Atomistic modeling of metallic thin films by modified embedded atom method

Accepted Manuscript Title: Atomistic modeling of metallic thin films by modified embedded atom method Authors: Huali Hao, Denvid Lau PII: DOI: Reference:

S0169-4332(17)31313-2 http://dx.doi.org/doi:10.1016/j.apsusc.2017.05.011 APSUSC 35946

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APSUSC

Received date: Revised date: Accepted date:

23-3-2017 22-4-2017 2-5-2017

Please cite this article as: Huali Hao, Denvid Lau, Atomistic modeling of metallic thin films by modified embedded atom method, Applied Surface Sciencehttp://dx.doi.org/10.1016/j.apsusc.2017.05.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Graphical abstract

Highlights 

The mechanical and thermal properties of different metals are predicted.



The potential parameters for binary system are developed by ab initio calculation.



The details of interfacial structure between films and substrate are revealed.



The work provides a useful guidance to analyze interface related behaviors.

Atomistic modeling of metallic thin films by modified embedded atom method Huali Haoa and Denvid Laua, b, * a

Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China. b

Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Abstract Molecular dynamics simulation is applied to investigate the deposition process of metallic thin films. Eight metals, titanium, vanadium, iron, cobalt, nickel, copper, tungsten, and gold, are chosen to be deposited on the substrate aluminum.

The second

nearest-neighbor modified embedded atom method potential is adopted to predict their thermal and mechanical properties.

When quantifying the screening parameters of the

potential, the error for Young’s modulus and coefficient of thermal expansion between simulated results and experimental measurements is less than 15%, demonstrating the reliability of the potential to predict metallic behaviors related to thermal and mechanical properties.

A set of potential parameters which governs the interactions between aluminum

and other metals in a binary system is also generated from ab initio calculation. The details of interfacial structures between films and substrate are successfully simulated with the help of these parameters.

Our results indicate that the preferred orientation of film growth relies

on the film crystal structure, and the inter-diffusion at the interface is related the cohesive energy parameter of potential for binary system.

Such finding provides an important basis

to further understanding upon interfacial science, which contributes to the improvement of the mechanical properties, reliability and durability of films. Keywords: Aluminum; Interface; Metallic thin film; Modified embedded atom method potential; Molecular dynamics simulation

Corresponding author. e-mail: [email protected]

1. Introduction Metallic thin films are widely deposited on Al for improving its low load bearing capacity, electrical conductivity, photoelectric property and low corrosion resistance [1-5]. Residual stress, which significantly affects the reliability and performance of metallic films, cannot be avoided during fabrication. by two reasons.

In general, residual stress in metallic films is caused

Firstly, due to the difference of thermal expansion coefficients (α) between

thin films and substrate, a thermal residual stress arises during the deposition process [5, 6]. Secondly, the lattice mismatch between thin film and substrate and defects within films (e.g. point defects, dislocations, grain boundaries) introduce intrinsic residual stress [7].

Some

straightforward methods such as X-ray diffraction and neutron diffraction methods are employed to measure the residual stress in the thin film [8], and the high-resolution transmission electron microscopy and scanning tunneling microscopy are applied to characterize and investigate the microstructure evolution of films [9, 10].

However,

experimental techniques are difficult to be adopted for measuring the residual stress in films with less than 100 nm thickness and display the details of interfacial microstructures, such as the inter-diffusion, defect, lattice mismatch, which are partial origins of the residual stress [11, 12]. Even during preparation of experimental specimen, defects are avoidably generated, resulting in the inaccuracy of characterizing and measuring residual stress.

An approach to

reveal microstructure and predict properties within several nano-size structures is necessary for a fundamental understanding of film residual stress, which contributes to the improvement of the durability, reliability and properties of thin films.

It is of technological

significance, which paves a way for material selection of metallic thin films and optimization of manufactory techniques. Molecular dynamics (MD) simulation provides powerful means for displaying atom configuration, predicting the materials properties, and quantifying the mechanisms of the structure-properties relationship [13-21].

