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Molecular dynamic simulation of Ag nanowires self-assembling on Si(7 7 17)-2 × 1 surface
Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 567–573
Molecular dynamic simulation of Ag nanowires self-assembling on Si(7 7 17)-2 × 1 surface Tao Ding a,b , Jin Zhang a,∗ , Yu-Quan Ma a , Li Zeng a , Yong-kang Chen a a
b
Department of Physics, Yunnan University, Kunming 650091, PR China Surface Physics Lab (National Key Lab), Fudan University, Shanghai 200433, PR China
Received 20 July 2005; received in revised form 9 November 2005; accepted 10 November 2005 Available online 10 January 2006
Abstract The tight binding molecular dynamic (TBMD) simulation method was used to detect the mechanism of Ag nanowires self-assembling on Si(7 7 17)-2 × 1 surface by mean of double step annealing. Firstly, the potential energy of Si(7 7 17)-2 × 1 surface was calculated, which explained the tetramer areas of (2 2 5) subunit sites of Si(7 7 17)-2 × 1 have the strongest attraction to Ag atoms adsorbed on the surface. And then, the experimental processes of double step annealing were studied by dynamic simulation. The results show that the first annealing at 450 ◦ C made most of Ag atoms move to lower potential sites on the Si(7 7 17)-2 × 1 surface, while the second annealing at 650 ◦ C kept Ag atom chains grew uniformly along tetramer rows. And the simulation results were good agreement with the experiment of Ag nanowires self-assembling on Si(7 7 17)-2 × 1 surface. © 2005 Elsevier B.V. All rights reserved. Keywords: Si(7 7 17)-2 × 1; Ag nanowire; Self-assembling; Molecular dynamic simulation
1. Introduction There has recently been much interest on ultra-thin film growing systems that exhibit favorable self-organization [1,2]. In particular, an attracting system is the growth of one-dimensional nanowires self-assembled on reconstructed Si surfaces [3]. Si(5 5 12)-2 × 1, a high-index surface, has row like structure with 5.35 nm long periodicity, which have been used as a template to grow metal nanowires [4]. Another high-index Si(7 7 17)-2 × 1 surface was also found be similar with Si(5 5 12)-2 × 1 only lack of one (3 3 7) subunit, and usually parasite on the terrace of Si(5 5 12)-2 × 1 surface. Thus, regular silver nanowires could be got by Ag atoms self-assembling in double step annealing method on the Si(7 7 17)-2 × 1 template [5]. However, the mechanism of Ag nanowire formation is not completely clear yet. It is well known that computer simulation is a strong tool for study the surface diffusion and nucleation. The bonding, migration and interaction of Ag atoms on the Si(1 0 0)-2 × 1 surface had been studied by the atom superposition and electron
∗
Corresponding author. Tel.: +86 871 5033697; fax: +86 871 5033697. E-mail address: [email protected] (J. Zhang).
0927-7757/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2005.11.026
delocalization-molecular orbital (ASED-MO) theory [6]. And cave sites of Si surfaces are determined to be the most stable adsorption sites. Yoshimichi et al. [7] √ had√studied the arrangement of Ag atoms of Ag–Si(1 1 1)- 3 × 3 surface by Monte Carlo simulation. So far most of simulation studies focused on low index silicon surfaces [8–10] while the similar study to high index surfaces has rarely been reported. In this paper, we calculated the potential map of Si(7 7 17)-2 × 1 surface in the tight binding method, and used molecular dynamic simulation to investigate Ag nanowires self-assembling on the high index Si(7 7 17)-2 × 1 surface. 2. Experimental The experiments were performed in an ultrahigh vacuum (UHV) system composed of a main and preparation chamber at Chonbuk National University, Korea. The main chamber contains a commercial scanning tunneling microscope (STM) with the sample heater and transfer mechanisms for sample and tip exchanges. The preparation chamber is equipped with the facility for metal deposition. The bass pressure was 2 × 10−10 mbar. The Si(5 5 12) wafers were cut and mounted on the sample holder for the row direction ([−1 1 0]) to be either parallel
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T. Ding et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 567–573
or perpendicular to the heating current-flowing direction. The mounted sample direction was confirmed by STM. The samples were cleaned by degassing at 700 ◦ C for a night and flashing to ∼1200 ◦ C for 2–3 s, some 100 times (P < 5 × 10−10 mbar), and then reconstructed by cooling down at 2 ◦ C/s from ∼1000 ◦ C or ∼700 ◦ C to room temperature (RT). The temperatures were measured with an infrared pyrometer (Minolta TR-630). Ag atoms were evaporated from a Ta basket onto Si substrates at RT, where the deposition rate was calibrated using a thickness monitor. Typical rates were ∼0.5 ML/min, with 1 ML (monolayer) equal to the atomic density of a reconstructed Si(5 5 12)-2 × 1 surface, or 5.84 × 1014 atoms/cm2 . To improve Ag row growth on Si(5 5 12) surface, a new method with the double step fabrication was used to make Ag nanowires. The method includes two post-annealing processes for Ag:Si systems: The first annealing was performed at lower temperature around 450 ◦ C for 10–15 min, the second annealing at 600–650 ◦ C for 10 min and then slow cooling down to RT. The samples here were heated directly by passing direct current (DC) through Si wafers. STM images of the filled electronic states were acquired at RT with a constant current of 0.5–0.8 nA and bias voltages between 1.5 V and 3 V. All images presented here are rendered topographies or error singles of the filled states. 3. Molecular dynamic simulation 3.1. Tight binding method As well known, in the adiabatic approximation the Hamiltonian of a system can be written as [11]: Htot = Ti + Te + Uee + Uei + Uii
(1)
where Ti and Te are the kinetic energy of atoms and electrons; Uee , Uei , Uii are the electron–electron, electron–ion and ion–ion interactions, respectively. Considering the theory of one electron moving in the presence of the average field due to the other valence electrons and ions, let H be the reduced a single electron Hamiltonian and |ψn be its nth eigenfunction, so the one electron Schr¨odinger equation is got: H|ψn = εn |ψn
(2)
