NANO LETTERS
Fabrication of Multiple Concentric Nanoring Structures
2009 Vol. 9, No. 10 3419-3424
C. Somaschini, S. Bietti, N. Koguchi, and S. Sanguinetti* L-NESS and Dipartimento di Scienza dei Materiali, UniVersita´ di Milano Bicocca, Via Cozzi 53, I-20125, Milano, Italy Received May 11, 2009; Revised Manuscript Received August 25, 2009
ABSTRACT We present the fabrication of GaAs/AlGaAs Multiple (from three to five) concentric nanoring structures by an innovative growth method based on droplet epitaxy and characterized by short time As supply to the Ga droplets at different substrate temperatures. The formation mechanism has been interpreted on the basis of a detailed ex situ and in situ characterization of nanostructure morphology and surface reconstruction. We introduce design criteria which will allow to obtain concentric quantum ring structures of the desired complexity.
Quantum mechanical experiments in ring geometries have long fascinated the physics community, as electrons confined in nanometric rings manifest a topological quantum mechanical coherence, the Aharonov-Bohm (AB) effect.1 Exciton AB effect has been predicted as well, due to the exciton nonzero electric dipole moment.2 Quantum ring molecules, made by concentric double quantum ring structures, permit to explore the magneto-optical excitations on the basis of the Rashba spin orbit interaction.3 Quantum rings have a peculiar and useful magnetic field level dispersion; unlike quantum dots the ground state total angular momentum changes from zero to nonzero by increasing the magnetic field.4,5 This also results in a different energy dispersion of the excitons for different ring radius. Since charge tunneling between states of different angular momentum is strongly suppressed by selection rules, double concentric quantum rings eventually offer the control of effective coupling of direct-indirect excitons,6 which is of the utmost relevance in the research of semiconductor-based quantum computational devices as it could pave the way to multiple two level states devices with switchable interaction. Recently, the ability to fill the ring with few electrons has offered the possibility to experimentally detect the AB effect by means of the magnetic oscillation in the persistent current carried by the single electron states.7 It is worth noticing that the AB effect was observed in self-assembled, singly connected, highly anisotropic semiconductor quantum ring structures,8 denoting that symmetry and topology (doubly connected) typical of ideal quantum rings is not strictly required to observe ring related quantum effects. The fabrication of GaAs/AlGaAs single and concentric double quantum rings by droplet epitaxy (DE)9,10 has pro* To whom correspondence
[email protected]. 10.1021/nl901493f CCC: $40.75 Published on Web 09/18/2009
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2009 American Chemical Society
vided suitable semiconductor quantum ring molecules for the investigation of these fundamental physical effects. In fact, Hanbury-Brown and Twiss interferometric measurements have recently demonstrated that concentric double quantum ring structures show single photon emission,11 thus proving that DE concentric double quantum rings can be considered as almost ideal quantum ring systems. The DE12,13 is a flexible growth method, based on the molecular beam epitaxy (MBE), which allows for the fabrication of a large variety of three-dimensional nanostructures with different geometries, such as quantum dots, quantum molecules, quantum rings, and concentric double quantum rings.9,10,14-18 In the case of GaAs growth by DE the substrate is irradiated by a Ga molecular beam flux first, leading to the formation of numerous, nanometer-size, Ga droplets on the surface with uniform size, which are subsequently crystallized into GaAs nanostructures by an As molecular beam supply. The intrinsic design flexibility of the DE variant of MBE is permitted mainly by such splitting in time of the III-column and V-column element supply. This allows an independent choice for each of the two elements of specific growth conditions. Despite being DE, a rather successful method for the fabrication of semiconductor quantum ring structures, the growth dynamics of these intriguing nanostructures from both growth and fundamental physics points of view still remains undisclosed. In this letter, we present through a detailed and extensive characterization of the DE growth process via in situ reflection high energy electron diffraction (RHEED) and ex situ atomic force microscopy (AFM) a model of the growth mechanism of complex nanoring structures, including concentric double quantum rings. The acquired knowledge allowed us to introduce an innovative DE growth procedure, which is an extension of the DE method used to produce
Figure 1. AFM images of the sample surface after the procedure of step 1 (a) and that of the sample surface fabricated by the 3-steps growth procedure (b).
