# Full 3D-3C velocity measurement inside a liquid immersion droplet

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## Abstract

We describe a tomographic PIV system for the measurement of the internal flow in a droplet over a stagnant and a moving surface. The flow condition is representative of the flow in an immersion droplet applied in a liquid immersion lithography machine. We quantify the accuracy and reliability of the measurements and compare the shape of the reconstructed measurement volume to shape measurements by means of shadowgraphy. First results indicate the internal flow pattern near the receding contact line, showing a small recirculation region.

## Keywords

Contact Angle Particle Image Velocimetry Capillary Number Particle Tracking Velocimetry Advance Contact Angle## 1 Introduction

In semiconductor fabrication, immersion lithography has been considered as a means to further improve the spatial resolution. By replacing the air (\({n}_{\rm air}\approx\,1.0\)) in the gap between a lens and an object (a silicon wafer) with water (\({n}_{\rm water}\approx\) 1.44) for 193 nm UV light, the optical resolution in the image plane is enhanced (French and Tran 2009). The spatial resolution is given by \(\delta\,=\,k\lambda/\hbox{NA}\) where *k* is the process coefficient with *k* ≃ *O* (1), λ the light wavelength, and NA the numerical aperture of the lens, \(\hbox{NA}\,=\,{n}\cdot\sin\theta\), where θ is the half viewing angle. Current immersion systems can improve the resolution quality down to the order of tens of nanometers (Mulkens et al. 2004; Owa and Nagasaka 2008), which is an enhancement of about 30–40%.

Besides the advantage of higher optical resolution, immersion lithography also poses a couple of difficulties and challenges. In semiconductor production, usually the substrate (wafer) is moved underneath the optical lithographic lens. The biggest challenge then is to keep the liquid phase uniform without defects. With speeds in the range of 1 m/s, the main concerns for wafer defects are (1) water left behind (watermarks) and (2) a loss of resist-water adhesion (air gap) and bubble entrainment at the leading edge of the immersion droplet. To further increase yield, manufacturers of lithographic immersed-lens scanners wish to increase the wafer speed even further. Schuetter et al. (2006) studied the transitions of the dynamic contact angle for the immersion droplet until the maximum substrate speed, about 0.4 m/s, where the droplet starts to break up. Riepen et al. (2008) reported the evolution of dynamic contact angles as a function of the rotational speed where the substrate is rotated with respect to a liquid immersion droplet. The receding contact angles evolve from a round shape to a cusp shape when the substrate has a velocity less than 0.73 m/s. Above the critical velocity, the liquid droplet begins to break up (‘pearling’) at the downstream side of the immersion droplet. This critical velocity depends on fluid, gap heights, contact angles, and so on.

In a different geometry, similar studies were performed on a moving droplet on an inclined substrate, albeit at a much lower Reynolds number (\(\hbox{Re}\,=\,O\)(1)), i.e., almost within the Stokes flow regime. Podgorski et al. (2001) showed that the initially rounded perimeter of the drop exhibits a singularity at the rear of the drop when the capillary number exceeds a critical value. Snoeijer et al. (2005) attempted to apply conventional planar particle image velocimetry (PIV) to measure the internal flow field. However, the measured flow field rather represents the average fluid motion over the whole depth of the droplet. A theoretical model was suggested to understand the mechanism of the droplet motion. In the Stokes flow regime, the theoretical model is derived from the lubrication theory taking into account the small slope of the liquid--air interface with respect to the solid plane (Limat and Stone 2004). However, in the case of the immersion droplet at a higher value of the Reynolds number, it is difficult to obtain a theoretical model.

Therefore, to allow for a further understanding of the fluid motion in a liquid immersion droplet under realistic conditions, the droplet flow field needs to be investigated experimentally. Kang et al. (2004) performed a quantitative measurement of lateral flow fields of an evaporating droplet by a direct ray tracing method, and Lu et al. (2008) measured the internal flow of electro-wetting-on-dielectric (EWOD)-driven droplet by conventional PIV. However, due to the complex nature in contact line dynamics, the volumetric measurement of all velocity components of the flow inside the entire droplet shape is desirable. To measure the volumetric flow field, several methods are proposed. Scanning light-sheet (Brücker 1995), holography (Hinsch 2002; Sheng et al. 2009), defocusing digital particle image velocimetry (DDPIV) (Pereira et al. 2000, 2007), tomographic particle image velocimetry (Elsinga et al. 2006), and 3D particle tracking velocimetry (Maas et al. 1993) are the most typical approaches. Recently, Pereira et al. (2007) investigated the 3D flows of evaporating droplet by using μDDPIV with an inverted microscope.