In the TB scheme, the eigenfunctions are represented as linear combinations of atomic orbital |φlα [12], n |ψn = clα |φlα (3) lα
where l is the quantum number indexing the orbital and α labels the atom. Slater-orbital basis functions have been employed to represent the valence electron orbital. According to variation principle, the secular equation was concluded n µ=1
[Hµν − εn Sµν ]Cµν = 0
(4)
and the secular determinant was |Hµν − εn Sµν | = 0
(5)
where Huv
⎧ ⎨ −Ii = 1 ⎩ k(Huu + Hvv )Suv 2
u=v u = v
(6)
and Suv , the overlap integral, got by “C Matrix” [13]. The parameters used in the calculation are taken from Ref. [6]. When the single electron energy εn was calculated, the total energy of system can be described as Etot = εn f (εn , T ) + Urep (7) n
where f(εn , T) is the Fermi-Dirac distribution function. The force fα needed to move atoms can now be straightforwardly evaluated from the TBMD Hamiltonian HTBMD =
p2 α + εn f (εn , T ) + Urep 2mα α n
and are given by ∂H ψn f (εn , T ) − ∂Urep ψn fα = − ∂rα ∂rα n
(8)
(9)
based on Hellmann–Feynman principle, the first term can be calculated as ∂H ψn f (εn, T ) ψn ∂r α
n
= −2
n
f (εn, T )
lγ l β
cln β
∂Hlγ,l β (rβγ ) n clγ ∂rα
(10)
where cln represent eigenvectors of the TB Hamiltonian matrix. 3.2. Structural models for Si(7 7 17)-2 × 1 surface The high-index Si(7 7 17) surface oriented between Si(0 0 1) and (1 1 1) possesses unique anisotropic row-like structures that do not exist on the well-known low-index surfaces. This plane similar to another high-index Si(5 5 12) surface, they have approach orientation of only 0.3◦ off and consist of (2 2 5) and (3 3 7) subunits [i.e., (5 5 12) = 2 × (3 3 7) + (2 2 5) and (7 7 17) = (3 3 7) + (2 2 5)]. Both of them, having onedimensional symmetric structures, could offer much more suitable templates for the growth of one-dimensional quantum wires. A model of the reconstructed Si(7 7 17)-2 × 1 surface was constructed according to the atom model proposed by Baski et al. [14], shown in Fig. 1, which can be viewed as a combination of a single (3 3 7) unit cell and one (2 2 5) unit cell. The (3 3 7) unit cells are always observed paired with a (2 2 5) unit, the combination equivalent to one unit cell of (7 7 17). A reconstructed (5 5 12) surface therefore consists of an equal number of (7 7 17) and ‘left-side’ (3 3 7) units [15].
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in the [−1 1 0] direction six (7 7 17) subunits were constructed. ˚ × 46.36 A. ˚ The total size of the simulated surface is 41.89 A 4. Results and discussion 4.1. Growth of Ag nanowires on the Si(7 7 17)-2 × 1 template
Fig. 1. Top and side views of the structure model of Si(7 7 17)-2 × 1 surface. Each (7 7 17) unit cell is equivalent to one unit cell of (3 3 7) plus one unit of (2 2 5). The 2 × 1 unit cell (unit cell = 0.77 nm × 3.78 nm) of (7 7 17) is outlined with a black rectangle. The constituent atomic structures are labeled as follows: D: dimmers; T: tetramers, and 6 (7): -bonded chains atop 6-membered (7membered) rings. In top view (the upper figure), black atoms represent chains, and gray atoms represent dimmer chain and tetramer chain labeled by D and T, respectively. Considering the periodic boundary condition, in the [6 6 −5] direction the right side of (3 3 7) subunit was added a 6 chain, which was corresponding to the 6 chain on the left side of (2 2 5), and in the [−1 1 0] direction six (7 7 17) units were constructed. In side view (the bottom figure), smaller black atoms at the bottommost stand for bulk atoms of Si substrate.
The STM images of clean reconstructed Si(5 5 12)-2 × 1 and Si(7 7 17)-2 × 1 surfaces are shown as Fig. 2a and b, respectively. In our experiment, we have often detected (7 7 17) domains parasitic on Si(5 5 12) surface. It reveals that (5 5 12) unit cells missed (3 3 7) units, resulting in two adjacent (7 7 17) units. Most of wide (7 7 17) domains appear in the terrace adjacent to the step parallel to [−1 1 0] row direction (labeled in Fig. 3c). Usually, the reconstruction of semiconductor surfaces are driven by a delicate energy balance between a variety of factors, the most importance of which are the elimination of dangling bonds and the minimization of surface stress. The role of surface stress has been suggested as a mechanism for the incorporation of extra or missing (3 3 7) unit cells on the vicinal (5 5 12) sample [15]. In addition, the temperature of surface reconstruction is one of important factors to result in thermal reconstruction of surface atoms. In our case, Si(5 5 12) wafers preferred to form the purer Si(5 5 12)-2 × 1 surface structure if they were reconstructed by cooling down at 2 ◦ C/s from ∼1000 ◦ C to RT, whereas appeared frequently the wide Si(7 7 17)-2 × 1 reconstruction domains parasitic on the Si(5 5 12) surface when they were cooled down at 2 ◦ C/s from ∼700 ◦ C to RT. Ag atoms were deposited onto Si(5 5 12)-2 × 1 surfaces with wide Si(7 7 17)-2 × 1 reconstruction domains, Ag rows also grew on Si(7 7 17)-2 × 1 structures. Fig. 3d shows that Ag atomic chains uniformly grow on Si(7 7 17) by the double step fabrication. The 2× periodicity of the Si(7 7 17)-2 × 1 reconstruction is
3.3. Details of molecular dynamic simulation In the dynamic simulation, the position and velocity of simulated atoms was updated by Velocity–Verlet algorithm. The temperatures of simulated system were controlled in the method of scaling atomic velocities. A time step adopted in simulation was 1 fs, and two-dimensional periodic boundary condition was used in x–y plane. The simulated Si(7 7 17)-2 × 1 surface was composed of (2 2 5) and (3 3 7) subunits, and possessed characteristic structure such as -bonded chains, dimmer and tetramer rows. The model for the simulation totally has 995 atoms, divided into 648 bulk atoms and 347 surface atoms of silicon, shown in Fig. 1. Considering the periodic boundary condition, in the [6 6 −5] direction the right side of (3 3 7) subunit was added a 6 chain corresponding to the 6 chain on the left side of (2 2 5), and
Fig. 2. Potential energy map of Si(7 7 17)-2 × 1 surface drawn by a single Ag ad-atom scanning the area of two 2 × 1 unit cells of the Si(7 7 17)-2 × 1 surface. The positions of nine typical potential wells on the surface were marked by A to I from left to right of the surface.
