Measuring aberrations in lithographic projection systems with phase wheel targets

A significant factor in the degradation of nanolithographic image fidelity is optical wavefront aberration. Aerial image sensitivity to aberrations is currently much greater than in earlier lithographic technologies, a consequence of increased resolution requirements. Optical wavefront tolerances are dictated by the dimensional tolerances of features printed, which require lens designs with a high degree of aberration correction. In order to increase lithographic resolution, lens numerical aperture (NA) must continue to increase and imaging wavelength must decrease. Not only do aberration magnitudes scale inversely with wavelength, but high-order aberrations increase at a rate proportional to NA2 or greater, as do aberrations across the image field. Achieving lithographic-quality diffraction limited performance from an optical system, where the relatively low image contrast is further reduced by aberrations, requires the development of highly accurate in situ aberration measurement. In this work, phase wheel targets are used to generate an optical image, which can then be used to both describe and monitor aberrations in lithographic projection systems. The use of lithographic images is critical in this approach, since it ensures that optical system measurements are obtained during the system\u27s standard operation. A mathematical framework is developed that translates image errors into the Zernike polynomial representation, commonly used in the description of optical aberrations. The wavefront is decomposed into a set of orthogonal basis functions, and coefficients for the set are estimated from image-based measurements. A solution is deduced from multiple image measurements by using a combination of different image sets. Correlations between aberrations and phase wheel image characteristics are modeled based on physical simulation and statistical analysis. The approach uses a well-developed rigorous simulation tool to model significant aspects of lithography processes to assess how aberrations affect the final image. The aberration impact on resulting image shapes is then examined and approximations identified so the aberration computation can be made into a fast compact model form. Wavefront reconstruction examples are presented together with corresponding numerical results. The detailed analysis is given along with empirical measurements and a discussion of measurement capabilities. Finally, the impact of systematic errors in exposure tool parameters is measureable from empirical data and can be removed in the calibration stage of wavefront analysis

Bayesian Analysis for Photolithographic Models

The use of optical proximity correction (OPC) as a resolution enhancement technique (RET) in microelectronic photolithographic manufacturing demands increasingly accurate models of the systems in use. Model building and inference techniques in the data science community have seen great strides in the past two decades in the field of Bayesian statistics. This work aims to demonstrate the predictive power of using Bayesian analysis as a method for parameter selection in lithographic models by probabilistically considering the uncertainty in physical model parameters and the wafer data used to calibrate them. We will consider the error between simulated and measured critical dimensions (CDs) as Student’s t-distributed random variables which will inform our likelihood function, via sums of log-probabilities, to maximize Bayes’ rule and generate posterior distributions for each parameter. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, the model’s parameter space is explored to find the most credible parameter values. We use an affine invariant ensemble sampler (AIES) which instantiates many walkers which semi-independently explore the space in parallel, which lets us exploit the slow model evaluation time. Posterior predictive checks are used to analyze the quality of the models that use parameter values from their highest density intervals (HDIs). Finally, we explore the concept of model hierarchy, which is a flexible method of adding hyperparameters to the Bayesian model structure

Control and signal processing for lithography

Ph.DDOCTOR OF PHILOSOPH

Advanced process/equipment control for thermal processing in lithography

Ph.DDOCTOR OF PHILOSOPH

Application of iterative feedback tuning

Master'sMASTER OF ENGINEERIN

In-situ measurement and control of photoresist processing in lithography

Ph.DDOCTOR OF PHILOSOPH

Modeling and analysis of extrusion-spin coating : an efficient and deterministic photoresist coating method in microlithography

