Structure of GaN quantum dots grown under “modified Stranski–Krastanow”conditions on AlNN. Gogneau, D. Jalabert, E. Monroy, T. Shibata, M. Tanaka, and B. Daudin Citation: Journal of Applied Physics 94, 2254 (2003); doi: 10.1063/1.1592866 View online: http://dx.doi.org/10.1063/1.1592866 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/94/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Strain relaxation dependent island nucleation rates during the Stranski–Krastanow growth of GaN on AlN bymolecular beam epitaxy Appl. Phys. Lett. 93, 243105 (2008); 10.1063/1.3046730 Investigation of AlN films grown by molecular beam epitaxy on vicinal Si(111) as templates for GaN quantumdots Appl. Phys. Lett. 89, 231903 (2006); 10.1063/1.2399940 Surfactant effect of gallium during the growth of GaN on Al N ( 000 1 ¯ ) by plasma-assisted molecular beamepitaxy Appl. Phys. Lett. 85, 1421 (2004); 10.1063/1.1782264 Linear alignment of GaN quantum dots on AlN grown on vicinal SiC substrates J. Appl. Phys. 93, 3108 (2003); 10.1063/1.1538334 Influence of AlN nucleation layers on growth mode and strain relief of GaN grown on 6H–SiC(0001) Appl. Phys. Lett. 74, 3660 (1999); 10.1063/1.123214

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Structure of GaN quantum dots grown under ‘‘modifiedStranski–Krastanow’’ conditions on AlN

N. Gogneau,a) D. Jalabert, and E. MonroyCEA-CNRS-UJF Research Group ‘‘Nanophysique et Semiconducteurs,’’ De´partement de RechercheFondamentale sur la Matie`re Condense´e, SP2M/PSC, CEA-Grenoble, 17 rue des Martyrs, 38054-Grenoblecedex 9, France

T. Shibata and M. TanakaCorporate Technical Center, NGK Insulators Ltd., 2-56 Suda-cho, Mizuho, Nagoya 467-8530, Japan

B. DaudinCEA-CNRS-UJF Research Group ‘‘Nanophysique et Semiconducteurs,’’ De´partement de RechercheFondamentale sur la Matie`re Condense´e, SP2M/PSC, CEA-Grenoble, 17 rue des Martyrs, 38054-Grenoblecedex 9, France

~Received 17 February 2003; accepted 27 May 2003!

We propose a procedure to grow GaN quantum dots~QDs! on AlN by using the Ga surfactant effectin plasma-assisted molecular beam epitaxy. Self-formed GaN islands were spontaneously generatedunder vacuum, after evaporation of the Ga bilayer stabilizing the two-dimensional GaN layer grownunder Ga-rich conditions. Island characteristics~size and density! are studied as a function of thenominal amount of GaN deposited. We demonstrate that the QD density can be controlled in the331010 cm22– 231011 cm22 range. It is shown that beyond a given amount of GaN nominallydeposited, there is a coexistence between elastic and plastic relaxation, with GaN islands beingformed on a partially relaxed two-dimensional GaN layer thicker than two monolayers. ©2003American Institute of Physics.@DOI: 10.1063/1.1592866#

INTRODUCTION

The control of the growth mode of nitride semiconduc-tors is an issue of major interest, which appears to be crucialfor the optimization of III-nitride heterostructures in opto-electronic devices. For instance, despite the large lattice mis-match of the AlN–GaN system (;2.5%), the versatility ofplasma-assisted molecular beam epitaxy~PAMBE! and theability to control both the growth mode and the elastic relax-ation mechanism opens the possibility of growing eitherquantum wells or quantum dots~QDs!, depending on thegrowth conditions.

Both the structural and the optical quality of III-nitrideheterostructures grown by PAMBE strongly depend ongrowth parameters. In the case of GaN grown on AlN, thesituation is complex due to the dependence of the growthmode on parameters like the metal/nitrogen ratio or the sub-strate temperature. Thus, growth can proceed by either alayer-by-layer~Frank–Van der Merwe! mode in Ga-rich con-ditions (Ga/N.1) or layer-by-layer growth followed rapidlyby three-dimensional~3D! islanding ~Stranski–Krastanowgrowth mode! in N-rich conditions (Ga/N,1).1 Hence, bycontrolling the growth mode one can obtain either quantumwells or quantum dots by the proper choice of Ga flux andsubstrate temperature, which emphasizes the role of kinetics~and not only of lattice mismatch! in the strain relaxationmechanisms of nitride heterostructures.

