Positronium Behavior In Porous Films

Implant Profile

Depth

Figure 3. Positronium formation in porous materials. The shape of a typical positron implantation profile is depicted in the lower panel.

The most important process a positron can undergo in an insulator is electron-capture to form the bound state of Ps. Ps formation in a porous insulator is depicted in Figure 3. The positron slows down through collisions in the material from its initial beam energy of several keV to several eV. It can either capture a bound molecular electron or recombine with free "spur" electrons generated by ionizing collisions during the slowing down process to form Ps. This Ps, which initially has a few eV of kinetic energy, begins to diffuse and thermalize in the insulator. In porous films it localizes in the void volume where the Ps binding energy is not reduced by the dielectric value of the surrounding material. However, even when it is thermalized in the pores, Ps is still colliding with the pore walls

Depth

Figure 3. Positronium formation in porous materials. The shape of a typical positron implantation profile is depicted in the lower panel.

and the resulting Ps lifetime is shortened by positron annihilation with molecularly bound electrons in addition to the captured electron. Furthermore, Ps may move in a diffusion-like motion over long distances that can be greater than the porous film thickness if the pores are interconnected. As a result Ps can easily escape from the film and into the surrounding vacuum as depicted in Figure 3 (bottom).

Figure 4. PALS spectra of uncapped and Al-capped porous silica films.

Ps escape from open pores is detected differently by the systems shown in Figure 1 and 2. In the electrostatic system, most of the Ps annihilates into three gamma rays with the vacuum lifetime of 142 ns, a telltale indicator that the pores in the film are interconnected. This is what has typically been found so far for porous silica films [5]. They have interconnected pores and Ps diffuses within the pore volume with most Ps finding its way into the vacuum. The lifetime may be shortened systematically when Ps atoms can reach the vacuum walls and pickoff annihilate there. To extract information from PALS on the average pore size (technically, the mean free path for Ps in the interconnected pores), it is necessary to deposit a thin capping layer on top of the film to keep the Ps contained in the porous film. Examples of lifetime spectra acquired with an aluminium-capped and an uncapped porous silica film are shown in Figure 4. The effect of the Ps diffusion barrier is clearly evident. In this example the 41 ns lifetime acquired in the capped film is the correct, pickoff-shortened lifetime to associate with Ps in the pores. Thus PALS gives a clear indication of pore interconnectivity and, once the film is capped, a single lifetime component corresponding to the average mean free path of Ps throughout the entire film is fitted.

A method for distinguishing interconnected pores (Ps escape) without the deposition of a capping layer has been developed for the magnetically guided system (Figure 2). A y-shield is inserted in front of the scintillator to dramatically reduce the probability of detecting photons from Ps annihilations outside of the sample. Data collected with and without the y-shield are compared. In one case, without the y-shield (Figure 2), escaping Ps can be detected with high probability. In the other (using the y-shield), the sensitivity to detecting escaping Ps is strongly suppressed due to the limited acceptance angle. A difference in the mean lifetimes between these two spectra indicates Ps escape [8]. Conversely, an identical mean lifetime signifies that all Ps annihilations occur within the film. Figure 5 shows the mean o-Ps lifetime (for details, see [8]) for a series of films with different degrees of porosity (directly related to the porogen load), obtained from spectra taken with and without the (open triangles and circles, respectively). For a comparison, capped samples were measured to assess the sensitivity of the system with the y-shield to escaping Ps. The results (solid diamonds) practically coincide with those obtained with the

Figure 5. Mean o-Ps lifetime (for t > 60 ns) from PALS spectra of mesoporous MSSQ films as a function of the porogen load. Uncapped films were measured without y-shield (sensitive to escaped Ps; open circles), and with y-shield (insensitive to escaped Ps; open triangles), and were compared to capped films (solid diamonds). The film dielectric value is given on the top scale.

