Coherent Acoustic Phonon Oscillations in Ge Using Pump-Probe Time-Resolved Spectroscopic Ellipsometry

Photoexcitation of bulk materials can create hot charge carriers that relax by transferring energy to the lattice, hence exciting phonons in the process. By photoexciting the material through femtosecond laser pulses, coherent acoustic phonon (CAP) oscillations at picosecond time scales are generated via this method. These CAP oscillations are related to an increase in charge carrier density, as well as strain triggered by the laser pulse, however details of this relationship are scarce in the literature. CAP oscillations affect the pseudo-dielectric function (DF) of the material, which makes time-resolved spectroscopic ellipsometry ideal to understand the processes in hand.



The present work aims to describe the relationship between CAP oscillations and charge carrier density, as well as surface orientation dependence via femtosecond pump-probe ellipsometry of Ge. Photoexcitation is induced by 800 nm laser pump pulses at different intensities, generating a strain pulse that travels normal to the surface within the ∼200 nm penetration depth in the semiconductor. Measurements in Ge at (100), (110), and (111) orientations and charge carrier concentrations ranging from ∼7.5×10²⁰ cm^-3 to ∼3.5×10²¹ cm^-3 were performed. The behavior of these oscillations is characterized by analyzing the changes in the pseudo-DF of Ge as a function of the delay time between the pump and probe pulse. Analyzing the E₁ and E₁+Δ₁ critical points (CP) and the variation of their parameters (energy, broadening, amplitude, and phase) with delay time, the behavior of phonon oscillations can be studied.



In order to determine these parameters, second derivatives of the pseudo-DF were calculated using a linear filter technique based on extended Gauss (EG) functions. The periods of these oscillations are deduced by tracking the energy of these CPs as a function of time.