- Email: [email protected]
The transition from ripples to islands in strained heteroepitaxial growth under low driving forces
j. . . . . . . .
ELSEVIER
CRYSTAL GROWTH
Journal of Crystal Growtla 183 (19981 305 310
The transition from ripples to islands in strained heteroepitaxial growth under low driving forces W . D o r s c h a'*, B. S t e i n e r b'l, M . A l b r e c h t a, H . P . S t r u n k a, H . W a w r a b, G . W a g n e r b alnstitutl~ir Werkstq[J~dssenschq//en VII, Lehrstuhl Mikrocharakterisierung, Unil'ersitiit Erlangen-Niirnberg, Cauerstr. 6, D-91058 Erlangen, Germany b lnstitut ~ r Kristallziichtung, Rudower Chaussee 6, 12489 Berlin, Germany
Received 6 June 1997: accepted 27 June 1997
Abstract
We investigate the morphological evolution during the growth of strained GexSil ~ layers from In solution (5 ~< x ~< 15%). Surface ripples develop due to elastic stress relaxation. These ripples self-organize in a way that a defined wavelength and a two-dimensional pattern aligned along (1 0 0) directions develops. During further growth, the ripples transform into pseudomorphic islands and island growth proceeds in vertical direction at constant island width. The ripple wavelength and the island size are controlled by the germanium content and verify energetical predictions. Further, the theoretical expectation is corroborated that island development occurs even at low misfits when deposition is controlled by energetics. 'C 1998 Elsevier Science B.V. All rights reserved.
1. I n t r o d u c t i o n
Planar surfaces of strained layers are unstable against surface undulations. The driving force for this instability results from the reduction of the Gibbs free energy as essentially given by the sum of surface energy and elastic strain energy. Whereas undulations increase the surface energy (extreme anisotropies excluded) the undulations redistribute
*Corresponding author. Fax: +49 9131 85 8602: e-mail: [email protected]. 1Present address: SPECS, Voltastr. 5, 13355 Berlin, Germany.
the strain energy such as to reduce it and overcompensate the additional surface energy. Experimental results point to two different morphologies essentially: (i) rippling of the surface of continuous layers [1 3] and (ii) islands [4 7] that can reside or not, depending on the initial wetting conditions on a pseudomorphic layer. Ripples were generally observed on layers with a comparably low misfit, and thus associated with this misfit regime. Islands were observed on comparably high misfit surfaces, and thus associated with this high misfit regime. However, theoretical work [8] indicates that a m a x i m u m strain energy relaxation is reached in all misfit regimes, when an islanded structure develops (at least beyond a corresponding critical thickness). This ultimate island state should be reached
0022-0248,,"98,/$19.00 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 0 2 4 8 ( 9 7 ) 0 0 4 3 0 - 2
306
W. Dorsch el al. /Journal c?f Cr),stal Growth 183 (1998) 305 310
once the growth follows essentially energetics, i.e. is not kinetically limited. In this paper we study the growth at low misfits f (0.2 ~
2. Experimental procedure We deposit the epitaxial GexSil x layers in a horizontal solution growth system. The epitaxy apparatus essentially consists of a graphite slider boat inside a quarz tube which is flowed through palladium-purified hydrogen. The saturation of the solutes in the solvent, in our case Si and Ge in ultra-pure In, proceeds in two steps: first the appropriate amount of germanium is dissolved and second the required amount of silicon for the intended composition of the GexSil _x layer is added (in our experiments x = 0.05, 0.10, 0.12 and 0.15 nominally). The substrate is cleaned by a RCA treatment and introduced into the growth chamber. After in situ oxide desorption and several hours of homogenization of the solution at the deposition temperature, in our case 930~C, the growth starts by pushing the substrate under the solution. The solution is kept in supersaturation by a constant cooling rate between 0.2 and 0.0°C min- 1 (for the limiting case of 0" see Ref. [9]), growth times range between 0.5 s and 15 min. The layer deposition ends by withdrawing the solution from the substrate. An intended slow withdrawal results in a thickness gradient along the layer with the thinnest part where the solution is removed first. Thus, we can compare the stages at different growth times on one sample for otherwise identical growth conditions. We control the nominal layer composition by energy dispersive X-ray spectroscopy of comparably thick layers ( ~ 5 gm thickness). We investigate the surface topologies of the a s 9 r o w n layers ex situ in a scanning force microscope (SFM, Park Scientific Instruments) under ambient
conditions. In addition, we use transmission electron microscopy (TEM, Philips CM 20 operated at 200 kV) of cross-sectional and plane-view specimens to evaluate layer thicknesses and the degree of plastic relaxation.