The Stranski–Krastanow~SK! growth mode is a widelyused method to synthesize self-organized quantum dots. In

this mode, the deposition of a strained two-dimensional~2D!wetting layer is followed by elastic relaxation through three-dimensional islanding above a given critical thickness. Thisgrowth mode has been observed for different semiconductorfamilies, such as~In, Ga!As on GaAs,2–4 InP on GaInP,5 Geon Si,6,7 and GaN on AlN.8–10 In the specific case of nitridesemiconductors grown by PAMBE, the SK mode is observedwhen growing GaN at high temperature (710– 750 °C) underN-rich conditions, the critical thickness being about twomonolayers~ML !.8,9 The formation of 3D GaN islands hasalso been observed in ammonia MBE. However, it must bestressed that in this case island formation does not obey theSK growth mode but requires a growth interruption.10 In-deed, this difference in growth mode, depending on the typeof nitrogen source in MBE, indicates that a detailed balanceof elastic and surface energy has to be considered, as will beextensively discussed in the present work.

As concerns metalorganic chemical vapor deposition~MOCVD!, formation of 3D GaN islands has been demon-strated when using Si as an antisurfactant.11 This methoddoes not require a large lattice mismatch between GaN andthe substrate, so GaN islands can be formed on AlGaN hav-ing low aluminum content. The shape and the density ofGaN QDs can be controlled by the Si dose, the growth tem-perature, the growth time, and the Al content of the AlGaNlayer below the islands.11–13 More recently, it has beenshown that the SK growth mode can also be used inMOCVD to grow GaN QDs on AlN,14 with the density ofGaN islands varying as a function of GaN coverage.

Returning to the central issue of the present article,which is the control of the growth mode of GaN on AlN, wea!Electronic mail: gogneau@drfmc.ceng.cea.fr

JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER 4 15 AUGUST 2003

22540021-8979/2003/94(4)/2254/8/$20.00 © 2003 American Institute of Physics

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recall that Ga can act as a surfactant during the growth ofGaN on AlN by PAMBE.1 In this case, the SK growth modeis inhibited by the presence of a self-regulated Ga film on thegrowing surface, similar to the case of InAs grown onGaAs15–17 or on InP,18 where the island formation is sup-pressed under excess In conditions.

Taking advantage of the Ga self-surfactant effect, wereport a method to grow GaN quantum dots. In particular, itis shown that the spontaneous rearrangement of a 2D GaNlayer into 3D islands can be induced by a growth interruptionunder certain growth conditions. We describe structural prop-erties of these GaN islands, and we show how to control theirdensity and size as a function of the GaN coverage. More-over, it is shown that beyond a given thickness of GaN layer,there is a coexistence between plastic strain relaxation~through misfit dislocations! and elastic strain relaxation~through island formation!.

EXPERIMENT

Samples were grown on AlN templates deposited byMOCVD on c-sapphire. After a standard chemical degreas-ing procedure and acid cleaning, the substrates were intro-duced in a MECA2000 molecular beam epitaxy chamberequipped with standard effusion cells for Al and Ga evapo-ration. Active nitrogen was produced by dissociation of N2 ina radio-frequency plasma cell. During growth, the substratetemperature was measured using a thermocouple in mechani-cal contact with the molybdenum sample holder, ensuringgood reproducibility. For all the samples in the present study,the substrate temperature was fixed at 750 °C and the growthrate was 0.23 ML/s. Each sample consisted of two GaN is-land layers, one embedded in AlN and the other one on thesurface.

The elastic relaxation induced by the 2D/3D transitionwas measuredin situ by reflection high-energy electron dif-fraction ~RHEED!.

The amount of GaN deposited on AlN was determinedby Rutherford backscattering spectroscopy~RBS! using a 2MeV 4He1 ion beam.

