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At least 973 records · Page 54

ROVIBRATIONAL LINE LISTS FOR NINE ISOTOPOLOGUES OF THE CO MOLECULE IN THE X {sup 1}Σ{sup +} GROUND ELECTRONIC STATE

Extensive rovibrational line lists were computed for nine isotopologues of the CO molecule, namely, {sup 12}C{sup 16}O, {sup 12}C{sup 17}O, {sup 12}C{sup 18}O, {sup 13}C{sup 16}O, {sup 13}C{sup 17}O, {sup 13}C{sup 18}O, {sup 14}C{sup 16}O, {sup 14}C{sup 17}O, and {sup 14}C{sup 18}O in the ground electronic state with v ≤ 41, Δv ≤ 11, and J ≤ 150. The line intensity and position calculations were carried out using a newly determined piece-wise dipole moment function (DMF) in conjunction with the wavefunctions calculated from an experimentally determined potential energy function from Coxon and Hajigeorgiou. A direct-fit method that simultaneously fits all the reliable experimental rovibrational matrix elements has been used to construct the dipole moment function near equilibrium internuclear distance. In order to extend the amount and quality of input experimental parameters, new Cavity Ring Down Spectroscopy experiments were carried out to enable measurements of the lines in the 4-0 band with low uncertainty as well as the first measurements of lines in the 6-0 band. A new high-level ab initio DMF, derived from a finite field approach has been calculated to cover internuclear distances far from equilibrium. Accurate partition sums have been derived for temperatures up to 9000 K. In addition to air- and self-induced broadening and shift parameters, those induced by CO{sub 2} and H{sub 2} are now provided for planetary applications. A complete set of broadening and shift parameters was calculated based on sophisticated extrapolation of high-quality measured data. The line lists, which follow HITRAN formalism, are provided as supplementary material.

74 ATOMIC AND MOLECULAR PHYSICS↗

Toward an understanding of foreground emission in the BICEP2 region

BICEP2 has reported the detection of a degree-scale B-mode polarization pattern in the Cosmic Microwave Background (CMB) and has interpreted the measurement as evidence for primordial gravitational waves. Motivated by the profound importance of the discovery of gravitational waves from the early Universe, we examine to what extent a combination of Galactic foregrounds and lensed E-modes could be responsible for the signal. We reanalyze the BICEP2 results and show that the 100 ×150 GHz and 150 ×150 GHz data are consistent with a cosmology with r=0.2 and negligible foregrounds, but also with a cosmology with r=0 and a significant dust polarization signal. We give independent estimates of the dust polarization signal in the BICEP2 region using a number of different approaches: (1) data-driven models based on Planck 353 GHz intensity, polarization fractions inferred from the same Planck data used by the BICEP2 team but corrected for CMB and CIB contributions, and polarization angles from starlight polarization data or the Planck sky model; (2) the same set of pre-Planck models used by the BICEP2 team but taking into account the higher polarization fractions observed in the CMB- and CIB-corrected map; (3) a measurement of neutral hydrogen gas column density N{sub HI} in the BICEP2 region combined with an extrapolation of a relation between HI column density and dust polarization derived by Planck; and (4) a dust polarization map based on digitized Planck data, which we only use as a final cross-check. While these approaches are consistent with each other, the expected amplitude of the dust polarization power spectrum remains uncertain by about a factor of three. The lower end of the prediction leaves room for a primordial contribution, but at the higher end the dust in combination with the standard CMB lensing signal could account for the BICEP2 observations, without requiring the existence of primordial gravitational waves. By measuring the cross-correlations between the pre-Planck templates used in the BICEP2 analysis and between different versions of a data-based template, we emphasize that cross-correlations between models are very sensitive to noise in the polarization angles and that measured cross-correlations are likely underestimates of the contribution of foregrounds to the map. These results suggest that BICEP1 and BICEP2 data alone cannot distinguish between foregrounds and a primordial gravitational wave signal, and that future Keck Array observations at 100 GHz and Planck observations at higher frequencies will be crucial to determine whether the signal is of primordial origin.

