Ž .Applied Surface Science 148 1999 86–91

Kinetic effects on the size homogeneity of Stranski–Krastanowislands

Jonas Johansson ), Werner SeifertSolid State Physics, Lund UniÕersity, Box 118, S-221 00 Lund, Sweden

Received 20 January 1999; accepted 9 February 1999

Abstract

Ž .In this study we present results concerning the size height homogeneity of self-assembled quantum dots grown in theStranski–Krastanow growth mode for different deposition conditions. 3.5 ML InP was deposited on a GaP-stabilized GaAssubstrate by metal organic vapor phase epitaxy for varying temperatures, 580–6408C, and varying deposition rates, 0.5–3.5MLrs. The average height decreases for increasing deposition rate and decreasing temperature. The width of the heightdistribution decreases with decreasing temperature and shows a non-monotonic behaviour with a minimum as a function ofthe deposition rate. q 1999 Elsevier Science B.V. All rights reserved.

PACS: 68.55.-a; 81.15.Gh

Keywords: Metal organic vapor phase epitaxy; Stranski–Krastanow growth; Self-assembling; Quantum dots

1. Introduction

During the recent years, intense interest has beenŽ .paid to the formation of coherent dislocation free ,

Ž .three dimensional 3D islands during heteroepitaxialgrowth of lattice mismatched semiconductors. Thisprocess which is an elegant way to fabricate zero

Ž .dimensional heterostructures quantum dots is com-monly referred to as self-assembling of dots or the

Ž . ŽStranski–Krastanow SK growth mode see Refs.w x .1–3 and references therein . It has been observedfor a wide range of materials combinations, includ-ing Ge Si on Si, In Ga As on GaAs, InP onx 1yx x 1yx

In Ga PrGaAs, and others.x 1yx

) Corresponding author. Tel.: q46-46-222-7671; Fax: q46-46-222-3637; E-mail: jonas.johansson@ftf.lth.se

In order to manipulate sizes and densities ofself-assembled quantum dots, detailed knowledgeabout the mechanism behind 3D island formation isneeded. Since the driving force for the 2D–3D tran-sition is the relaxation of misfit strain, numeroustheoretical as well as experimental investigationswere done in order to study the effect of strain on the

w xisland formation 4–6 . On the other hand, there existseveral investigations which show that size and den-sity of coherent islands vary primarily with the depo-sition conditions temperature and deposition rate, Rw x7–13 . These dependencies have been systemati-cally investigated for the materials combination

Ž .InPrGaInPrGaAs 001 and it was found that theŽ . zdensity follows a power law, rA RrD , with

w xzf1 for SK growth and not too high R 14 . D ishere the temperature-dependent surface diffusion

0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0169-4332 99 00127-0

( )J. Johansson, W. SeifertrApplied Surface Science 148 1999 86–91 87

Ž . 2parameter. It is given by D s 2k Trh a =BŽ .exp yE rk T , where k is Boltzmann’s constant,d B B

T is the absolute temperature, h is Planck’s constant,a is the lattice parameter of the wetting layer strainedto the substrate, and E is the energy barrier ford

surface diffusion, estimated from the slope of the ln r

w xversus 1rT dependence to 1.2 eV 14 . This propor-tionality between r and RrD is in agreement withthe rate equation formalism for 3D island formation

w xdeveloped in Ref. 15 and more detailed rate equa-w xtion calculations presented in Ref. 16 .

The island sizes develop after nucleation by distri-bution of excess material over the stable nuclei. Bythis materials balancing the average island size ismainly defined by the amount of material depositedand the density of stable nuclei. The consequence isan inverse relation between size and density. Duringthe evolution of sizes the detailed process parametersaffect the entire size distribution, concerning widthand modality. Experimental observations show thatthe distribution is bimodal during early stages. This

w xwas observed for InP dots on GaInP 17 , as well asw xInAs dots on InP 18 , and Ge Si dots on Six 1yx

w x19,20 . When the material supply and the tempera-ture are large enough, the initially created smallislands grow rapidly into fully developed ones andthe size distribution becomes unimodal.

The aim of this investigation is to show how theŽ .size height homogeneity of free standing InP is-

lands grown on GaAs by metal organic vapor phaseŽ .epitaxy MOVPE is affected by variations in the

deposition rate and the temperature. We find that thewidth of the height distribution increases with thetemperature and that it has a minimum for a certaindeposition rate.

2. Experimental

The experiments were carried out in a low-pres-Ž .sure 100 mbar , RF-heated MOVPE reactor.