concentric double quantum rings,9 based on short time As supply to the Ga droplets at different substrate temperatures. With this method, we can easily control the crystallization process of the Ga atoms, thus realizing complex nanostructures. We demonstrate the fabrication of GaAs multiple concentric nanorings (Multiple-CNRs) by DE with three and five concentric rings. The DE multiple-step growth process for the fabrication of the GaAs/AlGaAs CNRs is here introduced. The DE growth was carried out in a conventional GEN II MBE system equipped with an Arsenic valved cell by using GaAs (100) semi-insulating substrates. Arsenic cracking temperature was set at 600 °C, thus providing As4 molecular beam. We prepared the susbtrate by growing 750 nm thick GaAs buffer layer and of a 200 nm thick Al0.3Ga0.7 As barrier layer at 580 °C. The substrate temperature was then decreased to 350 °C and the As valve closed. At this temperature, the surface had an As-rich c(4 × 4)β surface reconstruction.19 Subsequently, we performed a sequential three-steps growth procedure. Step 1 corresponds to the supply of 10 MLs of Gallium at 350 °C in absence of As supply, step 2 corresponds to an As flux supply equal to 8 × 10-7 Torr at 250 °C for 20 s, and during step 3 an As flux is supplied of the same intensity at 300 °C for 20 min (thus until full crystallization of the deposited Ga). Figure 1 shows the AFM image of the sample surface fabricated by such three-steps growth procedure. Welldefined GaAs Triple CNR (T-CNR) structures with good rotational symmetry are usually formed from Ga droplets with the inner, middle, and outer ring diameters of around 80, 140, and 210 nm, respectively, and with heights around 7 nm for the inner rings, 4 nm for middle rings, and 3 nm for the outer rings. These T-CNRs show a slight elongation of ∼11% along the [0-11] direction, which could come from the anisotropic surface migration of Ga on the (100) GaAs 3420
Figure 2. AFM images of as-grown samples S1, S2, and S3 (left panels), etched samples S1-E, S2-E, and S3-E (center panels), and corresponding line profiles taken along [0-11] direction (right panels) after 10 MLs Ga supply at 350 °C (top panels), after 8 × 10-7 Torr As supply at 250 °C for 20 s (middle panels), and after 8 × 10 -7 Torr As supply at 300 °C for 20 min (bottom panels).
surface,20 and a finite fraction of them (around 40%) shows defected ring structures (see Figure 1b and sample S3 in Figure 2). The inner ring diameter is nearly equal to that of the original Ga droplet. The density of the T-CNRs structures matches that of the original droplets (around 8 × 108 cm-2), thus confirming that all Ga droplets transformed into GaAs triple rings at the end of the process. To determine the growth dynamics of such T-CNR structures, we followed their formation by stopping the process and quenching the samples just after each process step (samples S1, S2, and S3) and performing a morphological characterization via ex situ AFM measurements. Because, especially after step 1 and 2, a certain amount of unreacted Ga is present on the surface, to determine its distribution and to expose the surface of the already formed GaAs structure after each step, pieces of samples S1, S2 and S3 were selectively etched for pure metallic Ga. The etched samples were named S1-E, S2-E, and S3-E, respectively. In Figure 2, the AFM images and the typical line profiles of the six samples are reported. After the 10 MLs Ga supply at 350 °C (sample S1), numerous nearly hemispherical Gallium droplets were formed with an average diameter of around 80 nm, height around 35 nm, and a density of around 8 × 108 cm-2. After the etching treatment (sample S1-E), it is possible to identify the presence of a GaAs ring structure under the original droplet coming from the crystallization at the droplet’s edge. After step 2, that is, when the initial Ga droplets are irradiated with an arsenic flux of 250 °C for 20 s (sample S2), we observe a complex structure formed by a central dome with the same radius of the initial Ga droplet, surrounded by a shallow ring of ∼140 nm diameter. Because the short time supply of As cannot completely crystallize all the Ga atoms that were present in the droplet, we expected some unreacted Ga atoms on the surface. The morphological analysis of the corresponding etched sample (S2-E) clearly shows that the center dome was made by Nano Lett., Vol. 9, No. 10, 2009
