GPU-accelerated parallel image reconstruction strategies for magnetic particle imaging.

Objective. Image reconstruction is a fundamental step in magnetic particle imaging (MPI). One of the main challenges is the fact that the reconstructions are computationally intensive and time-consuming, so choosing an algorithm presents a compromise between accuracy and execution time, which depends on the application. This work proposes a method that provides both fast and accurate image reconstructions.Approach. Image reconstruction algorithms were implemented to be executed in parallel ingraphics processing units(GPUs) using the CUDA framework. The calculation of the model-based MPI calibration matrix was also implemented in GPU to allow both fast and flexible reconstructions.Main results. The parallel algorithms were able to accelerate the reconstructions by up to about6,100times in comparison to the serial Kaczmarz algorithm executed in the CPU, allowing for real-time applications. Reconstructions using the OpenMPIData dataset validated the proposed algorithms and demonstrated that they are able to provide both fast and accurate reconstructions. The calculation of the calibration matrix was accelerated by up to about 37 times.Significance. The parallel algorithms proposed in this work can provide single-frame MPI reconstructions in real time, with frame rates greater than 100 frames per second. The parallel calculation of the calibration matrix can be combined with the parallel reconstruction to deliver images in less time than the serial Kaczmarz reconstruction, potentially eliminating the need of storing the calibration matrix in the main memory, and providing the flexibility of redefining scanning and reconstruction parameters during execution.

Harmonic dependence of thermal magnetic particle imaging.

Advances in instrumentation and tracer materials are still required to enable sensitive, accurate, and localized in situ 3D temperature monitoring by magnetic particle imaging (MPI). We have developed a high-resolution magnetic particle imaging instrument and implemented a low-noise multi-harmonic lock-in detection method to observe and quantify temperature variations in iron oxide nanoparticle tracers using the harmonic ratio method for determining temperature. Using isolated harmonics for MPI and temperature imaging revealed an apparent dependence of imaging resolution on harmonic number. Thus, we present experimental and simulation studies to quantify the imaging resolution dependence on temperature and harmonic number, and directly validate the fundamental origin of MPI imaging resolution on harmonic number based on the concept of a harmonic point-spread-function.

Data-driven approaches to optical patterned defect detection.

Computer vision and classification methods have become increasingly wide-spread in recent years due to ever-increasing access to computation power. Advances in semiconductor devices are the basis for this growth, but few publications have probed the benefits of data-driven methods for improving a critical component of semiconductor manufacturing, the detection and inspection of defects for such devices. As defects become smaller, intensity threshold-based approaches eventually fail to adequately discern differences between faulty and non-faulty structures. To overcome these challenges we present machine learning methods including convolutional neural networks (CNN) applied to image-based defect detection. These images are formed from the simulated scattering of realistic geometries with and without key defects while also taking into account line edge roughness (LER). LER is a known and challenging problem in fabrication as it yields additional scattering that further complicates defect inspection. Simulating images of an intentional defect array, a CNN approach is applied to extend detectability and enhance classification to these defects, even those that are more than 20 times smaller than the inspection wavelength.

Evaluating the Effects of Modeling Errors for Isolated Finite 3D Targets.

Optical 3D nanostructure metrology utilizes a model-based metrology approach to determine critical dimensions (CDs) that are well below the inspection wavelength. Our project at the National Institute of Standards and Technology is evaluating how to attain key CD and shape parameters from engineered in-die capable metrology targets. More specifically, the quantities of interest are determined by varying the input parameters for a physical model until the simulations agree with the actual measurements within acceptable error bounds. As in most applications, establishing a reasonable balance between model accuracy and time efficiency is a complicated task. A well-established simplification is to model the intrinsically finite 3D nanostructures as either periodic or infinite in one direction, reducing the computationally expensive 3D simulations to usually less complex 2D problems. Systematic errors caused by this simplified model can directly influence the fitting of the model to the measurement data and are expected to become more apparent with decreasing lengths of the structures. In this paper we identify these effects using selected simulation results and present experimental setups, e.g., illumination numerical apertures and focal ranges, that can increase the validity of the 2D approach.

Optimizing the nanoscale quantitative optical imaging of subfield scattering targets.

The full 3-D scattered field above finite sets of features has been shown to contain a continuum of spatial frequency information and, with novel optical microscopy techniques and electromagnetic modeling, deep-subwavelength geometrical parameters can be determined. Similarly, by using simulations, scattering geometries and experimental conditions can be established to tailor scattered fields that yield lower parametric uncertainties while decreasing the number of measurements and the area of such finite sets of features. Such optimized conditions are reported through quantitative optical imaging in 193 nm scatterfield microscopy using feature sets up to four times smaller in area than state-of-the-art critical dimension targets.

Deep-subwavelength Nanometric Image Reconstruction using Fourier Domain Optical Normalization.

Quantitative optical measurements of deep sub-wavelength, three-dimensional, nanometric structures with sensitivity to sub-nanometer details address an ubiquitous measurement challenge. A Fourier domain normalization approach is used in the Fourier optical imaging code to simulate the full three-dimensional scattered light field of nominally 15 nm sized structures, accurately replicating the light field as a function of the focus position. Using the full three-dimensional light field, nanometer scale details such as a 2 nm thin conformal oxide and nanometer topography are rigorously fitted for features less than 1/30th of the wavelength in size. The densely packed structures are positioned nearly an order of magnitude closer than the conventional Rayleigh resolution limit and can be measured with sub-nanometer parametric uncertainties. This approach enables a practical measurement sensitivity to size variations of only a few atoms in size using a high throughput optical configuration with broad application in measuring nanometric structures and nanoelectronic devices.

Optimizing Hybrid Metrology: Rigorous Implementation of Bayesian and Combined Regression.

Hybrid metrology, e.g., the combination of several measurement techniques to determine critical dimensions, is an increasingly important approach to meet the needs of the semiconductor industry. A proper use of hybrid metrology may yield not only more reliable estimates for the quantitative characterization of 3-D structures but also a more realistic estimation of the corresponding uncertainties. Recent developments at the National Institute of Standards and Technology (NIST) feature the combination of optical critical dimension (OCD) measurements and scanning electron microscope (SEM) results. The hybrid methodology offers the potential to make measurements of essential 3-D attributes that may not be otherwise feasible. However, combining techniques gives rise to essential challenges in error analysis and comparing results from different instrument models, especially the effect of systematic and highly correlated errors in the measurement on the χ2 function that is minimized. Both hypothetical examples and measurement data are used to illustrate solutions to these challenges.

Improved grating reconstruction by determination of line roughness in extreme ultraviolet scatterometry.

The accurate determination of critical dimensions and roughness is necessary to ensure the quality of photoresist masks that are crucial for the operational reliability of electronic components. Scatterometry provides a fast indirect optical nondestructive method for the determination of profile parameters that are obtained from scattered light intensities using inverse methods. We illustrate the effect of line roughness on the reconstruction of grating parameters employing a maximum likelihood scheme. Neglecting line roughness introduces a strong bias in the parameter estimations. Therefore, such roughness has to be included in the mathematical model of the measurement in order to obtain accurate reconstruction results. In addition, the method allows to determine line roughness from scatterometry. The approach is demonstrated for simulated scattering intensities as well as for experimental data of extreme ultraviolet light scatterometry measurements. The results obtained from the experimental data are in agreement with independent atomic force microscopy measurements.

A maximum likelihood approach to the inverse problem of scatterometry.

Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 - 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.