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Fig. 3. Filled-state STM images of two high-index Si surfaces and Ag nanowires self-assembling by the double step fabrication. (a) Error signal image of clean ˚ × 200 A). ˚ The 2 × 1 unit cell (unit cell = 0.77 nm × 5.35 nm) of (5 5 12) is outlined with 68 surface atoms per 2 × 1 reconstructed Si(5 5 12)-2 × 1 surface (200 A unit cell, as well as the prominent structural units of this surface: tetramer rows, -chains, and adsorbed dimer defects. (b) Also error signal image of the clean ˚ × 90 A). ˚ (c) Topography image of wide (7 7 17) domain adjacent to the step parallel to the atomic row direction [−110] (360 A ˚ × 360 A). ˚ Si(7 7 17)-2 × 1 surface (90 A ˚ × 150 A). ˚ (d) Ag chains self-assembling on the Si(7 7 17)-2 × 1 surface by double step fabrication. (150 A
parallel to the row direction and a stronger 3× periodicity forms along their length, and the -chains of the underlying Si reconstruction remains on this surface. To distinguish Ag rows from Si rows, here we make a comparison between clean Si(7 7 17)-2 × 1 (Fig. 3b) and Ag:Si(7 7 17) system (Fig. 3d), Ag rows obviously grew along only one of two tetramers within each unit cell of Si(7 7 17) and form Ag atomic chains with strongly periodic corrugations (3× and 2×) along their length. These rows are the most ordered structures induced by Ag atoms at around 0.1 ML coverage. In addition, we can find out that the well-ordered Ag chains with relatively high aspect ratio were made by double step fabrication. 4.2. Potential energy map of Si(7 7 17)-2 × 1 surface The results of STM experiments show the one-dimensional symmetric structure of Si surface plays an important role in the Ag nanowires self-assembling process. To find the effect of Si substrate during Ag atoms diffusion, the tight bind method was used to calculate the distribution of surface potential energy (SPE). Calculations of the potential-energy surface of Si(7 7 17)2 × 1 were carried out by using an Ag atom as a virtual probe to
˚ y-direction: 17–33 A) ˚ of scanning the area (x-direction: 5–44 A, Si(7 7 17)-2 × 1 surface. Furthermore, this area, two 2 × 1 unit cells of the Si(7 7 17)-2 × 1 surface, was divided into 78 × 32 points equally and on each point of (x, y) the Ag atom, being a virtual probe, was moved from relatively infinite height near to silicon surface. At different height the total energy E of Ag:Si system were calculated, when E reached the minimum at z0 height, Ag atom would stop decreasing, and the value of Emin ( E = E(z0 ) − E(∞)) were recorded as the surface potential-energy of this point (x, y). As a result, the surface potential map is shown in Fig. 2. We find that there exist potential wells in nine typical positions on the surface from left to right: 7 chain A(14, 25.5), dimmer B(17.5, 21.5), the middle C(21.5, 25.5) of two tetramers of (2 2 5), the center D(22.5, 21.5) of tetramers of (2 2 5), the site E(26, 23.5) between tetramers and 6 chains, 6 chains F(29, 25.5), the middle G(36.5, 21.5) of two tetramers in (3 3 7), the center H(38, 25.5) of tetramers of (3 3 7), the site I(42, 23.5) between tetramers and 6 chains of (3 3 7) subunit. The corresponding potential energy of the nine typical positions is listed in Table 1, from which the deepest potential well located at the position C and resulted in the strongest attraction to Ag atoms.
T. Ding et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 567–573
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Fig. 4. Simulations of Ag nanowires self-assemble processes. (a) The top view (upper) and side view (bottom) of initial positions of Ag atoms (larger black atoms) deposited on Si(7 7 17)-2 × 1 surface (gray atoms). (b) Simulation of Ag:Si system heating from room temperature to 450 ◦ C. (c) Simulation of the Ag:Si system annealing at 450 ◦ C. (d) Simulation of the Ag:Si system annealing at 650 ◦ C.
