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Semiconductor Science and Technology

Coherent and incoherent charge carrier response in the femtosecond spectroscopy of semiconductors

Frank J. Adler, Peter Kocevar, J. Schilp, T. Kühn, Fausto Rossi

Published May 1, 1994• 6 citations
Publisher

Abstract

We theoretically estimate the possibility of detectable coherence effects in nonlinear femtosecond pump-and-probe absorption spectroscopy of semiconductors at high excitation energies and densities by hybridizing the quantum mechanical equations of motion for the intraband and interband density matrices of the photoexcited carriers with an ensemble Monte Carlo simulation of the detailed scattering dynamics. We predict realizable experimental scenarios for Rabi-type oscillations in the transient absorption change at the excitation frequency.

DOI
10.1088/0268-1242/9/5s/011

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We theoretically estimate the possibility of detectable coherence effects in nonlinear femtosecond pump-and-probe absorption spectroscopy of semiconductors at high excitation energies and densities by hybridizing the quantum mechanical equations of motion for the intraband and interband density matrices of the photoexcited carriers with an ensemble Monte Carlo simulation of the detailed scattering dynamics. We predict realizable experimental scenarios for Rabi-type oscillations in the transient absorption change at the excitation frequency.
Coherent optical phenomena such as the optical Stark effect, Rabi flopping, photon echo and quantum beating which are well-known in atomic spectroscopy can also be observed in semiconductors by using femtosecond laser pulses. On these short time scales, the quantum coherence of the optical excitations in the solid do not only influence the optical properties but change at the same time the relaxation and dephasing kinetics. The quasi-classical Boltzmann kinetics has to be replaced by quantum kinetics. Coherence leads to the appearance of memory in the scattering integrals. For femtosecond four-wave mixing and pump-and-probe spectroscopy the use of quantum kinetics for LO-phonon and for carrier-carrier scattering will be reviewed.
The influence of carrier correlation processes on the interaction and propagation of femtosecond optical pulses in an inverted semiconductor is theoretically investigated. Microscopically treated Coulomb scattering described from a first-principles theory, including both diagonal and nondiagonal dephasing, is seen to cause considerably different behavior on the dynamics than that modeled by employing a rate-equation approximation. Semiconductor intrinsic optical nonlinearities such as gain saturation and adiabatic following, controlled by microscopic dephasing and relaxation mechanisms, manifest dominantly in ultrafast transient effects that, experimentally, can appear as a typical Kerr-type (instantaneous) nonlinearity. It is shown that one cannot invoke an adiabatic elimination for the polarization equation on femtosecond time scales. The present self-consistent theory successfully explains recent experimental measurements without recourse to parametrized equations. The possible role of non-Markovian relaxation is also discussed.
The dynamics of electrons and holes in semiconductors and semiconductor heterostructures have been extensively discussed in the literature, and are governed by their mutual Coulomb interaction, by their interaction with lattice vibrations (phonons) and by their radiative recombination (for an overview see e.g. Ref. [1]). A powerful technique to study the carrier dynamics in semiconductors utilizes short optical pulses to photoexcite electrons from the valence to the conduction band (i.e. to create electron-hole pairs) that subsequently relax until the photon energy stored in the medium is dissipated and the system has recovered the thermal equilibrium. The dynamics of the carriers photoexcited by the short optical pulse can be followed by monitoring two main optical observables: the interband population difference and the induced polarization. Both quantities decay with time after the photoexcitation due to the carrier dynamics. While the induced polarization (which is an ensemble average over many photoexcited dipole moments) is sensitive to scattering events that break the phase relationship among the individual dipoles and/or with the light field creating them (dephasing processes), the population difference is sensitive only to events that change the energy state of the carriers. Transient coherent optical spectroscopy addresses the time-evolution of the induced polarization in the time-regime during and immediately following the photoexcitation by a short laser pulse, in which the photoexcited dipoles have retained a defined phase relationship among each other and with the exciting coherent radiation.
The availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.
We investigate the optical properties of a Coulomb-coupled double-quantum dot system excited by coherent light pulses. Basic effects of Coulomb coupling regarding linear and nonlinear optical processes are discussed. By numerically solving the Heisenberg equation of motion we are able to present the temporal evolution of the system's density matrix for a wide range of coupling parameters. The two main coupling effects in dipole approximation, biexcitonic shift and F\"orster energy transfer, are investigated and their qualitative and quantitative influence on absorption spectra, Rabi oscillations, and single- and two-pulse excitation is discussed. We present simulated differential transmission spectra to allow for comparison with recent experimental studies.
We investigate the resonance fluorescence spectrum of a bulk semiconductor subject to an injection current and an arbitrarily intense electromagnetic wave. We assume that the electron-hole system is in quasiequilibrium due to the rapid carrier-carrier intraband scattering. The analysis is based on the generalized Bloch equations for semiconductors. Although the fast carrier scattering heavily damps the electronic coherence, it nevertheless allows the total carrier density to adiabatically follow the relatively slowly varying field fluctuations. As a consequence, the resonance fluorescence spectra reveal an asymmetric peak generated by pump scattering from carrier-density pulsations induced by the interference between the pump and a vacuum mode. Similar to the two-level fluorescence and probe absorption, the semiconductor-probe absorption coefficient equals the difference between the resonance fluorescence and reabsorption coefficients. The results are important for nonlinear semiconductor spectroscopy and semiconductor laser instabilities.