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Ni (1 1¯ 1¯) heteroepitaxial growth
ARTICLE IN PRESS Journal of Crystal Growth 311 (2009) 2736–2741
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Misfit dislocations and adatom domain competitions in Cu/Ni (11¯ 1¯) heteroepitaxial growth Naigen Zhou a,b,, Huajian Gao b, Lang Zhou a a b
School of Materials Science and Engineering, Nanchang University, Nanchang 330031, China Division of Engineering, Brown University, 182 Hope Street, Providence, RI 02912, USA
a r t i c l e in f o
a b s t r a c t
Article history: Received 26 January 2009 Received in revised form 24 February 2009 Accepted 27 February 2009 Communicated by K.H. Ploog Available online 9 March 2009
Three-dimensional molecular dynamics simulations of Cu/Ni (11¯ 1¯) heteroepitaxy were carried out based on the Sutton–Chen EAM potential. It was found that the heteroepitaxial growth leads to the nucleation and competitive growth of FCC and HCP domains in the surface adatom monolayer, leading to a network of misfit dislocations along the domain boundaries. Analyses on surface diffusion energy barriers and energy differences between FCC and HCP domains provide explanations why such domain competition mechanisms and the associated misfit dislocations are expected to play a prevalent role in heteroepitaxial growth. & 2009 Elsevier B.V. All rights reserved.
PACS: 68.55.Ac 02.70.Ns Keywords: A1. Line defects A1. Molecular dynamics A1. Nucleation A1. Surface processes A3. Atomic layer epitaxy A3. Vapor-phase epitaxy
1. Introduction Misfit dislocations constitute one of the most important research topics for heteroepitaxial thin films. For nearly half a century, numerous theoretical and experimental investigations on misfit dislocations have been carried out. One of the most prominent achievements of theoretical investigations is the recognition of a critical thickness [1] beyond which misfit dislocations become thermodynamically favorable, in the sense that the total energy is reduced by the introduction of misfit dislocations whose selfenergy is lower than the strain energy released by them. Depending on the nucleation processes, misfit dislocations may readily form as soon as the film thickness exceeds its critical thickness, or may not form even after the film reaches more than ten times the critical thickness [2,3]. So far, a thorough understanding of misfit dislocation nucleation mechanisms has been elusive due to limitations in the existing experimental methods. Molecular dynamics (MD) simulations can track the trajectories of each atom in a system under precisely controlled
conditions, and are therefore ideally suited to investigate structural evolutions at atomistic scale. By means of MD simulations, researchers have shown that nucleation of misfit dislocations begins with the surface steps [4–6]. Two-dimensional MD simulations showed that misfit dislocations can be nucleated by squeezing out a single atom under compressive mismatch or by inserting an extra lattice atomic row under tensile mismatch [7]. Three-dimensional MD simulations with one dimensional mismatch showed that the nucleation starts with an ejected surface atom [5] or a squeezed-out inverse mini-tetrahedron [8] under compression and with an atom pressed into a thin film [9] or a cross-surface glide [6] under tension. However, these simulations are either two-dimensional MD or three-dimensional MD with one-dimensional mismatch. In the present study, three-dimensional MD simulations with two-dimensional mismatch were carried out to understand the nucleation mechanism of misfit dislocations in Cu/Ni (11¯ 1¯) heteroepitaxial films.