3. Results Fig. la-Fig, ld depicts the evolution of the surface topology during the growth of Ge0.osSi0.95 layers. The evolution starts with the formation of randomly distributed undulations with small amplitude, Fig. I a. These undulations become higher on further growth and align along ~1 0 0) directions, Fig. lb. It is interesting to note that at this stage areas with ripples exist that are comparatively high and that are always accompanied by troughs that are comparatively deep. During further growth, the average ripple amplitude continues to increase and eventually the highest surface ripples are accompanied by troughs that reach to the substrate surface, Fig. lc. The most advanced stage of this process constitutes an array of square-based islands, Fig. lc. Further, layer growth consists in the increase of the height of the islands while the island basis width stays constant. As an ultimate stage, the islands develop pronounced [1 1 11-, [ 1 1 0}- and { 1 0 0}-facettes and are regularly aligned, Fig. ld. Up to this stage of layer growth, no misfit dislocations have formed either in the surface ripples or in the islands, see the transmission electron micrograph in Fig. 2. In consequence of this island formation mechanism, the distance of the islands (measured in ~1 0 0) direction) is controlled by the wavelength of the initial surface ripples. The growth topologies of layers with 10 to 15% Ge develop analogously. We use the observations of the layer with 10% Ge content, see Fig. 3a and Fig. 3b, to exemplify the dependencies of the growth topologies on the Ge content. As qualitatively recognizable from a comparison of Fig. 3a Fig. la the wavelength of the ripples decreases with increasing Ge content. Also the alignment of the ripples is more accurate at higher Ge content. The amplitude of the surface ripples, just before they turn into islands, and the maximum
307
W Dorsch et al./Journal qfO3,stal Growth 183 (1998) 305 310
<110> ~- <1-10>
2Jam
<100>
<
<010>
Fig. 2. Facetted island in a Geo.osSio.gs layer. The growth is pseudomorphic until this stage of layer and island growth: no misfit dislocations are present. TEM plane view micrograph
island width shrink with higher Ge content. The measured values of this geometries are summarized in Table 1. The island width w and £ scale with the Ge content, i.e. the m i s f i t f o f the layer, with Z oc 1If 2 as theoretically predicted [10]. <100>
<
4. Discussion
<010>
<100>
<010>
<110>
<1-10> 25 ~m
In the following, we will discuss the observed development of the growth topologies of the GexSil x layers within the models for strained layer growth. We will focus on the energetics, since in our experiments we can assume the layers to practically exhibit, at any stage of growth, the lowest energy configuration. Modifications due to kinetics are negligible. This situation is a consequence of the liquid-phase epitaxy technique, where the diffusion coefficient is about 4 orders of magnitude higher [ l l I than in techniques with a "free" surface (such as molecular beam epitaxy). Further, the supersaturation used during growth is rather low (with an a n y w a y c o m p a r a b l y high growth velocity due to the easy diffusion) which
4 Fig. 1. Surface development of Geo.osSi0.~5 layers. (a) Surface ripples, partially alined in (l 00) directions. Scanning force micrograph (SFM) 40 x 40 I.tm 2, color scale (CS) 270 ,~,.(b) Aligned surface ripples with different amplitudes. SFM 40 x 40 gm2, CS 2500 A. (c) Transition between undulated layer growth and island growth. SFM 40 x 40 Jam 2, CS 1.2 pare. (d) Well-facetted islands aligned in ( 1 0 0) directions. Nomarski differential interference contrast image.
