Mat. Res. Soc. Symp. Proc. Vol. 677 © 2001 Materials Research Society
Dislocation Nucleation and Propagation During Deposition of Cubic Metal Thin Films W. C. Liu, Y. X. Wang, C. H. Woo, and Hanchen Huang @ Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong
ABSTRACT In this paper we present three-dimensional molecular dynamics simulations of dislocation nucleation and propagation during thin film deposition. Aiming to identify mechanisms of dislocation nucleation in polycrystalline thin films, we choose the film material to be the same as the substrate – which is stressed. Tungsten and aluminum are taken as representatives of BCC and FCC metals, respectively, in the molecular dynamics simulations. Our studies show that both glissile and sessile dislocations are nucleated during the deposition, and surface steps are preferential nucleation sites of dislocations. Further, the results indicate that dislocations nucleated on slip systems with large Schmid factors more likely survive and propagate into the film. When a glissile dislocation is nucleated, it propagates much faster horizontally than vertically into the film. The mechanisms and criteria of dislocation nucleation are essential to the implementation of the atomistic simulator ADEPT. INTRODUCTION Thin films, in particular polycrystalline thin films, are most ubiquitous to modern engineering, because of their important applications and their complexity. The performance of thin films is directly affected or controlled by their microstructures. Starting from the BCF theory in 1950’s [1] to the atomistic simulator [2] developed nowadays, the microstructure evolution of thin films has always been a focus of intensive investigations. The atomistic simulator ADEPT [2], which has been extended to simulate competition of two textures [3] and that of multiple textures [4], provides a tool to study the texture evolution during thin film deposition at the atomic level. Recent development and applications of this simulation are discussed in details in references [5-7]. So far, all the simulations using ADEPT have ignored direct contributions of stress to the microstructure development. Under stress, a thin film tends to generate dislocations so as to relax the stress and minimize the energy. The analytical formulation of Frank and van der Merwe [8], based on a balance of elastic energy due to stress and energy associated with a dislocation. In this theory, a simple model of one-dimensional springs on a periodically modulated substrate was used. A dislocation will be generated – nucleated and propagated to the film-substrate interface – if the dislocation’s presence leads to the reduction of the total energy. However, the theory tells nothing about how a dislocation nucleates and how it propagates. The mechanisms of dislocation nucleation and propagation would become clear if details of atomic trajectories are known during the deposition of thin films. Molecular dynamics simulations are idea for this purpose, except that the maximum physical time accessible is only nano-seconds. This limitation is also part of the reason why most of the atomistic simulations of the dislocation nucleation and propagation have been two-dimensional (2D) or quasi twodimensional. Nevertheless, the 2D molecular dynamics simulations provide useful insights to these unknown mechanisms. In a 2D molecular dynamics study, Dong et al [9] found that the critical thickness of dislocation nucleation depends not only on the magnitude, but also the sign @
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of mismatching. Under compression, a dislocation was found to nucleate by squeezing out one atom near a depression. Under tension, on the other hand, the first dislocation was found to nucleate by relative shift of two neighboring columns of atoms. In the 2D molecular dynamics simulations, two of the most important factors are ignored; they are geometry of a dislocation and effects of crystal structures. With the advancement of computer technology, it is now feasible to study the nucleation and propagation processing using 3D molecular dynamics method. Recently, we have taken tungsten as a prototype – because it is elastically isotropic and it does not have Shockley partial dislocations – to study dislocation nucleation and propagation [10,11]. Now, we extend the study to an FCC metal – aluminum. In Section 2, we briefly describe the simulation method used in the simulations of tungsten and aluminum. In Section 3, we start by summarizing the results of tungsten, and then present the results of aluminum in comparison. Finally, our conclusions and discussions are presented in Section 4. SIMULATION METHOD We choose tungsten and aluminum as prototypes of BCC and FCC metals, respectively, in this study of dislocation nucleation and propagation. Since our primary interest is in the deposition of polycrystalline thin films, we study the deposition of tungsten on tungsten and aluminum on aluminum. However, the substrate is stressed to mimic the condition of one grain under a stress by its neighboring grains. The interatomic interaction of tungsten atoms is described by the Ackland’s potential [12], and that of aluminum atoms by the Ercolessi-Adams potential [13]. Both potentials are based on the concept of embedding an atom in an electron sea, and provide a reasonably reliable description of bulk and surface properties. A typical simulation cell consists of fixed, thermostat, and film layers. Atoms in the bottom layers of the simulation cell are fixed to their perfect lattice positions – scaled according to thermal expansion and stress condition, which will be described in the next paragraph. The fixed layers are one cut-off – of the interatomic potential – in thickness, and they represent a background of perfect crystal to the newly grown thin film. Several thermostat layers of atoms – which are also one cut-off in thickness – sit right on top of the fixed layers to provide a constant temperature reservoir. Periodic boundary conditions are applied along the two horizontal directions to simulate deposition on a flat substrate. In the thermostat layers, atoms are subject to Langevin forces [14] so that a constant temperature is maintained in this region. To minimize the effects of momentum – for the sake of clarity, source atoms are assigned a small kinetic energy (less than 0.01 eV) and they are injected onto the substrate vertically. These atoms are deposited on top of the thermostat layers. Both the thermostat layers and the fixed layers use lattice constants that correspond to finite temperatures and imposed stress conditions. The temperature of the simulated system is brought to a desired value using the Langevin force, and thermal expansion and mechanical deformation of the simulation cell are accomplished using the Parrinello-Rahman constant stress algorithm [15]. The simulation cell is maintained at a high temperature – 2500K for tungsten and 500K for aluminum – to compensate for the extremely high deposition rate. In a typical experiment, the deposition rate is 1 micron per minute. In contrast, the deposition rate is a molecular dynamics simulation is about 1 meter per second. We choose the simulation temperature so that atomic diffusion in the simulation and that in the experiment are comparable.
