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Influence of step edges elastic relaxation on the
morphology of compressively and tensilely strained In
l-xGaxAs layers epitaxially grown on InP
P Krapf, Y. Robach, Michel Gendry, L. Porte
To cite this version:
ELSEVIER Journal of Crystal Growth 181 (1997) 337 342
j . . . C R Y S T A L G R O W T H
Influence of step edges elastic relaxation on the morphology
of compressively and tensilely strained In l-xGaxAs layers
epitaxially grown on InP
P. Krapf a, Y. Robach a, M. Gendry b, L.
P o r t e a'*"D~partement de Physico-Chimie des Mat#iavar, Ecole Centrale de Lyon, BP 163, F-69131 Ecully Cedex, France b Laboratoire d'Electronique, Automatique et Mesures Electriques, Associd au CNRS, UMR 5512, Ecole Centrale de Lyon, BP 163,
F-69131 Ecullv Cedex, France
Received 17 February 1997; accepted 18 April 1997
A b s t r a c t
The growth of compressively and tensilely strained In1 xGaxAs/InP(00 1) epilayers has been studied using the scanning tunneling microscope. For 2% compressive strain, a transition occurred after the epitaxy of five monolayers and three-dimensional islands were formed. A different type of surface roughening was observed for 2% tensile strain: three-dimensional holes were left within the terraces evolving towards the formation of chain-like surface structures. The shapes of self-assembled surface structures depend markedly on the sign of the strain imposed between mismatched materials. They can be explained by the elastic relaxation of strained unit cells, which occurs at step edges delimiting islands or holes.
K e y w o r d s : Scanning tunneling microscopy; Epitaxy; Strain; Surface structure; Surface morphology
1. I n t r o d u c t i o n
M o l e c u l a r beam epitaxy (MBE) is a powerful tool for designing s e m i c o n d u c t o r structures with tailored electronic or optical properties [1]. The epitaxial g r o w t h of lattice m i s m a t c h e d In1 - xGaxAs on I n P substrates enables the p r o d u c t i o n of b o t h compressively a n d tensilely strained layers which can be of use for device applications. A compres- sively strained q u a n t u m well can be used as a canal
* Corresponding author. E-mail: [email protected].
in p s e u d o m o r p h i c high-electron mobility transis- tors [ 2 - 4 ] . Tensilely strained layers are also of interest to p r o d u c e laser structures [5]. To m a k e efficient electronic and optoelectronic devices, sharp interfaces are needed and the layer-by-layer epitaxial g r o w t h m o d e is required. However, the g r o w t h of m i s m a t c h e d layers a c c u m u l a t e positive strain energy which can be relieved by dislocations when a critical thickness is attained. A n o t h e r w a y to relieve strains is the f o r m a t i o n of three-dimen- sional islands coherently strained a n d dislocation- free. This coherent Stranski K r a s t a n o v g r o w t h m o d e has been observed in various systems: Ge on 0022-0248,,'97/$17.00 ,~2, 1997 Elsevier Science B.V. All rights reserved
338 P. Krat)/'et al. /Journal o/'CEvstal Growth 181 (1997) 337 342
Si [6, 7], In(Ga)As on G a A s [8-12], G a l n P on I n P [13, 14]. The possibility to create self-assembled q u a n t u m structures has renewed interest on these systems [15 18].
Both the compressively and the tensilely strained lnl xGaxAs layers grown on I n P at a typical mis- match of 2% form three-dimensional structures after deposition of very few monolayers. This sur- face roughening was detected by a spotty aspect in reflection high-energy electron diffraction ( R H E E D ) lines [19]. In this work scanning tunnel- ing microscopy (STM) is used to compare the mor- phology of compressively and tensilely strained layers. We will show that changing the sign of the strain has striking influence on the m o r p h o l o g y and we will emphasize the important role of stress relaxation at step edges in determining the shapes of the three-dimensional structures.
