Porous low-k thin films




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  Closed Porosity

In 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 pore-size 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 non-porous MSSQ and porous MSSQ.  Only very short Ps lifetimes (1.5 and 6 ns) are fitted in the non-porous MSSQ.  They correspond to the nanovoids in the polymer matrix due to packing.  The porous film, however, shows long-lived 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 volume-to-surface 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 mean-free path, l, is given by 

where dNPs/dt is the Ps lifetime distribution and dt/dl is the pore size calibration from our extended Tao-Eldrup model.  

Figure 4 shows the pore volume distributions obtained from the lifetime distributions in Figure 3 using the extended Tao-Eldrup calibration model (the two pore geometry models are: an infinitely long, square-channel 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 non-porous MSSQ and porous MSSQ films

Figure 3.  Ps lifetime distribution in the porous MSSQ film

Figure 4. Deduced pore size distribution 

  • PALS can be used to detect closed pores in thin films.  Lifetime distributions can be converted into pore-size distributions. 


  • D. W. Gidley, T. L. Dull, W. E. Frieze, J. Sun, A. F. Yee, C. V. Nguyen, and D. Y. Yoon, Determination of Pore-Size Distribution in Low-Dielectric Thin Film, Applied Physics Letter, 76, 10, 1282 (2000)