308
I'K Dorsch et al. /Journal o#Crystal Growth 183 (1998) 305 310
<100>
<01 O>
Fig. 3. Surface development of Ge0.1oSiom0layers. (a) Surface ripples with a wavelength, obviously smaller than in the Ge0.0sSi0.gs layer. The surface ripples are well aligned in (1 0 0> directions. SFM 40 x 40 pm e, CS 900 A. (b) Transition stage between undulated layer and island growth. SFM 20 x 20 I_tm2. c s 3000 ~,.
essentially avoids kinetic effects. Thus, growth proceeds in our case according to the energetic conditions at the growth surface. These conditions, however, vary locally once the first surface ripples start to redistribute the strain [12] and therefore, to modify locally the surface potential and thus the growth driving force. Regions of low strain, i.e. essentially the crests of the surface undulations, have a c o m p a r a b l y high growth rate, regions with large strain, i.e. the troughs and the b o t t o m parts of islands, exhibit low growth rate. O u r observations can be analyzed with this notion. We first neglect the binary nature of the growing layer and assume, as observed, a dislocation-free strained state. The first ripples arise at r a n d o m from fluctuations in the growth of the p s e u d o m o r p h i c layer and grow rapidly in number. They also, on further growth increase in amplitude (the average thickness of the epitaxial layer grows as well) which is a selfsupporting mechanism with initially exponential time dependence [10, 13]. At a certain instance, when the n u m b e r density of the ripples is large enough, their strain fields overlap. In consequence, where two adjacent ripples are close to each other a c o m p a r a b l y high strain exists between them in the trough and growth is decelerated as c o m p a r e d to wider troughs. By this mechanism a regular arrangement of the ripples develops [14] with a wavelength ). as given by the linear stability analysis [10] (see sketch in Fig. 4). This state is approximately reached in Fig. lb and Fig. 3a. The transition from the rippled surface to islands (Fig. 5) can also be attributed to the strain in the troughs. This strain increases with the increase in amplitude of the ripple crests [10] (at constant
Table 1 Geometrical values of the growth topologies in layers with nominal Ge contents of 5 15%: wavelength 2 of the surface ripples, their amplitude A (peak to valley) before they turn into islands and the basis width w of the islands and their standard deviations Ge content
5%
10%
12%
15%
2 (~m) A (nm) w (Iam)
6.5 _+0.4 83.2 4- 37 5.5 + 0.4
2.1 -,- 0.17 37.5 -+ 19 1.7 + 0.1
1.58 _+0.1 19.6 + 5 1.38 _+0.05
1.08 _4_0.08 9.6 _+2 0.8l _+0.05
309
~: Dorsch et al. /Journal of Crystal Growth 183 (1998) 305 310
~ A
A ~ II I substrate
Fig. 4. Schematicrepresentation of the development of an equilibrium undulation wavelength ,;_ The overlapping strain fields between two islands that nucleated too close to another is comparatively high and causes comparatively low growth near this trough. The centers of the islands shift away from each other until equilibrium distances 2 are achieved.
wavelength 2). F r o m a certain value on, it compensates and then overcompensates the growth driving force given by the supersaturation. Thus, dissolution sets in, as observed (Fig. lc and Fig. 3b), which again is a self-supporting process because of the concomitant rapid increase in amplitude. This process is very dominant in our growth experiment because of the easy diffusion in the solution. It may be impeded in the cases of growth with a free surface (with or without surfactant). Due to the nature of this dissolution process, the troughs will deepen at least to the substrate surface, if not a little deeper into the substrate (within the substrate the strain due to misfitting islands decreases rapidly and therfore, also the driving force for dissolution [12]). The precise analysis of the final position of the dissolution front needs chemical characterization in the electron microscope and is under way. The most noteworthy aspect of this transformation of the ripple structure into an island array is that the characteristic distances and the regular arrangement of the ripple structure are inherited by the islands. Since the ripple wavelength of a given epitaxial layer is determined solely by the epitaxial strain, the island size and distance can be controlled by the appropriate choice of the misfit. This possibility holds also for layers that are partially relaxed by misfit dislocations [13, 15] (provided plastic relaxation can be controlled to the required degree). In any case this mechanism provides a number of possibilities to tailor regular island arrays. We still have to consider the complication that arises from the growth of binary (and multinary) epitaxial
Fig. 5. Schematic representation of the transition flcom undulated layer to island growth. After the development of an undulated layer with characteristicwavelength(I), the increasing amplitude results in a decrease of the growth velocity in the troughs (ll). The growth velocity in the troughs becomes zero and even negative (llI) resulting in the transition to island growth.