In this paper, the internal flow of the liquid immersion droplet on a moving substrate is investigated by means of tomographic PIV. This measurement technique is capable of simultaneously measuring all three velocity components (referred to as 3D-3C). The paper is structured as follows. First, the experimental setup and measurement technique are explained in detail. Next, the pre- and post-processing for 3D-3C data will be elucidated followed by a discussion of the measurement accuracy based on the assessment of the relative measurement examined by means of the continuity equation. Tomographic PIV is applied to determine the complex flow topology of the immersion droplet at Re = 200 for the first time. From this result, we can assess the internal flow field of the liquid immersion droplet. The results may lead to strategies that can achieve the flow control and to optimized designs of the immersion lithographic system.

## 2 Experimental setup

_{ s }≈ 90°) is used. The working fluid is distilled water with a dynamic viscosity μ = 10

^{−3}Pa\(\cdot\)s, a surface tension \(\gamma\,=\,70\,\hbox{mN}/\hbox{m}\), and a density \(\rho\,=\,10^{3}\,\hbox{kg}/\hbox{m}^{3}\). We consider a liquid immersion droplet with a diameter (

*D*) of 2 mm and a height (

*h*) of 200 μm as shown in Fig. 2a. The wafer spins with a velocity of \(V_{w}\,=\,1.0\,\hbox{m}/\hbox{s}\) at the position of the droplet, so that the flow conditions are characterized by a capillary number (\(\hbox{Ca}\,=\,\mu V_{w}/\gamma\)) of 0.014 and a Reynolds number (\(\hbox{Re}\,=\,\rho V_{w}h/\mu\)) of 200. At these conditions, the immersion droplet exhibits a wedge shape at the rear. In particular, Fig. 2b,c shows that the droplet begins to lose mass (referred to as ‘pearling’) at a critical velocity of around 1.4 m/s.

For the visualization of the motion of the fluid inside the droplet, the recirculating fluid is seeded with 1.28-μm tracer particles (Microparticle GmbH) that are fluorescent (Rhodamine-B) and that have a polyethylene glycol (PEG) coating. This coating avoids particle coagulation and attachment of particles to the wafer surface and to the free droplet surface. The fluorescence is excited by illumination with laser light from a pulsed frequency-doubled Nd:YLF laser, which emits light with a wavelength of 527 nm. A separate stirring device maintains a homogeneous particle density. The PEG-coated particles in water possess a slightly negative surface charge, whereas the immersion needle showed a weak positive charge promoting the attachment of particles to the surface. Therefore, the immersion needle is grounded to maintain electrical neutrality, which reduces the number of particles sticking to the surface significantly.

*N*

_{ I }) is \(5.38\,\times\,10^{-1},\,N_{I}\equiv CA_{I}\Updelta z_{0}/M_{0}^{2}\), where

*C*is the mean number of particles per unit volume (\(\hbox{m}^{-3}),\,M_{0}\), the magnification of the lens, \(\Updelta z_{0}\), the depth of field (m), and

*A*

_{ I }, the image interrogation area (\(\hbox{m}^{2}\)). In this experiment, the particle volume fraction is 2.5% in aqueous suspension of 0.2 ml and then the particles are diluted in 500 ml distilled water. In the present condition, there is a low image density condition,

*N*

_{ I }< 1. Directly counting particle images from raw images yields a value of around 0.034

*ppp*(particles per pixel), which corresponds to a source density

*N*

_{ S }≃ 0.09. The whole pre- and post-processing and calibration procedures are performed by means of a commercial code (Davis 7.4, LaVision GmbH).

*L*

_{ d }is almost 5 mm. As shown in Fig. 5, the custom-made microscope is installed below at about 30 mm from the wafer surface. The depth of field is given approximately by \(\Updelta z_{0}\cong4(1+1/M_{0})^{2}{f^{\#}}^{2}\lambda\), where \(\Updelta z_{0}\) is the depth of field;

*M*

_{0}, the magnification of the lens;

*f*

^{#}, the f-number of the lens; λ, the wavelength of the light. For the given optical parameters, we have \(\Updelta z_{0}\approx 120\) μm.

