Fluid Dynamics Problems
in Next-Generation Microlithography

Derek Bassett derek@che.utexas.edu Office: CPE 5.472 Phone: 512-471-5082

IMMERSION LITHOGRAPHY

In projection lithography, the smallest feature that can be produced b_min is determined by the Rayleigh equation,

Where k₁ is a process constant of order 1, λ is the wavelength of light used, n is the index of refraction of the medium between the lens and the photoresist, and θ is the incidence angle. In the past two decades, continually smaller features were produced primarily by reducing the wavelength of light used, from 436 nm to 365 nm to 248 nm to 193 nm. However further reduction of the wavelength is becoming prohibitively expensive. Recently industry has looked at using a fluid with a higher index of refraction than air in between the lens and resist. Water is the first obvious choice with an index of about 1.4 over air’s 1.0, giving about a 30% improvement in smaller feature size.

Using water or some other fluid in a similar matter is called immersion lithography. There are of course many engineering challenges to be worked out in order to implement immersion lithography, i.e. fluid management issues, fluid purity, barrier materials, etc. I have been focusing primarily on the dynamic stability of the system in order to determine what parameters affect how quickly the lens can move while keeping the fluid attached to it.

To simulate the scanning process, we built an experimental apparatus that mimics the motion of a scanner. We had a computer controlled x-table with a vacuum chuck to hold an 8" wafer, and above that we built a cantilever to hold a lens mount. This mount also had a vacuum chuck to hold a lens of any desired size and could be adjusted to any specific height. To observe the moving contact line, we used a CCD camera with backlighting.

Using an experimental apparatus that we built, we found there are two separate dynamic instabilities. As the lens moves faster across the scanning surface, either the advancing contact line becomes separated from the edge of the lens, or small droplets may be deposited on the resist behind the receding contact line.

Stable
Advancing Edge Instability
Receding Edge Instability

We conducted a series of experiments by varying the lens height and the lens diameter and found the maximum stable velocity for each configuration while noting the type of instability that occured. Using the following variables, there are three relevant dimensionless groups:

μ = viscosity
U = velocity
γ = surface tension
ρ = density
H = lens height above surface
D = lens diameter

Capillary number

Weber number

Aspect ratio

This helped us collapse our experimental data into the following graph:

The two instabilities clearly fall into two different regimes. Using a force balance approach, it is fairly straightforward to show that the advancing edge instability is caused by viscous forces becoming dominant over surface tension or capillary forces. Analysis of the receding edge instability has been more difficult however. Force balance analysis and lubrication analysis have been unable to quantify the nature of the instability. We are currently looking at using a full fluid dynamics simulation package to analyze the immersion fluid and understand what causes this instability.

NANOIMPRINT (STEP AND FLASH) LITHOGRAPHY

As projection lithographic techniques approach the physical limit, other methods of device fabrication are being looked at. One other approach is called nanoimprint or step and flash lithography. It uses the idea that if we can make a high-resolution template using a different process such as e-beam lithography, we can then use that same template as a mold to produce high-resolution features in a high-throughput process.

From a fluid dynamics perspective, there are many questions to be answered in how the photopolymerizable fluid fills the template. How quickly can the fluid fill the gap? How do we minimize air bubble entrapment? What kinds of pressure forces are necessary? It turns out that pressure forces are so high in the nanometer length scale gaps that deformation of the template and/or wafer is a real concern. Many of these questions have been investigated by Shravanthi Reddy, a former student in our same group. I am continuing her research and trying to answer some additional questions dealing with the fluid dynamics of this process.

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References

1. D. Bassett, J.C. Taylor, W. Conley, C. G. Willson, R. T. Bonnecaze, "Drag-a-drop: a characterization tool for immersion lithography," Proc. SPIE 6154, 182 (2006).
2. D. Bassett and R.T. Bonnecaze, "Immersion lithography for laser mask writing," J. Vac. Sci. Techno. B  24 2659 (2006).