Rene A. Claus

Transport of Intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes

We propose an alternative method for solving the Transport of Intensity equation (TIE) from a stack of through-focus intensity images taken by a microscope or lensless imager. Our method enables quantitative phase and amplitude imaging with improved accuracy and reduced data capture, while also being computationally efficient and robust to noise. We use prior knowledge of how intensity varies with propagation in the spatial frequency domain in order to constrain a fitting algorithm [Gaussian process (GP) regression] for estimating the axial intensity derivative. Solving the problem in the frequency domain inspires an efficient measurement scheme which captures images at exponentially spaced focal steps, significantly reducing the number of images required. Low-frequency artifacts that plague traditional TIE methods can be suppressed without an excessive number of captured images. We validate our technique experimentally by recovering the phase of human cheek cells in a brightfield microscope.

Quantitative phase retrieval with arbitrary pupil and illumination

We present a general algorithm for combining measurements taken under various illumination and imaging conditions to quantitatively extract the amplitude and phase of an object wave. The algorithm uses the weak object transfer function, which incorporates arbitrary pupil functions and partially coherent illumination. The approach is extended beyond the weak object regime using an iterative algorithm. We demonstrate the method on measurements of Extreme Ultraviolet Lithography (EUV) multilayer mask defects taken in an EUV zone plate microscope with both a standard zone plate lens and a zone plate implementing Zernike phase contrast.

The SEMATECH Berkeley MET: demonstration of 15-nm half-pitch in chemically amplified EUV resist and sensitivity of EUV resists at 6.x-nm

EUV exposures at the SEMATECH Berkeley Microfield Exposure Tool have demonstrated patterning down to 15 nm half pitch in a chemically amplified resist at a dose of 30 mJ/cm2. In addition, the sensitivity of two organic chemically amplified EUV resists has been measured at 6.7 nm and 13.5 nm and the sensitivity at 6.7 nm is shown to be a factor of 6 lower than the sensitivity at 13.5 nm. The reduction of the sensitivity of each resist at 6.7 nm relative to the sensitivity at 13.5 is shown to be correlated to a reduction of the mass attenuation coefficients of the elements involved with photoabsorption.

Partially Coherent Phase Recovery by Kalman Filtering

We demonstrate a Kalman filtering method to recover the phase of a thin object illuminated by partially coherent light. Our method is fast, efficient, robust to noise, and able to handle arbitrary source shapes when used in a microscope with Kohler illumination.

Phase measurements of EUV mask defects

Extreme Ultraviolet (EUV) Lithography mask defects were examined on the actinic mask imaging system, SHARP, at Lawrence Berkeley National Laboratory. A quantitative phase retrieval algorithm based on the Weak Object Transfer Function was applied to the measured through-focus aerial images to examine the amplitude and phase of the defects. The accuracy of the algorithm was demonstrated by comparing the results of measurements using a phase contrast zone plate and a standard zone plate. Using partially coherent illumination to measure frequencies that would otherwise fall outside the numerical aperture (NA), it was shown that some defects are smaller than the conventional resolution of the microscope. Programmed defects of various sizes were measured and shown to have both an amplitude and a phase component that the algorithm is able to recover.

Extreme ultraviolet mask roughness: requirements, characterization, and modeling

It is now well established that extremely ultraviolet (EUV) mask multilayer roughness can lead to wafer-plane line-edge roughness (LER) in lithography tools. It is also evident that this same effect leads to sensor plane variability in inspection tools. This is true for both patterned mask and mask blank inspection. Here we evaluate mask roughness specifications explicitly from the actinic inspection perspective. The mask roughness requirement resulting from this analysis are consistent with previously described requirements based on lithographic LER. In addition to model-based analysis, we also consider the characterization of multilayer mask roughness and evaluate the validity of using atomic force microscopy (AFM) based measurements by direct comparison to EUV scatterometry measurements as well as aerial image measurements on a series of high quality EUV masks. The results demonstrate a significant discrepancy between AFM results and true EUV roughness as measured by actinic scattering.

Mathematical model for calculating speckle contrast through focus

The significantly reduced wavelength and the reflective nature of EUV masks causes phase variations resulting from roughness on the mask to result in intensity variations when the wafer is out of focus. These variations should be understood and modeled to control LER and device yield. A typical approach to modeling the effects of roughness is to image many masks using a thin mask simulator. These images can then be statistically analyzed to get the speckle properties. A model already exists that can relate speckle contrast to LER. This paper presents a method to compute the speckle image intensity using a single convolution with the roughness. This can be used to compute speckle through focus quickly. The presented technique takes into account defocus and the illumination coherence. It can be applied to phase roughness and amplitude roughness (reflectivity variations). In addition to speed improvements, the convolution kernel provides insights into the interaction of the source mask and mask roughness showing that, depending on the illumination coherence and defocus, not all roughness frequencies are attenuated equally.

Predicting LER PSD caused by mask roughness using a mathematical model

EUV masks have replicated multilayer roughness from the substrate or the deposition process which cause line edge roughness (LER) during imaging. We have developed a model, based on the assumption that the roughness is small, that is able to analytically calculate the LER and LER Power Spectral Density (PSD) for any illumination source, defocus, and pitch. We evaluated the model for typical mask roughness values and varied illumination and other parameters to determine how the roughness induced LER behaves under different imaging conditions.

Examination of phase retrieval algorithms for patterned EUV mask metrology

We evaluate the performance of several phase retrieval algorithms using through-focus aerial image measurements of patterned EUV photomasks. Patterns present a challenge for phase retrieval algorithms due to the high- contrast and strong diffraction they produce. For this study, we look at the ability to correctly recover phase for line-space patterns on an EUV mask with a TaN absorber and for an etched EUV multilayer phase shift mask. The recovered phase and amplitude extracted from measurements taken using the SHARP EUV microscope at Lawrence Berkeley National Laboratory is compared to rigorous, 3D electromagnetic simulations. The impact of uncertainty in background intensity, coherence, and focus on the recovered field is evaluated to see if the algorithms respond differently.

Partially Coherent Quantitative Phase Retrieval for EUV Lithography

We present a phase recovery algorithm based on the Weak Object Transfer Function. The algorithm is iteratively extended to also apply to non-weak objects. We demonstrate the algorithm on an EUV multilayer defect imaged through-focus on SHARP with both a standard zone plate and a phase contrast zone plate.