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Dimensionality and critical sizes of GeSi on Si(100)
Thin Solid Films, 216 (1992) 199 202
199
Letter
Dimensionality and critical sizes of GeSi on Si(100) P. O. Hansson, ~ * M. Albrecht, b H. P. Strunk, b E. Bauser a and J. H. Werner ~ ~Max-Planck-lnstitut fiir FestkOrpe~)rschung, Heisenbergstrafie 1, W-7000 Stuttgart 80 (German)') b Universitiit Erlangen-Niirnberg, lnstitut fiir Werkstq,(li~qssenschafien VII, CauerstrqlSe 6, W-8520 Erlangen (Germany) (Received April 14, 1992; accepted May 8, 1992)
Abstract
Pseudomorphic heteroepitaxy close to equilibrium is investigated by transmission electron microscopy for GexSi~ ,, grown on Si(100) by liquid phase epitaxy. A transition from two-dimensional to island growth (i.e. Stranski Krastanov growth) at a thickness of h~ = 1.2nm (8 monolayers), is observed, which quantitatively validates theoretical assessments of Bauer [5] and Tersoff [8], based on assumptions of equilibrium. Results suggest that the true equilibrium phase of Stranski-Krastanov growth involves pseudomorphic islands, exclusively bound by {111} side facets. The critical island thickness h~. ~ = 30 nm exceeds predictions by a factor of two, supporting arguments of a kinetic barrier in the formation of the first misfit dislocation.
Heteroepitaxial semiconductor structures are fundamental for basic research as well as for device applications. Particularly interesting is the system Ge/Si [1]. The bulk lattice constant of Ge exceeds the one of Si by 4%, giving rise to misfit dislocations at the interface when the thickness h of the epitaxial layer (i.e. Ge or Ge,-Sil_ ,- alloy crystals) on an Si substrate exceeds a certain thickness, the so called critical thickness, h c. On the other hand, for h < hc, the lattice mismatch between the epitaxial layer and the substrate can be totally accommodated by elastic strain; such a system is termed pseudomorphic. The strain then depends essentially on the misfit between substrate and epitaxially grown layer. In strained superlattices, the thickness of the various layers is a further strain-adjusting parameter [2]. Tailoring of strain can thus be used to optimize physical properties (e.g. carrier mobilities [1], band
structure [2] or band offsets [3]) by variations of the thickness h and/or the composition x of the GexSi~ _,. layers. In order to provide for defect-free layers that fully utilize these possibilities for G e , S i l . , device structures, knowledge of the interdependence of growth mode and the limits for defect-free strain accommodation is essential. In this letter we report on specifically designed growth experiments of Ge.~.Si~ .,. on (100) oriented Si, to investigate the initial and subsequent stages of heteroepitaxial growth close to thermodynamical equilibrium. We present direct experimental observations of the crystallographic configuration of two-dimensional (2D) growth followed by three-dimensional (3D) island growth ( S t r a n s k i - K r a s t a n o v growth [4]). Our experimental observations quantitatively validate earlier theoretical models of stress induced growth mode transitions, presented by Bauer [5, 6], Mar~e [7], and Tersoff [8]. Additionally, our experiments allow the detailed study of the initial introduction of the first misfit dislocation. A critical island thickness hc.i 30 nm is observed for the initially pseudomorphic 3D islands. We use liquid phase epitaxy (LPE), which takes place close to thermodynamical equilibrium by crystallization from a metallic solution, to deposit Ge~Sit ~ on Si(100) [9, 10]. This technique has already shown its potential in growing GexSi~ x layers of low defect density on Si(111) substrates [9, 10]. To obtain epitaxial layers representing initial growth stages, growth times as short as 1 s are made necessary by the use of LPE. Therefore, a solution of the solvent Bi and the solutes Ge and Si is transported on and off the substrate by gravitational forces in a computer controlled boat. The (100) oriented Si substrate is initially cleaned by an RCA-treatment [l l], followed by a (2.5%) H F dip and an in situ oxide desorption under hydrogen atmosphere. After the saturation of the Bi Ge solution with Si, Ge08sSi01s (termed as GeSi from now on) is deposited at the saturation temperature 800 °C. Thus the driving force for crystallization due to a supercooling is negligible. We denote growth under these conditions as equilibrium growth. The nominal growth rate is around 2 nm per second; Bi as solvent yields n-type material with an electron concentration around 1016 c m -2 [9].