metallic Ga. The exposed GaAs surface of S2-E shows the formation of a double ring structure, whose inner ring was lying in S2 sample under the metallic Ga droplet just at the edge of it. The final As supply at 300 °C for 20 min (sample S3) completely crystallize the Ga atoms by forming the outermost third ring structure with a diameter of around 210 nm. At this point, a complete GaAs T-CNRs structure was obtained. After etching (sample S3-E), no evident change is found on the morphology of the surface, thus showing that no unreacted Ga is present. Let us discuss the phenomenology presented. We fabricated semiconductor nanostructures characterized by three concentric rings by using a 3-step process. However, the rings do not share the same origin. While the two external rings are formed during the two arsenization steps, the inner ring is already there just after the Ga droplet formation, when no intentional As flux is supplied to the sample (Figure 2). The inner ring lies underneath the Ga droplet at its edge and there it remains through all the fabrication process. We believe that the formation of the inner ring is due to the establishment of an internal convection flux that transports the incorporated As atoms toward the droplet edge. The internal convection flux can be caused by a gradient in the surface tension of the droplet. Indeed, some As atoms coming from the substrate can be dissolved at the bottom of the Ga droplets thus creating a difference in concentration respect to the top of the droplets. However, we cannot observe massive dissolution of As form the substrate in to the droplet with a consequent etching of the substrate below the droplet21 due to low (always below 350°) growth temperature. In fact, As solubility in liquid Ga can be estimated from the solubility data obtained by Rubenstein as 10-5 at 350 °C,22 thus meaning that in a typical droplet with 107 Ga atoms less than 100 As atoms can be incorporated in each metallic droplet. The gradient in As concentration results in a difference in the surface tension within the Ga droplets, which in turn originates the surface convection. Furthermore, during and after the Ga deposition lots of As atoms, coming from the residual As flux (∼1 × 10-9 Torr), impinging on the Ga droplet are dissolved into the liquid Ga and transported to the edge of the droplet by the internal surface convection, resulting in the formation of the GaAs inner ring at the droplet’s edge. This speculation is supported by the observation of an increase in the inner ring height when keeping the substrate temperature at 350 °C for 1 h after the Ga droplets deposition. Therefore, the inner ring structure might be the combined result of the low solubility of As in the metallic Ga and of the accretion due to internal convection flux of the GaAs tiny ring found just after the droplet deposition, thus preserving the same diameter for all the growth conditions. Its formation happens during the first T-CNR fabrication step. It is worth noting that because the mechanism formation of the inner ring structure does not depend on the specific conditions used during the arsenization step it shares the same origin of the inner ring in concentric double quantum rings.9 For the two outer rings, which are formed during the arsenization steps, we devise a different formation mechaNano Lett., Vol. 9, No. 10, 2009
Figure 3. Specular beam intensity change as a function of time (a) during the As supply of 8 × 10-7 Torr at 250 °C for 20 s in step 2 and (b) during the As supply of the same intensity at 300 °C in step 3.
nism. As a matter of fact, DE is a growth method of compound III-V semiconductors where a reservoir of the III-column species (the droplet) resides permanently on the growth subtrates and the V-column species is supplied in form of distributed flux. It is therefore the balance between the Ga migration from the droplet and As flux that determines the growth of the GaAs nanostructure. Then, in order to understand such mechanism, it is of the utmost importance to follow the changes in average surface reconstruction during the growth process. This has been determined through the analysis of the RHEED pattern for the determination of the surface reconstruction geometry and of the RHEED specular beam intensity (see Figure 3). During step 1, (4 × 6) surface reconstruction in the Ga-rich limit23 appeared just after 1.7 MLs supply of Ga