Factors influencing epitaxial growth of three-dimensional Ge quantum dot crystals on pit-

patterned Si substrate

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Nanotechnology 24 (2013) 015304 (7pp) doi:10.1088/0957-4484/24/1/015304

Factors influencing epitaxial growth ofthree-dimensional Ge quantum dotcrystals on pit-patterned Si substrate

Y J Ma, Z Zhong, X J Yang, Y L Fan and Z M Jiang

State Key Laboratory of Surface Physics, Key Laboratory of Micro- and Nano-Photonic Structures(Ministry of Education) and Department of Physics, Fudan University, Shanghai 200433,People’s Republic of China

E-mail: zmjiang@fudan.edu.cn

Received 18 September 2012, in final form 16 November 2012Published 7 December 2012Online at stacks.iop.org/Nano/24/015304

AbstractWe investigated the molecular beam epitaxy growth of three-dimensional (3D) Ge quantumdot crystals (QDCs) on periodically pit-patterned Si substrates. A series of factors influencingthe growth of QDCs were investigated in detail and the optimized growth conditions werefound. The growth of the Si buffer layer and the first quantum dot (QD) layer play a key rolein the growth of QDCs. The pit facet inclination angle decreased with increasing buffer layerthickness, and its optimized value was found to be around 21◦, ensuring that all the QDs in thefirst layer nucleate within the pits. A large Ge deposition amount in the first QD layer favorsstrain build-up by QDs, size uniformity of QDs and hence periodicity of the strain distribution;a thin Si spacer layer favors strain correlation along the growth direction; both effectscontribute to the vertical ordering of the QDCs. Results obtained by atomic force microscopyand cross-sectional transmission electron microscopy showed that 3D ordering was achievedin the Ge QDCs with the highest ever areal dot density of 1.2× 1010 cm−2, and that the lateraland the vertical interdot spacing were ∼10 and ∼2.5 nm, respectively.

(Some figures may appear in colour only in the online journal)

1. Introduction

In general, the term three-dimensional (3D) quantum dotcrystals (QDCs) refers to an array of quantum dots (QDs)positioned periodically in three spatial dimensions [1].However, precisely speaking, apart from the 3D ordering,other critical requirements must also be met to forma regimented QDC, i.e. that the QDs are small andhomogeneous, and that the interdot spacing is small enoughfor strong wavefunction overlapping [2, 3]. The QDs in3D artificial QDCs play a role similar to that of atomsin real crystals. The band offsets at the interfaces betweenthe QD and the matrix in the QDC also play a roleanalogous to that of the periodic potential in real crystals.When QDs are 3D ordered and in close proximity toone another, significant carrier wavefunction overlap occurs.QD ensembles under such regimented structure modification

will dramatically change the electronic structures and thecarrier transport properties. Theoretical investigations havedemonstrated interesting electronic and optical propertiesof the QDCs such as negative differential conduction [4],enhanced light absorption [5] and light-mass polaritons [6].Experimental work showed that 3D ordering of the PbSe/PbTeQDs dramatically enhanced the thermoelectric figure of meritas compared to the random alloys case due to increasedphonon scattering and reduced thermal conductivity [7].Similar behaviors can be expected in the Si/Ge QD systems.It has also been demonstrated that the 3D ordered Ge QDscan act as a nanoscaled phononic crystal with functionalacoustic properties [8]. The Si/Ge system is of special interestbecause of its excellent compatibility with conventional Siintegration technology. Meanwhile, the addressable QDs areattractive due to the potential applications in electronic andoptoelectronic devices [9] and even possibly in quantum

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Nanotechnology 24 (2013) 015304 Y J Ma et al

information processing [10, 11]. This requires lateral as wellas vertical coupling of Ge QDs, for which dense arrays of GeQDs at specified sites are needed.

Already, major progress in fabrication of site-controllableGe QDs has been achieved by the combination of nanopatternlithography and self-assembling growth techniques [2,12–18]. However, due to the limitations of pattern lithography,although 3D ordered Ge QD arrays have been reportedpreviously, the periodicities, and in particular the interdotspacings, were too large for neighboring QDs to have anycoupling effect. Growth of Ge QDCs with strong couplingneeds ordered pit patterns with small pit size and closeproximity of pit to pit. The recently developed patterningtechnique of polystyrene (PS) nanosphere lithography (NSL)is promising for the fabrication of densely ordered pitpatterns [13, 14]. Detailed growth investigations of uniformQD arrays with small dot size, high areal density andsmall interdot spacing are very desirable, which can providematerials support for both the fundamental physics and deviceapplication research into coupled QD systems.

