Neural network driven sensitivity analysis of diffraction-based overlay metrology performance to target defect features

Diffraction-based overlay (DBO) metrology has been successfully introduced to deal with the tighter overlay control in modern semiconductor manufacturing. Moreover, DBO metrology typically needs to be performed at multiple wavelengths to achieve accurate and robust measurement in the presence of overlay target deformations. In this Letter, we outline a proposal for multi-spectral DBO metrology based on the linear relation between the overlay errors and the combinations of off-diagonal-block Mueller matrix elements ΔM = Mij - ( - 1)jMji (i = 1, 2; j = 3, 4) associated with the zeroth-order diffraction of overlay target gratings. We propose an approach that can realize snapshot and direct measurement of ΔM over a broad spectral range without any rotating or active polarization component. The simulation results demonstrate the capability of the proposed method for multi-spectral overlay metrology in a single shot.

With the increase of process complexity in advanced nodes, the requirements of process robustness in overlay metrology continues to tighten. Especially with the introduction of newer materials in the film-stack along with typical stack variations (thickness, optical properties, profile asymmetry etc.), the signal formation physics in diffraction-based overlay (DBO) becomes an important aspect to apply in overlay metrology target and recipe selection. In order to address the signal formation physics, an effort is made towards studying the swing-curve phenomena through wavelength and polarizations on production stacks using simulations as well as experimental technique using DBO. The results provide a wealth of information on target and recipe selection for robustness. Details from simulation and measurements will be reported in this technical publication.

Background: An overlay target design is essential before performing overlay metrology and has a great impact on overlay performance. In addition, accurate overlay metrology is required to achieve high product yields in semiconductor manufacturing. When asymmetry of the overlay target occurs, it is necessary to increase the area of the pattern existing in the target and stabilize the optical aberration for stable measurement. For this reason, we propose an image-based overlay target design that can secure a larger area compared with the existing overlay target and stabilize the optical aberration by overlapping and exposing the upper and lower patterns of the overlay target.Aim: The effective area of the existing mark design is improved by proposing an overlay target and a measurement method used in image-based overlay measurement.Approach: The proposed overlay target design is configured by arranging different marks orthogonally to the upper and lower layers, and different two-dimensional information can be inserted in the same area. When necessary, single-dimensional information desired by the user can be obtained through a technique called projection, and it has the advantage of using a larger effective area than the existing overlay target.Results: Overlay can be measured using projected signal components, and the possibility and performance of the proposed target can be confirmed through simulation and test wafer. In addition, it was possible to bring about a 15% improvement in total measurement uncertainty performance compared with the existing advanced imaging metrology (AIM) target by taking a wider effective area.Conclusions: An overlay target design is proposed to solve the technical problems of the existing overlay target design. The proposed overlay target has a method that is capable of minimizing the size of the overlay target while maximally maintaining the signal density, a way of reducing the influence of aberration, and various other advantages.In addition, the proposed method provides a design rule that breaks the “lower pattern and upper pattern must not overlap” framework.

Background: Overlay (OV) is a very important indicator for characterizing the pattern position accuracy between two layers in an integrated circuit in the manufacturing industry. The self-aligned double-patterning (SADP) process, which is limited to the resolution of deep ultraviolet lithography, is being extensively used for the volume manufacturing of integrated circuits. However, compared to the planar process, the SADP process poses new challenges for OV control.Aim: We investigate the bottom grating asymmetry of a microdiffraction-based overlay (μDBO) target in the SADP process and its effect on OV measurement.Approach: The bottom grating of the OV metrology target is analyzed through scanning electron microscopy and transmission electron microscopy. The imbalance of the −1st- and +1st-order diffraction light intensities of the asymmetrical bottom OV target is characterized. Finally, the effects of light polarization and wavelength on the OV accuracy are simulated.Results: Asymmetric behavior of bottom OV grating is identified. OV dependency on the measurement-light polarization is determined. The simulation results indicate that wavelength and polarization affect the OV accuracy simultaneously.Conclusions: We studied the bottom grating asymmetry-induced inaccuracy in DBO measurement and can assist in understanding the mechanism of measurement light-interaction with the OV grating to enhance the DBO accuracy to a new level.

Overlay error in lithography refers to the positional deviation between the patterns of two exposures and is one of the key indicators for evaluating lithography quality. Traditional overlay metrology methods are limited by the intensity of higher-order diffraction energy and mostly rely on ±1st-order diffraction light for measurements, making them susceptible to variations in the mark structure. This project proposes a diffraction-order-enhanced overlay error metrology method utilizing multiple diffraction orders. First, the scalar diffraction theory is used to derive the method for enhancing grating diffraction efficiency and explain the advantages of higher diffraction orders. Then, the Rigorous Coupled-Wave Analysis (RCWA) algorithm is used to simulate the optimized overlay (OVL) mark, demonstrating the effectiveness of the design. This method can compensate for the issue of certain wavelengths being difficult to use due to large measurement errors, achieving sub-nanometer precision while reducing sensitivity to polarization direction. By using the method of shared multiple diffraction orders, it is possible to corrected situations that are unavailable when only using ±1st order, providing more recipe options for multi-wavelength Diffraction-Based Overlay (DBO) technology. Our study presents an ingenious approach to mark optimization, enabling practitioners to make more flexible choices when dealing with different product batches, thereby enhancing the accuracy and robustness of OVL measurement.

