1996 origin of rippled structures formed during growth of si on si(001) with mbe


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1996 origin of rippled structures formed during growth of si on si(001) with mbe

  1. 1. surface s c i e n c e ELSEVIER Surface Science 352-354 (1996) 641-645 Origin of rippled structures formed during growth of Si on Si(001) with MBE J. van Wingerden *, E.C. van Halen, K. Werner, P.M.L.O. Scholte, F. Tuinstra Solid State Physics, Department of Applied Physics, Delft University of Technology, Lorentzweg I, 2628 CJ Delft, The Netherlands Received 5 September 1995; accepted for publication 31 October 1995 Abstract During epitaxial growth of silicon on Si(001) with MBE a rippled structure is formed on the surface. This rippled structure is akin to ripples observed in sand when water has flown over it. Experiments combining X-ray crystallography, optical microscopy and atomic force microscopy have been used to determine the microscopic details of the rippled structure. We find that the rippled structure is caused by correlated kink bunching and not by step bunching. A model is presented for the microscopic mechanism yielding deviations of the kink distribution from the equilibrium distribution, which are large enough to cause step-step interactions. Keywords: Atomic force microscopy; Epitaxy; Faceting; Growth; Models of surface kinetics; Molecular beam epitaxy; Non-equilibrium thermodynamics and statistical mechanics; Silicon; Single crystal epitaxy; Stepped single crystal surfaces; Surface structure, morphology, roughness, and topography 1. Introduction period and orientation as a function of the sample misorientation. As the ripples disappear upon anneal- Molecular beam epitaxy (MBE) is a well-known ing at the growth temperature, their existence is technique to grow high-quality layers with well-de- determined by the growth kinetics. The effect of the fined properties. In general, growth is performed on high supersaturation on the minimum energy step vicinal substrates, i.e. substrates with a regular spac- configuration has been suggested as the origin of the ing b e t w e e n the steps, which are caused by the ripple formation [1]. However, since ripples form if misorientation of the macroscopic surface relative to growth proceeds by step flow, the adatom density the crystallographic plane. Under certain growth con- should be sufficiently low to let the adatoms stick to ditions a shallow ripple pattern develops during the a step edge before they meet each other and form an growth of a thick layer ( ~ 1 /xm) on such a flat immobile cluster [2]. This means that the actual substrate. adatom density on the surface cannot be large enough Pidduck et al. [1] have determined the ripple to change the relative energies of the step configura- tions. This stresses the need for a thorough study of the origin of the ripple formation, as it will con- * Corresponding author. Fax: +31 1578 3251; e-Mail: tribute to a better understanding of the basic micro- wing@duttfks.tn.tudelft.nl. scopic processes during growth. 0039-6028/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved SSDI 0039-6028(95)01219-2
  2. 2. 642 J. van Wingerden et a l . / Surface Science 352-354 (1996) 641-645 In this paper we will first present new experimen- bonds of the lower terrace have to be broken for tal evidence for the microscopic form of the steps on every other dimer attached to a kink site, stable the rippled surface. Furthermore, we present a new growth units consist of two dimers. For step flow model which shows that the inherent discreteness of growth no islands are formed on the terraces and growth can cause the onset of ripple formation. growth proceeds via attachment of growth units to the step edges, which occurs mainly at kink sites. For surfaces with alternating S A and S B step edges 2. The Si(001) surface this causes a much higher growth rate at Ss step edges so that they will catch up with the S n step The atoms of the Si(001) surface top layer form edges. dimers, which form rows in the (110) directions. The orientation of the dimer rows rotates over 90 degrees at single atomic height steps. In Fig. 1 an 3. The microscopic ripple structure STM image of the Si(001) surface is shown. We use the notation of Chadi [3] for the S A and S B step In this section we present the results of measure- edges, where the dimer rows of the upper terrace are ments, where atomic force microscopy, optical mi- parallel and perpendicular to the step edges, respec- croscopy, and X-ray crystallography have been used tively. to characterize the microscopic structure of the rip- Because S A step edges have the lowest energy [3], ples. For these experiments a 2 /xm thick layer was the introduction of kinks is energetically un- grown on Si(001) at 650°C with a rate of 1.4 .