Accuracy of the rotational table by varying rotational speeds where *V* _{ w } is the input value and *V* _{ m } is the measured value

| | Error (%) |
---|---|---|

0.20 | 0.2014 | 0.70 |

0.40 | 0.4028 | 0.70 |

0.60 | 0.6043 | 0.72 |

0.80 | 0.8057 | 0.71 |

1.00 | 1.0074 | 0.74 |

1.20 | 1.2090 | 0.75 |

1.40 | 1.4099 | 0.71 |

1.60 | 1.6121 | 0.76 |

## 3 Pre- and post-processing for 3D-3C data

### 3.1 Image processing

*i*is the index of the image, and

*N*is the total number of images. The result is shown in Fig. 7b. The aforementioned step is useful in the case of steady flow. Additionally, a spatial filtering is applied to remove the remaining noise in the images. A spatial 3 × 3 pixel sliding minimum filter, which subtracts the calculated local minimum from the local intensity, has been applied to all individual images. If necessary, the temporal and spatial filtering should be repeated until reasonable particle image fields are obtained. To enhance the visibility of the particle images with respect to the noisy image background, a 3 × 3 Gaussian smoothing filter is applied as a final step (Guezennec and Kiritsis 1990).

### 3.2 3D calibration and correction

*a*

_{ i }and

*b*

_{ i }depend on the depth position. Note that despite the image mapping and reconstruction via the calibration process, it is often impractical to achieve a perfect overlap of all reconstructed images in multi-camera PIV measurements. Therefore, in addition, to match corresponding particle images in the volume, the possible mismatch, or disparity, of the particle positions for each of the four cameras is resolved by applying a volumetric self-calibration. Wieneke (2008) first described a volumetric self-calibration that is based on the computation of the 3D positions of matching particles by triangulation. After applying this procedure, the average mapping errors for the case of stationary substrate are reduced from 0.03 to 0.01 pixels (see Fig. 8a, b). For the moving substrate, the errors decrease from 0.04 to 0.02 pixels (see Fig. 8c, d). In both cases, the disparity errors are less than 0.2 μm. In the case of the immersion droplet on the moving substrate, there is an image disagreement in image results caused by differences in refractive indexes. As a consequence, the disparity errors in both cases are a little bit different.

### 3.3 Tomographic reconstruction

To increase the effective particle image density, the reconstructed 3D intensity volumes are averaged over 25 individual reconstructed volume pairs. This is possible when the flow is steady. This effectively increases the seeding density while keeping relative low amount of ghost particles. The 3D-3C velocity vectors of each data set are obtained by means of 3D particle image pattern cross-correlation. The particle image displacement within a chosen interrogation volume (8 × 8 × 8 voxels) with 50% overlap is obtained by the 3D cross-correlation of the reconstructed particle distribution at the two exposures. The measured vector field contains 147 × 132 × 15 velocity vectors. The final vector results are averaged over 30 data sets (for the immersion droplet on a moving substrate) and 40 data sets (for the immersion droplet on a stagnant substrate).

The final result occasionally has vectors outside the liquid immersion droplet although actual particles must evidently be inside the droplet. This is due to ghost particles outside the measurement domain (Elsinga et al. 2010). In the case of tomographic PIV, the intensity information from actual and ghost particles both contribute to the cross-correlation. Therefore, further image processing is required to identify the internal flow field of the liquid immersion droplet. To eliminate spurious vectors, every vertical plane to a mask is applied by considering the largest intensity gradient that represents the position of the droplet interface using average reconstructed intensity field.

## 4 Results and discussion

### 4.1 Error estimation

*D*

_{ I }the dimension of the square and non-overlapping interrogation domain [pixel] in the cross-correlation procedure; and \(\Updelta t\) the time delay between two frames (\(\Updelta t=10\) μs). The relative measurement error in every sub-volume is considered. Figure 10 presents the histogram of the relative error in the form of the continuity equation. The width of the distribution in Fig. 10 indicates the error of the measurement; the fitted Gaussian distribution has a standard deviation of (a) 0.0246 [pixel/pixel] and (b) 0.0251 [pixel/pixel], respectively. Hence, given that

*D*

_{ I }= 8 pixel, it is found through (3) that \(\sigma_{\Updelta x}\,=\,0.2\) pixel. This error is consistent with a typical measurement uncertainty reported for tomographic PIV (Elsinga 2008).

Furthermore, we check the mass conservation at \(z\,=\,100\) μm of the immersion droplet on the stagnant substrate. Due to the characteristics of flow field, the mass flow rate must be zero at that plane. The mass flow rate for the inlet and outlet is 0.5 g/min. The relative error for the mass conservation at the middle plane of the stationary droplet is found to be about 2% with respect to the inlet flow, which is 39.34 g/min.

