2.1 Krypton adsorption

For quite a while physical adsorption of gases has been considered as a standard method to measure the pore properties of micro- and mesoporous materials [44]. Most of the studies on powdery nanoporous samples suggested the use of conventional BJH analysis as the method to estimate the PSD from the adsorption isotherm of N₂ or Ar. BJH analysis needs two pieces of information: the relationship between pore size and its capillary evaporation (or condensation) pressure, and the change of adsorbed film thickness with pressure in open pores. By studying mesoporous materials of ordered cylindrical mesochannels, the corrected Kelvin equation, modified Broekhoff–de Boer (BdB) method or a semi-molecular approach (NLDFT, the non-local density functional theory calculation) were found recently to be more appropriate to provide the required information for the first part in BJH analysis [42,44–47]. While the experimental t-curves of N₂ and Ar physisorption on an non-porous standard or the calculated values from Frenkel–Halsey–Hill (FHH) instead of classical Harkins and Jura or the Halsey equation are recommended to provide the second part information for the BJH analysis [46].

N₂ adsorption/desorption isotherm at 77 K has been used to estimate the porosity of mesoporous films [48]; due to its ability in reducing uncertainty related to equipment dead volume, adsorption of krypton (Kr) at 77 K has been considered as a means for obtaining PSD of low surface area materials such as thin films. However, there are expressed concerns in the literature about the correct values for the molar volume, the molecular cross-section area, the saturated pressure of Kr at 77 K (p₀). Considering that the triple point of bulk Kr is at 115.8 K, while it is at 77 K that p₀ of supercooled liquid equals 2.49 Torr and that of solid equals 1.77 Torr [47]. Furthermore, surface tension of adsorbed Kr in pores was found to be pore size dependent [49]. Consequently, even for the calculation of the Kelvin equation values of the parameters involved were considered uncertain. A more practical way was thus suggested using a series of ordered powdery mesoporous silicas [50] to experimentally establish the relationship between the pore radius (R_p, nm) determined from the N₂ adsorption isotherm and capillary condensation/evaporation pressure of Kr adsorption (x). The experimental x vs. R_p data were fitted and gave empirical equations with –ln(x) = 34.97 nm/R_p – 22.74 (1 – x)^1.259 for the analysis of desorption branch of Kr adsorption isotherm and –ln(x) = 16.13 nm/R_p – 8.40(1 – x)^0.316 for the analysis of adsorption branch of Kr adsorption isotherm [50]. Film thickness of Kr adsorbed on a low surface area non-porous standard was measured and fitted into an empirical Eq. (1) which, in turn, was employed as the thickness variation of Kr adsorbed with pressure on open pores.(1)

Kr adsorption isotherms of mesoporous SiO₂ films on (100) silicon wafer of thickness  = 600 μm (Fig. 1) were found to be similar to N₂ adsorption isotherm of 2D-hexagonal mesoporous SiO₂ films on (100) silicon wafer of thickness =8 μm) [48], and both gave a triangular hystersis loop. Such behavior could be caused by either an anisotropic shrinkage normal to the substrate surface [51], or mesoporous materials having cylindrical pores with bottlenecks [48]. Kr adsorption isotherm can further provide information on the Brunauer–Emmett–Teller (BET) surface area and pore volume. Surface area measured by Kr adsorption was calculated with molecular area of Kr = 0.21 nm² as suggested by Micromeritics Co. or 0.147 nm² by Muris et al. [52]. The BET surface area thus obtained depends strongly on the pressure range of choice, since multilayer adsorption in mesochannels might be different from that of flat surface. The general applicability of BET equation is within a relative pressure range of p/p₀ = 0.05–0.25 or 0.05–0.1.

