LO-phonon emission by hot electrons in terahertz quantum cascade lasers

Recently, a new design of Quantum Cascade Lasers (QCL) operating in the terahertz (THz) domain that combines the advantages of the bound-to-continuum approach together with the use of a LO-phonon resonance was proposed [1]. In this structure, the extraction miniband of the bound-to-continuum transition is aligned resonantly with the first excited state of a large coupled quantum well which exhibits a transition at roughly the LO-phonon energy hwLO. This large energy separation was supposed to significantly reduce the lower state lifetime by allowing optical phonon scattering of the electrons and also to reduce the thermal backfilling of the lower state. We present measurements performed on that particular structure under a strong magnetic field applied parallel to the growth axis. Each level of the QCL is split into a series of Landau levels (LLs). As previously reported, the lifetime of the upper state of the laser transition, and thus the output power, can be modulated by varying the magnetic field. A strong increase of the scattering rate, and therefore a output power minimum, is observed when two LLs are brought into resonance, since in that case electrons can scatter elastically, essentially as a result of the interface roughness. This leads to dramatic oscillations of the emission power which vary as B-1. Besides these features, a second series of oscillations is also clearly observed in this structure. Such minima cannot be accounted by inter-LL resonances or by resonant electron-electron scattering (Auger like effect) as previously observed in different structures. We show that they can be explained by LO-phonon emission from hot electrons injected in the LLs of the upper level. For critical values of the magnetic field, these electrons can resonantly emit one LO-phonon and relax directly to the fundamental LL of the laser transition, leading to a minimum in the output power. We are developing a simple model to calculate the magnetic-field dependence of the upper state lifetime. The first predictions of this model, including both the interface roughness scattering and the LO-phonon emission, account very well for the experimental data