Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “correlation function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Angular clustering properties of the DESI QSO target selection using DR9 Legacy Imaging Surveys

ABSTRACT The quasar target selection for the upcoming survey of the Dark Energy Spectroscopic Instrument (DESI) will be fixed for the next 5 yr. The aim of this work is to validate the quasar selection by studying the impact of imaging systematics as well as stellar and galactic contaminants, and to develop a procedure to mitigate them. Density fluctuations of quasar targets are found to be related to photometric properties such as seeing and depth of the Data Release 9 of the DESI Legacy Imaging Surveys. To model this complex relation, we explore machine learning algorithms (random forest and multilayer perceptron) as an alternative to the standard linear regression. Splitting the footprint of the Legacy Imaging Surveys into three regions according to photometric properties, we perform an independent analysis in each region, validating our method using extended Baryon Oscillation Spectroscopic Survey (eBOSS) EZ-mocks. The mitigation procedure is tested by comparing the angular correlation of the corrected target selection on each photometric region to the angular correlation function obtained using quasars from the Sloan Digital Sky Survey (SDSS) Data Release 16. With our procedure, we recover a similar level of correlation between DESI quasar targets and SDSS quasars in two-thirds of the total footprint and we show that the excess of correlation in the remaining area is due to a stellar contamination that should be removed with DESI spectroscopic data. We derive the Limber parameters in our three imaging regions and compare them to previous measurements from SDSS and the 2dF QSO Redshift Survey.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Energy-Resolved Information Scrambling in Energy-Space Lattices

Here, weakly interacting Fermi gases simulate spin lattices in energy space, offering a rich platform for investigating information spreading and spin coherence in a large many-body quantum system. We show that the collective spin vector can be determined as a function of energy from the measured spin density, enabling general energy-space resolved protocols. We measure an out-of-time-order correlation function in this system and observe the energy dependence of the many-body coherence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A non-perturbative pairwise-additive analysis of charge transfer contributions to intermolecular interaction energies

Energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs) decomposes the interaction energy between molecules into physically interpretable components like geometry distortion, frozen interactions, polarization, and charge transfer (CT, also sometimes called charge delocalization) interactions. In this work, a numerically exact scheme to decompose the CT interaction energy into pairwise additive terms is introduced for the ALMO-EDA using density functional theory. Unlike perturbative pairwise charge-decomposition analysis, the new approach does not break down for strongly interacting systems, or show significant exchange–correlation functional dependence in the decomposed energy components. Both the energy lowering and the charge flow associated with CT can be decomposed. Complementary occupied–virtual orbital pairs (COVPs) that capture the dominant donor and acceptor CT orbitals are obtained for the new decomposition. It is applied to systems with different types of interactions including DNA base-pairs, borane-ammonia adducts, and transition metal hexacarbonyls. While consistent with most existing understanding of the nature of CT in these systems, we report the results also reveal some new insights into the origin of trends in donor–acceptor interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Systematic study of projection biases in weak lensing analysis

We present a systematic study of projection biases in the weak lensing analysis of the first year of data from the Dark Energy Survey (DES) experiment. In the analysis we used a $\Lambda$CDM model and three two-point correlation functions. We show that these biases are a consequence of projecting, or marginalizing, over parameters like $h$, $\Omega_b$, $n_s$ and $\Omega_\nu h^2$ that are both poorly constrained and correlated with the parameters of interest like $\Omega_m$, $\sigma_8$ and $S_8$. Covering the relevant parameter space we show that the projection biases are a function of where the true values of the poorly constrained parameters lie with respect to the parameter priors. For example, biases in the position of the posteriors can exceed the 1.5$\sigma$ level if the true values of $h$ and $n_s$ are close to the top of the prior's range and the true values of $\Omega_b$ and $\Omega_\nu h^2$ are close to the bottom of the range of their priors. We also show that in some cases the 1D credible intervals can be over-specified by as much as 30% and coverage can be as low as 27%. Finally we estimate these projection biases for the analysis of three and six years worth of DES data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Accessing the strong interaction between Λ baryons and charged kaons with the femtoscopy technique at the LHC