*On leave from Lund University, Department of Solid State Physics, Professorsgatan 3B, S-221 00 Lund, Sweden.
0040-6090/92/$5.00
The sketch in Fig. 1 summarizes the topology of our samples as observed by transmission electron microscopy (TEM). Our LPE process yields a thin initial
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200
Letter
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Fig. 1. Sketch representing geometrical aspects of pseudomorphic GeSi epitaxial layer growth on (100) Si by liquid phase epitaxy. The Mands are exclusively bound by {lll}-facets as sideplanes. These ,ell-defined truncated pyramids occur in different sizes on the same tmple on top of a thin initial layer.
~i :1.2 nm GeSi (a)
Fig. 3. Bright-field TEM micrograph in plan-view (multibeam condilions along the (100) surface normal) of the same GeSi LPE layer as in Fig. 2. the d a r k m a t e r i a l c o n t r a s t o f this thin layer as c o m p a r e d to t h a t o f the Si s u b s t r a t e . E x t e n s i v e c o n t r a s t e x p e r i m e n t s s h o w t h a t n o d i s l o c a t i o n s are p r e s e n t in this layer a n d at the i n t e r f a c e , i.e. the l a y e r is p s e u d o m o r p h i c . I s l a n d s are f o r m e d o n t o p o f this h o m o g e n e o u s l y t h i n initial layer. T h e t w o islands visible in Fig. 2(b) h a v e a t h i c k n e s s h - 25 n m ; c o r r e s p o n d i n g m e a s u r e m e n t s o n o t h e r m i c r o g r a p h s s h o w t h a t at this s t a g e o f g r o w t h , the t h i c k n e s s h o f the islands r a n g e s b e t w e e n 20 a n d 35 nm. W i t h i n this r a n g e the islands e x h i b i t a c o n s t a n t a s p e c t r a t i o o f w / h v 2, w h e r e w is the b a s e w i d t h a n d h the thickness, i.e. the h e i g h t o f the islands. T h e p l a n - v i e w m i c r o g r a p h in Fig. 3 reveals t h a t t h e p y r a m i d a l islands are statistically d i s t r i b u t e d o n the s a m p l e surface; n o i n d i c a t i o n s exist f o r p r e f e r e n t i a l n u c l e a t i o n sites. T o s e a r c h for p o s s i b l e defects, we utilize w e a k - b e a m images, as in Fig. 4. All islands ( e x c e p t o n e , w h i c h will
(b) Fig. 2. Cross sectional TEM micrographs (bright-field image in (110} multibeam conditions) of a Geo.s>Sio.t~ layer grown in Stranski-Krastanov mode (1.5 s at 800 'C from a 0.2 K supercooled Bi Ge Si solution). The islands form on top of a h i = 1.2 nm thick pseudomorphic GeSi layer on the Si(100) substrate, This layer can easily be seen by dark material contrast in (a), which shows a magnified section of (b). The pyramidal islands have a constant base width w to thickness h aspect ratio w/h ~ 2.
l a y e r o f G e S i o v e r the w h o l e Si surface. O n t o p o f this l a y e r we find islands c o n s i s t i n g o f t r u n c a t e d t e t r a h e d r a l p y r a m i d s , the side faces o f w h i c h b e i n g e x c l u s i v e l y f o r m e d by { l l l } - f a c e t s , i n t e r s e c t i n g the (100) g r o w t h p l a n e a l o n g ( 1 1 0 } d i r e c t i o n s . F i g u r e s 2 ( a ) a n d 2(b) s h o w c r o s s - s e c t i o n a l T E M m i c r o g r a p h s o f a s a m p l e as o b t a i n e d a f t e r 1.5 s o f g r o w t h . T h e m i c r o g r a p h s a r e seen in p r o j e c t i o n a l o n g the (100) i n t e r f a c e . F i g u r e 2(a) d e m o n s t r a t e s a c o n t i n u o u s G e S i layer, h a v i n g a t h i c k ness h~ = 1.2 n m c o r r e s p o n d i n g to 8 m o n o l a y e r s . N o t e
Fig. 4. Area of a GeSi sample showing islands of different sizes: TEM weak-beam dark-field image in plan-view. All islands with the exception of that in the centre are free of dislocations. These islands show a broad patchy contrast at their corners due to local strain. The island at which the diffraction vector points, contains a single isolated msfit dislocation (Burger's vector b = ½ (011}) in the middle.