Ž . Ž .Trimethylgallium TMG , trimethylindium TMI ,Ž .PH , AsH and GaAs 001 substrates were used in3 3

H as the carrier gas. The process was controlled by2

a flow and pressure balanced ventrrun system.After growing the GaAs buffer layer a 2 ML thick

GaP layer was grown in order to reduce As carry

over effects. Then, on top of the GaP-stabilizedGaAs, 3.5 ML InP was deposited. Deposition ratesinvestigated were 0.5, 0.7, 1.2, and 3.5 MLrs for thetemperatures 580, 610, and 6408C. Samples for AFMmeasurements were annealed for 12 s under PH at3

deposition temperature before cooling down. AFMimages were recorded in contact mode. Due to thelimited lateral resolution of conventional contactmode measurements, we use the height as a measureof the island size. The island height distributionswere evaluated by measuring island heights on oneor two 2=2 mm2 scans until more than 100 islandswere evaluated. From these data, the widths of the

Žheight distributions the fluctuations in island height,. 2h , s , were calculated as standard deviations, s '2 2h yh , where the bars denote average.

3. Results and discussion

In Fig. 1, the height distributions for the 580 and6108C samples are shown. As the deposition rate, R,increases, the average height, h, decreases. In therange of 0.5 to 1.2 MLrs, the width of the distribu-tion, s , narrows. For the 3.5 MLrs samples aclearly bimodal height distribution is observed forthe 5808C sample and for the 6108C a wider distribu-tion than the one accounting for 1.2 MLrs. Byincreasing the temperature s also increases, see Fig.

Ž .1. The 6408C histograms not shown follow thesame trend as the ones accounting for 6108C.

In Fig. 2 the inverse relationship between averageŽ .size height and density is demonstrated. Here h is

plotted versus r, and a power fit yields the exponenty0.32. The 3.5 MLrs values, where we clearly seea bimodal size distribution, and consequently islands

Žof different aspect ratios hrw hsheight and ws.base width of the islands were excluded from this

fit. However, these values show the same slope onthe log log scale, although with a slightly lowerintercept.

w xSince the average quantities r 14 and h scalewith RrD it is reasonable to assume that also s isrelated to RrD. In Fig. 3, s is plotted versus RrD,for the three different temperatures and the insetshows r versus RrD for the same temperatures.For the 5808C, 3.5 MLrs sample s accounts for the

( )J. Johansson, W. SeifertrApplied Surface Science 148 1999 86–9188

Fig. 1. Height distribution histograms for the 580 and 6108C samples for the different deposition rates. The 5808C histograms are shown onŽ . Ž . Ž . Ž . Ž . Ž . Ž . Ž .the left panel and the 6108C histograms on the right: a and e 0.5 MLrs, b and f 0.7 MLrs, c and g 1.2 MLrs, and d and h 3.5

MLrs.

Ž .larger island branch see Fig. 1 . The dashed curve inFig. 3 shows that in the limit of low R, the curvesfor the three temperatures fall together into anasymptotic form, from which they diverge for largerR values. The inset in Fig. 3 shows that for high Rvalues the densities also deviate from the scaling

w xrelation between r and RrD 14 .

The relationship between average size and densitycan simply be explained by materials balancing overa unit area. If the island shape is approximated by aspherical cap, its volume may be written as V sisl

2 3Ž .wŽ . xpr6 3r4a q1 h , where a is the aspect ratioof the fully developed islands, defined as h dividedby the average base diameter. Now, rV sV yisl tot

( )J. Johansson, W. SeifertrApplied Surface Science 148 1999 86–91 89

ŽFig. 2. Average island height counting only the fully developed.islands versus density plotted on a log log scale. A power fit

yields the exponent y0.32. The 3.5 MLrs values are excludedŽ .from the fit see Section 3 .

V , where V is the total deposited volume andWL tot

V is the volume in the remaining wetting layer.WL

Rewriting this expression under the reasonable as-Žsumptions that V and a are constant the latterWL

condition is valid as long as we consider only the.fully developed islands, where af0.3 , yields hA

ry1r3. This is in agreement with the experimentalobservations shown in Fig. 2, with the exception ofthe 3.5 MLrs samples.

