Air Bubble Defects in Dispensing Nanoimprint Lithography

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1 Air Bubble Defects in Dispensing Nanoimprint Lithography Abstract We report a theoretical study and dynamic simulation to understand the dynamic behavior of the air bubble defects in Dispensing Nanoimprint Lithography (D-NIL), which is one of the biggest challenges in this technique. Continued with previous research report of air bubble formation and dissolution in dispensing nanoimprint lithography [5], which found mechanisms for air bubble formation (multi-droplet encircling) and air bubble dissolution as a function of time, we draw a hypnosis that the air bubble, instead of dissolving completely in the resist liquid, still remains in nano-scale and experience the surface energy relaxation. We developed theoretical and simulation evidence to support our hypoesis. Our key conclusions from the study, which has significant practical importance, is that air in a bubble can relax to the equilibrium position before completely dissolving in a resist liquid. Key Words Dispensing-based nanoimprint lithography, air bubble defect, air bubble surface energy relaxation 1. Introduction Nanoimprint lithography (NIL) is a proven technology with the key advantage of high resolution. It has shown the capability of patterning structures smaller than 10 nm with a high throughput [1, 2]. One of the NIL processes under current study is dispensing-based NIL (D-NIL), which generally describes a group of relevant and similar procedures using dispensed liquid resist including micromoulding in capillaries (MIMIC) [3], and step-and-flash imprint lithography (SFIL). In this technique, the resist liquid is dropped on the resist as droplets (Fig.1 ). Then a mold is used to push the droplets to merge together into a thin film (Fig.1 (b)).the resist liquid is then cured by either photos, heat, or both (Fig.1 (c)), and leave a solid imprint pattern on the substrat e(fig.1 (d)). 1

2 Figure 1: Schematic of dispensing nanoimprint lithography (D-NIL). However, there still challenges remaining in this process. One of the biggest challenges in this method is the air bubble defect. The air bubble defect is caused during the multiple droplets merging process, in which the air bubble is trapped in the center of the resist, due to the enclosure of the escape paths (Fig. 2). Figure 2: Schematic of bubble formation due to multi-droplet encircling 2. Dynamic Behavior of Air Bubble After the air bubble is trapped in the center of the resist, the dynamic behavior of air bubble is presented below as two stages: (2.1) dissolution stage and (2.2) surface energy relaxation stage The dynamic behavior in dissolution stage has already been well studied by Xiaogan Liang in 2007 using experimental and theoretical model (Fig.3, [5]). Our study is a continuous study based on this previous research and focus on the second stage: surface energy relaxation stage. 2.1 Dissolution Stage After the air bubble is trapped in the center of the resist, it will first experience the dissolution stage. Figure 3 shows the study results that air bubble can dissolve with time, using the real-time observation of the air bubble dissolution (Fig 3) and average bubble diameter as a function of 2

3 time (Fig 3(b)). However, the scale of this study is in micron meter and the bubble diameter did not reach zero, we could doubt the air bubble did not dissolve completely in the resist. An recent industrial from Seagate company proved our doubt by showing the nano-scale air bubble defects found in the resist pattern (Fig.4 ). So we developed further study to understand the dynamic behavior of air bubble in nano-scale after dissolution stage, where the most parts of bubble has been dissolved. (b) Figure 3: Real-time observation of an air bubble encircled by multiple droplets and the bubble shrinking due to the air dissolution into the resist. (b) The simulated ( ) and measured ( ) time evolution of average bubble diameter as a function of bubble initial size for a given set of NIL parameters [5]. 2.2 Surface Energy Relaxation Stage After the most parts of the air bubble dissolved in the resist liquid, we assume small parts of it still remain in nano-scale, and then experience surface energy relaxation stage. The hypothesis of the dynamic behavior of air bubble in this stage is made by assuming the bubble will spread out and relax follwing the dash line in figure.4 (b). 3

4 (b) Figure 4: Geometry of the Air bubble defects found in the resist pattern, and (b) hypothesis of the dynamic behavior of air bubble during surface energy relaxation: the bubble will spread out and relax follwing the dash line. 3. Theoretical and Simulation Study of the Air Bubble Surface Energy Relaxation Behavior We developed theoretical and simulation evidence to support our hypothesis of the surface energy relaxation of the air bubble. After dissolution, the model assumes a 100 nm single air bubble trapped at the central part of an already merged resist film; the outer boundary of the resist film is far away from the bubble; the fluidic flow can be described as laminar flow; the bubble relaxation and the resist flow around the bubble are axially symmetrical; the pressure is constant and the gas trapped in the bubbles is mainly composed of air. Figure 5 shows the geometry of the theoretical model, in which a single bubble is initially located at the center of a thin resist film sandwiched between a rigid mold and a substrate. (b) Figure 5: Geometry and parameters of a single air bubble initially located at the center of a resist liquid sandwiched between a mold and a substrate, and (b) the illustration of the final position of the air bubble after the surface energy relaxation. 3.1 Theoretical Study During the surface energy relaxation process, the dynamic behavior of air bubble is described by the Young's equation [6], which is obtained by projecting the equilibrium forces on the solid plane, and used to describe the surface tensions between three phases: solid, liquid, and gas (Fig.6). Where γ LS is the liquid-solid interfacial free energy, γ LG is the liquid-gas interfacial free energy, γ GS is gas-solid interfacial free energy, θ 1 and θ 2 is the contact angel. 4

