Coherent charge transport in semiconductor quantum cascade structures

Abstract

Quantum cascade structures have found extensive application in electrically driven semiconductor lasers working in the mid- to far-infrared spectral range. Optical amplification in such unipolar devices is based on a population inversion between quasi-two-dimensional conduction subbands in coupled quantum wells. The population inversion in the active region is generated by electrons tunnelling from an injector region through a barrier into the upper laser subband and by ultrafast extraction of these electrons out of the lower laser subband through a barrier into the next injector region. Such transport processes on ultrafast timescales have been the subject of extensive experimental and theoretical work without, however, reaching a clear physical picture of the microscopic electron dynamics. In this review, we report a comprehensive experimental study of electron transport in electrically driven quantum cascade structures. Ultrafast quantum transport from the injector into the upper laser subband is investigated by mid-infrared pump–probe experiments directly monitoring the femtosecond saturation and subsequent recovery of electrically induced optical gain. For low current densities, low lattice temperatures and low pump pulse intensities, the charge transport is dominantly coherent, leading to pronounced gain oscillations due to the coherent motion of electron wavepackets. For higher current densities, lattice temperatures, or pump intensities, the gain recovery shows an additional incoherent component, which essentially follows the pump-induced heating and subsequent cooling of the carrier gas in the injector.

Time-Resolved Investigations of Electronic Transport Dynamics in Quantum Cascade Lasers Based on Diagonal Lasing Transition

“…14; the experimentally relevant scattering rate is the average phonon scattering. Considering the lattice temperature is always higher than the heat sink temperature [33], the calculated tunneling rate is approximately two to three times smaller than the measurement results.…”

“…A rigorous understanding of the dynamical superlattice relaxation would require a full quantum-mechanical model coupled to Poisson's equation, with hot carrier effects included at the same level [33]. However, if the field across the superlattice injector is sufficiently low that the transport can be described in a low-field transport regime (mobility regime), then one can apply an approximate model to understand the essential features.…”

Density-matrix theory of the optical dynamics and transport in quantum cascade structures: The role of coherence

“…According In Ref. 31, the lifetime of the superposition of the two resonant states T scatt ≈ 1 ps which is much longer than the observed oscillation of T osc ≈ 500 fs, and thus 2Ω > Γ which is the regime where gain oscillations are expected. In Ref.…”

“…The question arises whether coherent optical effects after ultrafast optical excitation can be observed in the opposite regime, where coherences were shown not to be important in the stationary transport. Recently, optical pumpprobe measurements in mid-infrared 29,30,31,32 and THz QCLs 33 have shown an oscillatory behavior attributed to (coherent) resonant tunneling through the injection barrier. In this section, this effect is investigated with respect to the relation between the tunnel coupling and the level broadening.…”

Many-body interaction in resonant tunneling of terahertz quantum cascade lasers

“…The analysis of the gain recovery process is very important for understanding the physical mechanism in the terahertz QCLs. 11,12 The sequential resonant tunneling in a bound-to-continuum terahertz QCL has been proved and the gain recovery time has been given in the time-resolved measurements lately. 13 In the past decades, much effort has been made to develop theories and models for simulating the electron transport in terahertz quantum cascade structures.…”