To explain these observations let us consider somedetails of the 3D island growth mechanism. For highdeposition rates and lower deposition temperatures inthe here investigated materials combination we see aclearly bimodal size distribution of coherent islandsw x2,17 , as is visible from the size histogram of the5808C sample in Fig. 1d. This bimodal size distribu-tion seems to be a very general case during the earlystage of the 2D–3D transition, since it appears alsoat higher deposition temperatures if one depositslower amounts of material andror cools down the

w xsample very rapidly after island formation 2 . Wehave demonstrated that the smaller, low-aspect ratioislands are unstable and disappear during annealingprocesses, whereas the fully developed islands, trun-

� 4 � 4cated pyramids with 111 B and 110 side facetsŽ . w xand a 001 top-plane 21 are rather stable and

Žwithstand short-time annealing in the range of min-. w xutes 22 . The subject of this investigation is the size

distribution of these fully developed islands only.We believe that these islands are a result of ripeningof the smaller, low aspect ratio islands. A similarbehaviour has recently been reported for self-assem-

w xbled dots of Ge on Si 20 . However, in contrast tow xthe discussion in Ref. 20 , we observe this transition

into fully developed islands for very different islandŽvolumes, depending on R and T see the histograms

.in Fig. 1 . The nature of this transition is mostprobably the increase of the facet angle from origi-

� 4 � 4nally flat facets 11n and 10n , with nf3–6, to� 4 � 4the steeper 110 and 111 facets by deposition of

material at the most strain-relaxed apex area. With� 4 � 4the formation of these low-energy 110 and 111

facets further growth in lateral direction will beŽunfavourable due to facet nucleation barriers

w x. ² :23,24 , whereas growth in the vertical 001 direc-tion will still be driven by the gain in volume elasticenergy until the 3D islands reach their equilibriumshape. Total energy calculations predict shapes forInAs islands on GaAs which are very similar to the

Fig. 3. The standard deviation of the height of the fully developedislands, s , versus RrD. The curves are guides for the eye. The

Ž w x.inset shows the total island density versus RrD from Ref. 14 .

( )J. Johansson, W. SeifertrApplied Surface Science 148 1999 86–9190

truncated pyramid shapes of fully developed InPw xislands on GaAs 25 .

If this model is correct, then the only preconditionfor an efficient size regulation should be that thetransition into fully developed islands starts on thebase of laterally equally sized small islands. Thisdepends on the nucleation and materials transportconditions, i.e., on R and D. By changing theexperimental parameters R and T , the supersatura-tion at the onset of nucleation is altered. By deposit-ing the material fast, i.e., at high R, the supersatura-tion is high and the island nucleation is confined to ashort time span, leading to similar starting conditionsfor all islands and consequently a narrow size distri-

w xbution 26 . The same effect is achieved when de-positing the material at low T , since this will delaythe thermally activated nucleation and allow theformation of a thicker wetting layer before nucle-ation. Indeed, the kinetically defined critical thick-ness, i.e., the thickness of the wetting layer at theonset of nucleation, increases with increasing RrDw x27 . A high critical thickness gives a high initialsupersaturation, since in this case the islands growfast by capturing material from a thicker decompos-ing wetting layer.

Moreover, for efficient size regulation it is impor-tant to have a surface diffusion length that is consid-erably greater than the average inter-island distance.Then the islands that have not yet reached the equi-librium shape will preferentially collect the mobilematerial. Surface diffusion lengths of about 10 timesthe average island–island distance have been re-

w xported 28 .In the region where R is low, s follows RrD

asymptotically, see Fig. 3, indicating the relationbetween the supersaturation and the size homogene-ity. The increase in s for Rs1.2–3.5 MLrs aswell the offset of the 3.5 MLrs samples in Fig. 2 wesee as consequences of too less material available forformation of fully developed islands. We argue thatthere are more hidden flat islands in these high

Ždensity samples or a thicker remaining wetting.layer , difficult to detect by the AFM, which had no

chance to grow up into fully developed 3D islandsdue to too less material in relation to the large

Ž w x.number of islands see explanation in Ref. 16 .Thus, for these high density cases efficient sizeregulation was never achieved. One should also con-

sider that 3.5 MLrs InP deposition in MOVPE isextremely high in comparison to commonly useddeposition rates in order to obtain perfect material.

4. Conclusions

In conclusion, we have shown that not only thedensity and size of self-assembled quantum dots arekinetically controlled by the deposition conditions,temperature and deposition rate. Also the width

Ž .of the size height distribution of InPrGaAs Stran-ski–Krastanow islands is strongly affected by thedeposition conditions.

The average island height decreases with increas-ing deposition rate and decreasing temperature and isinversely related to the density via hAry1r3, fornot too high deposition rates. The width of the heightdistribution, here measured by the standard devia-tion, decreases with decreasing temperature andshows a non-monotonic behaviour as a function ofdeposition rate. For low deposition rates the standarddeviation decreases with increasing deposition rateand reaches a minimum, whereas upon further in-crease in the deposition rate the height distributionwidens again.

We attribute this optimum of high size homogene-ity to an optimum in the nucleation conditions, whichis characterized by a high supersaturation at theonset of nucleation.

