ELSEVIER Surface Science 352-354 (1996) 641-645

surface science

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. Introduct ion

Molecular beam epitaxy (MBE) is a well-known technique to grow high-quality layers with well-de- fined properties. In general, growth is performed on vicinal substrates, i.e. substrates with a regular spac- ing b e t w e e n the steps, which are caused by the misorientation of the macroscopic surface relative to the crystallographic plane. Under certain growth con- ditions a shallow ripple pattern develops during the growth of a thick layer ( ~ 1 /xm) on such a flat substrate.

Pidduck et al. [1] have determined the ripple

* Corresponding author. Fax: +31 1578 3251; e-Mail: wing@ duttfks.tn.tudelft.nl.

period and orientation as a function of the sample misorientation. As the ripples disappear upon anneal- ing at the growth temperature, their existence is determined by the growth kinetics. The effect of the high supersaturation on the minimum energy step configuration has been suggested as the origin of the ripple formation [1]. However, since ripples form if growth proceeds by step flow, the adatom density should be sufficiently low to let the adatoms stick to a step edge before they meet each other and form an immobile cluster [2]. This means that the actual adatom density on the surface cannot be large enough 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- tribute to a better understanding of the basic micro- scopic processes during growth.

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642 J. van Wingerden et a l . / Surface Science 352-354 (1996) 641-645

In this paper we will first present new experimen- tal evidence for the microscopic form of the steps on the rippled surface. Furthermore, we present a new model which shows that the inherent discreteness of growth can cause the onset of ripple formation.

2. The Si(001) surface

The atoms of the Si(001) surface top layer form 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 STM image of the Si(001) surface is shown. We use the notation of Chadi [3] for the S A and S B step edges, where the dimer rows of the upper terrace are parallel and perpendicular to the step edges, respec- tively.

Because S A step edges have the lowest energy [3], the introduction of kinks is energetically un- favourable due to the accompanying small pieces of S B step edge. Therefore, S A step edges are relatively straight with a density of thermally excited kinks which is in most cases much lower than the density of kinks enforced by the misorientation. On the other hand S B step edges are rough because of thermal excitation of kinks. If the step edge direction deter- mined by the misorientation of the macroscopic sur- face is close to the (110) direction, step edges are alternating of the S A and S B type. Under growth conditions adatoms as well as ad-dimers are mobile, and their diffusion is much faster along than perpen- dicular to the dimer rows [4,5]. Because two dimer

Fig. 1, STM image of Si(001) with S n and S B step edge seg- ments.

bonds of the lower terrace have to be broken for every other dimer attached to a kink site, stable growth units consist of two dimers. For step flow growth no islands are formed on the terraces and 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 this causes a much higher growth rate at Ss step edges so that they will catch up with the S n step edges.

3. The microscopic ripple structure

In this section we present the results of measure- ments, where atomic force microscopy, optical mi- croscopy, and X-ray crystallography have been used to characterize the microscopic structure of the rip- ples. For these experiments a 2 /xm thick layer was grown on Si(001) at 650°C with a rate of 1.4 .~/s . The vicinal angle of the sample (i.e. the angle be- tween the macroscopic surface and the crystallo- graphic surface) is determined to be 0.296 ___ 0.002 °. The angle between the average step edge direction and the [110] direction is 20.3 ___ 0.4 °. The average ripple direction has been determined from Nomarski microscope images (see Fig. 2a for a typical exam- pie). By measuring the ripple orientation and the crystallographic [110] orientation relative to the sam- ple holder, the angle between the ripple and the [110] orientation is determined to be 46 ___ 2 °. These orien- tations are drawn in Fig. 2f.

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 these directions it is clear that the steps run approxi- mately in the [1 I0] direction in those regions where

J. oan Wingerden et aL / Surface Science 352-354 (1996) 641-645 643

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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 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 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 of neighbouring steps lead to a rippled structure is demonstrated in the schematic drawings in Fig. 3a and Fig. 3b. Straight S A segments are formed along [110]. Kink bunches are shown as straight lines along [110] although they need not necessarily be straight.

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(a)

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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 correlations in the fluctuations of neighbouring steps. Straight segments along R10] indicate kinkbunches with many kinks and not individual kinks.

644 J. van Wingerden et aL / Surface Science 352-354 (1996) 641-645

Neighbouring steps exhibit similar bunches shifted over the same distance along the step edge. The magnitude of this shift determines the ripple direc- tion. In the next section we discuss the onset of the kinkbunching process in more detail.

4. Kink bunching

In thermodynamic equilibrium kinks are more or less uniformly distributed along the step edges. The rippled surface will return to this situation if growth is stopped, while the sample remains at the growth temperature [1]. In this section we propose a model that explains how during growth fluctuations in the kink distribution increase in such a way that devia- tions on large length scales become dominant. Here, we define a kink as the end of a single dimer row at an S A step edge.

