Background Metrology techniques with high accuracy and throughput are needed to address critical challenges in the characterization of periodic nanostructured materials. Copper interconnects are structures for which precise topography characterization is needed. Although common methods include atomic force and scanning electron microscopy, extreme-ultraviolet (EUV) scatterometry has unique capabilities for the characterization of structure parameters and material properties. Aim We study the effect of experimental design parameters (wavelength and incidence angle) on EUV scatterometry. We explore the fundamental sensitivity capabilities of EUV scatterometry for interconnect metrology when data are collected such that the information content in a single EUV diffraction pattern is maximized by tuning the wavelength and incidence angle.Approach We applied experimental design methods based on the Fisher information matrix to EUV scatterometry of an interconnect to obtain the optimized EUV wavelength and angles at which to obtain a single diffraction pattern. Using rigorous coupled wave analysis simulations and Monte Carlo uncertainty quantification, the accuracy of the parameter reconstructions under an optimal design is quantified. Results The uncertainty of the sample parameters depends strongly on wavelength and incidence angle, necessitating experimental design methods to achieve maximal sensitivity. When data are collected under an optimal experimental design, simulations indicate that sub-angstrom accuracy can be obtained from only a single diffraction pattern for the dishing depth of interconnect pads (0.02 nm standard deviation), and the substrate density can additionally be extracted (0.015 g/cm3 standard deviation). Decorrelation of the sample parameters is observed with optimal design, and 13.8 nm EUV light provides better sensitivity than longer wavelengths such as 30 nm. Conclusions Experimental design methods are an essential tool for ensuring that experimental data are collected under an optimal design that maximizes the information in the data. Implementing these methods opens further capabilities for fast and precise interconnect metrology with EUV scatterometry.

Extreme ultraviolet (EUV) scatterometry offers non-destructive, chemically specific, and high-resolution metrology for nanoscale structures in modern technology. Typically, EUV scatterometry experiments are conducted with fixed arbitrary designs or fixed optimal designs. Here, we reformulate EUV scatterometry as a closed-loop Bayesian adaptive experiment where measurement design and inference are performed sequentially using a Sequential Monte-Carlo (SMC) sampler. We first demonstrate efficient and accurate Bayesian inference using SMC sampler. Then we extend this methodology to design sequential measurements with Bayesian Adaptive Experiment Design (BAED), where we aim to extract the maximum amount of information with the fewest measurements. In a simulated experiment probing a 1 nm Hf grating buried under 70 nm of amorphous silicon, adaptive experiment design yielded sensitivity as low as 0.1 nm and 0.1g/cm(3)after 50 total measurements.

Luttinger liquids emerge in one-dimensional metals with strong electron interactions, exhibiting intriguing near-equilibrium properties such as spin-charge separation and power-law correlations. Although these interactions suggest fast, distinctive out-of-equilibrium dynamics, such phenomena remain largely unexplored on ultrashort timescales. Here, we use femtosecond laser excitation to weakly deplete the electron density in the Luttinger band of Li 0.9 Mo 6 O 17 and track the response via time- and angle-resolved photoemission spectroscopy. By fitting the measured electron distributions to a finite-temperature Luttinger liquid model, we observe a fast drop in the Luttinger exponent, quantifying the strength of electron interactions. Subsequently, unlike hot electrons in conventional Fermi liquids that slowly relax within picoseconds via electron-phonon coupling, hot electrons in Li 0.9 Mo 6 O 17 relax within a short time of ~100 femtoseconds, through the excitation of a nonequilibrium collective plasmon. The extremely fast evolution of the Luttinger exponent and electron temperature—including a tens of femtosecond time lag between excitation, recovery, and plasmon-driven modulation—reveals previously unidentified pathways for modulating quantum many-body interactions in low-dimensional materials.

Extreme ultraviolet (EUV) scatterometry is an increasingly important metrology that can measure critical parameters of periodic nanostructured materials in a fast, accurate, and repeatable manner and with high sensitivity to nanoscale structure and material composition. Because of this, EUV scatterometry could support manufacturing of semiconductor devices or polymer metamaterials, addressing the limitations of traditional imaging methods such as resolution and field of view, sample damage, throughput, or low sensitivity. Here we use EUV scatterometry to measure the profile of an industrially relevant 2D periodic interconnect structure, using λ = 29 nm light from a table-top high harmonic generation source. We show that EUV scatterometry is sensitive to out-of-plane features with single-nanometer sensitivity. Furthermore, we also apply a methodology based on the Fisher information matrix to optimize experimental design parameters, such as incidence angles and wavelength, to show how measurement sensitivity can be maximized. This methodology reveals the strong dependence of measurement sensitivity on both incidence angle and wavelength - even in a simple two-parameter case. Through a simultaneous optimization of incidence angles and wavelength, we determine that the most sensitive measurement of the quantities of interest can be made at a wavelength of ∼14 nm. In the future, by reducing sample contamination due to sample preparation, deep sub-nanometer sensitivity to axial profiles and 2D structures will be possible. Our results are an important step in guiding EUV scatterometry towards increased accuracy and throughput with a priori computations and by leveraging new experimental capabilities.