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Using the atomic positions during the deposition, we prepare an “atomic movie” to visualize the nucleation and propagation of dislocations. The von Mises atomic-level stress [16] is used to differentiate atoms near a dislocation from the rest. It is worthwhile emphasizing that the atomic movie provides only an initial guess about where the dislocation is and what its Burgers vector is. We rely on the atomic positions to define the Burgers vector and line vector of the dislocation. When positions of atoms in two periods are projected onto the residential plane, the dislocation is marked by an extended zone of mismatching projections. Onto any other planes, part or all of the dislocation will be missing. Once the residential plane is chosen, there are many ways of projecting atomic positions on the plane. The projection direction can be chosen so that the mismatching of the projections is zero along one direction in the residential plane. This leaves the plane that the Burgers vector resides uniquely defined. Taking one layers of atoms on this plane, one can finally determine the dislocation Burgers vector according to the SF/RH Burgers circuits [17]. SIMULATION RESULTS We start with the dislocation nucleation and propagation in tungsten. Under the uniaxial compression of 16 GPa, two types of nucleation events have been observed during the deposition. For the first type, an atom (circled in the top part of Figure 1a) near a step is ejected _
__
from a (0 1 1) surface layer, allowing atoms in the same layer to relax along the [1 11 ] direction (bottom part of Figure 1a). This process leads to the nucleation of a half loop having a Burgers 1 __ vector of [1 11 ] on the (101) plane. The half loop quickly propagates into the film and arrives 2 at the film-substrate interface. Due to the small size of the simulation cell, we do not attach much
[1 1 1] [2 1 1 ]
[1 1 1]
[111]
[1 11]
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(a) (b) Figure 1: Two types of dislocations nucleated under compression, with (a) being glissile, and (b) being sessile. The time sequence goes from top to bottom. importance to the details of the propagation, although the nucleation process is unlikely affected by the size. For the second type, one atom (circled in top and middle parts of Figure 1b) on the _
top (0 1 1) surface layer is ejected near a step, followed by another ejection from the layer below, allowing atoms to relax along the [111] direction (bottom part of Figure 1b. This process leads to 1 ___ [ 111 ] on the (011) plane. Because it the formation of a dislocation having a Burgers vector of 2 is sessile, this dislocation does not propagate into the film, but it grows upwards with the film. The observed phenomena are verified using simulation cells of various sizes. When a large AA7.32.3
simulation cell is used, both types of dislocations are observed in one simulation. Further, three common features in the two types of dislocations are: (1) both are nucleated on {110} planes with large Schmid factors; (2) both nucleate near surface steps; (3) the glissile dislocation propagate horizontally also along a surface step. It is more likely that the surface step guides the dislocation propagation, rather than that the propagating dislocation leads to the formation of the surface step; because the dislocation propagates horizontally very fast. Thermal annealing molecular statics simulations are underway to clarify the interplay of surface step and dislocation.
[1 11]
110
[111]
Figure 2: Dislocation nucleated under tension. The time sequence goes from left to right, and the Burgers circuit in shown on the final snapshot. In comparison to the compression case, only one type of dislocation nucleation has been observed during deposition of tungsten thin film under tension. An atom (circled in the first two _
snapshots of Figure2) right under the step is squeezed into the film along the [11 1 ] direction to take up the extra space – resulted from the substrate tension. The edge atom of the surface step moves down to form a smooth surface, eliminating the step (the final snapshot of Figure 2). This 1 __ process generates a dislocation having a Burgers vector of [ 11 1] on the (112) plane. The 2
B
A
C
[0 1 1]
[0 1 1]
[ 211]
O M [ 211]
N
[111]
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(a) (b) Figure 3: Slip planes with large Schmid factors. A, B, and C are (110), (101), and (011) planes, respectively. M, N, and O are (211), (121), and (112) planes, respectively.