79 ASTRONOMY AND ASTROPHYSICS↗

Future sensitivity of neutrino telescopes to dark matter annihilations from the cosmic diffuse neutrino signal

Cosmological observations and cold dark matter N-body simulations indicate that our Universe is populated by numerous halos, where dark matter particles annihilate, potentially producing Standard Model particles. In this paper we calculate the contribution to the diffuse neutrino background from dark matter annihilations in halos at all redshifts and we estimate the future sensitivity to the annihilation cross section of neutrino telescopes such as IceCube or ANTARES. We consider various parametrizations to describe the internal halo properties and for the halo mass function in order to bracket the theoretical uncertainty in the limits from the modeling of the cosmological annihilation flux. We find that observations of the cosmic diffuse neutrino flux at large angular distances from the galactic center lead to constraints on the dark matter annihilation cross section which are complementary to (and for some extrapolations of the astrophysical parameters, better than) those stemming from observations of the Milky Way halo, especially for neutrino telescopes not pointing directly to the Milky Way center, as is the case of IceCube.

79 ASTRONOMY AND ASTROPHYSICS↗

A critical reassessment of particle Dark Matter limits from dwarf satellites

Dwarf satellite galaxies are ideal laboratories for identifying particle Dark Matter signals. When setting limits on particle Dark Matter properties from null searches, it becomes however crucial the level at which the Dark Matter density profile within these systems is constrained by observations. In the limit in which the spherical Jeans equation is assumed to be valid for a given tracer stellar population, we study the solution of this equation having the Dark Matter mass profile as an output rather than as a trial parametric input. Within our new formulation, we address to what level dwarf spheroidal galaxies feature a reliable mass estimator. We assess then possible extrapolation of the density profiles in the inner regions and—keeping explicit the dependence on the orbital anisotropy profile of the tracer population—we derive general trends on the line-of-sight integral of the density profile squared, a quantity commonly dubbed J -factor and crucial to estimate fluxes from prompt Dark Matter pair annihilations. Taking Ursa Minor as a study case among Milky Way satellites, we perform Bayesian inference using the available kinematical data for this galaxy. Contrary to all previous studies, we avoid marginalization over quantities poorly constrained by observations or by theoretical arguments. We find minimal J -factors to be about 2 to 4 times smaller than commonly quoted estimates, approximately relaxing by the same amount the limit on Dark Matter pair annihilation cross section from gamma-ray surveys of Ursa Minor. At the same time, if one goes back to a fixed trial parametric form for the density, e.g. using a NFW or Burkert profile, we show that the minimal J can hardly be reduced by more than a factor of 1.5.

79 ASTRONOMY AND ASTROPHYSICS↗

Responses in large-scale structure

We introduce a rigorous definition of general power-spectrum responses as resummed vertices with two hard and n soft momenta in cosmological perturbation theory. These responses measure the impact of long-wavelength perturbations on the local small-scale power spectrum. The kinematic structure of the responses (i.e., their angular dependence) can be decomposed unambiguously through a ''bias'' expansion of the local power spectrum, with a fixed number of physical response coefficients , which are only a function of the hard wavenumber k . Further, the responses up to n -th order completely describe the ( n +2)-point function in the squeezed limit, i.e. with two hard and n soft modes, which one can use to derive the response coefficients. This generalizes previous results, which relate the angle-averaged squeezed limit to isotropic response coefficients. We derive the complete expression of first- and second-order responses at leading order in perturbation theory, and present extrapolations to nonlinear scales based on simulation measurements of the isotropic response coefficients. As an application, we use these results to predict the non-Gaussian part of the angle-averaged matter power spectrum covariance Cov{sup NG}{sub ℓ=0}( k {sub 1}, k {sub 2}), in the limit where one of the modes, say k {sub 2}, is much smaller than the other. Without any free parameters, our model results are in very good agreement with simulations for k {sub 2} ∼< 0.06 h Mpc{sup −1}, and for any k {sub 1} ∼> 2 k {sub 2}. The well-defined kinematic structure of the power spectrum response also permits a quick evaluation of the angular dependence of the covariance matrix. While we focus on the matter density field, the formalism presented here can be generalized to generic tracers such as galaxies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A signature of anisotropic cosmic-ray transport in the gamma-ray sky

