Theoretical Investigations into Self-Organized Ordered Metallic Semi-Clusters Arrays on Metallic Substrate
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Abstract
Using the energy minimization calculations based on an interfacial potential and a first-principles total energy method, respectively, we show that (2 × 2)/(3 × 3) Pb/Cu(111) system is a stable structure among all the [(n − 1) × (n − 1)]/(n × n) Pb/Cu(111) (n = 2, 3,…, 12) structures. The electronic structure calculations indicate that self-organized ordered Pb semi-clusters arrays are formed on the first Pb monolayer of (2 × 2)/(3 × 3) Pb/Cu(111), which is due to a strain-release effect induced by the inherent misfits. The Pb semi-clusters structure can generate selective adsorption of atoms of semiconductor materials (e.g., Ge) around the semi-clusters, therefore, can be used as a template for the growth of nanoscale structures with a very short periodic length (7.67 Å).
Keywords
Self-organized Template Interface potential Molecular dynamics First-principles calculationIntroduction
The microelectronics industries have refined the fabrication methods to make ever smaller devices, but these methods will soon reach their fundamental limits. A promising alternative way for the fabrication of nanometer functional systems is to grow self-organized atoms and molecules on well-defined surface templates with periodic structures. This idea is of great interest not only for its promising applications in technology but also for a fundamental study [1, 2, 3, 4, 5, 6, 7]. When the mechanisms controlling the self-organized phenomena are fully disclosed, the self-organized growth processes can be steered to create a wide range of surface nanostructures from metallic, semiconducting and molecular materials. Theoretically, the energetic driving forces for self-organization have been explained by various mechanisms, such as overlapping electric [8], magnetic [9], and bulk elastic strain fields [10, 11]. However, many of these systems are too complex to predict a new self-organized structure with sufficient accuracy. Besides, as far as we know, there are only a few first-principles studies on the self-organization template because the experimentally observed super cells are too large to perform such a time-consuming calculation, such as Cu bilayer on Pt(111) and Ag bilayer on Pt(111) with (25 × 25) super cells [2]. Recently, the ordered arrays of clusters on metallic substrate are reported experimentally [12, 13]. As the substrate of the ordered clusters, the self-organized template plays a vital role in the growth process of the ordered clusters arrays. Indeed, the detail properties of these self-organization phenomena need thoroughly theoretical research, such as the structure property of the first adsorbing layer under the second layer in metal-bilayer/metal(111) system, because they cannot be observed directly in experiment. Our previous works focused on the behavior of identical metallic clusters arrays on the clean metallic or clean semiconductor substrate [3, 4]. Now, we turn to the self-organized metallic substrate with metal-bilayer/metal(111) structure, which can be used as a template.
In this paper, we apply two methods to perform energy minimization respectively on a series of complex Pb/Cu(111) interfaces with [(n − 1) × (n − 1)]/(n × n) (n = 2, 3,…, 12) super cells to search a stable template and study its atomic and electronic structures. The two methods are molecular dynamics (MD) method based on Chen–Möbius inversion interfacial potential [14, 15, 16, 17, 18] and self-consistent first-principles method. Some experiments described a method to create almost monodisperse, equally spaced nanostructures through the self-organization of a fcc metal film on fcc metal (111) substrates with a periodic strain-relief template [2]. The nanostructures are stable, which are partly due to that the fcc metal (111) surface is a very stable surface with a very low surface energy [19]. Recently, there are increasing experiments studying the system of Pb atoms deposited on Cu(111) surface using the low-energy electron microscope (LEEM) and the scanning tunneling microscopy (STM) [20]. But as far as we know, very little theoretical study has been performed on the structure of Pb bilayer on Cu(111) surface. The lattice constant misfit ratio (37.1%) between Pb and Cu is very large, so the achievable periodicity of the Pb/Cu(111) template can be very short, if the system is stable. Thus, it will be easy to perform further theoretical study on the stable template with a very high density periodic structure, which may reveal important information for potential applications, e.g. in the high-density memory, catalysis or developing nanostructured device technology. In this paper, we identify a stable template of Pb bilayer on Cu(111) surface with a periodic nanometer structure and reveal the atomic and electronic structure properties of the template.
Calculation Method
In order to study the stability of the Pb/Cu(111) interface structures with misfit, the proper interfacial potentials are developed with Chen–Mőbius lattice inversion method [14, 15, 16, 17, 18], and then the potentials are applied to relax the interface structures with energy minimization method in Cerius2 software package. The interface structures are modeled in super cells of [(n − 1) × (n − 1)]/(n × n) Pb/Cu(111) (n = 2, 3,…, 12) to take the misfit into account. The (n − 1) × (n − 1) indicates the lateral super cell size of the Pb bilayer, and the (n × n) is for the super cell of Cu(111) substrate. The periodic length of the stable Pb/Cu(111) system is expected to be around the lease common multiple of the lattice constants of Pb and Cu. The [(n − 1) × (n − 1)]/(n × n) super cells with the increasing value of n will be easy to meet the lease common multiple condition.