By taking the pore volume calculated from N₂ isotherm as reference, one can derive the adsorbed Kr density. It becomes evident that different molar volumes for adsorbed Kr were needed to match the nitrogen and krypton isotherms of powdery mesoporous materials. The values of 35.19, 34.74 and 35.62 ml/mol were found for mesoporous silica MCM-41, MCM-48 and SBA-15, respectively [47]. All the values are smaller than the 36.43 ml/mol reported by Nonaka [53], but greater than the 31.04 ml/mol (2.7 g/cm³) cited by Takei and Chikazkwa [49]. Although the theory/principle used in the surface area and pore size analysis may be fine, the parameters involved in the estimation may warrant further study.

2.2 X-ray reflectivity

Specular XRR (with reflected angle equal to the angle of incident) is a non-destructive technique to measure thin film properties such as film thickness, laterally averaged electron density normal to surface and interfacial roughness [41]. The refractive index of matter in X-ray energy range is n = 1 – δ – iβ, δ = λ²r_eρ_e/2π and β = λμ_i/4π, where r_e is classical electron radius (r_e = 2.8 × 10^–6 nm), λ is X-ray wavelength, ρ_e is electron density of material and μ_i is linear absorption coefficient of film. Typical value for δ is 10^–5–10^–6 while β value is 10 times smaller [41]. Since the X-ray refractive index of air is 1 and that of mater is less than 1, when X-ray beam impinging from air to a flat surface with incident angle (θ_i) below a critical angle θ_c, it can be totally reflected with θc2 ≅ 2δ in the absence of absorption. The critical angle of total reflection is related to the electron density (ρ_e, in units e^–/nm³), thus, the mass density (ρ_m, in units g/cm³) and(2)

Densities of nanoporous films are smaller than that of silicon wafer (ρ_m = 2.3 g/cm³ and ρ_e = 708.3 e⁻/nm³), of which the angular position of total reflection critical angle is 0.221° for λ = 0.154 nm. The electron densities of polymethylsilsesquioxane (PMSSQ) films deposited on Si wafer were assumed to be uniform within a film and were observed to be 370–420 e^–/nm³, and they are dependent on porosity (0–20%) of films and curing temperatures [56]. Porosity of a film (P) can be derived from the average mass density of film (ρ_ave) and pore wall density (ρ_wall) as ρ_ave = ρ_wall (1 – P). Information on PSD was also considered to be derivable through XRR technique by mass uptake of probe molecules and by measuring the total reflection critical angle of thin film before and after exposing it to various partial vapor pressure of a probing molecule, and one such example is toluene for the hydrophobic nanoporous hydrogen silsesquioxane (HSQ) film [57,58]. The critical angle as a function of toluene uptake and the Kelvin equation were used to build the relationship between the pore size and partial pressure of toluene, the PSD could then be calculated.

Doshi et al. [59] found that the as-synthesized form of two-dimensional (2D) hexagonal thin film of cetyltrimethylammonium bromide (CTAB)-templated mesoporous silica (thickness ≅ 586 Å) gave an XRR curve resulting from periodic variation in the derivative of the electron density profile in the z-direction (normal to the Si (100) substrate surface). The presence of oscillation peaks at the high (near the film–substrate interface) and low (near the film–air interface) values of z while with the absence of peaks at intermediate values indicates the existence of a disordered region sandwiched between ordered regions at the substrate–film and film–air interfaces in the thin film. All these confirm the interfacial growth of the mesoporous film.

The as-synthesized form of free-standing film of CTAB-templated mesoporous silica grown on air/water interface consists of 21 layers as examined by XRR [60] and analyzed by a slab model. Which could approximately be separated into a series of two alternating layers: one corresponds to organic surfactant micelle in the cylindrical channel of layer thickness ≅ 3 nm and ρ_z ≅ 9 × 10^–4 nm^–2 and the other is associated with a low density silica phase of layer thickness ≅ 1.5 nm and ρ_z ≅ 10.5 × 10^–4 nm^–2 (where ρ_z is electron density per area); similar to the model in Fig. 3a.