~/s. favourable due to the accompanying small pieces of The vicinal angle of the sample (i.e. the angle be- S B step edge. Therefore, S A step edges are relatively tween the macroscopic surface and the crystallo- straight with a density of thermally excited kinks graphic surface) is determined to be 0.296 ___0.002 °. which is in most cases much lower than the density The angle between the average step edge direction of kinks enforced by the misorientation. On the other and the [110] direction is 20.3 ___0.4 °. The average hand S B step edges are rough because of thermal ripple direction has been determined from Nomarski excitation of kinks. If the step edge direction deter- microscope images (see Fig. 2a for a typical exam- mined by the misorientation of the macroscopic sur- pie). By measuring the ripple orientation and the face is close to the (110) direction, step edges are crystallographic [110] orientation relative to the sam- alternating of the S A and S B type. Under growth ple holder, the angle between the ripple and the [110] conditions adatoms as well as ad-dimers are mobile, orientation is determined to be 46 ___2 °. These orien- and their diffusion is much faster along than perpen- tations are drawn in Fig. 2f. dicular to the dimer rows [4,5]. Because two dimer AFM images of the rippled surface have been obtained under atmospheric conditions because no in situ scanning probe microscope is available in the equipment where the thick Si layers are grown. A large scan area AFM image is shown in Fig. 2b. The cross section perpendicular to the ripple direction (Fig. 2c) shows a ripple height of about 3 nm. Although the native silicon oxide layer on top limits the resolution, individual step edges are observed on a small scan area (Fig. 2d) and on the corresponding high pass filtered image (Fig. 2e). The orientations in Fig. 2f are found by drawing the [110] direction and the average step edge direction relative to the ripple direction observed in the AFM image. By comparing Fig. 1, STM image of Si(001) with Sn and S B step edge seg- these directions it is clear that the steps run approxi- ments. mately in the [1 I0] direction in those regions where
  3. 3. J. oan Wingerden et aL / Surface Science 352-354 (1996) 641-645 643 + + I0.0 + ?2 ..... 0 215 s:o 715 10.0 12'.5 (a) 0 2,5 5.0 7.5 I0.0 o (c) p.m IT 0 1.0 2.0 3.0 ~m 0 1.0 2,0 3.0 ~m Fig. 2. Nomarski microscope image (76 x 58 /xm 2) (a) and large scan area AFM image (b) with the corresponding cross section (c). Individual step edges are observed in the AFM image (3.6 x 3.6 /zm 2) before (d) and after high pass filtering (e). A step edge and the relevant directions are drawn schematically in (f). individual steps are resolved (the bright areas in Fig. 2e). Furthermore, to obtain the average step edge - - [11 O] direction corresponding to the vicinal orientation of the surface, we need to assume that in those parts where no individual step edges are resolved, the steps should on the average run along the [~10] direction. The fact that in these regions no steps are (a) observed is caused by the limited resolution, possibly in combination with a larger roughness of these step segments. Thus, the macroscopically visible ripples are not formed by the bunching of steps. Instead they are caused by "kink bunching" in combination with strong correlations in the fluctuations of neighbour- ing steps. That strong correlations in the fluctuations A ~ B (b) of neighbouring steps lead to a rippled structure is demonstrated in the schematic drawings in Fig. 3a Fig. 3. Schematic top view (a) and cross section (b) along the line AB of a surface where ripples are formed because of the strong and Fig. 3b. Straight SA segments are formed along correlations in the fluctuations of neighbouring steps. Straight [110]. Kink bunches are shown as straight lines along segments along R10] indicate kinkbunches with many kinks and [110] although they need not necessarily be straight. not individual kinks.
