Terahertz Emission from Quantum Cascade Lasers in the Quantum Hall Regime: Evidence for Many Body Resonances and Localization Effects Giacomo Scalari, * Ste ´phane Blaser, † and Je ´ro ˆme Faist ‡ Institute of Physics, University of Neucha ˆtel, CH-2000 Neucha ˆtel, Switzerland Harvey Beere, Edmund Linfield, and David Ritchie Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom Giles Davies School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom (Received 17 March 2004; revised manuscript received 14 July 2004; published 1 December 2004) A terahertz quantum cascade laser, operating at   159 m and exploiting the in-plane confine- ment arising from perpendicular magnetic field, is used to investigate the physics of electrons confined on excited subbands in the regime of a large ratio of the magnetic field confinement energy to the photon energy. As the magnetic field is increased above about 6 T, and the temperature lowered below 20 K, the devices are characterized by a very low threshold current density, with values as low as J th  1A=cm 2 , and an increase of gain by five times the low field value. We show that, as with the quantum Hall effect, the key physical process is the localization of the carriers. Evidences for resonant electron-electron scattering processes are directly obtained from light intensity and transport measurements. DOI: 10.1103/PhysRevLett.93.237403 PACS numbers: 78.60.Fi, 42.55.Px, 85.30.Tv, 95.85.Gn The quantum cascade (QC) laser [1] is a coherent source of infrared radiation based on quantum confine- ment and tunneling in semiconductor heterostructures. Gain arises from a population inversion between two- dimensional subbands. This continuum of available states provided by the free in-plane motion of the carriers is responsible for two strong limitations of quantum cascade lasers structures: the relatively short upper state lifetime and the waveguide losses arising from free carrier absorption. Strong in-plane quantization, through which the in- plane parabolic dispersion becomes a set of discrete lev- els, is potentially able to change this picture by acting on the fundamental process governing the lifetime  of the intersubband transition. The application of a strong per- pendicular magnetic field provides a tunable confinement, by breaking the free-electron in-plane dispersion, with energy E i;k  E i   h 2 k 2 =2m  , of each of the two- dimensional states into a set of equidistant Landau levels [ji;ni with E i;n  E i n  1 2   h! c ] separated by the cy- clotron energy  h! c   heB=m  . In previous experiments, modifications of the charac- teristics of a QC laser (both mid-IR and THz) have been studied for cyclotron energies smaller or equal to the photon energy [2–5]. In a recent work, the modification of scattering times by Landau levels has been exploited to enhance the population inversion in a QC laser [6] based on an intersubband transition between the first two ex- cited states of a thick quantum well. We investigate in this Letter such a device, designed to operate at 1.9 THz (7.9 meV ,  ’ 160 m) in the regime of strong magnetic con- finement. The temperatures, mobilities, and magnetic fields correspond to the physics of resonant tunneling in the quantum Hall regime [7]. In contrast to previous work, where an intermediate regime was achieved in which the magnetic confinement was strong enough to modulate the intersubband lifetime but no qualitative change was observed in the laser behavior, we are able to demonstrate two dramatic new features unique to devices operating in this strong field regime: a strong reduction of the waveguide losses and an increase in the gain attributed to carrier localization, and a resonant electron-electron scattering effect. As shown schematically in the inset of Fig. 1(a), the active region of our device, similar in concept to the one presented in Ref. [6], consists of a 55 nm thick undoped GaAs quantum well followed in sequence by a coupled well extractor and a three quantum well injector. The exact layer sequence is given in the caption of Fig. 1. As shown in Fig. 1(d), where a Landau fan of the active region is plotted, the device is originally designed to operate at a field of 2.9 T where the cyclotron energy matches the E 21 energy spacing, reducing the n  2 life- time. At the same time, the energy spacings E 32 and E 31 are, respectively, equal to one and a half times and two and a half times the cyclotron energy, enhancing the n  3 lifetime. This combination of level alignment therefore enhances the n  3 to n  2 population inversion. The structure was grown by molecular beam epitaxy on a semi-insulating GaAs substrate. One hundred peri- ods of the active region were deposited between 0:7 m thick (Si doped, 9  10 17 cm 3 ) lower and 0:08 m thick (Si doped, 5  10 18 cm 3 ) upper GaAs contact layers. The devices were then processed into 100–520 m wide and 0.5–4.7 mm long ridge stripes by wet chemical etching. After thinning to a substrate thickness of PRL 93, 237403 (2004) PHYSICAL REVIEW LETTERS week ending 3 DECEMBER 2004 0031-9007= 04=93(23)=237403(4)$22.50 237403-1  2004 The American Physical Society