Surface morphology was studiedex situby atomic forcemicroscopy~AFM! in tapping mode scanning a typical sur-face of 1mm31 mm. To perform the statistics we considerthree different positions in every sample, and data presentedcorresponds to an average of at list 300 islands, error barscorresponding to the standard deviation of the gaussian dis-tribution of experimental data. The dimensions of surfacecorrugations measured by AFM may be influenced by thefinite size of the probe tip. In general, the measured topog-raphy will be a convolution of the real surface and the tipshape. An exact deconvolution requires the precise knowl-edge of both the surface and the tip shape; however, a simplecorrection of the lateral size of an island, as measured byAFM, can be obtained assuming a spherical tip. Typicalopening angles of commercial AFM tips are of the order of15°, typical apex radii of the order of 5 nm. Supposing a tipradius of 5 nm and using the facet angle of 32° observed fortruncated pyramids~see later! a constant value of 3 nm canbe used to correct diameters of such pyramids measured by

AFM. Concerning the height of the islands, the effect israther difficult to estimate and no island height correction hasbeen performed in this work. It is important to remark thatmeasurements were performed with a number of differenttips without noticeable difference. Furthermore, the agree-ment between AFM measurements and the quantity of GaNmeasured by RBS demonstrate that further experimental er-rors are not significant.

GROWTH PROCEDURE

The experimental procedure for QD formation is sche-matized in Fig. 1. Prior to GaN deposition, a thin(;100 nm) AlN buffer layer was deposited on the pseu-dosubstrate. A GaN layer was grown under Ga-rich condi-tions at a fixed substrate temperature of 750 °C and a growthrate of 0.23 ML/s. The Ga flux was set high enough so that acontinuous Ga bilayer, about 2 ML thick, was present on thesurface of the growing GaN layer@Fig. 1~a!#.1,19–21 It hasbeen reported previously that the 2D/3D transition associatedwith the SK growth mode of GaN deposited on AlN is in-hibited in the presence of the excess Ga film.1 This filmfavored layer-by-layer growth~Frank–Van der Merwemode!.19 Thus, the GaN epilayer remained 2D even abovethe critical thickness for the SK transition ('2 ML), as evi-denced in the RHEED pattern, which remained streaky.When the N flux was suppressed, while maintaining the Gaflux, the adsorbed Ga film regenerated and the RHEED pat-tern remained unchanged@Fig. 1~b!#. However, when the Ga

FIG. 1. Schematic representation of the experimental procedure for growingself-formed GaN islands.~a! GaN growth under Ga-rich conditions withadsorbed excess Ga bilayer on the growing surface; the GaN epilayer is twodimensional and has a flat surface.~b! When we stop the growth under Gaflux, the surface remains 2D and the Ga film regenerates; the RHEED pat-tern remains unchanged.~c! Under vacuum, the Ga film desorbs in a fewseconds.~d! The GaN layer transforms into facetted 3D islands; the RHEEDpattern evidences this island formation by the presence of additional linescharacteristic of facets.

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flux was shuttered, the Ga adlayer desorbed in a few secondsunder vacuum@see Fig. 1~c!#. Then, the RHEED patternabruptly became spotty, a clear signature of the spontaneousrearrangement of the 2D GaN layer with formation of 3Dislands.22 Eventually, additional lines appeared in theRHEED pattern@~see Fig. 1~d!# which showed that the 3DGaN islands were hexagonal pyramids.

The islands were allowed to evolve for 2 min undervacuum, before being capped with AlN. After recovery of astreaky RHEED pattern, the operation was repeated. In thiscase, the GaN dots were left uncapped. The capped layer ofislands was deposited in order to measure cathodolumines-cence, which will be reported elsewhere. The second layer ofuncapped islands makes possible to perform the structuralcharacterization by atomic force microscopy. The AlN be-tween both dot layers was thick enough to prevent any cor-relation effect.

RESULTS AND DISCUSSION

GaN islands formed using the earlier procedure, schema-tized in Fig. 1, are hexagonal pyramids with$1-103% facets,since the angle deduced from the RHEED pattern isb532°. It is remarkable that this is the same shape as ob-served for GaN islands grown by the SK mode.8,9 Further-more, transmission electron microscopy~TEM! experimentshave revealed that a continuous 2D GaN layer~2 ML thick!is present, connecting the rearranged islands,22 which is simi-lar to the wetting layer existing below GaN QDs in the SKgrowth mode. Therefore, we propose that the method de-scribed in the present work be named ‘‘modified Stranski–Krastanow growth mode,’’ which refers to the earlier men-tioned similarities with the conventional SK mode.