### 4.2 3D Flow field

Two exemplary cases are examined: a drop on the stationary substrate and a drop on the moving substrate. Note that all figures in this section depict the fluid field in absolute velocity in the stationary frame of coordinates of the immersion needle. Very close to the substrate, this yields velocities identical to the local velocity of the wafer.

*x*,

*y*) vectors and the contours for the out-of-plane velocity. The flow pattern has a radial symmetry, although the velocity distribution is not perfectly axis-symmetric. This is because the outlet is connected only to one side of the immersion needle, and hence the flow field is slightly skewed to that side. Alternatively, a non-parallel alignment of the immersion needle and substrate could also be a reason for the asymmetry.

*x*−

*y*translation stage with micron resolution. The droplet has an advancing contact angle of about 145° and a receding contact angle of about 30°. The contact angle is measured from the image of the shadowgraph. At the rear of the droplet, the shape has an opening half-angle of about 60°. The superimposed vectors in Fig. 12 represent the 3D-3C velocity measured by tomographic PIV. The vector planes are cross-sectional results. The internal flow of the immersion droplet is shown, which exhibits a complex, but symmetric, flow pattern. There is a small circulation region near the corner of the droplet (see Fig. 12a). This region is related to the force balance of the viscous force, surface tension, and outlet pressure, as shown in Fig. 12c. The bottom result shown in Fig. 12b presents the flow field above the substrate (\(z\approx\) 10 μm). A detailed inspection of the flow near the moving contact line indicates that particles follow the contact line. The velocity gradient of the flow field is related to the substrate speed, surface tension and outlet pressure. Furthermore, there is a fast flow region near the rear outlet trench where the fluid is extracted from the droplet. Therefore, the rear trench of the immersion needle should be considered as an important parameter to extract fluid.

This experiment involves non-uniform optical properties of the media, e.g., different indices of refraction for air, substrate, and water. In Fig. 12, only few data could be obtained near the top of the advancing part of the droplet as a result of the rather large advancing contact angle, which limits the view in that part of the droplet.

*z*-direction, as shown in Fig. 14c, d. Figure 14e shows the fast flow region that is nearby the rear trench of the immersion needle, where there still is a small reversed flow region. Schuetter et al. (2006) and Riepen et al. (2008) showed that the droplet tail becomes longer as long as the substrate speed increases. The size of the reversed flow region near the corner of the droplet is related to the length of the droplet tail. The droplet will break up when the viscous force, surface tension, and outlet pressure are no longer balanced. Consider Fig. 2b, c, when the viscous drag force is further increased, i.e., the wafer speed approaches the critical velocity (\(V_{w}\,=\,1.4\,\hbox{m}/\hbox{s}\)), the liquid immersion droplet begins to show ‘pearling’.

## 5 Conclusion

For the first time, the complex internal flow of a liquid immersion droplet on a moving substrate has been investigated by using tomographic PIV. The technique allows to obtain the full 3D-3C velocity vector fields. Current results help to understand the internal flow field of the liquid immersion droplet at relatively high Reynolds number, (\(\hbox{Re}\,\gg1\)). The location of the measurement data is consistent with the shape of the droplet determined by means of shadowgraphy. The limited view on certain parts of the droplet can be improved, provided that the advancing contact angle is decreased. In addition, reducing the strong reflection light at the droplet interface improves the quality of the data near the free surface. The consistency of the measured data is quantified by means of the continuity equation for an incompressible fluid. We observe the separation flow region near the tail of the droplet. This is related to the droplet instability resulting in the rupture of the droplet tail. However, further investigation will be necessary to study these issues in detail. Future work will address a parameter study related to the flow instability as a function of the height of the droplet, different inlet and outlet conditions, different surface condition of the wafer (i.e., applied coatings), and the velocity of the substrate (wafer).

## Notes

### Acknowledgments

This work is part of the Industrial Partnership Programme (IPP) ‘Contact line control during wetting and dewetting’ (CLC) of the Foundation for Fundamental Research on Matter (FOM), which is supported financially by the Netherlands Foundation for Scientific Research (NWO). The IPP CLC is co-financed by ASML and Océ.

We would like to thank R. Lindken for valuable advice and discussions on the PIV measurements at an early stage of the project. We also thank M. Franken for his contribution to the experimental setup. Additionally, we acknowledge a very useful conversation with B. Wieneke from LaVision GmbH on 3D PTV and a good support of experimental setups of F. Evangelista and M. Verdonck from ASML Holding NV.

### Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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