2. Experimental procedure
In1 _~GaxAs epilayers were grown on ln0.53Ga0.47As buffer layers lattice matched to the InP(0 0 1) substrate. Buffer layers were realized in normal layer-by-layer growth mode. Strained layers (either 2% compressive for x = 0.18, or 2% tensile for x = 0.75) were deposited on the buffer layer. Epitaxial growth was carried out in a Riber 2300 M B E system connected under ultra-high vac- uum to a STM chamber adapted for a Beetle microscope. This system has been described else- where [20]. It allows the transfer between M B E and STM of epitaxially grown layers under ultra- high vacuum. Nominally flat n ÷ doped (Si, 5 x 1018 atoms/cm 3) I n P ( 0 0 1) substrates were used. After thermal desorption of the oxide, a 400 nm thick buffer layer was grown at 525':'C, with a V to Ill element ratio equal to 20, and at a growth rate of 0.4 gm/h. The buffer layer was also Si-doped at 5 x 10 is atoms/cm 3, but the last 5 nm were kept undoped. The buffer layer was main- tained at the growth temperature for 10 min under arsenic pressure. This allows an appreciable surface smoothing prior to the deposition of strained ma- terial [21]. Either compressive or tensile lattice mismatched epilayers were then deposited on the buffer layer at 5 2 5 C , for a V to I I I ratio equal to
70, and at a growth rate of 0.25 lam/h. Slow growth rate and high temperature were chosen in order to favor surface diffusion and obtain a surface mor- phology near to the t h e r m o d y n a m i c equilibrium.
Several thicknesses were realized, ranging from 0.5 to 17 M L ( M L = monolayer). Only represen- tative thicknesses will be presented, at both positive (tensile) and negative (compressive) strain. R H E E D patterns were registered during growth. F o r com- pressive layers R H E E D patterns showed the well documented 2 x 4 surface reconstruction. A spotty aspect appears in the R H E E D pattern at a critical thickness of 1.5 nm. It characterizes the transition to a three-dimensional growth mode. For tensilely strained layers no surface reconstruction is ob- served by R H E E D . Moreover, in that case no pre- cise critical thickness for the transition could be determined since the evolution of the diffraction lines towards the characteristic spotty aspect was progressive [19]. After the growth was finished the samples were quickly cooled to 300:C, while under arsenic pressure, so as to reduce large-scale surface reorganisation (i.e. step motions). However, the R H E E D patterns showed that the surface recon- struction evolves towards a 4 x 3 reconstruction during this cooling procedure for both signs of strain. This is attributed to arsenic absorption. Thereafter, samples were cooled under vacuum nearer to r o o m temperature and transferred to the STM chamber. STM images were recorded at posi- tive sample bias ( + 2 V), 0.2 nA of tunneling cur- rent, and using chemically etched Pt0.9Iro.x tips. These imaging conditions are chosen since they allow the obtention of well reproducible images whith a good definition of step edges. In these conditions, only the 1.2 nm (x3) periodicity of the 4 x 3 reconstruction was observed by STM.
3. Results and discussion
P. Kral)f et al. /Journal of Crystal Growth 181 (1997) 337 342 339
Fig. 1. STM images from lno.82Ga0.18As epitaxied in compres- sion on lattice matched Ino.53Gao.47As/InP(00 1), recorded after deposition of: (a) 4 ME; (b) 5 ML; (c) 10 ML
340 P. Kral?/'et al. /Journal o f Crystal Growth 181 (1997) 337 342
obtained from a layer-by-layer growth mode [21]. Up to the deposition of 4 M L (Fig. la) compress- ively strained material forms isolated fiat platelets 1 3 M L high, about 35 nm broad ([1 1 0] direc- tion) and 120 nm long ([1 - 1 0] direction) separ- ated by large 2D terraces. Thus, growth remains essentially 2D. Addition of one more M L (Fig. lb) leads to the formation of islands strongly elongated along [1 - 1 0] but getting similar width than the former platelets. They are higher than the nominal 5 ML thick deposit since up to 7 M L can separate minima and maxima. After this 2D to 3D transition, islands continue to grow and can reach 15-20 M L while 10 M L were deposited (Fig. lc).