Figure 5. Mean o-Ps lifetime (for t > 60 ns) from PALS spectra of mesoporous MSSQ films as a function of the porogen load. Uncapped films were measured without y-shield (sensitive to escaped Ps; open circles), and with y-shield (insensitive to escaped Ps; open triangles), and were compared to capped films (solid diamonds). The film dielectric value is given on the top scale.

Either method has systematic disadvantages. In a capped film larger beam energies are required to reach a certain depth in the film, causing a loss in depth resolution. A fraction of the implanted positrons annihilate from the cap and not the film; the signal rate drops [16]. The interaction of Ps with the cap can result in a new lifetime component, not inherent to the film. The effectiveness of the y-shield, on the other hand, may vary depending on the angular and velocity distribution of the escaping Ps atoms. The shield also reduces the count rate.

Regardless of the specific annihilation tool used the observed onset of Ps escape into vacuum correlates with the onset of the pore interconnectivity. For mesoporous MSSQ films shown here produced by the sacrificial porogen approach, the pore interconnectivity threshold occurs at ~20 wt% porogen load (as shown in Figure 5). The onset depends on the materials used and the details of the film preparation. Note that Ps escape can occur from pores as soon as a path to the surface is open, well before the entire film pores are interconnected. Therefore, pore interconnectivity precedes total percolation, as a function of porogen load. Considering the high probability for Ps escape (large mean free path compared to film thickness) and the size of the Ps atom (smaller than any probe used in gas absorption techniques), Ps can probe very narrow open channels, and is arguably the most sensitive probe for pore interconnectivity.

Figure 6. Left: Depth-profiles of the 3y Ps decay for films with different porosity (MSSQ denoted the value for an unfoamed film). Right: Fit to the data for 30% porosity, using a model [16] (thick line), accounting for Ps formation (thin solid line) and escape (dashed line).

The onset of Ps escape can also be measured by DBS in much reduced measurement times of V* -V% hour duration [17] by means of the "3y-to-2y" annihilation ratio. In vacuum all ortho-Ps annihilates into three photons. Inside a pore channel the chance for 3y decay compared to 2y pick-off annihilation decreases with the number of wall collisions necessary to reach vacuum (Figure 3, bottom). In a homogeneous film without interconnected pores the 3y-to-2y" ratio remains constant with implantation depth. When pores are connected the ratio decreases with a characteristic escape depth that is related to the length of the connected pore path. This is illustrated in Figure 6 left. The sharply decreasing 3y-signal at <0.1 urn is due to Ps created at the sample surface independent of the pore structure. This information is used to estimate the diffusion length of Ps and positrons, which governs the probability of populating the pores with positronium. At low porosity (<16%) the signal is constant in the layer. When the implantation depth exceeds 0.5 pm, positrons can reach the silicon substrate, where no Ps is formed.

The fractions of the open and closed porosities in a film can be evaluated from profiles in parallel with Ps escape (Figure 6, left). (Here, pores are open, when a path to the surface exists). Positronium is formed in the bulk material (MSSQ in this case). With increasing porosity an increasing fraction can reach the pores. The chance of annihilation increases as seen in Figure 6 left. If the Ps is in a pore with an open path to vacuum the change for 3y decay increases further. The model [16], producing the best least-square fit for depths <0.4 pm (thick line), evaluates the contributions from Ps formation (thin solid line) with a characteristic depth of ~14 nm, and Ps escape (dotted line) through an open channel to vacuum with a characteristic length of~120 nm.

The asymptotic value of the Ps formation curve (at large depth), depends on the average pore size and density, is a measure of the total film porosity. On the other hand, the asymptotic value of the Ps escape curve can be ascribed to the closed pore fraction, where Ps remains confined. For the given example, the fractions of open and closed porosity in the film are approximately 33% and 67%, respectively. The successful application ofthis analysis, however, relies on the ability to separate the formation and escape curves, whose correlation depends strongly on the near-surface data. While the Ps formation curve may carry a significant error, the Ps escape curve can be determined easily from the data for mean implantation depth, using a simple exponential model.

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