Self-Limiting Growth of Hexagonal and Triangular Quantum Dots on

Article pubs.acs.org/crystal

Self-Limiting Growth of Hexagonal and Triangular Quantum Dots on (111)A Masafumi Jo,*,† Takaaki Mano,† Marco Abbarchi,† Takashi Kuroda,† Yoshiki Sakuma,† and Kazuaki Sakoda†,‡ †

Photonic Materials Unit, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8577, Japan

‡

ABSTRACT: We report the formation of triangular GaAs quantum dots (QDs) on (111)A substrates using droplet epitaxy. Shape transition from hexagonal to triangular QDs is observed with increasing crystallizing temperature, as a result of different growth rates of step edges on a (111)A substrate. Size statistics illustrate the self-limiting growth of GaAs QDs whose characteristic size is determined by that of Ga droplets. Detailed structural analysis further reveals the three-dimensional structure of QDs. By decreasing the amount of Ga, low-density GaAs QDs are obtained while retaining the triangular shape, which allows the optical properties to be studied at a single QD level.

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conductor QDs.17,18 Since the dot formation does not rely on strain relaxation but on the large difference in metal/ semiconductor surface energies, droplet epitaxy can be applied to a wide variety of material combinations including homo/ hetero and strained/strain-free systems. In addition, the separate process of droplet formation and crystallization offers a higher degree of freedom in engineering the size and shape of QDs, which makes droplet epitaxy attractive for fabricating prismatic nanostructures.3,6,19−24 Recently we have successfully grown strain-free GaAs QDs on a (111)A substrate by employing droplet epitaxy.22 In accordance with the theory, those QDs show small fine-structure splitting compared to the QDs on (001), while the dot shape remains isotropic originating from semispherical Ga droplets. Here, we report the morphological control of GaAs QDs on (111)A substrates using droplet epitaxy. We have found that the shape of QDs can be controlled between hexagonal and triangular truncated pyramid by changing the crystallizing temperature, while the size and density are governed by that of Ga droplets. The shape transition is discussed in terms of the different growth rates of two step edges on a (111)A surface. Furthermore, size statistics on QDs reveal that highly anisotropic growth rates lead to the self-limiting growth of triangular QDs. By controlling the density of QDs, optical properties of single QDs are investigated in terms of microphotoluminescence (μ-PL).

INTRODUCTION Semiconductor quantum dots (QDs) and their families have attracted much attention due to their unique optical and electronic properties.1,2 In particular, the morphological diversity of QDs makes it possible to explore various physical properties by controlling electronic states in characteristic structures. For example, quantum ring structures have long attracted both theoretical and experimental interest in the context of the Aharonov−Bohm effect.3−6 Elongated QDs, or quantum dashes, show superior properties in terms of polarization, producing polarization-controlled devices.7−9 The formation of Wigner molecules is another interesting topic in polygonal QDs.10−12 Various shapes of QDs thus provide a wide platform on which to investigate the fundamental physical properties. One of the main factors determining the shape of QDs is the substrate orientation, the characteristic symmetry of which also modulates the electronic states of the QDs. Among many orientations, a (111) surface is an attractive orientation with high symmetry. Apart from a (001) orientation, (111) is the only orientation in which heavy- and light-hole states do not mix with each other. In addition, the purely longitudinal piezoelectric field induced by strain does not lower the in-plane symmetry of the dot potential, leading to the vanishing finestructure splitting which is useful for polarization-entangled photon emission.13,14 However, it is difficult to obtain QDs on (111) substrates by using the conventional Stranski−Krastanow growth mode because strain relaxation takes place via the introduction of dislocations instead of three-dimensional (3D) island formation.15,16 In this context, droplet epitaxy is another promising growth approach which is based on the formation of metallic droplets followed by crystallization into semi© 2012 American Chemical Society

Received: November 16, 2011 Revised: January 20, 2012 Published: January 27, 2012 1411

dx.doi.org/10.1021/cg201513m | Cryst. Growth Des. 2012, 12, 1411−1415

Crystal Growth & Design

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EXPERIMENTAL PROCEDURES Samples were grown on semi-insulating GaAs(111)A substrates by molecular beam epitaxy. After the growth of a 50-nm GaAs buffer layer at 500 °C, Ga droplets were formed at 450 °C by supplying four monolayers (MLs) of Ga at an equivalent rate of 0.1 ML s−1 on a (001) surface without As flux. Subsequently, the substrate was lowered or raised to the temperature at which the Ga droplets were crystallized into GaAs QDs by irradiating As flux of 2 × 10−6 Torr. Surface morphology of the QDs was then investigated using atomic force microscopy (AFM). For the optical measurements, GaAs QDs were embedded in the middle of a 100-nm Al0.3Ga0.7As layer. Optical properties of single QDs were studied by the conventional μ-PL setup using an He-flow cryostat. We would like to note that there was no significant difference in the size and density of QDs between GaAs and AlGaAs surfaces, as in the case of (311)A.25 Therefore, the following discussion can be applied to the QDs grown on AlGaAs.