molecular-beam, while during step 2 and 3 the surface reconstructions changed from the Ga-rich limit (4 × 6) to As-stabilized (2 × 4), and finally As-rich c(4 × 4) surface reconstruction begins to appear and progressively orders. Figure 3a,b shows the intensity change of specular-beams in RHEED, during step 2 and 3, respectively. In both steps, the specular-beam intensities increase first, showing the maximum after around 2 s supply of As flux, where we observe the formation of (2 × 4) surface reconstruction, then decrease to the minimum after further 3 s supply of the As fluxes, corresponding to the initiation of the c(4 × 4) reconstruction.24 Finally, the intensities show a gradual increase again, which is related to the establishment of an ordered c(4 × 4) surface reconstruction. Taking into account the AFM on as grown and etched samples and the RHEED analysis just presented, we propose a mechanism for the formation of CNR structures based on the interplay between the As adsorption on the Ga-rich (4 × 6) surface and the Ga migration on the As-stabilized (2 × 4). Figure 4 shows a schematic diagram of the proposed mechanism. Just after the 10 MLs Ga supply, droplets are formed on a Ga-rich (4 × 6) surface reconstruction, which appears just after 1.7 MLs supply to the c(4 × 4) reconstructed surface (Figure 4a). As soon as arsenic molecular 3421
Figure 4. Schematic explanation of the proposed growth mechanism for the formation of outer rings structures. Ga droplets are formed on a Ga-rich (4 × 6) surface reconstruction (a). During As supply, a (2 × 4) surface reconstruction appears all over the substrate on the top of which the Ga atoms, coming from the droplets, can migrate covering a mean displacement area of ∼Dτ (b). Far away from the droplet the surface turns to the As-rich c(4 × 4). The border of this area act as a pining site for the migration of the Ga atoms (c). The detailed atomic arrangements for the different surface reconstructions are ignored for simplicity.
beam is supplied, an As-stabilized (2 × 4) surface reconstruction starts to form on the substrate and nearly simultaneously some Ga atoms migrate from the droplet and laterally form a monolayer of GaAs25 (Figure 4b). Considering the cylindrical symmetry of the diffusion dynamics in our system, Ga atoms can cover a mean displacement area ≈ Dτ where D is the surface diffusion coefficient of Ga atoms and τ the average time interval between arrival and adsorption of As atoms at a specific site.26 At the same time, at the substrate surface far from the Ga droplets, the reconstruction changes to c(4 × 4), caused by the Arsenic adsorption on the surface without being affected by the Ga diffusion. The formation of the outer ring structure can be explained, considering that for the Ga atoms diffusing from the droplet on the As-stabilized (2 × 4) surface the border to the Asrich c(4 × 4) region acts as a pinning site for the growth, as here Ga atoms can easily find excess As atoms (Figure 4c). It is worth noting that step 2 and step 3 start from similar configurations with a reservoir of metallic Ga in the position of the droplet and a Ga-rich (4 × 6) surface reconstruction. The change in surface reconstruction from As-rich to Garich that happens during the time required to change and stabilize the temperature between step 2 and 3 might be due to a diffusion of Ga from the droplets on the As-rich, forming a 2D GaAs thin layer, in absence of an intentional As flux. It is worth noticing that, although the formation kinetics of the inner and outer rings is different, the composition of the rings is the same due to the crystallization, induced by the As flux, of the Ga contained in the droplets. To confirm our model proposal for the growth mechanism of multiple-CNR structures and to generalize our growth procedure, we realized a five concentric ring structure obtained with the technique previously described for the T-CNR, but extending the growth sequence including two 3422
Figure 5. (a) Two and (b) three-dimensional AFM images of F-CNRs. (c) Line profile along the [0-11] direction of a GaAs F-CNR structure. Starting from the inner and moving to the outermost ring, the ring radii of the structures are around 50, 90, 130, 170, and 210 nm, while the heights are around 13, 8, 7, 5.5, and 4.5 nm, respectively. (d) Arrhenius plot of outer ring radii vs arsenization temperature. The dotted line is a guide for the eyes.
