Size evolution of ion beam synthesized Pb nanoparticles in Al
© Wang and Zhu; licensee Springer. 2014
Received: 16 April 2014
Accepted: 27 June 2014
Published: 10 July 2014
The size evolution of Pb nanoparticles (NPs) synthesized by ion implantation in an epitaxial Al film has been experimentally investigated. The average radius R of Pb NPs was determined as a function of implantation fluence f. The R(f) data were analyzed using various growth models. Our observations suggest that the size evolution of Pb NPs is controlled by the diffusion-limited growth kinetics (R2∝f). With increasing implantation current density, the diffusion coefficient of Pb atoms in Al is evident to be enhanced. By a comparative analysis of the R(f) data, values of the diffusion coefficient of Pb in Al were obtained.
The novel properties of embedded metallic nanoparticles (NPs) are currently the subject of intense research activities driven both by fundamental interest and by their possible applications. Among different possible techniques, high fluence implantation of an insoluble element in a crystalline matrix proved to be suitable in obtaining NP-based materials. The size control of NPs during implantation and subsequent annealing is one of the challenging issues of this approach, since the resulting thermal, optical, magnetic, and superconducting properties of NPs are drastically dependent on their size [1–7]. Therefore, a better understanding of the influence of synthesis parameters, such as implantation fluence and temperature, on average particle size during implantation is of major importance.
In this research, we have investigated the growth kinetics of embedded Pb NPs in Al during the implantation process. The ion beam synthesized Pb NPs were observed to precipitate in a crystalline Al matrix at room temperature . By comparing with the theory of NP growth mechanism, a detailed description of the Pb NP nucleation and size evolution in Al is given. Finally, we obtain estimates for the following: (i) the concentration threshold for precipitation of ion beam synthesized Pb NPs in Al and (ii) the current density-dependent diffusion coefficient of Pb atoms in Al during the implantation at room temperature.
Epitaxial Al film deposition
Al films can be epitaxially grown on 7 × 7 reconstructed Si(111) . In this work, Si(111) wafers with resistivity of 8 to 12 Ωm were used as a substrate. The Si wafers were first cleaned ex situ in a 2% hydrofluoric acid solution and subsequently in situ using a two-step silicon-flux method (silicon beam clean) . This procedure results in a Si(111) surface which is free of contaminants and which exhibits the Si(111) 7 × 7 reconstruction, as confirmed by in situ reflection high energy electron diffraction and scanning tunneling microscopy. A 150-nm-thick Al layer was then evaporated at room temperature in a molecular-beam epitaxy setup with a base pressure of 5 × 10-11 Torr. The deposition rate (approximately 0.2 Å/s) was monitored in situ with a quartz crystal microbalance which is calibrated using X-ray reflectivity. After deposition, the sample was annealed in situ at 350°C for 2 h in order to improve the crystalline quality of Al films.
Ion implantation was performed at room temperature using Pb+ ions at 90 keV with implantation fluences ranging from 0.4 × 1016 to 1.2 × 1017 cm-2. In order to reduce the lattice damage, a channeling geometry was used . The implanted sample was fixed by a clamp pressing the wafer on the sample holder, which is made of stainless steel. By tuning the anode current, the beam current extracted from ion source was controlled. The current densities were maintained at 0.5, 1.0, and 2.0 μAcm-2, respectively, for each sample set with a current fluctuation < 5% during implantation.
Rutherford backscattering spectrometry (RBS) with a 2.023 MeV He+ beam was used to determine the Pb content and Pb depth distribution in the samples, whereas the crystallinity of the Al films is assessed by ion channeling, i.e., RBS with the ion beam directed along a high-symmetry crystal direction. The minimum yield χmin, which is the ratio of backscattering yield with aligned versus random beam incidence, is a direct measure of the crystalline quality of a film . The backscattered He+ particles were detected by two Au-Si surface barrier detectors with an energy resolution of about 15 keV, which were placed at backscattering angles of 10° and 72°, respectively.
Conventional room temperature X-ray diffraction (XRD) was performed on a Bruker D8 diffractometer using Cu Kα1 radiation with a wavelength of 0.1542 nm. We used θ-2θ scans to identify the orientation of the epitaxial Al film and the embedded Pb NPs and to estimate the average size of the embedded Pb particles from the width of diffraction peak using the Scherrer equation .
