Fundamental temperature-dependent properties of the Si nanocrystal band gap

Abstract

Ever since the first reports about low-temperature photoluminescence (PL) measurements of Si nanocrystals Si (NCs), a severe deviation from the equations commonly used to describe the temperature dependence of the band-gap energy for bulk materials was reported. Our analysis reveals that the formerly observed deviation is solely attributed to too high excitation power densities that cause a preferential emission enhancement of the smaller NCs within a size distribution, due to the temperature dependence of the radiative exciton lifetime. We report on the successful fit of the temperature-dependent band-gap energy of quantum-confined silicon. By means of four size-controlled Si NC samples (1.5 to 4.5 nm), we are able to prove the validity of these equations down to liquid He temperatures, if sufficiently low excitation power densities (500 $\ensuremath{\mu}$W/cm${}^{2}$) are used. Thereby, it is shown that the characteristics of the band-gap widening of quantum-confined nanocrystalline Si obeys to the same physical law as the bulk Si crystal. In addition, the previously observed decrease of the PL intensity for decreasing temperatures is demonstrated to have its origin in the same measurement artifact caused by excitation saturation.