more arsenization steps performed at different temperatures. This time 30 MLs Ga were supplied at 350 °C and four subsequent As supplies were performed respectively at 250, 300, and 325 °C for 20 s and finally at 350 °C for 20 min in order to achieve complete crystallization of the nanostructure. The AFM images and line profile, showing the Five-CNR (F-CNR) structures with good rotational symmetry, are shown in Figure 5. The realization of a F-CNR structure clearly shows the success of the DE procedure we propose in order to introduce new degrees of design in quantum ring structures. We observe a regular behavior in the dependence of outer ring radii on the temperature (see Figure 5d). This allows us to finely tune the radius of each ring in the CNR structure by a convenient choice of the substrate temperature during the arsenization step, thus providing a fundamental design parameter for CNR structures. The observed temperature activated dependence is in agreement with our model where the outer ring radius is determined by a diffusion limited process from the droplet during the arsenization step. The hole at the center of the five ring structures (see Figure 5c) has its bottom below the surface level outside the F-CNR. We believe this is the effect of two concurrent phenomena, (i) the As dissolution from the substrate that occurs below the droplet during the growth and (ii) the twodimensional growth that takes place during the outer rings formation. If on one side, the etching of the substrate below the Ga droplet is a well-established phenomena at high substrate temperatures,21 on the other side we observe a significant difference between the number of Ga atoms initially supplied and that contained in our multiple CNR, as determined via AFM measurements. In F-CNR, this Nano Lett., Vol. 9, No. 10, 2009
Figure 6. PL spectra of the T-CNR sample measured at T ) 14 K. The arrow indicates the theoretical prediction based on the AFM image reported in Figure 6.
difference corresponds to an equivalent amount of ∼10 MLs. This observation suggests that only a fraction of the initially supplied Ga atoms effectively concurs to the formation of the nanostructures, while the larger part might form a twodimensional GaAs thin layer all over the substrate.25 This is caused by a slow crystallization of Ga atoms diffusing from the droplets, even in the absence of an intentional As supply, due to the residual As pressure in the chamber. We believe this two-dimensional layer growth to be the more effective phenomena in determining the apparent depth of the hole, as the low subtrate temperature (always below 350 °C) strongly limits the etching activity of the Ga droplet. The presented model can easily explain also the formation dynamics of the concentric double quantum rings,9 as the concentric double quantum rings are realized via a two-step growth process which corresponds in a deposition of 3.75 MLs of Ga into droplets at 350 °C in absence of As flux followed by step where As with moderate flux (∼1 × 10-7 Torr BEP) is irradiated on the sample at 250 °C until full crystallization of the deposited Ga is achieved. The inner ring should be formed just after the droplet deposition, as it has, like in our T-CNR structure, the same radius of the initial droplet.9 The subsequent arsenization step is, on the other side, responsible of the formation of the outer ring. Finally, the ensemble optical emission of T-CNR structures embedded in a Al0.3Ga0.7 As matrix is shown in Figure 6. The photoluminescence was measured at T ) 14 K and excited in the Al0.3Ga0.7As barrier with a green laser (λ: exc ) 532 nm). A clear emission peak is visible at 1.56 eV with a full width at half-maximum 30 meV above the excitonic GaAs signature at 1.519 eV. To attribute this line, we performed electronic structure calculations following the method outlined in refs 27 and 28 within the effective mass approximation. We used the same materials parameters reported in ref 10 for GaAs and Al0.3Ga0.7As. In the calculations, the potential for quantum confinement was derived by imposing a cylindrical symmetry to the actual shape of a randomly chosen T-CNR, measured by AFM. The predicted T-CNR ground state energy is EGS ) 1.58 eV, thus within the bandwidth of the line at 1.56 eV, which allows us to safely attribute such band to the ensemble Nano Lett., Vol. 9, No. 10, 2009