2. Simulation setups Corresponding author at: Division of Engineering, Brown University, 182 Hope
Street, Providence, RI 02912, USA. Tel.: +1 401863 2628. E-mail address: [email protected] (N. Zhou). 0022-0248/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2009.02.047
The setup of the initial rigid structure of the simulation cell is shown in Fig. 1. The material of the substrate is nickel. The original
ARTICLE IN PRESS N. Zhou et al. / Journal of Crystal Growth 311 (2009) 2736–2741
size of the cell is 26d{11 0} 42d{11 2} 14d{111}, where d is the inter-planar distance. To simulate an infinite surface, periodic boundary conditions were applied along the [11 0] and [11¯ 2]. Four bottom atomic layers (one cutoff distance of the potential used) along [11¯ 1¯] were fixed. Atoms in the top 6 surface layers were allowed to move freely in accordance with Newton’s law. A thermal bath algorithm [10] was applied to atoms between the free top layers and the fixed bottom layers to maintain the set temperature. In simulating the depositional growth, Copper atoms with an initial downward velocity were randomly dropped, one at a time, from a height slightly more than one cutoff distance above the film surface. The initial kinetic energy of each depositing atom was set to be 0.33 eV. The frequency of the atom drop determines the deposition rate, which was set to be 13.7 atomic layers/ns in the present simulation. Such an extremely high deposition rate
2737
was a choice of compromise due to the limited time span that could be covered by MD simulations under current computation power. Higher deposition rate usually means shorter adatom life and less adatom motion, which might hinder the normal formation of film structures. To compensate the effect of the unrealistically high deposition rate on film structures, the current practice in MD simulations of film deposition is to raise the film temperature, so that the diffusivity of surface adatoms is raised to compensate the loss of their life time due to high deposition rates [7,11]. This practice is adopted here with an elevated deposition temperature of 700 K. The long-range Finnis–Sinclair EAM potential developed by Sutton and Chen [12,13] was used. In this work, the potential functions were truncated at a cutoff distance equal to 2.3 times the lattice constant of nickel. A predictor–corrector algorithm was adopted to solve the equation of motion. The time step was taken to be 10 3 ps. Every /111S growth plane contains four types of atomic sites: A, B, C and transition sites, as shown as colored circles in Fig. 2. Adatoms will be labeled according to the sites they occupy. For example, an A atom would occupy an A circle. Transition atoms sit outside the circles. The radius of every circle is taken to be 90% of that of closely packed spheres. For examination of the film structures at any time, the system is quenched to 0.001 K or lower, so that the noise from thermal vibrations is removed.
Cu Z:[111] Free layers
Y: [112]
Thermostated layers
Ni
3. Competing domains
Fixed layers
A [1 0 1] projection of the Cu/Ni (11¯ 1¯) heteroepitaxial system obtained after 800 ps of the simulated deposition is shown in Fig. 3, which indicates that a copper crystalline film has grown successfully on the nickel substrate. It was found that copper atoms in the third layer and above have the same structure as the second layer, and are therefore hidden in Fig. 4, which exhibits the structure of the first two copper layers above nickel. In order to identify the site relationship, atoms at different sites are assigned different colors. As shown in Fig. 4a, the first copper layer is an interim plane between nickel substrate and copper film. The atoms in this layer are divided into two different domains (A and C) by transit atoms. According to the FCC stacking order, C domain would be the normal FCC domain after the nickel surface, which is the B layer, while A domain is the HCP domain (stacking fault). The transition from FCC to HCP domains corresponds to an atomic shift of a /1 2 1S/6, where a refers to the lattice constant. Therefore, the transit regions are Shockley partial dislocations. The Burgers vectors of these dislocations are a /1 2 1S/6. So two half Shockley partial dislocation loops are formed in the first copper layer.
X:[110] Fig. 1. The simulation cell of Cu/Ni (11¯ 1¯) epitaxial growth.
A
A
Transition sites
B C
C A
A
A B
B C
A
A
Fig. 2. The atomic site relationship in an FCC {111} plane.
Cu
Disordered atoms Disordered atoms Ni
Fig. 3. The [1 0 1] projection of a snapshot of the Cu/Ni (11¯ 1¯) heteroepitaxial system taken after 800 ps of the simulation.
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Transit atoms
C
A
4. Nucleation of misfit dislocations
A B C
The 2nd Cu layer
C C A The 1st Cu layer
Ni substrate
Aβ
βC
βD βA
Dβ βC
layer between nickel substrate and copper film. Misfit dislocations lie in the first and second Cu layers.