The model is based on two assumptions. First of all the discreteness of the growth process causes shot noise fluctuations in the number of growth units attached to the kink sites. Therefore, the statistical deviations of the kink sites from an equidistant dis- tribution increase continuously during growth. How- ever, these deviations are uniformly distributed over all length scales.

The second assumption is that thermal equilib- rium is still maintained on short length scales. A growth unit will not stick at a kink site if the resulting local geometry is energetically un- favourable; i.e. if the growth unit has only one neighbouring growth unit in the (001) plane as de- picted in Fig. 4a.

A Monte Carlo simulation of the evolution of the kink distribution for a single step edge has been performed. As the fast diffusion direction on Si(001) is along the dimer rows, growth units are assumed to arrive exclusively at the S A segments (the step seg- ments along the [110] direction in Fig. 4a). The diffusion process itself has not been incorporated in the simulation. Instead the positions at which the growth units arrive at the [110] step edge segments are generated randomly using a uniform distribution. Each growth unit will stick to the closest of two neighbouring kink sites. However, the growth unit is removed if its addition to the kink site causes that kink to pass the neighbouring kink. In that case it

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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 standard deviation of the kink distribution during the simulated evolution of a single isolated step edge (b) with a typical example of a step edge profile after growth of 1000 S A layers (c). The straight lines indicate the neighbouring steps.

will stick in the same kinkbunch to the first kink which does not pass another one by adding the growth unit as shown in Fig. 4a. Using values corre- sponding to the sample studied experimentally (see Section 3) an average kink distance of 2.7 growth unit lengths is used and an average number of 197 growth units have to stick to each kink site for every S A layer.

Fig. 4b shows the increase: of the standard devia- tion of the kink distribution as growth proceeds. A typical step profile after growth of about 1000 S A layers is shown in Fig. 4c. Straight lines at both sides of the step edge indicate the distance to the neigh- bouring steps. This simulated step edge profile shows the formation of straight step edge segments in be- tween the kink bunches, which is consistent with the experimental observations.

5. Discussion

Our model describes the behaviour of a single isolated step. The step edge fluctuations remain an order of magnitude smaller than those observed ex-

J. van Wingerden et aL / Surface Science 352-354 (1996) 641-645 645

perimentally. However, before growth of 1000 S A layers is completed, the fluctuations have become larger than the terrace width so that interactions between neighbouring steps can no longer be ne- glected. Step-step interactions will be governed by the maintenance of local thermodynamic equilibrium in much the same way as kink-kink interactions. These step-step interactions also cause the corre- lated bunching of kinks, which yields the macro- scopic ripple structure.

Bales and Zangwill [6] have used a continuum model to show that for certain growth conditions surface diffusion can lead to step edge instabilities. During step flow growth on Si(001) S B steps con- 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 and Zangwill as growth from atoms of the lower terrace is unstable because of the larger attachment probability at the convex than at the concave step edge parts. Although the slow diffusion perpendicu- lar to the dimer rows strongly reduces the effect, it could still lead to instability. It should be noted that the local thermodynamic equilibrium incorporated in our model yields the highest growth rate at the concave parts of the step edges, which is the oppo- site of the diffusion effect. As already noted by Bales and Zangwill, numerical evaluation of their model to

determine the relevance of the diffusion effect is very difficult. This illustrates once more the need for a better knowledge of the basic microscopic pro- cesses during growth.

We conclude that microscopic evidence has been presented which confirms that ripple formation dur- ing MBE is caused by the formation of long straight step edge segments along [110]. Furthermore, we have presented a model to explain the onset of the ripple formation. This model shows the importance of the fluctuations caused by the inherent discrete- ness of the growth process. More investigations are needed to understand the relation between the ripple orientation and the step edge orientation.

References

[1] A.J. Pidduck, D.J. Robbins, I.M. Young and G. Patel, Thin Solid Films 183 (1989) 255.

[2] J. van Wingerden, Y.A. Wiechers, P.M.L.O. Scholte and F. Tuinstra, Surf. Sci. 331-333 (1995) 473.

[3] D.J. Chadi, Phys. Rev. Lett. 59 (1987) 1691. [4] G. Brocks, P.J. Kelly and R. Car, Phys. Rev. Lett. 66 (1991)

1729. [5] D. Dijkkamp, E.J. van Loenen and H.B. Elswijk, Proc. 3rd

NEC Syrup. on Fundamental Approach to New Material Phases, Vol. 17, Springer Ser. Mater. Sci. (Springer, Berlin, 1992) p. 85.

[6] G.S. Bales and A. Zangwill, Phys. Rev. B 41 (1990) 5500.