Section 6: Nanocomposite Thin Films and Coatings 1 C alculation of Dislocation Energy for Ni/Cu Thin Films A. Komijani, S. Sadatserky, A. Zolanvari 2 Preparation and Characterization of PU Clay Nanocomposites Gaurav Verma, Anupama Kaushik, Anup K. Ghosh 3 Improvement in Performance of Nano-Alumina Incorporated Polyester based Urethane Acrylate Clearcoat: An Investigation Pallavi Deshmukh, Prakash Mahanwar, Sunil Sabharwal 4 Fabrication and Characterization of MIS Diode of Al/Al2O3/PVA: n-CdSe Nanocomposite Film Mamta Sharma, S.K. Tripathi 5 Morphological and Thermal Degradation Behavior of Bionanocomposite Films based on Cellulose Nanofibrils Reinforced Thermoplastic Starch Mandeep Singh, Anupama Kaushik 6 Formation of Ordered Structures in Dewetting of Polymer Bilayer on Topographically Patterned Substrate Ravdeep Singh, Sudeshna Roy, Rabibrata Mukherjee 7 Sensing Mechanism of Acid on Zinc Phthalocyanine Thin Films Studied by Electrical Conductivity Sukhwinder Singh, G.S.S. Saini, S.K. Tripathi 8 Structural Study of CBD Deposited CdS Nanofilm Suresh Kumar, Pankaj Sharma, Vineet Sharma, P. B. Barman, S. C. Katyal 9 Growth and Characterization of PrCoO3 Thin Films Nanostructures Deposited by Pulsed Laser Deposition Ram Prakash 10 Improvement in Functional Properties of Potato Starch/NanoCellulose Particles Nanocomposite Films N.R. Savadekar, S.T. Mhaske
11 Z inc Oxide Thin Films Prepared by RF Sputtering at Different Oxygen Partial Pressures R. Subba Reddy, A. Sivasankar Reddy, S. Uthanna
1 Calculation of Dislocation Energy for Ni/Cu Thin Films A. Komijani, S. Sadatserky, A. Zolanvari Department of Physics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
ABSTRACT In recent years the structures of thin layers have been widely studied, because of their properties that are unattainable in bulk materials. The aim of this paper is to present the dislocation energy per unit length of the Nickel thin films deposited on Cu. The annealed Ni films show high flow strengths due to the presence of the rigid substrate. Dislocation energy per unit length of a 43 nanometer Nickel thin film have been calculated using low angle incident x-ray scattering. In the present work the value of the film thickness is larger than the prescribed numerical value of (tc). So, the misfit dislocation in Ni/Cu will be stable but do not necessarily form. Results obtained by the proposed experimental test, is then compared with the theoretical analysis data. The dislocation energy per unit length of the nickel thin films has been theoretically obtained equal to 5.3105 (nm)2 Gpa.
Introduction Mechanical properties of thin films have an important role in each application due to stability of thin film systems, depending on mechanical properties of films. Inconstancy of film occurs due to the residual stresses and inadequate coherence of film to substrate. In the last years, this matter has been indicative of researcher’s attention to mechanical properties of thin films. Inconsistency of lattice constants of film and substrate makes residual stresses in thin films. Dislocation energy is important issue in the range of mechanical properties. When the film thickness increases, it becomes energetically favorable for misfit dislocation at the interface between film and substrate to reduce the stress in the film. In spite of some limitations, like conducting substrates, the electrochemical methods has been used for preparation of such multilayer as Ni/Cu [1], NiCo/Cu[2], Co/Cu [3], NiFe/Cu [4], Co/Pt [5], in past decades.