The densities of P123 (H(OCH₂CH₂)₂₀(OCH₂CH₂CH₂)₇₀(OCH₂CH₂)₂₀OH block copolymer)-template-free mesoporous silica films deposited on Si (100) wafer were recently found by us to be lower than that of Brij-56 (C₁₆H₃₃(OCH₂CH₂)₁₀OH)-template-free films [61]. It was also noted that the XRR densities of these mesoporous films were sensitive to the water uptake due to the existence of hydrophilic Si–OH groups on the intrachannel surface. Thickness of P123 and Brij-56 template-free films was analyzed by the Kiessig fringes of XRR curves with a single layer model. Both the single layer model [55,61] and the multi-layer model [60] can be applied for a well-organized film with uniform pore packing arrangement throughout the film. The same frequency values of Kiessig fringes are obtained as shown in Fig. 3c. However, for the multi-layer model consisted of a series of two alternating layers, there are out of plane diffraction peaks on top of the oscillations of Kiessing fringes (profile B of Fig. 3c).

Another example of mesoporous film XRR profile fitted by single layer model is the CTAB or P123-templated mesoporous silica and alumina thin film prepared by Klotz et al. [62]. From the average mass density (ρ_ave) and the pore wall density (ρ_wall, 2.00 g/cm³) by pycnometry, they evaluated the porosity of mesoporous film according to the equation ρ_ave = ρ_wall (1 – P). The porosity derived from the XRR and pycnometer corresponds well with the porosity determined by nitrogen adsorption–desorption measurement.

Wall thickness and core radius of dip-coated CTAB-templated mesostructure silica film were measured by Gibaud et al. [63]. Through the combination of XRR and GIXD measurements, invaluable information such as the radius of the cylindrical rods and the distance between their cores of as-synthesized thin film of CTAB surfactant-templated 2D hexagonal mesoporous silica could be obtained. It has recently been demonstrated that the structural and physical properties of porous thin films deposited on silicon wafer up to 1.4 μm thick can be accurately characterized by high resolution specular XRR and small-angle neutron scattering [64].

In addition to specular reflectivity, there is an off specular characterization (reflected angle does not equal to the angle of incident): Brennan et al. [65] investigated the growth of silica-surfactant mesostructured film at the air/water interface using diffuse XRR technique. The changes of peak intensities of specular reflectivity and Yoneda wing with various CTABr/TMOS ratios and induction period were monitored to study the growth of CTAB-mesostructure films at the air/water interface.

XRR technique has been widely used in organosilane nanoporous films such as hydrogensilsesquioane (HSQ) and methylsilsesquioane (MSQ) to derive their film properties. [66,67] The XRR profiles of these nanoporous films were found to be similar to those of mesoporous films except the existence of Bragg peaks from the ordered pore arrangement of mesoporous films. Film properties such as porosity and pore wall density can thus be obtained.

