A Multi-scale Model for Copper Dishing in Chemical-Mechanical Polishing

The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.

Converting the nanodomains of a diblock-copolymer thin film from spheres to cylinders with an external electric field

We investigate the ability of an applied electric field to convert the morphology of a diblock-copolymer thin film from a monolayer of spherical domains embedded in the matrix to cylindrical domains that penetrate through the matrix. As expected, the applied field increases the relative stability of cylindrical domains, while simultaneously reducing the energy barrier that impedes the transition to cylinders. The effectiveness of the field is enhanced by a large dielectric contrast between the two block-copolymer components, particularly when the low-dielectric contrast component forms the matrix. Furthermore, the energy barrier is minimized by selecting sphere-forming diblock copolymers that are as compositionally symmetric as possible. Our calculations, which are the most quantitatively reliable to date, are performed using a numerically precise spectral algorithm based on self-consistent-field theory supplemented with an exact treatment for linear dielectric materials.

Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

Undulation instability in block-copolymer lamellae subjected to a perpendicular electric field

We examine the stability of lamellar stacks in the presence of an electric field, E-0, applied normal to the lamellae. Calculations are performed with self-consistent field theory (SCFT) supplemented by an exact treatment of the electrostatic energy for linear dielectric materials. The calculations identify a critical electric field, E-0*, beyond which the lamellar stack becomes unstable with respect to undulations. This E-0* rapidly decreases towards zero as the number of lamellae in the stack diverges. Our quantitative predictions for E-0* are consistent with previous experimental measurements by Xu and co-workers.

Radar scattering by aggregate snowflakes

The radar scattering properties of realistic aggregate snowflakes have been calculated using the Rayleigh-Gans theory. We find that the effect of the snowflake geometry on the scattering may be described in terms of a single universal function, which depends only on the overall shape of the aggregate and not the geometry or size of the pristine ice crystals which compose the flake. This function is well approximated by a simple analytic expression at small sizes; for larger snowflakes we fit a curve to Our numerical data. We then demonstrate how this allows a characteristic snowflake radius to be derived from dual wavelength radar measurements without knowledge of the pristine crystal size or habit, while at the same time showing that this detail is crucial to using such data to estimate ice water content. We also show that the 'effective radius'. characterizing the ratio of particle volume to projected area, cannot be inferred from dual wavelength radar data for aggregates. Finally, we consider the errors involved in approximating snowflakes by 'air-ice spheres', and show that for small enough aggregates the predicted dual wavelength ratio typically agrees to within a few percent, provided some care is taken in choosing the radius of the sphere and the dielectric constant of the air-ice mixture; at larger sizes the radar becomes more sensitive to particle shape, and the errors associated with the sphere model are found to increase accordingly.

Dipole modes on open periodic structures — an experimental study

An experimental study is made of the lower pass-band of waveguides built as necklaces of oblate spheroids. Short lengths of guide are tested in open resonators. The dominant mode is found to be a glow-wave dipole type having no low-frequency cut off. High Q factors indicate low attenuations. Perturbation measurements demonstrate this energy to be concentrated in the vicinity of the guide.

LDA or GGA? A combined experimental inelastic neutron scattering and ab initio lattice dynamics study of alkali metal hydrides

In a previous work, we carried out inelastic neutron scattering (INS) spectroscopy experiments and preliminary first principles calculations on alkali metal hydrides. The complete series of alkali metal hydrides, LiH, NaH, KH, RbH and CsH was measured in the high-resolution TOSCA INS spectrometer at ISIS. Here, we present the results of ab initio electronic structure calculations of the properties of the alkali metal hydrides using both the local density approximation (LDA) and the generalized gradient approximation (GGA), using the Perdew–Burke–Ernzerhof (PBE) parameterization. Properties calculated were lattice parameters, bulk moduli, dielectric constants, effective charges, electronic densities and inelastic neutron scattering (INS) spectra. We took advantage of the currently available computer power to use full lattice dynamics theory to calculate thermodynamic properties for these materials. For the alkali metal hydrides (LiH, NaH, KH, RbH and CsH) using lattice dynamics, we found that the INS spectra calculated using LDA agreed better with the experimental data than the spectra calculated using GGA. Both zero-point effects and thermal contributions to free energies had an important effect on INS and several thermodynamic properties.

