DOI: 10.1007/s00339-006-3799-2 Appl. Phys. A 86, 497–503 (2007)
Materials Science & Processing
Applied Physics A
h.-y. lai1,u p.-h. huang1 t.-h. fang2
Microscopic spallation mechanisms induced
by a pulse laser at the solid-state interface
1Department of Mechanical Engineering, National Cheng-Kung University, Tainan 701, Taiwan 2Institute of Mechanical and Electro-Mechanical Engineering, National Formosa University,
Yunlin 632, Taiwan
Received: 29 September 2006/Accepted: 16 November 2006 Published online: 23 December 2006 • © Springer-Verlag 2006 ABSTRACTThis paper presents a study of the transient behavior of structural dynamics and the associated innovatory micro-scopic spallation mechanism at the solid-state interface, induced by an incident femtosecond pulse laser. By detailed structural dynamic analysis, using the technique of molecular dynamics simulation, the spallation mechanism at the solid–solid interface is observed. The occurrence of structural spallation is mainly characterized by extraordinary expansion dynamics and tensile stress that induces interior structural void defect coalescence, eventually leading to cracking. The microscopic phenomenon of moderate ductile fracturing at the solid–solid interface is identi-fied. A high strain rate in the order of 109s−1is observed. Both aforementioned phenomena are analogous to the experimental results of metal-film spallation excited by a pulse laser. More-over, it is also shown that the critical value of the stain rate is one of the dominant factors that influences the occurrence and mechanism of structural spallation. The results of simulations reveal that the thin-film structure is safe if the strain rate is below certain critical values. The critical damage threshold is evalu-ated and technical suggestions to avoid interfacial fracture are also presented.
PACS02.70.Ns; 42.62.-b; 64.60.Ht; 61.72.Cc; 64.60.-i
1 Introduction
Due to its ultra-short duration time in operation, the femtosecond-laser has some invaluable traits (e.g. low thermal diffusion, small mechanical damage and high qual-ity micro-sculptures) which are superior to longer pulse laser. Thus, the technology has been quickly established in recent years and gradually become a crucial operational tool in the industries of semi-conductor and micromachining [1–3]. In particular, the application of pulsed laser for precision sur-face marking, direct writing and pattern formation on multi-layer film devices have emerged as an important approach for micromachining [4, 5]. However, the shock wave excited by pulse-laser is able to cause mechanical failure in terms of layer cracking and interfacial delaminating, and thus, often limit the life of thin film components [6, 7]. Moreover, the existent la-u Fax: +886-6-2352973, E-mail: [email protected]
tent defects in materials are invisible and difficult to detect. It can often cause accidental failure of multilayer film com-ponents. Therefore, it is of great importance to explore the fundamental mechanism of microscopic fracture at the solid– solid interface excited by pulse laser.
Numerous experimental methods have been studied to measure the interfacial quality, stress and thermal stability of multilayer films by the laser spallation technique [7, 8]. In this technique, a laser-generated compressive stress wave reflects into a tensile wave from the free surface of the coat-ing and pries off the interface surface at a critical ampli-tude. The critical interfacial stress σ is estimated accord-ing to one-dimensional longitudinal mechanics, expressed as σ(t) = 0.5V∂u(t)/∂t [9, 10], where is the density of the material and V denotes the velocity of the longitudinal wave. The partial differentiation of the displacement u(t) with re-spect to time defines the particle velocity of the longitudinal wave. However, the strength measurement at the interface be-tween the film and substrate by laser spallation technique can only stand for the dynamic adhesive strength at a high rate of strain [10], but in the present work measurement of the quasi-static interfacial strength still cannot be carried out by these methods.