ABSTRACTPROSAIL is a combination of the leaf optical properties spectra (PROSPECT) model and the scattering by arbitrarily inclined leaves (SAIL) canopy bidirectional reflectance model. When modelling forest canopy reflectance using the PROSAIL radiative transfer model, the sensitivities of parameters can affect the modelling accuracy. Traditionally, sensitivities have been assessed using local sensitivity analysis (LSA); however, drawbacks to this approach include a lack of consideration for coupled effects between different parameters. In this study, parameter sensitivities in the PROSAIL model were calculated using two global sensitivity analysis (GSA) methods (the Extended Fourier Amplitude Sensitivity Test (EFAST) method and the Morris method), field measurements, and Landsat 5 Thematic Mapper (TM) data for a Moso bamboo forest. The results of GSA were compared with those of LSA in order to identify the key parameters impacting the Moso bamboo forest canopy reflectance, and to provide a reference for model optimization and vegetation canopy inversion improvement. The results showed that: (1) the sensitivities of six major input parameters of the PROSAIL model were generally consistent with the sorting orders of the two GSA methods, but were not in accordance with those from the LSA method, especially in the mid-infrared band; (2) coupled effects among parameters acting on reflectance simulation in visible light bands were greater than those in infrared bands; (3) the simulated canopy reflectance was evaluated using Landsat 5 TM data, and the results simulated based on LSA analysis showed higher error than those based on GSA analysis, because the LSA method ignored the influence of some parameters on canopy reflectance, e.g. leaf mesophyll structure (N), average leaf angle (ALA), leaf water content (Cw), and leaf dry matter content (Cm). However, GSA was able to fully consider the coupled effects among parameters, and thus identified the sensitive parameters impacting on reflectance more accurately.

As the design rule of semiconductor devices shrinks to below 100nm dimensions, the degree of pattern alignment from different process levels has become a crucial factor affecting both process control and induced defect on unit process. Isolated and dense patterns were formed at process layers from front-end through to back-end on wafers using sub 100nm device process utilizing ArF lithography under various lithography conditions. As pattern size is reduced, overlay discrepancies become larger. The OL (overlay) error is very important because the pattern misalignment induces critical defects for the device. For many years, overlay metrology for process control has been measured by 4-corner box-in-box methods in chip. OL errors and CD (Critical Dimension) values have been measured on different tool. CD values have been measured on SEMs (Scanning Electron Microscope) and OL errors have been measured on optical tools. The accuracy of OL error metrology is limited by the resolution of tool, which is on the order of 1μm. In this paper we calculated the degree of overlay errors (current level to prior level errors) through a process patterns images obtained from a CD-SEM.

Intelligent sensitivity analysis framework based on machine learning for spacecraft thermal design

In 32nm/22nm advanced technology node, double patterning lithography is considered for semiconductor manufacturing. It necessitates tightened requirement of overlay measurement, i.e. to measure the position of a pattern with respect to that of a pattern in the underlying layer. The measurement target design plays a fundamental role in overlay precision and accuracy. Typical alignment target, such as bar-in-bar or box-in-box (BIB), has precision, accuracy, and size restrictions. This prompts us to look into better alignment targets. Recently, scatterometry-based metrology and profile model capability have been extended to measure multi-level grating structures. In addition, scatterometry has been shown to be the best choice for integrated metrology to perform wafer-to-wafer control. Therefore, it makes sense to consider using scatterometry for overlay measurement. In this research, the modeling analysis is performed on the spectra taken directly from a real pattern area with grating-ongrating structure. The critical dimension (CD) at the grating on top and the lateral shift between the top and the bottom gratings can be detected simultaneously. The lateral shift between the layers can be verified with the traditional overlay box. Unlike the traditional BIB target that has micrometer CD size, the CD size of the scatterometry overlay (S_OVL) target is much closer to that on the real device. So, it can much better reflect the overlay (OVL) shift on real devices. We also studied the non-model-based S_OVL measurement using a 673-nm semiconductor laser with a 10μm x 20μm target size, wafer-to-wafer control of CD and lateral shifts on some critical layers with grating-on-grating structure, as well as the CD and OVL variations within layer and from layer to layer for double patterning.

