Atomistic simulation of nanoformed metallic glass

Applied Surface Science 343 (2015) 153–159

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Atomistic simulation of nanoformed metallic glass Cheng-Da Wu ∗ Department of Mechanical Engineering, Chung Yuan Christian University, 200, Chung Pei Rd., Chung Li District, Taoyuan City, 32023, Taiwan

a r t i c l e

i n f o

Article history: Received 27 January 2015 Received in revised form 16 March 2015 Accepted 16 March 2015 Available online 23 March 2015 Keywords: Metallic glass Forming Mechanics Mechanical properties Molecular dynamics

a b s t r a c t The effects of forming speed and temperature on the forming mechanism and mechanics of Cu50 Zr25 Ti25 metallic glass are studied using molecular dynamics simulations based on the second-moment approximation of the many-body tight-binding potential. These effects are investigated in terms of atomic trajectories, flow field, slip vectors, internal energy, radial distribution function, and elastic recovery of nanoimprint lithography (NIL) patterns. The simulation results show that a shear transformation zone (STZ) forms at the substrate surface underneath the mold during the forming process. The STZ area increases with mold displacement (D). The movement speed of substrate atoms underneath the mold increases with increasing D value. The movement directions of substrate atoms underneath the mold are more agreeable for a larger D value. The stick-slip phenomenon becomes more obvious with increasing D value and imprint speed. The substrate energy increases with increasing imprint speed and temperature. Great NIL pattern transfer is obtained with unloading at low temperatures (e.g., room temperature). © 2015 Elsevier B.V. All rights reserved.

1. Introduction With progress in micro- and nanosystems, the requirement for high-resolution patterns on micro- and nanometer scales has greatly increased. Nanoimprint lithography (NIL) [1,2] is one of the most popular nanopatterning technology. It’s easy operation, high resolution (sub-10-nm feature size) [3,4], high throughput (patterning on a large substrate), and low cost have led to its application in various fields, such as data storage devices [5], flexible electronics [6], microelectronics [7], and biological devices [8]. NIL is a mechanical deformation process operated under suitable temperature and pressure, in which a mold with nanoscale patterns is directly replicated onto a polymer or thin metal film through imprinting and release. Metallic glass, also known as amorphous metal alloy, is a solid metallic material. It has a disordered atomic arrangement (noncrystalline structure) and thus lacks the typical defects found in metals, such as dislocations and grain boundaries [9]. Metallic glass has recently been applied for nanomolds [10,11] due to their unique physical properties, such as high strength and hardness [12–14], low friction, good corrosion resistance [15], and minimal shrinkage. Metallic glass is considered as an alternative to traditional materials [10], such as silicon and quartz, for nanomolds. However, few studies have been conducted on the forming mechanism and

∗ Tel.: +886 3 2654346. E-mail address: [email protected] http://dx.doi.org/10.1016/j.apsusc.2015.03.091 0169-4332/© 2015 Elsevier B.V. All rights reserved.

mechanics of metallic glass. Molecular dynamics (MD) simulation is a powerful tool for studying nanoscale material interactions. Atomic simulation avoids experimental noise and turbulence problems and can be used to analyze atomic trajectories, thermodynamics, and mechanical properties. Many nanosystems have been analyzed using MD, such as nanoscratching [16], nanoforming [17–19], and the bending of nanowires [20,21]. This work investigates the effects of forming speed and temperature on the forming mechanism and mechanics of Cu50 Zr25 Ti25 metallic glass using MD simulations. The simulation results are discussed in terms of atomic trajectories, slip vectors, flow field, internal energy, radial distribution function, and elastic recovery of NIL patterns. 2. Model and methodology The amorphous structure of Cu50 Zr25 Ti25 metallic glass (substrate) at a temperature of 300 K was simulated with the following parameter settings and heat treatments. First, 120,000 atoms were placed in a cubic box and arranged as a perfect face-centered cubic (fcc) single crystal. Each fcc unit cell consisted of two Cu atoms, one Zr atom, and one Ti atom. Three-dimensional periodic boundary conditions were applied. The simulations were carried out in the isobaric–isothermal ensemble (NPT) and the Nosé-Hoover thermostat was used to control the temperature and to maintain the external pressure at zero. The system was heated from 0 to 1700 K at a constant heating rate of 0.5 K/ps to simulate the melting process (to obtain a well-equilibrated liquid state). Before the cooling

