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Large-area ordered Ge-Si compound quantum dot molecules on dot-patterned Si (001) substrates

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Nanotechnology 25 345301 (http://iopscience.iop.org/0957-4484/25/34/345301) View the table of contents for this issue, or go to the journal homepage for more

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Nanotechnology Nanotechnology 25 (2014) 345301 (5pp)

doi:10.1088/0957-4484/25/34/345301

Large-area ordered Ge-Si compound quantum dot molecules on dot-patterned Si (001) substrates Hui Lei, Tong Zhou, Shuguang Wang, Yongliang Fan and Zhenyang Zhong State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People’s Republic of China E-mail: [email protected] Received 30 March 2014, revised 30 May 2014 Accepted for publication 10 June 2014 Published 31 July 2014 Abstract

We report on the formation of large-area ordered Ge-Si compound quantum dot molecules (CQDMs) in a combination of nanosphere lithography and self-assembly. Truncated-pyramidlike Si dots with {11n} facets are readily formed, which are spatially ordered in a large area with controlled period and size. Each Si dot induces four self-assembled Ge-rich dots at its base edges that can be fourfold symmetric along directions. A model based on surface chemical potential accounts well for these phenomena. Our results disclose the critical effect of surface curvature on the diffusion and the aggregation of Ge adatoms and shed new light on the unique features and the inherent mechanism of self-assembled QDs on patterned substrates. Such a configuration of one Si QD surrounded by fourfold symmetric Ge-rich QDs can be seen as a CQDM with unique features, which will have potential applications in novel devices. Keywords: compound quantum dot molecules, self-assembly, dot-patterned substrates, surface chemical potential, nanosphere lithography (Some figures may appear in colour only in the online journal) 1. Introduction

the QD formation is energetically favorable [5]. As a result, the site of self-assembled Ge-rich QDs can be precisely controlled on patterned substrates, and this can readily result in perfectly ordered Ge-rich QDs [5–8]. Moreover, the homogeneities of the size [6] and composition [9] of selfassembled Ge-rich QDs on patterned substrates are also substantially improved in comparison with those on normal flat substrates. Such ordered and uniformed Ge-rich QDs have exhibited unique optical properties [7, 8, 10]. Photo detectors based on ordered Ge-rich QDs also show promising features [11]. On the other hand, self-assembled Ge-rich QDs on patterned Si substrates are significantly affected by the growth conditions and the geometrical profiles of the pattern [12]. Depending on the growth conditions, three growth regimes on patterned substrates are suggested [13]. A collective shape oscillation of Ge-rich QDs on patterned substrates is observed with the increase of the deposited Ge amount [14]. On particular pit-patterned substrates, second-order Ge-rich QDs can

Self-assembled Ge-rich quantum dots (QDs) have been extensively investigated not only because of their potential device applications [1–3] that are compatible with sophisticated Si integration technology but also to understand the fundamental physics [4] during heteroepitaxial growth as a prototype model. To fully characterize QDs and functionalize and integrate QD-based devices, external addressability and uniformity of QDs are always in demand [3]. Such prerequisites are hardly satisfied with self-assembled QDs on normal flat substrates, which are always spatially random and have a broad size distribution. Tremendous effort has gone into trying to solve this problem. One promising solution is via heteroepitaxial growth on patterned substrates. The microstructure on the surface of patterned substrates can dramatically affect the nucleation and the evolution of selfassembled QDs. On pit-patterned Si (001) substrates, selfassembled Ge-rich QDs preferentially grow within pits, where 0957-4484/14/345301+05$33.00