layers. In general, the surface potential is different for the different species in the solution (say Si and Ge) and so is the dependence on the local strain. Therefore, we cannot expect a homogeneous composition in the ripples and islands. Especially, in systems with broad range of mixing such as GexSil-x local deviations from the composition as given by the equilibrium phase diagram (inclusive of the influence of the pseudomorphic strain) should be noticeable. Such experiments require an access to the chemical composition on a scale much smaller than the characteristic size of the investigated layers. We exploit currently, techniques such as Raman scattering, X-ray diffraction and with high local resolution composition-sensitive highresolution T E M [16] and convergent electron beam diffraction in combination with finite element analysis of the strained state.
5. Summary We analyze the temporal development of the epitaxial surface topology of growing SiGe strained layers on Si substrates. The analysis shows that pseudomorphic islands develop from the initial ripple structure. This observation is consistent with theoretical predictions according to which islands relax strain energy more efficiently than undulations (for the same effective layer thickness). Therefore, undulations should turn into islands if diffusion is possible: (i) during growth (even for lower germanium contents as described if the driving force for growth is further reduced) or (ii) by
310
w Dorsch et al. /Journal of C~stal Growth 183 (1998) 305 310
p o s t - g r o w t h a n n e a l i n g as r e c e n t l y f o u n d [-17]. T h i s t r a n s i t i o n leads to island a r r a y s t h a t i n h e r i t the c h a r a c t e r i s t i c w a v e l e n g t h a n d the r e g u l a r s t r u c t u r e of the ripples. T h i s m e c h a n i s m c a n be used to t a i l o r r e g u l a r island a r r a y s w i t h d e s i r e d island d i s t a n c e s by c h o o s i n g an a p p r o p r i a t e misfit.
Acknowledgements T h i s w o r k was p a r t i a l l y f u n d e d by the V o l k s w a g e n s t i f t u n g u n d e r C o n t r a c t N o . 1/71 181.
References I l l A.G. Cullis, D.J. Robbins, A.J. Pidduck, P.W. Smith, Mater. Res. Soc. Syrup. Proc., vol. 280, 1993, p. 383. [2] A.G. Cullis, Mater. Res. Soc. Syrup. Proc., vol. 399. 1996, p. 303. [3] M. Albrecht, S. Christiansen, J. Michler, W. Dorsch, H.P. Strunk, P.O. Hansson, E. Bauser, Appl. Phys. Len. 67 (1995) 1232.
[4] Y.-W. Mo, D.E. Savage, B.S. Swartzentruber, M.G. Lagally, Phys. Rev. Lett. 65 (1990) 1020. [5] D.J. Eaglesham, M. Cerullo, Phys. Rev. Lett. 64 (1990)
1943. [6] F.K. LeGoues, M.C. Reuter, J. Tersoff, M. Hammar, R.M. Tromp, Phys. Rev. Lett. 73 (1994) 300. [7] W. Dorsch, S. Christiansen, M. Albrecht, P.O. Hansson, E. Bauser, H.P. Strunk, Surf. Sci. 331-333 (1994) 896. [8] H. Gao, J. Mech. Phys. Solids 42 (19941 741. [9] P.O. Hansson, M. Albrecht, W. Dorsch, H.P. Strunk, E. Bauser, Phys. Rev. Lett. 73 (1994) 444. [10] D.J. Srolovitz, Acta Metallogr. 37 (1988) 621. [11] P. Breuer, G. Miiller-Vogt, 1994, private communication. [12] S. Christiansen, M. Albrecht, H. Michler, H.P. Strunk, Phys. Status Solidi (a) 156 (1996) 129. [13] H.P. Strunk, S. Christiansen, M. Albrecht, Mater. Res. Soc. Syrup. Proc., vol. 399, 1995, p. 313. [14] The alignment of the ripples follows the same principle but is not forced by the ripple distance but the anisotropy of the elastical constants of the layer material. [15] M. Albrecht. S. Christiansen, J. Michler, H.P. Strunk, P.O. Hansson, E. Bauser, J. Crystal Growth 167 (1996) 24. [16] D. Stenkamp, H.P. Strunk, Appl. Phys. A 62 (1996) 369. [17] C.S. Ozkan, W.D. Nix, H. Gao, Mater. Res. Soc. Syrup. Proc., vol. 399, 1996, p. 407.