Theoretical Theoretical formulation of the epitaxial stresses arise when films have perfectly coherent interfaces with their substrates, i.e., when the crystal lattices in films and substrates line up perfectly. The critical thickness on which it becomes favorable to form misfit dislocations: Address for Correspondence: Email:
[email protected]
2µ f µ s tc b = β tc µ f + µ s 4π (1 − ν ) M ε mf ln( ) b
(1)
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Calculation of Dislocation Energy
In the case in which the numerical value of dEtot at b = 0 , is smaller b s d( ) s than zero, the parameter (tc) is defined which represents the critical thickness of the film with two conditions: If t < tc: Misfit dislocation is not stable. If t > tc: Misfit dislocation is stable. where (t) represents the film thickness. Assuming enough symmetry, the misfit strain is given by [19]:
ε mf =
as − a f af
(2)
Where af and as are the lattice constants of film and substrate [19]. The expression, εmf only holds when the film is sufficiently thin so that the film assumes the lattice parameter of the substrate. When the film thickness increases, it becomes energetically favorable for misfit dislocation at the interface between film and substrate to reduce stress in the film. Strain in film is [19]:
ε = ε mf −
b s
(3)
Residual elastic Strain energy (per unit film area) of the film is [19]: b2 (4) ] tf s Ef For isotropic materials, Mf is equal to , where Ef and Vf are the 1 − vf young’s Es = M f [ε mf −
module and the Poisson’s ratio of the film respectively [9,19]. The total length of the burgers vector of the dislocation is mentioned by (b) and (s) is the spacing and tf is the thickness of the film [19]. The other energy existing in film is known as the dislocation energy.
Results and Discussion Dislocation energy per unit length is given by: E b2 = l 4 π ( 1 − vf
2µ f µ s
ln(
β tf
)
(5) 2s to 2 for a square Where l is the dislocation length per unit area and is = (lequal = ) s s2 2 2 s of edge dislocation: = (l ) = s s2 µf And µS represents the shear modulus of the film and substrate respectively [17, 19]. β Is a constant value which depends on the kind of film. i.e. is the characteristic parameter of the lattice [17, 8, 18]. Thus, the total energy of the film consisting of the dislocation and strain energies is defined as:
) ( µf
+ µs )
b
Nanotechnology553
Etot = M f [ε mf −
b2 b2 ] tf + s 4π ( 1 − vf
2µ f µ s
) ( µf
+ µs )
ln(
β tf b
)
(6)
Misfit dislocation will form, if the energy is decreased by doing so [19]: dEtot . < 0 b b =0 d( ) s s
(7)
In this situation, tc is defined as the critical thickness of the film which can be obtained, with to apply condition (7) to Etot [19]. Thus, the critical thickness at which it becomes favorable to form misfit dislocations:
2µ f µ s tc b = β tc ( µ f + µs ) 4π ( 1 − vf ) M f ε mf ln( ) b
(8)
In the case in which tc does not exist, misfit dislocations are not stable and never will form. If tf < tc: under thermodynamic equilibrium conditions, misfit dislocations are not stable and will not form upon deposition [19]. If tf > tc: under thermodynamic equilibrium conditions, misfit dislocations are stable upon deposition, but do not necessarily form [19]. The aim of this paper is to calculate the dislocation energy per unit length for Ni/Cu thin films. Nickel represents the film and copper is the substrate. The film’s thickness is 43 nanometers. Properties of Ni and Cu are listed in table (1) [8, 10 to 16]. Table 1: Material properties used in this study
Young’s modulus (Gpa)
Poisson’s ratio
shear’s modulus (Gpa)
lattice constants (nm)
β
Nickel
200
0.31
76
0.35
4.47
Copper
130
0.34
48
0.36
--------
Material
Fundamentals of the calculation of dislocation energy for Ni thin films are calculation of the miller indices’ and Burgers vector of Ni thin films. Fig1 is plotted by XRD unit for Ni/Cu thin films with 43nm thickness of Ni. The maximum intensity of Fig. 1 arises in 2θ = 50.46 with Miller index of (200) for Ni thin layer [6]. Thus, miller index of Ni film whit thickness of 43nm are (200). The total length of the burgers vector is calculated by [7, 19]:
b =
a 2
h2 + k2 + l2
(9)
Where h, k and l are the Miller indices and a, is the lattice constant. Using table1, the total length of the burgers vector of the Ni(200) film is:
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Calculation of Dislocation Energy
50.460[°] 50.301[°]
Counts/s 30000
0
95.039[°]
10000
43.174[°]
20000
50
60
70 80 90 Position [°2Theta]
100
110
Fig 1. XRD pattern result of Ni/Cu thin film at 25 oC.
