Thermal-strain-induced splitting of heavy- and light-hole exciton energies in CuI thin films grown by vacuum evaporation

Abstract

We have investigated thermal strain effects on excitons in CuI thin films with a thickness of 10--3000 nm grown by vacuum evaporation onto (0001) ${\mathrm{Al}}_{2}{\mathrm{O}}_{3},$ fused silica (quartz), and (001) NaCl substrates. The x-ray-diffraction patterns indicate that the crystalline thin film grown on every substrate is preferentially oriented along the $〈111〉$ crystal axis. All the absorption spectra for the films with a thickness of 10--100 nm clearly show a doublet structure of the heavy-hole and light-hole excitons which are degenerate under a strain-free condition: The heavy-hole exciton has the higher energy for the ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ and quartz substrates, while it has the lower energy for the NaCl one. The splitting energy increases as temperature decreases. This indicates that the in-plane strain, which results from the difference of the thermal expansion coefficients of CuI and the substrate, induces the splitting. The critical layer thickness for the thermal strain relaxation in the ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ substrate is estimated to be 400 nm from the observed exciton energies as a function of the layer thickness. The shifts of the exciton energies due to the thermal strain effects are successfully analyzed on the basis of a $k\ensuremath{\cdot}p$ perturbation theory.