Critical size, recovery, and mechanical property of nanoimprinted Ni–Al alloys
investigation using molecular dynamics simulation
Cheng-Da Wu, Te-Hua Fang
⇑, Po-Hsien Sung, Quang-Cherng Hsu
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan
a r t i c l e
i n f o
Article history: Received 11 July 2011
Received in revised form 12 September 2011
Accepted 19 September 2011 Available online 22 October 2011 Keywords: Nanoimprinting Alloy Composition Elastic recovery Molecular dynamics
a b s t r a c t
The nanoimprinting process of nickel–aluminum (Ni–Al) alloys is studied using molecular dynamics (MD) simulations based on the many-body tight-binding potential. The effects of the temperature, load-ing and unloadload-ing velocities, holdload-ing/dwellload-ing time, and composition of Ni–Al alloys are evaluated in terms of molecular trajectories, imprinting force, potential energy, stress, slip vector, and elastic recovery ratio. Simulation results show that the imprinting force increases with decreasing temperature and increasing loading velocity and Ni content. The average potential energy of a specimen decreases and its stress increases with increasing loading velocity. Slip planes of (1 1 0) and (1 1 0) form during Ni–Al alloy imprinting. During unloading, the adhesion force increases with increasing unloading velocity. The formability of a Ni–Al alloy can be enhanced by increasing the Ni content. Elastic recovery for a pat-tern can be avoided by decreasing the imprinting temperature and increasing the holding time. At a crit-ical line width of 6.5 nm, elastic recovery ratios can be maintained in a range of 8–11%.
Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
Nanoimprinting lithography (NIL) [1] is a low-cost, high-throughput, large-area [2–4], sub-10-nm manufacturing method
[5]with applications in nano-optical devices, electronics fabrica-tion, storage devices, bio-chemical devices, and microfluidic de-vices [6–11]. In NIL, nanoscale structures on an imprinting master template are directly replicated onto polymer substrates or resists repeatedly by their physical deformation under suitable temperature and pressure. A strong high-resolution mold is thus necessary for fabricating nanoscale patterns. Top-down nanoli-thography technologies, such as e-beam linanoli-thography (EBL) [12]
and focused ion beam (FIB) milling[13], are commonly used to fab-ricate NIL molds on silicon or quartz substrates.
NIL was originally developed for imprinting on a soft polymer. However, direct imprinting on hard materials, such as metal, has recently been proven to be feasible[14–16]using extremely hard molds, such diamond and SiC molds. Experimental studies of NIL are restricted due to complicated interfacial interactive forces. To better understanding the deformation and mechanics in NIL, ana-lytical methods need to be developed to allow better control and design of the process. Molecular dynamics (MD) simulation is an effective tool for studying material behavior and system design at the nanoscale, and it provides detailed deformation information at the atomic level. Atomic simulation avoids experimental noise
and turbulence problems and can be used to analyze molecular tra-jectories and thermodynamic properties. Many nano-systems have been analyzed using MD, such as nanoindentation[17,18], nanos-cratching[19], and nanoforming[20]. Related to NIL, we recently reported the effects of taper angle[21]and annealing[22]on metal specimens and found that both the specimen deformation force and the internal energy increased with increasing punch taper an-gle. The residual stress was released after the annealing process. Pei et al.[23]found that the formation of the (0 0 1) surface results in the lowest imprinting force, and that the formation of the (1 1 1) surface results in the highest imprinting force for the NIL of single-crystal copper. Kang et al.[24]studied the effect of aspect ratio on a poly(methyl methacrylate) (PMMA) pattern and found that the amounts of springback and friction increased with increasing as-pect ratio.
This work investigates the effects of the imprinting tempera-ture, loading and unloading velocities, composition, and holding/ dwelling time on the NIL process of Ni–Al alloys using MD simula-tion. The results are discussed in terms of molecular trajectories, imprinting force, potential energy, stress, slip vector, and elastic recovery ratio.
2. Methodology
Fig. 1a shows a three-dimensional NIL model. The NIL process is studied using an MD simulation at an isothermal state of 300 K. The physical model consists of two silicon punches and a specimen of Ni–Al alloy, as shown inFig. 1b. The punches are assumed to be 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.commatsci.2011.09.027
⇑ Corresponding author. Tel.: +886 7 3814526 5336. E-mail address:[email protected](T.-H. Fang).