A critical component of MD is the potential,

which determines the accurately in predicting properties of materials [22].

To analyze the

residual stress in metallic films, the potential enables to precisely predict physical phenomenon and thermal properties of film-substrate systems, such as defect formation, dislocations, elastic modulus and α.

Additionally, as deposited films on the substrate result

in the formation of an interface, the interface structure should be forecast by the potential. Recently, there are some literatures reported to apply MD to simulate the deposit process of thin film with different potentials.

For example, the tight-binding potential has been

employed to simulate Fe and Co atoms deposited on Cu substrate [23]. The embedded-atom method potential has been utilized to simulate the Al thin film deposited on Cu substrate [24]. However, the details of the interface structure, such as the lattice mismatch at the interface between thin film and substrate, cannot be revealed clearly by these potentials. The simulated thin films do not demonstrate the preferred orientation growth mechanism, and their natural crystal structures. Such simulated structure has deviated from the experiment, making it questionable for film residual stress analyzed.

The modified embedded atom method

(MEAM) potential is the first semi-empirical potential formalism that shows the possibility one single formalism can be applied to a wide range of elements by considering the

nearest-neighbor interactions [25].

MEAM potential has been successfully applied to

precisely estimate the formation energy of defect, the stacking faults energy, the surface energy, and structural transformation energy for metals with various crystal structures, expect body-centered-cubic (bcc) structure [26].

Because, the second nearest neighbor distance in

bcc structure, which is just 15% larger than the first nearest-neighbor distance, is neglected [26]. The second nearest-neighbor (2NN) MEAM potential has been developed based on the MEAM potential to consider both the first nearest-neighbor interactions and the second nearest-neighbor interaction, successfully reproducing many physical properties of bcc metals. The objective of this work is to predict the mechanical and thermal properties of different metals by 2NN MEAM potential, and generate the 2NN MEAM parameters for binary systems from ab initio calculation to predict the interfacial structure by simulating the deposit process.

Eight transition metals, Ti, V, Fe, Co, Ni, Cu, W and Au (sorted by

atomic number) are deposited on the substrate Al. Specifically, Ni, Cu and Au have a face-centered-cubic (fcc) structure, alike to the substrate Al; V, Fe, and W are of bcc structure; Ti and Co have hexagonal close-packed (hcp) structure.

The screening parameters are

firstly quantified on basis of already existed 2NN MEAM parameters to evaluate Young’s modulus (E) and α of deposited metals and substrate.

Subsequently, the calculated

properties are compared with available experimental data.

Following, the potential

parameters for interaction between Al and Ti, V, Fe, Co, Ni, Cu, W and Au are obtained by first-principles calculations.

Eventually, with the help of these parameters, the deposit

process of metallic films grown on substrate is simulated to display the details of interfacial structure.

It provides a new approach to characterize interfacial microstructures, such as

lattice mismatch, inter-diffusion, and reaction at interface, and predict the properties of metallic thin film/substrate systems, such as intrinsic residual stress, interfacial adhesive toughness and interfacial fracture energy.

This benefits the analysis of the interface related

behaviors, such as the crack prolongation and interfacial fracture, contributing to improve the performance and durability of thin films.

2. Simulation method The full description on the 2NN MEAM formalism has been published in details [27]. For pure elements, each pair interaction is characterized by a total of 14 independent parameters: the equilibrium nearest neighbor distance (re), the cohesive energy of atom (Ec), the bulk modulus (K), an adjustable parameter (d) for the universal equation of state, four exponential decay factors (β(0), β(1), β(2), β(3)) for the atomic density, three weight factors (t(1), t(2), t(3)) for the electron density, one parameter (A) for the embedding function, and two parameters (Cmin, Cmax) for many-body screening.

For a binary system, in addition to unary

potential parameters, another 13 independent parameters are involved: Ec, re, K, d, ρ0 (electron density ration between individual elements), four Cmin and four Cmax [28, 29].

