The THz spectral range (0.5–10 THz) lies in the gap between frequency ranges accessible with conventional semiconductor electronic and photonic devices. At the lower end of the THz gap, frequency multipliers using electronic devices have reached ∼1.6 THz with milliwatt (mW) optical power at room temperature.1,21. J. V. Siles, K. B. Cooper, C. Lee, R. H. Lin, G. Chattopadhyay, and I. Mehdi, “ A new generation of room-temperature frequency-multiplied sources with up to 10× higher output power in the 160-GHz–1.6-THz range,” IEEE Trans. THz. Sci. Technol. 8, 596–604 (2018). https://doi.org/10.1109/TTHZ.2018.28766202. I. Mehdi, J. V. Siles, C. Lee, and E. Schlecht, “ THz diode technology: Status, prospects, and applications,” Proc. IEEE 105, 990–1007 (2017). https://doi.org/10.1109/JPROC.2017.2650235 Both quantum cascade laser-pumped molecular lasers (QPMLs)33. P. Chevalier, A. Amirzhan, F. Wang, M. Piccardo, S. G. Johnson, F. Capasso, and H. O. Everitt, “ Widely tunable compact terahertz gas lasers,” Science 366, 856–860 (2019). https://doi.org/10.1126/science.aay8683 and difference-frequency generation (DFG)4,54. M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “ Terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007). https://doi.org/10.1038/nphoton.2007.705. Q. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “ Continuous operation of a monolithic semiconductor terahertz source at room temperature,” Appl. Phys. Lett. 104, 221105 (2014). https://doi.org/10.1063/1.4881182 have used infrared quantum cascade lasers (IR QCLs) to generate THz waves at room temperature indirectly. Quantum cascade lasers (QCLs) have several advantages compared to the nonlinear frequency upconversion and downconversion schemes. As fundamental oscillators, THz QCLs inherently have much higher power levels and efficiencies than nonlinear frequency conversions. At cryogenic temperatures, THz QCL systems can reach watt-level optical power in pulse mode6–86. L. Li, L. Chen, J. Freeman, M. Salih, P. Dean, A. Davies, and E. Linfield, “ Multi-Watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017). https://doi.org/10.1049/el.2017.06627. Y. Jin, J. L. Reno, and S. Kumar, “ Phase-locked terahertz plasmonic laser array with 2 W output power in a single spectral mode,” Optica 7, 708–715 (2020). https://doi.org/10.1364/OPTICA.3908528. L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. Davies, and E. Linfield, “ Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett. 50, 309–311 (2014). https://doi.org/10.1049/el.2013.4035 and tens of milliwatts in continuous wave operation with ∼1% efficiency.9,109. A. Khalatpour, J. L. Reno, and Q. Hu, “ Phase-locked photonic wire lasers by π coupling,” Nat. Photonics 13, 47–53 (2019). https://doi.org/10.1038/s41566-018-0307-010. A. Khalatpour, J. L. Reno, N. P. Kherani, and Q. Hu, “ Unidirectional photonic wire laser,” Nat. Photonics 11, 555–559 (2017). https://doi.org/10.1038/nphoton.2017.129 In addition, THz QCL gain medium can be used to develop THz sources, such as frequency combs11,1211. D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “ Terahertz laser frequency combs,” Nat. Photonics 8, 462–467 (2014). https://doi.org/10.1038/nphoton.2014.8512. M. Rösch, G. Scalari, M. Beck, and J. Faist, “ Octave-spanning semiconductor laser,” Nat. Photonics 9, 42–47 (2015). https://doi.org/10.1038/nphoton.2014.279 and radiation amplifiers.1313. T.