THz stimulated emission at interband transitions in HgTe/CdHgTe quantum wells

V.I.Gavrilenko, V.V.Rumyantsev, A.A.Dubinov, S.V.Morozov, N.N.Mikhailov, S.A.Dvoretsky, F.Teppe, C.Sirtori Institute for Physics of Microstructures, Nizhny Novgorod, Russia, gavr@ipmras.ru A.V.Rzhanov Institute of Semiconductor Physics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia Charles Coulomb Laboratory, University of Montpellier & CNRS, Montpellier, France Laboratory of Materials and Quantum Phenomena, University Paris-Diderot, Paris, France

. SE spectra at different temperatures (solid curves) obtained under pulsed pumping with 2.3 µm wavelength and 10 kW/cm 2 intensity for Structure #1 (at both temperatures) and 65 kW/cm 2 for Structure #2 at 175K. SE for Structure #2 at T = 8K was obtained at cw excitation with 0.9 µm wavelength 7 W/cm 2 intensity. Dash curves show PL spectra obtained with the same cw pumping source at 5 W/cm 2 intensity for Structure #1 and 1 W/cm 2 for Structure #2 at 8 K.
The corresponding thresholds are 5 kW/cm 2 and 120 W/cm 2 for SE wavelength ~20 µm (15 THz) and ~10 µm (30 THz) at low temperatures. However, these values are obtained for "below barrier" excitation (ħω < E g in barriers), i.e. when non-equilibrium carriers are generated in QWs only. Taking for estimation the QW absorption as 1% one can find the corresponding carrier density in each QW n th = 1.4×10 11 cm -2 for λ p = 2.3 µm and I th = 0.12 kW/cm 2 pumping intensity. This n th value agrees fairly well with our previous calculations 7 . It also allows estimating the equivalent threshold current density for 5 QWs placed into a p-n junction as j th = 5en th /τ pulse (e is the elementary charge), that for τ pulse = 10 ns gives j th = 11 A/cm 2 . This threshold is low enough to obtain SE under cw excitation: Fig 1. shows the corresponding spectrum, measured with cw pumping at 0.9 µm wavelength.
Obviously, the threshold grows with the SE wavelength and the maximum "operating" temperature T max gets lower. To understand the energetic scale that determines T max let us consider the energy spectrum of Structure #1, presented in Fig.2. One can see that the hole effective mass increases dramatically with k and the dispersion laws in the valence band and the conduction band are no longer quasi-symmetrical. When holes reach larger-mass region the Auger recombination becomes efficient. We have calculated the threshold energies E th for CCHC Auger process (the energetic threshold for CHHH process is high compared to CCHC process, therefore the latter is less important) given in Fig. 2. For both struc-tures under study we get k B Т max ≈ E th /2. In Fig. 2 one can see also that the detrimental impact of side maxima in the valence band can be reduced in QW of pure HgTe with the same bandgap as in Structure #1. As easy to see in this case the threshold energy increases significantly. Effective carrier temperature is affected by their heating by the pumping radiation. At the excitation with radiation wavelength 2.3 μm the carrier heating effect is noticeable already in QW structures emitting at wavelengths μm about 14 μm. For the Structure #1 emitting at λ ~ 20 μm the SE quenching with the increase of pumping power takes place just after the SE arising. We have demonstrated that the pumping with CO 2 -laser (λ = 10.6 μm) drastically decrease the carrier heating and the SE intensity monotonously grows with pump power. Thus, the effect of SE quenching with the pump power, observed in Ref.8 is not fundamental but results from using the short wavelength excitation.
Carrier lifetimes are expected to decrease for QW structures with narrower bandgap. The sub-nanosecond carrier lifetimes have been explored via the pump-probe measurements of a sample's transmission using THz free electron laser FELBE at Helmholtz-Zentrum Dresden-Rossendorf 9 . For HgCdTe QW with E g = 20 meV (f ~ 4.8 THz) the carrier lifetime proved to be about 100 ps for carrier density 10 11 cm -2 that is sufficient to achieve the population inversion. One can estimate a threshold pumping intensity of 10 kW/cm 2 for an optically pumped laser exploiting such QWs as an active media. Thus, HgCdTe QWs should be able to provide amplification of radiation at interband transitions down to 5 THz (λ = 60 μm).
In conclusion, we demonstrated stimulated emission at wavelengths up to 20.3 µm (14.7 THz) from HgCdTe based waveguide quantum well heterostructures. Nonradiative Auger recombination is shown to be suppressed compared to bulk HgCdTe solid solutions due to the "symmetry" of electron and hole energy-momentum laws. Results of time-resolved pave the way to obtain stimulated emission in wide THz range down to 5 THz.