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Table 1 Calculation results for the potential wells on Si(7 7 17)-2 × 1 surface Sites of potential wells
A
B
C
D
E
F
G
H
I
SPE (eV)
−2.74
−3.85
−4.25
−3.66
−3.65
−3.46
−3.72
−3.69
−3.39
On account of two-thirds potential wells distributed in (2 2 5) subunit, it could be concluded that the tetramer area of (2 2 5) has much stronger attraction to Ag atoms than that of (3 3 7) subunit. Furthermore, every kind of surface potential wells distributing in lines led to the surface an anisotropic attraction. That might be the reason why Ag ad-atoms diffused into tetramer areas of (2 2 5) subunits and formed Ag nanowries. 4.3. MD simulation of Ag nanowire self-assembling To understand the mechanism of Ag nanowire selfassembling, the Ag atom diffusion dynamic processes during the double step annealing were simulated by TBMD. The whole process of simulation was done by two main stages corresponding to the double step annealing. The first step simulated the Ag:Si system annealing process at 450 ◦ C, and the second step simulated the annealing at 650 ◦ C. Fig. 4 shows the results of simulations. The number of Ag atoms simulated is 25, same as Ag coverage at 0.1 ML used in our experiments, these Ag atoms randomly distributed on the Si surface, shown in Fig. 4a. Due to the silicon lattice almost no change on the base of experimental observations, to reduce the amount of computation and to focus attention on finding the effect of Si substrate to Ag atoms diffusion, we assumed the Si(7 7 17)-2 × 1 surface atoms did not move during the simulation. Firstly, we used 1.0 × 103 fs to simulate the heating process from room temperature to 450 ◦ C. After the relaxation of this process, the Ag atoms gradually assembled into a little of clusters (see Fig. 4b). Then, the subsequent annealing at 450 ◦ C, kept the temperature by scaling the atomic velocities, was simulated with 1.0 × 104 fs. Some of Ag clusters diffused and further assembled into four larger clusters at this time scale, shown in Fig. 4c. In the annealing simulation, when the time went to 4 × 103 fs the four clusters had been basically formed, and in the rest time these clusters just relaxed in their local places, which revealed the clusters had approached to an equilibrium state at 450 ◦ C. The second step of simulation was the Ag:Si system annealing at 650 ◦ C, which was realized by 3.0 × 104 fs. Since the Ag atoms on the Si surface obtaining larger kinetic energy during the annealing process, in Fig. 4c the independent cluster I linked with cluster II after diffusions, then the cluster III also diffused along the tetramer rows and closed to the cluster grew from I and II, formed a larger wire-like structure. Thus, these clusters in the Si(2 2 5) areas grew into longer wires. Through the relaxation of the Ag:Si system from 650 ◦ C to room temperature, much longer and regular nanowires appeared on the Si(7 7 17)-2 × 1 surface, shown in Fig. 4d. Ag wires in our simulation presented shorter than Ag rows with about 1.6 nm width and 30 nm length got in our experiments, the error mainly came from assuming the Si(7 7 17)-2 × 1 surface atoms did not move in the simulation,
because atomic movements of Si substrate may assist the diffusion of Ag atoms. 5. Conclusions UHV-STM experiment presents that wide Si(7 7 17)-2 × 1 domains parasitic on Si(5 5 12)-2 × 1 has row like structure with 3.78 nm long periodicity, which can be also used as a template to grow metal nanowires. When Ag coverage was at 0.1 ML, the first post-annealing temperature was around 450 ◦ C, then the subsequent annealing at 650 ◦ C and slow-cooling, such a process can promote the well-ordered Ag chains preferentially adsorbing on the tetramer sites, resulting in Ag wires with relatively high aspect ratio and an inter-row spacing of ∼3.78 nm on Si(7 7 17)-2 × 1 surface. We obtained the potential energy map of Si(7 7 17)-2 × 1 surface in the tight-binding method. The surface potential wells were divided into nine types. Two thirds of them existed at tetramer areas of (2 2 5) subunit and arranged in lines, from which we can get a clear picture of the anisotropic surface adsorptive attraction: the region of tetremer rows of (2 2 5) is the most reactive area in Si(7 7 17)-2 × 1 surface structures. Most of Ag atoms diffused to tops of tetramers and nucleate along the more reactive underlying Si tetramer rows, led to Ag nanowires self-assembling. The double step annealing for Ag nanowires self-assembling were simulated by means of TBMD, the results show the annealing temperature was an important factor for the growth of Ag nanowires on Si(7 7 17)-2 × 1 surface: In the double step annealing process, the lower temperature annealing is required for diffusions and cohesions of adsorbed Ag atoms and forming smaller Ag clusters; and the higher temperature annealing is for providing Ag clusters to the tetramer sites to grow longer and more regular Ag nanowires along the tetramer rows of (2 2 5) subunits. Acknowledgements The work was supported by the National Nature Science Foundation of China (No. 60261004, 60361001) and the Nature Science Foundation of Yunnan Province (2002E0008M). Jin Zhang is grateful for the support from KOSEF through the Brain Korea 21 Projects at Chonbuk National University. References [1] J.F. Jia, J.L. Li, X.J. Liang, J. Chin. Electron Microsc. Soc. 21 (3) (2002) 270. [2] H.H. Song, K.M. Jones, A.A. Baski, J. Vac. Sci. Tech. A 17 (4) (1999) 1696. [3] A.A. Baski, K.M. Jones, K.M. Saoud, Ultramicroscopy 86 (2001) 23.
T. Ding et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 567–573 [4] A.A. Baski, K.M. Jones, K.M. Saoud, Appl. Surf. Sci. 182 (2001) 216. [5] R.H. Zhou, P.L. Cao, L.Q. Lee, Surf. Sci. Lett. 290 (1993) L649. [6] J. Zhang, S.H. Cho, W.X. Quan, Y.Z. Zhu, J.M. Seo, J. Korea Vacuum Soc. Technol., JKVST 6 (2) (2002) 79. [7] N. Yoshimichi, K. Yuuki, K. Yuuki, N. Jun, W. Satoshi, Surf. Sci. 493 (2001) 206. [8] J.C. Okon, C. Joachim, Surf. Sci. 376 (1997) L409.