In addition to experimental studies, theoretical analysis of thermo conduction and stress propagation behaviors inside materials were presented by Chou, Qiu and Yilbus [10–12]. Their reports offer important information to infer the proper-ties of microstructures and to predict the films fracture. How-ever, the theoretical analysis, by having a key problem about the inter-coupling mechanisms of realistic physical quantities is complicated to handle. In this study, the fracture process ex-cited by the pulse laser is tightly time-dependent and energy accumulation correlated. Therefore, it is illogical if only the analysis of a single property or criterion is used to describe the fracture process without considering the coupling effect, i.e. to consider the overall coupling effects and to have relevant physical derivations are necessary but are difficult to achieve. Tremendous amounts of energy deposition excited by a pulse laser over a short time can cause high gradients in pressure and temperature, and also very complicated dynamic behaviors at the interface. Many of these complicated phe-nomena, such as interior microscopic mechanical fracture, transient structure evolvement phenomena, thermodynamic properties recordation and so on, are still unclear so far. The
498 Applied Physics A – Materials Science & Processing technique of molecular dynamics (MD) simulation has proven to be comprehensive for detailed study of these phenom-ena and the associated transient behaviors. In the past, MD methods have been successfully used for the study of sur-face ablation mechanisms and dynamic behavior excited by pulsed laser [13–17]. A two-dimensional MD simulation has been used to study surface ablation phenomena of solid argon (Ar) [13], thermodynamic trajectories, and the mechanism of cluster ejections [17]. The dynamic characteristic and surface spallation for organic molecules [16] and phase trajectories of metal [15, 18] excited by pulse laser ablation has also been re-ported. These results can be attributed to better understanding of the dynamic behavior at the atomic scale, the mechanism of cluster ejection, and the effect of photochemical and photo mechanics on target surface ablation between the laser and materials.
Although the aforementioned MD reports are confined to surface ablation, the approach can be further improved to study solid-state interfacial spallation processes excited by pulsed laser. In view of the need for further investigation on detailed interfacial spallation mechanisms, this paper focuses on the dynamic formation process of fractures at the solid-state structural interface when excited by pulse laser. Since this is the first use of the microscopic spallation process in-duced by pulse laser at the solid–solid interface by means of a MD approach, various laser incident energy densities and pulse durations are employed to characterise the dynamic behavior and interfacial evolution at the interface. The micro-scopic mechanism of interfacial fracture excited by expansive dynamics and tension stresses are investigated, and the rela-tions between the associated strain rate and interfacial failure are analysed. Finally, a critical damage threshold is evalu-ated. Technical suggestions to avoid interfacial fracture are also proposed.
2 Methodology 2.1 Computational model
In order to study and compare structural spallation mechanisms at the solid–solid interface excited by femtosec-ond pulse laser by using MD simulation, an argon crystal and the pair potential of Lennard–Jones (LJ) system [19, 20] was chosen for simulation and modeling. The potential and inter-molecular forces of the system are derived and evaluated in a time step of∆t = 5 fs with energy parameter ε = 1.653× 10−21J, equilibrium separationσ = 3.404 Å, and cutoff ra-dius rc= 2.5σ. The atomic velocities and accelerations are
estimated by means of Gear’s fifth-order predictor-corrector algorithm [19].
The bulk materials consist of two different parts of crys-talline planes of Ar, namely the (001) and (111) planes. The upper part of the structure, enduring the laser irradiation di-rectly, is the Ar(001) crystal that comprises 14× 10 × 50 face-centered cubic (FCC) unit cells in x, y and z directions, respectively. The lower part of the structure comprises 150 layers of Ar(111) plane in z direction. Between two struc-tures is an ideal flat interface. The system is constructed by 76 000 atoms, and the computational domain has a size of 75.8 × 54.1 × 736.7 Å in x, y and z directions, respectively. The domain sizes of Ar crystal in FCC lattice are calculated by
FIGURE 1 Schema of different modeling regions for MD simulation
means of the nearest-neighbor distance given by Broughton and Gilmer [21]. Periodic boundary conditions (PBC) are im-plemented for the surfaces in the x and y directions, and free boundary conditions in the z direction. The evaluation of the atomic force and potential near the PBC is compliant with the minimum imagined criterion [19]. The scheme of the simu-lation domain is given in Fig. 1. The bottommost layer of Ar(111) crystalline planes is designed as a fixed lattice that mimics a fixed substrate to stabilize the system. Such a static lattice may introduce strain and stress wave-rebounding into the system. Above the static lattice, the next four neighbor-ing layers are assigned to comprise the “heat bath” actneighbor-ing as a thermostat of Gauss’s principal of least constrain algo-rithm [20, 22]. The thermostat presents the temperature in a heat bath at a fixed value (taken as 50 K of the substrate tem-perature) and acts to diffuse the heat of the substrate outwards. Above the heat bath are the so-called free motion layers or dynamic sections. The atoms in the dynamic sections inter-act with the incoming energy “laser beam”, transferring heat, energy and force to the inside of the bulk materials.