2.3 Grazing incident X-ray diffraction

Reflection mode XRD, i.e. the θ – 2θ conventional XRD, is well-established for the characterization and the identification of structures of powdery mesoporous samples. However, the bundles of channels in mesoporous silica films are usually expected to pack and align themselves in a specific and preferred orientation at air–solution interface or on a flat substrate. With such ordering of pores, only lattice planes parallel to the surface, d_//s, can be detected by XRD patterns in θ – 2θ scan mode as shown in Fig. 4a [68]. To acquire information more than out-of-plane periodic lattice in the film, GIXD technique is employed (Figs. 4 and 5). Using GIXD technique, incident angle of X-ray (θ_i) should be set at a very small-angle, usually at the critical angle of total reflection (θ_i = θ_c) and the incident beam will be reflected in the direction having (90°– θ_i) angle with the normal to the surface in a specular geometry. For θ_is that are slightly higher than θ_c, the incident beam will penetrate into the film (Fig. 2b) and be diffracted along β axis if some periodicities normal to the film are in agreement with Bragg’s law (Fig. 4b). If a thin-film sample was aligned precisely parallel to incident X-ray beam at θ = 0° and θ_i could be set around θ_c, 2θ should then be set equal to twice that of θ_i in order to get higher reflected intensity during in-plane measurement. Normal axis of the thin film, α, and in-plane angle of the detector, β, together with the geometry of the in-plane diffraction are given in Fig. 4c. The d-spacings of periodicities normal to the surface, d_⊥s, can be obtained from in-plane XRD by nλ = 2 d sin(β/2). Furthermore, after the in-plane structural information is retrieved, the detector can be fixed at certain in-plane XRD peak position and let the sample rotate around the α-axis to obtain the direction distribution of grains in in-plane direction. Nevertheless, information from conventional or out-of-plane and in-plane XRD patterns give d-spacings of periodicity parallel (d_//) and normal to the film (d_⊥), respectively. To resolve the texture of the film, a 2D detector instead of a point detector is recommended for GIXD. An X-ray sensitive imaging plate or charge-coupled device (CCD) camera is used in a 2D GIXD experiment as illustrated in Fig. 4c [69,70]. Due to the absorption of substrate, only half of the diffraction data can be collected for a thin film deposited on a thick substrate. However, either a thin self-supported film [69] or a sample of very thin substrate [70], whole diffraction pattern can be collected. 2D GIXD patterns (Fig. 5) provide the structural information about both out-of-plane and in-plane lattices, as well as periodicities that are neither normal nor parallel to the film surface. By using real time detection through CCD camera and with a synchrotron X-ray source, in situ experiments can also be performed in a time scale less than 1 s [71].

Combining with GIXD and transmission mode XRD technique (Fig. 5) to analyze a mesoporous silica thin film dip-coated on a very thin substrate (10-mm thick Si wafer) [69], it was found that even the 2D planar unit cells were well aligned perpendicular to the surface of dip-coated samples, but the channel axes were still found to be randomly orientated within the plane parallel to the surface.

Miyata and Kuroda [31] found that the channels of mesoporous silica films with thickness less than 0.3 μm were aligned well in perpendicular direction to the rubbing-treated flat glass substrate and thus presenting a 2D hexagonal columnar structure. In this case, only (h00) reflections, i.e. (100), (200) etc. were observed by conventional out-of-plane XRD. The axial preferred orientation of the mesochannels was confirmed by the narrow full width at half maximum (FWHM of diffraction peak) values of the diffraction intensity with α-scan of the in-plane XRD.

Besson et al. recorded GIXD patterns at different incident angles for films derived from silica sols with different period of aging. Interior of the film was found to be organized with the presence of Bragg spots after the growth of ordered domains at the air–sol interface. They suggested that the growth of mesoporous film starts from the nuclei at the liquid–vapor interface [72].

A time-resolved GIXD was also used to study the very fast self-assembly process during film formation [73]. Time scale of the in situ GIXD experiments is less than 1 s and is considered suitable for investigating the growth of mesostructure in a dip-coated film under a controlled atmosphere. Gibaud et al., Grosso et al. and Chao et al. suggested [34,73–75] that the solvent evaporation rate could be controlled by environment and is also important for the formation of the final mesostructure.

The diffraction patterns of GIXD provide the bulk average information about lattice parameters of 2D structures in thin films, while the uniformity over the film thickness and the texture of film relative to the substrate were also viewed by the cross-sectional TEM and electron diffraction (ED) measurements by us [75]. The continuous mesoporous silica film deposited on silicon (100) wafer of 0.2 μm thickness was prepared by dip-coating of Brij-56 templated precursor and then calcined to 500 °C. The texture of template-free film was investigated by the cross-sectional TEM and GIXD and was found to have well-organized pore arrangement throughout the film. However, the directional distribution of bundles of mesochannels in the film as observed by both transmission mode XRD and top-view TEM revealed no preferred in-plane orientation [75], and this is similar to the structure of hexagonal mesophase silica films dip-coated on silica glass and silicon wafer substrates using F127 (OH(CH₂CH₂O)₁₀₆ (CHCH₃CH₂O)₇₀ (CH₂CH₂O)₁₀₆H, Pluronic block polymer) templated silica sol [70]. The results of both studies [70,75] suggested that even the structure of mesoporous silica and grain growth in a film could be direction-dependent, and the preferential ordering normal to the substrate could be disturbed by the deposition of precursor-sol grains on the substrate during the initial stage of coating process.

