Tracking defect type and strain relaxation in patterned Ge/Si(001) islands by x-ray forbidden reflection analysis

Plastic relaxation and formation of defects are crucial issues in the epitaxial growth of nanoparticles and thin films. Indeed, defects generate local stress in the crystalline lattice, which affects their surroundings and may lead to undesired effects such as reduced charge-carrier lifetime or nonradiative recombinations. Here, we use a nondestructive method based on x-ray diffuse scattering close to forbidden reflections to identify the defect types with a high sensitivity and quantify their average size and strain field. Combined with transmission electron microscopy, it offers opportunities to track both ensemble average and single defects inside three-dimensional structures. These techniques have been applied to partially embedded and high-Ge-content ($x_{\text{Ge}}=0.87\pm 0.06$) dots selectively grown in 20-nm-sized pits on Si(001) surfaces through openings in a SiO${}_2$ template. The stress in the 20-nm-wide Ge islands is relaxed not only by interfacial dislocations but also by microtwins and/or stacking faults located at the interface, proving the importance of {111} planes and twinning in the relaxation process of nanometer-size Ge dots.

Figure 1

Schematic illustration of the nanopatterning process for forming the self-assembled hexagonal cylindrical patterns of exposed Si areas (holes) in the SiO${}_2$ mask layer using self-assembled diblock copolymer of PS-$b$-MMA as template. (a) Si(001) substrate with diblock copolymers of PS-PMMA, (b) template after selective washing of PMMA, (c) RIE and polymer removal, (d) Ge growth, and (e) scanning electron microscopy image of the grown Ge islands after SiO${}_2$ etching. The inset in (e) shows a HRTEM cross section image in the [110] zone axis of a grown Ge island.

Figure 2

Geometry used to measure the diffuse x-ray scattering at grazing incidence ${\alpha }_i$ and exit ${\alpha }_f$ angles with 2$\theta$ the diffraction angle. The PSD is used for efficient reciprocal space mapping in the ($Q_{//}$ - $Q_z$) plane with $Q_{//}=\frac{2\pi }{a_{\mathrm{Si}}}\sqrt{h^2+k^2}$ and $Q_z=\frac{2\pi }{a_{\mathrm{Si}}}l$.

Figure 3

The intensity in the three figures is presented on a logarithmic scale. (a) (220) reciprocal space map of the Ge islands grown on the Si substrate template. The dashed lines labeled (b) and (c) denote the trajectory, along which the line scans in Figs. 2b and 2(c) were performed, respectively. The minimum and maximum intensity values are in dark and white, respectively. (b) Angular scan at the (220)Si substrate reflection along the correspondent line denoted in Fig. 2a. The inset shows a drawing of the hexagonal reciprocal lattice of the organized assembly of islands and the theoretical position of the correlation peaks (black circles). (c) Radial scan close to the (220)Si substrate reflection along the correspondent line denoted in Fig. 2a. The inset displays radial scans around the (440)Si Bragg peak measured below ($-50$ eV) and at the Ge $K$ edge ($E=11103$ eV).

Figure 4

HRTEM cross-sectional images taken along the [110] zone axis and associated geometrical phase images. (a) Initial HRTEM image. A Burgers circuit has been drawn around the dislocation located at the bottom Ge/Si interface. The Burgers vector of the dislocation is $\frac{1}{2}$[$\overline{1}$10]. The black arrows point to the {111} Si/Ge interfacial planes. (b) and (c) Geometrical phase images obtained with selected g vectors equal to ($\overline{1}$,1,1) and (1,$\overline{1}$,1), respectively. The phase images contain discontinuities that ends either at the surface or at a dislocation core. The phase outside the sample in the glue part (at the top) has been set to zero by using a mask computed from the phase image (see Fig. 5). (d) and (e) {111} lattice parameter maps obtained respectively with the ($\overline{1}$11) [see Fig. 3d] and (1$\overline{1}$1) [see Fig. 3e] g vector. The average values of the interatomic distance between (111) planes inside the Si substrate (noise changes the reference value of 0.314 nm for the Si {111} interplane distance) and in the center of the Ge dot are written. (f) and (g) {111} angle maps obtained respectively using the (−1,1,1) [see Fig. 3f] and (1,−1,1) [see Fig. 3g] g vectors. The local angles measure the local rotation of the {111} planes. (h) Numerical power spectrum used in the GPA analysis to select a given g diffraction spot with an aperture.

Figure 5

Illustration of phase suppression outside the sample. (a) Original phase image. The phase in the glue part is just random noise and prevents to see clearly the dot. (b) Phase image after noise suppression. One can notice that the discontinuity at the right side of the dot just falls at the boundary between the glue and the dot. (c) Original amplitude image obtained with GPA. (d) Binary mask (0 and 1) obtained by thresholding the amplitude image.

Figure 6

HRTEM images of two Ge dots that contain defects on one side of their {111} interfaces as indicated by the arrows and the white circles.

Figure 7

(a) Three-dimensional intensity distribution around $\mathbf{h}=2$. The scattered intensity, which is represented on a logarithmic scale, is concentrated in streaks along $\langle 111\rangle$ directions, perpendicular to the fault planes. (b) In-plane reciprocal space map of diffuse scattering measured around the Si basis-forbidden reflection (200). The intensity, which is displayed on a logarithmic scale, was measured by a position sensitive detector collecting the diffracted signal between ${\alpha }_f\sim$0${}^{\circ }$ and ${\alpha }_f\sim$1.5${}^{\circ }$. The minimum and maximum values are in dark and white, respectively.

Figure 8

(a) Measured integrated intensity (logarithmic scale) along $\langle 111\rangle$ rods passing through the (1$\overline{1}$1)Ge, (200)Ge, and (311)Ge Bragg peaks. A part of the signal was not collected in the vicinity of the (200)Ge reciprocal space position due to limitations of the used scattering geometry. (b) Reciprocal space map of crystal twinning. The (1$\overline{1}$0) plane is drawn: all the peaks verify $h-k=2$. The fourfold symmetry around the [001] direction has been taken into account. The Bragg peaks of the direct and indirect stackings are symbolized by a red $\Delta$ and a blue $\nabla$ markers, respectively. The experimentally observed twin Bragg peaks at $\frac{1}{3}\left(5\overline{1}1\right)$ and $\frac{1}{3}\left(822\right)$ are circled in red.

Figure 9

(a) Si and Ge scattered intensities ($|F_{\mathrm{Si}}{|}^2$ and $|F_{\mathrm{Ge}}{|}^2$) calculated along the $\langle 111\rangle$ rods linking the (1$\overline{1}$1)Si and (311)Si Bragg peaks and passing through the reciprocal space lattice point $\mathbf{h}=(200$) for a pure and defect-free Ge dot grown on a Si substrate. (b) Simulated $|F_{\mathrm{Ge}}{|}^2$ intensity scattered by a Ge dot having a single stacking-fault, with the Si substrate free of defects [see Fig. 9c] and the simulated $|F_{\mathrm{Si}}{|}^2$ intensity scattered by the Si substrate containing one single stacking fault, with a defect-free Ge island [see Fig. 9d]. The atomic positions inside the Ge dot and the Si substrate were obtained by atomistic simulations. Qualitatively, the simple shape chosen for the simulated islands does not influence the obtained results.