Relativistic Doppler frequency up-conversion and probing the initial relaxation of a non-equilibrium electron-hole plasma in silicon

We demonstrate experimentally the relativistic Doppler frequency up-conversion of the THz pulses from the counter-propagating ionized plasma front in silicon. The observed frequency up-conversion can be well modeled by the 1D FDTD simulations if significant short scattering time (well below 10 fs) in the plasma is assumed. To further elucidate the scattering rate in the electro-hole plasma, we performed pump probe experiment employing ultra-broadband (150 THz) THz-Mid-Infrared pulse. The results show the scattering time decreases from ~200 fs down to ~20 fs when the carrier density increases up to 10¹⁹-cm^-3, and then saturates for higher densities. Such scattering time dependence on plasma carrier density can be very well fitted by the Drude model for thermalized electron-holes, and the saturation behavior is attributed to electron-hole phase-space restriction as the plasma becomes degenerate. The resultant much shorter scattering time measured with non-thermalized plasma is in good accordance with the Doppler experiment, which demonstrates Doppler geometry an effective method for probing non-equilibrium plasma dynamics.