Chemical, physical and electrical properties of aged dodecylbenzene 3: thermal ageing of mixed isomers in nitrogen and under sealed conditions

Commercial dodecylbenzene cable fluid was aged at temperatures of 105 and 135 degrees C in dry oxygen-free nitrogen. In addition, selected samples were aged at 135 degrees C under sealed conditions where air was excluded from the headspace above the oil. A variety of analytical techniques, such as ultra-violet visible and infra-red spectroscopy, acid number and water content measurements, were then used to characterize the aged oils. In addition, their electrical properties were assessed by dielectric spectroscopy. Compared with ageing in air, the ageing rate was reduced significantly and, as expected, no major oxidation peaks were detected in the infrared spectrometer. Significantly, very little absorbance at 680 nm ("red absorbers") was detected in samples aged with copper and, consequentially, no large increases in dielectric loss were recorded within the ageing times considered here. This study compliments previous investigations on cable fluid and 1-phenyldodecane aged in air and show that the same ageing indicators are valid in oils aged under conditions which more closely resemble those found in high voltage plant.

Chemical, physical and electrical properties of aged dodecylbenzene: thermal ageing of mixed isomers in air

A commercial dodecylbenzene (DDB) cable oil was aged at temperatures between 90 and 135 degrees C in air and was analyzed using various analytical techniques including optical and infra-red spectroscopy and dielectric analysis. On ageing, the oil darkened, significant oxidation features were found by infra-red spectroscopy and the acid number, water content and dielectric loss all increased. Ageing in the presence of paper or aluminum did not affect the ageing process, whereas ageing was significantly modified by the presence of copper. An absorption at 680 nm ("red absorbers") was detected by ultra-violet/visible spectroscopy followed by the production of an opaque precipitate. A reaction between copper and the acid generated on ageing is thought to produce copper carboxylates, and X-ray fluorescence confirmed that copper was indeed present in both the aged oil and the precipitate. Significantly, once red absorbers were detected, the dielectric loss increased to catastrophically high values and, therefore, the appearance of these compounds may serve as a useful diagnostic indicator. The development of acidity on ageing appears to be key in initiating the destructive copper conversion reaction and hence the control of oil acidity may be key to prolonging the life of DDB cable oils.

Chemical, physical and electrical properties of aged dodecylbenzene 2: thermal ageing of single isomers in air

The linear isomer of dodecylbenzene (DDB), 1-phenyldodecane, was aged at temperatures of 105 and 135 degrees C in air and the resultant products were analyzed using a range of analytical techniques. On ageing, the 1-phenyldodecane darkened, the acid number, dielectric loss and water content increased and significant oxidation peaks were detected in the infrared spectrum. When aged in the presence of copper, a characteristic peak at 680 nm was also detected by UV/visible spectroscopy but, compared with previous studies of a cable-grade DDB, the strength of this peak was much increased and no appreciable precipitate formation occurred. At the same time, very high values of dielectric loss were recorded. On ageing in the absence of copper, an unusually strong infrared carbonyl band was seen, which correlates well with the detection of dodecanophenone by gas chromatography / mass spectrometry and nuclear magnetic resonance spectroscopy. It was therefore concluded that the ageing process proceeds via the initial production of aromatic ketones, which may then be further oxidized to carboxylic acids. In the presence of copper, these oxidation products are present in lower quantities, most of these oxidation products being combined with the copper present in the oil to give copper carboxylates. The behavior is described in terms of a complex autoxidation mechanism, in which copper acts as both an oxidizing and a reducing agent, depending on its oxidation state and, in particular, promotes elimination via the oxidation of intermediate alkyl radical species to carbocations.

Characterisation of blends based on hydroxyethylcellulose and maleic acid-alt-methyl vinyl ether

Hydrophilic polymeric films based on blends of hydroxyethylcellulose and maleic acid-co-methyl vinyl ether were produced by casting from aqueous solutions. The physicochemical properties of the blends have been assessed using Fourier transform infrared spectroscopy, thermal gravimetric analysis, differential scanning calorimetry, dielectric spectroscopy, etc. The pristine films exhibit complete miscibility due to the formation of intermacromolecular hydrogen bonding. The thermal treatment of the blend films leads to cross-linking via intermacromolecular esterification and anhydride formation. The cross-linked materials are able to swell in water and their swelling degree can be easily controlled by temperature and thermal treatment time. The formation of the crosslinks is apparent in the dynamic properties of the blends as observed through the mechanical relaxation and dielectric relaxation spectra. The dielectric characteristics of the material are influenced by the effects of change in the local structure of the blend on the ionic conduction processes and the rate of dipolar relaxation. Separation of these processes is attempted using the dielectric modulus method. Significant deviations from a simple additive rule of mixing on the activation energy are observed consistent with hydrogen bonding and crosslinking of the matrix. This paper indicates a method for the creation of films with good mechanical and physical characteristics by exposing the blends to a relatively mild thermal treatment.