βA
Cβ
Fig. 4. Domain structures and misfit dislocations in Cu/Ni (11¯ 1¯) heteroepitaxy. (a) The structure of the first two copper atomic layers grown on nickel (11¯ 1¯) substrate (Every atom is assigned a color according to its site: A atoms are red, B atoms are green, C atoms are blue and transit atoms are yellow; the interplanar distance of Cu layers are artificially magnified; and the third and upper Cu layers are not displayed for clarity.) and (b) the structure of the misfit dislocation network in the second Cu layer (Burgers vectors marked). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
In the second Cu layer, there are three different domains, A, B and C, which are also separated by transit atoms (Fig. 4a). Among these, A and B are normal stacking domains above the corresponding C and A domains in the first Cu layer, while C domains correspond to a stacking fault above the A domains in the first Cu layer. The boundaries of these domains, i.e. the transit regions, form a network of Shockley partial dislocations. The Burgers vectors of these misfit dislocations marked according to the Thompson Tetrahedron are shown in Fig. 4b. Note that the misfit dislocations network here does not have the shape of regular triangles as analyzed in [14]. A probable reason is that this network was formed during the dynamic process of deposition, and has not reached equilibrium before being covered and restricted by upper atomic layers. It is also interesting to compare the number of atoms in every (11¯ 1¯) plane, which was found to be 728 for the nickel substrate, 688 for the first Cu plane and 675 for the second Cu plane and beyond. This indicates that the first Cu layer serves as a transit
Fig. 5 displays a series of snapshots tracking back to the early stage of the formation of the first Cu layer on Ni substrate. Fig. 5a shows various dimer, trimer, tetramer and larger Cu adatom domains. Besides, a few of them on transit sites, most Cu adatoms sit on either FCC sites (C) or HCP sites (A) of the nickel (11¯ 1¯) surface. The amount of FCC adatoms is approximately equal to that of HCP adatoms. As the deposition process proceeds, larger domains swallow up smaller domains, and both FCC and HCP domains grow and eventually impinge on each other, as shown in Fig. 5b and c. Three possible scenarios may result from the competition between different types of domains: the first is that FCC domains that may win the competition and cover the entire surface, as in normal epitaxial growth. The second is that HCP domains that may win the competition and cover the entire surface, forming a twin boundary [15]. The last is that FCC and HCP domains that would coexist stably, separated by a network of Shockley partial dislocations. The first Cu layer observed here seems to be the last scenario, with two half dislocation loops separating the A and C domains (Fig. 5d). Fig. 6 shows snapshots of the atomic structures of the second Cu layer during the simulated Cu/Ni (11¯ 1¯) heteroepitaxial growth. The simulations show that the formation of the second Cu layer also involves a domain competition process: adatom domains grow and converge together to form misfit dislocations. A difference from the first layer is that there are now four types of domains due to the underneath plane having multiple domains. Transit atoms connect each other into a network of Shockley partial dislocations and separate A, B and C domains. Similar analysis shows that the formation of subsequent growth planes is also a process of domain competition. However, the competitive results are usually the first type, i.e. dominance of FCC domains. Occasionally, the second scenario occurs, resulting in the formation of a twin boundary. The third scenario did not occur after the second layer. To understand the reason why HCP domains of Cu would form frequently on the nickel (11¯ 1¯) plane, we performed a simulation of a single Cu adatom moving on the nickel (11¯ 1¯) plane, and monitor its trajectories and changes in system energy. In every simulation step, the adatom was allowed to move 2% of the distance from its original site to the destination site, and the system is relaxed for 1 ps. The results are shown in Fig. 7. When the adatom moves from a FCC site to the adjacent HCP site, the trajectory is a straight line with an energy barrier of 0.073 eV. However, when moving to another FCC site, the adatom usually passes through an adjacent HCP site before reaching the destination, and the energy barrier would remain the same as that in moving from a FCC site to a HCP site. If the adatom is forced to move from one FCC site to another following a straight trajectory, the energy barrier would be much higher. By fixing the Y coordinate of the adatom during its motion in Fig. 7, we found this energy barrier to be as high as 0.225 eV, which is over three times the corresponding value of moving from an FCC site to an HCP site. In fact, the energy of a Cu adatom on an HCP site of nickel (11¯ 1¯) plane is found to be 0.012 eV lower than that on an FCC site (Fig. 7b). Similar simulations were also performed for a Cu adatom originally sat on an HCP site of nickel (11¯ 1¯). The trajectory of HCP–HCP diffusion was found to pass through an FCC site, with the same energy barrier as in Fig. 7. Therefore, we imagine the following scenario: as Cu adatoms are dropped
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Fig. 5. A top oblique view of some snapshots of the Cu/Ni (11¯ 1¯) system during heteroepitaxial growth (Every atom is assigned a color according to its site, as in Fig. 4. Atoms above the first Cu layer are not displayed for clarity.). (a) 20ps, (b) 50ps, (c) 70ps, and (d) 300ps. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. The structure evolution of the second Cu layer during heteroepitaxial growth on Ni (11¯ 1¯) (Every atom is assigned a color according to its site, as in Fig. 4.). (a) 100ps, (b) 120ps, (c) 160ps, and (d) 360ps. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Move along X Axis, Fixed Y coordinate
0.5
Move along X Axis, Free Y coordinate
-37594.20 0.4 HCP site 0.3 FCC site
0.2
System Energy / eV
Y: [112] Direction / nm
Move along Y Axis, Free X coordinate
Origin site (FCC site)
-37594.25 -37594.30
0.225 eV
-37594.35 -37594.40
HCP site 0.1
0.073 eV -37594.45
0.012 eV
Surface nickel atom 0.0 -0.2
0.0 X: [110] Direction / nm
0
0.2
10
20
30 Time / ps
40
50
60
Fig. 7. Diffusion of a single Cu adatom on the Ni (11¯ 1¯) surface. (a) The atomic trajectory and (b) energy evolution.