As

Cmin and Cmax determine the extent of screening of an atom from the interaction between two neighbor atoms, there are four different types of interaction (i.e. A-B-A, B-A-B, A-A-B and A-B-B) in a binary system consisting of elements A and B [29]. Particularly, the model

parameters Ec, re and K for binary systems are determined either from experimental data or first-principle calculation based on a reference structure. The MD simulations are carried out using the parallel MD code LAMMPS [30].

2NN

MEAM parameters for pure elements of deposited films and substrate are applied as the starting point, shown in Table 1[14, 26, 27, 31, 32].

During the parameterization, the

parameter Cmin for Cu is reduced from original 1.21 to 0.8, and Cmax for Co is increased from original 2.0 to 2.8.

This is to ensure the MEAM predictions of α not deviating noticeably

from the experimental data.

Such an adjustment has no effect on other properties.

All ab

initio calculations are performed in the Materials Studio by using generalized gradient approximation pseudopotential to develop the potential parameters [33].

During the

uniaxial tensile deformation, the tensile loading is implemented by subjecting the simulation box of 10a × 10a × 20a (a = lattice constant) with a constant strain rate 108 s-1 along the z-coordinate at 300 K.

The thermal expansion coefficient is calculated as the average

thermal expansion in each direction and is given by the following formula [34]: 1 1 dlx (T ) 1 dly (T ) 1 dlz (T ) α(T )  [      ] 3 lx (T ) dT ly (T ) dT lz (T ) dT

(1)

where lx, ly and lz are the size of the simulation box in the x, y, and z directions at temperature of T. Specifically, the x, y and z directions are parallel to the [100], [010] and [001] direction of crystal.

To obtain this information, a model is developed in which periodic

boundary conditions are applied to a unit cell of in three directions. The simulation box (i.e. 10a × 10a × 10a) suffers from elevating temperature from 300 K to 500 K.

The three

dimensions of the simulation box are allowed to vary independently from one another under

zero external pressure.

By examining the root-mean-square displacement (RMSD) of the

atoms, which keeps at a constant level before the 200 ps NVT equilibrium run completes at different temperatures, it implies that the equilibrated state has been obtained. Metallic thin films, Ti, V, Fe, Co, Ni, Cu, W and Au are deposited on the substrate Al with the simulation size of 24.3 Å × 24.3 Å × 16.2 Å, where the temperature of substrate is of small fluctuation during deposit simulation process.

The lowest two layers of the substrate

are fixed to prevent the substrate from shifting due to the momentum transfer during atom impact.

The middle layers are called thermal control layers, the atom temperature of which

is rescaled every ten steps according to the prescribed substrate temperature 300 K.

The

atom velocities of the thermal control layers are given by Maxwell-Boltzmann distribution at the substrate temperature.

The top three layers are free motion layers to simulate the

interactions of atoms after the impacts of the deposited atoms. are imposed for the x and y directions of simulation box.

Periodic boundary conditions

A free boundary condition is used

for the z direction, where the substrate atoms at surface enable to move free.

Specially, the x,

y and z directions parallel to the [100], [010] and [001] directions of Al crystal, respectively. The atoms of films randomly deposit on the substrate surface from the position with 121.5 Å above the Al surface. picosecond.

Deposition is performed with a deposition rate of 1 atom per

Then a relaxation process is conducted to enable the deposited system to

equilibrate. The root-mean-square displacement of the atoms becomes stable after relaxed, indicating that the system has reached equilibrium state.

3. Simulation results and discussion 3.1 The mechanical and thermal properties for pure metals Besides the substrate Al, the simulated property curves for three representative film materials with different structures, namely, Cu with fcc structure, Fe with bcc structure and Co with hcp structure are particularly demonstrated.

The overall stress and strain relations

for the represented materials, Al, Cu, Fe, and Co are shown in Fig. 1.

The stress of these

materials demonstrates a linear response to the applied strain at the early stage (elastic stage). For metal Al, Cu, and Co, when the strain is over a specific value (about 0.05), the samples have a non-linear relationship between strain and stress with uniform deformation, which indicates they suffer from plastic deformation.

However, the strain-stress curve for metal Fe

is different from the other three kinds with non-uniform deformation.

