J. Phys. Chem. C 2010, 114, 15343–15346
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Formation Mechanisms of Multiple Concentric Nanoring Structures upon Droplet Epitaxy X. L. Li* MOE Key Laboratory of Laser Life Science & Institute of Laser Life Science, College of Biophotonics, South China Normal UniVersity, Guangzhou 510631, China ReceiVed: June 3, 2010; ReVised Manuscript ReceiVed: August 2, 2010
We have developed a theoretical model to elucidate the formation mechanisms of multiple concentric nanoring structures upon droplet epitaxy. On the basis of the developed model, we performed the shape evolution of GaAs nanostructures during the multistep crystallization process. Theoretical analyses indicated the rapid growth region at the periphery of the diffusion region is pushed outward by increasing growth temperature, which results in the formation of an outer ring. In addition, according to our model, we proposed that multiple concentric nanoring structures can also be obtained via reducing element flux intensity using a multistep crystallization procedure which may be more advantageous than that via increasing temperature. 1. Introduction In recent years, there has been growing interest in the studies of ring structures in the nanoscale, since they provide ideal systems to be potentially used in mesoscopic physics and fabrication of nanodevices. Because of their particular topology, ring nanostructures show unique electronic, optical, and magnetic properties in one-dimensional confinement.1-4 In order to attain perfect ring nanostructures, various methods have been employed to control the sizes and shapes of nanorings in the past few years.5-17 Recently, droplet epitaxy has been intensively investigated as an important fabrication method of nanostructures with various shapes, such as dot shape,5,6 single-ring shape,5-8 concentric double-ring shape,7-9 and hole shape.9-12 This method has advantages over other methods based on the Stranski-Krastanow growth mode. Droplet epitaxy is applicable to the formation of nanostrutures not only in lattice-mismatched systems such as InGaAs/GaAs18,19 but also in lattice-matched systems such as GaAs/AlGaAs.5-12 The process of droplet epitaxy consists of forming numerous III-column element liquid droplets with a uniform size of less than 100 nm on the substrate surface first, and then crystallizing the droplets to produce epitaxial nanostructures by a V-column element molecular beam supply. By controlling the intensity of V-column element flux and the crystallization temperature, we can dominate the geometry of final nanostructures. Besides the four types of nanostructures mentioned above (dot, singlering, concentric double-ring, and hole), very recently Somaschini et al. reported that the GaAs multiple (from three to five) concentric ring nanostructures have been fabricated by a multistep growth process upon droplet epitaxy.20 Although much progress has been made in fabrications upon droplet epitaxy, the formation mechanisms of these intriguing nanostructures, especially multiple concentric ring nanostructures, still are not well understood. In this contribution, we present a developed model to pursue the formation mechanisms of multiple concentric nanoring structures upon droplet epitaxy. Theoretical analyses reveal that the outer ring of multiple concentric structures is the result that the rapid growth region at the periphery of the diffusion region * Corresponding author. E-mail:
[email protected].
Figure 1. Schematic illustration of the crystallization process of the Ga droplet with As ambience. The growth of GaAs has a higher rate on the boundary of the Ga droplet (region A) and at the periphery of the diffusion region (region C) than in the diffusion region (region B).