  4. 4. 644 J. van Wingerden et aL / Surface Science 352-354 (1996) 641-645 Neighbouring steps exhibit similar bunches shifted unstable over the same distance along the step edge. The magnitude of this shift determines the ripple direc- iL~[11 o] (a) tion. In the next section we discuss the onset of the kinkbunching process in more detail. stable I.._ L-. = N120 4. Kink bunching ~1 O0 ¢~ 80 • ~ 60 -u (b) In thermodynamic equilibrium kinks are more or -~ 40 less uniformly distributed along the step edges. The rippled surface will return to this situation if growth 0 2 4 6 8 10 12 x 1000 SA Layers is stopped, while the sample remains at the growth temperature [1]. In this section we propose a model [~t o] that explains how during growth fluctuations in the kink distribution increase in such a way that devia- ~100~) Growth Uni~ Lengths~ 1o] (c) tions on large length scales become dominant. Here, we define a kink as the end of a single dimer row at Fig. 4. Removal of a growth unit at a kinkbuneh with 3 kinks from an unstable to a stable configuration (a). The increase of the an S A step edge. standard deviation of the kink distribution during the simulated The model is based on two assumptions. First of evolution of a single isolated step edge (b) with a typical example all the discreteness of the growth process causes shot of a step edge profile after growth of 1000 SA layers (c). The noise fluctuations in the number of growth units straight lines indicate the neighbouring steps. attached to the kink sites. Therefore, the statistical deviations of the kink sites from an equidistant dis- tribution increase continuously during growth. How- will stick in the same kinkbunch to the first kink ever, these deviations are uniformly distributed over which does not pass another one by adding the all length scales. growth unit as shown in Fig. 4a. Using values corre- The second assumption is that thermal equilib- sponding to the sample studied experimentally (see rium is still maintained on short length scales. A Section 3) an average kink distance of 2.7 growth growth unit will not stick at a kink site if the unit lengths is used and an average number of 197 resulting local geometry is energetically un- growth units have to stick to each kink site for every favourable; i.e. if the growth unit has only one S A layer. neighbouring growth unit in the (001) plane as de- Fig. 4b shows the increase: of the standard devia- picted in Fig. 4a. tion of the kink distribution as growth proceeds. A A Monte Carlo simulation of the evolution of the typical step profile after growth of about 1000 S A kink distribution for a single step edge has been layers is shown in Fig. 4c. Straight lines at both sides performed. As the fast diffusion direction on Si(001) of the step edge indicate the distance to the neigh- is along the dimer rows, growth units are assumed to bouring steps. This simulated step edge profile shows arrive exclusively at the S A segments (the step seg- the formation of straight step edge segments in be- ments along the [110] direction in Fig. 4a). The tween the kink bunches, which is consistent with the diffusion process itself has not been incorporated in experimental observations. the simulation. Instead the positions at which the growth units arrive at the [110] step edge segments are generated randomly using a uniform distribution. 5. Discussion Each growth unit will stick to the closest of two neighbouring kink sites. However, the growth unit is Our model describes the behaviour of a single removed if its addition to the kink site causes that isolated step. The step edge fluctuations remain an kink to pass the neighbouring kink. In that case it order of magnitude smaller than those observed ex-
  5. 5. J. van Wingerden et aL / Surface Science 352-354 (1996) 641-645 645 perimentally. However, before growth of 1000 S A determine the relevance of the diffusion effect is layers is completed, the fluctuations have become very difficult. This illustrates once more the need for larger than the terrace width so that interactions a better knowledge of the basic microscopic pro- between neighbouring steps can no longer be ne- cesses during growth. glected. Step-step interactions will be governed by We conclude that microscopic evidence has been the maintenance of local thermodynamic equilibrium presented which confirms that ripple formation dur- in much the same way as kink-kink interactions. ing MBE is caused by the formation of long straight These step-step interactions also cause the corre- step edge segments along [110]. Furthermore, we lated bunching of kinks, which yields the macro- have presented a model to explain the onset of the scopic ripple structure. ripple formation. This model shows the importance Bales and Zangwill [6] have used a continuum of the fluctuations caused by the inherent discrete- model to show that for certain growth conditions ness of the growth process. More investigations are surface diffusion can lead to step edge instabilities. needed to understand the relation between the ripple During step flow growth on Si(001) S B steps con- orientation and the step edge orientation. sume most of the atoms of the upper terrace to follow the S A steps, which therefore grow mainly by incorporating atoms from the lower terrace. This does yield the unstable situation described by Bales References and Zangwill as growth from atoms of the lower terrace is unstable because of the larger attachment [1] A.J. Pidduck, D.J. Robbins, I.M. Young and G. Patel, Thin probability at the convex than at the concave step Solid Films 183 (1989) 255. [2] J. van Wingerden, Y.A. Wiechers, P.M.L.O. Scholte and F. edge parts. Although the slow diffusion perpendicu- Tuinstra, Surf. Sci. 331-333 (1995) 473. lar to the dimer rows strongly reduces the effect, it [3] D.J. Chadi, Phys. Rev. Lett. 59 (1987) 1691. could still lead to instability. It should be noted that [4] G. Brocks, P.J. Kelly and R. Car, Phys. Rev. Lett. 66 (1991) the local thermodynamic equilibrium incorporated in 1729. our model yields the highest growth rate at the [5] D. Dijkkamp, E.J. van Loenen and H.B. Elswijk, Proc. 3rd NEC Syrup. on Fundamental Approach to New Material concave parts of the step edges, which is the oppo- Phases, Vol. 17, Springer Ser. Mater. Sci. (Springer, Berlin, site of the diffusion effect. As already noted by Bales 1992) p. 85. and Zangwill, numerical evaluation of their model to [6] G.S. Bales and A. Zangwill, Phys. Rev. B 41 (1990) 5500.