Pore size distributions in low‐k dielectric thin films from X‐ray porosimetry

X‐ray reflectivity has been used to determine the mass uptake of probe molecules in porous thin films supported on thick silicon wafers. The adsorption occurs by capillary condensation when the films are exposed to probe vapor at controlled partial vapor pressures. The probe solvent partial pressure was varied by mixing saturated air and dry air at constant temperature or by changing sample temperature at a constant vapor concentration. Pore size distribution in the films can be calculated from the probe uptake with typical porosimetric approaches such as the application of the Kelvin equation to convert partial pressure into pore size. For illustration, the pore size distribution of three different nanoporous thin films, the primary candidate of ultra‐low‐k interlevel dielectrics in the next generation of integrated circuit chips, was determined with this technique. These samples represent different generations of low‐k dielectrics developed by industry. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2170–2177, 2002     

Moisture absorption and absorption kinetics in polyelectrolyte films: influence of film thickness

Specular X-ray reflectivity (XR) and quartz crystal microbalance (QCM) measurements were used to determine the absorption of water into thin poly(4-ammonium styrenesulfonic acid) films from saturated vapor at 25 degrees C. The effect of film thickness on the absorption kinetics and overall absorption was investigated in the range of thickness from (3 to 200) nm. The equilibrium swelling of all the films irrespective of film thickness was (0.57+/-0.03) volume fraction. Although the equilibrium absorption is independent ofthickness, the absorption rate substantially decreases for film thickness < 100 nm. For the thinnest film (3 nm), there is a 5 orders of magnitude decrease in the diffusion coefficient for water.     

Dynamics of thin polymer films: Recent insights from incoherent neutron scattering

Incoherent neutron scattering is presented as a powerful tool for interpreting changes in molecular dynamics as a function of film thickness for a range of polymers. Motions on approximately nanosecond and faster timescales are quantified in terms of a mean-square atomic displacement (〈u²〉) from the Debye–Waller factor. Thin-film confinement generally leads to a reduction of 〈u²〉 in comparison with the bulk material, and this effect becomes especially pronounced when the film thickness approaches the unperturbed dimensions of the macromolecule. Generally, there is a suppression (never an enhancement) of 〈u²〉 at temperatures T above the bulk calorimetric glass-transition temperature (T_g). Below T_g, the reduction in the magnitude of 〈u²〉 depends on the polymer and the length scales being probed. Polymers with extensive segmental or local mobility in the glass are particularly susceptible to reductions of 〈u²〉 with confinement, especially at the Q vectors probing these longer length scales, whereas materials lacking these sub-T_g motions are relatively insensitive. Moreover, a reduced 〈u²〉 value correlates with reduced mobility at long time and spatial scales, as measured by diffusion in these thin polymer films. Finally, this reduced thin-film mobility is not reliably predicted by thermodynamic assessments of an apparent T_g, as measured by discontinuities or kinks in the T dependence of the thermal expansion, specific volume, index of refraction, specific heat, and so forth. These measurements illustrate that 〈u²〉 is a powerful and predictive tool for understanding dynamic changes in thin polymer films. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3218–3234, 2004     

Cumulant functions in optical coherence theory

Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders greater than some numberN ₀ vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would need to introduce cumulant tensors.     

Glass transition of miscible binary polymer-polymer thin films

The average glass transition temperatures, Tg, of thin homopolymer films exhibit a thickness dependence, Tg(h), associated with a confinement effect and with polymer-segment-interface interactions. The Tg's of completely miscible thin film blends of tetramethyl bisphenol-A polycarbonate (TMPC) and deuterated polystyrene (dPS), supported by SiO(x)/Si, decrease with decreasing h for PS weight fractions phi >0.1. This dependence is similar to that of PS and opposite to that of TMPC thin films. Based on an assessment of Tg(h, phi), we suggest that the Tg(h, phi) of miscible blends should be rationalized, additionally, in terms of the notion of a self-concentration and associated heterogeneous component dynamics.     