with the B sides longer than the A sides are formed as seen in Figure 1b, and this trend is pronounced at high temperatures. At 400 °C, the B sides grow further while the A sides diminish, resulting in an almost triangular base. Finally, at 500 °C, the A sides totally disappear and equilateral-triangular QDs of 100 nm side are obtained as shown in Figure 1d. It is noteworthy that every triangle points in the same direction with only the B sides visible, implying that the island shape is governed by the C3v symmetry of the (111)A. Indeed, such a morphological transition between hexagonal and triangular islands has been observed in Pt/Pt(111)26 and GaN/GaN(0001),27 which is explained in terms of the different growth rates of step edges on a (111) surface. Figure 2

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RESULTS AND DISCUSSION Figure 1 shows AFM images of GaAs QDs crystallized at different temperatures: (a) 200, (b) 300, (c) 400, and (d) 500

Figure 1. 500 × 500-nm AFM images of GaAs QDs crystallized at different temperatures: (a) 200, (b) 300, (c) 400, and (d) 500 °C. Transition from hexagonal to triangular QDs is visible. Height scale is different for each image: (a) 30, (b) 22, (c) 14, and (d) 10 nm.

°C. Constant dot density of 3 × 109 cm−2 is observed for all samples, since the dot density is governed by the droplet density formed at a constant temperature of 450 °C. Contrastingly, the dot shape greatly varies with the crystallizing temperature. At 200 °C, laterally isotropic QDs of polygonal pyramids with six or more sides are obtained. The base diameter and height are 70 and 20 nm on average, respectively. The dot diameter is slightly larger than that of original Ga droplets of 60 nm. For the hexagonal pyramid, the base is almost a regular hexagon with the side normal to the equivalent six {112̅} directions. When the temperature is increased to 300 °C, the hexagonal feature becomes more distinct. However, the sides are no longer equivalent but split up into two groups: A sides, perpendicular to the [1̅1̅2] direction and equivalent [1̅21̅] and [21̅1̅] directions, and B sides, perpendicular to the [112̅], [12̅1], and [2̅11] directions. Then, distorted hexagonal QDs

Figure 2. Schematic drawing of a GaAs(111)A surface. (a) Crosssectional view along the [11̅0] direction. (b) (111)A plan view. (c) Shape evolution of a GaAs QD from hexagon to triangle.

illustrates schematic pictures of an ideal GaAs(111)A surface without reconstruction:28 (a) cross-sectional view along the [11̅0] direction, and (b) (111)A plan view. As shown in Figure 2a,b, there are two types of steps on a GaAs(111)A surface. The A step, which is perpendicular to the A side, has two dangling bonds per edge atom, whereas the B 1412