The interaction between baryons and kaons/antikaons is a crucial ingredient for the strangeness $S$ = 0 and $S$ = -2 sector of the meson–baryon interaction at low energies. In particular, the $Λ\overline{K}$ might help in understanding the origin of states such as the $Ξ$(1620), whose nature and properties are still under debate. Experimental data on $Λ–K$ and $Λ–\overline{K}$ systems are scarce, leading to large uncertainties and tension between the available theoretical predictions constrained by such data. In this Letter we present the measurements of $Λ–K$ + ⊕ $\overline{Λ}–K$ - and $Λ–K$ - ⊕ $\overline{Λ}–K$ + correlations obtained in the high multiplicity triggered data sample in pp collisions at $\sqrt{s}$ = 13 TeV recorded by ALICE at the LHC. The correlation function for both pairs is modeled using the Lednický–Lyuboshits analytical formula and the corresponding scattering parameters are extracted. The $Λ–K$ - ⊕ $\overline{Λ}–K$ + correlations show the presence of several structures at relative momenta k above 200 MeV/c, compatible with the $Ω$ baryon, the $Ξ$(1690), and $Ξ$(1820) resonances decaying into $Λ–K$ - pairs. The low $k^*$ region in the $Λ–K$ - ⊕ $\overline{Λ}–K$ + also exhibits the presence of the $Ξ$(1620) state, expected to strongly couple to the measured pair. The presented data allow to access the $ΛK$ + and $ΛK$ - strong interaction with an unprecedented precision and deliver the first experimental observation of the $Ξ$(1620) decaying into $ΛK$ - .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Comments on the quantum field theory of the Coulomb gas formalism

The holomorphic Coulomb gas formalism, as developed by Feigin-Fuchs, Dotsenko-Fateev and Felder, is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of quantum field theory. We begin with a careful examination of the timelike linear dilaton. Although the background charge of the model breaks the scalar field’s continuous shift symmetry, the exponential of the action remains invariant under a discrete shift because the background charge is imaginary. Gauging this symmetry makes the dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to the anti-holomorphic completion of the BRST current first introduced by Felder, and the full left/right cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the degenerate Fock space of the linear dilaton. The “supertrace” in the BRST complex reproduces the minimal model partition function and exhibits delicate cancellations between states with both momentum and winding. The model at the radius $R=\sqrt{pp^{\prime }}$ has two marginal operators corresponding to the Dotsenko-Fateev “screening charges”. Deforming by them, we obtain a model that might be called a “BRST quotiented compact timelike Liouville theory”. The Hamiltonian of the zero-mode quantum mechanics of this model is not Hermitian, but it is PT -symmetric and exactly solvable. Its eigenfunctions have support on an infinite number of plane waves, suggesting an infinite reduction in the number of independent states in the full quantum field theory. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlation functions. In contrast to spacelike Liouville, these “resonance correlators” are finite because the zero mode is compact. We comment on subtleties regarding the reflection operator identification, as well as naive violations of truncation in correlators with multiple reflection operators inserted. This work is part of an attempt to understand the relationship between the JT model of two dimen- sional gravity and the worldsheet description of the (2 , p ) minimal string as suggested by Seiberg and Stanford.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Centrality dependence of Lévy-stable two-pion Bose-Einstein correlations in $\sqrt{𝑠{𝑁⁢𝑁}}$ = 200 GeV Au + Au collisions

The PHENIX experiment measured the centrality dependence of two-pion Bose-Einstein correlation functions in $\sqrt{𝑠{𝑁⁢𝑁}}$ = 200 GeV Au + Au collisions at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. The data are well represented by Lévy-stable source distributions. The extracted source parameters are the correlation-strength parameter 𝜆, the Lévy index of stability 𝛼, and the Lévy-scale parameter 𝑅 as a function of transverse mass 𝑚 𝑇 and centrality. The 𝜆⁡(𝑚 𝑇 ) parameter is constant at larger values of 𝑚 𝑇 , but decreases as 𝑚 𝑇 decreases. The Lévy-scale parameter 𝑅⁡(𝑚 𝑇 ) decreases with 𝑚 𝑇 and exhibits proportionality to the length scale of the nuclear overlap region. The Lévy exponent 𝛼⁡(𝑚 𝑇 ) is independent of 𝑚 𝑇 within uncertainties in each investigated centrality bin, but shows a clear centrality dependence. At all centralities, the Lévy exponent 𝛼 is significantly different from that of Gaussian (𝛼 = 2) or Cauchy (𝛼 = 1) source distributions. Comparisons to the predictions of Monte-Carlo simulations of resonance-decay chains show that, in all but the most peripheral centrality class (50%–60%), the obtained results are inconsistent with the measurements, unless a significant reduction of the in-medium mass of the 𝜂′ meson is included. Finally, in each centrality class, the best value of the in-medium 𝜂′ mass is compared to the mass of the 𝜂 meson, as well as to several theoretical predictions that consider restoration of U 𝐴⁢ (1) symmetry in hot hadronic matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Random insights into the complexity of two-dimensional tensor network calculations