size in the Cu/Ni (11¯ 1¯) system, and HCP domains larger than 37 adatoms are more stable in the Cu/Ni (11¯ 1¯) system than those in the homoepitaxial Cu/Cu (11¯ 1¯) and Ni/Ni (11¯ 1¯) systems. These results suggest there will be opportunities for HCP domains of significant size to come in contact with FCC domains during growth, and the resulting domain boundaries correspond to Shockley partial dislocations. From an alternative point of view, misfit dislocations in the Cu/Ni (11¯ 1¯) heteroepitaxial system will decrease the misfit strain energy at the cost of dislocation selfenergy, and the resulting stable dislocation network leads to coexisting FCC and HCP domains in one growth plane. In contrast, since misfit dislocations are energetically unfavorable in homoepitaxy, it would be impossible to maintain a stable network of dislocations, the consequence being no coexistence of FCC and HCP domains.
0.09 -Cu adatoms on Ni(111) surface -Ni adatoms on Ni(111) surface -Cu adatoms on Cu(111) surface
0.08 0.07
EHCP - EFCC / eV
0.06 0.05 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 0
5
10
15
20
25
30
35
40
Number of adatoms Fig. 8. The energy difference between an HCP domain and an FCC domain as a function of the number of adatoms in the domain.
randomly onto the nickel (11¯ 1¯) surface, they hit the sites with the same probability as the HCP sites. Because the energy barrier associated with shuttling an adatom between FCC and HCP sites is lower than that between two FCC (or HCP) sites, the surface diffusion of Cu adatom tends to change between FCC and HCP sites. So for a single Cu adatom, the probability of holding an FCC site is approximately equal to or even less than that of holding an HCP site. To further understand the evolution of domain competition, we measure the energy difference between HCP and FCC domains in regular hexagon shapes as a function of the number of adatoms. The results are shown in Fig. 8. The corresponding results for Cu/Cu (11¯ 1¯) and Ni/Ni (11¯ 1¯) homoepitaxy are also shown for comparison. The energy difference between HCP and FCC domains in the Cu/Ni (11¯ 1¯) system is generally lower than that in both Cu/Cu (11¯ 1¯) and Ni/Ni (11¯ 1¯) systems. Furthermore, the HCP domains have lower energy than the FCC domains when the number of adatoms is less than 37 in the Cu/Ni (11¯ 1¯) system. During the initial growth process, HCP domains with less than 37 adatoms are expected to dominate over FCC domains of similar
5. Conclusion Three-dimensional molecular dynamics simulation of Cu/Ni (11¯ 1¯) heteroepitaxy has been performed based on the Sutton– Chen EAM potential. A network of misfit dislocations is observed in the first and the second epitaxial Cu layers that is identified to be associated with a domain competition mechanism. According to this mechanism, Cu adatoms are deposited randomly on the FCC or HCP sites of nickel (11¯ 1¯) surface, and form FCC domains and HCP domains with the same probabilities. Two types of domains grow competitively. In the first two Cu layers, FCC domains coexist with HCP domains, and Shockley partial dislocations form along the domains boundaries. Analysis on the energy indicates that when a Cu domain contains less than 37 Cu adatoms on the nickel (11¯ 1¯) surface, an HCP domain is energetically more favorable than an FCC domain. Consideration of single Cu adatom diffusion barrier shows that Cu adatoms can hold an HCP site as well as an FCC site.
Acknowledgement The authors are grateful for the support of the present work by the National Natural Science Foundation of China (Grant no. 10502024).
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References [1] [2] [3] [4] [5] [6] [7]
D.C. Houghton, J. Appl. Phys. 70 (1991) 2136. T. Yao, Optoelectronics 6 (1991) 37. J.C. Bean, Phys. Today 39 (1986) 36. M. Ichimura, J. Narayan, Philos. Mag. A 72 (1995) 281. W.C. Liu, S.Q. Shi, H. Huang, C.H. Woo, Comput. Mater. Sci. 23 (2002) 155. N.G. Zhou, L. Zhou, Mater. Chem. Phys. 100 (2006) 168. L. Dong, J. Schnitker, R.W. Smith, D.J. Srolovitz, J. Appl. Phys. 83 (1998) 217.