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be achieved [15]. Four regularly arranged Ge-rich QDs can be obtained within a large inverted truncated-pyramid pit as opposed to a single QD in a small pit [16, 17]. When the slope of the pit sidewall is increased, the preferential site of Ge-rich QDs can be transferred from the bottom to the rim of the pit [12, 18]. Quantum dot molecules (QDMs) are also observed at the edges of pits [19]. Recently, controlled Ge-rich QDs were obtained on the top terrace of sub-micro Si pillars [20]. Apparently, self-assembled QDs on patterned substrate are more complex than those on flat substrates due to the substantial effects of surface microstructure on strain relaxation, the variation in surface energy [5, 18, 19, 21], the diffusion of adatoms [12, 13, 22, 23], the interaction among QDs [19, 21], and so forth. Despite significant progress, the growth of QDs on patterned substrates is still in the process of becoming fully understood, and consequently, the capability to deliberately design patterns for manipulating self-assembled QDs in desired configurations has yet to be achieved. In this report, we develop a way to fabricate ordered Si dot patterns on a large scale via nanosphere lithography. After thermal treatment and Si buffer growth, truncated-pyramidlike Si dots are readily formed. The size and the period of the Si dots can be intentionally controlled. Around each Si dot, four Ge-rich QDs are induced near the centers of the four base edges. These four QDs can be uniform and show fourfold symmetry along directions. Detailed analyses of the surface chemical potential (SCP) clearly demonstrate four minima of the SCP around the centers of the four base edges of the Si dot, where Ge adatoms preferentially diffuse toward and aggregate at the beginning of the Ge deposition. Accordingly, four well-arranged Ge-rich QDs are formed around an Si dot. Our results disclose the critical effect of surface curvature on the diffusion and aggregation of Ge adatoms and further clarify the unique features and the inherent mechanism of self-assembled QDs on patterned substrates. Such a configuration of one Si QD at the center and fourfold symmetric Ge-rich QDs at the edges can be referred to as a Ge-Si compound quantum dot molecule (CQDM) due to the strong interaction among them and the unique confinement of electrons in the center Si QD and of the holes in the edge Ge-rich QDs. Such Ge-Si CQDMs will have unique properties and will be promising candidates for use in novel devices, e.g., quantum cellular automata.

gas to obtain periodic Si dots, as shown in figure 1(c). Finally, the remaining PS spheres were removed by RIE, with pure Si dots left on the substrate, as shown in figure 1(d). The obtained Si dots were arranged in a hexagonal lattice. By optimizing the processes during the self-assembly of the PS spheres in the first step, a very large area (on the centimeter scale) of the substrate was able to be covered by the periodic Si dots except for some domain boundaries. In addition, the period of the Si dot pattern was exactly the same as the diameter of the PS spheres, which can be intentionally changed. The size of the Si dots can also be readily controlled by modifying the parameters of RIE. The dot-patterned Si (001) substrates were then cleaned using the RCA method followed by hydrogen fluoride treatment before being loaded into the MBE chamber. After thermal treatment at 780 °C for 4 min to desorb hydrogen, a 50 nm-thick Si buffer was grown at 360 °C with a growth rate of 0.3 Å s−1 to obtain a smooth and impurity-free surface for the remaining dot pattern. Subsequently, 5 monolayers (MLs) of Ge were deposited at a growth rate of 0.05 Å s−1 and the substrate temperature was increased from 400 °C to 480 °C. The reference samples on flat substrates were also grown under identical conditions. The surface morphologies of the samples were characterized using atomic force microscopy (AFM) (Veeco DI Multimode V SPM) in tapping mode.

2. Experimental section

3. Results and discussion

Samples were grown on dot-patterned Si (001) substrates by molecular beam epitaxy (MBE). Periodic Si dots were fabricated via nanosphere lithography, as schematically illustrated in figure 1. First, a single monolayer of polystyrene (PS) spheres (Duke Scientific Corp.) were compactly self-assembled on an Si (001) substrate by use of the modified Langmuir-Blodgett (LB) technique [24], as shown in figure 1(a). Then the size of the PS spheres was reduced by reactive ion etching (RIE) using oxygen as the reactive gas, as shown in figure 1(b). The remaining PS spheres served as masks for subsequent RIE, which used carbon tetrafluoride as reactive