A crucial process in Galactic cosmic-ray (CR) transport is the spatial diffusion due to the interaction with the interstellar turbulent magnetic field. Usually, CR diffusion is assumed to be uniform and isotropic all across the Galaxy. However, this picture is clearly inaccurate: several data-driven and theoretical arguments, as well as dedicated numerical simulations, show that diffusion exhibits highly anisotropic properties with respect to the direction of a background (ordered) magnetic field (i.e., parallel or perpendicular to it). In this paper we focus on a recently discovered anomaly in the hadronic CR spectrum inferred by the Fermi-LAT gamma-ray data at different positions in the Galaxy, i.e. the progressive hardening of the proton slope at low Galactocentric radii. We propose the idea that this feature can be interpreted as a signature of anisotropic diffusion in the complex Galactic magnetic field: in particular, the harder slope in the inner Galaxy is due, in our scenario, to the parallel diffusive escape along the poloidal component of the large-scale, regular, magnetic field. We implement this idea in a numerical framework, based on the DRAGON code, and perform detailed numerical tests on the accuracy of our setup. We discuss how the effect proposed depends on the relevant free parameters involved. Based on low-energy extrapolation of the few focused numerical simulations aimed at determining the scalings of the anisotropic diffusion coefficients, we finally present a set of plausible models that reproduce the behavior of the CR proton slopes inferred by gamma-ray data.

79 ASTRONOMY AND ASTROPHYSICS↗

On the implementation of the spherical collapse model for dark energy models

In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity δ{sub c}, which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δ{sub c} for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.

79 ASTRONOMY AND ASTROPHYSICS↗

GROUND LEVEL ENHANCEMENT IN THE 2014 JANUARY 6 SOLAR ENERGETIC PARTICLE EVENT

We present a study of the 2014 January 6 solar energetic particle event which produced a small ground level enhancement (GLE), making it the second GLE of this unusual solar cycle 24. This event was primarily observed by the South Pole neutron monitors (increase of ∼2.5%) while a few other neutron monitors recorded smaller increases. The associated coronal mass ejection (CME) originated behind the western limb and had a speed of 1960 km s{sup –1}. The height of the CME at the start of the associated metric type II radio burst, which indicates the formation of a strong shock, was measured to be 1.61 Rs using a direct image from STEREO-A/EUVI. The CME height at the time of the GLE particle release (determined using the South Pole neutron monitor data) was directly measured as 2.96 Rs based on STEREO-A/COR1 white-light observations. These CME heights are consistent with those obtained for GLE71, the only other GLE of the current cycle, as well as cycle-23 GLEs derived using back-extrapolation. GLE72 is of special interest because it is one of only two GLEs of cycle 24, one of two behind-the-limb GLEs, and one of the two smallest GLEs of cycles 23 and 24.

79 ASTRONOMY AND ASTROPHYSICS↗

STAR FORMATION AT 4 < z < 6 FROM THE SPITZER LARGE AREA SURVEY WITH HYPER-SUPRIME-CAM (SPLASH)

Using the first 50% of data collected for the Spitzer Large Area Survey with Hyper-Suprime-Cam observations on the 1.8 deg{sup 2} Cosmological Evolution Survey we estimate the masses and star formation rates of 3398 M {sub *} > 10{sup 10} M {sub ☉} star-forming galaxies at 4 < z < 6 with a substantial population up to M {sub *} ≳ 10{sup 11.5} M {sub ☉}. We find that the strong correlation between stellar mass and star formation rate seen at lower redshift (the ''main sequence'' of star-forming galaxies) extends to z ∼ 6. The observed relation and scatter is consistent with a continued increase in star formation rate at fixed mass in line with extrapolations from lower-redshift observations. It is difficult to explain this continued correlation, especially for the most massive systems, unless the most massive galaxies are forming stars near their Eddington-limited rate from their first collapse. Furthermore, we find no evidence for moderate quenching at higher masses, indicating quenching either has not occurred prior to z ∼ 6 or else occurs rapidly, so that few galaxies are visible in transition between star-forming and quenched.

