Super-diffusion of excited carriers in semiconductors

The ultrafast spatial and temporal dynamics of excited carriers are important to understanding the response of materials to laser pulses. Here we use scanning ultrafast electron microscopy to image the dynamics of electrons and holes in silicon after excitation with a short laser pulse. We find that the carriers exhibit a diffusive dynamics at times shorter than 200 ps, with a transient diffusivity up to 1,000 times higher than the room temperature value, D₀≈30 cm²s^-1. The diffusivity then decreases rapidly, reaching a value of D₀ roughly 500 ps after the excitation pulse. We attribute the transient super-diffusive behaviour to the rapid expansion of the excited carrier gas, which equilibrates with the environment in 100-150 ps. Numerical solution of the diffusion equation, as well as ab initio calculations, support our interpretation. Our findings provide new insight into the ultrafast spatial dynamics of excited carriers in materials.