Computational Materials Science 53 (2012) 321–328
Contents lists available atSciVerse ScienceDirect
Computational Materials Science
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m m a t s c iideally rigid atoms to simplify the imprinting problem and to focus on the formation mechanism of patterns and the mechanics. The dimensions of the specimen are 25.5 (length) 1.8 (width) 6.0 (height) nm, and those of a single punch are 5.0 (length) 1.8 (width) 5.0 (height) nm with a taper angle of 15°. The punches comprise 9268 silicon atoms, and the specimen comprises 18,900 Ni and Al atoms in various proportions. A Cartesian coordinate sys-tem is used in the proposed syssys-tem. The origin is at the center of the lower-left atom of the specimen. A periodic boundary condi-tion (PBC) is imposed on the x-axis and z-axis. In mathematical models and computer simulations, a PBC[25]is often used to sim-ulate a large system by modeling a small part that is far from its edge. On the y-axis, the real specimen height is used; however, four layers of atoms at the specimen bottom are fixed to support the en-tire system. To further simplify the NIL model, only five unit cells of atoms are considered on the z-axis. The simulation of a three-dimensional NIL process is thus simplified into a two-three-dimensional process. In the simulation, the punches have constant unit dis-placements of 5 105and 2 104nm per time step along the y-axis for loading and unloading, respectively.
The forces and energy are calculated using interatomic poten-tials. Morse potential is used to simulate the interaction between the silicon punches and the Ni–Al alloy. The two-body Morse po-tential is adopted to simulate the interatomic energy. It is ex-pressed as:
UðrijÞ ¼ D exp 2f f
a
ðrij r1Þ 2 exp fa
ðrij r1Þ ð1Þwhere U(rij) is the pair potential energy function, rijis the distance between atom i and j, r1is the equilibrium distance between two atoms, D is the bonding energy between two atoms, and
a
is the material parameter. The Morse potential parameters evaluated by the mixed rule are listed inTable 1 [26,27]. For a Ni–Al alloy spec-imen, the second-moment approximation of the many-body tight-binding (TB) potential[28]is adopted to describe Ni/Ni interactions and Al/Al interactions, and the mixed rule is used for Ni/Al interac-tions. The TB potential form is:ES ¼X
i ðEiRþ E
i
BÞ ð2Þ
where EiBdenotes the bond-structure energy of atom i and E i R de-notes the repulsive energy of atom i; they are respectively ex-pressed as: Ei B¼ X j–1 n2 e2qððrij=r0Þ1Þ ( )1=2 ð3Þ Ei R¼ X j A epððrij=r0Þ1Þ ð4Þ
where r0is the first neighbor distance, and A, n, p, and q are adjust-able parameters governing the interaction between those atoms. The related parameters are listed inTable 2 [28].
The time integration of motion is performed using Gear’s fifth-order predictor–corrector method[25]with a time step of 1 fs. To increase calculation efficiency, the Verlet neighbor-list method
[25]is used. The lists of neighbor atoms are calculated every 10 time steps with a cut-off radius of 0.65 nm. To investigate the ef-fect of composition on the NIL process, Ni and Al atoms in a specific ratio were randomly located on the site of each lattice in the spec-imen. A series of thermal annealing procedures were run to reach thermodynamic equilibrium before the NIL process.
3. Results and discussion
3.1. Forming behavior during NIL process
Fig. 2a–f shows snapshots of the NIL process at a temperature of 300 K with loading and unloading velocities of 50 and 200 m/s, respectively. The NIL process can be divided into three stages: loading (imprinting), holding, and unloading. The loading process develops within the time period of 0–80 ps; atoms of the specimen deform and are extruded gradually into the cavities by the punches. At the initial loading stage, the balance of the specimen is disturbed due to the action of van der Waals (VDW) forces be-tween the atoms of the surfaces of the punches and the specimen just as the punches comes in contact with the specimen surface, as shown inFig. 2a. The contact surface of the specimen thus exhibits slight compressive deformation due to compressive loading from the punches, whereas the other surface is extruded upward by reactive forces. With increasing compressive loading, the extent of deformation of the specimen gradually increases, as shown in
Fig. 2b. When the punches reach the bottom point of imprinting at a depth of 1.7 nm (Fig. 2c), they are held motionless until 95 ps (Fig. 2d) to make the distribution of pressure more uniform. Fig. 1. (a) Schematic three-dimensional NIL model and (b) two-dimensional MD model (units: nm).