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[8] N.G. Zhou, L. Zhou, D.X. Du, J. Crys. Growth 289 (2006) 681. [9] W.C. Liu, S.Q. Shi, C.H. Woo, H. Huang, Comput. Modeling Eng. Sci. 3 (2002) 213. [10] S. Toxvared, Phys. Rev. E 47 (1993) 343. [11] X.W. Zhou, H.N.G. Wadley, Surf. Sci. 487 (2001) 159. [12] A.P. Sutton, J. Chen, Philos. Mag. Lett. 61 (1990) 139. [13] H. Rafii-Tabar, A.P. Sutton, Philos. Mag. Lett. 63 (1991) 217. [14] D. Cheng, Z.J. Yan, L. Yan, Thin Solid Films 515 (2007) 3698. [15] X.W. Zhou, H.N.G. Wadley, Acta Mater. 47 (1999) 1063.
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Misfit dislocations and adatom domain competitions in Cu/Ni (11¯ 1¯) heteroepitaxial growth Naigen Zhou a,b,, Huajian Gao b, Lang Zhou a a b
School of Materials Science and Engineering, Nanchang University, Nanchang 330031, China Division of Engineering, Brown University, 182 Hope Street, Providence, RI 02912, USA
a r t i c l e in f o
a b s t r a c t
Article history: Received 26 January 2009 Received in revised form 24 February 2009 Accepted 27 February 2009 Communicated by K.H. Ploog Available online 9 March 2009
Three-dimensional molecular dynamics simulations of Cu/Ni (11¯ 1¯) heteroepitaxy were carried out based on the Sutton–Chen EAM potential. It was found that the heteroepitaxial growth leads to the nucleation and competitive growth of FCC and HCP domains in the surface adatom monolayer, leading to a network of misfit dislocations along the domain boundaries. Analyses on surface diffusion energy barriers and energy differences between FCC and HCP domains provide explanations why such domain competition mechanisms and the associated misfit dislocations are expected to play a prevalent role in heteroepitaxial growth. & 2009 Elsevier B.V. All rights reserved.
PACS: 68.55.Ac 02.70.Ns Keywords: A1. Line defects A1. Molecular dynamics A1. Nucleation A1. Surface processes A3. Atomic layer epitaxy A3. Vapor-phase epitaxy
1. Introduction Misfit dislocations constitute one of the most important research topics for heteroepitaxial thin films. For nearly half a century, numerous theoretical and experimental investigations on misfit dislocations have been carried out. One of the most prominent achievements of theoretical investigations is the recognition of a critical thickness [1] beyond which misfit dislocations become thermodynamically favorable, in the sense that the total energy is reduced by the introduction of misfit dislocations whose selfenergy is lower than the strain energy released by them. Depending on the nucleation processes, misfit dislocations may readily form as soon as the film thickness exceeds its critical thickness, or may not form even after the film reaches more than ten times the critical thickness [2,3]. So far, a thorough understanding of misfit dislocation nucleation mechanisms has been elusive due to limitations in the existing experimental methods. Molecular dynamics (MD) simulations can track the trajectories of each atom in a system under precisely controlled
conditions, and are therefore ideally suited to investigate structural evolutions at atomistic scale. By means of MD simulations, researchers have shown that nucleation of misfit dislocations begins with the surface steps [4–6]. Two-dimensional MD simulations showed that misfit dislocations can be nucleated by squeezing out a single atom under compressive mismatch or by inserting an extra lattice atomic row under tensile mismatch [7]. Three-dimensional MD simulations with one dimensional mismatch showed that the nucleation starts with an ejected surface atom [5] or a squeezed-out inverse mini-tetrahedron [8] under compression and with an atom pressed into a thin film [9] or a cross-surface glide [6] under tension. However, these simulations are either two-dimensional MD or three-dimensional MD with one-dimensional mismatch. In the present study, three-dimensional MD simulations with two-dimensional mismatch were carried out to understand the nucleation mechanism of misfit dislocations in Cu/Ni (11¯ 1¯) heteroepitaxial films.