An important parameter governing the formation of GaNQDs in the modified Stranski–Krastanow growth mode is theGaN coverage,Q, defined as the quantity of 2D GaN depos-ited before stopping the growth. QD characteristics~densityand size! have been investigated for varying GaN coveragefrom 2.8 to 13 ML. First of all, it has been found that belowa given threshold coverage (;2.5 ML) no transformation ofthe 2D GaN layer into 3D facetted islands is observed.22

AFM images of GaN QDs obtained by varyingQ from2.8 to 13 ML are displayed in Fig. 2. The figure shows avariation of the GaN island density withQ. In Fig. 3 we canobserve that the island density increases rapidly (2.8 ML<Q<5 ML) before saturation (6 ML<Q<10 ML), fol-lowed by a slow decrease for larger coverages (Q>11 ML). Interestingly, it appears that the QD density canbe controlled over about one order of magnitude (331010 cm22– 231011 cm22 range! for coverages varyingfrom 2.8 to 6 ML. As a comparison, the density of GaN QDsgrown in the SK mode saturates at 231011 cm22 for a cov-erage of only 3 ML,23 and is already 131011 cm22 for acoverage of 2.8 ML.

The relative variation of the in-plane lattice parameter(Da/a0), during the transformation of the 2D GaN layer intoGaN 3D facetted islands has been determinedin situ fromthe RHEED pattern. The result is plotted in Fig. 4, wherea0

is the lattice parameter of the relaxed AlN buffer andDa is

FIG. 2. 1mm31 mm AFM images of the GaN QDs grown atTS5750 °Cand a growth rate of 0.23 ML/s. The GaN coverages are:~a! Q52.8 ML,~b! Q56 ML, ~c! Q510 ML, and~d! Q513 ML. Thez scale is 8 nm forall images.

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the variation due to the elastic relaxation of the GaN layer. Inthis Fig. 4, error bars correspond to the dispersion observedin four different samples. This figure shows that the elasticrelaxation increases forQ varying from 2.8 to 8 ML and thendecreases slowly for greater coverages. The existence ofthese different regimes suggests a change of the relaxationprocess of the 2D GaN layer when the deposited amount ofGaN increases.

The shape of the GaN QDs is also affected by the nomi-nal GaN coverage. Figure 5 shows the variation of the aver-age island characteristics as a function of the nominalamount of GaN coverage. Island height, diameter, and aspectratio follow a single gaussian distribution, within the limitsof statistical error and the error bars in Fig. 5 correspond tothe full width at half maximum of the gaussian fit in eachcase. The average island height, plotted in Fig. 5~a!, in-creases with the GaN coverage up to 8 ML. On the contrary,for a GaN coverage between 9 and 11 ML, the island heightdecreases and remains approximately constant for greatercoverages. As regards the island base diameter, Fig. 5~b!shows its variation as a function of GaN coverage. Withinthe statistical error, the diameter remains approximately in-dependent of GaN coverage, with a slight increase for thick-est coverages. Finally, Fig. 5~c! shows the variation of theaspect ratioh, defined as island height/island diameter. Thedashed line corresponds to the aspect ratio of a nontruncatedhexagonal pyramid, which demonstrates that the self-formedGaN islands are truncated hexagonal pyramids. Since the

diameter remains approximately constant with the GaN cov-erage, the aspect ratio follows the behavior of island height,i.e., it increases up to 8 ML before decreasing markedly forhigher coverages.

The results displayed in Figs. 4 and 5~c! reveal a strongcorrelation between the QD aspect ratio and the strain relax-ation. Actually, one may wonder what the strain state of the2D GaN layer is just before island formation. In particular,one may expect that plastic relaxation associated with misfitdislocations occurs for sufficiently thick 2D GaN layers.

