Subnanometer-scale size effects in electronic spectra ofSi∕SiO2multiple quantum wells: Interferometric second-harmonic generation spectroscopy

Abstract

Resonant electronic structure of amorphous-$\mathrm{Si}∕\mathrm{Si}{\mathrm{O}}_{2}$ multiple quantum wells (MQWs) is studied by means of second-harmonic generation (SHG) spectroscopy and SHG interferometric spectroscopy of the MQW samples with the Si quantum well thickness $d$ ranging from $1.00\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}0.25\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The observed modification of the SHG spectra upon decreasing $d$ is interpreted using a combination of the resonant two-subband approximation for the nonlocal optical response of each quantum well with the generalized transfer-matrix formalism for the description of light propagation across the whole MQW structure. Agreement with the experiment shows that the description of the quadratic optical response of the MQW structure within the model of a nonlocal piecewise-continuous medium remains valid on the subnanometer scale.