Outliers detection by fuzzy classification method for model building

International audienceOptical Proximity Correction (OPC) is used in lithography to increase the achievable resolution and pattern transfer fidelity for IC manufacturing. Nowadays, immersion lithography scanners are reaching the limits of optical resolution leading to more and more constraints on OPC models in terms of simulation reliability. The detection of outliers coming from SEM measurements is key in OPC [1]. Indeed, the model reliability is based in a large part on those measurements accuracy and reliability as they belong to the set of data used to calibrate the model. Many approaches were developed for outlier detection by studying the data and their residual errors, using linear or nonlinear regression and standard deviation as a metric [8]. In this paper, we will present a statistical approach for detection of outlier measurements. This approach consists of scanning Critical Dimension (CD) measurements by process conditions using a statistical method based on fuzzy CMean clustering and the used of a covariant distance for checking aberrant values cluster by cluster. We propose to use the Mahalanobis distance [2] in order to improve the discrimination of the outliers when quantifying the similarity within each cluster of the data set. This fuzzy classification method was applied on the SEM CD data collected for the Active layer of a 65 nm half pitch technology. The measurements were acquired through a process window of 25 (dose, defocus) conditions. We were able to detect automatically 15 potential outliers in a data distribution as large as 1500 different CD measurement. We will discuss about these results as well as the advantages and drawbacks of this technique as automatic outliers detection for large data distribution cleaning

Bragg spectroscopy of a superfluid Bose-Hubbard gas

Bragg spectroscopy is used to measure excitations of a trapped, quantum-degenerate gas of 87Rb atoms in a 3-dimensional optical lattice. The measurements are carried out over a range of optical lattice depths in the superfluid phase of the Bose-Hubbard model. For fixed wavevector, the resonant frequency of the excitation is found to decrease with increasing lattice depth. A numerical calculation of the resonant frequencies based on Bogoliubov theory shows a less steep rate of decrease than the measurements.Comment: 11 pages, 4 figure

Excitations of quantum gases in optical lattices

textThis thesis describes experiments that studied the excitations of an ultra-cold atomic Rb gas in an optical lattice using Bragg spectroscopy. A Bose-Einstein condensate (BEC) of 87Rb was formed in a cloverleaf trap. An optical lattice of cubic symmetry, formed by the interference of six laser beams, was superimposed on the Rb BEC and turned on adiabatically. Such a system is well described by the Bose-Hubbard model, which predicts a quantum phase transition from a superfluid to a Mott insulator state at a critical lattice depth. In the first experiment, we studied the superfluid regime. The superfluid admits sound waves as phonon excitations. In two photon Bragg spectroscopy two laser beams intersecting at angle on the condensate create such excitations. The excitation spectrum of BEC was measured in a three dimensional optical lattice as a function of lattice strength. In the second experiment we studied the excitation spectrum of the Mott insulator. The lowest energy excitations in such a system are particlehole excitations. These correspond to the hopping of atoms from one lattice site to another. The insulating phase is characterized by a gap in the excitation spectrum and we measured this particle-hole gap by Bragg spectroscopy. The precise nature of our measurement allowed us to study the opening of the excitation gap that has previously eluded experimental verification.Physic

Best focus shift mitigation for extending the depth of focus

International audienceThe low-k1 domain of immersion lithography tends to result in much smaller depths of focus (DoF) compared to prior technology nodes. For 28 nm technology and beyond it is a challenge since (metal) layers have to deal with a wide range of structures. Beside the high variety of features, the reticle induced (mask 3D) effects became non-negligible. These mask 3D effects lead to best focus shift. In order to enhance the overlapping DoF, so called usable DoF (uDoF), alignment of each individual features best focus is required. So means the mitigation of the best focus shift. This study investigates the impact of mask 3D effects and the ability to correct the wavefront in order to extend the uDoF. The generation of the wavefront correction map is possible by using computational lithographic such Tachyon simulations software (from Brion). And inside the scanner the wavefront optimization is feasible by applying a projection lens modulator, FlexWaveTM (by ASML). This study explores both the computational lithography and scanner wavefront correction capabilities. In the first part of this work, simulations are conducted based on the determination and mitigation of best focus shift (coming from mask 3D effects) so as to improve the uDoF. In order to validate the feasibility of best focus shift decrease by wavefront tuning and mitigation results, the wavefront optimization provided correction maps are introduced into a rigorous simulator. Finally these results on best focus shift and uDoF are compared to wafers exposed using FlexWave then measured by scanning electron microscopy (SEM)

Accurate mask model implementation in optical proximity correction model for 14-nm nodes and beyond

International audienc

Accurate mask model for advanced nodes

International audienc

Accurate mask model implementation in OPC model for 14nm nodes and beyond

International audienc