In this paper, we demonstrated the molecular beamepitaxy (MBE) growth of 3D Ge QDCs on pit-patterned Sisubstrates via NSL, and investigated in detail how growthconditions influence the nucleation, ordering both laterallyand vertically, and size uniformity of Ge QDs in QDCs andtheir microstructures. The growth of the Si buffer layer andthe first QD layer were found to be the determining factorsin the growth of QDCs. Also, spacer layer thickness wasfound to be crucial in the layer stacking growth of QDCs.Furthermore, it is demonstrated that a low Si growth ratecould dramatically promote the overall QD homogeneity inthe QDCs. By optimizing the growth conditions, ten-layer 3Dordered Ge QDCs were achieved with a dot size dispersionof 10% and an areal density of 1.2 × 1010 cm−2. Atomicforce microscopy (AFM) and cross-sectional transmissionelectron microscopy (XTEM) were used to investigate themicrostructures of the QDCs.

2. Experimental details

We start with the fabrication of a densely ordered pitpattern on Si (001) substrate via NSL. PS spheres withmean diameter of 100 nm were self-assembled to form ahexagonal close-packed ordered monolayer (ML) on the Si(001) substrates in a large area, as shown in figure 1(a).The same ordered nanopits were obtained after multiplesteps including final selective etching of the Si with a KOHsolution, as shown in figure 1(b). The nanopits have aninverted pyramid shape. The mean lateral size and depthof the nanopits were ∼50 and ∼20 nm, respectively. Thelateral period of the pit pattern is around 100 nm, the sameas the diameter of the PS spheres. Before loading into asolid source MBE chamber, the pre-patterned Si substrateswere cleaned by the standard RCA method and passivatedwith HF. The procedures of growth of the Ge QDCs are asfollows. The patterned substrate was first heated to 780 ◦Cfor 5 min to desorb the passivating hydrogen. Then the Sibuffer layer was deposited. The first QD layer was grown by

Figure 1. AFM images of (a) the self-assembled, hexagonalclose-packed single ML PS sphere pattern and (b) the orderednanopit pattern on a Si substrate.

depositing Ge with increasing substrate temperature, followedby Si spacer layer deposition. The subsequent QD layers weregrown one by one, separated by Si spacer layers of the samethickness. After growth, the samples were cooled down toroom temperature immediately. The surface morphologies ofthe samples were characterized using AFM. XTEM imageswere also obtained to provide more detailed information onthe microstructures of the Ge QDCs.

Generally, the shape and size uniformity of the Ge QDsgrown are correlated with a number of growth parameters.In achieving size uniform Ge QDCs on pit-patterned Sisubstrates with high structural perfection, the crucial pointsare the growth of the Si buffer layer, that of the first QD layerand that of the Si spacer layer. In this section, a number ofgrowth parameters and conditions, including the depositionamount, deposition temperature and rate, were systematicallystudied for growing well-structured QDCs, together with theirmicrostructure investigation.

2.1. Buffer layer thickness and temperature

The growth rates of Si and Ge were initially set to be0.5 and 0.06 A s−1, respectively. After deposition of theSi buffer layer at 450 ◦C, 5 ML thick Ge was depositedwith ramping the substrate temperature from 450 to 550 ◦C,followed by the deposition of additional 3 ML thick Ge at550 ◦C, which led to the formation of the first layer QDsas shown in figures 2(a)–(c) on Si buffer layers of differentthicknesses: 30, 70 and 90 nm, respectively. As can be seenin figure 2(a), only a proportion of the pits were filled withGe dots while for figure 2(b) almost all the pits were filledwith Ge dots, forming an array of Ge QDs. As for figure 2(c),due to an overdose growth of the Si buffer layer (90 nm),the nanopits became very shallow or even flattened after theSi buffer layer deposition. Large dome-shaped QDs wereformed within some shallow pits due to a reduced pit-fillingeffect, and some pits remained flat. These different resultsoriginate from the different pit profiles after the buffer layergrowth. Figure 2(f) illustrates the pit profiles obtained byAFM and the corresponding pit facet inclination angles α(the angle between the pit facet and the substrate surface,i.e. 0◦, corresponds to a facet parallel to the substrate surface)to the buffer layer thickness. The inclination angle decreasedwith increasing buffer layer thickness.