emission from T-CNR. The ground-state wave function is completely localized in the inner ring, while wave functions localized within the two external rings can be found for more excited states. In conclusion, we have fabricated GaAs multiple (three and five) CNRs by DE introducing an innovative growth method based on short time As supply to the Ga droplets at different substrate temperatures. The growth mechanism has been interpreted on the basis of the morphological evolution of the nanostructures and in situ RHEED analysis of surface reconstruction during the growth. The formation of inner rings structures is explained as due to As transport to the droplet edge by convection fluxes at the surface of the droplet, while the growth of outer rings is shown to be governed by the interplay between As adsorption on the Ga-stabilized surface and Ga migration from the droplet on the As-stabilized surface surronding the droplet. The presented DE technique is capable of producing single addressable, self-assembled nanostructures with the potential capability of fabricating multiple ring structures that could pave the way to multiple two level states devices with switchable interaction. Acknowledgment. We thank M. Gurioli for useful discussions. This work was supported by the CARIPLO Foundation through the QUADIS Project. References (1) Aharonov, Y.; Bohm, D. Phys. ReV. 1959, 115, 485. (2) Grochol, M.; Grosse, F.; Zimmermann, R. Phys. ReV. B 2006, 74, 115416. (3) Kuan, W.-H.; Tang, C.-S.; Chang, C.-H. Phys. ReV. B 2007, 75, 155326. (4) Lorke, A.; Luyken, R. J.; Govorov, A. O.; Kotthaus, J. P.; Petroff, P. M. Phys. ReV. Lett. 2000, 84, 2223. (5) Fuhrer, A.; Lu¨scher, S.; Ihn, T.; an K. Ensslin, T. H.; Wegscheider, W.; Bichler, M. Nature 2001, 413, 822. (6) Dias da Silva, L. G. G. V. M.; Villas-Boas, J.; Ulloa, S. E. Phys. ReV. B 2007, 76, 155306. (7) Kleemans, N. A. J. M.; Bominaar-Silkens, I. M. A.; Fomin, V. M.; Gladilin, V. N.; Granados, D.; Taboada, A. G.; Garcı´a, J. M.; Offermans, P.; Zeitler, U.; Christianen, P. C. M.; Maan, J. C.; Devreese, J. T.; Koenraad, P. M. Phys. ReV. Lett. 2007, 99, 146808. (8) Offermans, P.; Koenraad, P. M.; Wolter, J. H.; Granados, D.; Garcı´a, J. M.; Fomin, V. M.; Gladilin, V. N.; Devreese, J. T. Appl. Phys. Lett. 2005, 87, 131902. (9) Mano, T.; Kuroda, T.; Sanguinetti, S.; Ochiai, T.; Tateno, T.; Kim, J.; Noda, T.; Kawabe, M.; Sakoda, K.; Kido, G.; Koguchi, N. Nano Lett. 2005, 5, 425. (10) Kuroda, T.; Mano, T.; Ochiai, T.; Sanguinetti, S.; Sakoda, K.; Kido, G.; Koguchi, N. Phys. ReV. B 2005, 72, 205301. (11) Abbarchi, M.; Mastrandrea, C. A.; Vinattieri, A.; Sanguinetti, S.; Mano, T.; Kuroda, T.; Koguchi, N.; Sakoda, K.; Gurioli, M. Phys. ReV. B: Condens. Matter 2009, 79, 085308. (12) Koguchi, N.; Takahashi, S.; Chikyow, T. J. Cryst. Growth 1991, 111, 688. (13) Koguchi, N.; Ishige, K. Jpn. J. Appl. Phys. 1993, 32, 2052. (14) Watanabe, K.; Koguchi, N.; Gotoh, Y. Jpn. J. Appl. Phys. 2000, 39, L79. (15) Sablon, K. A.; Lee, J. H.; Wang, Z. M.; Shultz, J. H.; Salamo, G. J. Appl. Phys. Lett. 2008, 92, 203106. (16) Alonso-Gonza´lez, P.; Fuster, P.; Gonzales, L.; Martı´n-Sa´nchez, J.; Gonzales, Y. Appl. Phys. Lett. 2008, 93, 183106. (17) Wang, Z. M.; Holmes, K.; Mazur, Y. I.; Ramsey, K. A.; Salamo, G. J. Nanoscale Res. Lett. 2006, 1, 57. (18) Yamagiwa, M.; Mano, T.; Kuroda, T.; Tateno, T.; Sakoda, K.; Kido, G.; Koguchi, N.; Minami, F. Appl. Phys. Lett. 2006, 89, 113115. (19) Ohtake, A.; Koguchi, N. Appl. Phys. Lett. 2003, 83, 5193. (20) Ohta, K.; Kojima, T.; Nakagawa, T. J. Cryst. Growth 1989, 95, 71. 3423
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(26) It’s worth stressing that D and τ in the DE should be different from the typical MBE values, due to the dissimilar growth kinetics. Detailed studies on this topic are in progress. (27) Marzin, J. Y.; Bastard, G. Solid State Commun. 1994, 92, 437–442. (28) Sanguinetti, S.; Watanabe, K.; Kuroda, T.; Minami, F.; Gotoh, Y.; Koguchi, N. J. Cryst. Growth 2002, 242, 321.
NL901493F
Nano Lett., Vol. 9, No. 10, 2009
