The pump-probe technique is a powerful tool for probing and characterizing the electronic and structural properties of short-lived excited states of materials. Upon the absorption of photons of the pump, excited states of the materials are established. Relaxation of these states reflects many physical aspects of the materials which can be tracked by a consequent beam – the probe. In this study, we present a conventional pump-probe technique at the University of Amsterdam and its application for tracking relaxation of charge carriers in thin films containing Si and Ge nanocrystals embedded in SiO2 matrix. The pump beam is obtained from a 150-fs laser pulse with the photon wavelength at 340 nm. The probe beam is constituted from a white-light beam in the wavelength range from approximately 900 - 1300 nm (0.9 - 1.4 eV). The photon-generated charge carriers feature with multi-exponent decay dynamics, involving to different physical characteristics. The fast decay components of about few ps time scale arise from defect-related trapping or Auger processes, while the slow decay components of about few hundred ps come from relaxation of the exciton left in the semiconductor nanocrystals. The deep-insight characterization of the materials involving to individual relaxation processes are presented and discussed.