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Figure 2. AFM images of the surface after the growth of the first QD layer. The thickness of the Si buffer layer is 30, 70, 90, 64 and 64 nmfor (a), (b), (c), (d) and (e) respectively. (f) Pit profiles and the corresponding pit facet inclination angles (α) with the buffer layer thickness.Detailed growth parameters and conditions are listed in table 1.

Table 1. Growth parameters and conditions for the samples shown in figures 2(a)–(e).

SampleBuffer layerthickness (nm)

Buffer layer growthtemperature (◦C)

Ge depositionamount (ML)

Ge depositiontemperature (◦C)

a 30 450 8 450→ 550b 70 450 8 450→ 550c 90 450 8 450→ 550e 64 450 8 450→ 570f 64 400 8 450→ 550

Generally, the site-selective nucleation nature of the Geislands originates from the different local surface chemicalpotentials on patterned substrate [19]. The local surfacechemical potentials are closely related to the local surfacecurvatures. Ge islands preferentially nucleate in the siteswith local minima in the surface chemical potential [20].Theoretical investigations have demonstrated how the pitfacet inclination influences the nucleation of islands on pit-patterned substrates from the viewpoint of elastic energy [21,22], and concluded that the pit facet inclination angle criticallyaffects island positioning. For the dense pit pattern in ourexperiments, appropriate growth conditions for the first QDlayer should be close to the case in figure 2(b) (17.5◦). Less(figure 2(a)) or more (figure 2(c)) buffer layer thickness wouldlead to both a partially random dot nucleation and a pooruniformity. However, as shown in figure 2(b) there are a fewlarge dome-shaped QDs, showing a less perfect ordering;further optimized buffer layer thickness was found to be 64nm with a pit facet inclination angle of 21.6◦. Figures 2(d)and (e) show the surface morphologies of the first Ge QD

layer grown on the 64 nm thick Si buffer layer, and thegrowth temperatures for the buffer layer were different, 450and 400 ◦C, respectively. The growth conditions for the firstGe QD layer in figures 2(d) and (e) were kept the sameas in figures 2(a)–(c) except for a slightly higher growthtemperature of 570 ◦C for (d). The detailed growth parametersfor figures 2(a)–(e) are listed in table 1. Both figures 2(d) and(e) show that all the dots nucleate inside the pits with nearlyperfect in-plane dot ordering and good dot size uniformity.The optimized pit facet inclination angle (21.6◦) obtainedin our experiments agrees well with theoretical predictionsof around 20◦, at which the elastic energy density has localminima at the bottom of the pits [21]. Besides, it is worthwhileto point out that a lot of flat surface of the wetting layerin figure 2(e) is seen, which is due to the low growthtemperatures (note the different scales of the color bars forfigures 2(d) and (e)). The smooth surface of the wetting layercertainly has smaller surface chemical potential fluctuations,which will benefit the subsequent growth of QDCs.

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Figure 3. Surface morphologies after the growth of three Ge QD layers with different Ge deposition amounts in the first QD layer. (a)8 ML and (b) 10 ML.

2.2. The Ge deposition amount in the first QD layer

With the optimized thickness and growth temperature of theSi buffer, layer stacking growth was performed for verticalordering of QDs. Figures 3(a) and (b) show AFM images afterthe growth of three-layer Ge QDs for vertical ordering of QDs.The thickness of the Si spacer layer was first chosen to be12 nm. The difference for the samples shown in figures 3(a)and (b) is for the deposition amount of the first Ge QDlayer. For the sample shown in figure 3(a), 5 ML thick Gewas first deposited with increasing the temperature from 450to 550 ◦C, and additional 3 ML thick Ge was deposited at550 ◦C, whereas for figure 3(b) additional 5 ML thick Ge wasdeposited at 550 ◦C, 2 ML more in the total Ge deposition.Figure 3(a) reveals that not all the pits are filled by QDs: alarge proportion of pits remain empty, and no ordering in thegrowth plane is observed. In contrast, as shown in figure 3(b),ordered Ge QDs are observed and the QDs have a pyramidshape with {105} facets. This difference in the lateral orderingcan be interpreted on the basis of strain build-up by QDs inthe first layer and the strain transferring in the layer stacking.

