Dielectric constant reduction in silicon nanostructures

Abstract

We performed a systematic measurement of the dielectric function of Si nanoslabs as a function of their thickness using spectroscopic ellipsometry from $0.73\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ $(1700\phantom{\rule{0.3em}{0ex}}\mathrm{nm})\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}4.58\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ $(270\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$. The Si nanoslabs were obtained by repeatedly thinning down the top Si layer in silicon-on-insulator wafers by successive oxidation and HF etching. As predicted by the theories, both real and imaginary parts of the dielectric function are reduced as the thickness decreases. The dielectric constant of $3.3\text{\ensuremath{-}}\mathrm{nm}$-thick nanoslabs measured at $0.73\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, below the band gap energy of bulk Si, is reduced by $\ensuremath{\sim}13%$ (from 12 to 10.4) compared to the bulk value. The measured size dependence is in qualitative but not quantitative agreement with the most applicable theory.