Electron-phonon interaction in quantum cascade lasers probed by Landau level spectroscopy

Resonant electron-LO phonon assisted depopulation of the lower lasing state is one of the common approaches to ensure population inversion and gain of quantum cascade lasers (QCLs) [1]. As a consequence, understanding of the dominating energy relaxation channels is important for development and optimizing of the active region of QCLs, especially built with new or modified materials. In this work we present a method to study the energy of the phonon modes responsible for nonradiative energy relaxation of electrons in the active zone of QCLs. The method is based on the spectrum analysis of the oscillations pattern of QCLs emission intensity as a function of magnetic field applied along the growth direction. These oscillations known as intersubband magnetophonon resonance (IMPR) originate from the resonant phonon assisted scattering of electrons from the upper lasing state into the Landau ladders of lower subbands whenever it is allowed by energy conservation [2] (Fig.1). The IMPR oscillations are periodic in the reciprocal magnetic field. Each lower subband and each phonon mode results in a maximum of the oscillation spectra. Each maximum corresponds to resonant scattering of electrons into the first Landau level of one of the bottom subbands, therefore the difference between intersubband and cyclotron energies gives the energy of phonon modes ensuring the relaxation.
In our experiments we have studied three sets of samples. The first two ones are GaAs/AlGaAs QCLs with different Al concentration in the barriers (33% and 45%) [3]. We clearly demonstrated that in the case of high Al concentration the relaxation via AlAs-like LO phonon can be significant (Fig. 2.). The third set is a In0.73Ga0.27As/AlAs short-wavelength QCL [4]. In this case we found that in spite of the high Al concentration in the barriers and the low GaAs contents in the wells, the nonradiative energy relaxation happens principally via GaAs-like or InAs-like (or mixed modes) phonon emission, while a clear signature of AlAs-like phonons was not observed.

[1] J. Faist et al., IEEE J. Quantum Electronics 38, 533 (2002).
[2] D. Smirnov et al., Phys. Rev. B 66, 125317, (2002); D. Smirnov et al., Phys. Rev. B 66, 121305(R) , (2002)
[3] P. Kruck et al. Appl. Phys. Lett. 76, 3340 (2000) ; H. Page et al., Appl. Phys. Lett. 78, 3529 (2001)
[4] M. P. Semtsiv et al., Appl. Phys. Lett. 85, 1478 (2004).