Experimental verification of dielectric constant decrease in silicon nanostructures

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During the design of devices using Si nanostructures, it is often important to precisely know the dielectric function ε, since it determines many of their electrical and optical properties. Several theoretical studies have predicted a reduction in the dielectric constant ε as the nanostructure size decreases. Two competing physical mechanisms have been proposed for the reduction: quantum confinement and surface effects (due to a breaking of polarizable bonds on the surface). There have been only a few experimental works on the size dependence of ε, in which ε was measured only for one particular average size. In our work, we have measured the size-dependent ε of thin crystalline slabs at different sizes using variable angle spectroscopic ellipsometry from 270 nm to 1700 nm at the incident angles of 65°, 70° and 75°. The thin crystalline slabs of different thicknesses (~ 15 nm to 2.5 nm) were fabricated by repeatedly subjecting the top Si layer of SOI wafers to plasma oxidation and BOE etching. Ellipsometry and surface profile measurements were performed between each etching step. At the wavelength of 1700 nm, for which silicon is transparent and bulk ε is 11.7, we found thatε was reduced to 7.5 for a 2.5 nm thick Si slab. Our results represent the first systematic measurement of the dielectric function of Si nanostructures as a function of size and represent the first test of the theories.