Space-time study of microplasmas inside silicon induced by infrared ultrashort laser pulses

Full text: Long-wavelength femtosecond lasers are highly desirable for three-dimensional (3D) microfabrication applications in semiconductors that are opaque at the fundamental wavelength of Ti:sapphire lasers. However, experiments show that the intrinsic properties of narrow gap materials prevent the occurrence of confined breakdown in the bulk with tightly focused interaction arrangements. We perform a pump-probe microscopy experiment at 1300-nm wavelength and ≈50 fs pulse duration to investigate the specificity of microplasmas formed by two-photon ionization when the beam is focused below the surface of silicon crystals (NA=0.3). An image of a plasma acquired for a delay of 10 picoseconds after the interaction of a pulse of ≅ 10 nJ energy. This allows us to study the space-time characteristics of the plasmas for laser intensities up to 10¹² W/cm². The measurements reveal a self-limitation of the excitation at a maximum free-carrier density of ≅ 10¹⁹ cm³, which is more than one order of magnitude below the threshold for permanent modification. In parallel, we perform a pump self-absorption measurement to translate the observations in terms of energy balance inside the material and discuss the potential factors that prevent bulk micromachining. We observe that the plasma develops in a pre-focal region for pump pulse energies exceeding 40 nJ leading to a clamping of the intensity at the focus. This is a major reason for the saturation of the maximum free-carrier density that can be achieved. At higher pulse energies, the shape of the microplasma is changed progressively. The observation likely relies on nonlinear propagation effects due to the low threshold for self-focusing in silicon. The overall results underline the limits in local control of silicon excitation, which are inherent to the use of single near-infrared ultrashort Gaussian pulses. In addition, the experiment allows us also to study directly free-carrier dynamics in bulk silicon. We observe that the plasma cylinders expand in 2D and we measure a microplasma lifetime of ≅ 1.5 ns. By combining the observations with simulations, we extract directly the free-carrier diffusion coefficient and recombination time in bulk silicon as a function of free-carrier density up to ≅ 10¹⁹ cm³. This provides an original set of experimental data which must be beneficial for modelling the responses of silicon in various contexts. (author)