Intrinsic interfacial thickness, interface between

As mentioned in Sect. 2.2.2, the effective interfacial width wD characterizing the bilayer structure may be broadened beyond its intrinsic value w, yielded by a mean field theory (Eqs. 10 and 12). This is due to the capillary wave excitations causing the lateral fluctuation of the depth Ie(x,y) corresponding to the midpoint of the internal interface between coexisting phases. This fluctuation is opposed by the forces due to external interfaces, which try to stabilize the position Ie(x,y) in the center of the bilayer [6, 224, 225]. It was suggested recently [121] that the spectrum of capillary waves for a soft mode phase should be cut off by qb and y. This leads to the conclusion that the effective interfacial width wD should depend on the film thickness D as (wD/2)2= b2+ bD/4. Experimental data [121] obtained for olefinic blends (at T close to Tc) indeed show remarkable increase of the measured interfacial width from wd(D=160 nm)=14.4(3) nm to wd=45(12) nm for thickness D-660 nm, where wD levels off (because is comparable with lateral sample dimensions). This trend is in qualitative agreement with the formula due to capillary oscillations in the soft mode phase . However... 

It has been reported that the permittivity of a material decreases with decreasing film thickness. As a result, the capacitance increase is not as large as expected based on the inverse relation between C and t. The reason is the existence of dielectric dead layers at the dielectric s surface and interfaces, or interfacial layers between the dielectric and its neighboring materials, which in both cases are characterized by a much lower permittivity. As the dead layer is in series with the dielectric, the effective permittivity is reduced as well. In the case of MOS devices, a notorious interfacial reaction is the formation of silicates between the dielectric and silicon, hence the importance of the thermodynamic stability of the dielectric on Si. In the case of MIM (metal-insulator-metal) devices, alloy formation or in-diffusion of the electrode is a possibility, for example, in the case of Pt. However, also in case no secondary phases are formed, permittivity can be thickness dependent. Possible reasons include breaking of the lattice periodicity or the presence of ion vacancies at the interface, which disturb or inhibit the soft phonon mode and other intrinsic effects [6]. It was shown that electrodes with a shorter electronic screening length, for example, Pt or Au, lead to a smaller dead layer effect compared with, for instance, SrRuOs electrodes [13]. 

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