2. Simulation setups Corresponding author at: Division of Engineering, Brown University, 182 Hope
Street, Providence, RI 02912, USA. Tel.: +1 401863 2628. E-mail address: [email protected] (N. Zhou). 0022-0248/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2009.02.047
The setup of the initial rigid structure of the simulation cell is shown in Fig. 1. The material of the substrate is nickel. The original
ARTICLE IN PRESS N. Zhou et al. / Journal of Crystal Growth 311 (2009) 2736–2741
size of the cell is 26d{11 0} 42d{11 2} 14d{111}, where d is the inter-planar distance. To simulate an infinite surface, periodic boundary conditions were applied along the [11 0] and [11¯ 2]. Four bottom atomic layers (one cutoff distance of the potential used) along [11¯ 1¯] were fixed. Atoms in the top 6 surface layers were allowed to move freely in accordance with Newton’s law. A thermal bath algorithm [10] was applied to atoms between the free top layers and the fixed bottom layers to maintain the set temperature. In simulating the depositional growth, Copper atoms with an initial downward velocity were randomly dropped, one at a time, from a height slightly more than one cutoff distance above the film surface. The initial kinetic energy of each depositing atom was set to be 0.33 eV. The frequency of the atom drop determines the deposition rate, which was set to be 13.7 atomic layers/ns in the present simulation. Such an extremely high deposition rate
2737
was a choice of compromise due to the limited time span that could be covered by MD simulations under current computation power. Higher deposition rate usually means shorter adatom life and less adatom motion, which might hinder the normal formation of film structures. To compensate the effect of the unrealistically high deposition rate on film structures, the current practice in MD simulations of film deposition is to raise the film temperature, so that the diffusivity of surface adatoms is raised to compensate the loss of their life time due to high deposition rates [7,11]. This practice is adopted here with an elevated deposition temperature of 700 K. The long-range Finnis–Sinclair EAM potential developed by Sutton and Chen [12,13] was used. In this work, the potential functions were truncated at a cutoff distance equal to 2.3 times the lattice constant of nickel. A predictor–corrector algorithm was adopted to solve the equation of motion. The time step was taken to be 10 3 ps. Every /111S growth plane contains four types of atomic sites: A, B, C and transition sites, as shown as colored circles in Fig. 2. Adatoms will be labeled according to the sites they occupy. For example, an A atom would occupy an A circle. Transition atoms sit outside the circles. The radius of every circle is taken to be 90% of that of closely packed spheres. For examination of the film structures at any time, the system is quenched to 0.001 K or lower, so that the noise from thermal vibrations is removed.
Cu Z:[111] Free layers
Y: [112]
Thermostated layers
Ni
3. Competing domains
Fixed layers
A [1 0 1] projection of the Cu/Ni (11¯ 1¯) heteroepitaxial system obtained after 800 ps of the simulated deposition is shown in Fig. 3, which indicates that a copper crystalline film has grown successfully on the nickel substrate. It was found that copper atoms in the third layer and above have the same structure as the second layer, and are therefore hidden in Fig. 4, which exhibits the structure of the first two copper layers above nickel. In order to identify the site relationship, atoms at different sites are assigned different colors. As shown in Fig. 4a, the first copper layer is an interim plane between nickel substrate and copper film. The atoms in this layer are divided into two different domains (A and C) by transit atoms. According to the FCC stacking order, C domain would be the normal FCC domain after the nickel surface, which is the B layer, while A domain is the HCP domain (stacking fault). The transition from FCC to HCP domains corresponds to an atomic shift of a /1 2 1S/6, where a refers to the lattice constant. Therefore, the transit regions are Shockley partial dislocations. The Burgers vectors of these dislocations are a /1 2 1S/6. So two half Shockley partial dislocation loops are formed in the first copper layer.
X:[110] Fig. 1. The simulation cell of Cu/Ni (11¯ 1¯) epitaxial growth.
A
A
Transition sites
B C
C A
A
A B
B C
A
A
Fig. 2. The atomic site relationship in an FCC {111} plane.
Cu
Disordered atoms Disordered atoms Ni
Fig. 3. The [1 0 1] projection of a snapshot of the Cu/Ni (11¯ 1¯) heteroepitaxial system taken after 800 ps of the simulation.
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Transit atoms
C
A
4. Nucleation of misfit dislocations
A B C
The 2nd Cu layer
C C A The 1st Cu layer
Ni substrate
Aβ
βC
βD βA
Dβ βC
layer between nickel substrate and copper film. Misfit dislocations lie in the first and second Cu layers.
