Periodic Porous Structures Research Articles

Influence of Humidity on Electrical Characteristics of Self-Assembled Porous Silica Low-k Films

The influence of humidity on the dielectric constant and leakage current of self-assembled porous silica films which have two-dimensional hexagonal periodic porous structures was investigated quantitatively by proposing a new water adsorption model. The amount of adsorption was calculated by the modified Rayleigh model, where molecules are assumed to be adsorbed on the inner surface of cylindrical porous silica structures and form a dispersal concentric double-layer dielectric cylinder system. The amount of calculated by the proposed model was consistent with the measured dielectric constant and thermogravimetry data. It suggests that inner-surface coverage of the cylindrical porous silica wall with a hydrophobic group is the most effective way to suppress water adsorption. Hexamethyldisilazane as a surface coverage molecule was introduced to the periodic cylindrical porous silica film and the leakage current was suppressed by a factor of even below 0.5% relative humidity, resulting in the improvement of time-dependent dielectric breakdown lifetime by a factor of 30.

Discussion: “A Numerical Study of Thermal Dispersion in Porous Media” and “Numerical Determination of Thermal Dispersion Coefficients Using a Periodic Porous Structure”

In the two papers 12, Kuwahara et al. investigated thermal dispersion in convective flow in porous media by using a two-dimensional periodic model of porous structure. In their study, a macroscopically uniform flow is assumed to pass through a collection of square rods placed regularly in an infinite space, where a macroscopic temperature gradient is imposed perpendicularly and in parallel to the macroscopic flow direction, respectively. Due to the periodicity of the model, only one structure unit is taken for a calculation domain to resolve an entire domain of porous medium. Exhaustive numerical computations were conducted for thermal dispersion conductivity. The transverse thermal dispersion conductivity results were correlated as the following expression 1: (26a)kdisyykf=0.022 PeD1.71−ε1/4forPeD<10and the longitudinal thermal dispersion conductivity results were correlated as 2(16a)kdisxxkf=0.022 PeD21−εforPeD<10(16b)kdisxxkf=2.7 PeDε1/2forPeD>10where PeD=Pe1−ε1/2. Equation (26a) was also summarized together with their longitudinal thermal dispersion conductivity results, Eq. (16), in their later paper 2. The parameters used in this discussion are defined as the same as those applied by Ref. 12; see also the Nomenclature in this discussion. However, correlations (26a), (16a) and (16b) are questionable. Here is my detailed analysis. According to the definition on the Peclet number given by Refs. 12, the Peclet number Pe should be expressed as (1)Pe=ρCpfumH/kfHowever, the generally applied definition on the Peclet number is 34567(2)Peg=ρCpfumD/kfIf the generally applied definition on the Peclet number, Eq. (D2), is applied to Eqs. (26a), (16a) and (16b), Eqs. (26a), (16a) and (16b) will present the unreasonable results due to the structural unit applied by Kuwahara et al. 12. The structural unit applied by Kuwahara et al. 12 in their numerical experiments is shown in Fig. 1. According to Fig. 1, the total volume of the structural unit is (3)Vt=H2The pore volume of the unit is (4)Vp=H2−D2So, the porosity of the unit can be expressed as (5)ε=Vp/Vt=1−D2/H2From Eq. (D5), we have (6)D/H=1−ε1/2or (7)H=D/1−ε1/2Equation (D7) indicates that H is a function of porosity. Inserting Eq. (D7) into Eq. (D1) yields (8)Pe=ρCpfumD/[kf1−ε1/2]Due to the generally applied definition for the Peclet number Eq. (D2), Eq. (D8) can be written as (9)Pe=Peg/1−ε1/2Equation (D9) establishes the relation between the Peclet number, Eq. (D1), defined by Refs. 12 and the generally applied Peclet number, Eq. (D2) 34567. According to PeD=Pe1−ε1/2 (defined by Refs. 12) and Pe=Peg/1−ε1/2 (i.e. Eq. (D9)), we obtain (10)PeD=PegInserting Eq. (D10) into Eqs. (26a), (16a) and (16b) results in (11)kdisyykf=0.022 Peg1.71−ε1/4forPeD<10(12a)kdisxxkf=0.022 Peg21−εforPeD<10(12b)kdisxxkf=2.7 Pegε1/2forPeD>10where Peg=ρCpfumD/kf is the generally defined definition for the Peclet number given by Eq. (D2). From the above analysis, it is seen that the equations (D11), (D12a) and (D12b) are equivalent to Eqs. (26a) and (16a) and (16b). Equations (D11) and (D12) are transverse and longitudinal thermal dispersion conductivities, respectively, which are expressed in terms of porosity and generally defined Peclet number Peg. However, Eqs. (D11) and (D12) present unreasonable results. For example, the thermal dispersion conductivities given by Eqs. (D11) and (D12a) increase with the increase of porosity. If porosity is 1, Eqs. (D11) and (D12a) present the infinite values for transverse and longitudinal thermal dispersion conductivities, while Eq. (D12b) presents nonzero longitudinal thermal dispersion conductivity. These are inconsistent with physical situation because the thermal dispersion should be reduced with the increase of porosity, and when porosity is 1, there is no dispersion and thermal dispersion conductivity should be zero. In conclusion, it seems to me that the transverse and longitudinal thermal dispersion conductivity correlations, Eq. (26a), Eq. (16a) and (16b) given by Refs. 12, are questionable because they present unreasonable results. This work was supported by the National Natural Science Foundation of China through Grant No. 10272052. D= size of square rod or size of particle H= size of structural unit k= thermal conductivity Pe= Peclet number based on H and the macroscopically uniform velocity defined by Refs. 12Peg= generally defined Peclet number given by Eq. (D2) um= the macroscopically uniform velocity V= volume ε = porosity Subscriptsdis= dispersion f= fluid xx= longitudinal direction yy= transverse direction g= generally applied t= total p= pore

