CRYSTAL GROWTH & DESIGN
Evolution of Holed Nanostructures on GaAs (001)
2009 VOL. 9, NO. 6 2941–2943
Alvason Zhenhua Li,* Zhiming M. Wang,* Jiang Wu, Yanze Xie, Kim A. Sablon, and Gregory J. Salamo Institute of Nanoscale Science and Engineering, UniVersity of Arkansas, FayetteVille, Arkansas 72701 ReceiVed February 14, 2009; ReVised Manuscript ReceiVed April 12, 2009
ABSTRACT: We studied the evolution of holed nanostructures by gallium droplet epitaxy on a GaAs surface. A linear relationship between the height and diameter of outer rings from holed nanostructures was found. Further, an empirical rule to predict the ratio of height to outer ring diameter for Ga and In holed nanostructures was established. This rule provides deeper insights to quantum rings formation from droplet materials. Introduction Self-assembled semiconductor quantum rings have become the focus of intensive research owing to their unique electronic and magneto-optical properties in basic physics and solid-state devices, for example, Aharonov-Bohm interferometer and quantum computing applications.1-7 Among various selfassembled growth methods, droplet epitaxy is shedding new light on the fabrication of such advanced semiconductor devices and peculiar nanostructures.8,9 One of the great advances of droplet epitaxy growth is that it can be used in either homoepitaxy growth or heteroepitaxy growth. Therefore, it has revealed itself as a flexible technique that is applicable to both latticemismatched and lattice-matched systems. Extensive efforts of this unique method have led to dot-like,10-12 ring-like,13-15 and hole-like nanostructures16 since initial research in this direction began by Koguchi et al.17 Here, “hole-like” or “holed” nanostructures is specifically referred to as a ring nanostructure with a hole beneath the substrate, while a “ring-like” nanostructure is specifically referred to as a ring nanostructure with a hole above the substrate. Among them, holed nanostructure, first demonstrated by Wang et al.,18 has great potential to achieve uniform and low-density quantum rings.19-21 However, the growth mechanism of holed nanostructures is not clear, and device quality quantum-ring formation and control process remain very challenging.22 Further investigation is needed to provide a deeper insight of this simple and novel molecular beam epitaxy (MBE) growth process. In this paper, the evolution of GaAs holed nanostructures by high temperature gallium (Ga) droplet epitaxy on GaAs substrate is presented in detail. The relationship between the height and diameter of quantum-ring under various annealing conditions are investigated. This work is for topography/morphography study instead of quantum confinement study, and previous experiences suggest that the resulting nanostructures from Ga-droplet-epitaxy on either GaAs or AlGaAs substrate are not different in many aspects. Therefore, this present work on the homoepitaxial GaAs system keeps the growth system as simple as possible, which will enable the researcher to get deep insight into the underlying physics of droplet epitaxy growth without losing its essential features and worrying about too many parameters. Experimental Procedures Samples were grown on semi-insulating GaAs(001) substrates by MBE. Following thermal deoxidization, a 500 nm thick GaAs buffer layer was * To whom correspondence should be addressed. E-mail: alvali@ uark.edu (A.Z.L.);
[email protected] (Z.M.W.).
grown at 580 °C. The substrate was cooled to 500 °C. Under an ultralow arsenic background pressure of 5.0 × 10-9 Torr, a Ga molecular beam was supplied to the substrate surface, leading to Ga droplet formation. The total amount of deposited Ga was equivalent to three monolayers (ML) of GaAs growth at a growth rate of 1 ML/s. Thereafter, the substrate temperature was increased to 600 or 620 °C as soon as possible (the actual temperature ramp up rate was around 50 °C/min here). Keeping the arsenic background pressure of MBE growth chamber ultralow (around 5.0 × 10-9 Torr), the Ga droplets were annealed under various temperature conditions to be described later.
Results Figure 1 depicts three atomic force microscope (AFM) images (in tapping mode) of various thermal annealing conditions: (a) 0 s at 600 °C, (b) 0 s at 620 °C, (c) 60 s at 620 °C. The matrix of annealing experiments demonstrates the evolution of holed nanostructures. Initially, the deposited Ga atoms form droplets of varying sizes on the substrate surface in order to decrease the surface energy on the wetting layer. The Ga droplets then etch into the GaAs substrate to form various sizes of holed nanostructure, in which liquid droplets transform into crystallized holed nanostructures. Consequently, the initial sizes and shapes of holed nanostructure directly correspond to the initial sizes of droplet, as shown in Figure 1. In the comparison of the different annealing temperatures between Figure 1a,b, a ripening phenomenon is more easily observed at the lower annealing temperature of Figure 1a, in which nanorings, nanoholes, and ripened nanodots coexist, because low temperature results in a slow ripening progress. In increasing the annealing temperature, the ring-size ripened nanodots lessen and eventually disappear. Consequently, bigger ripened nanoislands or even ripened microislands appear. Meanwhile, in comparison of the different annealing times between Figure 1b,c, the significant changes are the following: the smaller rings have disappeared and the depth of holes becomes shallower over time. Further details of the process parameters influencing the diameter and height of the holed nanostructures will follow. For a quantitative analysis of holed nanostructures, we characterize their AFM profiles by height, D1 (inner ring diameter), and D2 (outer ring diameter),16 as illustrated in Figure 2. Because of limitations of current AFM measurements, it is difficult to produce exact and consistent results of the depth of holes. Therefore, in this paper, we have neglected this important parameter, which typically has a maximum depth of ∼18 nm. In this analysis, we do not consider holed nanostructures with a height of less than one monolayer. As shown in Figure 3, the
10.1021/cg900189t CCC: $40.75 2009 American Chemical Society Published on Web 04/30/2009
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Figure 1. AFM images (each is 2 µm × 2 µm) after annealing at various conditions: (a) 0 s at 600 °C, there are two ripening droplet dots sitting in the hole sites, (b) 0 s at 620 °C, (c) 60 s at 620 °C.