-Y. Kao, J. L. Reno, and Q. Hu, “ Amplifiers of free-space terahertz radiation,” Optica 4, 713–716 (2017). https://doi.org/10.1364/OPTICA.4.000713 Another advantage of THz QCLs is that they enable cavities with unique radiation properties. For instance, the local oscillator at 4.74 THz for GUSTO,1414. C. Walker, C. Kulesa, A. Young et al., “ Gal/Xgal U/LDB spectroscopic/stratospheric THz observatory: GUSTO,” in Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy XI ( SPIE, 2022), Vol. 12190. which is a NASA balloon-borne mission, has been developed using a tunable unidirectional cavity that achieves ∼10 mW of CW power with less than 1.8 W dissipated power, and it is cooled with a compact Stirling cooler (CryoTel®CT) weighing as little as 5 kg.1515. A. Khalatpour, A. K. Paulsen, S. J. Addamane, C. Deimert, J. L. Reno, Z. R. Wasilewski, and Q. Hu, “ A tunable unidirectional source for GUSTO's local oscillator at 4.74 THz,” IEEE Trans. THz. Sci. Technol. 12, 144–150 (2022). https://doi.org/10.1109/TTHZ.2021.3124310 The required size for cooling and the system's vibration will be significantly reduced by using thermoelectric (TE) coolers. Compact, hand-held, TE-cooled THz QCLs were made possible by a record high operating temperature of Tmax ∼ 250 K.1616. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “ High-power portable terahertz laser systems,” Nat. Photonics. 15, 16–20 (2021). https://doi.org/10.1038/s41566-020-00707-5 Here, we report on further improvement to the maximum operating temperature Tmax ∼ 261 K.Figure 1(a) shows a schematic of a three-level laser to illustrate the dominant scattering processes in THz QCLs.1717. J. Faist, Quantum Cascade Lasers ( Oxford University Press, Oxford, 2013). Here, the upper lasing level, the lower lasing level, and the ground states in the nth module are denoted by |un⟩, |ln⟩, and |gn⟩, respectively. IFR, imp, e–e, LOem, and LOabs represent interface roughness scattering, impurity scattering, electron–electron scattering, LO-phonon emission, and LO-phonon absorption, respectively. In this scheme, electrons are injected into |un⟩ and extracted from |ln⟩ through resonant tunneling and scattering with LO-phonons in the heterostructure. The peak gain of intersubband transitions Gp can be described by the oscillator strength ful, the population inversion between the upper and the lower lasing level ΔN, and the transition linewidth Δν as Gp∝ΔNfulΔν. The linewidth is defined as Δν=12π(1τu+1τl+2T*) in which τu, τl, and T* are the upper-state lifetime, the lower-state lifetime, and pure dephasing times. The oscillator strength is essentially a wavefunction overlap integral between the upper and lower lasing levels and is defined as ful=(2m*ΔEℏ2)|⟨u|z|l⟩|2, in which z is the growth direction, m* is the effective mass, and ΔE is the energy separation between the two levels. The explicit temperature dependence of ΔN arises from thermally activated, non-radiative LO-phonon emission,1717. J. Faist, Quantum Cascade Lasers ( Oxford University Press, Oxford, 2013). and the so-called thermal backfilling due to LO-phonon absorption from |gn⟩ to |ln⟩.1818. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “ 3.4 THz quantum cascade laser based on LO-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015 (2003). https://doi.org/10.1063/1.1554479 Although the form factors for the emission of photon and LO-phonon are different, both strongly depend on the overlap of wavefunctions between |un⟩ and |ln⟩.1717. J. Faist, Quantum Cascade Lasers ( Oxford University Press, Oxford, 2013). Hence, suppressing LO-phonon emission from the upper state comes at the cost of reducing the optical gain. Consequently, designs with higher ful (vertical designs) have shorter τu than those with a lower ful (diagonal designs). In diagonal designs, a higher carrier concentration (higher doping) can be used to compensate for the reduced optical gain. However, increasing the doping leads to an increase in Δν due to the reduction of τu and T* due to nonradiative elastic processes, including e–e and imp scattering. Therefore, the figure of merit fulτuΔν appears to limit the performance of diagonal designs targeting high temperatures.1919. C. W. I. Chan, A. Albo, Q. Hu, and J. L. Reno, “ Tradeoffs between oscillator