It has been shown that relaxation is purely elastic forsmall dots (Q53 ML), and no dislocations have been foundto be associated with the rearrangement of the 2D GaNlayer.22 As elastic relaxation is, in first approximation, pro-portional to the aspect ratio of the islands,24 the increasingaspect ratio observed up to 8 ML is consistent with the in-

FIG. 3. Total density of GaN QDs formed by spontaneous re-arrangement ofa 2D GaN layer under vacuum, at a substrate temperature of 750 °C fordifferent GaN coverages.

FIG. 4. Relative variation of the in-plane lattice parameter (Da/a0) mea-sured during the rearrangement of the GaN 2D layer into 3D facetted is-lands, as a function of the nominal GaN coverage.

FIG. 5. Variation of the average height~a!, diameter~b!, and aspect ratio~c!of the GaN QDs formed using the modified SK growth mode, as a functionof the GaN coverage. The dashed line in figure~c! indicates the aspect ratioof nontruncated pyramids.

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crease of elastic relaxation observed in Fig. 4. For a GaNcoverage thicker than 8 ML, both the aspect ratio and theelastic relaxation~during island formation! decrease. Alongthe views detailed in the article of Kern and Mu¨ller,24 thisbehavior could indicate a decreasing strain of the 2D layer~before rearrangement! when its thickness exceeds 8 ML.Above this nominal amount of GaN, we propose that thethickness of the 2D layer below the islands exceeds the 2 MLthat correspond to the so-called wetting layer. Moreover, wepropose that the strained 2D GaN layer~connecting the is-lands! is then partially relaxed~contrary to the 2-ML-thickwetting layer which is perfectly matched to AlN for the SKgrowth mode! due to the presence of dislocations.

The earlier hypothesis is strongly supported by a com-parison between the total amount of GaN deposited, mea-sured by RBS, and the amount of material in the QDs, ex-tracted from AFM data. Figure 6 shows the total quantity ofGaN measured by RBS as a function of the nominal amountdeposited. We must take into account that, at 750 °C, wehave a GaN dissociation/desorbtion rate of 0.18 ML/min un-der vacuum. The dashed line indicates the nominal amountof GaN contained in a 2D layer grown under Ga-rich condi-tions ~presence of a Ga bilayer on the growing surface!, cor-rected by 0.36 ML of GaN, which corresponds to the GaNdecomposition during the annealing under vacuum~2 minafter the 2D/3D transition!. The close agreement between thecalculation and the experimental data confirms that theamount of GaN present on AlN is the nominal amount ofGaN deposited corrected by the GaN decomposition.

We have extracted from the AFM data the total amountof GaN contained in the islands as a function of nominallydeposited GaN. The results are plotted in Fig. 7~a!. The solidline indicates the expected behavior assuming that a 2-ML-thick 2D GaN layer is present below the islands. The dashedline corresponds to the case when no 2D GaN layer ispresent. We can observe that for GaN coverages up to 8 ML,the experimental data are consistent with the presence of a2-ML-thick wetting layer, which corroborates high-resolution transmission electron microscopy~HRTEM!

measurements.22 In contrast, for coverages higher than 8ML, the deviation from a linear behavior is the signature ofthickening of the 2D layer. In fact, from Fig. 7~a!, it is foundthat forQ.8 ML the amount of GaN contained in dots tendsto saturate to about 6 ML. This amount is limited by geo-metrical considerations, as the aspect ratio cannot exceed thevalue corresponding to a full pyramid (h50.27). However,as shown in Fig. 5~c!, for an 8 ML GaN coverage, the aspectratio is still slightly below its theoretical maximum value.This further suggests that the change in the island formationregime observed around 8 ML GaN coverage is related moreto kinetic factors during the rearrangement of the 2D GaNlayer and the island formation, such as a temperature-dependent capture radius. This is supported by the observa-tion, shown in Fig. 2, that dots are clearly separated fromeach other even forQ as high as 13 ML.

From the comparison between RBS and AFM data, wecan estimate the thickness of the 2D layer below the GaNislands. Figure 7~b! shows the evolution of the thickness ofthis layer, as a function of the nominal amount of GaN de-posited. For low coverages (2.8 ML<Q<8 ML), the 2Dlayer is approximately 2 ML thick, in agreement with HR-TEM measurements shown in Ref. 22. However, for largecoverages (Q.8 ML), due to the incomplete transformationof GaN into islands, the 2D GaN layer starts to thicken.

