Terahertz scattering-type near-field microscopy quantitatively determines the conductivity and charge carrier density of optically doped and impurity-doped silicon

Abstract

A terahertz scattering-type scanning near-field optical microscope is used for nano-scale non-invasive conductivity measurements on bulk silicon samples. We first investigate the case where the density of charge carriers is determined by optical interband excitation. We show that the amplitude and phase of the near-field signal are reproduced by simulations based on an established near-field interaction model, which takes the Drude conductivity, ambipolar carrier diffusion, and known recombination properties of photo-excited carrier pairs in Si into account. This study is then extended to impurity-doped Si. We demonstrate that the phase of the near-field signal, which can easily be measured in absolute terms, allows us to quantitatively determine the conductivity of the specimens, from which the carrier density is derived based on the known carrier momentum relaxation time. A measurement at a single properly chosen terahertz frequency is sufficient. The technique proposed here holds promise for the spatially resolved quantitative characterization of micro- and nanoelectronic materials and devices.