Let ter
be considered later) in this area are free of dislocations. This means that not only the initial layer, but also the islands grow pseudomorphically. (The pronounced broad and patchy contrast is caused by local strain at the corners of the islands.) Plan-view observations, as in Fig. 3, are ideally suited to measuring the critical island thickness he. 1. The base width w of those islands that already contain one misfit dislocation is characteristic of the critical island thickness h~.~, due to the constant aspect ratio w/h ~ 2 . From islands of the type shown in the centre of Fig. 4 we obtain an experimental value h ~ , ~ 30 nm for the critical island thickness. Contrast analyses by T E M of islands, containing one isolated misfit dislocation, imply a Burger's vector b =~t ~011 ) of these dislocations, the detailed arrangement of which is presented separately [12]. Our experiments allow us to quantify Stranski-Krastanov growth in a direct way, i.e. the transition of two-dimensional growth (of the thin initial layer) to three-dimensional growth (of the pyramidal islands). Heteroepitaxial growth modes have been discussed in terms of surface energy arguments [5-7], originally presented by Bauer [5, 6]. He suggested that the equilibrium growth mode is determined by the balance between the surface free energies of the substrate 7~, the epitaxial layer 7e and the interface ~i. Mar6e later applied this theory to misfitting layers, adding an energy term ~ that accounts mainly for the stress influence of lattice strain on the energy [7]. Two-dimensional growth ( F r a n k - v a n der Merwe growth [13]) takes place when the epitaxial layer wets the substrate, i.e. when the energy of surface plus interface and stress contribution is smaller than the surface energy of the substrate, the following must hold: 7e -? )'i + O" ~ 7~.
(1)
During pseudomorphic growth, the stress and thus increase with the number of epitaxially deposited monolayers. After a certain number of monolayers, the magnitude of the left hand terms in eqn. (1) therefore exceeds Vs, resulting in the onset of 3D growth ( V o l m e r - W e b e r growth [14]). Recent calculations by Tersoff showed that 2D growth of Ge on Si(100) is energetically favourable for a Ge coverage of up to 4 monolayers [8]. (The areal elastic energy of a 4 monolayer thick Ge0.ssSi0.~5 layer equals that of a 3 monolayer thick Ge layer.) Both quoted models of epitaxial growth are based on the assumption of thermodynamical equilibrium. Clearly, this condition is fulfilled for our LPE process. The experiments permit a direct comparison to these theories and a transition to pseudomorphic island growth after deposition of 8 monolayers is found. The results suggest the equilibrium growth mode transition from 2D to 3D growth occurs at a later
201
stage of growth than most previous results obtained by (non-equilibrium) vacuum deposition techniques suggested [7, 15 20]. The side faces of the equilibrium grown pseudomorphic islands, formed by Stranski-Krastanov growth, without exception consist of { 111 }-facets terminated by a (100)-oriented top face. We do not observe any intermediate phases between the initial 2D layer and the final {111}-faceted islands; only differences in island size occur. By the use of various vacuum deposition techniques, the formation of islands of complex facet structures, mostly consisting of {ll3}-facets, has been observed [15, 18, 19]. Scanning tunnelling microscopy studies have shown the existence of a 3D cluster phase of a different facet configuration. These clusters consist of perfect {105}-facets and coexist with larger islands [18]. Our LPE experiments, therefore, indicate that the faceting of an island by Stranski Krastanov growth depends on the conditions of deposition. The near-equilibrium conditions of growth associated with LPE obviously lead to the formation of the stable { 111 }-facets of low free energy. We speculate that the [ l l l ] - f a c e t e d islands represent the true equilibrium phase of Strans k i - K r a s t a n o v growth, probably minimizing the total free energy. The kinetics of the initial formation of these {lll}-facets and thus the transition to the 3D island phase is, however, not deducible from the present experiments. The transition of the pseudomorphic islands into the dislocated state is now discussed in terms of critical thickness. Application of the mechanical equilibrium theory according to Frank and van der Merwe [13, 21] to our system yields a critical thickness he. Mr: ~ 3 nm. However, our experimental value of critical island thickness h~. 