ELSEVIER
CRYSTAL GROWTH
Journal of Crystal Growtla 183 (19981 305 310
The transition from ripples to islands in strained heteroepitaxial growth under low driving forces W . D o r s c h a'*, B. S t e i n e r b'l, M . A l b r e c h t a, H . P . S t r u n k a, H . W a w r a b, G . W a g n e r b alnstitutl~ir Werkstq[J~dssenschq//en VII, Lehrstuhl Mikrocharakterisierung, Unil'ersitiit Erlangen-Niirnberg, Cauerstr. 6, D-91058 Erlangen, Germany b lnstitut ~ r Kristallziichtung, Rudower Chaussee 6, 12489 Berlin, Germany
Received 6 June 1997: accepted 27 June 1997
Abstract
We investigate the morphological evolution during the growth of strained GexSil ~ layers from In solution (5 ~< x ~< 15%). Surface ripples develop due to elastic stress relaxation. These ripples self-organize in a way that a defined wavelength and a two-dimensional pattern aligned along (1 0 0) directions develops. During further growth, the ripples transform into pseudomorphic islands and island growth proceeds in vertical direction at constant island width. The ripple wavelength and the island size are controlled by the germanium content and verify energetical predictions. Further, the theoretical expectation is corroborated that island development occurs even at low misfits when deposition is controlled by energetics. 'C 1998 Elsevier Science B.V. All rights reserved.
1. I n t r o d u c t i o n
Planar surfaces of strained layers are unstable against surface undulations. The driving force for this instability results from the reduction of the Gibbs free energy as essentially given by the sum of surface energy and elastic strain energy. Whereas undulations increase the surface energy (extreme anisotropies excluded) the undulations redistribute
*Corresponding author. Fax: +49 9131 85 8602: e-mail: [email protected]. 1Present address: SPECS, Voltastr. 5, 13355 Berlin, Germany.
the strain energy such as to reduce it and overcompensate the additional surface energy. Experimental results point to two different morphologies essentially: (i) rippling of the surface of continuous layers [1 3] and (ii) islands [4 7] that can reside or not, depending on the initial wetting conditions on a pseudomorphic layer. Ripples were generally observed on layers with a comparably low misfit, and thus associated with this misfit regime. Islands were observed on comparably high misfit surfaces, and thus associated with this high misfit regime. However, theoretical work [8] indicates that a m a x i m u m strain energy relaxation is reached in all misfit regimes, when an islanded structure develops (at least beyond a corresponding critical thickness). This ultimate island state should be reached
0022-0248,,"98,/$19.00 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 0 2 4 8 ( 9 7 ) 0 0 4 3 0 - 2
306
W. Dorsch el al. /Journal c?f Cr),stal Growth 183 (1998) 305 310
once the growth follows essentially energetics, i.e. is not kinetically limited. In this paper we study the growth at low misfits f (0.2 ~
2. Experimental procedure We deposit the epitaxial GexSil x layers in a horizontal solution growth system. The epitaxy apparatus essentially consists of a graphite slider boat inside a quarz tube which is flowed through palladium-purified hydrogen. The saturation of the solutes in the solvent, in our case Si and Ge in ultra-pure In, proceeds in two steps: first the appropriate amount of germanium is dissolved and second the required amount of silicon for the intended composition of the GexSil _x layer is added (in our experiments x = 0.05, 0.10, 0.12 and 0.15 nominally). The substrate is cleaned by a RCA treatment and introduced into the growth chamber. After in situ oxide desorption and several hours of homogenization of the solution at the deposition temperature, in our case 930~C, the growth starts by pushing the substrate under the solution. The solution is kept in supersaturation by a constant cooling rate between 0.2 and 0.0°C min- 1 (for the limiting case of 0" see Ref. [9]), growth times range between 0.5 s and 15 min. The layer deposition ends by withdrawing the solution from the substrate. An intended slow withdrawal results in a thickness gradient along the layer with the thinnest part where the solution is removed first. Thus, we can compare the stages at different growth times on one sample for otherwise identical growth conditions. We control the nominal layer composition by energy dispersive X-ray spectroscopy of comparably thick layers ( ~ 5 gm thickness). We investigate the surface topologies of the a s 9 r o w n layers ex situ in a scanning force microscope (SFM, Park Scientific Instruments) under ambient
conditions. In addition, we use transmission electron microscopy (TEM, Philips CM 20 operated at 200 kV) of cross-sectional and plane-view specimens to evaluate layer thicknesses and the degree of plastic relaxation.