Figure 2(a) shows the surface morphology of the periodic Si dots on Si (001) substrate before growth. The Si dots are quite uniform and are arranged in a hexagonal lattice with periods of 220 nm. They look like cones with no particular facets and have typical heights of ∼22 nm, as shown in figure 2(b). After thermal treatment and Si buffer layer growth, Si dots with the same arrangement and uniformity remain on the substrate, as demonstrated in figure 2(c). The shape of the Si dots evolves into a truncated pyramid, as exhibited in figure 2(d). The sidewalls of the Si dot are composed of {11n} facets, based on their slopes. The height of the Si dots is also considerably

Figure 1. Schematic illustration of the fabrication of a dot-patterned

Si (001) substrate: (a) a close-packed monolayer of PS nanospheres on a clean Si substrate, (b) after RIE of O2, (c) after RIE of CF4, and (d) after removal of the PS spheres.

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which has also been observed in the case of pit-patterned substrates [12, 15, 17]. In addition, such shape evolution may become more pronounced for smaller dots [20]. Figure 3(a) shows the surface morphology of the sample after 5 ML Ge depositions. Interestingly, clusters of dots are regularly arranged in the same lattice as that of the former Si dots in figures 2(a) and (c). Each cluster of dots is generally composed of one small mount-like dot in the center and four dome-like dots at the edge, as demonstrated in figure 3(b). The mount-like dot in the center originates from the former Si dot. The four dome-like dots are ascribed to Ge-rich dots after Ge deposition. The height profile across the center dot and two edge dots along the direction is shown in figure 3(c). It can be seen that the four Ge-rich dots around the center dot can be symmetrically located with respect to directions, as shown in figures 3(b) and (c). In addition, the four Ge-rich dots are preferentially located around the centers of the base edges of the center dots, where the intersections between the (001) and {11n} facets of the former Si dot are. The center Si dot evolves from a truncated pyramid to a mount shape. This is attributed to the formation of a thin Ge surface layer on the former Si dots [25], which can result in the appearance of other facets, e.g., {105} [14, 15]. The size of the center dot is considerably diminished in comparison with the former Si dot due to the diffusion of Si and Ge atoms outward from the center dot during Ge deposition. This outdiffusion can become more pronounced after the formation of the four Ge-rich dots, which introduce remarkable compressive strain on the center dot. Such a configuration of one Si dot surrounded by fourfold symmetric Ge-rich dots can be referred to as a Ge-Si CQDM. These Ge-Si CQDMs are well ordered in a large area because their sites are predetermined by the ordered Si dots. They are substantially different from those on the flat substrate, which exhibit many small hut clusters and a few domes in a random distribution, as shown in figure 3(d). They are also considerably different from those on the pit-patterned substrates [5–18]. Our results are also distinctly different from previous ones related to the growth of Ge on mesa-patterned Si substrates [25–27], which manifest the formation of QDs on the top rather than on the base edge of the mesas. It is argued that the preferential growth of Ge QDs on the top of Si mesas is attributed to the efficient strain relaxation there [25–27]. It appears that this argument cannot account for the preferential growth of Ge QDs at the base of the Si dots in our case, where the strain cannot be efficiently accommodated [22, 26]. The main reason is that the effect of surface curvature on surface energy is neglected in the previous model. Considering both effects, the later models propose that both the top and the foot of the mesas can be the favorable sites for Ge-Si QDs on patterned Si substrates [23, 28], whereas the preferential growth of Ge-Si QDs on patterned substrates is significantly affected by the geometrical profiles of the pattern [12, 17, 18, 20]. The issue of where the Ge-Si QDs nucleate first around the Si mesas has not been similarly clarified. This issue is critical to actually achieving site-controlled growth of Ge-Si QDs on pattern substrates. The unique Ge-Si CQDM

Figure 2. AFM images of (a) the Si dot-patterned substrate

(1 × 1 μm2), (b) an enlarged single Si dot before growth, (c) the Si dot-patterned substrate (1 × 1 μm2), and (d) an enlarged single Si dot after Si buffer layer growth. The height profiles along the dashed lines in (a) and (c) are shown in figure 3(c).