The Cu(111) surface is modeled by repeated slabs with five Cu layers separated by a vacuum region equivalent to twelve Cu layers. Each metal layer in the super cell contains n × n Cu atoms that form a (n × n) surface cell. Two Pb bilayers are adsorbed symmetrically on both sides of the Cu slab. Such a super cell can well simulate the system of Pb bilayer on the Cu(111) surface, including a good description of the interaction between the two sides of the interface. All the Cu atoms are initially located at their bulk positions with the equilibrium lattice constant 3.61 Å. Upon Pb bilayer adsorptions, all the atoms in the unit cell except for the central Cu layer are fully relaxed. The Pb atoms in the Pb bilayer are also initially located at their bulk positions with the equilibrium lattice constant 4.95 Å. The same super cell models are used for the following first-principles calculations.
Then, for the stable structures that are found with energy minimization method based on the interfacial potentials, the first-principles calculations are carried out on these stable structures, which is based on a density functional theory implemented in a projector augmented wave (PAW) representation [21, 22, 23]. The exchange–correlation effect is treated with the generalized gradient approximation (GGA) [24, 25].The plane wave kinetic energy cutoff employed is 25.73 Ry, and the Monkhorst–Park k-point mesh is 2 × 2 × 1 [26]. The total energy convergences with respect to the energy cutoff and the number of k points have been tested. Optimizations of the atomic structures are done by the conjugate-gradient technique, using the calculated Hellmann–Feynman forces as guidance [27]. All the atomic geometries are fully relaxed, except the fixed center Cu layer, till the forces on all relaxed atoms are less than 0.01 eV/Å.
Results and Discussions
The parameters of Φ_{Cu–Pb}, Φ_{Cu–Cu} and Φ_{Pb–Pb} for the Pb bilayer/Cu(111) structure
Pb/Cu(111) | D_{0}(eV) | R_{0}(Å) | y | a_{1}(eV) | b_{1}(Å^{−1}) | c_{1}(Å) | a_{2}(eV) | b_{2}(Å^{−1}) | c_{2}(Å) | a_{3}(eV) | b_{3}(Å^{−1}) | c_{3}(Å) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Φ_{Cu–Pb} | 53.04 | 1.00 | 1.74 | 45.42 | 8.56 | 0.01 | −4.95 | 1.56 | 2.21 | −2.62 | 2.88 | 2.34 |
Φ_{Cu–Cu} | 626.96 | 1.00 | 0.50 | 4082.02 | 3.42 | 0.73 | −476.68 | 0.50 | 1.62 | −669.59 | 1.00 | 1.04 |
Φ_{Pb–Pb} | 370.36 | 1.00 | 1.02 | 4082.02 | 2.64 | 1.09 | −476.68 | 1.05 | 1.02 | −669.59 | 1.33 | 0.17 |
Conclusions
In summary, we find a stable periodic strain-relief template by using energy minimizations with the MD calculations and the self-consistent first-principles calculations. The (2 × 2)/(3 × 3) and (3 × 3)/(4 × 4) Pb bilayer/Cu(111) are stable structures among the [(n − 1) × (n − 1)]/(n × n) Pb bilayer/Cu(111) (n = 2, 3,…, 12) structures, which are calculated with MD simulations based on Chen–Möbius inversion potential. However, first-principles calculations show that the (3 × 3)/(4 × 4) Pb bilayer/Cu(111) is fully covered by Pb atoms with almost (1 × 1) atomic and electronic structures on the surface of Pb bilayer, and thus it is not suitable to be used as a periodic template. For the (2 × 2)/(3 × 3) Pb bilayer/Cu(111) stable structure, the ordered Pb semi-clusters are found to show a high-density array on the first Pb atoms layer, and the high and zero electron charge density areas periodically locate in the second Pb layer. These different areas with different atomic and electronic structure will lead to the selective adsorption of atoms on the surface of (2 × 2)/(3 × 3) Pb bilayer/Cu(111) structure. The further calculations on the eight adsorptions sites of Ge atoms on (2 × 2)/(3 × 3) Pb bilayer/Cu(111) structure also confirm this conclusion. Ge atoms prefer to adsorb on the S3, S4 and S6 sites. This stable periodic template can be realized under certain experimental conditions. As a result, the strain-relief periodic (2 × 2)/(3 × 3) Pb bilayer/Cu(111) structure is a promising candidate for the new self-organized template to assemble ordered quantum dots on it with a very high density, and may be one of the new platforms for studying next-generation microelectronics. Our method may be useful for the search of other stable templates for quantum structure arrays, that is, superlattice of nanostructures with size and period much smaller than the wavelength of an electron.
Notes
Acknowledgments
We thank Prof. Qi-Kun Xue and Yu-Gui Yao for very helpful discussions. The work at Tsinghua University was supported by the Nature Science Foundation of China (NSFC, No. 50531050), the 973 Project (No.2006CB605100), and China Postdoctoral Science Foundation funded project (No. 20090450426). The work of YZ was partially supported by CRI of UNC-Charlotte.
Open Access
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