Theory of Coherent Phonon Oscillations in Bulk GaAs

Abstract

In this chapter we discuss the theory of coherent phonon oscillations in semiconductors with emphasis on bulk GaAs. We first present and solve a phenomenological model that predicts oscillations after carriers are rapidly created by an ultrafast laser pulse. Next, we present a microscopic justification of the phenomenological model that is applicable to both polar and nonpolar semiconductors. We show that for nonpolar semiconductors such as Ge, the coherent lattice displacement is related to a quantum-mechanical average of a single phonon creation operator, and we derive the equation of motion for the coherent phonon amplitude. Our results show that the coherent oscillations are not caused by synchronous motion between different modes, but are instead due to a multiphonon process within a single mode that leads to a macroscopic occupation of that mode. Finally, we look at the specific case of GaAs, which is a polar material. In GaAs the driving force for the oscillations is the screening of a DC surface depletion electric field by photoexcited electrons and holes. We formulate and present a microscopic theory for the plasmon-phonon oscillations. Our results show that for an idealized situation with homogeneous plasma density, plasmon-like oscillations should dominate the transient behavior over the LO phonon oscillations. This does not agree with experiments. To get agreement with experiment, the inhomogeneous density-distribution generated by the laser pulse must be taken into account. When one accounts for the inhomogeneous density of the laser pulse, then the density-dependent plasmon oscillations average out, leaving only density-independent LO phonon oscillations present in the transient optical response.