 $\{111\}⟨110⟩$ glide systems (planes and BV orientations indicated in the four schemes), according to FE calculations. Stress values between $-2$ and 8 MPa are obtained. The systems with the lowest stresses $|{\tau }_{\{111\}⟨110⟩}^{\mathrm{th}}|$ fit the suppressed activation for $\mathbf{b}\propto [1\overline{1}0]$ (purple) and $\mathbf{b}\propto [110]$ (pink) observed in (a).

Figure 3

(a) Surface map of the regions $A$, $C$, and $D$ [compare Fig. 1], showing the location of all steps detected in the CDIC data and their relation to the individual dislocations inside the $(\overline{1}11)$ and $(1\overline{1}1)$ slip bands in the bulk below. The visualization is $10\times$ compressed along $\pm [110]$. As illustrated in (b), all steps are represented by lines colored according to the BV of the associated dislocations, the end point positions of which are marked by white dots. (c) Isolated view on the $(1\overline{1}1)$ slip band [see Fig. 2] with the half-loops $\alpha$, $\beta$, and $\gamma$ highlighted. Identical BV, similarity, concentricity, and end point positions compatible with a common glide plane [indicated in (a)] suggest their emission from a regenerative dislocation source. (d) Macroscopic plastic deformation of the wafer (scheme). The dislocation-free pyramid is moved to the rear side, finally elevating there an undisturbed square area.

Figure 4

(a) CDIC micrograph of the indentation damage in region $D$ [see Figs. 1 and 3], including the positions of all active glide planes within the $(\overline{1}11)$ and $(1\overline{1}1)$ slip bands. Two main subbands intersect the left facet of the triangular imprint (red) and a crack tip (blue) at the edge of a breakout. At $S$, many short surface steps are visible. (b) RSS ${\tau }_{(1\overline{1}1)[011]}^{\mathrm{ind}}$ during indentation, calculated using the Hertz contact stress model (contact radius $R=1$), normalized to the mean contact pressure ${\overline{p}}_c$, and in a depth of $(R/3)$ below the surface.