2.4 Transmission electron microscopy

TEM technique is usually conducted with ED or Fourier transformation (FT) calculation simulation for a direct view of pore structures of mesoporous materials. For those who are interested in observing preferred orientation of mesoporous grain to the substrate and the pore morphology of mesochannels affected by substrate and anisotropic shrinkage from heat treatment [70], thin film specimen should always be together with its host substrate. To prepare ‘on-substrate’ thin film specimens for cross-sectional TEM characterization, a sample can first be cleaved into small pieces, and two pieces can be glued together through face-to-face contact. The glued stacks are then ground, polished and milled. At the thin section of a TEM specimen containing the interface of mesoporous silica and substrate, electron transparency can be achieved. A top-view TEM can also be examined using on-substrate sample, which, in turn, has been polished to achieve good electron transparency. It is to be noted that TEM result is localized; therefore, it is desirable to further examine its consistency with XRD investigation.

3.1 Low-k dielectric

As integrated circuit (IC) technology rapidly advances towards sub-100 nm nodes, ultra-low dielectric constant (k) materials are badly needed to minimize RC delay, signal cross-talk and power dissipation in ULSI devices [76]. Over the past few years, tremendous research on those new interlayer dielectrics (ILD) have been performed in order to replace the conventional Al(Cu)/SiO₂ metallization. Reduction of the k value of ILD relative to SiO₂ (k = 4.0) can be achieved by lowering density and polarizability of materials [36,77]. High electronegativity of F atom reduces the polarizability of C–F bonds. While the density of dielectric materials can be lowered by incorporating either lighter atoms or more void space for air (k = 1). Two types of films have been developed for low-k application, one is the composites of SiO₂-based materials of k = 1.3–3.5, such as SiO₂F_y, HSQ, MSQ, mesoporous organosilicas, porous silica, nanoporous silica in aerogel/xerogel, porous silicas with porogens, and molecularly templated mesoporous silica; and the other is the C-based materials of k = 1.9–3.6, such as polytetrafluoethylene (PTFE), F-doped polyimides, poly (aryl ether) and nanofoams. Among the various low-k dielectrics, nanoporous silica materials are widely believed to be the most promising ILD material for sub-100 nm technology nodes because of their tunable ultra-low k value and their similar chemical composition as the conventional SiO₂ dielectric [22]. Besides, porous silica films have high thermal stability and are compatible with silicon wafer and related materials in the existing IC technology [23,78,79].

Due to its high porosity and channel microstructure, calcined spin-on mesoporous silica films are generally hydrophilic and, therefore, have very poor stability in dielectric properties. Trimethylsilylation by hexamethyldisilazane (HMDS) vapor post-treatment and trimethylchlorosilane (TMCS) mixed with the organic-templated silica sol precursor were adopted to improve the hydrophobicity and thus to stabilize the dielectric properties of the nanoporous silica films [80,23]. Ultralow dielectric constants of 1.4–2.5 were obtained on spin-on hydrophobic mesoporous silica films. Of which the hydrophobic property was found to be thermally stable at temperatures as high as 400–500 °C by thermal desorption mass spectrometry. Trimethylsilyl groups (–Si(CH₃)₃) bonded on the intrapore surface of the mesoporous silica film is susceptible to degradation upon exposing to reactive plasmas used for capping, etching, and ashing processes. Plasma can induce chemical modifications in the film, causing film densification, and formation of dangling bonds and defects. All of these can increase the k-value or cause other integration problems. Patterned nanoporous silica films by reactive ion etching were prepared, and a combination of post-annealing, hydrogen plasma treatment, and HMDS vapor treatment was found to be effective to alleviate damages caused by dry etching. The structure of nanoporous silica films was detected by X-ray diffraction and was found to be well in order even after the dry etching process, this suggests that the nanoporous silica can withstand the plasma dry etching [81,82].