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C.-D. Wu / Applied Surface Science 343 (2015) 153–159 Table 1 Tight-binding potential parameters used in simulation [22]. Parameter

A (eV)

 (eV)

p

q

˚ r0 (A)

Cu–Cu Ti–Ti Zr–Zr

0.0855 0.1519 0.1934

1.2240 1.8122 2.2792

10.960 8.6200 8.2500

2.278 2.390 2.249

2.56 2.890 3.170

where EBi and ERi denote the bond-structure energy and repulsive energy of atom i, respectively; they are respectively expressed as:

⎧ ⎨

EB i = −

⎩

ER i =

 j

j= / i



 2 · exp −2q



A · exp −p

r

ij

r0

r

ij

r0

⎫1 ⎬ 2

−1

⎭

(2)



−1

(3)

where rij is the distance between atoms i and j, r0 is the firstneighbor distance, and  is an effective hopping integral. The parameters A, p, q, and  are determined from experimental data of cohesive energy, lattice parameter, bulk modulus, and two shear elastic constants (C44 and C  = 12 (C11 − C12 )), respectively. The TB potential parameters are listed in Table 1 [22]. A cut-off radius of 0.65 nm was used for the TB potential. 3. Results and discussion Fig. 1. Schematic of nanoforming model of Cu50 Zr25 Ti25 metallic glass (unit: nm).

process began, the melting system was equilibrated at 1700 K for 300 ps. Finally, the system was cooled from 1700 to 300 K at a high cooling rate of 5 K/ps and then equilibrated at 300 K for 300 ps. The radius distribution function of the obtained amorphous structure is in good agreement with that reported by Dalgic et al. [22]. Samples for the forming test were cut from a large cubic-shaped amorphous sample, as shown in Fig. 1, in which the substrate atoms are colored according to the element type. The substrate dimensions are 11.0 nm (length) × 2.5 nm (width) × 10.5 nm (height). The mold, made of tungsten (W), consisted of a perfect body-centered cubic single crystal with a lattice constant of 0.316 nm. The feature size of the mold was 5.0 × 5.2 nm. The whole mold was assumed to be an ideally rigid object to simplify the forming problem and focus on the deformation of the substrate. Two kinds of atoms were set in the substrate, namely Newtonian atoms and boundary atoms (fixed atoms). The boundary atoms of the four layers at the substrate bottom were used to support the whole system. Periodic boundary conditions were applied in the X and Y directions in the model. The NTV ensemble was employed in the simulation. The equations of motion were integrated with steps of 1 fs using Gear’s fifthorder predictor-corrector method [23]. A constant displacement of 3 × 10−5 nm per time step along the Z-axis was set for the mold for imprinting, followed by a holding process for 50 ps. Finally, the mold was instantly unloaded to simulate an ideal unloading process without adhesion action between the mold and the substrate. The second-moment approximation of the many-body tightbinding (TB) potential [22] was adopted to describe the ternary Cu–Zr–Ti system. The TB potential can effectively predict the glass transition temperature for the ternary Cu–Zr–Ti system [22] via the change of the radial distribution function (g(r)) and the volume with temperature. The TB potential (Es ) is expressed as: ES =

 i

ER i + EB i



(1)