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2001.Includes bibliographical references (p. 173-178).In the fabrication of microelectronic chips, microlithography is used to transfer a pattern of circuit geometry from mask to semiconductor wafer. An important step in this process is the deposition of a thin and uniform layer of photoresist (often called resist) on which the lithographic image is exposed. Typical photoresist layers are less than 1 pum thick with a variation of 5 [angstroms] for advanced chips. Spin coating is the prevalent coating method to produce the required thickness and uniformity, but it typically wastes over 90% of the photoresist applied. A more efficient method needs to be developed for two reasons. The first is that 80% of the photoresist is an environmentally hazardous solvent. The second is the cost increase of photoresist. As the target of semiconductor industry moves toward the fabrication of smaller devices with larger capacity, the trend in photoresist shifts from i-line to deep UV resists, which allow for narrower linewidths on a chip. The price of this new resist is four to ten times higher than that of i-line resists. Reducing photoresist waste is desirable for both environmental and economical reasons. The current spin coating method has another problem in addition to low coating efficiency. Results from spin coating are unpredictable. The relationships between the inputs (process variables) and outputs (coating thickness and uniformity) can only be obtained by trial and error. Thus, a number of experiments have to be conducted to attain a certain coating thickness and uniformity. A more effective method would yield the predictable coating thicknesses and uniformities for given inputs.(cont.) Both the cost and time required for process development can be reduced this way. Extrusion-spin coating achieves high coating efficiency with predictable coating results. This new method uses an efficient extrusion coating technique to apply a thin film of resist to a wafer before spinning. spinning. This initial layer of photoresist eliminates the spreading phase, the most inefficient step of spin coating. The initial layer also provides the existing spin coating models with determined initial conditions and thereby renders its results predictable. A prototype extrusion-spin coater has been designed and fabricated. Initial experiments have been conducted to determine, test and optimize process variables. One variable, the solvent concentration degree in the environment, is most critical. As the initial coating layer deposited by extrusion coating is only 20-40 [mu]m, solvent contained in the photoresist evaporates rapidly at the absence of a solvent concentration in the environment. Evaporation causes the viscosity of photoresist to be nonuniform over the wafer. The outcome of the spin coating process becomes less uniform. Experimental results are compared with Emslie et al.'s predictive models of spin coating. A solvent concentration of 80% or higher in the environment was found to be necessary to attain a predictable coating thickness with 5 [angstrom] uniformity. With optimized process variables, mean coating thickness matches theoretical predictions with a variation of 0.01 [mu]m. Defect-free coating results with coating efficiencies as high as 40% were achieved.by Sangjun Han.Ph.D

Doctor of Philosophy

dissertationOptics is an old topic in physical science and engineering. Historically, bulky materials and components were dominantly used to manipulate light. A new hope arrived when Maxwell unveiled the essence of electromagnetic waves in a micro perspective. On the other side, our world recently embraced a revolutionary technology, metasurface, which modifies the properties of matter-interfaces in subwavelength scale. To complete this story, diffractive optic fills right in the gap. It enables ultrathin flat devices without invoking the concept of nanostructured metasurfaces when only scalar diffraction comes into play. This dissertation contributes to developing a new type of digital diffractive optic, called a polychromat. It consists of uniform pixels and multilevel profile in micrometer scale. Essentially, it modulates the phase of a wavefront to generate certain spatial and spectral responses. Firstly, a complete numerical model based on scalar diffraction theory was developed. In order to functionalize the optic, a nonlinear algorithm was then successfully implemented to optimize its topography. The optic can be patterned in transparent dielectric thin film by single-step grayscale lithography and it is replicable for mass production. The microstructures are 3?m wide and no more than 3?m thick, thus do not require slow and expensive nanopatterning techniques, as opposed to metasurfaces. Polychromat is also less demanding in terms of fabrication and scalability. The next theme is focused on demonstrating unprecedented performances of the diffractive optic when applied to address critical issues in modern society. Photovoltaic efficiency can be significantly enhanced using this optic to split and concentrate the solar spectrum. Focusing through a lens is no news, but we transformed our optic into a flat lens that corrects broadband chromatic aberrations. It can also serve as a phase mask for microlithography on oblique and multiplane surfaces. By introducing the powerful tool of computation, we devised two imaging prototypes, replacing the conventional Bayer filter with the diffractive optic. One system increases light sensitivity by 3 times compared to commercial color sensors. The other one renders the monochrome sensor a new function of high-resolution multispectral video-imaging