The correlation of thickening of the 2D layer with theelastic relaxation results in Fig. 4 suggests that elastic and

FIG. 6. Amount of GaN contained the layer present on AlN, measured byRBS as a function of the nominal GaN deposited. The dashed line representsthe nominal amount to GaN in a 2D layer corrected by 0.36 ML correspond-ing of GaN dissociation/desorption~amount of GaN decomposed after 2 minof annealing under vacuum!.

FIG. 7. ~a! Total volume contained in GaN islands as a function of thenominal amount of deposited GaN. The solid line corresponds to a 2-ML-thick GaN layer below the islands, the dashed line corresponds to the casewithout the 2D layer.~b! Variation of the GaN 2D layer thickness as afunction of the nominal amount of GaN.

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plastic relaxation coexist for a nominal GaN coverage above8 ML. However, one may wonder if plastic relaxation occursduring the growth of the 2D GaN layer, above a criticalthickness of about 2 ML, or during the Ga-film evaporation,with the 2D GaN layer being completely strained on AlNbefore evolving under vacuum. To answer this question, wehave donein situ measurements of the strain state of a 2DGaN layer grown on AlN under Ga-bilayer conditions atTS

5750 °C. Figure 8 shows the relative variation of the in-plane lattice parameter, measured by RHEED, as a functionof the layer thickness. First, a sudden decrease of the in-plane lattice parameter is observed, followed by its rapidincrease. The inset in Fig. 8 shows the same measurementbut, in this case, the GaN surface has been exposed to a Gaflux prior to GaN growth. We observe a similar transientbefore opening the N cell, which demonstrates that this rapidvariation of (Da/a0) corresponds to the formation of the Gabilayer on the surface. Thus, this experiment gives a furtherdemonstration that a slow relaxation process, tentatively as-signed to progressive introduction of misfit dislocations,starts from the beginning of the growth.25 Although a precisevalue is difficult to extract, the critical thickness should bevery small, as will be discussed later. On the other hand,HRTEM measurements reveal that for small dots (Q53 ML), the relaxation is purely elastic without anydislocations.22 This suggests that during island formation, thestrain state of the 2D GaN layer is modified, which impliesthe disappearance of misfit dislocations during the mass re-arrangement, as schematized in Fig. 9. Based on the set ofexperimental data, we tentatively propose that the first 2 MLof GaN remain strained on the AlN layer during the growth@Fig. 9~a!#. This situation persists as long as the amount ofGaN deposited remains smaller than@Fig. 9~b!# or equal to@Fig. 9~c!# 8 ML, since all the GaN material above the 2DGaN layer is transformed into islands@see Fig. 7~a!#. Forhigher coverages, because the amount of GaN evolving inislands is limited, misfit dislocations are not totally elimi-nated during rearrangement@Fig. 9~d!#, and a residual plasticrelaxation takes place. This relaxation increases with the 2Dlayer thickness@Fig. 9~e!#.

We believe that the model presented in Fig. 9 opensprospects in the controversial issue of the critical thicknessof GaN grown on AlN. Values reported in the literature varyfrom about 0.5 nm~2 ML!26 to more than 5 nm~20 ML!,27

including several determinations around 3–4 nm.28,29 Thiswide scatter further illustrates, that determination of the criti-cal thickness in nitride growth is intricate and dependent onthe growth technique. In this context, our data suggest thatthe critical thickness of GaN on AlN could be of the order of2 ML, whatever the growth mode. For the SK mode, this isverified exactly as 3D islanding occurs above about 2 ML.For the Frank–Van der Merwe growth mode, direct observa-tion of misfit dislocations by TEM is not yet available, butthe interpretation of the present data schematized in Fig. 9 isconsistent with the idea that the 2D layer connecting theislands is partly relaxed above about 2 ML, which shouldthen correspond to the plastic critical thickness.

At this stage, one may discuss the possible mechanismgoverning the 2D/3D transition in the modified SK growthmode. We recall that the GaN layer remains 2D in presenceof the Ga surfactant film. The evaporation under vacuum ofthe Ga adatoms leads to a rapid transformation of the bareGaN layer into 3D facetted islands. Such a behavior, i.e.,inhibition of the island formation by a surfactant, has previ-ously been shown for other semiconductor families and canbe of kinetic or energetic origin.

