Coherent-diffraction imaging of single nanowires of diameter 95 nanometers

Photonic or electronic confinement effects in nanostructures become significant when one of their dimension is in the 5–300 nm range. Improving their development requires the ability to study their structure-shape, strain field, and interdiffusion maps. We have used coherent-diffraction imaging to record the three-dimensional scattered intensity of single silicon nanowires with a lateral size smaller than 100 nm. We show that this intensity can be used to recover the hexagonal shape of the nanowire with a 28 nm resolution. This paper also discusses the limits of the method in terms of radiation damage.

Figure 1

Scanning electron microscopy images of a silicon nanowire, with an hexagonal-shaped section. The gold droplet used as a catalyst for the synthesis can be seen at the top of the wire (upper view). The bottom view shows the facets and nanofacetting for the same wire.

Figure 2

(Color online) 3D coherent-diffraction image of a single $\text{Si}⟨111⟩$ nanowire shown as a projection of multiple semitransparent isosurface layers, with the intensity increasing logarithmically from blue to green and red (from light to dark gray). The hexagonal symmetry of the wire is visible in the 3D diffraction image. The scale is given for $k=2\text{sin}\theta /\lambda$.

Figure 3

(Color) Simulation of the truncation effect on the reconstruction of a NW shape. (a) Original hexagonal shape of the NW; (b) FT of the NW shape: as the original shape is centrosymmetric, the FT is real, here depicted with positive regions in red and negative in blue; (c) truncation of the FT and (d) resulting NW shape calculated by inverse FT, in which dips (representing $\approx 15\%$ of the average density) can be clearly seen due to the truncation.

Figure 4

(Color) The real shape (the projection of the electronic density) of the NW can be reconstructed from the measured scattered amplitude by recovering the lost phase information either by predicting the [(a)–(c)] phase values or by using [(d)–(f)] iterative phase retrieval algorithms (see text for details). (a) Projection of the experimental scattered amplitude, with model phases—the saturation corresponds to the logarithm of the intensity and the color to the phase. Relative coordinates around the (111) reflection are given in $k=2\text{sin}\theta /\lambda$ units. (b) NW density cross section obtained by inverse Fourier transform of (a); the distance between opposite facets is equal to $\approx 95\text{nm}$. (c) Density profiles along the horizontal $\left({\rho }_x\right)$ and vertical $\left({\rho }_y\right)$ directions, which demonstrate (the real components being positive and the imaginary one being negligible) that the choice of alternating $(+)$ and $(-)$ signs for successive rings is correct. The dips of the density inside the NW are due to the limited extent of the intensity scattered by the silicon NW. (d) Experimental amplitude with the phase recovered using ab initio Fourier-recycling algorithms. (e) The best reconstruction obtained and (f) the corresponding cross sections (positivity is imposed in the algorithm).

Figure 5

(Color online) Effect of radiation damage: [(a)–(c)] evolution of the 3D diffraction pattern of a single Si NW around the (111) reflection for successive scans, with a total exposure time of $4000\text{s}$ per scan (a fourth scan is not presented here). The projection is presented in the direction perpendicular to the NW axis, using a logarithmic color (grayscale) scheme. The short vertical oscillations are due to the finite length of the wire and almost disappear in later scans due to the damage to the NW. The fringes which can be seen parallel to the diagonal of the image correspond to the FT of the NW cross section, as seen in Fig. 2 for another wire. The split of the main diffraction peak could be due to the breaking of the NW: (d) simulated scattered amplitude around the (111) reflection of a broken wire, with two parts with an equal length of 400 nm along $⟨111⟩$ and a width of 105 nm along $⟨1\overline{1}0⟩$, with a separation between the two parts equal to half the interplanar distance $d_{111}$. This separation leads to two maxima at the (111) reflection position.