Processing and Characterization of Silica Xerogel Films for Low-K Dielectric Applications
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solution of TMCS in hexane. All the films were then dried at rate of 1 °C/min. to 200 'C in air. The thickness and refractive index (R.I.) of the films were measured by ellipsometry at X = 632.8 nm, 0 = 700. Interferometry and profilometry were used to obtain an estimate of the film thickness to determine the correct ellipsometric period. The porosity of the films was obtained from the R.I. using effective medium theory [10]. Rheological Measurements Rheological measurements of the acid-base catalyzed sols were performed from the time of addition of base catalyst (t = 0) to gelation. Gelation is defined as the time at which an abrupt rise in viscosity occurs and which leads to a loss of fluidity in the material. Practically, a viscosity of 70 cP was adequate to define the gel time to within a second or so. The measurements were performed in a rotating cylinder rheometer. At a constant shear rate, viscosity and shear stress with time were measured. The shear rate was varied from sample to
sample to obtain viscosity versus shear rate as well as shear stress vs. shear rate plots over times ranging from 1 minute after the addition of base catalyst to gelation (about 14 minutes at 300 C for all R = 2 samples). Five xerogel films, spun from sols at different stages of polymerization, were used to assess the thickness uniformity of the resulting films [11]. The spin coater was sealed and the atmosphere above the wafer was saturated with ethanol to eliminate solvent evaporation from the wafer surface during spinning. Spinning was done at 2000 rpm for 10s so spin coating was complete well before the sol gelled. The samples were aged in EtOH/ 0.25 M NH 4OH solutions for 2 hrs. at 50' C. The effect of spin speed on the final film thickness was also considered. Films (0.0 7 tgei, R=2) were spin-coated in a saturated atmosphere at spin speeds ranging from 1000 to 5900 rpm for 10 sec. Following spin coating, each film was aged, silylated and dried exactly as described above. The gradual transition from a Newtonian to a shear thinning fluid observed by Sacks and Sheu [12] for acid as well as base catalyzed gels, holds true for the two-step acid-base catalyzed gels as well. Figure 1 shows the shear stress as a function of the shear rate at five different stages of polymerization for the sol. Best fit straight lines have been drawn through the data in accordance with a power-law model. The slope of each line represents the power law index, n, and the intercept is the natural log of the power-law parameter g.. The sol remains Newtonian (n - 1) for a time up to about 0.7 tgel and then changes to shear thinning (n
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