Modified Stranski-Krastanov Growth in Stacked Layersof Self-Assembled Cubic GaN/AlN Quantum Dots

E. Martinez-Guerrero (a), R. Beneyton (b), C. Adelmann (a),B. Daudin (a), Le Si Dang (b), G. Mula (a, c), and H. Mariette1) (b)

(a) CEA–CNRS research group ‘‘Nanophysique et Semiconducteurs“,Departement de Recherche Fondamentale sur la Matiere Condensee, CEA/Grenoble,17 rue des Martyrs, F-38054 Grenoble Cedex 9, France

(b) CEA–CNRS research group ‘‘Nanophysique et Semiconducteurs“,Laboratoire de Spectrometrie Physique, Universite J. Fourier, Grenoble I,CNRS-UMR5588, BP87, F-38402 Saint Martin d’Heres, France

(c) INFM and Dipartimento di Fisica, Universita degli studi di Cagliari,Cittadella Universitaria, I-09042 Monserrato Italy

(Received June 25, 2001; accepted July 7, 2001)

Subject classification: 68.37.Ps; 68.55.Jk; 68.65.Hb; 81.07.Ta; 81.15.Hi; S7.14

In a stacked structure of cubic GaN/AlN islands grown in a Stranski-Krastanov mode, the criticalthickness for the GaN islanding (2D–3D transition) decreases by a factor of up to 10 between theinitial dot layer and the third one. This variation of the critical thickness is strongly dependent onthe AlN spacer thickness. Moreover, we observe systematically a change of the quantum dot strainstate and an increase of island size, depending on the GaN island layer number.

Introduction One of the main challenges in the fabrication of self-assembled semicon-ductor quantum dots (QDs) is to control their size distribution together with their or-dering on the substrate surface. A widely used approach to reduce this size inhomo-geneity is to stack several dot layers on top of each other, where each dot layer isseparated from the previous one by a spacer layer of thickness ts. It has been pointedout that, if ts is kept thin enough, anisotropic strain fields of underlying islands create astrain energy modulation at the surface, and induce stacks of vertically aligned andmore homogeneous islands.However, recent experiments [1, 2] on Ge/Si(001) quantum dots in multilayer struc-

tures clearly demonstrated that the critical thickness in the second dot layer is signifi-cantly lower than that in the first one. It was also observed in this system, that such adecrease of the critical thickness in the upper dot layers was strongly dependent on thethickness of the Si spacer layer. A quantitative analysis has been proposed very re-cently to account for these results [3]: by calculating the strain distribution within con-tinuous elasticity framework, it has been demonstrated that the critical thickness forplanar growth in stacked layers is reduced and that excess material due to a thinnerwetting layer accumulates to form larger islands.The first experimental results on this issue are reported here for cubic GaN/AlN quan-

tum dots, a promising system for ultraviolet optoelectronic devices [4]. We directly evi-dence that strain fields generated by underlying islands reduce drastically the critical

1) Corresponding author; Tel.: ++33.(0)4.38.78.56.88; Fax: ++33.(0)4.38.78.51.38;e-mail mariette@drfmc.ceng.cea.fr

phys. stat. sol. (a) 188, No. 2, 711–714 (2001)

# WILEY-VCH Verlag Berlin GmbH, 13086 Berlin, 2001 0031-8965/01/18811-0711 $ 17.50þ.50/0

thickness for all but the initial dot layer in a stack of coherent GaN islands grown inthe Stranski-Krastanov (SK) mode, if the thickness ts of the AlN spacer layer is keptsmaller than a certain value t0. As a consequence, a decrease of the strain relaxation isobserved in the upper QD layers, together with an increase of the dot size as a func-tion of the dot plane number. Knowing this effect of modified SK growth, we proposea method to improve the homogeneity of the GaN quantum dots in a GaN/AlN multi-layer structure.

Sample Growth The samples were grown by plasma-assisted molecular-beam epitaxy.The metal fluxes were provided by conventional effusion cells, while active nitrogenresulted from radio-frequency dissociation of N2 using a plasma cell. The substrate con-sisted of a 3 mm thick 3C-SiC(001) layer grown by chemical vapor deposition on Si(001)[5]. The growth was monitored in situ using reflection high-energy electron diffraction(RHEED). In particular, the strain relaxation of the GaN QDs was continuously fol-lowed by analyzing the streak spacing in the RHEED pattern. A smooth AlN bufferlayer was first obtained after the deposition of about 5 nm as evidenced by the streakyRHEED pattern, for a growth temperature of Ts ¼ 720�C.Figure 1 shows both the time tc corresponding to the onset of the 2D–3D transition

and the maximum strain relaxation Da=a0 of GaN as a function of the dot layer num-ber, for a stack of eleven GaN dot layers separated to each other by 5 nm of AlN. Themaximum strain relaxation for each dot layer is deduced from real-time measurementsof the in-plane lattice parameter by recording the relative variation of the RHEEDstreak separation Da=a0, with respect to the initial AlN lattice parameter a0. For fullyrelaxed GaN on AlN, Da=a0 is about 2.8%. The inset in Fig. 1 shows the variation ofDa=a0 during the growth of one given GaN QD layer. This puts in evidence the charac-teristic time tc corresponding to the critical thickness (the wetting layer) at which therelaxation starts to occur: during this initial stage of GaN growth, the RHEED patternremains streaky [4]. At the onset of the relaxation, the RHEED pattern changesabruptly into Bragg spots, revealing both the formation of GaN islands during a timet3D and the yield of relaxation achieved for this QD plane number. Interestingly, Fig. 1shows that after three QD planes, a steady-state equilibrium is reached, for which boththe critical thickness and the strain state in the dots exhibit a stable value.