1 ~ 30 nm is a factor of 10 higher. Mechanical equilibrium theory [ 13, 21, 22] assumes an infinitely extended epitaxial layer; an assessment that may not be applicable for our case of laterally well-separated islands. In order to consider the stress reduction caused by island formation (and thus a further increase of critical thickness he. ME) we use a theoretical analysis developed by Luryi and Suhir [23]. The most significant result here is that the expected strain reduction is a function of the aspect ratio w/h. For our case of w/h ~ 2, the strain is reduced to 55% of the value for an infinitely extended layer. Within the mechanical equilibrium approach [13, 21], this strain reduction corresponds to a theoretical critical island thickness of he, vr = 15 nm, which still is a factor of two smaller than our experimental value he. l ~ 30 nm [24] (a possible contribution to strain reduction in epitaxial islands due to an elastic strain in the substrate material adjacent to the interface as discussed in ref. 24 can be neglected in this case since no corresponding strain contrasts are observed). Strain reduction due to local pyramidal
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island formation, therefore, does not alone explain the observed discrepancy. We attribute the still remaining difference to a kinetic barrier which has to be overcome in the formation process of the first misfit dislocation. In conclusion, a specifically designed growth technique has been presented, taking place close to thermodynamical equilibrium, for detailed studies of any state in the early epitaxial growth process and thus also in the formation of the first misfit dislocation. Our electron microscopy study shows for GeSi on (100) Si, that after 8 monolayers of 2D growth the system changes to 3D island growth. These islands are bound by stable {lll}-oriented side facets and grow pseudomorphically up to a critical island thickness h~, ~ ~ 30 nm; then isolated misfit dislocations appear. Our experimental value for the h~. ~ exceeds theoretical predictions by a factor of two. This discrepancy supports arguments for a kinetic barrier in the formation process for misfit dislocations.
Acknowledgments The authors gratefully acknowledge the continuous support of H. G. Grimmeiss and H. J. Queisser. One of us, P.O.H. is supported by the Swedish National Board for Technical Development. Support by the Deutsche Forschungsgemeinschaft under contract STR 277/1 is gratefully acknowledged.
References 1 S. S. Iyer, G. L. Patton, J. M. C. Stork, B. S. Meyerson and D. L. Harame, IEEE Trans. Electron Dev., ED-36 (1989) 2043 and references therein.
2 S. Satpathy, R. M. Martin and C. G. Van de Walle, Phys. Rev. B, 38 (1988) 13237. 3 C. G. Van de Walle, Phys. Re~'. B, 39(1989) 1871 and references therein. 4 1. N. Stranski and V. L. Krastanov, Akad. Wiss. Lit. Mainz Math.-Natur. Kl. lib, 146 (1939) 797. 5 E. Bauer, Z. Krist., 110(1958) 372. 6 E. Bauer and J. H. van der Merwe, Phys. Rev. B, 33 (1986) 3657. 7 P. M. J. Mar6e, K. Nakagawa, F. M. Mulders, J. F. van der Veen and K. U Kavanagh, Su~jace Science, 191 (1987) 305. 8 J. Tersoff, Phys. Rev. B, 43 (1991) 9377. 9 P. O. Hansson, J. H. Werner, L. Tapfer, k. P. Tilly and E. Bauser, J. Appl. Phys., 68 (1990)2158. 10 M. Albrecht and H. P. Strunk, in J. H. Werner and H. P. Strunk (eds.), Polyco,stalline Semiconductors I1 Grain Boundaries, Dislocations and HeterointerJ~wes, Springer Proceedings" in Physics, Vol. 54, Springer, Heidelberg, 1991, p. 503. 11 W. Kern and D. A. Puotinen, RCA Re~., 6(1670) 187. 