Virgin Al film on Si(111)
Determination of the implanted Pb content and depth distribution
Size evaluation of Pb nanoparticles in Al
In order to explain the size evolution of the Pb NPs under our experimental conditions, the classical nucleation and growth theory which has been developed for ion implanted systems can be used [24–26]. The formation and growth of NPs during ion implantation can be divided into three distinct stages:
At the early stage of implantation, the impurity atoms are found as dissolved monomers. Depending mainly on the mobility of the implanted atoms, they can either remain ‘frozen’ in their final position or may subsequently diffuse through the lattice. During implantation, the concentration of monomers C m increases linearly with time. Since ion implantation is not a thermodynamic equilibrium process, the solubility limit of the implanted ions in the host can be largely exceeded, achieving impurity concentrations higher than the bulk solubility, C∞.
In the case of non-zero mobility, as C m increases further and exceeds a critical value C C , small agglomerates of impurity atoms (i.e., dimers and trimers) start to form. Consequently, the increase of C m slows down. Subsequently, these tiny agglomerates constitute a pool of nucleation sites and some of them grow (by statistical fluctuations) beyond a critical radius RC, thus forming stable precipitates. Here, RC represents the critical radius above which a particle spontaneously grows and below which it dissolves. These stable precipitates act as sinks for diffusing monomers. Despite the fact that the impurity atoms are continuously implanted, C m starts to decrease and eventually drops below the concentration threshold C C .
where k is the rate of monomer absorption at the particle surface, ϵ-1 = DV a /k is the screening length which compares bulk diffusion to surface integration effect, D is the diffusion coefficient of Pb atoms in Al, and V a is the molar volume of Pb precipitates.
To retrieve the particle growth law in the growth regime, we assume R ≫ R C . The product ϵR = kR/DV a is the key parameter determining the growth mechanism. When kR ≪ DV a , the interface integration is the rate-determining step. In this case, integration of Eq. (2) reveals that the particle size increases linearly with time during the growth regime, i.e., R∝t, with a slope of k(C m - C∞). On the other hand, when kR ≫ DV a , the growth is purely diffusion limited and presents different kinetic behavior as R2∝t with a slope of 2DV a (C m - C∞). While, if kR is comparable with DV a , the growth rate is determined by both diffusion and interface absorption, the precipitates evolve as (ϵR2 + 2R) ∝t. For ion implantation with a constant current density since implantation fluence f∝t, it can be seen that the scaling law of the average particle radius R with implantation fluence f provides a distinct signature for distinguishing the growth kinetics of the embedded NPs. In addition, the important values of the absorption rate k (in the interface kinetic limited case) and the diffusion coefficient D (in the diffusion limited case) during implantation can be deduced.
Size evolution of Pb nanoparticles
Due to the extremely small value of C∞ for Pb in Al (0.19 at.% at 601 K) , the supersaturation and nucleation regimes should already be finished after a short implantation time, i.e., at a low implantation fluence. It was observed that Pb NPs with average radius about 2.1 nm are formed with an implantation fluence of 7 × 1015 cm-2 and a current density at 2.0 μAcm-2 (Figure 6). Thus, the upper limit of the critical monomer concentration for particle nucleation to occur C C can be estimated to be 6 at.% in Al, i.e., 6.2 × 10-3 mol/cm3, by assuming that all the implanted Pb atoms (7 × 1015 cm-2) are dissolved monomers in the Al layer (Figure 4). In addition, since C m < C C in the growth regime, one can safely assume the upper limit of C m = C C = 6.2 × 10-3 mol/cm3 during the implantation process.
We have investigated the clustering process of Pb atoms implanted in a single crystalline Al layer grown on Si(111). By analyzing the average particle radius R as a function of implantation fluence f, we observed the diffusion limited growth of ion beam synthesized Pb NPs during the implantation process. Moreover, with a decreasing implantation current density from 2.0 to 0.5 μAcm-2, a lower limit of the diffusivity of Pb in Al ranging from 0.15 to 0.04 nm2/s was obtained. This phenomenon indicates that implantation current density is one of the parameters which can be applied to tune the particle size during the implantation process.
The work was supported by the National Nature Science Foundation of China 11275175.
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