is pushed outward by increasing growth temperature in the multistep crystallization procedure. 2. Theoretical Model Taking the GaAs/AlGaAs system as an example, we elucidate the formation mechanisms of GaAs ring-like nanostructures upon droplet epitaxy based on the established kinetic model. In our model, we assume that (i) the evaporation of Ga atoms from the droplet surface is neglected because of the low vapor pressure of Ga,21 (ii) the bulk diffusion of As atoms into Ga droplets is neglected in the case of low As flux intensity,14 and (iii) there is no nucleation of GaAs on the surface of the Ga droplet.22 Accordingly, the loss of Ga atoms only is caused by surface crystallization with As atoms deposited on the boundary of the Ga droplet and on the surface of the substrate, as shown in Figure 1. In the case of crystallization on the boundary of the Ga droplet (region A in Figure 1), As atoms deposited on the droplet surface can arrive at the boundary of the droplet via surface diffusion and crystallize with Ga atoms of the droplet. The crystallization on the surface of the substrate can be classified as two types according to the kinds of crystallized As atoms. The first is crystallization between the As atoms directly from the gas flux and the diffused Ga atoms away from the droplet in the Ga diffusion region (region B in Figure 1), and the other crystallization occurs at the periphery of the
10.1021/jp105094q 2010 American Chemical Society Published on Web 08/24/2010
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diffusion region (region C in Figure 1) where the Ga atoms diffused to the periphery of the diffusion region can crystallize with the As atoms trapped by diffused Ga atoms from the substrate surface around the region. The size of the diffusion region, i.e., region B in Figure 1, is determined by the diffusivity of Ga atoms and the trapping ability to As atoms. According to the experimental observations,5,7 final GaAs nanostructures have a distinct borderline, which means that the diffusing Ga atoms are confined in a finite region and crystallize with As atoms. Therefore, we can consider that the concentration of Ga atoms at the periphery of the diffusion region is zero and all the diffusing Ga atoms from the droplet to the periphery of the diffusion region crystallize with the trapped As atoms. On the basis of our previous theory,22,23 in order to satisfy the condition that all the diffusing Ga atoms from the droplet to the periphery of the diffusion region can crystallize with the trapped As atoms and the concentration of Ga atoms at the periphery of the diffusion region is zero, the amount of the diffusing Ga atoms to the periphery of the diffusion region should be equal to the amount of the trapped As adatoms by the diffusion region. According to Fick’s law, the amount of diffusing Ga atoms from the droplet to the periphery of the diffusion region per unit time can be written as NGa ) 2πh0DGaC0 ln(rGa/rc), where rGa is the radius of the Ga droplet, C0 refers to the concentration of Ga atoms on the droplet boundary, h0 is the thickness of the monolayer, and DGa represents the diffusion coefficient of Ga atoms which is given by DGa ) D0Ga exp(-EGa/kT) (D0Ga is the prefactor, EGa is the diffusion activation energy, and k is the Boltzmann constant). The amount of the trapped As atoms by the diffusion region from the substrate surface around the region per unit time can be calculated by NAs ) 2πrca0Rυ1/υ0 exp[(Ea - Ed)/kT], where a0 is the space between surface sites, υ0 and υ1 are the thermal vibration frequencies for the upward direction and lateral direction, Ea and Ed are the adsorption energy and an energy barrier to hopping between surface sites, and R is the amount of impacting As atoms on the substrate per unit time, which can be written as R ) P/(2πmkT)1/2 (P is the intensity of As flux, and m is the mass of an As atom). Therefore, fromNGa ) NAs, the size of the diffusion region, rc, can be calculated as follows
( )
rc ln
h0D0GaC0υ0 √2πmkT exp(∆E/kT) rc ) rGa a0υ1 P
(1)
where ∆E ) -EGa - Ea + Ed. According to eq 1, the ratio of rc/rGa can be obtained by
rc /rGa ) Lambert w ×
{ [ exp
h0D0GaC0υ0√2πmkT exp(∆E/kT) a0υ1rGaP
]}
(2)
where Lambert w(x) represents the Lambert W function which is also called the omega function and is the inverse function of f(W) ) WeW. 3. Results and Discussion The ratio between the size of the diffusion region and the radius of the droplet, i.e., rc/rGa, intensely affects the shape of the final nanostructure.22,23 Because of mass accumulation of As and Ga atoms in the regions A and C, the growth of GaAs
Figure 2. Simulation results of three different shapes of final GaAs nanostructures: (a) single ring; (b) double rings; (c) hole. The crystallization conditions for the three shapes correspond to (a) 1 × 10-5 Torr As supply at 200 °C, (b) 4 × 10-6 Torr As supply at 200 °C, and (c) 1 × 10-6 Torr As supply at 300 °C, and the distances of the Ga droplets are 300 nm. (d) The calculated values of rc/rGa as a function of the intensity of As flux under different temperatures based on eq 2.