The evolution of the morphology appears quite different for the tensile case. When 5 M L of strained material are deposited (Fig. 2a) a great number of small 2D platelets, l M L high, 5-15 nm broad and 10-80 nm long, are formed along with narrow holes which exhibit a high aspect ratio. This rough patchy surface is still observed after deposition of 9 ML, with a deepening of the holes (Fig. 2b). After deposit of 13 ML, highly anisotropic structures, 1 0 - 1 5 n m large, are obtained. They extend all across the image, forming zig-zag chains which separate several M L deep holes (Fig. 2c). These chains appear to result from the coalescence, along the [1 - 1 0] direction, of the former small 2D platelets, while lower terraces are not completed. It is noteworthy that the upper part of these chains would create a unique (may be two) terrace(s) if material was allowed to fill the holes. Thus, the roughness of tensilely strained epilayers increases along with the deposited thickness. Roughening appears to be rather continuous from the onset of the growth of the strained layer. This contrasts with the sharp transition observed for compressive layers. Holes which are observed in the growing terrace from the beginning, are not efficiently filled by subsequent material deposition. They appear to be the starting point of the larger holes which finally separate the zig-zag chains. Thus, while 3D structures develop for both compressive and tensile layers, a striking difference is also observed: Com- pressive layers form 3D islands but tensile layers leave 3D holes within terraces. Fig. 3 presents im- ages recorded at higher magnification from both such islands and holes. Isohypses 1 M L apart are
!!!jl!r
iiiii~iiiiiiiiiiiiiiiiiiii
:~:: }} :: : :::: { }: { {{~:
Fig. 3. S T M images from: (a) An island created after deposition of 10 M L of compressively strained lno.82GaoslsAs epitaxied on lno.53Gao.4vAs lattice matched to lnP(0 0 1) substrate. (b) A hole created after deposition of 13 M L of tensilely strained Ino.25Gao.TsAs epitaxied on Ino.53Gao,4vAs lattice matched to InP(0 0 1) substrate. Isohypses 1 M L apart ( ~ 3 ]i) are drawn to show the terrace shapes of the three-dimensional islands or holes which have formed during epitaxial growth.
P. Krat)f et al. // Journal o f Co,stal Growth 181 (1997) 337--342 341
Steps delimiting islands or holes exhibit clearly a mean curvature. While steps of compressively strained islands a d o p t a convex curvature, steps of tensilely strained holes a d o p t a concave curvature (the curvature is defined with respect to the upper terrace; steps are convex (concave) if the upper terrace is inside (outside) the curvature).
A surface delimiting two fluids supporting differ- ent internal pressures adopts a curvature whose radius R is given by the Young Laplace relation- ship: AP =
?/R,
where AP is the pressure difference and ? the surface tension. It can be demonstrated [22] that a strained 2D terrace delimited by a step corresponds to a special two-dimensional case of the Y o u n g - L a p l a c e relationship, which then writes:Affii =
ai/R.
The pressure difference has been re-placed by the two-dimensional stress difference Acrll on both sides of the step, and the surface tension 7 by the line stress ai along a step. Thus, a step delimiting a strained terrace should experi- ence some curvature.