Acknowledgements

This work was performed within the NanometerStructure Consortium in Lund and was supported bygrants from the Swedish National Board for Indus-

Ž .trial and Technical Development NUTEK , theŽ .Swedish Natural Science Research Council NFR ,

and the Swedish Research Council for EngineeringŽ .Sciences TFR .

References

w x1 P.M. Petroff, S.P. DenBaars, Superlattices Microstruct. 15Ž .1994 15.

w x2 W. Seifert, N. Carlsson, M. Miller, M.-E. Pistol, L. Samuel-Ž .son, L.R. Wallenberg, Prog. Cryst. Growth Charact. 33 1996

423.

( )J. Johansson, W. SeifertrApplied Surface Science 148 1999 86–91 91

w x Ž .3 R. Notzel, Semicond. Sci. Technol. 11 1996 1365.¨w x4 C.W. Snyder, B.G. Orr, D. Kessler, L.M. Sander, Phys. Rev.

Ž .Lett. 66 1991 3032.w x5 B.G. Orr, D. Kessler, C.W. Snyder, L. Sander, Europhys.

Ž .Lett. 19 1992 33.w x Ž .6 A.-L. Barabasi, Appl. Phys. Lett. 70 1997 2565.´w x7 P. Chen, Q. Xie, A. Madhukar, L. Chen, A. Konkar, J. Vac.

Ž .Sci. Technol. B 12 1994 2568.w x8 G.S. Solomon, J.A. Trezza, J.S. Harris Jr., Appl. Phys. Lett.

Ž .66 1995 991.w x9 G.S. Solomon, J.A. Trezza, J.S. Harris Jr., Appl. Phys. Lett.

Ž .66 1995 3161.w x10 M. Sopanen, H. Lipsanen, J. Ahopelto, Appl. Phys. Lett. 67

Ž .1995 3768.w x11 W. Seifert, N. Carlsson, J. Johansson, M.-E. Pistol, L.

Ž .Samuelson, J. Cryst. Growth 170 1997 39.w x Ž .12 R.E. Welser, L.J. Guido, Appl. Phys. Lett. 68 1996 912.w x13 G. Abstreiter, P. Schittenhelm, C. Engel, E. Silveira, A.

Ž .Zrenner, Semicond. Sci. Technol. 11 1996 1521.w x Ž .14 J. Johansson, N. Carlsson, W. Seifert, Physica E 2 1998

667.w x Ž .15 J.A. Venables, Surf. Sci. 299–300 1994 798.w x16 H.T. Dobbs, D.D. Vvedensky, A. Zangwill, J. Johansson, N.

Ž .Carlsson, W. Seifert, Phys. Rev. Lett. 79 1997 897.

w x17 S.P. DenBaars, C.M. Reaves, V. Bressler-Hill, S. Varma, H.Ž .Weinberg, P.M. Petroff, J. Cryst. Growth 145 1994 721.

w x18 A. Ponchet, A.L. Corre, H. L’Haridon, B. Lambert, S. Salaun,¨Ž .Appl. Phys. Lett. 67 1995 1850.

w x19 G. Medeiros-Ribeiro, A.M. Bratkovski, T.I. Kamins, D.A.A.Ž .Ohlberg, R.S. Williams, Science 279 1998 353.

w x20 F.M. Ross, J. Tersoff, R.M. Tromp, Phys. Rev. Lett. 80Ž .1998 984.

w x21 K. Georgsson, N. Carlsson, L. Samuelson, W. Seifert, L.R.Ž .Wallenberg, Appl. Phys. Lett. 67 1995 2981.

w x22 J. Johansson, W. Seifert, V. Zwiller, T. Junno, L. Samuels-Ž .son, Appl. Surf. Sci. 134 1998 47.

w x23 D.E. Jesson, G. Chen, K.M. Chen, S.J. Pennycook, Phys.Ž .Rev. Lett. 80 1998 5156.

w x24 T.-M. Ahn, S. Purushothaman, J. Phys. Chem. Solid 37Ž .1976 777.

w x25 E. Pehlke, N. Moll, A. Kley, M. Scheffler, Appl. Phys. A 65Ž .1997 525.

w x Ž .26 J.-M. Gerard, in: E. Burstein, C. Weisbuch Eds. , ConfinedElectrons and Photons, Plenum, New York, 1995, p. 357.

w x27 C.W. Snyder, J.F. Mansfield, B.G. Orr, Phys. Rev. B 46Ž .1992 9551.

w x28 M. Hata, T. Isu, A. Watanabe, Y. Kajikawa, Y. Katayama, J.Ž .Cryst. Growth 114 1991 203.