Investigation of the spontaneous lateral modulation in InAs/AlAs short-period superlattices by grazing-incidence x-ray diffraction

O. Caha¹, P. Mikulík¹, J. Novák¹, V. Holý², and S. C. Moss³

¹Institute of Condensed Matter Physics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
²Department of Electronic Structures, Charles University, Ke Karlovu 5, 121 19 Prague, Czech Republic
³Department of Physics, University of Houston, Houston TX 77204, USA

Processes of self-organization during the epitaxial growth of strained semiconductor heteroepitaxial systems represent a possible route for fabricating semiconductor quantum wires and dots. In a short-period superlattice nearly lattice-matched to a buffer layer underneath, such a process leads to a spontaneous modulation of the thicknesses of individual layers [1].

Theoretical description of the modulation process is based on two different models. If the crystallographic miscut of the substrate surface is large (above 1^o), the density of monolayer steps on the vicinal surface is large. In this case a stress-induced bunching of the steps takes place creating a nearly periodic sequence of atomically flat terraces divided by bunches of monolayer steps [2]. If the miscut is small, the mean distance between the neighboring monolayer steps is larger than the diffusion length of the migrating adatoms. Then, the bunching process does not occur and the spontaneous modulation of the layer thicknesses is caused by a morphological instability of the growing surface – the Asaro-Tiller-Grinfeld instability (ATG) [3,4].

The serie of four samples of InAs/AlAs superlattices grown by molecular beam epitaxy (MBE) on an InP(001) substrate was studied; the substrate was prepared without any nominal miscut. The samples have 2, 5, 10 and 20 superlattice periods; the InAs and AlAs thicknesses were nominally 1.9 monolayers in all samples. For all samples, we have measured the intensity distribution of the grazing-incidence 400 and 040 diffraction in the q_xq_y plane of the reciprocal space, i.e. parallel to the sample surface. The x-ray measurements have been carried out at the beamline ID01 of the European Synchrotron Radiation Facility (ESRF, Grenoble). In Fig. 1 are shown the reciprocal space maps of all samples taken in diffraction 400. In all cases except of the 2-period sample, the intensity distributions exhibit two side maxima in direction few degrees from [100] and [010] caused by the periodicity of the composition modulation. The intensity of side maxima increase with the number of the superlattice periods, so that the lateral composition modulation becomes stronger.

Since the intensity of the diffracted intensity depends on the chemical composition and the elastic deformation field in the supperlattice, we developed a theoretical description of x-ray scattering that makes it possible to determine the degree of the lateral modulation directly from the measured data without assuming any structure model [5]. The dependences of the modulation amplitude Cdq and width dq of the satellites on the number of superlattice periods are plotted in Fig. 2. From the measurements it follows that the mean period <L>=(267 ± 15) Å of the modulation remains constant during the growth, the integrated amplitude increases with the number N of the periods, while the width dq of the lateral satellites decreases with N as N^-0.2. From this behavior it follows that the first stages of the spontaneous modulation of the average chemical composition of a short-period superlattice cannot be explained as a result of the bunching of monolayer steps at the interfaces. Most likely, this behavior can be ascribed to the ATG instability, in which the critical wavelength of the surface corrugation, L_crit depends on the stress in the growing layer, elastic constants and its surface energy. In periodic multilayers, such an instability was investigated theoretically in Ref. [4]; using this approach we obtain L_crit » 200 Å for these samples, which roughly corresponds to the obtained mean period L. However this approach gives much faster growth of the composition modulation than that obtained from the measurements; this will be the subject of further investigation.

References

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Fig. 1. The reciprocal space maps of the diffracted intensity measured in diffraction 400 of samples with 2 to 20 superlattice periods. The diffraction vector is parallel to the q_x-axis, the numbers of periods are denoted in the maps.

Fig. 2. The scaling behavior of the modulation amplitudes Cdq and widths dq of the lateral satellites as functions of the number of the superlattice periods.