Positronium annihilation in mesoporous thin films

Abstract

Depth-profiled positronium lifetime spectroscopy is used to probe the pore characteristics ͑size, distribution, and interconnectivity͒ in porous, low-dielectric silica films. The technique is sensitive to the entire void volume, both interconnected and isolated, even if the film is buried beneath a metal or oxide layer. Our extension of a simple quantum mechanical model of Ps annihilation in a pore adequately accounts for the temperature and pore size dependence of the Ps lifetime for pore sizes in the range from 0.1 nm to 600 nm. It is applicable to any porous media. ͓S0163-1829͑99͒51932-2͔ Submicron thin films of porous silica and organosilicates are vigorously being developed as low-dielectric, interlayer insulators for use in future high-speed microelectronic devices. 1 Voids are introduced into the film to produce porosity and hence to lower the dielectric constant. Pores must be plentiful to lower the dielectric constant of solid silica from 4 to less than 2, yet they must be small relative to the device element size which is expected to approach 100 nm in the next decade. Important pore characteristics such as average size, size distribution, and degree of interconnectedness are difficult to probe with standard techniques ͑such as gas absorption͒ because of the submicron film thickness, the presence of a thick Si substrate and, in some cases, by the lack of pore interconnectivity ͑i.e., inaccessibility to gas absorption͒. A less standard technique, positronium annihilation lifetime spectroscopy ͑PALS͒, is well known as a bulk probe of subnanometer voids in polymers and insulators and has recently been extended to probe very thin polymer films using keV beams of positrons. 2 The technique looks promising for probing porous films since it is readily applicable to films less than 0.1 m thick, does not rely on any pore interconnectivity/accessibility, and is expected to be sensitive to pore sizes in the 0.3 nm to 100 nm range.In this paper we will explore the capability of PALS to probe the pores in two different types of porous silica films that are spin-cast on Si substrates. The first is a 0.5-m-thick silica-organic composite in which the organic component is removed by thermal decomposition to create pores after the silica component is fully cured and crosslinked. The second is a 0.9-m-thick film, formed using a sol-gel ͑aerogel/ xerogel͒ technique. We determined the film porosities using Rutherford backscattering spectroscopy to be 52% and 77%, respectively. Details on the methodology of depth-profiled PALS has been presented elsewhere. 2 Briefly, a focussed beam of several keV positrons forms positronium ͑Ps, the electron-positron bound state͒ throughout the film thickness. The binding energy of Ps ͑6.8 eV in vacuum͒ is reduced in the solid dielectric and thus Ps tends to localize in the pores.The natural ͑vacuum͒ lifetime of Ps ͑142 ns͒ is reduced by annihilation with molecular electrons during collisions with the pore surface and thus pore size information can be deduced from measuring this lifetime, ͑...

Positronium formation via excitonlike states on Si and Ge surfaces

“…Thus, the colder the emitted Ps, the less there will be, and the longer it will take to leave the sample [29]. Since Ps emission times can be comparable to the lifetime in the pores, which may be 10's of ns or more [30], Ps produced by this method may not be optimal for some experiments (for example, excitation with laser pulses that are much shorter than the Ps emission time). Moreover, such materials can be highly susceptible to laser damage even at room temperature [31]; this situation is likely to be worse at lower temperatures [32], and may even lead to significant damage being created by the incident positron beam if it is intense enough [33].…”

Some Aspects of Free Volume Studies in Molecular Substances Using Positron Annihilation Experiments

“…3) were useful for checking possibility to apply contemporary theoretical models, connecting EFV size and positronium lifetimes, to our experimental results. We mean here extended Tao-Eldrup (ETE) model suggested by Goworek et al [16,17] and so-called "classical regime", considering Ps atom as a classical particle in a large hole [18,19]. Analysis of our TD-data shows that the classical free path concept Distribution of the free volume holes sizes in polymeric sorbent LPS200X found from the sorption experiments.…”

Positronium as a probe of small free volumes in crystals, polymers and porous media

“…For the first time such an attempt was presented for porous Vycor glass of relatively narrow pores [204]; the value of ∆ = η = (0,191 ± 0.008) nm was obtained. Gidley et al [199] have found for silica films the value 0.18 nm. A precise test was performed by Kallmann et al [205] for cylindrical pores etched in Vycor glass.…”

“…One can easily extend the Eq.30 for cuboid to describe the o-Ps annihilation rate from individual state (n 1 , n 2 , n 3 ) for arbitrary number of halfwaves n i between the walls: (Eq. 59 is equivalent to a similar equation given by Gidley et al [199], where x i = a i +2∆). In porosimetry the rectangular geometry is rarely used, but it is easier in calculations (sine wavefunctions instead of more complex ones).…”