Because, different

from other kinds of metals (i.e. fcc, hcp), the bcc metals typically do not obey Schmidt’s law during deformation, where slip occurs on crystallographic planes other than the one with the maximum resolved shear stress [35-37].

The strain-stress curves from simulation for these

metals are in accordance with experimental tensile tests that stress-strain curves for fcc and hcp metals have no yield phenomenon, while for bcc metal, it yields with non-homogenous deformation [38].

Based on the obtained stress-strain curves, E is calculated by performing

a linear regression analysis on the stress-strain data ranging at elastic stage.

The E of pure

Al, Cu, Fe and Co are 76.3 GPa, 128.1 GPa, 226.0 GPa and 217.8 GPa, respectively. Thermal expansion in the x, y, and z directions keeps practically identical change rate for metals Al, Cu, Fe and Co, due to their periodical prefect crystalline structure.

The

representative length change in x directions at specific temperature is shown in Fig. 2. length of simulation box grows steadily with the increment of temperature.

The

Based on the

equation (1), the typical α of metal Al, Cu, Fe, and Co at 300 K are 21.2, 15.9, 12.6 and 11.8 (× 10-6 K-1), respectively. The values of E and α for all simulated materials are summarized in Table 2, compared with the experimental data. the experimental values.

For all these metals, the simulation results of E are higher than

This is because the strain rate in MD simulation is several orders

of magnitude higher, making less contribution of thermal motions to the mechanical response of the material [39].

Additionally, the constructed model is free of structural defects and

voids, which are normally existed in the macroscopic samples.

All these result in the

overestimation of elastic moduli. The error between the simulation results and experimental values is less than 10%. Nevertheless, the predicted α is subtly lower than the experiment. This underestimation is possibly due to imperfections of the structure for the real materials [40]. The errors of α for different metals are less than 15%.

The error is much lower than

simulated results with other potentials [42, 43]. This indicates the reliability of MEAM potential to predict the mechanical and thermal properties of materials film materials, Ti, V, Fe, Co, Ni, Cu, W, Au and substrate material Al.

3.2. Interfacial structure between films and substrate Al with developed 2NN MEMA potential To describe the interface interaction in a bi-layer system, the main task is to estimate the

thirteen potential parameters for a binary system mentioned in above.

According to phase

diagram, different intermetallic compounds between Al and element of thin films are possible to form [41].

However, when simulated films deposited on the Al substrate, the types of

intermetallic compounds formed are not all available from experiment, or highly depend on the experimental conditions [44].

Furthermore, some formed compounds in experiment are

too complex to simulate. For example, Al5W with hP12 structure is formed, when W film has been coated on Al [45].

The intermetallic compounds with high atom ratio of Al are

selected as the reference structure to determine the parameters Ec, re and K for binary systems. Generally, the substrate is thicker than the film, with a higher atom ratio between substrate and thin films, resulting in intermetallic compounds with high content of Al are preferential to form.

The finally determined 2NN MEAM parameter for Al-Cu, Al-Fe and Al-Co

systems are presented in Table 3.

The first three parameters, which are computed by first

principle and available in literature [32, 38]; the other parameters are calculated through the corresponding equations in Table 3.

Specifically, d is related to the atom ratio for the

reference structure; Cmin and Cmax for type A-B-A and B-A-B are equivalent to those of pure B and pure A, respectively.

Other Cmin and Cmax for type A-A-B and A-B-B directly are

deduced from the equations shown in Table 3, which are based on values of Cmin and Cmax for pure elements A and B.

The value of ρ0 normally equals 1.

Table 4 shows the parameters

Ec, re and K for binary systems between Al and other elements (i.e. Ni, Au, W, V and Ti) which are calculated by first principle and based on literatures [46, 47].

Such developed

potential parameters are effective to explicitly display the interface structure, and make

possible the study of interfacial diffusion, reaction, lattice mismatch which is difficult to characterize by experiments [5]. The deposition process is simulated with the developed 2NN MEAM potential parameters for Al and other metals in Table 3 and Table 4.