712 E. Martinez-Guerrero et al.: Modified Stranski-Krastanov Growth in Stacked Layers

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Structural Characterization Figure 2 evidences the variation observed by atomic-forcemicroscopy for the various dot planes: the first one was grown on a thick AlN bufferlayer, whereas the second and third ones were grown on the top of one and two dotlayers, respectively, capped by a AlN spacer layers of 5 nm. The striking features de-duced from these observations are that (i) the dot size increases versus the dot planenumber with a diameter changing from 23 nm for the first plane to 33 nm for the thirdone; (ii) the density decreases by a factor 2; (iii) the aspect ratio of the dots is changingfrom a value of about 6 to 12 together with a dispersion of the dot size which increasesbetween the first plane and the third one.To further examine the influence of the dot plane number, we report in Fig. 3 the strain

relaxation deduced from an analysis of the RHEED patterns for the first three dot layerscapped by 5 nm thick AlN spacers. Figure 3a shows a strong variation of the relaxation ofthe dot layers when the GaN deposition time is the same for all three layers: the GaNQDs in the first layer reach a maximum strain relaxation of 2.8 % on the 50 nm thick AlNbuffer layer, whereas the relaxation is only 2.1% and 1.4% for the second and the thirdQD layer, respectively. Such an evolution of the relaxation in the dot planes is well consis-tent with the variation of the dot aspect ratio obtained from the AFM data.However, if the GaN deposition time is adjusted to the variation of the critical thick-

ness in order to ensure that the GaN quantity deposited after the 2D–3D transition isconstant, the relaxation of the first three layers is similar, varying only between 2.1%and 1.8% (see Fig. 3b). This shows that such a modification of the deposition timesmay lead to more homogeneous QDs in the different layers.

phys. stat. sol. (a) 188, No. 2 (2001) 713

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Fig. 2. AFM results of cubic GaN QDs grown on AlN thick layer (first plane) and 5 nm AlNlayers (second and third planes), respectively. The QD density and aspect ratio are varing by afactor 2 between the first and the third dot planes

Discussion All these results evidence the strong variation of both the critical thicknessand the strain state in the first three dot layers. This indicates that the strain fieldinduced by the buried GaN dot layers and mediated by the AlN spacer layer is themain parameter which governs the quantum dot formation and leads to a steady-stateregime after deposition of three dot layers. Such elastic interaction has been calculatedrecently by Priester [3] in the case of Si/Ge: it can explain a decrease of the criticalthickness by several monolayers between the first dot plane and the second one.Knowing this effect, namely the decrease of the GaN critical thickness in the upper

layers, one can get rid of this variation in order to improve the homogeneity of the dotsin all layers. If one does not keep the GaN deposited amount constant in all layers, butadjusts this amount according to the effective critical thickness in subsequent layers,this can lead to the formation of islands having a better homogeneity. This is shown inFig. 3b where the GaN deposition time has been varied by a factor 4 in order toaccount for the variation of the critical thickness ts. The strain state in the three dotlayers varies now by less than 50% in contrast to the former case (constant amount ofGaN deposited) for which the strain state variation was more than 100%. Such results,giving a hint of islands having almost the same size and height distribution in all layers,should be confirmed by transmission electron microscopy study.

References

[1] V. Le Thanh, V. Yam, P. Boucaud, F. Fortuna, C. Ulysse, D. Bouchier, L. Vervoort, andJ.M. Lourtioz, Phys. Rev. B 60, 5851 (1999).

[2] O.G. Schmidt, O. Kienzle, Y. Hao, K. Eberl, and F. Ernst, Appl. Phys. Lett. 74, 1272 (1999).[3] C. Priester, Phys. Rev. B 63, 153303 (2001).[4] E. Martinez-Guerrero, C. Adelmann, F. Chabuel, J. Simon, N. T. Pelekanos, G. Mula, B. Daudin,

G. Feuillet, and H. Mariette, Appl. Phys. Lett. 77, 809 (2000).[5] G. Ferro, H. Vincent, Y. Monteil, D. Chaussende, and J. Bouix, Mater. Sci. Forum 264, 227

(1998).

714 E. Martinez-Guerrero et al.: Modified Stranski-Krastanov Growth in Stacked Layers

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Fig. 3. Variation of the in-plane lattice parameter Da=a0 during the growth of three GaN dot layerswith a spacer of 5 nm thick AlN: a) GaN deposition time is kept constant for the three dot planes,b) GaN deposition time has been varied by a factor 4 between the first QD plane and the twoother ones in order to compensate the variation of the critical thickness