12 M. Albrecht, H. P. Strunk, P. O. Hansson and E. Bauser, Mat. Res. Soc. Syrup. Proc., in the press. 13 F. C. Frank and J. H. van der Merwe, Proc. Roy. Soc. (Lomhm) A. 198(1949) 216. 14 M. Volmer and A. Weber, Z. Phys. (77em., 119 (1926) 277. 15 C. Tatsuyama, T. Terasaki, H. Obata, T. T a n b o and H. Ueba. J. Crystal Growth, 115 (1991) 112. 16 S. A. Chambers and V. A. Loebs, Phys. Ret:. B, 42 (1990) 5109. 17 J.-M. Baribeau, Appl. Phys. Lett., 57 (1990) 1748. 18 Y.-W. Mo, D. E. Savage, B. S. Swartzentruber and M. G. Lagally, Phys. Ret. Lett., 65(1990) 1020. 19 Y. Koide, S. Zaima, N. Oshima and Y. Yasuda, Jap. J. Appl. Phys., 28 (1989) L690. 20 H.-J. G o s s m a n n and L. C. Feldman, Sur/2lce. Science, 155 (1985) 413. 21 J. H. van der Merwe, J. Appl. Phys. 34(1963) 123. 22 J. W. Matthews and A. E. Blakeslee, J. Co, st. Growth, 27(1974) 118. 23 S. Luryi and E. Suhir, Appl. Phys. Lett., 49 (1986) 140. 24 D. J. Eaglesham and M. Cerullo, Phys. Rev. Lett., 64 (1990) 1943.
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Dimensionality and critical sizes of GeSi on Si(100) P. O. Hansson, ~ * M. Albrecht, b H. P. Strunk, b E. Bauser a and J. H. Werner ~ ~Max-Planck-lnstitut fiir FestkOrpe~)rschung, Heisenbergstrafie 1, W-7000 Stuttgart 80 (German)') b Universitiit Erlangen-Niirnberg, lnstitut fiir Werkstq,(li~qssenschafien VII, CauerstrqlSe 6, W-8520 Erlangen (Germany) (Received April 14, 1992; accepted May 8, 1992)
Abstract
Pseudomorphic heteroepitaxy close to equilibrium is investigated by transmission electron microscopy for GexSi~ ,, grown on Si(100) by liquid phase epitaxy. A transition from two-dimensional to island growth (i.e. Stranski Krastanov growth) at a thickness of h~ = 1.2nm (8 monolayers), is observed, which quantitatively validates theoretical assessments of Bauer [5] and Tersoff [8], based on assumptions of equilibrium. Results suggest that the true equilibrium phase of Stranski-Krastanov growth involves pseudomorphic islands, exclusively bound by {111} side facets. The critical island thickness h~. ~ = 30 nm exceeds predictions by a factor of two, supporting arguments of a kinetic barrier in the formation of the first misfit dislocation.
Heteroepitaxial semiconductor structures are fundamental for basic research as well as for device applications. Particularly interesting is the system Ge/Si [1]. The bulk lattice constant of Ge exceeds the one of Si by 4%, giving rise to misfit dislocations at the interface when the thickness h of the epitaxial layer (i.e. Ge or Ge,-Sil_ ,- alloy crystals) on an Si substrate exceeds a certain thickness, the so called critical thickness, h c. On the other hand, for h < hc, the lattice mismatch between the epitaxial layer and the substrate can be totally accommodated by elastic strain; such a system is termed pseudomorphic. The strain then depends essentially on the misfit between substrate and epitaxially grown layer. In strained superlattices, the thickness of the various layers is a further strain-adjusting parameter [2]. Tailoring of strain can thus be used to optimize physical properties (e.g. carrier mobilities [1], band
structure [2] or band offsets [3]) by variations of the thickness h and/or the composition x of the GexSi~ _,. layers. In order to provide for defect-free layers that fully utilize these possibilities for G e , S i l . , device structures, knowledge of the interdependence of growth mode and the limits for defect-free strain accommodation is essential. In this letter we report on specifically designed growth experiments of Ge.