on the boundary of the Ga droplet and at the periphery of the diffusion region has a higher rate than that in other regions,23 as shown in Figure 1. Therefore, the distance between regions A and C, i.e., the size of the diffusion region, determines the shape of the GaAs nanostructure. Figure 2a-c shows the simulation results of three typical final shapes under different values of rc/rGa in the case of the initial Ga droplet with a spherical cap shape (the contact angle with the substrate is 50°, and the base radius is 50 nm; note that all of the initial Ga droplets in the following simulations have the same shape and size based on experimental observations) based on our previous considerations.23 When rc/rGa is close to 1, the regions of A and C with a high growth rate can overlap as the size of the Ga droplet decreases during the crystallization process. In other words, there is only one region (i.e., the boundary of the Ga droplet) with a high growth rate, which results in the formation of a single ring, as shown in Figure 2a. When the values of rc/rGa become rather large, the regions of A and C are separated from each other by region B all the time. The rapid growth in the two regions leads to the formation of the concentric double rings, as shown in Figure 2b. However, when the value of rc is larger than the distance between droplets, region C does not exist because there are no trapped As atoms from the substrate surface around the diffusion region. In this case, the high growth rate at the boundary of the droplet leads to the formation of single ring-like structures which are actually holed nanostructures (Figure 2c). Figure 2d shows the values of rc/rGa as a function of intensity of As flux P under different temperatures T based on eq 2. We can note that the low pressure and the high temperature lead to the rc/rGa increase, and contrarily, the high pressure and the low temperature result in the rc/rGa decrease. According to the analysis above, we can obtain the direction that we can control the shapes of nanostructures from single ring to double rings then to holed structures via reducing the intensity of As flux or increasing the temperature. The nanostructures with varied shapes mentioned above are fabricated only by a one-step crystallization procedure; i.e., both the intensity of As flux and growth temperature are immovable during the crystallization process. If the intensity of As flux or growth temperature are altered during the crystallization process, because of the change of rc/rGa values, the final nanostructures may have more complicated shapes. Recently, Somaschini et al. presented the fabrication of GaAs multiple (from three to five) concentric ring nanostructures by a multistep growth
Multiple Concentric Nanoring Structures
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Figure 3. Schematic illustration of the shape evolution during the twostep crystallization process. Step 1 has the same intensity of As flux and growth temperature as that of fabricating double rings, and step 2 corresponds to increasing growth temperature or reducing intensity of As flux where the value of rc/rGa becomes larger than that in step 1.
process upon droplet epitaxy.20 The innovative growth method is based on time-phased As supply to the Ga droplets at different substrate temperatures. In detail, the crystallization process is divided into multiple steps by the change of substrate temperatures. Our model can also be carried out to elucidate the formation mechanism of the multiple concentric ring structures upon droplet epitaxy. Taking concentric triple rings as an example, the crystallization process is divided into two steps: the first step is keeping the same intensity of As flux and growth temperature as that of fabricating double rings (Figure 3a), and the second step corresponds to increasing growth temperature in order to increase the values of rc/rGa. During step 1, there are two rapid growth regions. The first region is the boundary of the Ga droplet (region A in Figure 1). The rapid growth in the region results in the formation of an inner ring and is caused by the crystallization of the Ga droplet with As atoms which are deposited on the droplet surface and can arrive at the boundary of the droplet via surface diffusion. The second rapid growth region is the periphery of the diffusion region (region C in Figure 1). The rapid growth at the periphery of the diffusion region results in the formation of an outer ring and is caused by the crystallization between the Ga atoms diffused to the periphery of the diffusion region and the As atoms trapped by diffused Ga atoms from the substrate surface around the diffusion region. However, when the growth temperature increases during step 2, the size of the diffusion region becomes large due to the increase of the surface diffusivity of the Ga atoms, which causes the rapid growth region at the periphery of the diffusion region to be pushed outward. The diffusing Ga atoms from the droplet can arrive at the periphery of the new large diffusion region and crystallize with As atoms trapped from around the new diffusion region. In this case, the outer ring formed in step 1 (i.e., the second ring) stops rapid growth because of the lack of trapped As atoms, and the periphery of the new large diffusion region becomes a new rapid growth region. The rapid growth at the periphery of the new diffusion region leads to the formation of the third ring beyond the first double rings formed in step 1, as shown in Figure 3b. Therefore, after the two-step crystallization process, concentric triple rings can be obtained. Figure 4 shows the results of simulations for the fabrication of multiple concentric rings based on the kinetic growth model.23
Figure 4. Simulation results of the surface of GaAs nanostructures during the multistep crystallization process: (a) after the procedure of step 1 (4 × 10-6 Torr As supply at 180 °C for 10 s); (b) after step 2 (growth temperature increased to 210 °C under the same intensity of As flux after step 1 until full crystallization of the Ga droplet); (c) after the four-step crystallization procedure (step 1, 180 °C for 10 s; step 2, 210 °C for 10 s; step 3, 225 °C for 10 s; step 4, 240 °C until full crystallization of the Ga droplet; all the steps are under the same As supply of 4 × 10-6 Torr).