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (“not too entangled”) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work, we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at a large bond dimension. Through this statistical-mechanics lens, we argue that (i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, and (ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. Furthermore, these results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

DESI DR2 Results IV: Alcock-Paczyński Measurements from the Lyman Alpha Forest and Cosmological Constraints

We present Alcock-Paczyński (AP) measurements from the full shape of Lyman-$α$ (Ly$α$) forest correlation functions measured from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI). Our measurements include information from the Ly$α$ forest auto-correlation and its cross-correlation with quasars. We constrain the AP effect with $1\%$ precision at an effective redshift $z_\mathrm{eff}=2.33$, which is twice as tight as the Baryon Acoustic Oscillation (BAO) constraint from the same data. When using the joint Ly$α$ AP and BAO results, we measure the ratios $D_\text{H}(z_\mathrm{eff})/r_\text{d}=8.600 \pm 0.066$ and $D_\text{M}(z_\mathrm{eff})/r_\text{d}=39.32 \pm 0.33$, where $D_\text{M}$ is the transverse comoving distance, $D_\text{H}$ is the Hubble distance, and $r_\text{d}$ is the sound horizon at the drag epoch. Assuming $Λ$CDM, Ly$α$ forest measurements combined with a nucleosynthesis prior produce a constraint on the Hubble constant $H_0=66.5\pm1.3\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The Ly$α$ AP result corresponds to a matter fraction constraint $Ω_\text{m}=0.325\pm0.018$ in $Λ$CDM, which is $1.4σ$ higher than DESI BAO. This impacts the DESI results relative to the Cosmic Microwave Background (CMB), slightly reducing their discrepancy from $2.4σ$ to $2.2σ$. We present updated constraints on extended models using the joint DESI DR2 BAO and Ly$α$ forest full shape data, together with external data sets. When considering a time-evolving dark energy equation of state parametrized by $w_0$ and $w_a$, we find it is preferred over $Λ$CDM at $2.7σ$ for the combination of DESI and CMB data, and at $3.2σ$ when also including supernovae. With the new Ly$α$ AP measurement, DESI provides its most precise anchor for the expansion history at $z > 1$ in the matter-dominated Universe.

Adame, A. G. [Vienna U.] (ORCID:0009000505949391)↗
DOE OSTI2020

Convergent momentum-space OPE and bootstrap equations in conformal field theory

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Two-particle Bose-Einstein correlations and their Lévy parameters in PbPb collisions at s N N = 5.02 TeV

Two-particle Bose–Einstein momentum correlation functions are studied for charged-hadron pairs in lead-lead collisions at a center-of-mass energy per nucleon pair of s NN = 5.02 TeV . The data sample, containing 4.27 × 10 9 minimum bias events corresponding to an integrated luminosity of 0.607 nb − 1 , was collected by the CMS experiment in 2018. The experimental results are discussed in terms of a Lévy-type source distribution. The parameters of this distribution are extracted as functions of particle pair average transverse mass and collision centrality. These parameters include the Lévy index or shape parameter α , the Lévy scale parameter R , and the correlation strength parameter λ . The source shape, characterized by α , is found to be neither Cauchy nor Gaussian, implying the need for a full Lévy analysis. Similarly to what was previously found for systems characterized by Gaussian source radii, a hydrodynamical scaling is observed for the Lévy R parameter. The λ parameter is studied in terms of the core-halo model. ©2024 CERN, for the CMS Collaboration 2024 CERN

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Two-particle correlations in azimuthal angle and pseudorapidity in central $^7\hbox {Be}+{}^9\hbox {Be}$ collisions at the CERN Super Proton Synchrotron

A measurement of charged hadron pair correlations in two-dimensional $\Delta \eta \Delta \phi $ space is presented. The analysis is based on total 30 million central Be + Be collisions observed in the NA61/SHINE detector at the CERN SPS for incident beam momenta of 19A, 30A, 40A, 75A, and 150A $\text {Ge} \text {V}/c$. Measurements were carried out for unlike-sign and like-sign charge hadron pairs independently. The $C(\Delta \eta ,\Delta \phi )$ correlation functions were compared with results from a similar analysis on p + p interactions at similar beam momenta per nucleon. General trends of the back-to-back correlations are similar in central Be + Be collisions and p + p interactions, but are suppressed in magnitude due to the increased combinatorial background. Predictions from the Epos and UrQMD models are compared to the measurements. Evolution of an enhancement around $(\Delta \eta ,\Delta \phi ) = (0,0)$ with incident energy is observed in central Be + Be collisions. It is not predicted by both models and almost non-existing in proton–proton collisions at the same momentum per nucleon.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Stellar-reddening-based Extinction Maps for Cosmological Applications