[9] [10] [11] [12] [13]
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T. Katsunori, T. Masaru, Surf. Sci. 384 (1997) 308. H.C. Gregorio, T. Noboru, Surf. Sci. 504 (2002) 101. C. Luciano, Comp. Mater. Sci. 12 (1998) 278. J.C. Slater, G.F. Koster, Phys. Rev. 94 (1954) 1498. H.W. Jones, C.A. Weatherford, Int. J. Quantum Chem. Symp. 12 (1978) 483. [14] A.A. Baski, S.C. Erwin, L.J. Whitman, Science 269 (1995) 1556. [15] A.A. Baski, S.C. Erwin, L.J. Whitman, Surf. Sci. 392 (1997) 69.
Molecular dynamic simulation of Ag nanowires self-assembling on Si(7 7 17)-2 × 1 surface Tao Ding a,b , Jin Zhang a,∗ , Yu-Quan Ma a , Li Zeng a , Yong-kang Chen a a
b
Department of Physics, Yunnan University, Kunming 650091, PR China Surface Physics Lab (National Key Lab), Fudan University, Shanghai 200433, PR China
Received 20 July 2005; received in revised form 9 November 2005; accepted 10 November 2005 Available online 10 January 2006
Abstract The tight binding molecular dynamic (TBMD) simulation method was used to detect the mechanism of Ag nanowires self-assembling on Si(7 7 17)-2 × 1 surface by mean of double step annealing. Firstly, the potential energy of Si(7 7 17)-2 × 1 surface was calculated, which explained the tetramer areas of (2 2 5) subunit sites of Si(7 7 17)-2 × 1 have the strongest attraction to Ag atoms adsorbed on the surface. And then, the experimental processes of double step annealing were studied by dynamic simulation. The results show that the first annealing at 450 ◦ C made most of Ag atoms move to lower potential sites on the Si(7 7 17)-2 × 1 surface, while the second annealing at 650 ◦ C kept Ag atom chains grew uniformly along tetramer rows. And the simulation results were good agreement with the experiment of Ag nanowires self-assembling on Si(7 7 17)-2 × 1 surface. © 2005 Elsevier B.V. All rights reserved. Keywords: Si(7 7 17)-2 × 1; Ag nanowire; Self-assembling; Molecular dynamic simulation
1. Introduction There has recently been much interest on ultra-thin film growing systems that exhibit favorable self-organization [1,2]. In particular, an attracting system is the growth of one-dimensional nanowires self-assembled on reconstructed Si surfaces [3]. Si(5 5 12)-2 × 1, a high-index surface, has row like structure with 5.35 nm long periodicity, which have been used as a template to grow metal nanowires [4]. Another high-index Si(7 7 17)-2 × 1 surface was also found be similar with Si(5 5 12)-2 × 1 only lack of one (3 3 7) subunit, and usually parasite on the terrace of Si(5 5 12)-2 × 1 surface. Thus, regular silver nanowires could be got by Ag atoms self-assembling in double step annealing method on the Si(7 7 17)-2 × 1 template [5]. However, the mechanism of Ag nanowire formation is not completely clear yet. It is well known that computer simulation is a strong tool for study the surface diffusion and nucleation. The bonding, migration and interaction of Ag atoms on the Si(1 0 0)-2 × 1 surface had been studied by the atom superposition and electron
∗
Corresponding author. Tel.: +86 871 5033697; fax: +86 871 5033697. E-mail address: [email protected] (J. Zhang).
0927-7757/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2005.11.026
delocalization-molecular orbital (ASED-MO) theory [6]. And cave sites of Si surfaces are determined to be the most stable adsorption sites. Yoshimichi et al. [7] √ had√studied the arrangement of Ag atoms of Ag–Si(1 1 1)- 3 × 3 surface by Monte Carlo simulation. So far most of simulation studies focused on low index silicon surfaces [8–10] while the similar study to high index surfaces has rarely been reported. In this paper, we calculated the potential map of Si(7 7 17)-2 × 1 surface in the tight binding method, and used molecular dynamic simulation to investigate Ag nanowires self-assembling on the high index Si(7 7 17)-2 × 1 surface. 2. Experimental The experiments were performed in an ultrahigh vacuum (UHV) system composed of a main and preparation chamber at Chonbuk National University, Korea. The main chamber contains a commercial scanning tunneling microscope (STM) with the sample heater and transfer mechanisms for sample and tip exchanges. The preparation chamber is equipped with the facility for metal deposition. The bass pressure was 2 × 10−10 mbar. The Si(5 5 12) wafers were cut and mounted on the sample holder for the row direction ([−1 1 0]) to be either parallel
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T. Ding et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 567–573