In the layer stacking growth of Ge QDs, when next GeQD layer grows on the surface of the Si spacer layer, the QDsnucleate preferentially and precisely over the underlying QDsdue to the strain effect, suggesting that the strain induced bythe underlying QDs can transfer upwards to the surface ofthe Si spacer layer and result in the Si on the top of QDsbeing tensile, which ensures the vertical ordering. However,for QDCs with small lateral periodicities, due to the lateralstrain-field interferences generated by the buried periodicQD array [23], uniform strain-field distribution must also beachieved for vertical dot ordering. A larger deposition amountof Ge in the first QD layer favors the strain build-up, onthe one hand; on the other hand, a little more Ge depositionamount helps improve the dot size uniformity and thus theperiodicity of the strain-field distribution induced by the QDs.So, the ordering of QDs after the stacking of three Ge QDlayers in figure 3(b) can be attributed to the larger strainbuild-up together with a good periodicity of the strain-field

distribution. This result also means that the Ge depositionamount in the first QD layer is a determining factor in thegrowth of 3D QDCs. Considering that the dot ordering infigure 3(b) is still not perfect, some dots are missing in theregular sites, and some large QDs appear, investigations onother growth parameters are needed for better ordering.

2.3. Si spacer layer thickness and growth rates

In this subsection, the Si spacer layer thickness and growthrate were studied for further ordering of QDs in QDCs. Inlayer stacking QD growth, the QDs preferentially nucleate inthe sites with strain energy minima on the surface of the spacerlayer, which is due to the strain induced by lattice mismatchof the underlying dots. The strain induced by the underlyingdots can penetrate upwards only a limited thickness in thespacer layer and the strain penetration thickness is strictlyproportional to the underlying dot height and composition.Both theoretical and experimental studies have revealed thatin the epitaxial growth of multi-layer Ge QDs, the verticalalignment probability of QDs is inversely proportional to theSi spacer layer thickness [24, 25]. A thick Si spacer layerwill diminish the strain induced by the underlying QDs onthe surface of the Si spacer layer, and worsening in verticalalignment of QDs will occur [26]. In contrast, too thin a Sispacer layer will also destroy the vertical ordering, since athin Si spacer layer could not cover the whole QDs with noSi spacer layer on the top of QDs. An optimized Si spacerlayer thickness should exist for the vertical ordering of theQDCs. Figures 4(a)–(c) show AFM images after ten-layer GeQD growth. The Si spacer layer thickness for the samples infigures 4(a)–(c) is 12, 8 and 5.5 nm, respectively. The Si spacerlayers were grown with the temperature ramping from 450 to550 ◦C during the deposition in order to reduce intermixing ofGe and Si, especially at the initial capping, and have a smoothsurface for the Si spacer layer. The Ge deposition amountfor the second layer was 8 ML, and was reduced by 0.5 MLafter every three layers in order to suppress the enlargementof the QDs due to strain accumulation in the subsequent dot

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Figure 4. Surface morphologies after the growth of ten QD layers with different spacer layer thicknesses and Si growth rates. (a) 12 nm,0.5 A s−1. (b) 8 nm, 0.5 A s−1. (c) 5.5 nm, 0.5 A s−1. (d) 5.5 nm, 0.3 A s−1. The inset of (d) shows the FFT image of (d). (e) 3D AFMimage of a small area in (d). (f) Statistical height distribution of the QDs shown in (d).

layers [16]. Progressive improvement in dot size uniformityis clearly seen for figures 4(a)–(c) with decreasing Si spacerlayer thickness. 5.5 nm is the optimized thickness of the Sispacer layer. A suitable thickness of the Si spacer layer shouldlead to a strong strain transfer in the layer stacking, on theone hand; on the other hand, it should ensure coverage of thewhole QDs. In this case QDCs with a good QD homogeneitywill be realized.