3.1. Forming mechanism Fig. 2 shows snapshots of the nanoforming process of the metallic glass at a temperature of 300 K at mold displacements (D) of 0.9, 3.3, 4.5, 5.0, 5.3, and 5.8 nm, respectively. The substrate atoms are colored according to the magnitude of their slip vectors. The slip vector of an atom was evaluated as the difference of the atomic positions between a specific time step and the time step after the equilibration at 300 K, which provides a clear description of the strain field for a deformed nanomaterial. At D = 0.9 nm (Fig. 2(a)), a few surface atoms of the substrate adsorbed onto the mold due to van der Waals (VDW) attractive forces, leading to a slight expansion at the substrate surface. When D increased to 3.3 nm (Fig. 2(b)), a shear transformation zone (STZ) formed at the substrate surface (light blue atoms) underneath the mold. The STZ, whose structure is independent and disordered, is the fundamental unit of plastic deformation in metallic glasses [24]. The STZ is considered as a point defect with high stress. However, for metallic crystals, the deformation mechanism originates from the nucleation and propagation of dislocations (line defects). Therefore, there is no formation of dislocations [25] in Fig. 2. When D further increased, as shown in Figs. 2(c)-(f), three main domains with high slip vector values appeared at the surface: one underneath the mold and the others at the two sides of the mold, respectively. The former is subjected to compressive stress from the mold whereas the latter are subjected to tensile stress, which leads to the atoms being extruded upwards. Interestingly, some surface atoms at the two sides of the mold have extremely low slip vector values, which indicates that they remained almost stationary during the forming process, forming a dead metal area, due to adhesion interaction with the mold. The slip vector of atoms significantly increases with D value. Fig. 3(a)–(d) show snapshots of the flow field of the surface atoms of the substrate underneath the mold at D = 3.3, 4.5, 5.0, and 5.8 nm, respectively. In Fig. 3, the length of the arrows is proportional to the magnitude of the flow speed of atoms and their direction indicates the flow direction at the present time step during the forming process. At a shallow imprint depth of 3.3 nm (Fig. 3(a)), the atoms moved irregularly at low speed. With an

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Fig. 2. Snapshots of whole forming process for D values of (a) 0.9, (b) 3.3, (c) 4.5, (d) 5.0, (e) 5.3, and (f) 5.8 nm at temperature of 300 K. Substrate atoms are colored according to magnitude of their slip vectors.

Fig. 3. Snapshots of flow field of surface atoms of substrate underneath mold for D values of (a) 3.3, (b) 4.5, (c) 5.0, and (d) 5.8 nm at temperature of 300 K.

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Fig. 4. Variation of (a) loading force and (b) internal energy per substrate atom versus D value for imprint speeds of 5, 30, 60, and 90 m/s at temperature of 300 K.

increase in the D value, the speed of atomic movement increased, with more atoms moving toward the bottom. Almost all the atoms at the surface moved downward when D reached 5.8 nm. The surface atoms attached to the mold had the highest flow speeds. 3.2. Effect of imprint speed Fig. 4(a) shows the variation of loading force versus D value for imprint speeds of 5, 30, 60, and 90 m/s at a temperature of 300 K. The interaction between the mold and the substrate begins at D = 0.6 nm. At first, a negative force up to 160 nN appears, indicating the maximum of the VDW attractive force interaction. The force then becomes a positive value and rapidly increases (repulsive force) with D value due to the increase in the number and accumulation amount of defects inside the substrate. The irregular oscillation on the force curves indicates a stick-slip phenomenon [26]. That is, the required loading force from the mold keeps increasing when the defects are being formed and accumulated; this force then drops during the relaxation of the defects. Fig. 4(a) shows that the stick-slip phenomenon is velocity dependent, increasing (larger oscillation) with the increasing imprint speed. The required loading force slightly increases with imprint speed. Fig. 4(b) shows the variation of internal energy per substrate atom versus D value for the tested imprint speeds. The internal energy of an atom consists of its potential energy and kinetic energy. In Fig. 4(b), the energy curves overlap before D reaches 1.5 nm. An energy drop appears as D = 0.6 nm, which indicates that the substrate is being relaxed through the VDW interaction with the mold, leading to a structure adjustment at the surface. The energy curves then rise with increasing D value because the amount of deformation increases. For forming at a given imprint temperature, the increase in energy during the forming process can be considered as the required energy to form the pattern. The required deformation energy for a sample with a slower imprint speed is less due to more time for relaxation. Fig. 5 shows the g(r) curve of the formed substrate for D values of 0.9, 4.5, 5.3, and 5.8 nm, respectively. The g(r) curve indicates how the atomic density varies as a function of the distance away from a particular atom. In Fig. 5, the first peak for the various D values appears at around 0.25 nm, which is close to that of equilibrated Cu50 Zr25 Ti25 metallic glasses [22]. However, the first peak slightly shifts to the left with increasing D value, indicating an increase in the extent of structural compactness. The height of the peaks also increases with the increasing D value, except for the first peak. This