5 γ LS + γ LG cosθ 1 = γ GS (1) When γ LS + γ LG cosθ 1 > γ GS as the initial condition (Fig.6 ), the air bubble will spreads driven by the unbalanced surface tension. When γ LS + γ LG cosθ 1 = γ GS (Fig.6 (b)), the air bubble will stop spreading and stay its equilibrium position which has lowest its surface energy. (b) Figure 6.Schemetic interface tensions between solid(mold), liquid(resist), and gas(air bubble); in initial condition, air bubble will spreads because the unbalanced surface energy in order to lower surface energy, until (b) the air bubble will stop spreads and keep staying its equilibrium position which has lowest its surface energy. The pressure difference between the inside and outside of bubble, P b P o, is described by Laplace pressure equation (Eq. (2)), which depends upon the surface tension σ, the radius R of the bubble. Where P b is the pressure inside the bubble and P o is the ambient pressure. During this spreading out process, the pressure difference decrease because the radius of the bubble increase. Thus dissolution decrease and bubble will stay in this equilibrium condition for a long time that formed air bubble defects in the resist. P b P o = 4σ R (2) 3.2 Simulation Study The dynamic behavior of air bubble surface energy relaxation was simulated by computational fluid dynamics (CFD) using ANSYS 16.1-Fluent. Since the minimum scale of this simulation software IS millimeter, dimensional analysis is used for scaling the parameters between theoretical prototype above and simulation model. We assume the viscosity μ of the resist flow depended on Eq. (3): μ = f(ρ, V, L, σ), where ρ is the density of the resist, V is the resist flow velocity, L is the characteristic length, and σ is the surface tension. With dimensional group analysis, we can immediately reduce Eq. (3) to the equivalent form of dimensionless groups. 5

6 ρvl μ = g( P ρv2l 1, ρv2 2 Re = g( Eu, We) Nan Li σ ) (4, 5) To achieve dynamic similarity requires duplication of these dimensionless groups, where subscripts m and p mean model and prototype. Re m = Re p, Eu m = Eu p, We m = We p (6) V p V m = ρ m ρ p μ p μ m L m L p = ρ ml m ρ p L p (7,8) μ m μ p = ρ ml m ρ p L p Assuming ρ m = ρ p, L m = 1 mm, L p = 100 nm, so μ m = 100. Since the material properties of μ p the resist liquid and air bubble was assumed water and air, the viscosity of the resist liquid and air bubble was set 100 times bigger than the standard viscosity properties (Table 1. ). Other numerical parameters, setting-up and geometry is presented in table 1 and figure 7 below. Physical parameters Symbols Value Surface tension σ Radius of the bubble R 0.42 mm Pressure inside the bubble P b Ambient pressure P o Pa Density of the resist ρ kg/m 3 Resist flow velocity V Characteristic length L 1 mm Contact angel θ degree 6

7 (b) Setting-Up Parameters General Pressure-based, Transient Volume of Fluid: two phases Models Laminar Bubble: standard air form default database, Viscosity [kg/m-s]: Materials Resist: standard water-liquid form default database, Viscosity [kg/m-s]: Pressure outlet: water backflow fraction:1 Boundary conditions Axisymmetric Solution Method Simple C Table 1: Numerical values of physical parameters, and (b) model set-up parameters used in the simulation. Figure 7: Axisymmetric geometry of the used in the simulation at equilibriums condition. The axis boundary type is used as the centerline (marked in dash line ) of the geometry. The simulatyion result regarding the volume fraction of the air bubble and pressure evolution of the air bubble with a function of time, during the air bubble surface energy relaxation stage, is presented in figure 8. We can see from the sec to 0.01 sec, the pressure difference between the bubble inside and outside is large since the energy contours cross a large range. After 0.02s, the pressure difference becomes less since the smaller range of enegy contours. Refering the volume fraction of the air bubble, we can draw the conclusion the bubble reached its equilibrium condition and formed air bubble defects in the resist. 7

8 Figure 8: The volume fraction of the air bubble in red color (left) and pressure evolution of the air bubble (right) with a function of time. 8

9 Conclusion Nanoimprint lithography has key adavantage in high resolution comparing to the conventional technics such as optical lithography. However, one of the biggest chanllege in this manufacturing process is the air bubble defects fomed in the resist. Our objective of this paper is to understand the dynamica behavior of air bubble. The air bubble is found to experience two stages: dissolosion and surface energy relaxation. Our project focus on the second stage and made hypoesis of the air bubble s daynamic havior. Finally we developed theoretical and simulation evidence to support our hypoesis that air in a bubble can relax to the equilibrium position before completely dissolving in a resist liquid. 9

10 References [1] S. Y. Chou, P. R. Krauss, and P. J. Renstrom, Imprint of sub-25 nm vias and trenches in polymers, Appl. Phys. Lett. Applied Physics Letters, pp [2] S. Y. Chou, P. R. Krauss, and P. J. Renstrom, Imprint Lithography with 25-Nanometer Resolution, Science, pp , [3] E. Kim, Y. Xia, and G. M. Whitesides, Polymer microstructures formed by moulding in capillaries, Nature, pp , [4] M. Colburn, S. C. Johnson, M. D. Stewart, S. Damle, T. C. Bailey, B. Choi, M. Wedlake, T. B. Michaelson, S. V. Sreenivasan, J. G. Ekerdt, and C. G. Willson,, Emerging Lithographic Technologies III, [5] X. Liang, H. Tan, Z. Fu, and S. Y. Chou, Air bubble formation and dissolution in dispensing nanoimprint lithography, Nanotechnology, pp , [6] ramé-hart Contact Angle, ramé-hart Contact Angle. [Online]. Available at: [Accessed: Feb-2015]. [7] M. C. Weinberg, Surface tension effects in gas bubble dissolution and growth, Chemical Engineering Science, pp [8] R. W. Fox and R. W. Fox, Fox and McDonald's introduction to fluid mechanics, 8th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2011, p

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