1. Nan Li
University of Michigan
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 (a)). 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)).

2. Nan Li
University of Michigan
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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(a)) and average bubble diameter as a function of

3. Nan Li
University of Michigan
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 email from Seagate company proved our doubt by showing the nano-scale air bubble
defects found in the resist pattern (Fig.4 (a)). 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.
(a) (b)
Figure 3: (a) 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).
(a)
(a)

4. Nan Li
University of Michigan
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(b)
Figure 4: (a) 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.
(a)
(b)
Figure 5: (a) 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 γLS is the liquid-solid interfacial free energy, γLG is the liquid-gas interfacial free energy,
γGS is gas-solid interfacial free energy, θ1and θ2 is the contact angel.

5. Nan Li
University of Michigan
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γLS + γLGcosθ1 = γGS (1)
When γLS + γLGcosθ1 > γGS as the initial condition (Fig.6 (a)), the air bubble will spreads driven
by the unbalanced surface tension. When γLS + γLGcosθ1 = γGS (Fig.6 (b)), the air bubble will
stop spreading and stay its equilibrium position which has lowest its surface energy.
(a)
(b)
Figure 6.Schemetic interface tensions between solid(mold), liquid(resist), and gas(air bubble);(a)
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, Pb − Po, is described by Laplace
pressure equation (Eq. (2)), which depends upon the surface tension σ, the radius 𝑅 of the bubble.
Where Pbis the pressure inside the bubble and Pois 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.
Pb − Po =
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.

6. Nan Li
University of Michigan
6
ρVL
μ
= g(
∆P
1
2
ρV2
,
ρV2L
σ
)
(4, 5)
Re = g( Eu, We)
To achieve dynamic similarity requires duplication of these dimensionless groups, where
subscripts 𝑚 and 𝑝 mean model and prototype.
Rem = Rep,
Eum = Eup,
Wem = Wep
(6)
Vp
Vm
=
ρm
ρp
μp
μm
Lm
Lp
= √
ρmLm
ρpLp (7,8)
μm
μp
= √
ρmLm
ρpLp
Assuming ρm = ρp, Lm = 1 mm, Lp = 100 nm, so
μm
μp
= 100. Since the material properties of
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. (a)). Other
numerical parameters, setting-up and geometry is presented in table 1 and figure 7 below.
(a)
Physical parameters Symbols Value
Surface tension σ
Radius of the bubble R 0.42 mm
Pressure inside the
bubble
Pb
Ambient pressure Po 1.01× 105
Pa
Density of the resist ρ 998.2 kg/m3
Resist flow velocity V
Characteristic length L 1 mm
Contact angel θ1 160 degree

7. Nan Li
University of Michigan
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(b)
Setting-Up Parameters
General Pressure-based, Transient
Models
Volume of Fluid: two phases
Laminar
Materials
Bubble:
standard air form default database,
Viscosity [kg/m-s]:0.00179
Resist:
standard water-liquid form default database,
Viscosity [kg/m-s]: 0.1003
Boundary conditions
Pressure outlet: water backflow fraction:1
Axisymmetric
Solution Method Simple C
Table 1: (a) 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 0.0001sec 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.

8. Nan Li
University of Michigan
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.

9. Nan Li
University of Michigan
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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.

10. Nan Li
University of Michigan
10
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