βA
Cβ
Fig. 4. Domain structures and misfit dislocations in Cu/Ni (11¯ 1¯) heteroepitaxy. (a) The structure of the first two copper atomic layers grown on nickel (11¯ 1¯) substrate (Every atom is assigned a color according to its site: A atoms are red, B atoms are green, C atoms are blue and transit atoms are yellow; the interplanar distance of Cu layers are artificially magnified; and the third and upper Cu layers are not displayed for clarity.) and (b) the structure of the misfit dislocation network in the second Cu layer (Burgers vectors marked). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
In the second Cu layer, there are three different domains, A, B and C, which are also separated by transit atoms (Fig. 4a). Among these, A and B are normal stacking domains above the corresponding C and A domains in the first Cu layer, while C domains correspond to a stacking fault above the A domains in the first Cu layer. The boundaries of these domains, i.e. the transit regions, form a network of Shockley partial dislocations. The Burgers vectors of these misfit dislocations marked according to the Thompson Tetrahedron are shown in Fig. 4b. Note that the misfit dislocations network here does not have the shape of regular triangles as analyzed in [14]. A probable reason is that this network was formed during the dynamic process of deposition, and has not reached equilibrium before being covered and restricted by upper atomic layers. It is also interesting to compare the number of atoms in every (11¯ 1¯) plane, which was found to be 728 for the nickel substrate, 688 for the first Cu plane and 675 for the second Cu plane and beyond. This indicates that the first Cu layer serves as a transit
Fig. 5 displays a series of snapshots tracking back to the early stage of the formation of the first Cu layer on Ni substrate. Fig. 5a shows various dimer, trimer, tetramer and larger Cu adatom domains. Besides, a few of them on transit sites, most Cu adatoms sit on either FCC sites (C) or HCP sites (A) of the nickel (11¯ 1¯) surface. The amount of FCC adatoms is approximately equal to that of HCP adatoms. As the deposition process proceeds, larger domains swallow up smaller domains, and both FCC and HCP domains grow and eventually impinge on each other, as shown in Fig. 5b and c. Three possible scenarios may result from the competition between different types of domains: the first is that FCC domains that may win the competition and cover the entire surface, as in normal epitaxial growth. The second is that HCP domains that may win the competition and cover the entire surface, forming a twin boundary [15]. The last is that FCC and HCP domains that would coexist stably, separated by a network of Shockley partial dislocations. The first Cu layer observed here seems to be the last scenario, with two half dislocation loops separating the A and C domains (Fig. 5d). Fig. 6 shows snapshots of the atomic structures of the second Cu layer during the simulated Cu/Ni (11¯ 1¯) heteroepitaxial growth. The simulations show that the formation of the second Cu layer also involves a domain competition process: adatom domains grow and converge together to form misfit dislocations. A difference from the first layer is that there are now four types of domains due to the underneath plane having multiple domains. Transit atoms connect each other into a network of Shockley partial dislocations and separate A, B and C domains. Similar analysis shows that the formation of subsequent growth planes is also a process of domain competition. However, the competitive results are usually the first type, i.e. dominance of FCC domains. Occasionally, the second scenario occurs, resulting in the formation of a twin boundary. The third scenario did not occur after the second layer. To understand the reason why HCP domains of Cu would form frequently on the nickel (11¯ 1¯) plane, we performed a simulation of a single Cu adatom moving on the nickel (11¯ 1¯) plane, and monitor its trajectories and changes in system energy. In every simulation step, the adatom was allowed to move 2% of the distance from its original site to the destination site, and the system is relaxed for 1 ps. The results are shown in Fig. 7. When the adatom moves from a FCC site to the adjacent HCP site, the trajectory is a straight line with an energy barrier of 0.073 eV. However, when moving to another FCC site, the adatom usually passes through an adjacent HCP site before reaching the destination, and the energy barrier would remain the same as that in moving from a FCC site to a HCP site. If the adatom is forced to move from one FCC site to another following a straight trajectory, the energy barrier would be much higher. By fixing the Y coordinate of the adatom during its motion in Fig. 7, we found this energy barrier to be as high as 0.225 eV, which is over three times the corresponding value of moving from an FCC site to an HCP site. In fact, the energy of a Cu adatom on an HCP site of nickel (11¯ 1¯) plane is found to be 0.012 eV lower than that on an FCC site (Fig. 7b). Similar simulations were also performed for a Cu adatom originally sat on an HCP site of nickel (11¯ 1¯). The trajectory of HCP–HCP diffusion was found to pass through an FCC site, with the same energy barrier as in Fig. 7. Therefore, we imagine the following scenario: as Cu adatoms are dropped
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Fig. 5. A top oblique view of some snapshots of the Cu/Ni (11¯ 1¯) system during heteroepitaxial growth (Every atom is assigned a color according to its site, as in Fig. 4. Atoms above the first Cu layer are not displayed for clarity.). (a) 20ps, (b) 50ps, (c) 70ps, and (d) 300ps. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. The structure evolution of the second Cu layer during heteroepitaxial growth on Ni (11¯ 1¯) (Every atom is assigned a color according to its site, as in Fig. 4.). (a) 100ps, (b) 120ps, (c) 160ps, and (d) 360ps. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Move along X Axis, Fixed Y coordinate
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-37594.20 0.4 HCP site 0.3 FCC site
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System Energy / eV
Y: [112] Direction / nm
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30 Time / ps
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Fig. 7. Diffusion of a single Cu adatom on the Ni (11¯ 1¯) surface. (a) The atomic trajectory and (b) energy evolution.