strength and lifetime in terahertz quantum cascade lasers,” Appl. Phys. Lett. 109, 201104 (2016). https://doi.org/10.1063/1.4967244Meanwhile, the escape of electrons to the continuum bands has been postulated as an unaccounted mechanism in THz QCLs for their temperature degradation.2020. A. Albo, Y. V. Flores, Q. Hu, and J. L. Reno, “ Two-well terahertz quantum cascade lasers with suppressed carrier leakage,” Appl. Phys. Lett. 111, 111107 (2017). https://doi.org/10.1063/1.4996567 To counteract the escape to the continuum, higher barrier compositions have been used in THz QCL designs.16,20–2316. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “ High-power portable terahertz laser systems,” Nat. Photonics. 15, 16–20 (2021). https://doi.org/10.1038/s41566-020-00707-520. A. Albo, Y. V. Flores, Q. Hu, and J. L. Reno, “ Two-well terahertz quantum cascade lasers with suppressed carrier leakage,” Appl. Phys. Lett. 111, 111107 (2017). https://doi.org/10.1063/1.499656721. L. Bosco, M. Franckié, G. Scalari, M. Beck, A. Wacker, and J. Faist, “ Thermoelectrically cooled THz quantum cascade laser operating up to 210 K,” Appl. Phys. Lett. 115, 010601 (2019). https://doi.org/10.1063/1.511030522. B. Wen and D. Ban, “ High-temperature terahertz quantum cascade lasers,” Prog. Quantum Electron. 80, 100363 (2021). https://doi.org/10.1016/j.pquantelec.2021.10036323. V. Rindert, E. Önder, and A. Wacker, “ Analysis of high-performing terahertz quantum cascade lasers,” Phys. Rev. Appl. 18(4), L041001 (2022). https://doi.org/10.1103/PhysRevApplied.18.L041001 To reduce the increased impact of IFR scattering—which scales quadratically with barrier composition—the number of barriers involved in electron transport should be minimized to reduce Δν. The most straightforward design in this direction is the so-called two-well scheme based on direct phonon depopulation, as illustrated in Fig. 1(b).24,2524. S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “ Two-well terahertz quantum-cascade laser with direct intrawell-phonon depopulation,” Appl. Phys. Lett. 95, 141110 (2009). https://doi.org/10.1063/1.324345925. G. Scalari, M. I. Amanti, C. Walther, R. Terazzi, M. Beck, and J. Faist, “ Broadband THz lasing from a photon–phonon quantum cascade structure,” Opt. Express 18, 8043–8052 (2010). https://doi.org/10.1364/OE.18.008043Figure 1(c) shows the probability density functions of subband states in a THz QCL with a two wells scheme. Here, the injection barrier, radiation well, radiation barrier, and phonon well are labeled, ib,rw,rb, and pw respectively. Due to a shorter module length in this scheme, undesired coupling between neighboring modules may occur at the injection alignment, |in−1⟩→|un⟩. The coupling between |in−1⟩, |un⟩ and the bound states in the neighboring modules, |p1,n⟩, |p2,n⟩, |p1,n+1⟩, and |p2,n+1⟩ was investigated, and by suppressing them, a record-high Tmax=250 K was achieved.1616. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “ High-power portable terahertz laser systems,” Nat. Photonics. 15, 16–20 (2021). https://doi.org/10.1038/s41566-020-00707-5 The energy separation between |in−1⟩ and |p1,n⟩ (denoted as Ei,pp) can be made arbitrarily high to reduce a possible leakage from |in−1⟩ to |p1,n+1⟩.1616. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “ High-power portable terahertz laser systems,” Nat. Photonics. 