From the kinetic viewpoint, island inhibition observedfor Ge on Si in presence of As or Sb30,31 and for~Ga, In!Ason GaAs using Te32,33 has been assigned to a surfactant-induced decrease of the diffusion length of the growing spe-cies. However, in our case, the presence of the Ga film re-

FIG. 8. Relative variation of the in-plane lattice parameter during thegrowth of GaN on AlN under Ga-rich conditions, at a fixed substrate tem-perature of 750 °C and a growth rate of 0.23 ML/s. For the main figuregrowth was started directly, whereas in the inset we have exposed the sur-face to the Ga flux for 5 s before starting the GaN growth.

FIG. 9. Schematic of GaN growth on AlN under Ga-rich conditions atTS

5750 °C. ~a! The initial 2 ML two-dimensional GaN film is dislocationfree. ~b! and ~c! Relaxation is purely elastic without any dislocations.~d!and ~e! Elastic and plastic relaxation coexist.

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sults in an increased diffusion length of N adatoms,according toab initio calculations.34 This enhancement ofthe surface mobility is consistent with the disappearance ofRHEED oscillations during the growth of the 2D GaN layerunder Ga-rich conditions, which indicates a step-flow growthmode.20 Moreover, when we stop the growth under Ga flux,the GaN layer remains 2D. This behavior establishes verywell that the 2D/3D growth mode transition is not kineticallyinhibited for the GaN/AlN system grown under Ga-rich con-ditions.

The 2D/3D transition can also be affected by changingthe energy balance of the system, depending on growth con-ditions. Hence, suppression of island formation when grow-ing ~Ga, In!As on GaAs15,35 or on InP18 under In-rich condi-tions has been assigned to an increase of surface tension dueto the presence of an adsorbed In layer. Higher surface ten-sion implies a higher energy cost for island creation. How-ever, such an explanation does not hold in the case of thegrowth of GaN on AlN, sinceab initio calculations haveshown that the Ga surfactant actually decreases the surfaceenergy fromg0001

stoichiometric5100 meV/Å2 @bare ~0001! GaNsurface# to g0001

Ga rich525 meV/Å2 ~GaN surface in presence ofthe Ga adlayer!.19 The terms stoichiometric and Ga rich referto the Ga/N ratio value during growth, i.e., Ga/N;1 andGa/N@1, respectively. More generally, it has been found thata surfactant may alternately result in a decrease of surfaceenergy. Such a decrease should foster island creation pro-vided the surface energy is isotropic. However, an aniso-tropic distribution of surface energies has been proposed asthe origin of the 2D/3D transition in the Ge/Si system.36 Therole of surface energy anisotropy on the formation, shape andstability of islands has been analyzed in detail by Zhang37 ina complete theoretical study of the Si/Ge system.

As discussed earlier, the reduction in surface energy dueto the presence of the Ga film should favor island formation,in contrast with experimental observations. To overcome thisapparent contradiction, one must do a more detailed analysisof the energy balance, taking into account the facet energy ofGaN islands. Actually, the total energy per unit surface of the~GaN/AlN! system consists of three terms: the elastic energyEelastic, the surface energyEsurface, and the edge energyEedge.

38,39 For simplicity, Eedgewill be neglected.In the case of a 2D layer growing along the~0001! axis,

the total energy is given by

ET2D5Eelastic1g0001, ~1!

whereg0001 is the surface energy for the@0001# plane, whichdepends on growth conditions. In the case of 3D islanding,the relaxation of elastic energy is somewhat compensated bythe generation of a larger surface, which results in an in-crease of the surface energy. The expression of the total en-ergy is then given by

ET3D5Eelastic8 1g0001~12a!1a

g1 – 103

cosb, ~2!

whereg1-103 is the surface energy of$1-103% facets andacorrespond to the surface ratio covered by the facets@facetangle b532° with respect to the~0001! surface as men-tioned earlier#.

