Full 3D-3C velocity measurement inside a liquid immersion
Gerrit E. Elsinga
Received: 27 September 2010 / Revised: 26 January 2011 / Accepted: 1 February 2011 / Published online: 23 February 2011
Ó The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract We describe a tomographic PIV system for the
measurement of the internal ﬂow in a droplet over a stag-
nant and a moving surface. The ﬂow condition is repre-
sentative 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.
In semiconductor fabrication, immersion lithography has
been considered as a means to further improve the spatial
resolution. By replacing the air (n
% 1:0) in the gap
between a lens and an object (a silicon wafer) with water
% 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 d ¼ kk=NA where k
is the process coefﬁcient with k ^ O (1), k the light
wavelength, and NA the numerical aperture of the lens,
NA ¼ n Á sin h, where h 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 litho-
graphic 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 scan-
ners 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 evo-
lution 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 down-
stream 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 (Re ¼ 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.
H. Kim (&) Á S. Große Á G. E. Elsinga Á J. Westerweel
Laboratory for Aero and Hydrodynamics,
Delft University of Technology, Leeghwaterstraat 21,
2628, CA, Delft, The Netherlands
Exp Fluids (2011) 51:395–405