We present the use of high harmonic generation (HHG) to achieve sub-nanometer sensitivity to out-of-plane geometric features on an industrially relevant damascene sample with extreme ultraviolet (EUV) scatterometry. We also demonstrate a methodology to take advantage of the tuneability of HHG by selecting experimental conditions that maximize the sensitivity of EUV scatterometry. The method uses the Fisher information matrix to encode prior knowledge about the sample into a robust mathematical framework that enables automated selection of the optimal experimental conditions such as wavelength and incidence angles. Importantly, HHG allows us to use wavelength tunability across the EUV spectrum through precisely controlled phase matching to achieve these conditions. We apply this to our damascene sample to show that EUV light at similar to 13nm will maximize the sensitivity of our scatterometry measurements and the angle selection will break correlations between parameters to enable a reliable solution to the inverse problem. Using this approach, we are able to take full advantage of the wavelength tunability of HHG based EUV sources to support accurate metrology for next generation semiconductor devices.

Background: The industry is developing extreme-ultraviolet wavelength (EUV) techniques to measure critical dimensions (CDs) in logic fabrication. As nascent approaches are unveiled, evaluations against reference metrologies are essential to motivate development at higher speeds using industrially relevant length scales. Aim: The parametric geometries determined from EUV diffractometry data using a tabletop coherent high-harmonic generation (HHG) source are compared against dimensions from synchrotron-based CD small angle x-ray scattering (CD-SAXS) for four line-space arrays with CDs below 50 nm. Approach: An EUV imaging reflectometer captures the 0th order reflection and the 1st order diffraction intensities as functions of grazing angle. The 1st order intensities are functions of five wavelengths from the spectral comb of this HHG source. Fits to these data using rigorous couple-wave analysis (RCWA) electromagnetic simulations yield parametric values and uncertainties. Results: EUV diffractometry simulations match well in general with the measured data after accounting for cross-sectional geometry and experimental conditions. EUV diffractometry line widths correlate well against those of CD-SAXS at the mid-height of the latter. Conclusions: These promising results were obtained using a general-purpose prototype coherent EUV reflectometer. Routes for further enhancing the sensitivity and accuracy are presented and are in progress.

Femtosecond laser light can transfer spin angular momentum between magnetic subspecies that exhibit hybridized valence bands within an alloy or compound, and represents the fastest route for manipulating the magnetization of a material. To date, ultrafast spin transfer has predominantly been explained in terms of the initial and final states available for laser excitation. Here, by comparing the measured and calculated dynamics across the entire $M$-edges of two very similar Heusler compounds, $Co_2MnGa$ and $Co_2MnGe$ as well as a sample of elemental Co, we find that simply accounting for the initial and final electron states available for laser excitation cannot alone explain the experimental observations. The influence of spin lifetimes must also be included, due to the shifting of the Fermi level upon replacing Ga with Ge, or the presence of crystalline disorder. This explains why the ordered $L2_1$ phase of $Co_2MnGa$ demonstrates strong laser-induced magnetic signal enhancements across the entire Co-edge, while similar enhancements were not observed in partially disordered $Co_2MnGe$. Although intra-site spin-transfers were expected in the minority channel in pure Co due to the presence of many more available states in the minority channel above the Fermi level, no such signal was observed due to very short few-femtosecond spin lifetimes in a metal. Finally, we identify key regions in the magnetic asymmetry where a transiently enhanced signal could be misinterpreted as a light-induced spin-transfer signature.