Figure 2. Cross-sectional AFM line-scanning profile of a typical holed nanostructure: characterized by height, D1 as inner ring diameter, and D2 as outer ring diameter.
Figure 3. Plots of height versus D2 (outer ring diameter) for three annealing conditions. The straight lines are the linear fit of corresponding annealing conditions. Among these data sets, the highest correlation coefficient of height and outer ring diameter is close to 0.9.
plotting of height versus D2 reveals clearly two important relationships between the height and diameter of outer rings: (1) The height is linearly proportional to the D2. The correlation coefficient of height and outer ring diameter for each data set are as follows: 0.753 (for 600 °C, 0 min annealing sample), 0.863 (for 620 °C, 0 min annealing sample), and 0.858 (for 620 °C, 1 min annealing sample) respectively. (2) Both higher annealing temperature and longer annealing time result in bigger outer rings while the average height decreases. For example, for rings of D2 ) 185 nm, the average height is ∼4 nm (for 600 °C, 0 min annealing sample), ∼3 nm (for 620 °C, 0 min annealing sample), and ∼2 nm (for 620 °C, 1 min annealing sample), respectively.
Figure 4. Plots of height versus D1 (inner ring diameter) for three annealing conditions.
Figure 5. D1 versus D2 (inner ring diameter against outer ring diameter) for three different annealing conditions.
In contrast to the significant results of D2, the plots of height versus D1 for each individual annealing condition, as shown in Figure 4, are diffused; there is no clear relationship between the height and diameter of the inner rings. After the data from three annealing conditions were plotted, the comparison indicates the trend that higher annealing temperature and longer annealing time result in bigger inner rings. Furthermore, as shown in Figure 5, the plots of D1 versus D2 have no clear relationship between the diameters of inner and outer rings for each annealing condition. The correlation coefficient of D1 and D2 for each data set are 0.19 (for 600 °C, 0 min annealing sample), 0.32 (for 620 °C, 0 min annealing sample), and 0.1 (for 620 °C, 1 min annealing sample), respectively. However, if all three data sets were taken together as one, it indicates a linear relationship between inner and outer diameter of the ring,
Evolution of Holed Nanostructures
Crystal Growth & Design, Vol. 9, No. 6, 2009 2943
nanostructures. Further investigation of this empirical rule is in progress.
Figure 6. Approximate ratio of height/diameter for droplet holed nanostructure: the three thin lines are the linear fit for Ga droplet experimental data sets from various annealing conditions. The thick arrow bar is the prediction ratio of the height to the outer ring diameter.
and the correlation coefficient of D1 and D2 for such united data set is 0.56. Discussion The insignificance in the relationship between the height and D1 indicates that the evolution of inner rings involves much complex processes than the outer ring. On the other hand, the strong linearity between the height and D2 suggests the following: (1) The diffusion of Ga atoms is the central process during the formation of the outer ring: higher temperature f higher diffusion rate f reduced height. (2) Nucleation is forced on the skirt (boundary area around the interface between solid substrate and liquid droplet)18,22 of the droplet and plays a key role to solidify the height: longer skirt interface area f higher crystallization f increased height. Very interestingly, based on our experimental data as shown in Figure 3, the following simple linear fit equation was acquired:
y ) 0.043x + c
(1)
where y is the height, x is the diameter of outer ring D2, and c is a constant which is related to annealing conditions (such as, c ) -5 nm for 620 °C, 0 min annealing sample). This approximate equation predicts that the maximum height corresponding to 600 nm diameter outer ring is close to 20 nm, as shown in Figure 6. We found that this prediction is nicely consistent with the experimental data of indium droplet from Stemmann et al.16 This may imply that eq 1 will serve as an empirical rule to predict an approximate ratio of height to diameter of outer ring D2 for general Ga and In holed
Conclusions In conclusion, we investigated the evolution of holed nanostrustures on a GaAs surface by high temperature gallium droplet epitaxy. The height and diameter of the outer rings from holed nanostructures were tuned both by annealing temperature and time, whereas a linear relationship was found. An empirical rule to predict the approximate ratio of height to D2 for general Ga and In holed nanostructures was derived. It is expected that this empirical rule from statistical fit will give further hints of the growth mechanism of droplet epitaxy.
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