Design optimization of phase-shifting point diffraction interferometer

The phase-shifting point diffraction interferometer (PS/PDI) has recently been developed to address the problem of at-wavelength metrology of extreme ultraviolet (EUV) optical systems. Although extremely accurate, the fact that the PS/PDI is limited to use with coherent EUV sources, such as undulator radiation, is a drawback for its widespread use. An alternative to the PS/PDI, with relaxed coherence requirements, is lateral shearing interferometry (LSI). Here we describe various LSI implementations and demonstrate the use of a cross-grating, carrier-frequency configuration to characterize a large-field 4×-reduction EUV lithography optic. The results obtained are directly compared with PS/PDI measurements.

In order to improve the measuring accuracy of the visible light phase-shifting point diffraction interferometer (PS/PDI) for the extreme ultraviolet lithography (EUVL) aspheric mirrors, the main measuring errors will be discussed in this paper. At first, the elementary configuration and measuring principle of the visible light phase-shifting point diffraction interferometer are introduced briefly, then the different errors which are possible to affect the measuring result are summed up, the errors include PZT phase-shifting error, detector nonlinearity error, detector quantization error, wavelength instability error and intensity instability error of the laser source, vibration error, air refractivity instability error and so on. Through detailed analysis and simulation, the magnitude of these errors can be obtained. By analysing the reasons which cause these errors and the relationship between these errors and interferometer configuration parameters, some methods are put forward to avoid or restrain these errors accordingly.

The performance of the recently developed EUV phase-shifting point diffraction interferometer (PS/PDI) depends heavily on the characteristics of the grating beamsplitter used in the implementation. Ideally, such a grating should provide throughput of better than 25% and diffraction efficiency, defined as the ratio of the first-diffracted-order power to the zero-order power, variable in the range from approximately 10 to 500. The optimal method for achieving these goals is by way of a phase grating. Also, PS/PDI system implementation issues favor the use of transmission gratings over reflection gratings. Here, the design, fabrication, and characterization of a recently developed transmission phase grating developed for use in EUV interferometry is described.

A phase-shifting point diffraction interferometer is being developed for at-wavelength testing of extreme ultraviolet lithographic optical systems. The interferometer was implemented to characterize the aberrations of a 10× Schwarzschild multilayer-coated reflective optical system at the operational wavelength of 13.4 nm. Chromatic vignetting effects are observed and they demonstrate the influence of multilayer coatings on the wave front. A subaperture of the optic with a numerical aperture of 0.07 was measured as having a wave front error of 0.090 wave (1.21 nm) root mean square (rms) at a 13.4 nm wavelength. The wave front measurements indicate measurement repeatability of ±0.008 wave (±0.11 nm) rms. Image calculations that include the effects of the measured aberrations are consistent with imaging performed with the 10× Schwarzschild optic on an extreme ultraviolet exposure tool.

At-wavelength interferometric characterization of a new 4×-reduction lithographic-quality extreme ultraviolet (EUV) optical system is described. This state-of-the-art projection optic was fabricated for installation in the EUV lithography Engineering Test Stand (ETS) and is referred to as the ETS Set-2 optic. EUV characterization of the Set-2 optic is performed using the EUV phase-shifting point diffraction interferometer (PS/PDI) installed on an undulator beamline at Lawrence Berkeley National Laboratory’s Advanced Light Source. This is the same interferometer previously used for the at-wavelength characterization and alignment of the ETS Set-1 optic. In addition to the PS/PDI-based full-field wave front characterization, we also present wave front measurements performed with lateral shearing interferometry, the chromatic dependence of the wave front error, and the system-level pupil-dependent spectral-bandpass characteristics of the optic; the latter two properties are only measurable using at-wavelength interferometry.

The standard silicon (Si) capping layer used for extreme ultra-violet lithography (EUVL) multilayer (ML) mask blanks has some shortcomings, such as low oxidation resistance, low chemical resistance, low etch selectivity in either the SiO₂ buffer layer etch to the capping layer or the absorber etch (e.g., TaN) to the capping layer. These performance and process issues with Si capped ML mask blank will reduce the mask lifetime and require tighter process control during EUVL mask fabrication. Alternative capping materials have been investigated for both EUVL optics and for mask applications.^1-5 It has been initially demonstrated that Ru capping layers have high oxidation resistance and high mask process margin as compared to Si ML cap. In this paper, we will present a detailed evaluation of Ru and ion beam deposited (IBD) diamond-like-carbon (DLC) for EUVL mask application. Performance evaluations of the DLC mask blank capping layer and Ru capping layer were made in the area of reflectivity performance, shelf-life, and EUV exposure stability. It has been shown that EUV exposure induced capping layer change depends upon the exposure conditions. However, we found that as long as the induced relative change in the ML cap material are the same (e.g., the same amount of oxidation), regardless of exposure time and exposure conditions, the resulting reflectivity change is about the same. In the case of the two capping layer materials we evaluated, the capping surface reaction with active oxygen is the primary cause for the reflectivity degradation.