The snapshots of deposited films

Cu and Fe on substrate Al at different time are shown in Fig. 3 and Fig. 4, respectively.

The

first monolayer of the films is identical with the natural deposited films’ lattice, and then the next monolayer grows.

The growth mode for the films is nearly layer-by-layer.

Eventually, this growth process provides the lattice of the deposited films resembles to their natural crystal structure.

Moreover, the atoms of Fe penetrate or insert into substrate at the

beginning of the deposition process as the circles shown in Fig. 4a, while there are no deposited Cu atoms penetrating substrate (Fig. 3a). As the Co atoms, similar to the case of film Fe, diffuse into the substrate at the beginning deposit stage, the detailed snapshots of deposited film Co are not shown.

Fig. 5 shows the finial interfacial structures between the

representative metallic thin films (Cu, Fe and Co) and substrate Al.

The microstructures

demonstrate the growth of films with preferred orientations, developing a coherent interface with the substrate. The orientation relationships between Cu and Al are Cu (100) // Al (100), Cu (010) // Al (010), the film Cu exhibiting a strong growth preference on (001) plane (Fig. 5a). Fig. 5 (b) shows the interfacial structure between Fe and Al, where the preferred orientation of thin film Fe is (001) plane. and Fe (1 1 0) // Al (010).

There are relationships of bcc Fe (110) // Al (100)

The film of hcp Co prefers to deposit on (011) plan and grow

along the [011] directions as shown in Fig. 5 (c).

The different preferred orientation of film

growth highly depends on the minimum surface energy of crystal structures and the discrepancy of lattice mismatch between thin films and substrate.

Comparing with film Cu,

the films Fe, Co have higher lattice mismatch with Al, resulting in the films prefers to grow on the surface with minimize surface energy. are also shown in Fig. 5.

The details of inter-diffusion at the interface

Films Fe and Co inter-mix with substrate Al, as the circles shown

in Fig. 5 (b) and (c), while there is no inter-diffusion between Cu and Al.

This correlates to

the cohesive energy of the reference structure in bi-nary systems, as represented in Table 3. The cohesive energy for Al-Fe and Al-Co is higher than pure Fe-Fe and Co-Co, resulting in diffusion, whereas the cohesive energy for Al-Cu is lower than pure Cu-Cu, leading to Cu atoms prone to aggregate on the substrate surface.

Such a detailed and clear display of

interfacial structure provides an approach to study the interfacial properties, such as interfacial adhesive strength and residual stress at interface, and analyze the effect of crystal structure on the interface related behavior, i.e. the interface cracking prolongation, interface fracture and detachment. This has great significances to improve the performance and durability of films and provide a guideline for films material design.

4. Conclusion In summary, the 2NN MEAM potential is employed to simulate the tensile and thermal behaviors of substrate material Al and different film materials, Ti, V, Fe, Co, Ni, Cu, W and Au. The discrepancy for Young’s modulus and coefficient of thermal expansion between simulated results and measurement is less than 15%, by quantifying the screening parameter

of the potential. The potential parameters, such as cohesive energy, lattice constant and bulk modulus, for the binary systems between Al and other elements are generated from ab initio calculation.

The deposit process of metallic thin films deposited on substrate Al is

successfully simulated.

Metallic thin films with different crystal structures are preferable to

grow on different planes. Cu (010) // Al (010).

The film Cu grows on (001) plane with Cu (100) // Al (100) and

Although the preferred orientation of the film Fe is also (001) plane,

the Fe [110] and [1 1 0] directions parallel Al [100] and [010], respectively. a strong preferred orientation on (011) plane with inter-mixing at interface.

The film Co has The successful

prediction of interface structures contributes to further study interface related behaviors, impossible to be in-situ observed by the experimental methods, and predict the properties of thin films, difficult to be measured.

This work provides an approach to study the basic

factors of these interfacial phenomena, which is of significance to improve the systems’ performance and durability, expanding their industrial applications.