Overlay control for recording head manufacturing is becoming increasingly challenging as design geometry specifications tighten in the transition to advanced Heated Assisted Magnetic Recording (HAMR) devices. As overlay control requirements for critical patterning layers tighten below 5nm, the need for accurate and robust overlay metrology is key to enabling the patterning roadmap and improving yields. This work focuses on improving Imaged Based Overlay (IBO) metrology to ensure accurate overlay measurements for critical lithography steps in the recording head fabrication process. Selection of the optimal settings for color filter and Numeric Aperture (NA) parameters can have a significant impact on overlay measurement accuracy and Total Measurement Uncertainty (TMU) when setting up a new overlay metrology recipe1-2. These overlay metrology recipe parameters can be selected to minimize the influence of process induced overlay target imperfections on the measured overlay 3. This paper reports our revised workflow for selecting IBO measurement conditions and evaluating pre-existing recipes for robustness. We utilize metrics such as the overlay model residuals, Tool Induced Shift (TIS), and Qmerit error in identifying recipes requiring improvement. The new “Train Log” feature available on KLA’s Archer™ IBO metrology tool platform can be used to compare the through focus contrast precision of different illumination conditions at the time of recipe creation. In this study, we show that an optimization workflow that utilizes the “Train Log” collection of the contrast precision metric and imageless recipes in selecting color filter and numeric aperture settings can significantly improve the overlay measurement repeatability and tool to tool matching.

Simulation of fate and transport mechanisms in the porous systems from contaminant transport models are affected by uncertainty associated with input model parameters. Sensitivity analysis (SA) provides tools to quantify the sources of uncertainty to the variations in the model output metrics. To quantify the uncertainty associated with physical non-equilibrium contaminant transport model, global SA was conducted for the problem mimicking reactive transport in the saturated soil column conditions. Five global SA methods, namely Morris, RSA (Regionalized Sensitivity Analysis), Sobol, FAST (Fourier Amplitude Sensitivity Test), and PAWN, were tested based on the temporal moments of contaminant concentrations for two output metrics: zeroth temporal moment (ZTM) and mean residence time (MRT). The ranking order of ten input model parameters from global SA methods for two output metrics was compared. Morris SA implied that the ZTM at outlet of the soil column is highly sensitive to sorption distribution coefficient in the mobile and immobile regions and less sensitive to dispersion coefficient and degradation rate constant in the immobile region. The mass-transfer coefficient showed highest non-linear interactions with other flow and transport parameters based on the highest value of standard deviation of elementary effects (EEs) for ZTM output metric. The sorption distribution coefficient in the mobile region and mass-transfer coefficient showed highest sensitivity and non-linear effect toward MRT based on the Morris method. The comparison of global SA methods revealed that the top two sensitive parameters affecting ZTM and MRT were the same from all the considered methods. However, large difference in the ranking order of bottom three sensitive parameters was observed. The sorption distribution coefficient of mobile region and mass-transfer coefficient were observed as the most sensitive parameters affecting ZTM and MRT based on the comparison of all five global SA methods. Overall results suggest that the non-linear contaminant transport model should be examined based on multiple sensitivity output metrics via a multi-model approach. The multi-model global SA approach implemented in this study highlighted its significance in quantifying the interplay of non-linear model parameters.

Uncertainty and sensitivity analysis of cooling and heating loads for building energy planning

Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

This paper presents an application of the Global Sensitivity Analysis (GSA) method in evaluating performance of impedance measurement algorithms implemented in modern Intelligent Electronic Devices (IEDs) when affected by uncertainty. To be specific, the GSA is applied in testing an algorithm for distance protection of a single transmission line in a system with two lines on the same towers. Factors contributing to uncertainty are discussed in the paper. The GSA method decomposes variance of the estimation error according to the factors and their interactions, and in this way identifies the factors that have the highest impact on the estimation error. Computation of the GSA sensitivity indices relies on the Quasi-Monte Carlo (QMC) technique with Sobol's quasi-random sampling. This is time-consuming for large number of factors therefore, fast pre-screening process based on the Morris method is implemented to remove non-influential parameters and reduce the factor space before running the QMC. The methodology is implemented using fault simulation software DIgSILENT PowerFactory to calculate fault impedance as a function of uncertain parameters (i.e. factors) as well as voltage and current signals that are inputs to an IED under test. In this simulation, factor space is sampled using Sobol's quasi-random sequence generated with the standard GSA software tool called SIMLAB. All simulations of the transmission line faults for various parameter values and calculation of the performance indices (i.e. sensitivities) is automated using the program developed in DIgSILENT Programming Language (DPL). This testing technique is applied to study the fault impedance measurement implemented in SEL-421. (6 pages)

The double exponentially weighted moving average (EWMA) controller is a popular algorithm for on-line quality control of semiconductor manufacturing processes. The performance of the closed-loop system hinges on the adequacy of the two weight parameters of the double EWMA equations. In 2004, Su and Hsu presented an approach based on the neural technique for ‘on-line’ tuning the weight of the single EWMA equation in the single-input single-output (SISO) system. The present paper extends the neural network on-line tuning scheme to the double EWMA controller for the non-squared multiple-input multiple-output (MIMO) system, and validates the control performance by means of a simulated chemical–mechanical planarization (CMP) process in semiconductor manufacturing. Both linear and non-linear equipment models are considered to evaluate the proposed controller, coupling with the deterministic drift, the Gaussian noise and the first-order integrated moving average (IMA) disturbance. It has been shown from a variety of simulation studies that the proposed method exhibits quite competitive control performance as compared with the previous control system. The other merit of the proposed approach is that the tuning system, if sufficient training in a neural network is available, can be practicably applied to complex semiconductor processes without undue difficulty.