~.Si~ .,. on (100) oriented Si, to investigate the initial and subsequent stages of heteroepitaxial growth close to thermodynamical equilibrium. We present direct experimental observations of the crystallographic configuration of two-dimensional (2D) growth followed by three-dimensional (3D) island growth ( S t r a n s k i - K r a s t a n o v growth [4]). Our experimental observations quantitatively validate earlier theoretical models of stress induced growth mode transitions, presented by Bauer [5, 6], Mar~e [7], and Tersoff [8]. Additionally, our experiments allow the detailed study of the initial introduction of the first misfit dislocation. A critical island thickness hc.i 30 nm is observed for the initially pseudomorphic 3D islands. We use liquid phase epitaxy (LPE), which takes place close to thermodynamical equilibrium by crystallization from a metallic solution, to deposit Ge~Sit ~ on Si(100) [9, 10]. This technique has already shown its potential in growing GexSi~ x layers of low defect density on Si(111) substrates [9, 10]. To obtain epitaxial layers representing initial growth stages, growth times as short as 1 s are made necessary by the use of LPE. Therefore, a solution of the solvent Bi and the solutes Ge and Si is transported on and off the substrate by gravitational forces in a computer controlled boat. The (100) oriented Si substrate is initially cleaned by an RCA-treatment [l l], followed by a (2.5%) H F dip and an in situ oxide desorption under hydrogen atmosphere. After the saturation of the Bi Ge solution with Si, Ge08sSi01s (termed as GeSi from now on) is deposited at the saturation temperature 800 °C. Thus the driving force for crystallization due to a supercooling is negligible. We denote growth under these conditions as equilibrium growth. The nominal growth rate is around 2 nm per second; Bi as solvent yields n-type material with an electron concentration around 1016 c m -2 [9].
*On leave from Lund University, Department of Solid State Physics, Professorsgatan 3B, S-221 00 Lund, Sweden.
0040-6090/92/$5.00
The sketch in Fig. 1 summarizes the topology of our samples as observed by transmission electron microscopy (TEM). Our LPE process yields a thin initial
,t') 1 9 9 2
Elsevier Sequoia. All rights reserved
200
Letter
/'I'l
( ~ i ) ~
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- [o111 J
Fig. 1. Sketch representing geometrical aspects of pseudomorphic GeSi epitaxial layer growth on (100) Si by liquid phase epitaxy. The Mands are exclusively bound by {lll}-facets as sideplanes. These ,ell-defined truncated pyramids occur in different sizes on the same tmple on top of a thin initial layer.
~i :1.2 nm GeSi (a)
Fig. 3. Bright-field TEM micrograph in plan-view (multibeam condilions along the (100) surface normal) of the same GeSi LPE layer as in Fig. 2. the d a r k m a t e r i a l c o n t r a s t o f this thin layer as c o m p a r e d to t h a t o f the Si s u b s t r a t e . E x t e n s i v e c o n t r a s t e x p e r i m e n t s s h o w t h a t n o d i s l o c a t i o n s are p r e s e n t in this layer a n d at the i n t e r f a c e , i.e. the l a y e r is p s e u d o m o r p h i c . I s l a n d s are f o r m e d o n t o p o f this h o m o g e n e o u s l y t h i n initial layer. T h e t w o islands visible in Fig. 2(b) h a v e a t h i c k n e s s h - 25 n m ; c o r r e s p o n d i n g m e a s u r e m e n t s o n o t h e r m i c r o g r a p h s s h o w t h a t at this s t a g e o f g r o w t h , the t h i c k n e s s h o f the islands r a n g e s b e t w e e n 20 a n d 35 nm. W i t h i n this r a n g e the islands e x h i b i t a c o n s t a n t a s p e c t r a t i o o f w / h v 2, w h e r e w is the b a s e w i d t h a n d h the thickness, i.e. the h e i g h t o f the islands. T h e p l a n - v i e w m i c r o g r a p h in Fig. 3 reveals t h a t t h e p y r a m i d a l islands are statistically d i s t r i b u t e d o n the s a m p l e surface; n o i n d i c a t i o n s exist f o r p r e f e r e n t i a l n u c l e a t i o n sites. T o s e a r c h for p o s s i b l e defects, we utilize w e a k - b e a m images, as in Fig. 4. All islands ( e x c e p t o n e , w h i c h will
(b) Fig. 2. Cross sectional TEM micrographs (bright-field image in (110} multibeam conditions) of a Geo.s>Sio.t~ layer grown in Stranski-Krastanov mode (1.5 s at 800 'C from a 0.2 K supercooled Bi Ge Si solution). The islands form on top of a h i = 1.2 nm thick pseudomorphic GeSi layer on the Si(100) substrate, This layer can easily be seen by dark material contrast in (a), which shows a magnified section of (b). The pyramidal islands have a constant base width w to thickness h aspect ratio w/h ~ 2.