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step, normal to the B side, provides only one dangling bond per atom. Because of the difference in binding energy between the two steps, A steps will grow faster than B steps. First, arriving Ga adatoms are more easily incorporated at the A steps than at the B steps in view of the binding energy. The lower binding energy of the B step also enhances adatom diffusion along the B step compared to the A step, which facilitates the accumulation and incorporation of adatoms at the A steps. In addition, there may be an asymmetry in corner diffusion: the rate of adatom transport from B to A across the corner will be greater than that from A to B, leading to a net flux from B to A steps.29,30 As a result of these effects, the growth rate of the step becomes anisotropic, causing the characteristic shape transition as shown in Figure 2c. In the present model, we assume that both steps are terminated by As atoms. While the A step may be terminated by Ga atoms under a Ga-rich condition during droplet epitaxy, the B step remain As-terminated because the B step covered with Ga is very unstable with having three dangling bonds. In addition, both of the As- and Ga-terminated A steps have two dangling bonds per edge atom. Therefore, the main mechanism of the different growth rates can be discussed using the As-terminated model in Figure 2. For the QDs crystallized at 200 °C, an isotropic multisided shape was observed, which indicates that the difference in the step growth rate is not manifest during the dot formation. At such a low temperature, the diffusion rate of Ga atoms from droplets is significantly smaller compared with the incorporation rates at step edges. In this diffusion-limited regime, the step growth rate is determined by the diffusion from droplets, resulting in the formation of isotropic QDs which reflect the hemispherical shape of Ga droplets [Figure 1a]. As the crystallizing temperature increases, both edge and corner diffusion become activated, and anisotropy in the step growth rate between the steps increases. Then, the A sides of the QD grow faster than the B sides, resulting in a distorted hexagonal QD [Figure 1b,c]. At a sufficiently high temperature, the A sides eventually disappear, leaving behind a triangular QD bounded by B sides [Figure 1d]. Previously, the characteristic formation of triangular islands on GaAs(111)A was observed only for two-dimensional island growth.31,32 The clear observation of triangular QDs in the present study confirms the model that the A steps grow faster on GaAs(111)A, as was pointed out in ref 27. In Figure 3a, we plot the lengths of the A side (LA) and B side (LB) of the QDs, along with the sum of the two lengths (2LA + LB) as a function of the crystallizing temperature. As observed above, LB monotonically increases while LA decreases with increasing temperature. The point to note is that 2LA + LB is almost constant for all temperatures, which means that the B sides hardly grow during the morphological change. In other words, the anisotropy in the growth rate is so large that the growth of triangular GaAs QDs proceeds self-limitingly, and their characteristic size is determined by that of the original droplets. The self-limiting growth as well as the compact dot shape at temperatures above 300 °C implies that the edge and corner diffusion of Ga adatoms along the B sides is sufficiently large when the diffusion is activated. In fact, if the diffusion length along a step is smaller than half the length of the step, the initial straight step would grow into a jagged step edge. Thus the lower limit of the diffusion length may roughly be estimated by measuring the B side length. Figure 3(b) shows a logarithmic plot of half the length of the B sides as a function of the

Figure 3. (a) Plots of the lengths of the {1̅1̅2} sides (LA) and the {112}̅ sides (LB) as a function of crystallizing temperature, along with the sum of 2LA + LB. The inset depicts schematics of a hexagonal QD and a triangular QD. Since many of the QDs have a pyramidal shape with more than six sides at 200 °C, both LA and LB are set to half the diameter of the QDs at 200 °C. Also, LA is set to zero for QDs crystallized at 500 °C. (b) Logarithmic plot of LB/2 versus crystallizing temperature. An exponential fit (line) to the data above 200 °C gives an activation energy of 0.16 eV.

crystallizing temperature. It can be seen that LB increases exponentially with increasing temperature except for the diffusion-limited regime at 200 °C. An exponential fit to the data above 200 °C gives an activation energy of 0.16 eV for the diffusion anisotropy on GaAs(111)A, which shall be compared with the theoretical calculation in further work. Now we again refer to the atomic configuration of the steps on (111)A in order to explain the extraordinary step anisotropy that causes the self-limiting growth. In general, a step can be recognized as a microfacet on the surface. Specifically, the A step is a (001) microfacet and the B step is a (110) microfacet, as seen in Figure 2a. The stability of the steps and the shape evolution of the islands can qualitatively be estimated by the surface energy of the corresponding microfacets. Under a Garich condition, the surface energy of the different low-index surfaces of GaAs are γ(110) = 52 meV/Å2, γ(111)A = 54 meV/Å2, and γ(001) = 64 meV/Å2.33 Accordingly, the B steps will not grow to form a (111)A terrace but instead retain the (110) facet. In contrast, the A steps easily grow because of the lower surface energy of (111)A than that of (001). Thus, the QD is expected to have three {110} side facets. To access the 3D structure of the QDs, we performed a structural analysis based on the AFM measurements. Figure 4a shows a close-up AFM image of the QDs crystallized at 300 °C. QDs in the transition regime show a truncated hexagonal-pyramid shape. To clearly visualize the surface, we show in Figure 4b the local surface slope |n| of the AFM image, in which n = ▽f is the surface gradient and f(x, y) is the surface height at position (x, y).34,35 It can be seen that the top of the QDs is more triangular in shape than the base, with the side facet angle of around 30°. This is confirmed by cross-sectional analysis of the AFM image. Figure 4c plots the cross section of a QD along the [112̅] direction. The obtained angle of 35° for the B side facet is very close to the side-facet angle for a (110) plane (35.2°). Interestingly, the other three sides show almost the same slope of 35°, indicating the formation of the (114) plane for the A 1413