Acknowledgments The authors are grateful to the support from Croucher Foundation through the Start-up Allowance for Croucher Scholars with the Grant No. 9500012, and the support from the Research Grants Council (RGC) in Hong Kong through the General Research Fund (GRF) with the Grant No. 11255616.

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Table 1. Parameters for 2NN MEAM potential of substrate material Al, and film materials Ni, Cu, Au, V, Fe, W, Ti and Co are represented.

The units of the sublimation energy Ec, the

equilibrium nearest-neighbor distance re and the bulk modulus K are eV, Å and × 1011 Pa, respectively.

Al [26]

Ni [26]

Cu [31]

Au [26]

V [31]

Fe [32]

W [27]

Ti [14]

Co [32]

Ec

3.36

4.45

3.54

4.08

5.30

4.29

8.66

4.87

4.41

re

2.86

2.49

2.56

3.93

2.62

2.48

2.74

2.92

2.50

K

0.79

1.88

1.38

1.80

1.57

1.67

3.14

0.91

1.95

A

1.16

0.94

0.94

1.00

0.73

0.5

0.40

0.70

0.90

β(0)

3.20

2.56

3.83

5.77

4.74

3.67

6.54

2.30

3.50

β(1)

2.6

1.5

2.2

2.2

1.0

1.0

1.0

1.0

0.0

β(2)

6.0

6.0

6.0

6.0

2.5

1.0

1.0

6.5

0.0

β(3)

2.6

1.5

2.2

2.2

1.0

1.0

1.0

1.0

4.0

t(1)

3.1

3.1

2.7

2.9

3.3

2.1

-0.6

3.5

3.0

t(2)

0.5

1.8

3.0

1.6

3.2

1.0

0.3

0.1

5.0

t(3)

7.8

4.4

2.0

2.0

-2.0

-8.5

-8.7

-10

-1.0

Cmin

0.49

0.81

0.80

1.53

0.49

0.16

0.49

1.0

0.49

Cmax

2.80

2.80

2.80

2.80

2.80

2.80

2.80

1.44

2.80

d

0.05

0.0

0.05

0.05

0.00

0.05

0.00

0.00

0.00

Table 2. Predicted Young’s modulus E and coefficient of thermal expansion α by 2NN MEAM, compared with the experimental results [41].

α (× 10-6 K-1) (at room temperature)

E (GPa) MEAM

Experiment

Error

MEAM

Experiment

Error

Al

76.3

70.6

8.1%

21.2

23.1

8.2%

Ni

201.4

199.5

1.0%

11.8

13.4

11.9%

Cu

128.1

125.6

2.0%

15.9

16.5

2.2%

Au

86.1

78.5

9.7%

12.1

14.2

14.8%

V

142.8

127.6

11.9%

9.9

8.4

17.9%

Fe

226.0

208

8.7%

12.6

11.8

6.8%

W

432.8

411

5.3%

5.3

4.5

17.8%

Ti

132.3

120.2

10.1%

7.4

8.6

14.0%

Co

217.8

211

3.2%

11.8

13.6

13.2%

Note: The error is the ratio between the difference of experimental data and MEAM results and the experimental data.

Table 3. 2NN MEAM potential parameters set for the binary Al-M (M represents Cu, Fe, and Co) systems are garnered from ab initio calculation.

The units of the energy Ec, the

equilibrium nearest-neighbor distance re and the bulk modulus K are eV, Å and × 1011 Pa, respectively.

Selected Values Reference B1-AlCu

L12-AlFe3

B1-AlCo

state ΔEc

c

l

c

u

- 0.19 [31]

c

l

c

e

c

l

c

o

K

1.09

1.59

1.62

re

2.53 [31]