b =
0 . 35 nm 2
4
Thus, the numerical value of the Burgers vector for Ni(200) film is 0.35nm. With attention to table1, dislocation energy per unit length for Ni(200)/Cu thin films with 43nm thickness is calculated by Eq. (5). (0 . 35 nm)2 2 × 76 Gpa × 48 Gpa 4 . 47 × 43 nm E ) = ln( 0 . 35 nm l 4 π (1 − 0 . 31) (76 Gpa + 48 Gpa) The numerical value of dislocation energy per unit length for the prescribed thin films is 5.31(nm2) Gpa. With attention to table1 and Eq. (2), Misfit strain in Ni/Cu thin films is given by: ε mf =
0 . 36 nm − 0 . 35 nm 0 . 35 nm
Numerical value of the misfit strain in Ni/Cu thin films is 0.026. Using Eq. (8), the critical thickness of Ni(200) film can be found by the following manner: 2 × 76 Gpa × 48 Gpa 0 . 35 nm tc = 4 .47 × tc 200 Gpa (76 Gpa + 48 Gpa) ) ln( 4 π ( 1 − vf ) × × 0 . 02 0 . 35 nm ( 1 − vf ) Solving the above equation for tc, the critical thickness of the film is 0.112 nm. Using Eq. (5), dislocation energy for Ni (200)/Cu with tc=0.112 nm is: (0 . 35 nm)2 2 × 76 Gpa × 48 Gpa 4 . 47 × 0 .1 1 nm E ) = ln( 0 . 35 nm l 4 π (1 − 0 . 31) (76 Gpa + 48 Gpa) The dislocation energy per unit length in Ni(200)/Cu thin films with the prescribed value of the thickness is 0.29(nm2) Gpa.
Nanotechnology555 Dislocation energy per unit length for Ni(200)/Cu thin films with 43nm thickness of film and Ni(200)/Cu thin films with tc=0.112 of Ni(200) film are 5.31(nm2) Gpa and 0.29(nm2) Gpa, respectively. When the nickel film thickness, increases to tc, the dislocation energy per unit length, will increase to 0.29(nm2) Gpa. Then, when the film thickness, increases from tc to 2tc, dislocation energy per unit length increases from 0.29(nm2) Gpa to 0.88(nm2) Gpa. It means that, with increase of the thickness, from tc to 2tc, dislocation energy increases to the value of 0.58(nm2) Gpa rather than 0.29(nm2) Gpa. Figs. 2 and 3 show the dislocation energy versos the film thickness for Ni(200)/Cu thin films. Fig.2 shows slope of the line between the points (0.29(nm2) Gpa, tc) and (0.88(nm2) Gpa, 2tc), is less than the slope of line connecting the point (0.21(nm2) Gpa, 0.1nm) to (0.29(nm2) Gpa, tc). This matter occurs due to the state (state of the graph is the ln) of the graph. Thus, with increase of the thickness of Ni(200) film in the Ni/Cu thin films, from 0.1 to tc, dislocation energy increases by the harsh slope. On the other hand, with increases of thickness of Ni(200) film, from tc to 2tc, or, with increase of the thickness of Ni(200) film, from tc to the, tf >tc, dislocation energy increases by the mild slope. In Fig.3, dislocation energy for Ni(200)/Cu thin films, when the thickness of Ni(200) film, increases for one stage, (0.1 → 43nm), or increases to several stages, (for example: 0.1 → 10nm → 30nm → 43nm), are equal to each other. Fig. 2 and Fig. 3 show that, in the extent of the very modicum thicknesses (for
Fig 2. Graph of Eq. (5) Ni thickness, from 0.1nm-1nm. example: 0.1nm to 20nm), the dislocation energy changes acutely, but in the extent of the thicknesses of largish (for example: 20nm to 43nm), the dislocation energy will change slowly. The numerical value of critical thickness of the Ni(200) film at which it becomes favorable to form misfit dislocation is 0.112nm. Thus, value of
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Calculation of Dislocation Energy
Fig 3. Graph of Eq. (5) Ni thickness, from 1nm-45nm. (tc= 0.112nm) the Ni(200) film with 43nm thickness, is too large than the prescribed numerical value of . So the misfit dislocation in Ni(200)/Cu will be stable upon deposition, but do not necessarily form.
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