3. Results Fig. la-Fig, ld depicts the evolution of the surface topology during the growth of Ge0.osSi0.95 layers. The evolution starts with the formation of randomly distributed undulations with small amplitude, Fig. I a. These undulations become higher on further growth and align along ~1 0 0) directions, Fig. lb. It is interesting to note that at this stage areas with ripples exist that are comparatively high and that are always accompanied by troughs that are comparatively deep. During further growth, the average ripple amplitude continues to increase and eventually the highest surface ripples are accompanied by troughs that reach to the substrate surface, Fig. lc. The most advanced stage of this process constitutes an array of square-based islands, Fig. lc. Further, layer growth consists in the increase of the height of the islands while the island basis width stays constant. As an ultimate stage, the islands develop pronounced [1 1 11-, [ 1 1 0}- and { 1 0 0}-facettes and are regularly aligned, Fig. ld. Up to this stage of layer growth, no misfit dislocations have formed either in the surface ripples or in the islands, see the transmission electron micrograph in Fig. 2. In consequence of this island formation mechanism, the distance of the islands (measured in ~1 0 0) direction) is controlled by the wavelength of the initial surface ripples. The growth topologies of layers with 10 to 15% Ge develop analogously. We use the observations of the layer with 10% Ge content, see Fig. 3a and Fig. 3b, to exemplify the dependencies of the growth topologies on the Ge content. As qualitatively recognizable from a comparison of Fig. 3a Fig. la the wavelength of the ripples decreases with increasing Ge content. Also the alignment of the ripples is more accurate at higher Ge content. The amplitude of the surface ripples, just before they turn into islands, and the maximum
307
W Dorsch et al./Journal qfO3,stal Growth 183 (1998) 305 310
<110> ~- <1-10>
2Jam
<100>
<
<010>
Fig. 2. Facetted island in a Geo.osSio.gs layer. The growth is pseudomorphic until this stage of layer and island growth: no misfit dislocations are present. TEM plane view micrograph
island width shrink with higher Ge content. The measured values of this geometries are summarized in Table 1. The island width w and £ scale with the Ge content, i.e. the m i s f i t f o f the layer, with Z oc 1If 2 as theoretically predicted [10]. <100>
<
4. Discussion
<010>
<100>
<010>
<110>
<1-10> 25 ~m
In the following, we will discuss the observed development of the growth topologies of the GexSil x layers within the models for strained layer growth. We will focus on the energetics, since in our experiments we can assume the layers to practically exhibit, at any stage of growth, the lowest energy configuration. Modifications due to kinetics are negligible. This situation is a consequence of the liquid-phase epitaxy technique, where the diffusion coefficient is about 4 orders of magnitude higher [ l l I than in techniques with a "free" surface (such as molecular beam epitaxy). Further, the supersaturation used during growth is rather low (with an a n y w a y c o m p a r a b l y high growth velocity due to the easy diffusion) which
4 Fig. 1. Surface development of Geo.osSi0.~5 layers. (a) Surface ripples, partially alined in (l 00) directions. Scanning force micrograph (SFM) 40 x 40 I.tm 2, color scale (CS) 270 ,~,.(b) Aligned surface ripples with different amplitudes. SFM 40 x 40 gm2, CS 2500 A. (c) Transition between undulated layer growth and island growth. SFM 40 x 40 Jam 2, CS 1.2 pare. (d) Well-facetted islands aligned in ( 1 0 0) directions. Nomarski differential interference contrast image.