It is known that atoms relax elastically at step edges on the upper terrace since they are less strongly linked to the substrate than atoms within the terrace [9]. F o r compressively strained layers, relaxed zones have a larger in-plane lattice par- ameter than unrelaxed ones, while the reverse oc- curs for tensilely strained layers where the in-plane lattice p a r a m e t e r is allowed to decrease in relaxed zones. The formation of coherent three-dimen- sional structures depends on the balance between the positive energy for creating terrace steps and the negative energy which originates from elastic relaxation of the lattice at step vicinity [17]. Thus, the formation of islands in compression or holes in tension appears to be first driven by the relaxation at terrace edges. Fig. 4 intends to illustrate sche- matically the relation between strain and step cur- vature on the basis of simple geometric arguments. Starting from a regular surface lattice one can ob- tain two types of terraces by breaking the bonds crossing a closed line drawn on the surface. A con- cave terrace shape is obtained by removing atoms inside the line, i.e., creating a hole within the ter- race, while a convex terrace shape is obtained by removing atoms outside the line, i.e., creating an island. It is noteworthy that the concave terrace has more atoms on the step edge than the convex one.
(a) • ° • ° ° ° • ° ° ° ° • ° • • ° ° ° ° ° ° o • • ° • • • • ° ° • ° '((/'A I 1 1 V/,,/.. 111III111 • • ° ° • • • , ° ° ° • • • ° • • • ° • • •
(b)
i ! ! l l l l l
J!~
(c)
Fig. 4. Illustration of the relation between strain relaxation and step curvature. (a) Two types of structures can be obtained by breaking the bonds crossing a closed line drawn on a terrace.
(b) Island at compressive strain: The volume of the island in-
creases due to relaxation of unit cells near step edges. Steps determine a general convex curvature (the curvature is defined versus the upper terrace). (c) Hole at tensile strain: The volume
of the terrace surrounding the hole decreases due to relaxation of unit cells near step edges. Steps determine a general concave curvature. Dots: lower terrace; square grid: upper terrace; hatched area: relaxed units.
Thus, atoms on the edge of convex terraces have more place to expand than on concave terraces. When an island is formed from a compressively strained terrace, unit cells at step edges can relax by extending the bonds outwards (Fig. 4b). Volume expansion is the natural trend towards stability for a compressive island, and the island shape will be determined by terraces whose steps have a general convex curvature. On the contrary, when a hole is created from a tensilely strained terrace the unit cells at step edges can relax by retracting the bonds inwards (Fig. 4c). In that case, the volume of the terrace surrounding the hole decreases, thus in- creasing the stability.
342 P. Krapf et al. /Journal of Crystal Growth 181 (1997) 337 342
efficiently than the convex one. As the terrace tends to retract, its steps will have a tendency to adopt a general concave curvature. Thus, the natural re- laxation trend for strained material leads to the formation of islands surrounded by convex steps in the case compression and the formation of holes limited by concave steps in the case tension. One can finally remark that, following the Y o u n g - Laplace relation, the curvature radius of the step increases (decreases) when strain decreases (in- creases). This general trend is also given by the Asaro-Tiller-Grinfeld model [23, 24]. However, the latter gave only a limit of stability of the size of islands which could not be predicted accurately. This behavior may be of general use to control the size of three-dimensional structures. While several combinations of compressively strained materials have been used to grow small island structures [-6, 8, l0 15], tensilely strained systems appear to have been quite ignored for this purpose. This work shows that a tensile system offers specific possibili- ties for the creation of self-assembled surface struc- tures. It suggests that structures of controlled nanometric width should be grown by appropriate choice of the mismatch between the substrate and the epitaxial deposit.
4. Conclusions
The epitaxial growth of In1 xGaxAs layers on a lattice matched buffer layer In0.53Ga0.47As/ I n P ( 0 0 1) was investigated using the STM, for both 2% compressive strain (x = 0.18) and 2% tensile strain (x = 0.75). As surface roughening occurred during the growth, a striking difference was observed between epilayers grown at op- posite strains: Compressive layers induced the formation of 3D islands while tensile layers left 3D holes within terraces. Moreover, steps delimit- ing the 2 D terraces from islands or holes exhibited a mean convex curvature (islands) for a compressive strain and a mean concave curva- ture (holes) for a tensile strain. These trends can be explained by the relaxation of strained unit cells at step edges. The shape of self-assembled surface structures which develop during epitaxial
growth of two mismatched materials is controlled by the imposed strain.
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