Modeling and Simulation of Nanofabrication

Most manufacturing has historically been based on top-down fabrication and assembly. With rapid advances in nanotechnology, there is increasing interest in potential construction methods based on self-assembly of nanostructures, particularly approaches incorporating nanoparticles, nanorods, carbon nanotubes, DNA molecules, and block copolymers. Regardless of which approach is chosen, the competitive requirement of rapid fire manufacturing advances will force most industries to re-evaluate both traditional and theoretical approaches to nanoscale construction on an ongoing basis, with detailed attention to the underlying physics and required metrology. In response to this need, we are developing analytical and numerical models of specific top down and bottom up nanofabrication techniques and processes, as well as models and simulations of their associated metrology challenges.

While self-assembly is still in its relative infancy with respect to practical use, with much additional research required to reach maturity, the more widely utilized top-down methods will continue to require advances and modifications to improve current nanomanufacturing techniques. This modeling and simulation project is therefore focused in the following three areas:

Self-assembly of block copolymers. While fairly well developed in the lab, self-assembly does not have the speed and robustness required for use in mass production nanomanufacturing. Specifically, self-assembled patterns contain errors such as pattern defects and roughness on a scale which is unacceptable for use in industry. In this area, we are working to both understand what drives these errors, and how best to quantifiably measure them. For example, one obstacle to accurate measurement of such errors is the limitations of specific imaging techniques such as optical fluorescence microscopy, x-ray scattering, or electron microscopy. We are using self consistent field theory to model self-assembly processes to predict errors and to determine how those errors manifest themselves in x-ray scattering measurements. 

Optical microscopy is an extremely well developed, robust, and convenient technique for imaging microscopic structures. Unfortunately the resolution is inherently limited by the wavelength of light used to produce the image, so that structures smaller than that wavelength cannot be clearly resolved. However, there are certain cases where the wavelength is not a limitation, such as when researchers must only determine the relative positions of widely separated nanoparticles. If the microscope optics are well corrected and/or characterized, and it is possible to collect enough light or photons from each particle, then it is possible to locate particle positions with a precision significantly smaller than the wavelength. In spite of the fact that the images of well separated nanoparticles are still blurry, the ability to precisely locate these nanoparticles on a scale much smaller than the wavelength indicates that such an image can contain extractable information about the size, shape, and orientation of the various structures within. Here, our goal is to determine how to accurately extract this information. To accomplish this goal, we are building an analytical and numerical model using Green’s functions to describe how light is scattered from any given nanoparticle and/or structure and then propagated and collected by the microscope to produce an image. The model will be used to quantitatively determine the limitations of measuring the size, shape, and orientation of a given particle or structure as a function of the wavelength(s) used, the numerical aperture, aberrations, illumination pattern of the microscope, and the number of photons collected, among other factors. 

Photonics. Ideally, photonic structures would have perfectly smooth edges. However, it is very difficult to fabricate micro- and nanoscale structures that do not have some amount of error or edge roughness. This roughness causes the light to scatter out of the structure, thereby degrading its performance. Scanning electron microscope (SEM) images can be processed to yield a detailed quantitative description of the edge roughness in terms of its power spectrum. Although the light scattering can be directly measured once a photonic device has been completely fabricated, it would be very useful to be able to predict the scattering directly from the SEM image itself. To accomplish this objective, we are working on two tasks. The first task is to determine which of the many SEM image processing algorithms produces the most accurate representation of the roughness. The second is to develop an electromagnetic computer code based on the boundary element technique that will enable one to rapidly predict the scattering in two and three dimensions given a roughness power spectrum determined from an SEM image.