size in the Cu/Ni (11¯ 1¯) system, and HCP domains larger than 37 adatoms are more stable in the Cu/Ni (11¯ 1¯) system than those in the homoepitaxial Cu/Cu (11¯ 1¯) and Ni/Ni (11¯ 1¯) systems. These results suggest there will be opportunities for HCP domains of significant size to come in contact with FCC domains during growth, and the resulting domain boundaries correspond to Shockley partial dislocations. From an alternative point of view, misfit dislocations in the Cu/Ni (11¯ 1¯) heteroepitaxial system will decrease the misfit strain energy at the cost of dislocation selfenergy, and the resulting stable dislocation network leads to coexisting FCC and HCP domains in one growth plane. In contrast, since misfit dislocations are energetically unfavorable in homoepitaxy, it would be impossible to maintain a stable network of dislocations, the consequence being no coexistence of FCC and HCP domains.
0.09 -Cu adatoms on Ni(111) surface -Ni adatoms on Ni(111) surface -Cu adatoms on Cu(111) surface
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EHCP - EFCC / eV
0.06 0.05 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 0
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Number of adatoms Fig. 8. The energy difference between an HCP domain and an FCC domain as a function of the number of adatoms in the domain.
randomly onto the nickel (11¯ 1¯) surface, they hit the sites with the same probability as the HCP sites. Because the energy barrier associated with shuttling an adatom between FCC and HCP sites is lower than that between two FCC (or HCP) sites, the surface diffusion of Cu adatom tends to change between FCC and HCP sites. So for a single Cu adatom, the probability of holding an FCC site is approximately equal to or even less than that of holding an HCP site. To further understand the evolution of domain competition, we measure the energy difference between HCP and FCC domains in regular hexagon shapes as a function of the number of adatoms. The results are shown in Fig. 8. The corresponding results for Cu/Cu (11¯ 1¯) and Ni/Ni (11¯ 1¯) homoepitaxy are also shown for comparison. The energy difference between HCP and FCC domains in the Cu/Ni (11¯ 1¯) system is generally lower than that in both Cu/Cu (11¯ 1¯) and Ni/Ni (11¯ 1¯) systems. Furthermore, the HCP domains have lower energy than the FCC domains when the number of adatoms is less than 37 in the Cu/Ni (11¯ 1¯) system. During the initial growth process, HCP domains with less than 37 adatoms are expected to dominate over FCC domains of similar
5. Conclusion Three-dimensional molecular dynamics simulation of Cu/Ni (11¯ 1¯) heteroepitaxy has been performed based on the Sutton– Chen EAM potential. A network of misfit dislocations is observed in the first and the second epitaxial Cu layers that is identified to be associated with a domain competition mechanism. According to this mechanism, Cu adatoms are deposited randomly on the FCC or HCP sites of nickel (11¯ 1¯) surface, and form FCC domains and HCP domains with the same probabilities. Two types of domains grow competitively. In the first two Cu layers, FCC domains coexist with HCP domains, and Shockley partial dislocations form along the domains boundaries. Analysis on the energy indicates that when a Cu domain contains less than 37 Cu adatoms on the nickel (11¯ 1¯) surface, an HCP domain is energetically more favorable than an FCC domain. Consideration of single Cu adatom diffusion barrier shows that Cu adatoms can hold an HCP site as well as an FCC site.
Acknowledgement The authors are grateful for the support of the present work by the National Natural Science Foundation of China (Grant no. 10502024).
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