Lateral and Vertical Ordering of PbSe Self-Assembled Quantum Dots in PbSe/PbEuTe Superlattices
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Figure 1: Sketch of the GISAXS method for studying the morphology of the arrays of self-assembled quantum dots consists in small angle x-ray scattering. This non-destructive method can investigate both the free-standing and buried dots, and in contrast to TEM and x-ray diffraction, it is not sensitive to elastic deformation. A small-angle x-ray scattering experiment yields a distribution of the scattered intensity in reciprocal space. In the usual coplanar arrangement, the wave vectors K2 ,f of the primary and scattered beam as well as the surface normal of the sample lie in the same plane (scattering plane). In this arrangement, the accessible part of reciprocal space is limited by the conditions aij > 0, where aij are the angles of incidence and exit of the radiation with respect to the sample surface. Thus, for a given scattering angle 20 = ai + af, one can detect the dots of a minimum characteristic size and/or distance Lmin > 22.
(1)
Since the maximum value of 0 is limited by the intensity of scattering to few degrees, this conditions represents a substantial limitation of the application of the coplanar arrangement. In grazing incidence small-angle x-ray scattering (GISAXS) geometry, the plane of the vectors K1 ,f is nearly parallel to the sample surface (see Fig. 1) and no limitation of the dot size exists [9]. In addition, changing the incidence and/or exit angles ai, we can tune the depth, where the scattered radiation comes from (the information depth). Especially in materials with heavy atoms such as PbEuTe the information depth can be small and the investigation of buried dots can be performed only using conventional coplanar x-ray diffraction (XRD). In this case, however, the scattered intensity is influenced also by the strain status of the surrounding host crystal, which makes data analysis more difficult. In this paper we use both the GISAXS and XRD methods for the investigation of the shape and the positions of self-assembled PbSe quantum dots in PbSe/PbEuTe superlattices and compare the results with AFM and TEM investigations published previously [6, 7, 8]. EXPERIMENTS The samples were grown by molecular beam epitaxy on PbTe buffer layers deposited on (111) BaF 2 cleaved substrates. All samples consisted of 5 monolayers PbSe and Pbl_,Eu=Te 162
Table 1: Parameters of the PbSe/PbEuTe samples Sample No # 966 # 925 # 906
period D (A) 355 470 660
number of periods N 30 60 60
stacking type vertical trigonal random
spacer layers with the superlattice periods D ranging from 350 to 650 A. Because of the -5.4 % lattice mismatch of PbSe with respect to PbTe, island growth in the Stranski-Krastanow growth mode occurs once the critical thickness of 1.5 monolayers is exceeded. During the overgrowth of the islands, a rapid replanarization occurs and a completely flat surface is regained after the growth of 200 A PbEuTe. The concentration x of Eu was adjusted in order to achieve a complete strain symmetrization of the superlattice period with respect to the PbTe buffer. The strain symmetrization prevents
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