Si / Ge Nanowires by MBE
Abstract
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P. Werner, N.D. Zakharov, L. Sokolov, and K. Nguyen-Duc
There is a large interest nowadays in different kinds of nanostructures supported by the possibility to explore quantum size effects. For this purpose the size of structural elements should be comparable with the de Broglie wavelength λ charge carriers, which is about 10 nm. Usually such bandgap engineering is implemented by local variation of composition of the crystal. At the same time modern growth techniques such as MBE, MOCVD and others open the way to create the artificial structures where the local composition varies at the atomic scale (formation of QDs, QWs and so on). In this situation to monitor the compositional variations in such structures an adequate method for chemical analysis characterised by atomic spatial resolution has to be used. TEM was used to monitor the composition of thin Ge layers incorporated into Si nanowhiskers grown by molecular beam epitaxy (MBE) on <111> Si substrates. The goal of this investigation is to show the possibility of Si/Ge heterostructure formation in Si whiskers by MBE.
Fig.1(a) Three Ge layers with nominal thickness 0.5, 1.0 and 1.5 nm were deposited in equal time interval. The variation of Ge concentration x in whisker and substrate was analysed along CD and AB respectively. (b) 5 Ge layers with nominal thickness 1 nm were deposited with the same time interval.
Fig.2. Variation of Ge concentration along AB (a) and CD (b) (see Fig. 1 a) in substrate and whisker respectively.
Three thin layers of Ge 0.5 nm, 1 nm and 1.5 nm thick were deposited during whiskers growth in equal time intervals. The concentration profiles measured along A-B in the substrate and C-D in the whisker (see Fig.1a) are shown in Fig.2 a,b respectively. One can see that the peak’s half-widths in Figs. 2a, b are approximately 2 and 10 times larger than deposited layer thickness respectively. There is an obvious difference between the Ge concentration profiles measured in substrate and whisker. In the first case Ge concentration almost momentarily reaches its maximum value after Ge flashing and then drops slowly due to Ge atom segregation. In the case of the whisker, the situation is practically reversed. The increase of the Ge concentration x occurs relatively slow after flashing and then drops sharply. The slow growth of the Ge concentration in the first stage is due to the time needed for Ge atoms to be transported from the gold droplet surface to the Si/Au interface, where the growth occurs.
Fig.3. (a) Compositional profile measured along CD in Fig.1 b. (b) Variation of the distances between Ge layers in (a). N-(N+1)-distance between N and N+1 Ge layers. The Si growth rate decreases due to incorporation of Ge layers.
It has been found that the incorporation of Ge decreases the growth rate of whiskers. To investigate the dynamics of this phenomenon we deposited 5 Ge layers 1 nm thick each as time markers with the same time interval (Fig.1b). Fig.3a depicts the Ge concentration profile in one of such whisker. The graph in Fig.3b demonstrates decreasing of the interlayer distance from 15.5 to 11 nm with the layer number. This can be explained by the the reduction of supersaturation γ to additional elastic energy introduced by Ge atoms into the Si matrix 
(Nabarro 1940), where G - shear modulus, 
=(rm-ri)/rm - atomic misfit parameter, rm and ri - the atomic radii of Si and Ge respectively, x-concentration, ω-atomic volume. Thus, the real supersaturation γ can be written as:
γ = (μ- μe)/kT
Hence, there is a critical impurity concentration xc at which the supersaturation gets zero and whiskers stop growing. We observed such a growth interruption for xc = 0.05. Thin Ge layers can be incorporated into whisker, however the interfaces are very much diffused. Widening of the Ge layers is explained by the time needed for Ge atoms to be transported from the gold droplet surface to the Si/Au interface. Ge doping reduces the supersaturation and slows down whisker growth.
Further information in:
N.Zakharov, P.Werner, G.Gerth, L.Schubert, L.Sokolov and U.Gösele “TEM investigation of Si/Ge multilayer structure incorporated into MBE grown whiskers” Proceedings of the 14th Conference “Microscopy of Semiconducting Materials” April 11-14, 2005, Oxford, UK, Eds. A.G.Cullis, J.L.Hutchison, Springer 2005, pp.103-106.
N.D.Zakharov, P.Werner, G.Gerth, L.Schubert, L.Sokolov, U. Gösele “Growth phenomena of Si and Si/Ge nanowires on Si(111) by molecular beam epitaxy” Journal of Crystal Growth 290, 6-10 (2006).