indicates that the order of the whole structure increases when subjected to an external force. After unloading, the g(r) curves almost overlap, which indicates that the effect of imprint speed on the transferred pattern is insignificant, as shown in Fig. 6. 3.3. Effect of imprint temperature The effect of imprint temperature was studied by forming the substrate at constant temperatures of 300, 500, 700, and 900 K, respectively. Fig. 7 shows the variation of internal energy per atom of the substrate versus D value for the tested temperatures. All the energy curves exhibit similar trends. However, the energy increases with the temperature because kinetic energy is directly related to temperature. Fig. 8 shows the g(r) curves of the transferred pattern after unloading at various temperatures. The first peak of the g(r) curves has a common value of around 0.25 nm; however, its height decays with increasing temperature, indicating a decrease in the structural order at higher temperatures. A comparison between the g(r) curves before (Fig. 3) and after (Fig. 8) unloading indicates that the

Fig. 5. Radial distribution function of formed substrate for D values of 0.9, 4.5, 5.3, and 5.8 nm at temperature of 300 K.

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Fig. 6. Formed substrates after unloading for imprint speeds of 5, 30, 60, and 90 m/s at temperature of 300 K.

peaks before unloading are sharper and narrower than those after unloading. This indicates that the substrate after unloading relaxes, the relaxation increasing with temperature. In the nanoforming process, the amount of elastic recovery of a pattern after unloading determines its quality. The elastic recovery strongly depends on a few factors, including the adhesion between the mold and the substrate [27], the size of the mold [28], and temperature [29]. This section focuses on the effects of temperature on

the outcome of pattern transfer and the evaluation of elastic recovery. Fig. 9 shows a series of snapshots of the transferred pattern at various temperatures. The amount of elastic recovery significantly increases with increasing temperature. This is because the atoms have greater flow ability (larger kinetic energy) at higher temperatures. In order to quantify the elastic recovery of the pattern, several parameters are defined: WT and WB are the width of the pattern at

Fig. 7. Variation of internal energy per substrate atom versus D value for imprint temperatures of 300, 500, 700, and 900 K at imprint speed of 30 m/s.

Fig. 8. Radial distribution function of formed substrate for imprint temperatures of 300–900 K at imprint speed of 30 m/s.

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C.-D. Wu / Applied Surface Science 343 (2015) 153–159

Fig. 9. Formed substrates after unloading for imprint temperatures of 300–900 K at imprint speed of 30 m/s.

the top and the bottom, respectively, and h is the height of the pattern. Subscripts 1 and 2 represent the pattern size before and after elastic recovery, respectively. Three elastic recovery ratios () are defined as: WT =

WT 1 − WT 2 WB1 − WB2 h1 − h2 , WB = , h = WT 1 WB1 h1

(4)

Fig. 10 shows the evaluation of  values for various temperatures. Positive  values represent shrinkage in the dimension whereas negative ones represent expansion. Both WT and h

increases significantly with increasing temperature, and WB decreases. The results indicate that to obtain good pattern transfer, unloading at high temperatures is unsuitable. To confirm this result, an additional case forming at 700 K and unloading at 300 K was simulated. A quite low elastic recovery was obtained, whose characteristics are very similar to those of the pattern shown in Fig. 9(a). 4. Conclusion MD simulations were used to investigate the effects of forming velocity and temperature on the forming mechanism and mechanics of Cu50 Zr25 Ti25 metallic glass. The following conclusions were obtained: (1) The STZ forms at the substrate surface underneath the mold and the STZ area increases with D value. (2) For a larger D value, the substrate atoms underneath the mold have higher movement speed with more agreeable movement directions. (3) During the forming process, the stick-slip phenomenon becomes more obvious with increasing imprint speed. (4) The substrate energy increases with increasing imprint speed and temperature. (5) Great pattern transfer is obtained with unloading at low temperatures (e.g., room temperature). Acknowledgments

Fig. 10. Evaluation of  values for various temperatures.

This work was supported by the Ministry Science and Technology of Taiwan under grant MOST 103-2218-E-033-003.

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