Table 1
Morse potential parameters used in the simulation[26,27]. Parameter D (eV) a(101nm1) r
0(101nm)
Si–Ni 1.177 1.910 1.314
Si–Al 0.944 1.782 2.802
Table 2
Tight-binding potential parameters used in the simulation[28].
Parameter A (eV) n(eV) p q r0(101nm)
Ni–Ni 0.0376 1.070 16.999 1.189 2.491
Al–Al 0.1221 1.316 8.612 2.516 2.864
Ni–Al 0.0678 1.187 12.805 1.8525 2.6775 322 C.-D. Wu et al. / Computational Materials Science 53 (2012) 321–328
Before and after the brief holding period at 80–95 ps, the specimen exhibits similar filling height, but its internal component distribu-tions show a slight difference due to energy relaxation and struc-ture adjustment. After unloading, the places underneath the punches have severe deformation zones, which have significant defects such as dislocations and atomic packing. An elastic force causes elastic recovery, as shown inFig. 2e and f.
3.2. Effect of temperature
The effect of temperature on the NIL process is investigated by simulating a Ni 80%–Al 20% alloy specimen at temperatures of 300, 500, 700, and 1000 K.Fig. 3shows the variation of imprinting force with respect to punch displacement for the tested temperatures. A significant attractive force of 1000 nN between the punches and the specimen appears before they come in contact due to the inter-action of VDW forces, displacing the surface atoms of the specimen slightly upward. At the loading stage (punch displacement of 2.7– 4.0 nm), the imprinting force increases gradually with punch dis-placement because the atoms of the specimen near the region in contact with the punches experience increasing plastic deforma-tion. The curves of the imprinting force inFig. 3exhibit different developments after the punch displacement passes 3 nm due to the effect of temperature. The oscillation and magnitude of the imprinting force start to decay with increasing imprinting temper-ature, which is in agreement with nanoscale material forming pro-cesses[22]. This is due to the kinetic energy of atoms and plastic flow increasing with increasing temperature. The highest required imprinting forces are 4738, 4787, 4292, and 3399 nN for tempera-tures of 300, 500, 700, and 1000 K, respectively. At the beginning of the unloading stage, the imprinting force for all temperatures quickly decreases to 2100 nN due to a strong adhesion force;
the imprinting forces gradually return to 0 nN with further punch retraction. The snapshots of NIL patterns inFig. 3clearly show that the amount of elastic recovery of the specimen increases with tem-perature. In these cases, the height of the pattern largely increased when the imprinting temperature was increased to 1000 K.
Fig. 4shows snapshots of the NIL process when the punches reach an imprinting depth of 1.7 nm for the tested temperatures. The atoms of the specimen in the snapshots are colored according to the magnitude of their potential energy during the NIL process to clearly indicate the behavior of atomic deformation in each characteristic region. The simulation shows that most high-energy Fig. 2. MD simulation of a Ni 80%–Al 20% alloy nanoimprinted at a temperature of 300 K with loading and unloading velocities of 50 and 200 m/s, respectively, at time steps of (a) 60, (b) 70, (c) 80, (d) 95, (e) 105 and (f) 115 ps.
Fig. 3. Relationship between imprinting force and punch displacement for a Ni 80%–Al 20% alloy for various imprinting temperatures.
(1) The imprinting force increases with decreasing temperature and increasing loading velocity and Ni content.
(2) The average potential energy of a specimen decreases and its stress increases with increasing loading velocity.
(3) The adhesion force during unloading increases with increas-ing unloadincreas-ing velocity.
(4) The formability of a Ni–Al alloy can be enhanced by increas-ing the Ni content.
(5) A low imprinting temperature and a short holding time lead to low elastic recovery.
(6) At a critical line width of 6.5 nm, elastic recovery ratios can be maintained in a range of 8–11%.
Acknowledgments
This work was supported by the National Science Council of Tai-wan under Grants NSC2628-E-151-003-MY3 and NSC -100-2221-E-151-018-MY3.
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