l a y e r o f G e S i o v e r the w h o l e Si surface. O n t o p o f this l a y e r we find islands c o n s i s t i n g o f t r u n c a t e d t e t r a h e d r a l p y r a m i d s , the side faces o f w h i c h b e i n g e x c l u s i v e l y f o r m e d by { l l l } - f a c e t s , i n t e r s e c t i n g the (100) g r o w t h p l a n e a l o n g ( 1 1 0 } d i r e c t i o n s . F i g u r e s 2 ( a ) a n d 2(b) s h o w c r o s s - s e c t i o n a l T E M m i c r o g r a p h s o f a s a m p l e as o b t a i n e d a f t e r 1.5 s o f g r o w t h . T h e m i c r o g r a p h s a r e seen in p r o j e c t i o n a l o n g the (100) i n t e r f a c e . F i g u r e 2(a) d e m o n s t r a t e s a c o n t i n u o u s G e S i layer, h a v i n g a t h i c k ness h~ = 1.2 n m c o r r e s p o n d i n g to 8 m o n o l a y e r s . N o t e
Fig. 4. Area of a GeSi sample showing islands of different sizes: TEM weak-beam dark-field image in plan-view. All islands with the exception of that in the centre are free of dislocations. These islands show a broad patchy contrast at their corners due to local strain. The island at which the diffraction vector points, contains a single isolated msfit dislocation (Burger's vector b = ½ (011}) in the middle.
Let ter
be considered later) in this area are free of dislocations. This means that not only the initial layer, but also the islands grow pseudomorphically. (The pronounced broad and patchy contrast is caused by local strain at the corners of the islands.) Plan-view observations, as in Fig. 3, are ideally suited to measuring the critical island thickness he. 1. The base width w of those islands that already contain one misfit dislocation is characteristic of the critical island thickness h~.~, due to the constant aspect ratio w/h ~ 2 . From islands of the type shown in the centre of Fig. 4 we obtain an experimental value h ~ , ~ 30 nm for the critical island thickness. Contrast analyses by T E M of islands, containing one isolated misfit dislocation, imply a Burger's vector b =~t ~011 ) of these dislocations, the detailed arrangement of which is presented separately [12]. Our experiments allow us to quantify Stranski-Krastanov growth in a direct way, i.e. the transition of two-dimensional growth (of the thin initial layer) to three-dimensional growth (of the pyramidal islands). Heteroepitaxial growth modes have been discussed in terms of surface energy arguments [5-7], originally presented by Bauer [5, 6]. He suggested that the equilibrium growth mode is determined by the balance between the surface free energies of the substrate 7~, the epitaxial layer 7e and the interface ~i. Mar6e later applied this theory to misfitting layers, adding an energy term ~ that accounts mainly for the stress influence of lattice strain on the energy [7]. Two-dimensional growth ( F r a n k - v a n der Merwe growth [13]) takes place when the epitaxial layer wets the substrate, i.e. when the energy of surface plus interface and stress contribution is smaller than the surface energy of the substrate, the following must hold: 7e -? )'i + O" ~ 7~.
