High-resolution imaging of nanoislands with hard X-rays is an experimental challenge due to the dramatic reduction of the scattered X-ray intensity from a sample when its size is in the submicrometre range. The lack of focusing optics with a nanometre focal spot at high X-ray energies is another bottleneck for a full-field imaging of nanoislands. In our work we use coherent X-rays in a grazing-incidence small-angle X-ray scattering (GISAXS) geometry to image SiGe nanoislands grown by liquid phase epitaxy (LPE) on Si(001). A significantly enhanced diffraction pattern is obtained from an average island as a result of the sum of the coherent scattering from individual islands. This is due to the narrow size distribution, identical shape, and orientation of the islands. We use iterative phase retrieval techniques for the reconstruction of the projected electron density of the islands with typical dimensions in the 100 nm range. We obtained a spatial resolution of 10 to 15 nm for such islands which is not achievable by other X-ray imaging methods.

In a conventional approach based on X-ray scattering methods, the structural information (shape, strain, and composition) is obtained indirectly by fitting the measured diffraction patterns with simulated ones derived from a realistic modelling of the nanostructures. Our model independent approach yields high resolution imaging of nanostructures. As an example, we determined the electron density of epitaxial SiGe nanoislands using coherent scattering in GISAXS geometry (Figure 88). In this scattering geometry, the recorded intensity distribution depends on the electron density distribution and the island shape and size, but not on strain. The GISAXS geometry provides an additional advantage to the conventional scattering techniques.The limited penetration of the X-rays into the substrate results in a considerable enhancement of the sensitivity to the nanoislands on the sample surface.

Fig. 88: Schematic diagram of the experiment in GISAXS geometry on a single island in the form of a truncated pyramid with a square base.

The experiments were performed at beamline ID01. The incidence angle ai was taken equal to the critical angle ac for the Si substrate i = c = 0.22°, for an X-ray energy of 8 keV. We used SiGe islands of 140 nm and 200 nm size as a model system. All islands exhibit a truncated pyramidal shape with a square base (see insets in Figure 89). In addition these islands typically have a narrow size distribution and the same crystallographic orientation on a Si surface. In GISAXS geometry with an incoming beam of a few hundreds of micrometres in size, a large number of SiGe islands, typically 106, are illuminated simultaneously. Diffraction patterns measured under these experimental conditions are shown in Figure 89.

Fig. 89: GISAXS diffraction patterns measured for different island sizes, a) 140 nm and b) 200 nm. SEM images of the samples with different magnification are presented in the insets. c) and e) Results of the reconstruction of the islands electron density projections obtained from experimental GISAXS data. d) and f) The reconstruction of a single island electron density obtained from a simulated GISAXS pattern. The size of the rectangular support region used in each reconstruction is indicated by a black line.

Results of the reconstruction of the islands electron density projection are presented in Figure 89. For comparison, a reconstruction of the island shape obtained from a simulated GISAXS pattern is also shown on the same Figure. We see that for our scattering conditions the projection of the electron density, the island shape, and their size are well reproduced.

We have demonstrated how the coherent GISAXS technique can be used to image nanometre-sized objects. The high resolution obtained in our experiment of about 10 to 15 nm is strongly related to the enhancement of the scattered signal from the simultaneous illumination of a large number of uniform islands. This approach does not depend on the crystalline structure of such an object and can, in principle, be applied to any material system. An important extension of this technique is its application to the collection of 3D data measured by rotating the sample around its axis perpendicular to the substrate surface, while maintaining grazing incidence conditions [1]. Such data can then be used for the reconstruction of the full 3D electron density of nanoislands [2].


Principal publication and authors

A.V. Zozulya (a), O.M. Yefanov (a), I.A. Vartanyants (a), K. Mundboth (b,c), C. Mocuta (b), T.H. Metzger (b), J. Stangl (c), G. Bauer (c), T. Boeck (d), M. Schmidbauer (d), Phys. Rev. B Rapid Commun. 78, 121304(R) (2008).
(a) HASYLAB at DESY, Hamburg (Germany)
(b) ESRF
(c) Institut für Halbleiterphysik, Johannes Kepler Universität Linz, Linz (Austria)
(d) IKZ, Berlin (Germany)


[1] I.A. Vartanyants, et al., Phys Rev. B 77, 115317 (2008).
[2] O.M. Yefanov and I.A Vartanyants, Eur. Phys. J. Special Topics 168, 81 (2009).