Integrated optics for nulling interferometry in the thermal infrared

Modal filtering is based on the capability of single-mode waveguides to transmit only one complex amplitude function to eliminate virtually any perturbation of the interfering wavefronts, thus making very high rejection ratios possible in a nulling interferometer. In the present paper we focus on the progress of Integrated Optics in the thermal infrared [6-20 mu m] range, one of the two candidate technologies for the fabrication of Modal Filters, together with fiber optics. In conclusion of the European Space Agency's (ESA) "Integrated Optics for Darwin" activity, etched layers of clialcogenide material deposited on chalcogenide glass substrates was selected among four candidates as the technology with the best potential to simultaneously meet the filtering efficiency, absolute and spectral transmission, and beam coupling requirements. ESA's new "Integrated Optics" activity started at mid-2007 with the purpose of improving the technology until compliant prototypes can be manufactured and validated, expectedly by the end of 2009. The present paper aims at introducing the project and the components requirements and functions. The selected materials and preliminary designs, as well as the experimental validation logic and test benches are presented. More details are provided on the progress of the main technology: vacuum deposition in the co-evaporation mode and subsequent etching of chalcogenide layers. In addition., preliminary investigations of an alternative technology based on burying a chalcogenide optical fiber core into a chalcogenide substrate are presented. Specific developments of anti-reflective solutions designed for the mitigation of Fresnel losses at the input and output surface of the components are also introduced.

Investigation of cadmium alternatives in thin-film coatings - art. no. 62860C

The health risks associated with the inhalation or ingestion of cadmium are well documented([1,2]). During the past 18 years, EU legislation has steadily been introduced to restrict its use, leaving a requirement for the development of replacement materials. This paper looks at possible alternatives to various cadmium II-VI dielectric compounds used in the deposition of optical thin-films for various opto-electronic devices. Application areas of particular interest are for infrared multilayer interference filter fabrication and solar cell industries, where cadmium-based coatings currently find widespread use. The results of single and multilayer designs comprising CdTe, CdS, CdSe and PbTe deposited onto group IV and II-VI materials as interference filters for the mid-IR region are presented. Thin films of SnN, SnO2, SnS and SnSe are fabricated by plasma assisted CVD, reactive RF sputtering and thermal evaporation. Examination of these films using FTIR spectroscopy, SEM, EDX analysis and optical characterisation methods provide details of material dispersion, absorption, composition, refractive index, energy band gap and layer thicknesses. The optimisation of deposition parameters in order to synthesise coatings with similar optical and semiconductor properties as those containing cadmium has been investigated. Results of environmental, durability and stability trials are also presented.

Towards a THz osmometer

This work discusses the use of a THz-transient spectrometer for the measurement of tissue water content. The relation of both mammalian- and plant-cell water content to the osmotic potential is discussed. The process of equilibration of tissue water potential with the water potential of water vapor in an osmometer cuvette is described. Observation of the THz transmittance through the water vapor provides a measure of the water activity and water potential in the sample. The possibility of performing dielectric relaxation measurements of the liquid water in the tissue at THz frequencies directly and the use of proline as marker of water stress in tissue are discussed.

Comparison of subspace and ARX models of a waveguide's terahertz transient response after optimal wavelet filtering

A quasi-optical deembedding technique for characterizing waveguides is demonstrated using wide-band time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time-domain responses were discretized and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an AutoRegressive with eXogenous input (ARX), as well as with a state-space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize both signal distortion, as well as the noise propagating in the ARX and subspace models. The optimal filtering procedure used in the wavelet domain for the recorded time-domain signatures is described in detail. The effect of filtering prior to the identification procedures is elucidated with the aid of pole-zero diagrams. Models derived from measurements of terahertz transients in a precision WR-8 waveguide adjustable short are presented.