79 ASTRONOMY AND ASTROPHYSICS↗

Watch and learn—a generalized approach for transferrable learning in deep neural networks via physical principles

Transfer learning refers to the use of knowledge gained while solving a machine learning task and applying it to the solution of a closely related problem. Such an approach has enabled scientific breakthroughs in computer vision and natural language processing where the weights learned in state-of-the-art models can be used to initialize models for other tasks which dramatically improve their performance and save computational time. Here we demonstrate an unsupervised learning approach augmented with basic physical principles that achieves fully transferrable learning for problems in statistical physics across different physical regimes. By coupling a sequence model based on a recurrent neural network to an extensive deep neural network, we are able to learn the equilibrium probability distributions and inter-particle interaction models of classical statistical mechanical systems. Our approach, distribution-consistent learning, DCL, is a general strategy that works for a variety of canonical statistical mechanical models (Ising and Potts) as well as disordered interaction potentials. Using data collected from a single set of observation conditions, DCL successfully extrapolates across all temperatures, thermodynamic phases, and can be applied to different length-scales. This constitutes a fully transferrable physics-based learning in a generalizable approach.

97 MATHEMATICS AND COMPUTING↗

Assessment of Accelerated Stress Testing Data for Silicon Photovoltaics Using Tensor Decomposition Methods

In this work, we examine the use of high-order tensor decompositions to analyze degradation pathways emerging from accelerated stress testing of silicon photovoltaic (PV) modules. Matrix-based decompositions are powerful tools for studying two-dimensional data arrays and form the foundation of a host of classical data analysis techniques. Tensors are high-order extrapolations of matrices that are able to account for more parameter dimensions, and a variety of tensor decomposition methods have been developed that similarly seek to extend insights from matrix decompositions to higher dimensions. Applying and interpreting tensor decomposition methods to sequences of PV module image data, we seek to uncover and isolate different degradation modes occurring from accelerated stress testing procedures. Further, we consider the contributions of different modes to PV module performance degradations.

data analysis↗

Connect the Dots: In Situ 4-D Seismic Monitoring of CO 2 Storage With Spatio-Temporal CNNs

4-D seismic imaging has been widely used in CO 2 sequestration projects to monitor the fluid flow in the volumetric subsurface region that is not sampled by wells. Ideally, real-time monitoring and near-future forecasting would provide site operators with great insights to understand the dynamics of the subsurface reservoir and assess any potential risks. However, due to obstacles such as high deployment cost, availability of acquisition equipment, exclusion zones around surface structures, only very sparse seismic imaging data can be obtained during monitoring. That leads to an unavoidable and growing knowledge gap over time. The operator needs to understand the fluid flow throughout the project lifetime and the seismic data are only available at a limited number of times. This is insufficient for understanding reservoir behavior. To overcome those challenges, we have developed spatio-temporal neural-network-based models that can produce high-fidelity interpolated or extrapolated images effectively and efficiently. Specifically, our models are built on an autoencoder, and incorporate the long short-term memory (LSTM) structure with a new loss function regularized by optical flow. We validate the performance of our models using real 4-D post-stack seismic imaging data acquired at the Sleipner CO 2 sequestration field. We employ two different strategies in evaluating our models. Numerically, we compare our models with different baseline approaches using classic pixel-based metrics. We also conduct a blind survey and collect a total of 20 responses from domain experts to evaluate the quality of data generated by our models. Finally, via both numerical and expert evaluation, we conclude that our models can produce high-quality 2-D/3-D seismic imaging data at a reasonable cost, offering the possibility of real-time monitoring or even near-future forecasting of the CO 2 storage reservoir.