or perpendicular to the heating current-flowing direction. The mounted sample direction was confirmed by STM. The samples were cleaned by degassing at 700 ◦ C for a night and flashing to ∼1200 ◦ C for 2–3 s, some 100 times (P < 5 × 10−10 mbar), and then reconstructed by cooling down at 2 ◦ C/s from ∼1000 ◦ C or ∼700 ◦ C to room temperature (RT). The temperatures were measured with an infrared pyrometer (Minolta TR-630). Ag atoms were evaporated from a Ta basket onto Si substrates at RT, where the deposition rate was calibrated using a thickness monitor. Typical rates were ∼0.5 ML/min, with 1 ML (monolayer) equal to the atomic density of a reconstructed Si(5 5 12)-2 × 1 surface, or 5.84 × 1014 atoms/cm2 . To improve Ag row growth on Si(5 5 12) surface, a new method with the double step fabrication was used to make Ag nanowires. The method includes two post-annealing processes for Ag:Si systems: The first annealing was performed at lower temperature around 450 ◦ C for 10–15 min, the second annealing at 600–650 ◦ C for 10 min and then slow cooling down to RT. The samples here were heated directly by passing direct current (DC) through Si wafers. STM images of the filled electronic states were acquired at RT with a constant current of 0.5–0.8 nA and bias voltages between 1.5 V and 3 V. All images presented here are rendered topographies or error singles of the filled states. 3. Molecular dynamic simulation 3.1. Tight binding method As well known, in the adiabatic approximation the Hamiltonian of a system can be written as [11]: Htot = Ti + Te + Uee + Uei + Uii
(1)
where Ti and Te are the kinetic energy of atoms and electrons; Uee , Uei , Uii are the electron–electron, electron–ion and ion–ion interactions, respectively. Considering the theory of one electron moving in the presence of the average field due to the other valence electrons and ions, let H be the reduced a single electron Hamiltonian and |ψn be its nth eigenfunction, so the one electron Schr¨odinger equation is got: H|ψn = εn |ψn
(2)
In the TB scheme, the eigenfunctions are represented as linear combinations of atomic orbital |φlα [12], n |ψn = clα |φlα (3) lα
where l is the quantum number indexing the orbital and α labels the atom. Slater-orbital basis functions have been employed to represent the valence electron orbital. According to variation principle, the secular equation was concluded n µ=1
[Hµν − εn Sµν ]Cµν = 0
(4)
and the secular determinant was |Hµν − εn Sµν | = 0
(5)
where Huv
⎧ ⎨ −Ii = 1 ⎩ k(Huu + Hvv )Suv 2
u=v u = v
(6)
and Suv , the overlap integral, got by “C Matrix” [13]. The parameters used in the calculation are taken from Ref. [6]. When the single electron energy εn was calculated, the total energy of system can be described as Etot = εn f (εn , T ) + Urep (7) n
where f(εn , T) is the Fermi-Dirac distribution function. The force fα needed to move atoms can now be straightforwardly evaluated from the TBMD Hamiltonian HTBMD =
p2 α + εn f (εn , T ) + Urep 2mα α n
and are given by ∂H ψn f (εn , T ) − ∂Urep ψn fα = − ∂rα ∂rα n
(8)
(9)
based on Hellmann–Feynman principle, the first term can be calculated as ∂H ψn f (εn, T ) ψn ∂r α
n
= −2
n
f (εn, T )
lγ l β
cln β
∂Hlγ,l β (rβγ ) n clγ ∂rα
(10)
where cln represent eigenvectors of the TB Hamiltonian matrix. 3.2. Structural models for Si(7 7 17)-2 × 1 surface The high-index Si(7 7 17) surface oriented between Si(0 0 1) and (1 1 1) possesses unique anisotropic row-like structures that do not exist on the well-known low-index surfaces. This plane similar to another high-index Si(5 5 12) surface, they have approach orientation of only 0.3◦ off and consist of (2 2 5) and (3 3 7) subunits [i.e., (5 5 12) = 2 × (3 3 7) + (2 2 5) and (7 7 17) = (3 3 7) + (2 2 5)]. Both of them, having onedimensional symmetric structures, could offer much more suitable templates for the growth of one-dimensional quantum wires. A model of the reconstructed Si(7 7 17)-2 × 1 surface was constructed according to the atom model proposed by Baski et al. [14], shown in Fig. 1, which can be viewed as a combination of a single (3 3 7) unit cell and one (2 2 5) unit cell. The (3 3 7) unit cells are always observed paired with a (2 2 5) unit, the combination equivalent to one unit cell of (7 7 17). A reconstructed (5 5 12) surface therefore consists of an equal number of (7 7 17) and ‘left-side’ (3 3 7) units [15].
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in the [−1 1 0] direction six (7 7 17) subunits were constructed. ˚ × 46.36 A. ˚ The total size of the simulated surface is 41.89 A 4. Results and discussion 4.1. Growth of Ag nanowires on the Si(7 7 17)-2 × 1 template
Fig. 1. Top and side views of the structure model of Si(7 7 17)-2 × 1 surface. Each (7 7 17) unit cell is equivalent to one unit cell of (3 3 7) plus one unit of (2 2 5). The 2 × 1 unit cell (unit cell = 0.77 nm × 3.78 nm) of (7 7 17) is outlined with a black rectangle. The constituent atomic structures are labeled as follows: D: dimmers; T: tetramers, and 6 (7): -bonded chains atop 6-membered (7membered) rings. In top view (the upper figure), black atoms represent chains, and gray atoms represent dimmer chain and tetramer chain labeled by D and T, respectively. Considering the periodic boundary condition, in the [6 6 −5] direction the right side of (3 3 7) subunit was added a 6 chain, which was corresponding to the 6 chain on the left side of (2 2 5), and in the [−1 1 0] direction six (7 7 17) units were constructed. In side view (the bottom figure), smaller black atoms at the bottommost stand for bulk atoms of Si substrate.