Figure 3. (a) AFM image (1 × 1 μm2) of the Ge-Si CQDMs after

deposition of 5 ML Ge on Si dot-patterned substrate; (b) an enlarged single Ge-Si CQDM; (c) the height profiles along the dashed lines in (a) and in figures 2(a) and (c); (d) AFM image (1 × 1 μm2) of the Ge QDs after deposition of 5 ML Ge on a flat substrate.

reduced, to about 5 nm. Such shape evolution mainly results from the redistribution of Si atoms during thermal treatment and the preferential incorporation of Si during buffer layer growth to form energetically favorable facets of Si dots [22], 3

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constant, τ is the time interval for adatom diffusion, a is the lateral motion corresponding to each hop of the adatom, υ is a prefactor, E denotes the diffusion barrier for the Ge adatoms, kB is the Boltzmann constant, and T is the growth temperature [13, 20, 22]. Under the current growth conditions, the surface diffusion length L (∼250 nm at 400 °C) of the Ge adatoms is larger than the period (220 nm) of the patterned Si dots. Therefore, at the beginning of Ge deposition, Ge adatoms preferentially diffuse toward and aggregate at the centers of the base edges of the patterned Si dot, where the SCP is at a minimum. Accordingly, the Ge layer in the regions at the base edges of the Si dot grows much faster than other Ge layers. The Ge-rich dots then readily nucleate there beyond the critical thickness. Further growth of Ge ripens the Ge-rich dots. In the ideal case of a perfectly smooth surface in between Si dots and identical facets of the sidewalls of the Si dots, four identical Ge-rich dots are expected to grow at the center of the four base edges of the Si dot, which results in a Ge-Si CQDM with fourfold symmetry along directions. In the current case, the uniformity of the Ge-Si CQDMs is not exactly ideal in spite of their rather good spatial ordering, as shown in figure 3(a). The main reason is that our growth conditions have not been optimized. Accordingly, some regions of the surface are not particularly smooth, and the Si dots are not all suitably fourfold symmetric. As a result, the minimum of the SCP can appear not exactly at the centers of base edges and their values may differ around some Si dots. The former will result in the formation Ge-rich dots deviating from the center of the base edge. The latter can cause the timing of nucleations of Ge-rich dots to vary, which always results in varying sizes of QDs. By optimizing the patterning processes and the growth conditions, ideal Ge-Si CQDMs on dot-patterned Si (001) substrates can be achieved. In addition, regular arrangement and uniformity of Ge-rich QDs around the Si dot can be improved during the ripening process due to repulsion interaction between Ge-rich QDs and their selflimiting growth [19], particularly for a smaller Si dot. Our results clearly demonstrate that self-assembled Gerich QDs first grow at the base edges of well-separated small Si dots because surface curvature plays the dominant role at the beginning of Ge growth. It is worth noting that the SCP around the Si dots or mesas is considerably changed with the increase in Ge layer thickness. With sufficient Ge growth, the minima of the SCP appear around the top corner of the mesas because strain relaxation plays the dominant role in the SCP for the thick Ge layer [20]. This accounts for the previous results of Ge QDs on the tops of Si pillars or mesas [20, 25–27]. The fact that no Ge QD is observed at the base of the mesas previously is mainly attributed to the limited aggregation of Ge there due to the existence of the SiO2 layer or the rather rough surface without Si buffer layer growth [25–27]. For an Si pillar of considerably large height and diameter, insufficient Ge is deposited at its base because part of the incident Ge flux is blocked by the neighboring pillars during growth. As a result, no Ge QD is observed around the base of the Si pillar [20]. The four Ge-rich dots around each patterned Si dot can significantly increase the density of the dots. More important,