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which the deposition of a capping layer significantly modifies the morphology and composition of the QDs. Furthermore, the size and density of QDs can be controlled independently of the shape in droplet epitaxy. On the (111)A substrate, the density of Ga droplets varies from 108 to 1011 cm−2 by changing the amount of Ga.22,23 We then fabricated small triangular QDs with low density by decreasing the amount of Ga to 0.05 ML. Other growth parameters were set to the same as those of triangular QDs in Figure 1d: crystallized at 500 °C and As4 flux of 2 × 10−6 Torr. The inset of Figure 5 shows an AFM image of GaAs QDs. The density is 8 × 108 cm−2 and the base length is 40 nm. In polarization-resolved μ-PL spectra, sharp emission lines from exciton (X) and biexciton (XX) are observed along with that from charged exciton (X*). Typical line width of the emission line is 40 μeV. In addition, the highly symmetric morphology of QDs as well as the atomic symmetry of the (111)A substrate considerably reduce the fine-structure splitting to 10 μeV. Thus, the good controllability of droplet epitaxy, as well as the applicability to a strain-free system, allows us to access the properties of single QDs with flexible shape.

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CONCLUSION In conclusion, we have demonstrated the formation of triangular GaAs QDs on (111)A substrates by droplet epitaxy. The dot shape can be controlled from hexagonal to triangular truncated pyramid depending on the crystallizing temperature. The difference in binding energy between {112̅} and {1̅1̅2} step edges on a (111)A surface is responsible for the shape evolution. Size statistics of the QDs show that the dot grows mostly in the {1̅1̅2} direction due to the highly anisotropic growth rate between the two steps, eventually leading to the formation of self-limiting triangular QDs. Structural analysis based on the AFM measurements reveals the 3D morphology of the QDs: the triangular QDs have three {110} side facets with a truncated (111)A top, while the hexagonal QDs have other {114} side facets. In addition to the shape design, the density can be successfully controlled by changing the amount of Ga. As a result, we can measure the PL properties of single QDs using low-density and small-size QDs, in which considerably small fine-structure splitting of 10 μeV is obtained due to the highly symmetric QDs on (111)A. The (111) substrates are also frequently used for nanowire growth, which is another promising quantum structure. Recently, a self-assisted nanowire growth method without Au catalyst was developed,36 and superior optical qualities compared to Au-assisted nanowires were reported.37 The growth of the self-assisted GaAs nanowire is closely related to that of droplet epitaxy, in which incorporation of Ga and As atoms as well as the crystallization of GaAs occurs beneath and around the Ga droplets. The results obtained here provide further insight into the mechanism of self-assisted nanowire growth, paving the way to controlling nanowire morphologies.

Figure 4. Surface morphology of GaAs QDs crystallized at 300 °C. (a) 360 × 343-nm AFM image of GaAs QDs. (b) Local surface slope with respect to the (111)A plane (tangent of the inclination α). Steeper facets appear darker. (c) Cross-section of a QD along [112̅] (A-B) in Figure 3a. (d) Schematic representation of the QD. Different facets are denoted by different gray tones.

side facet. When the temperature is increased, the (114) and equivalent side facets diminish with the A sides vanishing. Eventually, the triangular QDs at 500 °C have three {110} side facets with a truncated (111)A top. Thus, self-limiting growth of the QD is caused by the high stability of the (110) microfacet steps on GaAs(111)A. Finally, we show the optical emission from a single triangular QD in Figure 5. In the GaAs/AlGaAs system, the absence of

Figure 5. Vertically (blue) and horizontally (red) polarized PL spectra of a single triangular GaAs QD at low temperature. Here, H and V denote the two orthogonal directions in linearly polarized PL. Note that the polarization axes are randomly distributed in the QDs on (111)A, consistent with the results of highly symmetric QDs in ref 38. Three peaks correspond to emission from the exciton (X), biexciton (XX), and charged exciton (X*). Fine-structure splitting of 10 μeV is significantly smaller compared to usual QDs on (001), as a result of high symmetry both in substrate and dot shape. The inset shows an AFM image of the QDs.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.

strain allows QDs to be embedded with their shape retained. This is in stark contrast to strained QDs such as InAs/GaAs, in 1414



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(36) Fontcuberta i Morral, A.; Colombo, C.; Abstreiter, G.; Arbiol, J.; Morante, J. R. Appl. Phys. Lett. 2008, 92, 063112. (37) Breuer, S.; Pfuller, C.; Flissikowski, T.; Oliver, B.; Grahn, H. T.; Geelhaar, L.; Riechert, H. Nano Lett. 2011, 11, 1276. (38) Abbarchi, M.; Mastrandrea, C. A.; Kuroda, T.; Sakoda, K.; Koguchi, N.; Sanguinetti, S.; Vinattieri, A.; Gurioli, M. Phys. Rev. B 2008, 78, 125321.

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Self-Limiting Growth of Hexagonal and Triangular Quantum Dots on

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