The STM images of clean reconstructed Si(5 5 12)-2 × 1 and Si(7 7 17)-2 × 1 surfaces are shown as Fig. 2a and b, respectively. In our experiment, we have often detected (7 7 17) domains parasitic on Si(5 5 12) surface. It reveals that (5 5 12) unit cells missed (3 3 7) units, resulting in two adjacent (7 7 17) units. Most of wide (7 7 17) domains appear in the terrace adjacent to the step parallel to [−1 1 0] row direction (labeled in Fig. 3c). Usually, the reconstruction of semiconductor surfaces are driven by a delicate energy balance between a variety of factors, the most importance of which are the elimination of dangling bonds and the minimization of surface stress. The role of surface stress has been suggested as a mechanism for the incorporation of extra or missing (3 3 7) unit cells on the vicinal (5 5 12) sample [15]. In addition, the temperature of surface reconstruction is one of important factors to result in thermal reconstruction of surface atoms. In our case, Si(5 5 12) wafers preferred to form the purer Si(5 5 12)-2 × 1 surface structure if they were reconstructed by cooling down at 2 ◦ C/s from ∼1000 ◦ C to RT, whereas appeared frequently the wide Si(7 7 17)-2 × 1 reconstruction domains parasitic on the Si(5 5 12) surface when they were cooled down at 2 ◦ C/s from ∼700 ◦ C to RT. Ag atoms were deposited onto Si(5 5 12)-2 × 1 surfaces with wide Si(7 7 17)-2 × 1 reconstruction domains, Ag rows also grew on Si(7 7 17)-2 × 1 structures. Fig. 3d shows that Ag atomic chains uniformly grow on Si(7 7 17) by the double step fabrication. The 2× periodicity of the Si(7 7 17)-2 × 1 reconstruction is
3.3. Details of molecular dynamic simulation In the dynamic simulation, the position and velocity of simulated atoms was updated by Velocity–Verlet algorithm. The temperatures of simulated system were controlled in the method of scaling atomic velocities. A time step adopted in simulation was 1 fs, and two-dimensional periodic boundary condition was used in x–y plane. The simulated Si(7 7 17)-2 × 1 surface was composed of (2 2 5) and (3 3 7) subunits, and possessed characteristic structure such as -bonded chains, dimmer and tetramer rows. The model for the simulation totally has 995 atoms, divided into 648 bulk atoms and 347 surface atoms of silicon, shown in Fig. 1. Considering the periodic boundary condition, in the [6 6 −5] direction the right side of (3 3 7) subunit was added a 6 chain corresponding to the 6 chain on the left side of (2 2 5), and
Fig. 2. Potential energy map of Si(7 7 17)-2 × 1 surface drawn by a single Ag ad-atom scanning the area of two 2 × 1 unit cells of the Si(7 7 17)-2 × 1 surface. The positions of nine typical potential wells on the surface were marked by A to I from left to right of the surface.
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Fig. 3. Filled-state STM images of two high-index Si surfaces and Ag nanowires self-assembling by the double step fabrication. (a) Error signal image of clean ˚ × 200 A). ˚ The 2 × 1 unit cell (unit cell = 0.77 nm × 5.35 nm) of (5 5 12) is outlined with 68 surface atoms per 2 × 1 reconstructed Si(5 5 12)-2 × 1 surface (200 A unit cell, as well as the prominent structural units of this surface: tetramer rows, -chains, and adsorbed dimer defects. (b) Also error signal image of the clean ˚ × 90 A). ˚ (c) Topography image of wide (7 7 17) domain adjacent to the step parallel to the atomic row direction [−110] (360 A ˚ × 360 A). ˚ Si(7 7 17)-2 × 1 surface (90 A ˚ × 150 A). ˚ (d) Ag chains self-assembling on the Si(7 7 17)-2 × 1 surface by double step fabrication. (150 A
parallel to the row direction and a stronger 3× periodicity forms along their length, and the -chains of the underlying Si reconstruction remains on this surface. To distinguish Ag rows from Si rows, here we make a comparison between clean Si(7 7 17)-2 × 1 (Fig. 3b) and Ag:Si(7 7 17) system (Fig. 3d), Ag rows obviously grew along only one of two tetramers within each unit cell of Si(7 7 17) and form Ag atomic chains with strongly periodic corrugations (3× and 2×) along their length. These rows are the most ordered structures induced by Ag atoms at around 0.1 ML coverage. In addition, we can find out that the well-ordered Ag chains with relatively high aspect ratio were made by double step fabrication. 4.2. Potential energy map of Si(7 7 17)-2 × 1 surface The results of STM experiments show the one-dimensional symmetric structure of Si surface plays an important role in the Ag nanowires self-assembling process. To find the effect of Si substrate during Ag atoms diffusion, the tight bind method was used to calculate the distribution of surface potential energy (SPE). Calculations of the potential-energy surface of Si(7 7 17)2 × 1 were carried out by using an Ag atom as a virtual probe to
˚ y-direction: 17–33 A) ˚ of scanning the area (x-direction: 5–44 A, Si(7 7 17)-2 × 1 surface. Furthermore, this area, two 2 × 1 unit cells of the Si(7 7 17)-2 × 1 surface, was divided into 78 × 32 points equally and on each point of (x, y) the Ag atom, being a virtual probe, was moved from relatively infinite height near to silicon surface. At different height the total energy E of Ag:Si system were calculated, when E reached the minimum at z0 height, Ag atom would stop decreasing, and the value of Emin ( E = E(z0 ) − E(∞)) were recorded as the surface potential-energy of this point (x, y). As a result, the surface potential map is shown in Fig. 2. We find that there exist potential wells in nine typical positions on the surface from left to right: 7 chain A(14, 25.5), dimmer B(17.5, 21.5), the middle C(21.5, 25.5) of two tetramers of (2 2 5), the center D(22.5, 21.5) of tetramers of (2 2 5), the site E(26, 23.5) between tetramers and 6 chains, 6 chains F(29, 25.5), the middle G(36.5, 21.5) of two tetramers in (3 3 7), the center H(38, 25.5) of tetramers of (3 3 7), the site I(42, 23.5) between tetramers and 6 chains of (3 3 7) subunit. The corresponding potential energy of the nine typical positions is listed in Table 1, from which the deepest potential well located at the position C and resulted in the strongest attraction to Ag atoms.