Figure 4. (a) The SCP around a single Si dot (195 × 195 nm), and (b) the SCP along the line AB (across the center of the Si dot) and the line CD (along the base edge of the Si dot) in (a) and the height profile across the center of the Si dot. The SCP along the line CD is shifted upward by 8 meV to clearly show the features of all curves in (b). The atomic volumes of Ge are 13.6 cm3 · mol−1. The surface energy, the elastic constant, and the misfit strain of the Ge layer are 1.835 J · m−2, 1.03 × 1011 N · m−2, and 0.04, respectively. The fitting parameter (Zs − Z0) is 0.2 nm. For simplicity, we adopt μ0 = 0.

induced by the small Si dot has not been observed and predicted. In general, the nucleation of Ge-rich QDs is intimately associated with the diffusion and the aggregation of Ge adatoms, which are controlled by the SCP. For simplicity, the SCP is given by [17, 20, 23],

μ = μ0 + Ωγκ + ΩEs ES = −

⎞ 2 C⎛ κ ⎡ 2 ⎜ ⎣ κ ( ZS −Z 0 ) ⎤⎦ − ε ⎟ ⎠ 2 ⎝ κ

where μ0 is the SCP of a flat surface, Ω is the atomic volume, γ is the surface energy per unit area, κ is the surface curvature, Es is the local strain-relaxation energy, C is the elastic constant, and (ZS − Z0) is the parameter corresponding to the nominal thickness of the Ge film. The two-dimensional surface curvature κ can be derived from the AFM images [17, 20]. Figure 4(a) shows the SCP around a single truncated-pyramid-like dot, as shown in figure 2(d). Evidently, there are four local minima of the SCP around the four edges of the Si dot at the beginning of Ge growth. The SCP along the line AB (across the center of the Si dot) is shown in figure 4(b), which clearly demonstrates the minimum of the SCP just at the base of the Si dot. Moreover, the minimum of the SCP generally appears at the center of the base edge, as manifested by the SCP along the line CD (along the base edge) in figure 4(b). The variation of SCP along the base edge is mainly induced by the change of the surface curvature, particularly approaching the convex base corners. The maximum of the SCP appears at the convex top corners of the Si dots. Such a distribution of the SCP around the Si dots is mainly determined by the local surface curvature at the beginning of Ge growth, when the strain relaxation effect is quite small due to the very thin Ge layer. This unique distribution of the SCP sheds light on the scenario of the formation of Ge-Si CQDMs. We estimate the surface diffusion length L of the Ge adatoms by L = (Dτ )1/2 , D = a 2υ exp ( − E /kB T ), where D denotes the diffusion 4

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References

such novel configurations of Ge-Si CQDMs may result in the confinement of electrons in the center Si QDs and of holes in the fourfold symmetrical edge Ge-rich QDs. Although further studies are required, these Ge-Si CQDMs will give rise to much more promising features than other configurations of QDs due to the unique confinement of electrons and holes and the strong interaction among them. Accordingly, such Ge-Si CQDMs can be referred to as unique ‘artificial molecules’, which have a promising future in novel devices. In addition, the four Ge-rich QDs in the Ge-Si CQDM have the proposed symmetry of a building block for QD cellular automata [29], which will have potential applications in the field of quantum information and processing.

