Ultrafast, high resolution spatiotemporal mapping of energy transport dynamics for determination of energy transport properties in silicon

The spatiotemporal dynamics of energy carriers in silicon is studied under ultrafast laser excitation. A subpicosecond temporal resolution and precise, 10 nm spatial resolution system is used to study the spatiotemporal optical response of silicon. Two distinct sets of temporal information from a single experiment are obtained: the evolution of the peak amplitude and the spatial width of the optical reflectance trace. A modified two-temperature energy transport model incorporating the changes of carrier density under ultrafast laser excitation is used to describe the underlying carrier relaxation, carrier-phonon interaction, and energy diffusion process, and is integrated into an optical model to extract fundamental energy transport dynamics and properties. By tracking the evolution of the peak amplitude change and the spatial width with the high accuracy spatiotemporal pump probe system, the underlying relaxation rates and diffusion coefficients can be simultaneously determined. In this work, the ambipolar diffusion coefficient and the carrier-phonon scattering rate coefficient of silicon are found to be $7.3\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ and $3\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$, respectively. Additionally, an ambipolar Auger recombination coefficient in the range of ${10}^{\ensuremath{-}31}\ensuremath{-}{10}^{\ensuremath{-}30}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{6}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ is obtained. This method will be useful to determine transport dynamics and properties in many newly developed semiconductor materials.