Closure to Discussion: “A Numerical Study of Thermal Dispersion in Porous Media” (Kuwahara, F., Nakayama, A., and Koyama, H., 1996, ASME J. Heat Transfer, 118, pp. 756–761) and “Numerical Determination of Thermal Dispersion Coefficients Using a Periodic Porous Structure” (Kuwahara, F., and Nakayama, A., 1999, ASME J. Heat Transfer, 121, pp. 160–163)

Closure to Discussion: “A Numerical Study of Thermal Dispersion in Porous Media” (Kuwahara, F., Nakayama, A., and Koyama, H., 1996, ASME J. Heat Transfer, 118, pp. 756–761) and “Numerical Determination of Thermal Dispersion Coefficients Using a Periodic Porous Structure” (Kuwahara, F., and Nakayama, A., 1999, ASME J. Heat Transfer, 121, pp. 160–163)

The compaction of blended aggregates of non-spherical linear viscous particles

The approximate discrete-element model [Comput. Methods Appl. Mech. Engrg. 192 (2003) 4929] used to analyze global behavior of single-material aggregates of non-spherical linear viscous particles is extended to simulate compactions of blended granular systems. Based on the triangular mesh system, a new mesh reorganization algorithm for composite aggregates is generated. To verify accuracy of stress calculation in each time step, a multi-zone boundary element method is developed as an analytical model. Solutions of a patch test from two different models are in a great agreement. Infinitesimal area errors during the compaction also demonstrated preciseness of the simulation. Several comparisons among examples of different element number, of various material properties, and of different density are made. A homogenization theory with the finite element modeling is used to investigate the effect of void shape on a periodic porous structure. Results indicate that the factor has considerable effects on overall responses of the whole admixture.

Enhancement of Structural Stability of Mesoporous Silica Thin Films Prepared by Spin-Coating

A mesoporous silica film was prepared on a silicon substrate using a spin-coating process followed by a tetraethyl orthosilicate (TEOS) vapor treatment. The TEOS-treated mesostructured silica film did not contract during calcination, showing high structural stability. Thermal treatment without TEOS vapor was not effective to enhance the structural stability of mesostructured films. A flat mesoporous silica film about 250 nm thick was grown from the silicon substrate. No silica particle was deposited from TEOS vapor on the surface of the film, suggesting the penetration of TEOS vapor into the film. A periodic porous structure was observed in the FE-SEM image of the cross section of the mesostructured film. This indicates that the channels run predominantly parallel to the surface of the silicon substrate. FTIR studies suggested that the silanol groups in the film significantly decreased after the TEOS treatment. TEOS molecules penetrate into an originally deposited silicate film and react with the silanol ...

Electromagnetic propagation in periodic porous structures

A variational technique is employed to compute approximate propagation constants for electromagnetic waves in a dielectric structure which is periodic in the X− Y plane and translationally invariant in the Z-direction. The fundamental cell, in the periodic structure, is composed of a pore and the surrounding host media. The pore is a circle of radius R 0 filled with a dielectric ϵ 1 and the host dielectric characterized by ϵ 2. The size of the cell is characterized by the length A which is ∼ R 0. Two limiting cases are considered. In the first, the pore size is assumed to be much smaller than the wavelength; this limit is motivated by microwave heating of porous material. The approximate propagation constants are explicitly computed for this case and are shown to depend upon the two dielectric constants, the relative areas of the two regions in the cell, and on a modal number. They are not given by a simple mixture formula. In the second limit, the pore size is taken to be of the same order as the wavelength; this limit is motivated by the propagation of light in a holey fiber. In this case our argument directly yields the dispersion relationship recently derived by Ferrando et al. [Opt. Lett. 24 (1999) 276], using intuitive and physical reasoning. Thus, our method puts theirs into a mathematical framework from which other approximations might be deduced.

