Magnetic-field-assisted terahertz quantum cascade laser operating up to 225 K

Advances in semiconductor bandgap engineering have resulted in the recent development of the terahertz quantum cascade laser1. These compact optoelectronic devices now operate in the frequency range 1.2–5 THz, although cryogenic cooling is still required2,3. Further progress towards the realization of devices operating at higher temperatures and emitting at longer wavelengths (sub-terahertz quantum cascade lasers) is difficult because it requires maintaining a population inversion between closely spaced electronic sub-bands (1 THz 4 meV). Here, we demonstrate a magnetic-field-assisted quantum cascade laser based on the resonant-phonon design. By applying appropriate electrical bias and strong magnetic fields above 16 T, it is possible to achieve laser emission from a single device over a wide range of frequencies (0.68–3.33 THz). Owing to the suppression of inter-Landau-level non-radiative scattering, the device shows magnetic field assisted laser action at 1 THz at temperatures up to 215 K, and 3 THz lasing up to 225 K. In quantum cascade lasers (QCLs), radiative transitions take place between size-quantized sub-bands within the conduction band of a multi-quantum well system. Quantum well thickness can therefore be varied, allowing the emission wavelength to be tailored, using the same material, to cover a broad range of frequencies. Since the first demonstration of a mid-infrared (MIR) QCL in 1994 (ref. 4), rapid progress has been made in QCL design and materials growth, with the result that QCLs have become the dominant MIR semiconductor laser source5–7. In a terahertz QCL, the photon emission energy is smaller than the longitudinal-optical (LO) phonon energy in the semiconductor material of the quantum well, hn , hv 36 meV (GaAs). In the resonant-phonon design scheme, the population inversion is ensured by selectively injecting electrons through resonant tunnelling into the upper state of the laser transition. Relaxation from the lower radiative state occurs on a subpicosecond timescale into the injector states through LO-phonon emission8–10. This scheme has the highest operation temperature of any terahertz QCL design to date (Tmax 1⁄4 178 K)9,10. Achieving high-temperature operation in terahertz QCLs is difficult, because although hn , hvLO, as the temperature increases, electrons in the upper radiative state gain sufficient in-plane energy to emit an LO-phonon, which results in a fast thermally activated scattering process and a reduction in gain. The use of zero-dimensional confinement in quantum cascade structures has been proposed as a mechanism to suppress non-radiative intersub-band/level relaxation and achieve lower threshold and higher temperature operation11–14. Although appropriate technology does not exist at this time, a magnetic field is an effective tool to analyse and improve the performance of MIR15,16 and terahertz17–19 QCLs in the zero-dimensional limit. A magnetic field changes the two-dimensional parabolic energy dispersion of each size-quantized sub-band 1n(k) into a set of discrete, equidistant, zero-dimensional-like Landau levels (LLs), 1n,N 1⁄4 En þ (N þ 1/2)hvc, separated by the cyclotron energy hv 1⁄4 heB/m*, where n is the sub-band index, N is the LL index, B is the magnetic field, and m* is the energy-dependent electron effective mass. As a result, both radiative and non-radiative transitions are either reduced or resonantly enhanced by the inelastic (LO-phonon assisted15) or (quasi)-elastic (interface roughness, acoustical phonons or impurities16) scattering between different LL states jn,Nl. Here, we exploit this approach of ‘Landau-level engineering’ to explore the ultimate limits of terahertz QCL operation. The samples used were GaAs/Al0.15Ga0.85As terahertz QCLs based on 178 four-quantum-well modules, similar to those in refs 9 and 10. Figure 1a illustrates QCL operation at the designed zerofield operational bias. The laser transition takes place between levels j6l and j5l (E6,5 13 meV ! 3.1 THz) followed by a fast, LO-phonon assisted relaxation towards the triplet ground states j3l, j2l and j1l. A magnetic field allows controlled modulation of the lifetime of the laser transition states when the resonance condition is fulfilled (1i,021j,N2phvc 1⁄4 0), where i is either the upper or lower lasing level, j is a lower sub-band, and p is 0 for elastic scattering and 1 for inelastic scattering. When the upper lasing state is off resonance (quenched non-radiative relaxation) and the lower state is on resonance (enhanced relaxation), population inversion between levels j6,0l and j5,0l increases, thus reducing the lasing threshold current, and increasing laser power and operational temperature. Electronic structure calculations show that such a resonant enhancement of the j6,0l ! j5,0l transition ( 3 THz), 14,0213,1 1⁄4 0, takes place near 20 T and in a range of voltage biases between 50 and 70 mV per period (Fig. 1). When the voltage bias is increased above 60 mV per period, levels j5,0l and j4,0l are separated, but still have a large dipole-matrix element, resulting in the possibility of dual-wavelength ‘cascaded’ laser transitions: j6,0l ! j5,0l ( 3 THz) followed by j5,0l ! j4,0l ( 1 THz). Further increasing the voltage bias separates levels j8,0l, j7,0l and j6,0l. At these biases, both j8,0l ! j7,0l and j5l ! j4l transitions have large dipole-matrix elements, and can be enhanced by a LL resonance at 31 T (Fig. 1e) and 23 T (see also Supplementary Information, Discussion). Following the model of inhomogeneous LL broadening caused by the macroscopic fluctuations of quantum well parameters20, a phenomenological Gaussian broadening of the LLs with a width of d1⁄4 4 meV is introduced, which is consistent with previous estimates in mid-infrared and terahertz QCLs of 2–6 meV (refs 16, 19, 20). The electrical characteristics, current density J, voltage/period V, emitted optical power P as well as emission spectra were