Mechanical strength of porous films is expected to be weaker than their fully dense analogues. Low-k porous materials with low mechanical properties will have difficulties to endure integrating cycles such as chemical, mechanical polishing (CMP), dry etching, and packaging processes. Such porous materials as ILD candidates for IC process will constantly face the trade-off in dielectric constant and mechanical properties. Porosity, pore structure and intrapore surface properties of a porous material have all been found to affect the dielectric constant of thin silica film as well as its mechanical strength [37,80].

It is reported that the Cu/low-k interconnect integration has some integration problems in thermal copper diffusion and agglomeration of narrow Cu interconnect at high temperature, so, its processing temperature should be kept low. The application of low temperature photocalcination [83], O₂-plasma [84] and ozone ashing [37,85] treatments in contrast to the conventional thermal calcination were thus studied during the removal of organic templates.

3.2 Photoluminescence

Although bulk silicon is extremely inefficient at emitting light, silicon nanocrystals and highly porous silicon can emit red, green and even weak blue light when stimulated by light of shorter wavelength [86]. Since silicon nanocrystals have energy bandgaps wide enough to produce visible light (2–3 eV) than the 1 eV in bulk silicon. Many efforts have thus been devoted to exploit Si-related light sources including Si/SiO₂ superlattice [87] and Si clusters in mesoporous SiO₂ film [88]. The silicon clusters of ~1 nm size in orientated hexagonal mesoporous silica film displayed yellow–orange photoluminescence (PL) with a UV excitation at 308 nm.

The nature and the role in PL of walls among pores in mesoporous SiO₂ materials were studied recently [89,90]. The PL from mesoporous silica with the pore size of ~6 nm and the thickness of wall among pores of ~1 nm was induced by Nd:YAG laser at λ = 266, 354.7 or 532 nm and observed at room temperature [89]. Since bulk SiO₂ is a wide band gap insulator (the band gap of bulk silica E_g ≅ 11 eV), it was suggested that PL has been derived from a direct one-photon excitation of hydrogen-related species and non-bridging oxygen hole centers on the pore wall of mesoporous silica. PL induced by ultraviolet (UV) or vacuum UV light of mesoporous SiO₂ may be similar to that of surface-oxidized nanocrystals and porous silicon.

3.3 Other applications

The semiconducting polymer, poly [2-methoxy-5(2′-ethyl-hexyloxy)-1, 4-phonylene vinylene] (MEH-PPV) was incorporated in aligned mesochannels of a mesoporous film prepared by the rubbing polyimide method [31] and it showed highly polarized luminescence [91]. Highly aligned mesoporous silica films filled with guest conducting polymers that are intrinsically anisotropic in their intramolecular conductance and luminescence polarization may have potential for photonic applications and other optical applications [92], as they are optically clear and can emit polarized light.

The mesochannels of thin films are easily accessible by the external environment and increases the performances for sensing applications. Electrical current variation with relative humidity was observed on template-free mesoporous films [18]. In addition, mesoporous film loaded with Pt/Pd can act as efficient filter to improve the selectivity and stability of SnO₂-based gas sensors [19]. Mesoporous film was used as a pH-sensor, by incorporating pH-sensitive dye [20] and was integrated into the surface photovoltage gas sensing system for NO detection [21], as well as coated for anti-reflection of light [39].