A double-rings-like surface configuration of GaAs structure appears after the crystallization procedure of step 1 (4 × 10-6 Torr As supply at 180 °C for 10 s), as shown in Figure 4a. The formation mechanism of the double-rings-like shape is that the rapid growth in the two regions (boundary of the droplet and periphery of the diffusion region) results in the formation of the concentric double rings, as shown in Figure 3a. When the growth temperature is increased to 210 °C under the same intensity of As flux after step 1 until full crystallization of the Ga droplet, the initial double-rings-like shape during step 1 becomes a triple-rings-like shape after step 2 (Figure 4b). If we keep the growth temperature at 210 °C only for 10 s (step 2) and increase it to 225 °C for 10 s (step 3), and then keep it at 240 °C until full crystallization of the Ga droplet (step 4), a 5-fold rings-like structure can be obtained, as shown in Figure 4c. The main reason of multiple rings formation is that the value of rc/rGa increases with increasing temperature, which induces the rapid growth region at the periphery of the diffusion region to be pushed outward and results in the formation of an outer ring. The increase of rc/rGa can also be achieved via reducing the As flux intensity. We simulate the formation of concentric triple rings by a two-step crystallization procedure. Step 1 corresponds to an As supply of 4 × 10-6 Torr at 180 °C for 10 s, and during step 2, the As supply is decreased to 8.6 × 10-7 Torr at the same temperature until full crystallization of the Ga droplet. In the two-step crystallization procedure, step 1 is the same as that shown by Figure 4a, and the case of 8.6 × 10-7 Torr As supply at 180 °C during step 2 has the same value of rc/rGa (about
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Li do the simplification that the activation energy is a constant during the growth process. In our simulations, the diffusion activation energy of Ga atoms is set to 0.77 eV23 which is slightly lower than that of Ga atoms on the GaAs(001)-(2 × 4) surface reported by Deluca et al. (0.73 eV).25 4. Conclusion
Figure 5. (a) Simulation results of the final shape of GaAs nanostructures after the two-step crystallization procedure (step 1, 4 × 10-6 Torr As supply at 180 °C for 10 s; step 2, 8.7 × 10-7 Torr As supply at 180 °C until full crystallization of the Ga droplet). (b) Line profiles of final GaAs nanostructures shown in Figure 5a (red line) and Figure 4b (black line).
1.53) as that in the case of 4 × 10-6 Torr As supply at 210 °C. After the two-step procedure, a triple-rings-like shape appears, as shown by Figure 5a. The triple-rings-like structure in Figure 5a is similar to that in Figure 4b, as shown by the comparison of the two cases in Figure 5b. Though the multiple concentric rings can be obtained via either increasing growth temperature or decreasing As flux intensity, the two methods have different crystallization times. For example, the time of full crystallization of the Ga droplet during step 2 in the case of 4 × 10-6 Torr As supply at 210 °C is 75 s; however, the time in the case of 8.6 × 10-7 Torr As supply at 180 °C is 290 s. The longer crystallization time is caused by the decrease of As supply per unit time in the case of low As flux intensity. The information suggests that we should reasonably extend crystallization times, especially for each step in the case of a multistep growth process when multiple ring structures are fabricated via decreasing As flux intensity. Because the multistep growth process via decreasing As flux intensity allows more time for manipulation to shift growth conditions, the method may be more advantageous than that via increasing temperature to fabricate multiple ring structures. Noticeably, in our model, we consider that the velocity of the chemical reaction between Ga atoms and As atoms