Calculation of Pore Size Distribution in the Ellipsometric Porosimetry: Method and Reliability
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where y and VL are surface tension and molar volume of the liquid adsorbate, respectively. The curvature radius rm is close to the pore radius. A method of wide application is an adsorption porosimetry with the use of nitrogen adsorption near the boiling temperature and weighing of the adsorbate condensed in pores. However, the sensitivity of the traditional microbalance technique allows to work only with large samples. In order to characterise the PSD in thin films, the film must be scratched off from tens of substrates in order to get enough material. The very low temperature which is necessary for nitrogen porosimetry creates additional problems. This is a reason why development of a non-destructive and room temperature porosimetry for the thin film application is extremely valuable. 81 Mat. Res. Soc. Symp. Proc. Vol. 565 ©1999 Materials Research Society
Several publications related with the measurement of the pore size distribution in thin films are available. In these papers the measurement of the adsorption/desorption processes were carried out by the quartz crystal microbalance (QCM) [2,3], surface acoustic wave sensor (SAW) [4,5] and ellipsometry [6,7]. In the case of QCM and SAW the porous film should be deposited on top of a special sensor. These versions of the adsorption porosimetry in principle are close to the classical one because they use the mass determination of the adsorbed vapors. These methods can not be used for films deposited onto a silicon substrate. The ellipsometric porosimetry is more promising: 1. All measurements can be carried out on a porous film, deposited directly on top of a silicon wafer or any solid substrate. Technological layers between the silicon substrate and porous dielectrics do not induce any problems for the measurements. 2. Because of laser probe is used, small surface areas can be analyzed. Therefore the ELP can be used on patterned wafers and compatible with microelectronic technology. 3. Room temperature PSD measurements have been performed using ELP. Therefore, results of the measurements do not have any distortions, related with the used of low temperature nitrogen porosimetry. However, the ELP needs in more sophisticated software. The adsorbate amount is calculated from the measured change of the optical characteristics of porous film during the vapor adsorption/desorption. There are several methods for performing of these calculations based on the equations of Lorentz-Lorenz, Newton-Laplace, Bragg-Pippard etc. [8]. The optical characteristics of the solid part of the porous media and of the liquid adsorbate are used in these calculations. All these equations give quite close results. However, the Lorentz-Lorenz equation is more widely used. The correct choice of a proper adsorbate for the room temperature porosimetry is an additional important issue. This adsorbate should be a volatile liquid, because of the need to work near P=Po. It was shown [2,3,5-7] that vapor of some organic solvents can be used for this purpose. Non-polar solvents without permanent
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