(1)
During pseudomorphic growth, the stress and thus increase with the number of epitaxially deposited monolayers. After a certain number of monolayers, the magnitude of the left hand terms in eqn. (1) therefore exceeds Vs, resulting in the onset of 3D growth ( V o l m e r - W e b e r growth [14]). Recent calculations by Tersoff showed that 2D growth of Ge on Si(100) is energetically favourable for a Ge coverage of up to 4 monolayers [8]. (The areal elastic energy of a 4 monolayer thick Ge0.ssSi0.~5 layer equals that of a 3 monolayer thick Ge layer.) Both quoted models of epitaxial growth are based on the assumption of thermodynamical equilibrium. Clearly, this condition is fulfilled for our LPE process. The experiments permit a direct comparison to these theories and a transition to pseudomorphic island growth after deposition of 8 monolayers is found. The results suggest the equilibrium growth mode transition from 2D to 3D growth occurs at a later
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stage of growth than most previous results obtained by (non-equilibrium) vacuum deposition techniques suggested [7, 15 20]. The side faces of the equilibrium grown pseudomorphic islands, formed by Stranski-Krastanov growth, without exception consist of { 111 }-facets terminated by a (100)-oriented top face. We do not observe any intermediate phases between the initial 2D layer and the final {111}-faceted islands; only differences in island size occur. By the use of various vacuum deposition techniques, the formation of islands of complex facet structures, mostly consisting of {ll3}-facets, has been observed [15, 18, 19]. Scanning tunnelling microscopy studies have shown the existence of a 3D cluster phase of a different facet configuration. These clusters consist of perfect {105}-facets and coexist with larger islands [18]. Our LPE experiments, therefore, indicate that the faceting of an island by Stranski Krastanov growth depends on the conditions of deposition. The near-equilibrium conditions of growth associated with LPE obviously lead to the formation of the stable { 111 }-facets of low free energy. We speculate that the [ l l l ] - f a c e t e d islands represent the true equilibrium phase of Strans k i - K r a s t a n o v growth, probably minimizing the total free energy. The kinetics of the initial formation of these {lll}-facets and thus the transition to the 3D island phase is, however, not deducible from the present experiments. The transition of the pseudomorphic islands into the dislocated state is now discussed in terms of critical thickness. Application of the mechanical equilibrium theory according to Frank and van der Merwe [13, 21] to our system yields a critical thickness he. Mr: ~ 3 nm. However, our experimental value of critical island thickness h~. 1 ~ 30 nm is a factor of 10 higher. Mechanical equilibrium theory [ 13, 21, 22] assumes an infinitely extended epitaxial layer; an assessment that may not be applicable for our case of laterally well-separated islands. In order to consider the stress reduction caused by island formation (and thus a further increase of critical thickness he. ME) we use a theoretical analysis developed by Luryi and Suhir [23]. The most significant result here is that the expected strain reduction is a function of the aspect ratio w/h. For our case of w/h ~ 2, the strain is reduced to 55% of the value for an infinitely extended layer. Within the mechanical equilibrium approach [13, 21], this strain reduction corresponds to a theoretical critical island thickness of he, vr = 15 nm, which still is a factor of two smaller than our experimental value he. l ~ 30 nm [24] (a possible contribution to strain reduction in epitaxial islands due to an elastic strain in the substrate material adjacent to the interface as discussed in ref. 24 can be neglected in this case since no corresponding strain contrasts are observed). Strain reduction due to local pyramidal
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island formation, therefore, does not alone explain the observed discrepancy. We attribute the still remaining difference to a kinetic barrier which has to be overcome in the formation process of the first misfit dislocation. In conclusion, a specifically designed growth technique has been presented, taking place close to thermodynamical equilibrium, for detailed studies of any state in the early epitaxial growth process and thus also in the formation of the first misfit dislocation. Our electron microscopy study shows for GeSi on (100) Si, that after 8 monolayers of 2D growth the system changes to 3D island growth. These islands are bound by stable {lll}-oriented side facets and grow pseudomorphically up to a critical island thickness h~, ~ ~ 30 nm; then isolated misfit dislocations appear. Our experimental value for the h~. ~ exceeds theoretical predictions by a factor of two. This discrepancy supports arguments for a kinetic barrier in the formation process for misfit dislocations.
Acknowledgments The authors gratefully acknowledge the continuous support of H. G. Grimmeiss and H. J. Queisser. One of us, P.O.H. is supported by the Swedish National Board for Technical Development. Support by the Deutsche Forschungsgemeinschaft under contract STR 277/1 is gratefully acknowledged.
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