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Fig. 4. Simulations of Ag nanowires self-assemble processes. (a) The top view (upper) and side view (bottom) of initial positions of Ag atoms (larger black atoms) deposited on Si(7 7 17)-2 × 1 surface (gray atoms). (b) Simulation of Ag:Si system heating from room temperature to 450 ◦ C. (c) Simulation of the Ag:Si system annealing at 450 ◦ C. (d) Simulation of the Ag:Si system annealing at 650 ◦ C.
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Table 1 Calculation results for the potential wells on Si(7 7 17)-2 × 1 surface Sites of potential wells
A
B
C
D
E
F
G
H
I
SPE (eV)
−2.74
−3.85
−4.25
−3.66
−3.65
−3.46
−3.72
−3.69
−3.39
On account of two-thirds potential wells distributed in (2 2 5) subunit, it could be concluded that the tetramer area of (2 2 5) has much stronger attraction to Ag atoms than that of (3 3 7) subunit. Furthermore, every kind of surface potential wells distributing in lines led to the surface an anisotropic attraction. That might be the reason why Ag ad-atoms diffused into tetramer areas of (2 2 5) subunits and formed Ag nanowries. 4.3. MD simulation of Ag nanowire self-assembling To understand the mechanism of Ag nanowire selfassembling, the Ag atom diffusion dynamic processes during the double step annealing were simulated by TBMD. The whole process of simulation was done by two main stages corresponding to the double step annealing. The first step simulated the Ag:Si system annealing process at 450 ◦ C, and the second step simulated the annealing at 650 ◦ C. Fig. 4 shows the results of simulations. The number of Ag atoms simulated is 25, same as Ag coverage at 0.1 ML used in our experiments, these Ag atoms randomly distributed on the Si surface, shown in Fig. 4a. Due to the silicon lattice almost no change on the base of experimental observations, to reduce the amount of computation and to focus attention on finding the effect of Si substrate to Ag atoms diffusion, we assumed the Si(7 7 17)-2 × 1 surface atoms did not move during the simulation. Firstly, we used 1.0 × 103 fs to simulate the heating process from room temperature to 450 ◦ C. After the relaxation of this process, the Ag atoms gradually assembled into a little of clusters (see Fig. 4b). Then, the subsequent annealing at 450 ◦ C, kept the temperature by scaling the atomic velocities, was simulated with 1.0 × 104 fs. Some of Ag clusters diffused and further assembled into four larger clusters at this time scale, shown in Fig. 4c. In the annealing simulation, when the time went to 4 × 103 fs the four clusters had been basically formed, and in the rest time these clusters just relaxed in their local places, which revealed the clusters had approached to an equilibrium state at 450 ◦ C. The second step of simulation was the Ag:Si system annealing at 650 ◦ C, which was realized by 3.0 × 104 fs. Since the Ag atoms on the Si surface obtaining larger kinetic energy during the annealing process, in Fig. 4c the independent cluster I linked with cluster II after diffusions, then the cluster III also diffused along the tetramer rows and closed to the cluster grew from I and II, formed a larger wire-like structure. Thus, these clusters in the Si(2 2 5) areas grew into longer wires. Through the relaxation of the Ag:Si system from 650 ◦ C to room temperature, much longer and regular nanowires appeared on the Si(7 7 17)-2 × 1 surface, shown in Fig. 4d. Ag wires in our simulation presented shorter than Ag rows with about 1.6 nm width and 30 nm length got in our experiments, the error mainly came from assuming the Si(7 7 17)-2 × 1 surface atoms did not move in the simulation,
because atomic movements of Si substrate may assist the diffusion of Ag atoms. 5. Conclusions UHV-STM experiment presents that wide Si(7 7 17)-2 × 1 domains parasitic on Si(5 5 12)-2 × 1 has row like structure with 3.78 nm long periodicity, which can be also used as a template to grow metal nanowires. When Ag coverage was at 0.1 ML, the first post-annealing temperature was around 450 ◦ C, then the subsequent annealing at 650 ◦ C and slow-cooling, such a process can promote the well-ordered Ag chains preferentially adsorbing on the tetramer sites, resulting in Ag wires with relatively high aspect ratio and an inter-row spacing of ∼3.78 nm on Si(7 7 17)-2 × 1 surface. We obtained the potential energy map of Si(7 7 17)-2 × 1 surface in the tight-binding method. The surface potential wells were divided into nine types. Two thirds of them existed at tetramer areas of (2 2 5) subunit and arranged in lines, from which we can get a clear picture of the anisotropic surface adsorptive attraction: the region of tetremer rows of (2 2 5) is the most reactive area in Si(7 7 17)-2 × 1 surface structures. Most of Ag atoms diffused to tops of tetramers and nucleate along the more reactive underlying Si tetramer rows, led to Ag nanowires self-assembling. The double step annealing for Ag nanowires self-assembling were simulated by means of TBMD, the results show the annealing temperature was an important factor for the growth of Ag nanowires on Si(7 7 17)-2 × 1 surface: In the double step annealing process, the lower temperature annealing is required for diffusions and cohesions of adsorbed Ag atoms and forming smaller Ag clusters; and the higher temperature annealing is for providing Ag clusters to the tetramer sites to grow longer and more regular Ag nanowires along the tetramer rows of (2 2 5) subunits. Acknowledgements The work was supported by the National Nature Science Foundation of China (No. 60261004, 60361001) and the Nature Science Foundation of Yunnan Province (2002E0008M). Jin Zhang is grateful for the support from KOSEF through the Brain Korea 21 Projects at Chonbuk National University. References [1] J.F. Jia, J.L. Li, X.J. Liang, J. Chin. Electron Microsc. Soc. 21 (3) (2002) 270. [2] H.H. Song, K.M. Jones, A.A. Baski, J. Vac. Sci. Tech. A 17 (4) (1999) 1696. [3] A.A. Baski, K.M. Jones, K.M. Saoud, Ultramicroscopy 86 (2001) 23.
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