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_
horizontal propagation goes through a zig-zag line along the [ 3 11] direction involving two atomic planes. Another similar phenomena are observed with the reversed step on the (121) 1 _ plane with Burgers vector [ 11 1]. Again, the interplay between a dislocation and a surface step 2 is observed, as in the case of compression. For easy reference of the slip systems, those with large Schmid factors – based on {110} and {112} planes – are shown in Figures 3a and 3b, respectively. Our preliminary studies on aluminum indicate that a complete dislocation is nucleated, 1 when the substrate is subject to compression of 6 GPa. The Burgers vector – [10 1] – can be 2 seen from the (111) atomic layer. This dislocation resides on the (111) plane, the projection on which along the [110] direction is shown on the left of Figure 4. It is interesting to note that the dislocation nucleated is a complete one, instead of one partial after another. This feature may be accounted for by three possible factors. First, the existence of a surface in a thin film may prefer a complete dislocation. Second, a partial dislocation may be difficult to nucleate. Finally, the mixed nature of the dislocation may be the last factor that favors non-dissociation. Unlike the simulations of tungsten, we have not tested the simulation cell size dependence of the aluminum simulations. Therefore, it is impossible to rule out the possibility that this is due to the small simulation cell size – for the aluminum results only. Studies are under way to test various factors.
[1 01]
10 1 101
[111]
[1 1 0]
[110]
[01 1 ]
Figure 4: Atoms in a (111) layer – left, and projections of atoms on the (111) plane along the [110] direction. SUMMARY Using the molecular dynamics method, we have studied the nucleation of dislocation during deposition of cubic metal thin films. Our studies of tungsten films indicate that: (1) both glissile and sessile dislocations can be nucleated; (2) dislocations nucleate on both {110} and {112} planes; (3) dislocation nucleation is intimately related to surface steps; and (4) all the observed dislocations are on slip systems with large Schmid factors (even the sessile one). One interesting phenomenon is observed in aluminum: a complete dislocation instead of one partial after another is nucleated.
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ACKNOWLEDGEMENT The work described in this paper was substantially supported by a central research grant from the Hong Kong PolyU (G-V698), partially by grants from the Research Grants Council of the Hong Kong Special Administrative Region (PolyU 1/99C, PolyU 5146/99E and PolyU 5152/00E). REFERENCES 1. W. Burton, N. Cabrera, and F. Frank, Trans. Roy. Soc. London A243, 299 (1951). 2. H. Huang, G. H. Gilmer and T. Diaz de la Rubia, J. Appl. Phys. 84, 3636 (1998). 3. G. H. Gilmer, H. Huang, T. Diaz de la Rubia, J. D. Torre and F. Baumann, Thin Solid Films 365, 189 (1999). 4. H. Huang and G. H. Gilmer, J. Computer Aided Materials Design 6, 117 (1999). 5. G. H. Gilmer, H. Huang, T. Diaz de la Rubia and C. Roland, Comp. Mater. Sci. 12, 354 (1998). 6. H. Huang and G. H. Gilmer, J. Computer Aided Materials Design 7 (2001) in press. 7. F. H. Baumann, D. L. Chopp, T. Diaz de la Rubia, G. H. Gilmer, J. E. Greene, H. Huang, S. Kodambaka, P. O’Sullivan, and. I. Petrov, MRS Bulletin 26, 182 (2001). 8. F. C. Frank and J. H. van der Merwe, Proc. Roy. Soc. A198, 205 (1949). 9. L. Dong, J. Schnitker, R. W. Smith and D. J. Srolovitz, J. Appl. Phys. 83, 217 (1998). 10. W. C. Liu, S. Q. Shi, C. H. Woo and Hanchen Huang, Comp. Mater. Sci. (2001) accepted. 11. W. C. Liu, S. Q. Shi, C. H. Woo, and Hanchen Huang, Computer Modeling in Engineering & Sciences (2001) submitted. 12. G. J. Ackland and R. Thetford, Phil. Mag. A56, 15 (1987). 13. F. Ercolessi and J. Adams, Europhys. Lett. 26, 583 (1994). 14. A. Nyberg and T. Schlick, J. Chem. Phys. 95, 4989 (1991). 15. M. Parrinello and A. Rahman, J. Appl. Phys. 52, 7182 (1981). 16. H. Huang, M. Caturla, L. Marques, and T. Diaz de la Rubia, “Formulation of Atomic Level Stress Tensor in Silicon”, LLNL Report UCRL-ID-231669, 1998. 17. B. A. Bilby, R. Bullough and E. Smith, Proc. Roy. Soc. A231, 263 (1955).
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