308
I'K Dorsch et al. /Journal o#Crystal Growth 183 (1998) 305 310
<100>
<01 O>
Fig. 3. Surface development of Ge0.1oSiom0layers. (a) Surface ripples with a wavelength, obviously smaller than in the Ge0.0sSi0.gs layer. The surface ripples are well aligned in (1 0 0> directions. SFM 40 x 40 pm e, CS 900 A. (b) Transition stage between undulated layer and island growth. SFM 20 x 20 I_tm2. c s 3000 ~,.
essentially avoids kinetic effects. Thus, growth proceeds in our case according to the energetic conditions at the growth surface. These conditions, however, vary locally once the first surface ripples start to redistribute the strain [12] and therefore, to modify locally the surface potential and thus the growth driving force. Regions of low strain, i.e. essentially the crests of the surface undulations, have a c o m p a r a b l y high growth rate, regions with large strain, i.e. the troughs and the b o t t o m parts of islands, exhibit low growth rate. O u r observations can be analyzed with this notion. We first neglect the binary nature of the growing layer and assume, as observed, a dislocation-free strained state. The first ripples arise at r a n d o m from fluctuations in the growth of the p s e u d o m o r p h i c layer and grow rapidly in number. They also, on further growth increase in amplitude (the average thickness of the epitaxial layer grows as well) which is a selfsupporting mechanism with initially exponential time dependence [10, 13]. At a certain instance, when the n u m b e r density of the ripples is large enough, their strain fields overlap. In consequence, where two adjacent ripples are close to each other a c o m p a r a b l y high strain exists between them in the trough and growth is decelerated as c o m p a r e d to wider troughs. By this mechanism a regular arrangement of the ripples develops [14] with a wavelength ). as given by the linear stability analysis [10] (see sketch in Fig. 4). This state is approximately reached in Fig. lb and Fig. 3a. The transition from the rippled surface to islands (Fig. 5) can also be attributed to the strain in the troughs. This strain increases with the increase in amplitude of the ripple crests [10] (at constant
Table 1 Geometrical values of the growth topologies in layers with nominal Ge contents of 5 15%: wavelength 2 of the surface ripples, their amplitude A (peak to valley) before they turn into islands and the basis width w of the islands and their standard deviations Ge content
5%
10%
12%
15%
2 (~m) A (nm) w (Iam)
6.5 _+0.4 83.2 4- 37 5.5 + 0.4
2.1 -,- 0.17 37.5 -+ 19 1.7 + 0.1
1.58 _+0.1 19.6 + 5 1.38 _+0.05
1.08 _4_0.08 9.6 _+2 0.8l _+0.05
309
~: Dorsch et al. /Journal of Crystal Growth 183 (1998) 305 310
~ A
A ~ II I substrate
Fig. 4. Schematicrepresentation of the development of an equilibrium undulation wavelength ,;_ The overlapping strain fields between two islands that nucleated too close to another is comparatively high and causes comparatively low growth near this trough. The centers of the islands shift away from each other until equilibrium distances 2 are achieved.
wavelength 2). F r o m a certain value on, it compensates and then overcompensates the growth driving force given by the supersaturation. Thus, dissolution sets in, as observed (Fig. lc and Fig. 3b), which again is a self-supporting process because of the concomitant rapid increase in amplitude. This process is very dominant in our growth experiment because of the easy diffusion in the solution. It may be impeded in the cases of growth with a free surface (with or without surfactant). Due to the nature of this dissolution process, the troughs will deepen at least to the substrate surface, if not a little deeper into the substrate (within the substrate the strain due to misfitting islands decreases rapidly and therfore, also the driving force for dissolution [12]). The precise analysis of the final position of the dissolution front needs chemical characterization in the electron microscope and is under way. The most noteworthy aspect of this transformation of the ripple structure into an island array is that the characteristic distances and the regular arrangement of the ripple structure are inherited by the islands. Since the ripple wavelength of a given epitaxial layer is determined solely by the epitaxial strain, the island size and distance can be controlled by the appropriate choice of the misfit. This possibility holds also for layers that are partially relaxed by misfit dislocations [13, 15] (provided plastic relaxation can be controlled to the required degree). In any case this mechanism provides a number of possibilities to tailor regular island arrays. We still have to consider the complication that arises from the growth of binary (and multinary) epitaxial
Fig. 5. Schematic representation of the transition flcom undulated layer to island growth. After the development of an undulated layer with characteristicwavelength(I), the increasing amplitude results in a decrease of the growth velocity in the troughs (ll). The growth velocity in the troughs becomes zero and even negative (llI) resulting in the transition to island growth.