Visible Frequency Thin Film Photonic Crystals from Colloidal Systems of Nanocrystalline Titania and Polystyrene Microspheres

This work describes a simple and novel ceramic processing technique to form periodic ordered structures in ceramic materials with a uniform pore size distribution. This material shows photonic gaps at visible/near‐IR wavelengths. Monodisperse colloidal polystyrene microspheres are self‐organized into a crystalline structure of close‐packed spheres in a suspension of nanocrystalline titania. The nanoparticle titania fills the intersphere region simultaneously during colloidal crystallization. Removal of the polystyrene microspheres by calcination at a temperature of 520°C results in a periodic porous structure with a high refractive index background material. Crystals having ordered regions, a few millimeters across with typical grain sizes of 50–70 μm, are grown as thin films on substrates including glass and silicon. Optical reflectivity measurements indicate peaks at the stop band wavelengths that scale with the pore size. Visual inspection and optical microscopy reveal uniform colored regions for crystals with periodicity comparable to visible wavelengths. Despite the presence of cracks resulting from drying and heat treatment as well as numerous grain boundaries, optical characterization clearly demonstrates a photonic band gap. Reflectance peaks due to a pseudogap can be shifted by application of high pressure. In the following sections we will describe the experimental procedure and discuss optical reflectance and transmission measurements that can reveal information about the crystals, namely, the lattice constant, the refractive index, and the filling fraction of the background material.

A New Approach of Thin-Film X-Ray Diffraction / Scattering Analysis for Ultra-Low-k Dielectrics with Periodic Pore Structures

AbstractWe propose and demonstrate experimentally a structural characterization technique for ultra-low-dielectric-constant thin films with periodic porous structures [1-3] by employing X-ray diffraction / scattering measurements. The analytical approach that we propose here takes into account specular reflection, incoherent scattering from random distribution of electron density, and coherent scattering from periodically modulated distribution of electron density. From the analysis, inter-pore distances and pore diameters in the directions perpendicular and parallel to the film surface are determined with which the film porosity is calculated. Thus obtained porosity is then used to discuss the film density and dielectric constant in comparison to those of non-porous reference sample.

Synthesis of Ordered Nanoporous Silica Film With High Structural Stability

AbstractA mesoporous silica film was prepared on a silicon substrate using a spin-coating process followed by a tetraethyl orthosilicate (TEOS) vapor treatment. The stability of a formed silica network before TEOS treatment is thought to be insufficient because the rate of the condensation reaction is not high at temperatures below 453 K. The density of silica wall surrounding surfactant assembly could be low, resulting in the structural contraction with the formation of a silica network. On the other hand, the TEOS-treated mesoporous silica film did not contract during calcination, showing high structural stability. In the TEOS treatment, TEOS molecules penetrate into an originally deposited silicate film and react with silanol groups. The densified silica wall has high structural stability and hardly contracts under a calcination process. A flat mesoporous silica film about 250 nm thick was grown from the silicon substrate. A periodic hexagonal porous structure was observed in the FE-SEM image of the cross section of the TEOS-treated film. This indicates that the channels run predominantly parallel to the surface of the silicon substrate. The developed film is a promising material such as chemical sensors, low-k films and other optoelectronic devices.

A reconstruction technique for three-dimensional porous media using image analysis and Fourier transforms

A truncated gaussian method based on Fourier transforms is proposed to generate periodic 3D porous structure from a 2D image of the sample. This technique improves a previous method developed by Quiblier [Quiblier, J.A., 1984. A new three-dimensional modeling technique for studying porous media. J. Colloid Interface Sci 98, 84–102] and Adler et al. [Adler, P.M., Jacquin, C.G., Quiblier, J.A., 1990. Flow in simulated porous media. Int. J. Multiphase Flow 16 (4), 691–712]. The difference between the present method and previous work [Adler, P.M., 1992. Porous Media: Geometry and Transports. Butterworth-Heinemann, New York] is that the gaussian field is directly generated from its autocorrelation function and the use of a linear filter transform is avoided. It is not required to solve a set of nonlinear equations associated with this transform. In addition, memory requirements are reduced because non-correlated gaussian field data are not needed. Porous structure is described by the porosity and autocorrelation function, which are measured from a 2D binarized image of a thin section of the sample. When the autocorrelation function is positive–definite, the corresponding gaussian field can be generated using Fourier transforms. Phase angle distribution is assumed to be random and does not affect the autocorrelation function. 3D porous media are generated by truncating the gaussian distribution. Using the fast Fourier transform makes this algorithm more efficient. Both processing time and computer memory requirements are improved. Results for a Berea sandstone sample show that the mean pore size distribution, obtained taking several serial cross-sections of the reconstructed 3D porous structure into account, is in good agreement with the original thresholded 2D image.