[1] Wang K L, Cha D H, Liu J L and Chen C 2007 Proc. IEEE 95 1866 [2] Katsaros G, Spathis P, Stoffel M, Fournel F, Mongillo M, Bouchiat V, Lefloch F, Rastelli A, Schmidt O G and De Franceschi S 2010 Nat. Nanotechnol. 5 458 [3] Kasper E, Kirfel O and Karmous A 2011 Horizons in world physics Positioning of Ge-Dots on Si for Device Applications vol 273 ed A Reimer (New York: Nova Science Publisher) pp 171–85 [4] Tersoff J and Legoues F K 1994 Phys. Rev. Lett. 72 3570 [5] Zhong Z, Schwinger W, Schäffler F, Bauer G, Vastola G, Montalenti F and Miglio L 2007 Phys. Rev. Lett. 98 176102 [6] Zhong Z and Bauer G 2004 Appl. Phys. Lett. 84 1922 [7] Grutzmacher D et al 2007 Nano Lett. 7 3150 [8] Ma Y, Zhong Z, Lv Q, Zhou T, Yang X, Fan Y, Wu Y, Zou J and Jiang Z 2012 Appl. Phys. Lett. 100 153113 [9] Schulli T U et al 2009 Phys. Rev. Lett. 102 025502 [10] Chen Y, Pan B, Nie T, Chen P, Lu F, Jiang Z and Zhong Z 2010 Nanotechnology 21 175701 [11] Lavchiev V, Holly R, Chen G, Schaffler F, Goldhahn R and Jantsch W 2009 Opt. Lett. 34 3785 [12] Grydlik M, Langer G, Fromherz T, Schaffler F and Brehm M 2013 Nanotechnology 24 105601 [13] Zhong Z, Chen P, Jiang Z and Bauer G 2008 Appl. Phys. Lett. 93 043106 [14] Zhang J J et al 2010 Phys. Rev. Lett. 105 166102 [15] Zhong Z, Schmidt O G and Bauer G 2005 Appl. Phys. Lett. 87 133111 [16] Dais C, Solak H H, Müller E and Grützmacher D 2008 Appl. Phys. Lett. 92 143102 [17] Chen H M, Kuan C H, Suen Y W, Luo G L, Lai Y P, Wang F M and Chen S T 2012 Nanotechnology 23 015303 [18] Vastola G, Grydlik M, Brehm M, Fromherz T, Bauer G, Boioli F, Miglio L and Montalenti F 2011 Phys. Rev. B 84 155415 [19] Gray J L, Singh N, Elzey D M, Hull R and Floro J A 2004 Phys. Rev. Lett. 92 135504 [20] Zhou T, Zeng C, Ma Q, Ma Y, Fan Y, Jiang Z, Xia J and Zhong Z 2014 Nanoscale 6 3925 [21] Hu H, Gao H J and Liu F 2012 Phys. Rev. Lett. 109 106103 [22] Zhong Z, Halilovic A, Mühlberger M, Schäffler F and Bauer G 2003 J. Appl. Phys. 93 6258 [23] Yang B, Liu F and Lagally M 2004 Phys. Rev. Lett. 92 025502 [24] Chen P, Fan Y and Zhong Z 2009 Nanotechnology 20 095303 [25] Jin G, Liu J L and Wang K L 2000 Appl. Phys. Lett. 76 3591 [26] Kitajima T, Liu B and Leone S R 2002 Appl. Phys. Lett. 80 497 [27] Nguyen L H et al 2004 Appl. Surf. Sci. 224 134 [28] Hu H, Gao H J and Liu F 2008 Phys. Rev. Lett. 101 216102 [29] Orlov A O, Amlani I, Bernstein G H, Lent C S and Snider G L 1997 Science 277 928

4. Conclusion In summary, large-area ordered Si dots of controlled size and period are realized on Si (001) substrates via nanosphere lithography. Fourfold symmetric Ge-rich dots along directions can be readily induced around the centers of the base edges of the truncated-pyramid-like Si dots. This promising feature of self-assembled Ge-rich dots on dot-patterned Si (001) substrates is explained by a model based on surface chemical potential. Our results demonstrate that surface curvature plays a critical role in the diffusion and aggregation of Ge adatoms at the beginning of Ge deposition and shed new light on the unique features and the inherent mechanism of self-assembled QDs on patterned substrates. The obtained Ge-Si CQDMs will have much more promising physical properties in comparison with other configurations of QDs due to the unique confinement and strong interaction of electrons and holes. Accordingly, such Ge-Si CQDMs will have great potential in device applications.

Acknowledgements Hui Lei and Tong Zhou contributed equally to this paper. This work was supported by the special funds for the Major State Basic Research Project (No. 2011CB925601) of China.

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Large-area ordered Ge-Si compound quantum dot molecules on dot-patterned Si (001) substrates.

We report on the formation of large-area ordered Ge-Si compound quantum dot molecules (CQDMs) in a combination of nanosphere lithography and self-asse...
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