In addition to adjusting the Si spacer layer thickness,a reduced growth rate of 0.3 A s−1 in the Si spacer layergrowth was tried; the result is shown in figure 4(d). Muchimprovement in the QD size uniformity and the lateral

ordering are clearly seen, compared to figure 4(c). The insetshows the fast Fourier transform (FFT) image of figure 4(d),indicating a good in-plane dot ordering. Such remarkableimprovement can be attributed to the enhanced adatom surfacemigration length at low growth rates [27]. Figure 4(e) is the3D AFM image for a small area in figure 4(d); the pyramidshape for the dots can be seen and the dots are well positionedin a hexagonal lattice, which should be identical to that of thepit pattern on the substrate (figure 1(b)). This means that thevertical alignment of QDs in the layer stacking is realized. Theareal dot density of the QDCs is 1.2 × 1010 cm−2, which isthe highest ever achieved in an ordered Ge QD system. The

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Figure 5. (a) XTEM image of the QDCs with ten Ge QD layersshown in figure 4(d). (b) HRTEM image of a QD column shown in(a).

statistical size distribution of QDs in figure 4(d) is shown infigure 4(f); the size distribution can be fitted with a Gaussianfunction with a dispersion of 10%.

2.4. Microstructures

To obtain more detailed information on the microstructuresof the 3D Ge QDCs, XTEM investigation was performed forthe sample shown in figure 4(d). The vertical alignment ofthe QDs is clearly shown in figure 5(a). Figure 5(b) showsa high resolution XTEM (HRTEM) image of a QD columnalong the growth direction. Due to the filling of the pits,the dots in the first layer have a higher aspect ratio than theones in the subsequent layers (as indicated by the dashedlines in figure 5(b)). From figure 5(a), the lateral interdotspacing is estimated to be 10 nm. From figure 5(b), thevertical interdot spacing and the periodicity in the centerlineof a QD column are determined to be ∼7 and ∼2.5 nm,respectively, as indicated in the figure. It is worth noting thatthe vertical interdot spacing of 2.5 nm is much smaller thanthe average growth thickness of 5.5 nm for the Si spacer layer.This means that there is not much room for further reducingthe growth thickness of the Si spacer layer to increase thestrain transferral for vertical ordering. Actually 5.5 nm isthe optimized thickness for the Si spacer layer for verticalordering and size homogeneity of QDs. The vertical interdotspacing of 2.5 nm is the smallest interdot spacing that hasever been achieved in ordered Ge QD systems. According totheoretical studies, 2.5 nm spacing is in the range of the strongcoupling regime [28, 29] and could give rise to extendedelectronic states or even minibands [3, 30].

In addition, it should be noted that the mean QD heightof 7.8 nm in figure 4(f) extracted from AFM line-profile

statistical analysis is for the tenth-layer (topmost) uncappedQDs. The QD height extracted from the HRTEM in figure 5(b)is 4.5 nm in the centerline of a QD column. This reducedQD height in the underlying QD layers is mainly caused bythe Si spacer layer growth process, in which surface-mediatedatomic intermixing would reduce the height of the QDs [31].

3. Conclusions

In summary, this work systematically investigated the MBEgrowth of 3D Ge QDCs on pit-patterned Si substrates and theirmicrostructures. The ordering and uniformity of the QDCs arefound to critically rely on the growth conditions for the Sibuffer layer, the first QD layer and the Si spacer layer. Anoptimized pit facet inclination angle of 21◦ after buffer layergrowth was found for the QDC growth. Besides, a low growthrate of Si also yields much improvement in the ordering andoverall homogeneity of the QDCs. With optimized growthconditions, 3D Ge QDCs with good dot ordering and highdot size uniformity are achieved. The highest ever QD arealdensity of 1.2×1010 cm−2 and the so far smallest 3D interdotspacing of 2.5 nm were achieved in the 3D ordered Ge QDsystem.

Acknowledgments

This work was supported by the special funds for theMajor State Basic Research Project (Nos 2011CB925601 and2009CB929300) of China, and the Natural Science Foun-dation of China (NSFC) under Project Nos 61274016 and10974031. Y J Ma also thanks for support Fudan University,under the Research Support Project for Outstanding PhDStudents.

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