4-D seismic imaging↗

SU-E-T-104: An Examination of Dose in the Buildup and Build-Down Regions

Purpose: To examine dose in the buildup and build-down regions and compare measurements made with various models and dosimeters Methods: Dose was examined in a 30×30cm {sup 2} phantom of water-equivalent plastic with 10cm of backscatter for various field sizes. Examination was performed with radiochromic film and optically-stimulated-luminescent-dosimeter (OSLD) chips, and compared against a plane-parallel chamber with a correction factor applied to approximate the response of an extrapolation chamber. For the build-down region, a correction factor to account for table absorption and chamber orientation in the posterior-anterior direction was applied. The measurement depths used for the film were halfway through their sensitive volumes, and a polynomial best fit curve was used to determine the dose to their surfaces. This chamber was also compared with the dose expected in a clinical kernel-based computer model, and a clinical Boltzmann-transport-equation-based (BTE) computer model. The two models were also compared against each other for cases with air gaps in the buildup region. Results: Within 3mm, all dosimeters and models agreed with the chamber within 10% for all field sizes. At the entrance surface, film differed in comparison with the chamber from +90% to +15%, the BTE-model by +140 to +3%, and the kernel-based model by +20% to −25%, decreasing with increasing field size. At the exit surface, film differed in comparison with the chamber from −10% to −15%, the BTE-model by −53% to −50%, the kernel-based model by −55% to −57%, mostly independent of field size. Conclusion: The largest differences compared with the chamber were found at the surface for all field sizes. Differences decreased with increasing field size and increasing depth in phantom. Air gaps in the buildup region cause dose buildup to occur again post-gap, but the effect decreases with increasing phantom thickness prior to the gap.

60 APPLIED LIFE SCIENCES↗

Clinical introduction of image lag correction for a cone beam CT system

Purpose: Image lag in the flat-panel detector used for Linac integrated cone beam computed tomography (CBCT) has a degrading effect on CBCT image quality. The most prominent visible artifact is the presence of bright semicircular structure in the transverse view of the scans, known also as radar artifact. Several correction strategies have been proposed, but until now the clinical introduction of such corrections remains unreported. In November 2013, the authors have clinically implemented a previously proposed image lag correction on all of their machines at their main site in Amsterdam. The purpose of this study was to retrospectively evaluate the effect of the correction on the quality of CBCT images and evaluate the required calibration frequency. Methods: Image lag was measured in five clinical CBCT systems (Elekta Synergy 4.6) using an in-house developed beam interrupting device that stops the x-ray beam midway through the data acquisition of an unattenuated beam for calibration. A triple exponential falling edge response was fitted to the measured data and used to correct image lag from projection images with an infinite response. This filter, including an extrapolation for saturated pixels, was incorporated in the authors’ in-house developed clinical CBCT reconstruction software. To investigate the short-term stability of the lag and associated parameters, a series of five image lag measurement over a period of three months was performed. For quantitative analysis, the authors have retrospectively selected ten patients treated in the pelvic region. The apparent contrast was quantified in polar coordinates for scans reconstructed using the parameters obtained from different dates with and without saturation handling. Results: Visually, the radar artifact was minimal in scans reconstructed using image lag correction especially when saturation handling was used. In patient imaging, there was a significant reduction of the apparent contrast from 43 ± 16.7 to 15.5 ± 11.9 HU without the saturation handling and to 9.6 ± 12.1 HU with the saturation handling, depending on the date of the calibration. The image lag correction parameters were stable over a period of 3 months. The computational load was increased by approximately 10%, not endangering the fast in-line reconstruction. Conclusions: The lag correction was successfully implemented clinically and removed most image lag artifacts thus improving the image quality. Image lag correction parameters were stable for 3 months indicating low frequency of calibration requirements.

61 RADIATION PROTECTION AND DOSIMETRY↗

SU-C-206-07: A Practical Sparse View Ultra-Low Dose CT Acquisition Scheme for PET Attenuation Correction in the Extended Scan Field-Of-View

Purpose: To further reduce CT dose, a practical sparse-view acquisition scheme is proposed to provide the same attenuation estimation as higher dose for PET imaging in the extended scan field-of-view. Methods: CT scans are often used for PET attenuation correction and can be acquired at very low CT radiation dose. Low dose techniques often employ low tube voltage/current accompanied with a smooth filter before backprojection to reduce CT image noise. These techniques can introduce bias in the conversion from HU to attenuation values, especially in the extended CT scan field-of-view (FOV). In this work, we propose an ultra-low dose CT technique for PET attenuation correction based on sparse-view acquisition. That is, instead of an acquisition of full amount of views, only a fraction of views are acquired. We tested this technique on a 64-slice GE CT scanner using multiple phantoms. CT scan FOV truncation completion was performed based on the published water-cylinder extrapolation algorithm. A number of continuous views per rotation: 984 (full), 246, 123, 82 and 62 have been tested, corresponding to a CT dose reduction of none, 4x, 8x, 12x and 16x. We also simulated sparse-view acquisition by skipping views from the fully-acquired view data. Results: FBP reconstruction with Q. AC filter on reduced views in the full extended scan field-of-view possesses similar image quality to the reconstruction on acquired full view data. The results showed a further potential for dose reduction compared to the full acquisition, without sacrificing any significant attenuation support to the PET. Conclusion: With the proposed sparse-view method, one can potential achieve at least 2x more CT dose reduction compared to the current Ultra-Low Dose (ULD) PET/CT protocol. A pre-scan based dose modulation scheme can be combined with the above sparse-view approaches, which can even further reduce the CT scan dose during a PET/CT exam.