layers. In general, the surface potential is different for the different species in the solution (say Si and Ge) and so is the dependence on the local strain. Therefore, we cannot expect a homogeneous composition in the ripples and islands. Especially, in systems with broad range of mixing such as GexSil-x local deviations from the composition as given by the equilibrium phase diagram (inclusive of the influence of the pseudomorphic strain) should be noticeable. Such experiments require an access to the chemical composition on a scale much smaller than the characteristic size of the investigated layers. We exploit currently, techniques such as Raman scattering, X-ray diffraction and with high local resolution composition-sensitive highresolution T E M [16] and convergent electron beam diffraction in combination with finite element analysis of the strained state.
5. Summary We analyze the temporal development of the epitaxial surface topology of growing SiGe strained layers on Si substrates. The analysis shows that pseudomorphic islands develop from the initial ripple structure. This observation is consistent with theoretical predictions according to which islands relax strain energy more efficiently than undulations (for the same effective layer thickness). Therefore, undulations should turn into islands if diffusion is possible: (i) during growth (even for lower germanium contents as described if the driving force for growth is further reduced) or (ii) by
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p o s t - g r o w t h a n n e a l i n g as r e c e n t l y f o u n d [-17]. T h i s t r a n s i t i o n leads to island a r r a y s t h a t i n h e r i t the c h a r a c t e r i s t i c w a v e l e n g t h a n d the r e g u l a r s t r u c t u r e of the ripples. T h i s m e c h a n i s m c a n be used to t a i l o r r e g u l a r island a r r a y s w i t h d e s i r e d island d i s t a n c e s by c h o o s i n g an a p p r o p r i a t e misfit.
Acknowledgements T h i s w o r k was p a r t i a l l y f u n d e d by the V o l k s w a g e n s t i f t u n g u n d e r C o n t r a c t N o . 1/71 181.
References I l l A.G. Cullis, D.J. Robbins, A.J. Pidduck, P.W. Smith, Mater. Res. Soc. Syrup. Proc., vol. 280, 1993, p. 383. [2] A.G. Cullis, Mater. Res. Soc. Syrup. Proc., vol. 399. 1996, p. 303. [3] M. Albrecht, S. Christiansen, J. Michler, W. Dorsch, H.P. Strunk, P.O. Hansson, E. Bauser, Appl. Phys. Len. 67 (1995) 1232.
[4] Y.-W. Mo, D.E. Savage, B.S. Swartzentruber, M.G. Lagally, Phys. Rev. Lett. 65 (1990) 1020. [5] D.J. Eaglesham, M. Cerullo, Phys. Rev. Lett. 64 (1990)
1943. [6] F.K. LeGoues, M.C. Reuter, J. Tersoff, M. Hammar, R.M. Tromp, Phys. Rev. Lett. 73 (1994) 300. [7] W. Dorsch, S. Christiansen, M. Albrecht, P.O. Hansson, E. Bauser, H.P. Strunk, Surf. Sci. 331-333 (1994) 896. [8] H. Gao, J. Mech. Phys. Solids 42 (19941 741. [9] P.O. Hansson, M. Albrecht, W. Dorsch, H.P. Strunk, E. Bauser, Phys. Rev. Lett. 73 (1994) 444. [10] D.J. Srolovitz, Acta Metallogr. 37 (1988) 621. [11] P. Breuer, G. Miiller-Vogt, 1994, private communication. [12] S. Christiansen, M. Albrecht, H. Michler, H.P. Strunk, Phys. Status Solidi (a) 156 (1996) 129. [13] H.P. Strunk, S. Christiansen, M. Albrecht, Mater. Res. Soc. Syrup. Proc., vol. 399, 1995, p. 313. [14] The alignment of the ripples follows the same principle but is not forced by the ripple distance but the anisotropy of the elastical constants of the layer material. [15] M. Albrecht. S. Christiansen, J. Michler, H.P. Strunk, P.O. Hansson, E. Bauser, J. Crystal Growth 167 (1996) 24. [16] D. Stenkamp, H.P. Strunk, Appl. Phys. A 62 (1996) 369. [17] C.S. Ozkan, W.D. Nix, H. Gao, Mater. Res. Soc. Syrup. Proc., vol. 399, 1996, p. 407.