Cosmological surveys must correct their observations for the reddening of extragalactic objects by Galactic dust. Existing dust maps, however, have been found to have spatial correlations with the large-scale structure of the Universe. Errors in extinction maps can propagate systematic biases into samples of dereddened extragalactic objects and into cosmological measurements such as correlation functions between foreground lenses and background objects and the primordial non-Gaussianity parameter f NL . Emission-based maps are contaminated by the cosmic infrared background, while maps inferred from stellar reddenings suffer from imperfect removal of quasars and galaxies from stellar catalogs. Thus, stellar-reddening-based maps using catalogs without extragalactic objects offer a promising path to making dust maps with minimal correlations with large-scale structure. We present two high-latitude integrated extinction maps based on stellar reddenings, with a point-spread functions of FWHMs 6'. 1 and 15'. We employ a strict selection of catalog objects to filter out galaxies and quasars and measure the spatial correlation of our extinction maps with extragalactic structure. Our galactic extinction maps have reduced spatial correlation with large-scale structure relative to most existing stellar-reddening-based and emission-based extinction maps.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Evaluating the Chemical Reactivity of DFT-Simulated Liquid Water with Hydrated Electrons via the Dual Descriptor

Modeling the various properties of liquid water, particularly its reactivity, has been a longstanding challenge for simulation methods. Recently, ab initio simulations based on density functional theory (DFT) have come to the fore as tenable methods for calculating the properties and reactivity of water, with varying degrees of success for different exchange-correlation functionals. In particular, hybrid-GGA and meta-GGA functionals have been shown to reproduce many of the structural, dynamical, and energetic properties of water to a high degree of accuracy relative to their computational cost. Here, we show that the dual descriptor (DD) measure of nucleophilicity and electrophilicity, which is sometimes used to elucidate organic chemistry reaction mechanisms, can also be used to characterize the reactivity of DFTsimulated liquid water. The DD is especially apt for understanding the reactivity of excess electrons with water as its calculation explicitly involves adding and removing an excess electron from a reference system. We use the DD to explore the reactivity of water simulated using three different DFT functionals: the LDA functional (LDA), a hybrid-GGA functional (PBE0), and a hybrid meta- GGA functional (SCAN0). Using the DD, we show that the SCAN0 functional with the standard 25% Hartree–Fock exchange produces simulated liquid water with many regions that are far more reactive than either PBE0 or LDA. To understand the implications of these highly reactive regions, we then add a strong nucleophile in the form of an excess electron and find that although PBE0 and LDA predict stable hydrated electrons, the excess electron reacts nearly instantaneously with SCAN0 water via proton abstraction to form a hydrogen atom and hydroxide ion. We show that the DD provides the ability to not only predict whether or not liquid water will react with a hydrated electron but also which particular waters will be involved solely from analyzing pure water configurations generated with each functional. We rationalize this result in terms of the known trap-seeking behavior of injected hydrated electrons, which are able to find the most electronegative region in bulk water. These results highlight the utility of the dual descriptor as a fast and interpretable method for investigating condensed-phase reactivity with excess electrons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Dark Energy Survey Year 3 results: A 2.7% measurement of baryon acoustic oscillation distance scale at redshift 0.835

We present angular diameter measurements obtained by measuring the position of baryon acoustic oscillations (BAO) in an optimized sample of galaxies from the first three years of Dark Energy Survey data (DES Y3). The sample consists of 7 million galaxies distributed over a footprint of 4100 deg 2 with 0.6 < z photo < 1.1 and a typical redshift uncertainty of 0.03 ( 1 + z ) . The sample selection is the same as in the BAO measurement with the first year of DES data, but the analysis presented here uses three times the area, extends to higher redshift, and makes a number of improvements, including a fully analytical BAO template, the use of covariances from both theory and simulations, and an extensive preunblinding protocol. We used two different statistics; angular correlation function and power spectrum, and validate our pipeline with an ensemble of over 1500 realistic simulations. Both statistics yield compatible results. We combine the likelihoods derived from angular correlations and spherical harmonics to constrain the ratio of comoving angular diameter distance D M at the effective redshift of our sample to the sound horizon scale at the drag epoch. We obtain D M ( z eff = 0.835 ) / r d = 18.92 ± 0.51 , which is consistent with, but smaller than, the Planck prediction assuming flat Λ CDM , at the level of 2.3 σ . The analysis was performed blind and is robust to changes in a number of analysis choices. It represents the most precise BAO distance measurement from imaging data to date, and is competitive with the latest transverse ones from spectroscopic samples at z > 0.75 . When combined with DES 3 x 2 pt + SNIa , they lead to improvements in H 0 and Ω m constraints by ∼ 20 % .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Regularized machine learning on molecular graph model explains systematic error in DFT enthalpies

