Porous lowk thin films

Closed PorosityIn closed pore systems, thermalized Ps collides with the pore walls and the resulting Ps lifetime is shortened by positron annihilation with molecularly bound electrons in addition to the captured electron, as shown in Figure 1. The reduced Ps lifetime is related to the pore size. A shorter lifetime will be produced if Ps is trapped in a smaller pore. Furthermore, a distribution of Ps lifetimes may result if there is a distribution of pore sizes. We have developed a physical model of the trapping, diffusion, and annihilation of Ps in porous films in order to determine the poresize distribution from the PALS spectrum. The sample films to illustrate this methodology is the porous MSSQ films supplied by IBM. Figure 2 are the PALS lifetime spectra of the nonporous MSSQ and porous MSSQ. Only very short Ps lifetimes (1.5 and 6 ns) are fitted in the nonporous MSSQ. They correspond to the nanovoids in the polymer matrix due to packing. The porous film, however, shows longlived Ps events that can not be adequately fitted with a singer lifetime, i.e., a distribution of Ps lifetime is required. To focus on the mesoporous part of the time spectrum, we fit data for t beyond 60 ns, thus avoiding the short components with lifetimes less than 6 ns. Using a fitting program CONTIN, we can get the lifetime distribution in the porous MSSQ as shown in Figure 3. Given a statistically acceptable Ps lifetime distribution, we transformed it into a pore size distribution, or more specifically, the specific pore volume as a function of mean free path, which is proportional to the volumetosurface area ratio (l=4V/S). A key step in the transformation is a correction that must be made for Ps diffusing to and preferentially trapping in pores of large surface area. The fractional pore volume distribution as a function of meanfree path, l, is given by
where dN_{Ps}/dt is the Ps lifetime distribution and dt/dl is the pore size calibration from our extended TaoEldrup model. Figure 4 shows the pore volume distributions obtained from the lifetime distributions in Figure 3 using the extended TaoEldrup calibration model (the two pore geometry models are: an infinitely long, squarechannel 2D pore model, and a 3D cubic pore model). The systematically larger pore sizes deduced using the channels as compared with the cubic pores is indicative of the typical systematic error that would be assinghed in the determination of these distributions. Presumably, the "correct" distribution falls somewhere between these limiting cases of pore dimensionality.


Figure 1. Ps behavior in closed pores.


Figure 2. PALS spectra of nonporous MSSQ and porous MSSQ films 

Figure 3. Ps lifetime distribution in the porous MSSQ film 

Figure 4. Deduced pore size distribution 

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