2.2 Laser absorption mechanism
The mechanism of energy transfer between laser and materials strongly depends on the character of the irradi-ations and material properties. Energy transform [13, 17, 23] is the most commonly used technique to model the interac-tion between laser and argon material in the LJ system. The laser energy is absorbed by the target and converted into ki-netic energy by scaling the velocities of all atoms in each structural cell with an appropriate factor. The target is sepa-rated into many “layers” perpendicular to the incident light. The layers are chosen to be one-cell thick. The amount of energy deposited in each cell that exponentially decreases in the direction of incident light is calculated by means of
LAIet al. Microscopic spallation mechanisms induced by a pulse laser at the solid-state interface 503
FIGURE 10 Partially enlarged diagram of Fig. 9 (175 ps). Roman
numer-als identify different regions: (I) cluster aggregation and deposition; (II)
solid–liquid coexistence region; (III) non-ablated parts of Ar(001) crystal (in
purple); (IV) spallation at interface; (V) Ar(111) crystal (in gray)
perfect except for the cluster aggregation region (I) and the ab-lation region (II). However, in region (V) the Ar(111) crystal appears comparatively disordered, indicating that the struc-ture becomes unstable due to stress confinement effects. In region (IV) of the interfacial spallation, since the interaction between tension stress and binding force of molecular poten-tial energy, a special failure phenomenon, called “moderately ductile fracture” [25], is presented. A large fracture strain of more than 12% is observed before the fracture occurs, and the mechanism of spallation starts formation with the coalescence of voids. However, cross-sectional area reduction is less ap-parent. It is thus named as “moderately ductile fracture”. The above-mentioned mechanism is analogous to experimental re-sults reported in literature of spallation in aluminum coating excited by a pulse laser [28].
The fundamental mechanism of interfacial fracture can be further summarized. Interfacial spallation is a result of inter-nal failure in void defect creation, followed by consistent en-largement induced by expansive dynamics and tension stress. The macroscopic strain and strain rate are evaluated. The fun-damental failure mechanism is also analyzed. Finally, based upon the results of simulation, a critical damage threshold is evaluated and obtained as 8.5 J/m2(as shown in Fig. 8). 4 Conclusion
This paper reveals the mechanism of interfacial spallation and the transient behavior of a solid-state interface excited by a femtosecond pulse laser using the MD simulation technique. Based on the results of simulations, the interfa-cial spallation is found to be caused by expansive dynamics
and tension stresses inducing interior void defect enlargement that eventually leads to cracking, and even fracture. More-over, a high strain rate deformation with the order of 109s−1
induced by the compressive and expansive dynamics is ob-served. The microscopic mechanism of moderate ductile frac-turing is also identified. Both aforementioned phenomena are analogous to the experimental results of metal coating by the laser spallation technique. However, the high strain rate formation is another crucial factor to be concerned with for further study of the mechanism of fracture in materials.
The model presented in this paper is useful for predict-ing failure and to evaluate the critical damage threshold of multilayer devices in a pulse laser ablation process. In order to reduce the damage induced by thermal stress, moderate energy dissipation, by using substrate materials of high ther-mal conductivity and excellent vibrating absorption ability, is proposed. Such material can also be used to avoid unex-pected mechanical failure and to prolong the life of thin films in a pulse laser ablation process.
ACKNOWLEDGEMENTS The authors gratefully acknowledge the support provided for this research by the National Science Council of the Republic of China under Grant No. NSC94-2212-E-006-016.
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