Abstract A major goal of materials research is the discovery of novel and efficient heterogeneous catalysts for various chemical processes. In such studies, the candidate catalyst material is modeled using tens to thousands of chemical species and elementary reactions. Density Functional Theory (DFT) is widely used to calculate the thermochemistry of these species which might be surface species or gas-phase molecules. The use of an approximate exchange correlation functional in the DFT framework introduces an important source of error in such models. This is especially true in the calculation of gas phase molecules whose thermochemistry is calculated using the same planewave basis set as the rest of the surface mechanism. Unfortunately, the nature and magnitude of these errors is unknown for most practical molecules. Here, we investigate the error in the enthalpy of formation for 1676 gaseous species using two different DFT levels of theory and the ‘ground truth values’ obtained from the NIST database. We featurize molecules using graph theory. We use a regularized algorithm to discover a sparse model of the error and identify important molecular fragments that drive this error. The model is robust to rigorous statistical tests and is used to correct DFT thermochemistry, achieving more than an order of magnitude improvement.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Structures of glass-forming liquids by x-ray scattering: Glycerol, xylitol, and D-sorbitol

In this work, synchrotron X-ray scattering has been used to investigate three liquid polyalcohols of different sizes (glycerol, xylitol and D-sorbitol) from above the glass transition temperatures $T_g$ to below. We focus on two structural orders: the association of the polar OH groups by hydrogen bonds (HBs) and the packing of the non-polar hydrocarbon groups. We find that the two structural orders evolve very differently reflecting the different natures of bonding. Upon cooling from 400 K, the O$\cdots$O correlation at 2.8 Å increases significantly in all three systems, indicating more HBs, until kinetic arrest at $T_g$; the increase is well described by an equilibrium between bonded and non-bonded OH with ΔH = 9.1 kJ/mol and ΔS = 13.4 J/mol/K. When heated above $T_g$, glycerol loses the fewest HBs per OH, followed by xylitol and by D-sorbitol, in the same order the number of OH groups per molecule increases (3, 5, and 6). The pair correlation functions of all three liquids show exponentially damped density modulations of wavelength 4.5 Å, which are associated with the main scattering peak and with the intermolecular C$\cdots$C correlation. In this respect, glycerol is the most ordered with the most persistent density ripples, followed by D-sorbitol and by xylitol. Heating above $T_g$ causes faster damping of the density ripples with the rate of change being the slowest in xylitol, followed by glycerol and by D-sorbitol. Given the different dynamic fragility of the three liquids (glycerol being the strongest and D-sorbitol the most fragile), we relate our results to the current theories of the structural origin for the difference. We find that the fragility difference is better understood on the basis of the thermal stability of HB clusters than that of the structure associated with the main scattering peak.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Early stage growth of amorphous thin film: Average kinetics, nanoscale dynamics, and pressure dependence

We used the coherent grazing incidence small angle x-ray scattering technique to study the average kinetics and nanoscale dynamics during early-stage a-WSi 2 sputter deposition. The kinetic and dynamic properties are examined as a function of pressure, which is known to be a critical factor in determining final surface roughness. Surface growth kinetics and dynamics are characterized by time parameters extracted from the height-height structure factor and correlation functions. The roughness at a given length scale reaches a maximum before relaxing down to a steady state. The lateral length scale dependence and pressure dependence are then compared among the measured kinetics and dynamics time parameters. Surfaces grown at lower pressures are smoother, leading to longer correlation times. The time parameters to reach a dynamic steady state and a kinetic steady state show contrasting pressure dependence. A dynamic steady state is reached earlier than the kinetic steady state at high pressure. A more random deposition direction and lower kinetic energy at higher pressures can explain these phenomena, along with the hypothesis that larger nanoclusters form in vapor before arriving at the surface. Here, a continuum model is applied to simulate the overall behavior with mixed success.

36 MATERIALS SCIENCE↗