2.51

2.48 [32]

d

0.5dAl+0.5dCu

0.75 dAl +0.25 dFe

0.5dAl+0.5dCo

ρ0

ρAl/ρCu=1

ρAl/ρFe=1

ρAl/ρCo=1

Al  M  Al Cmin

CAl min =0.49

CAl min =0.49

CAl min =0.49

M  Al  M Cmin

CCu min =0.80

CFe min =0.16

CCo min =0.49

Al  Al  M Cmin

[

12 12 (CAl  (CCu min ) min ) ]2 =0.64 2

M  Al  Al Cmin

[

12 12 (CAl  (CCu min ) min ) ]2 2

=0.64

[

12 12 (CAl  (CFe min ) min ) ]2 =0.30 2

[

12 12 (CAl  (CFe min ) min ) ]2 =0.30 2

[

[

12 (CAlmin )1 2  (CCo min ) ]2 =0.49 2

12 12 (CAl  (CCo min ) min ) ]2 =0.49 2

Al  M  Al Cmax

CAl max =2.8

CAl max =2.8

CAl max =2.8

M  Al  M Cmax

CCu max =2.8

CFe max =2.8

CCo max =2.0

Al  Al  M Cmax

M  Al  Al Cmax

[

[32]

12 12 (CAl  (CCu max ) max ) ]2 =2.8 2

[

12 12 (CAl  (CFe max ) max ) ]2 =2.8 2

[

12 12 (CAl  (CCo max ) max ) ]2 =2.4 2

12 12 (CAl  (CCu max ) max ) ]2 =2.8 2

[

12 12 (CAl  (CFe max ) max ) ]2 =2.8 2

[

12 12 (CAl  (CCo max ) max ) ]2 =2.4 2

[

Table 4. Parameters Ec, re, and K set for binary Al-M (M represents Ni, Au, V, W and Ti) systems are obtained by ab initio calculation.

The units of the energy Ec, the equilibrium

nearest-neighbor distance re and the bulk modulus K are eV, Å and ×1011 Pa, respectively.

Selected Values Reference L12-Al3Ni

L12-Al3Au

L12-Al3V

B1-AlW

L12-Al3Ti

Ec

3.86

3.71 [45]

3.94

6.46 [46]

3.34 [47]

re

2.73

2.88 [45]

2.93

2.49 [46]

2.77 [47]

K

1.15

1.59

0.83

1.97

1.18

state

Fig. 1. Stress-strain curves for different pure metals by MD simulations: (a) pure Al; (b) pure Cu; (c) pure Fe; and (d) pure Co.

When the strain ε is less than 0.05, there is a linear

relationship between strain ε and stress σ. Young’s modulus

The slope of red line represents the value of

Fig. 2. The length deviation in x direction, plotted as a function of temperature: (a) pure Al; (b) pure Cu; (c) pure Fe; and (d) pure Co. (As there is no defects in the simulation box, the change rate along y and z directions is similar to x direction.)

Fig. 3. MD snapshots of the deposition process at different time for film Cu deposited on Al (a) 50 ps; (b) 100 ps; (c) 200 ps; (d) 800 ps; (e) 1400 ps.

The Cu atoms are located at the

lattice points of the fcc structure during deposit process.

The growth mode of thin film is

nearly layer-by-layer.

Fig. 4. MD snapshots of the deposition process at different time for film Fe deposited on Al: (a) 50 ps; partial Fe atoms penetrate the substrate and replace Al atoms at the beginning stage of deposit process; (b) 200 ps; (c) 800 ps; (d) 1400 ps. lattice point of bcc structure during deposit process.

The Fe atoms are located at the The inter-diffusion mainly occurs

between the uppermost layer of substrate Al and the lowest two monolayers of film Fe.

Fig. 5. The interfacial structure between films and substrate Al simulated with 2NN MEAM potential: (a) the film Cu; (b) the film Fe; (c) the film Co.

The growth of films shows a

preferred orientation, with a coherent interface developed between the films and substrate. The film Cu grows on (001) plane with Cu (100) // Al (100) and Cu (010) // Al (010).

The

preferred orientation of film Fe is (001) plane, with Fe (110) // Al (100) and Fe [11 0] // Al [010]. The film Co has a strong preferred orientation on (011) plane.

The inter-diffusion

is observed in the films Fe and Co deposited on Al substrate, because the cohesive energy of Al-Fe and Al-Co is higher than the cohesive energy of Fe-Fe and Co-Co, respectively.