Efficient thermal management is critical to device performance and reliability for energy conversion, nanoelectronics, and the development of quantum technologies. The commonly-used diffusive model of heat transport breaks down for confined nanoscale geometries, and advanced theories beyond diffusion are based on disparate assumptions that lead to conflicting predictions. Here, we outline and contrast the two predominant formulations of the Boltzmann equation for heat transport in semiconductors, namely, the ballistic and hydrodynamic models. We examine these methods in light of experiments and atomistic calculations of heat fluxes and temperature profiles in phononic systems with nanometer-sized features. We argue that reconciling the hydrodynamic and ballistic formulations is an outstanding necessity to develop a unifying theory of confinement effects on phonon flow, which will ultimately lead to optimal strategies for thermal management in nanodevices.

Spatiotemporal optical vortices (STOV) are space-time structured light pulses with a unique topology that couples spatial and temporal domains and carry transverse orbital angular momentum (OAM). Up to now, their generation has been limited to the visible and infrared regions of the spectrum. During the last decade, it was shown that through the process of high-order harmonic generation (HHG) it is possible to up-convert spatial optical vortices that carry longitudinal OAM from the near-infrared into the extreme-ultraviolet (EUV), thereby producing vortices with distinct femtosecond and attosecond structure. In this work we demonstrate theoretically and experimentally the generation of EUV spatiotemporal and spatiospectral vortices using near infrared STOV driving laser pulses. We use analytical expressions for focused STOVs to perform macroscopic calculations of HHG that are directly compared to the experimental results. As STOV beams are not eigenmodes of propagation, we characterize the highly-charged EUV STOVs both in the near and far fields, to show that they represent conjugated spatiotemporal and spatiospectral vortex pairs. Our work provides high-frequency light beams topologically coupled at the nanometer/attosecond scales domains with transverse OAM, that could be suitable to explore electronic dynamics in magnetic materials, chiral media, and nanostructures.

Spatiotemporal optical vortices (STOVs) are light pulses with unique topologies that couple spatial and temporal domains, previously limited to low-order topological charges in the visible and infrared spectral regimes. Our research demonstrates the generation of high-topological charge STOVs in the extreme ultraviolet (EUV) region through high harmonic generation (HHG). We develop analytical expressions for focused STOVs to perform advanced macroscopic HHG calculations, which are directly compared against our experimental results. HHG has been demonstrated in the last decade as a robust mechanism to up-convert structured light beams from the infrared/visible domains into the EUV/soft x-rays. However, the up-conversion of angular momentum properties within such highly nonlinear mechanism is not trivial. In this work, the generation process involves focusing an infrared Hermite-lobed driving field into a low-density argon gas jet. The nonlinear up-conversion allows to create highly charged EUV STOVs. However, as STOVs are not eigenmodes of propagation, their characterization is far from trivial. Upon characterization in the near and far fields, we demonstrate a duality between the generated harmonic spatio temporal and spatiospectral optical vortices (SSOVs). Our findings reveal that the topological charge of the harmonic vortices scales linearly with the driving laser field, providing new light beams with intrinsic spatiotemporal coupling at nanometer and attosecond scales. Our work confirms the theoretical predictions through advanced quantum HHG simulations and experimental validation, showcasing the generation of high-topological charge STOVs and SSOVs. These beams are particularly suitable for probing ultrafast electronic dynamics in systems with coupled spatial and temporal responses, such as magnetic materials, chiral media, and nanostructures. This advancement opens up new avenues for exploring complex light-matter interactions at unprecedented resolutions

Dynamic scattering and imaging with coherent, ultrafast, extreme ultraviolet (EUV) light sources can resolve charge, phonon and spin processes on their intrinsic length and time scales. However, full field coherent diffraction imaging requires scanning of the sample combined with computational phase retrieval, making it challenging to quickly acquire a large series of dynamic frames. In this work, we demonstrate a technique for extracting dynamic 1D images of the average unit cell in a periodic sample from traditional EUV scatterometry data by analyzing the changing intensities of the far field diffracted orders. Starting from a system of equations relating small changes in far field diffraction to phase and amplitude perturbations at the sample plane, it is shown that under certain conditions, changes to the nth diffracted order map exclusively onto the nth Fourier component of the perturbation via a closed-form relation. We show through rigorous coupled-wave analysis simulations that our method can provide a good approximation even outside the scalar diffraction theory framework in which it is derived. Finally, we experimentally demonstrate this reconstruction method by exiting 1D nickel nanowires on a diamond substrate using an infrared laser pump pulse, and measuring their relaxation using a time-delayed EUV probe pulse, to visualize nanoscale phonon dynamics.