Gas phase activation energy for unimolecular dissociation of biomolecular ions determined by focused RAdiation for gaseous multiphoton ENergy transfer (FRAGMENT)

We present a novel approach for the determination of activation energy for the unimolecular dissociation of a large (>50 atoms) ion, based on measurement of the unimolecular dissociation rate constant as a function of continuous-wave CO(2) laser intensity. Following a short ( approximately 1 s) induction period, CO(2) laser irradiation produces an essentially blackbody internal energy distribution, whose 'temperature' varies inversely with laser intensity. The only currently available method for measuring such activation energies is blackbody infrared radiative dissociation (BIRD). Compared with BIRD, FRAGMENT: (a) eliminates the need to heat the surrounding ion trap and vacuum chamber to each of several temperatures (each requiring hours for temperature equilibration); (b) offers a three-fold wider range of effective blackbody temperature; and (c) extends the range of applications to include initially cold ions (e.g., gas-phase H/D exchange). Our FRAGMENT-determined activation energy for dissociation of protonated bradykinin, 1.2 +/- 0.1 eV, agrees within experimental error to the value, 1.3 +/- 0.1 eV, previously reported by Williams et al. from BIRD experiments. Copyright 1999 John Wiley & Sons, Ltd.     

Characterization of pore structure in a nanoporous low-dielectric-constant thin film by neutron porosimetry and X-ray porosimetry

A small-angle neutron scattering (SANS) porosimetry technique is presented for characterization of pore structure in nanoporous thin films. The technique is applied to characterize a spin-on organosilicate low dielectric constant (low-k) material with a random pore structure. Porosimetry experiments are conducted using a "contrast match" solvent (a mixture of toluene-d8 and toluene-h8) having the same neutron scattering length density as that of the nanoporous film matrix. The film is exposed to contrast match toluene vapor in a carrier gas (air), and pores fill with liquid by capillary condensation. The partial pressure of the solvent vapor is increased stepwise from 0 (pure air) to P0 (saturated solvent vapor) and then decreased stepwise to 0 (pure air). As the solvent partial pressure increases, pores fill with liquid solvent progressively from smallest to largest. SANS measurements quantify the average size of the empty pores (those not filled with contrast match solvent). Analogous porosimetry experiments using specular X-ray reflectivity (SXR) quantify the volume fraction of solvent adsorbed at each step. Combining SXR and SANS data yields information about the pore size distribution and illustrates the size dependence of the filling process. For comparison, the pore size distribution is also calculated by application of the classical Kelvin equation to the SXR data.     

Nanostructural evidence of mechanical aging and performance loss in ballistic fibers

It is understood that the ballistic resistance of aromatic polyamide fibers is related to the fiber's ultimate tensile strength, strain‐to‐failure, and Young's modulus. Ideal high‐performance ballistic materials maximize these properties while minimizing material density. Equally important is long‐term mechanical and chemical stability: the fibers should not exhibit performance loss over their lifetime. However, less is known quantitatively about their modes of degradation, and experimental methods to quantify the aging and degradation in these fibers are critical. Multiple variations of next generation high‐performance fibers have been investigated under chemical and mechanical accelerated aging conditions. Performance losses have been empirically correlated to chemical degradation of the polymer chain and nanostructural changes in the fiber morphology through X‐ray photoelectron spectroscopy (XPS). Here, we introduce positron annihilation lifetime spectroscopy measurements as a sensitive method to quantify the early onset of damage in the flexed fibers as quantified through changes in the nanoscale void structure in the material. Published 2017.^? J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 1711–1717     

Lobby index as a network centrality measure

We study the lobby index (l$l$-index for short) as a local node centrality measure for complex networks. The l$l$-index is compared with degree (a local measure), betweenness and Eigenvector centralities (two global measures) in the case of a biological network (Yeast interaction protein–protein network) and a linguistic network (Moby Thesaurus   II). In both networks, the l$l$-index has a poor correlation with betweenness but correlates with degree and Eigenvector centralities. Although being local, the l$l$-index carries more information about its neighbors than degree centrality. Also, it requires much less time to compute when compared with Eigenvector centrality. Results show that the l$l$-index produces better results than degree and Eigenvector centrality for ranking purposes.     

Brillouin scattering studies of polymeric nanostructures *

For a range of applications, polymers are now being patterned into nanometer‐sized features. In these applications, the robust mechanical properties of the nanostructures are critical for performance and stability. Brillouin light scattering is presented as a nondestructive, noncontact tool used to quantify the elastic constants in such nanostructures. We demonstrate this through a series of thin films and parallel ridges and spacings (gratings) with ridge widths ranging from 180 to 80 nm. For the set of films and structures presented here, the room‐temperature elastic moduli did not change with decreasing film thickness or grating ridge width, and this implied that one‐dimensional and two‐dimensional confinement‐induced changes of the mechanical properties were not significant down to feature sizes of 80 nm. Additionally, Brillouin spectra of submicrometer gratings revealed new modes not present in the spectra of thin films. The origin of these new modes remains unclear. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1106–1113, 2004