The 2D/3D transition is determined by the energy differ-ence between the 2D and 3D structures

DET5ET3D2ET

2D5DEelastic1aS g1 – 103

cosb2g0001D , ~3!

whereDEelastic5Eelastic8 2Eelastic8 .Let us first consider the case of GaN growth under Ga-

rich conditions. The GaN layer remains 2D, which impliesthat the difference of the total energies,DET , is positive, asthe difference of the elastic energy variation,DEelastic, isnegative~3D islanding implies strain relaxation!. Using Eqs.~1! and ~2!, one can then deduce the following relation:

g1 – 103.g0001Ga rich

•cosb. ~4!

Let us now consider the case of GaN under vacuum. TheGa film is rapidly evaporated and the bare 2D GaN evolvesinto islands. Then,DET becomes negative. Further analysiswould require a detailed calculation ofDEelastic, which isbeyond the scope of the present work. However, this diffi-culty can be circumvented by noticing that, when exposing abare~0001! GaN surface under vacuum at a temperature suf-ficiently high for thermal decomposition to occur, roughen-ing is observed due to the formation of$1-103% facets, simi-lar to those of rearranged GaN dots. In the case of athermally roughened thick GaN layer, there is no differenceapriori in the elastic energy stored in smooth or rough film,allowing one to write

g1 – 103,g0001stoichiometric

•cosb. ~5!

This experiment supports the idea that the surface energy ofsuch facets is lower than the energy of~0001! surface. Then,combining Eqs.~4! and ~5! leads to

g0001Ga rich

•cosb,g1 – 103,g0001stoichiometric

•cosb ~6!

providing the limits between whichg1 – 103might be situated,i.e., 21 meV/Å2,g1 – 103,83 meV/Å2 to allow re-arrangement of a 2D GaN layer into 3D islands possibleunder vacuum.

Thus, in this framework, it is concluded that the 2D/3Dtransition in the modified SK growth mode is energeticallyinhibited, provided that the value ofg1 – 103 lies in the abovewindow.

CONCLUSION

We have described a procedure to grow GaN QDs onAlN by PAMBE, using the Ga surfactant effect. It has beendemonstrated that the Ga film, about 2 ML thick, present onthe growing surface, inhibits the SK transition, due to thedecreased surface energy and the increased adatom diffusionlength which favors a layer-by-layer growth~Frank–Van derMerwe growth mode!. The GaN island formation resultsfrom a spontaneous rearrangement of the 2D GaN layer into3D facetted islands when a growth interruption is performedunder vacuum. The quantum dots obtained with this methodare hexagonal truncated pyramids with a shape similar to thatobserved for GaN islands grown by the SK growth mode.

2260 J. Appl. Phys., Vol. 94, No. 4, 15 August 2003 Gogneau et al.

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Their facets are$1-103% planes inclined by 32° with respectto ~0001!. The existence of a 2D GaN layer inserted betweenthe AlN layer and the QDs has been shown.

The influence of the GaN coverage on the GaN islandcharacteristics has been studied, demonstrating the possibil-ity of controlling the island density in the 331010 cm22– 231011 cm22 range. We have also established that theamount of GaN nominally deposited affects both the islandshape and the strain relaxation (Da/a0) that occurs duringthe QD formation.

For an amount of GaN up to 8 ML, the relaxation hasbeen found to be purely elastic, with no dislocations associ-ated with the rearrangement of the 2D GaN layer in islands.By contrast, for higher GaN coverages, a plastic strain relax-ation occurs simultaneously with 3D island formation. Thecoexistence of elastic and plastic relaxation is assignedmainly to the limitation, at 6 ML, of the amount of GaNtransformed into islands, which induces a thickening of the2D layer beyond 2 ML for GaN coverages higher than 8 ML.Then, it has been tentatively suggested that 2 ML can beconsidered as the critical thickness of GaN deposited onAlN, with subsequent islanding~in the case of the SK growthmode! or misfit dislocation formation~in the case of theFrank–Van der Merwe growth mode! being partly deter-mined by kinetic conditions prevailing during the growth.

ACKNOWLEDGMENTS

The authors acknowledge Y. Genuist and M. Falco fortechnical support. Useful discussions with Dr. C. Adelmannand Dr. J. M. Gerard are also acknowledged.

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