Topological materials are of great interest because they can support metallic edge or surface states that are robust against perturbations, with the potential for technological applications. Here, we experimentally explore the light-induced non-equilibrium properties of two distinct topological phases in NaCd4As3: a topological crystalline insulator (TCI) phase and a topological insulator (TI) phase. This material has surface states that are protected by mirror symmetry in the TCI phase at room temperature, while it undergoes a structural phase transition to a TI phase below 200 K. After exciting the TI phase by an ultrafast laser pulse, we observe a leading band edge shift of >150 meV that slowly builds up and reaches a maximum after ∼0.6 ps and that persists for ∼8 ps. The slow rise time of the excited electron population and electron temperature suggests that the electronic and structural orders are strongly coupled in this TI phase. It also suggests that the directly excited electronic states and the probed electronic states are weakly coupled. Both couplings are likely due to a partial relaxation of the lattice distortion, which is known to be associated with the TI phase. In contrast, no distinct excited state is observed in the TCI phase immediately or after photoexcitation, which we attribute to the low density of states and phase space available near the Fermi level. Our results show how ultrafast laser excitation can reveal the distinct excited states and interactions in phase-rich topological materials.

We use soft x-ray vector-ptychographic tomography to determine the three-dimensional magnetization field in superparamagnetic nanoparticles self-assembled at the liquid-liquid interface and reveal the magnetic order induced by layered structure. The spins in individual nanoparticles become more aligned with increasing number of layers, resulting in a larger net magnetization. Our experimental results show a magnetic short-range order in the monolayer due to the proliferation of thermally induced magnetic vortices and a magnetic long-range order in the bilayer and trilayer, stemming from the strengthened dipolar interactions that effectively suppress thermal fluctuations. We also observe a screening effect of magnetic vortices and the attractive interaction between the magnetic vortices with opposite topological charges. Our work demonstrates the crucial role of layered structure in shaping the magnetization of nanoparticle assemblies, providing new opportunities to modulate these properties through strategic layer engineering.

High-harmonic generation (HHG) is an extreme nonlinear optical process that can map the properties of an infrared driving laser beam onto short wavelength attosecond pulse trains. However, current techniques for generating circularly polarized high harmonics for probing magnetic materials and chiral systems have limitations: two-color collinear counter-rotating driving lasers result in a low cutoff photon energy, while single-color noncollinear counter-rotating schemes suffer from low conversion efficiency. In this work, we generate circularly polarized attosecond pulse trains by using a structured laser driver which has a rotating polarization and phase grating along the azimuthal coordinate. Our experimental and numerical results demonstrate the production of left and right circularly polarized harmonics, which naturally separate upon propagation. Our approach uses a single laser color in a collinear geometry, that can be scaled for high efficiency. Simulations show this scheme can extend into the soft X-ray region when driven by mid-infrared driving lasers, while preserving the same high phase-matching cutoff photon energy as for linearly polarized high harmonics.

We present a method for achieving hyperspectral magnetic imaging in the extreme ultraviolet (EUV) region based on high-harmonic generation (HHG). By interfering two mutually coherent orthogonally-polarized and laterally-sheared HHG sources, we create an EUV illumination beam with spatially-dependent ellipticity. By placing a magnetic sample in the beamline and sweeping the relative time delay between the two sources, we record a spatially resolved interferogram that is sensitive to the EUV magnetic circular dichroism of the sample. This image contains the spatially-resolved magneto-optical response of the sample at each harmonic order, and can be used to measure the magnetic properties of spatially inhomogeneous magnetic samples.

We report a compact and reliable ultrafast fiber laser system optimized for seeding a high energy, 2 μ m pumped, 3 μ m wavelength optical parametric chirped pulse amplification to drive soft X-ray high harmonics. The system delivers 100 MHz narrowband 2 μ m pulses with >1 nJ energy, synchronized with ultra-broadband optical pulses with a ∼1 μ m FWHM spectrum centered at 3 μ m with 39 pJ pulse energy. The 2 μ m and 3 μ m pulses are derived from a single 1.5 μ m fiber oscillator, fully fiber integrated with free-space downconversion for the 3 μ m. The system operates hands-off with power instabilities <0.2% over extended periods of time.

We characterize nanoscale out-of-plane features on an industrially relevant semiconductor sample using a coherent extreme ultraviolet high harmonic generation source at 29nm. The advantages of using 13.5nm light are also shown.

We theoretically and experimentally demonstrate the generation of high-topological charge, extreme-ultraviolet (EUV) spatiotemporal optical vortices (STOV) from high-order harmonic generation. EUV-STOVs are unique structured light tools for exploring ultrafast topological laser-matter interactions.