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Semiconductor Science and Technology

Coherent dynamics of continuum and bound states in germanium

Thomas Rappen, U. Peter, Georg Mohs, W. Schäfer, Martin Wegener

Published May 1, 1994• 1 citation
Publisher

Abstract

We investigate the coherent dynamics of excitons and continuum states at the direct gap of bulk germanium using femtosecond four-wave mixing. In particular, the dependence on the polarization of the incident beams is studied. Spectrally resolving the diffracted wave exposes a strikingly different behaviour of excitons and continuum states. We explain the different polarization dependences on the basis of the recently discussed density-induced dephasing. Applying a high magnetic field substantially changes the coherent response of the underlying system. This manifests itself in a significant modulation of the spectrally integrated four-wave mixing signal, which is interpreted as the time-resolved cyclotron motion of carriers.

DOI
10.1088/0268-1242/9/5s/004

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physica status solidi (b)•Mar 1, 1996•39 citations
We investigate the coherent dynamics of excitons and continuum states at the direct gap of bulk germanium using femtosecond four-wave mixing. In particular, the dependence on the polarization of the incident beams is studied. Spectrally resolving the diffracted wave exposes a strikingly different behaviour of excitons and continuum states. We explain the different polarization dependences on the basis of the recently discussed density-induced dephasing. Applying a high magnetic field substantially changes the coherent response of the underlying system. This manifests itself in a significant modulation of the spectrally integrated four-wave mixing signal, which is interpreted as the time-resolved cyclotron motion of carriers.
The coherent dynamics of continuum states and their interplay with excitons at the direct gap of germanium (T=1.8 K) is studied by femtosecond four-wave mixing. In order to unambiguously distinguish between the contribution of continuum states and excitons, we spectrally resolve the diffracted wave as a function of time delay for different excitation photon energies. For excitation many binding energies above the direct gap, the spectra exhibit two clearly separated maxima, one narrow line at the exciton and a much broader contribution of the continuum states. Surprisingly, the continuum contribution persists to longer time delays than the exciton. The experimental results are explained in the framework of the semiconductor Bloch equations.
We have studied the coherent emission from bulk semiconductors by spectrally resolved and spectrally integrated four-wave mixing (FWM) with broadband 16-fs pulses in the carrier density range from $1\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ to $6\ifmmode\times\else\texttimes\fi{}{10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ In GaAs, only continuum transitions are excited, while both excitonic and continuum transitions are excited in Al0.06Ga0.94As.{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}.Al0.06​Ga0.94​As. The decay of the FWM signal for positive time delays unambiguously reflects the dephasing of the continuum, irrespective of the excitation of excitonic transitions. We find identical ultrafast sub-20-fs decay times of the coherent emission from continuum transitions in GaAs and Al0.06Ga0.94As,{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As},Al0.06​Ga0.94​As, independent of the excess excitation energy. These decay times depend only weakly on the carrier density for densities below ${10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ The continuum dephasing is analyzed considering carrier-carrier and carrier-LO-phonon scattering in a relaxation rate approach. The excitonic transitions in Al0.06Ga0.94As{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}Al0.06​Ga0.94​As dominate the FWM signal at negative time delays.
We present a unified microscopic approach to four-wave mixing (FWM) in semiconductors on an ultrashort time scale. The theory is valid for resonant excitation in the vicinity of the excitonic resonance and at low densities. The most important many-particle effects, i.e., static and dynamical exciton-exciton interaction as well as biexcitonic effects are incorporated. The internal fields resulting from these interaction processes give rise to pronounced many-particle effects in FWM signals. Our results explain the dependence of FWM signals on the polarization geometry, especially if biexcitons contribute. Time-resolved (TR) FWM experiments show that the diffraction of the interaction induced fields dominate the FWM signals completely. This dominance of the interaction induced field at low temperatures is true regardless of density, detuning, or polarization geometry. While spectrally resolved FWM (-FWM) shows biexcitonic or bound excitonic contributions under various experimental conditions, TR-FWM is always completely delayed, peaking roughly at the dephasing time after both beams passed through. \textcopyright{} 1996 The American Physical Society.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.
Coherent transient spectroscopy of semiconductor nanostructures has become an active field of research in recent years. Most such experiments are analyzed in terms of a simple two-level model in which the effects of interaction and induced fields are ignored. We discuss two very different cases where inclusion of these generally-neglected effects leads to large and important modification in the temporal response of the system. In the first case, interactions between excitons strongly modify the temporal response of four-wave-mixing (FWM) signals from quantum wells. This is the temporal analog of well-known effects in the spectral domain, such as bleaching of the exciton absorption and bandgap renormalization. In the second case, the shape of a low-intensity pulse is severely distorted after transmission through a typical quantum well sample. Interferometric measurements show that reradiation of induced polarization is responsible for the distortion. The distortion depends strongly on the dephasing time and has important implications for all time-resolved measurements. 1.
Abstract This paper studies coherent excitons in the presence of alloy disorder by femtosecond degenerate four‐wave mixing on ternary (ZnCd)Se/ZnSe quantum wells. The use of very low excitation densities enables to uncover an impurity‐mediated exciton dephasing time of (16 ± 2) ps and a related homogeneous exciton width of only 80 μeV. At higher densities, the coherence loss speeds up dramatically due to exciton‐exciton interaction. Separating the contributions from inhomogeneous (photon echo) and homogeneous broadening to the spectrally resolved decay transients allows to deduce the energy dependence of the dephasing time across the disorder broadened exciton ensemble. Further, pronounced biexciton resonances are observed in the signal spectrum which exhibit characteristic polarization properties. For cross‐polarized pulses, the biexciton signal shows a striking stimulation when the excitation density is increased.