60 APPLIED LIFE SCIENCES↗

SU-D-204-03: Comparison of Patient Positioning Methods Through Modeling of Acute Rectal Toxicity in Intensity Modulated Radiation Therapy for Prostate Cancer. Does Quality of Data Matter More Than the Quantity?

Purpose: To determine if differences in patient positioning methods have an impact on the incidence and modeling of grade >=2 acute rectal toxicity in prostate cancer patients who were treated with Intensity Modulated Radiation Therapy (IMRT). Methods: We compared two databases of patients treated with radiation therapy for prostate cancer: a database of 79 patients who were treated with 7 field IMRT and daily image guided positioning based on implanted gold markers (IGRTdb), and a database of 302 patients who were treated with 5 field IMRT and daily positioning using a trans-abdominal ultrasound system (USdb). Complete planning dosimetry was available for IGRTdb patients while limited planning dosimetry, recorded at the time of planning, was available for USdb patients. We fit Lyman-Kutcher-Burman (LKB) model to IGRTdb only, and Univariate Logistic Regression (ULR) NTCP model to both databases. We perform Receiver Operating Characteristics analysis to determine the predictive power of NTCP models. Results: The incidence of grade >= 2 acute rectal toxicity in IGRTdb was 20%, while the incidence in USdb was 54%. Fits of both LKB and ULR models yielded predictive NTCP models for IGRTdb patients with Area Under the Curve (AUC) in the 0.63 – 0.67 range. Extrapolation of the ULR model from IGRTdb to planning dosimetry in USdb predicts that the incidence of acute rectal toxicity in USdb should not exceed 40%. Fits of the ULR model to the USdb do not yield predictive NTCP models and their AUC is consistent with AUC = 0.5. Conclusion: Accuracy of a patient positioning system affects clinically observed toxicity rates and the quality of NTCP models that can be derived from toxicity data. Poor correlation between planned and clinically delivered dosimetry may lead to erroneous or poorly performing NTCP models, even if the number of patients in a database is large.

60 APPLIED LIFE SCIENCES↗

Contribution of the Δ-isobar excitation mechanism to the pp → {pp}{sub s} π{sup 0} reaction

The differential cross section of the reaction pp → {pp}{sub s} π{sup 0}, where {pp}{sub s} is the proton pair in the {sup 1}S{sub 0} state at a small excitation energy E{sub pp} < 3 MeV, is calculated using the box diagram with the excitation of the Δ-isobar. The model demonstrates a clear bump observed in the experimental data at the beam energy of ∼0.6 GeV and the zero diproton outgoing angle; however, its absolute value strongly depends on the off-shell extrapolation of the πNΔ vertex factor and underestimates the data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Composition and optical properties of amorphous a-SiO{sub x}:H films with silicon nanoclusters

The phase composition and optical properties of hydrogenated amorphous films of silicon suboxide (a-SiO{sub x}:H) with silicon nanoclusters are studied. Ultrasoft X-ray emission spectroscopy show that silicon- suboxide films with various oxidation states and various amorphous silicon-cluster contents can be grown using dc discharge modulation. In films with an ncl-Si content of ∼50%, the optical-absorption edge is observed, whose extrapolation yields an optical band gap estimate of ∼3.2–3.3 eV. In the visible region, rather intense photoluminescence bands are observed, whose peak positions indicate the formation of silicon nanoclusters 2.5–4.7 nm in size in these films, depending on the film composition.

36 MATERIALS SCIENCE↗