In our previous works, we have found the optimal window size for ALOS2-PALSAR2 data is $7 \times 7$ (or other window size settings including around 50 pixels). Such an optimal window size is fixed for the whole observation area. However, the optimal window size for different types of targets are actually different. In order to improve general interpretation performance, we propose a “target-wise” window size optimization algorithm. The process is like automatically zooming and finding the particular optimal window sizes for different target areas. The results show that the proposed algorithm has higher interpretation performance than fixed-type window size optimization.

Empirical investigation of optimal window size using the least squares image matching method

LiDAR is a useful technology for gathering point cloud data from its environment and has been adapted to many applications. We use a cost-efficient LiDAR system attached to a moving object to estimate the location of the moving object using referenced linear structures. In the stationary state, the accuracy of extracting linear structures is low given the low-cost LiDAR. We propose a merging scheme for the LiDAR data frames to improve the accuracy by using the movement of the moving object. The proposed scheme tries to find the optimal window size by means of an entropy analysis. The optimal window size is determined by finding the minimum point between the entropy indicator of the ideal result and the entropy indicator of the actual result of each window size. The proposed indicator can describe the accuracy of the entire path of the moving object at each window size using a simple single value. The experimental results show that the proposed scheme can improve the linear structure extraction accuracy.

Evaluation of surface roughness of ULE® substrates machined by Ar+ ion beam

Using multiple indexes for efficient subsequence matching in time-series databases

Due to the limitation from the uncertainty principle, the window size consistently affects the resolution of time–frequency distributions. Determining the optimal window size is crucial for time–frequency analysis. In this work, we propose the concept of the reliable window width range along time and frequency axes, which simplifies the process of determining the optimal window size and the search range for adaptive methods. Moreover, in existing work, adaptive time–frequency analyses apply either time- or frequency-varying windows. In this study, we utilize a multitaper technique to integrate time- and frequency-varying windows. The proposed concept of the reliable window width range can be applied to any window-based time–frequency analysis method and enhance post-processing methods in the time–frequency plane. Subsequently, together with the reliable window width range, we propose the multitaper adaptive time–frequency windowed synchroextracting transform. It can estimate the optimal window size for time and frequency axes simultaneously and achieve a more energy-concentrated time–frequency analysis result.

We investigate clustered orthogonal frequency-division multiplexing (OFDM) with adaptive antenna arrays for interference suppression. To calculate weights for interference suppression, instantaneous correlations of the received signals and channel responses corresponding to the desired signals have to be estimated. However, due to smaller size of each cluster for clustered OFDM than for classical OFDM, the discrete Fourier transform (DFT)-based estimator has large leakage and results in severe performance degradation. Therefore, a polynomial-based parameter estimator is proposed to combat the severe leakage of the DFT based estimator. We study the impact of the polynomial order and window size on the estimation error. An approximately optimal window size for the polynomial-based estimator is obtained and an adaptive algorithm for the optimal window size is developed. With the adaptive algorithm, the polynomial-based estimator has no leakage and does not require channel statistics. Simulation results show that the developed algorithm improves the performance significantly.

What is the optimal shape and size of a cortical window that least affects bone strength? A biomechanical study.

Media access control plays a critical role in cognitive radio networks (CRNs). In our previous work, we have proposed a fairness-oriented media access control (FMAC) protocol to achieve fair and efficient coexistence of infrastructure-based CRNs. In this paper, we enhance FMAC to be used for coexisting ad hoc CRNs, where no centralized base stations exist, and secondary users (SUs) access channel independently. In FMAC, the contention window size is essential to network performance such as throughput. We first derive the optimal contention window size, which can then be used by SUs to achieve optimal throughput. However, the optimal contention window size is closely related to the total number of users of all CRNs, which is typically unknown to each individual SU of coexisting ad hoc CRNs. We attack this problem by building a bridge between the average number of consecutive idle time slots and optimal contention window size, since the average number of consecutive idle time slots can be easily observed by each individual SU. Hence, SUs can independently adjust their contention window size by observing their current average number of consecutive idle time slots and eventually approach the optimal contention window without the information of the total number of SUs. Extensive simulations are conducted and the results verify that the enhanced FMAC is able to significantly improve the fairness among coexisting ad hoc CRNs while maintaining good throughput.Keywordscoexistingcognitive radio networksfairnessthroughput