is much higher than that of surface diffusion. Thus, the effect of the chemical reaction is neglected in our simulations. Additionally, to simplify our simulations, the exchange between different atoms is also not considered. In fact, the diffusion activation energy is influenced by surface reconstruction and surface orientation which dominate not only under static conditions but also during the growth process.24 In other words, the activation energy is variable before and after surface reconstruction during the growth process. However, it is difficult to estimate the degree of surface reconstruction and the true surface orientation because the surface morphology is continuously metamorphic during the growth process of GaAs nanostructures. Thus, we are forced to
In summary, in order to gain a better understanding of formation mechanisms of multiple concentric nanoring structures upon droplet epitaxy, we have developed a kinetic model to investigate the growth process by a multistep crystallization procedure. Theoretical analyses showed the rapid growth region at the periphery of the diffusion region is pushed outward by increasing growth temperature, which results in the formation of an outer ring. In addition, according to our model, we proposed that multiple concentric nanoring structures can also be obtained via reducing the As flux intensity using a multistep crystallization procedure. References and Notes (1) Aharonov, Y.; Bohm, D. Phys. ReV. 1959, 115, 485. (2) Bayer, M.; Korkusinski, M.; Hawrylak, P.; Gutbrod, T.; Michel, M.; Forchel, A. Phys. ReV. Lett. 2003, 90, 186801. (3) Yang, N.; Dai, Z. S.; Zhu, J. L. Phys. ReV. B 2008, 77, 245321. (4) Ouyang, G.; Wang, C. X.; Yang, G. W. Chem. ReV. 2009, 109, 4221. (5) Mano, T.; Koguchi, N. J. Cryst. Growth 2005, 278, 108. (6) Huang, S. S.; Niu, Z. C.; Fang, Z. D.; Ni, H. Q.; Gong, Z.; Xia, J. B. Appl. Phys. Lett. 2006, 89, 031921. (7) Mano, T.; Kurada, T.; Sanguinetti, S.; Ochiai, T.; Tateno, T.; Kim, J.; Noda, T.; Kawabe, M.; Sakoda, K.; Kido, G.; Koguchi, N. Nano Lett. 2005, 5, 425. (8) Gong, Z.; Niu, Z. C.; Huang, S. S.; Fang, Z. D.; Sun, B. Q.; Xia, J. B. Appl. Phys. Lett. 2005, 87, 093116. (9) Lee, J. H.; Wang, Z. M.; Abuwaar, Z. Y.; Strom, N. W.; Salamo, G. J. Nanotechnology 2006, 17, 3973. (10) Wang, Z. M.; Holmes, K.; Skultz, J. L.; Salamo, G. J. Phys. Status Solidi A 2005, 8, R85. (11) Tong, C. Z.; Yoon, S. F. Nanotechnology 2008, 19, 365604. (12) Li, A. Z.; Wang, Z. M.; Wu, J.; Xie, Y.; Sablon, K. A.; Salamo, G. J. Cryst. Growth Des. 2009, 9, 2941. (13) Keyser, U. F.; Fu¨hner, C.; Borck, S.; Haug, R. J.; Bichler, M.; Abstreiter, G.; Wegscheider, W. Phys. ReV. Lett. 2003, 90, 196601. (14) Granados, D.; Garcia, J. M. Appl. Phys. Lett. 2003, 82, 2401. (15) Hanke, M.; Mazur, Yu. I.; Marega, E.; AbuWaar, Z. Y., Jr.; Salamo, G. J.; Scha¨fer, P.; Schmidbauer, M. Appl. Phys. Lett. 2007, 91, 043103. (16) Yu, L. W.; Chen, K. J.; Song, J.; Xu, J.; Li, W.; Li, X. F.; Wang, J. M.; Huang, X. F. Phys. ReV. Lett. 2007, 98, 166102. (17) Robinson, J. T.; Evans, P. G.; Liddle, J. A.; Dubon, O. D. Nano Lett. 2007, 7, 2009. (18) Gong, Z.; Niu, Z. C.; Huang, S. S.; Fang, Z. D.; Sun, B. Q.; Xia, J. B. Appl. Phys. Lett. 2005, 87, 093116. (19) Lee, J. H.; Wang, Z. M.; Ware, M. E.; Wijesundara, K. C.; Garrido, M. G.; Stinaff, E. A.; Salamo, G. J. Cryst. Growth Des. 2008, 8, 1945. (20) Somaschini, C.; Bietti, S.; Koguchi, N.; Sanguinetti, S. Nano Lett. 2009, 9, 3419. (21) Tersoff, J.; Johnson, M. D.; Orr, B. G. Phys. ReV. Lett. 1997, 78, 282. (22) Li, X. L.; Yang, G. W. J. Phys. Chem. C 2008, 112, 7693. (23) Li, X. L.; Yang, G. W. J. Appl. Phys. 2009, 105, 103507. (24) Pristovsek, M.; Menhal, H.; Zettler, J.; Richter, W. Appl. Surf. Sci. 2000, 166, 433. (25) DeLuca, P. M.; Labanda, J. G. C.; Barnett, S. A. Appl. Phys. Lett. 1999, 74, 1719.
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