Effect of Auger recombination on transient optical properties in XUV and soft X-ray irradiated silicon nitride

Spatially encoded measurements of transient optical transmissivity became a standard tool for temporal diagnostics of free-electron-laser (FEL) pulses, as well as for the arrival time measurements in X-ray pump and optical probe experiments. The modern experimental techniques can measure changes in optical coefficients with a temporal resolution better than 10 fs. This, in an ideal case, would imply a similar resolution for the temporal pulse properties and the arrival time jitter between the FEL and optical laser pulses. However, carrier transport within the material and out of its surface, as well as carrier recombination may, in addition, significantly decrease the number of carriers. This would strongly affect the transient optical properties, making the diagnostic measurement inaccurate. Below we analyze in detail the effects of those processes on the optical properties of XUV and soft X-ray irradiated Si$${_3}$$ 3 N$$_4$$ 4 , on sub-picosecond timescales. Si$${_3}$$ 3 N$$_4$$ 4 is a wide-gap insulating material widely used for FEL pulse diagnostics. Theoretical predictions are compared with the published results of two experiments at FERMI and LCLS facilities, and with our own recent measurement. The comparison indicates that three body Auger recombination strongly affects the optical response of Si$${_3}$$ 3 N$$_4$$ 4 after its collisional ionization stops. By deconvolving the contribution of Auger recombination, in future applications one could regain a high temporal resolution for the reconstruction of the FEL pulse properties measured with a Si$${_3}$$ 3 N$$_4$$ 4 -based diagnostics tool.