15, 16–20 (2021). https://doi.org/10.1038/s41566-020-00707-5 However, as discussed in the supplementary material, the suppression of intermodule leakage (by increasing the Ei,pp) places an unfavorable upper limit on fulτLO−emu, where τLO−emu is the lifetime due to nonradiative LO-phonon emission. In addition, if intermodule leakage is not suppressed, the transport simulations using a non-equilibrium Green function (NEGF) solver predicted results that substantially deviated from experiments.In THz QCLs, a helpful graph to show the coupling between various channels is an anticrossing graph. An example of such a graph for several designs considered in this section is shown in Fig. 2(a). This graph shows the anticrossing curves over a wide range of module biases. Minima in the anticrossing correspond to a resonant alignment of two levels in energy, and the anticrossing gap is a measure of the coupling strength between those two levels. In an optimum scenario, the injection anticrossing (represented by the minima in the solid line) corresponding to alignment |in−1⟩→|un⟩ should be close to the dephasing rate. The spontaneous emission's radiation linewidth is related to this dephasing rate. To estimate the linewidth, one can use Fourier transform infrared (FTIR) spectroscopy combined with step-scan techniques. This method results in an approximate value of 4 meV for the linewidth in terahertz quantum cascade lasers (THz QCLs).2626. B. S. Williams, “Terahertz quantum cascade lasers,” Ph.D. dissertation ( Massachusetts Institute of Technology, 2003). It is crucial to highlight that this value does not directly correspond to the dephasing rate, and it may vary depending on factors, such as device design.2727. S. Kumar and Q. Hu, “ Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009). https://doi.org/10.1103/PhysRevB.80.245316 Therefore, it should be regarded as a general guideline rather than an absolute value. The transparency of the injection barrier ensures the minimum required doping to achieve population inversion and reduces the linewidth broadening due to imp scattering.1919. C. W. I. Chan, A. Albo, Q. Hu, and J. L. Reno, “ Tradeoffs between oscillator strength and lifetime in terahertz quantum cascade lasers,” Appl. Phys. Lett. 109, 201104 (2016). https://doi.org/10.1063/1.4967244 However, increasing the transparency of the injection barrier comes at the cost of an increase in the parasitic channels corresponding to the coalignment between |in−1⟩, |un⟩ and the bound states in the neighboring modules, |p1,n⟩, |p2,n⟩, |p1,n+1⟩, and |p2,n+1⟩ (minima in the dot lines).1616. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “ High-power portable terahertz laser systems,” Nat. Photonics. 15, 16–20 (2021). https://doi.org/10.1038/s41566-020-00707-5 Here, we optimized ζ=Ωin−1,unΩun,p1,n+1 as a figure of merit to achieve both objectives. In semiconductor lasers, such as THz QCLs, the rate of increase in the threshold current density (Jth) with temperature carries information on the leakage into the parasitic channels.17,20,2817. J. Faist, Quantum Cascade Lasers ( Oxford University Press, Oxford, 2013).20. A. Albo, Y. V. Flores, Q. Hu, and J. L. Reno, “ Two-well terahertz quantum cascade lasers with suppressed carrier leakage,” Appl. Phys. Lett. 111, 111107 (2017). https://doi.org/10.1063/1.499656728. H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, “ 300-K operation of a GaAs-based quantum-cascade laser at λ ≈ 9 μm,” Appl. Phys. Lett. 78, 3529–3531 (2001). https://doi.org/10.1063/1.1374520 In addition, Jmax−T can be used to evaluate the transparency of the injection barrier. In a so-called lifetime limited transport, where the maximum current density through the injection barrier is limited by the upper state lifetime, Jmax is temperature dependent. On the other hand, in tunneling-limited transport, the Jmax is mainly limited by dephasing processes and is temperature-independent.29,3029. R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “ Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett. 79, 3920–3922 (2001). https://doi.org/10.1063/1.142377730. H. Callebaut and Q. Hu, “ Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005). https://doi.org/10.1063/1.2136420 A slight decrease in Jmax with temperature in diagonal designs indicates lifetime limited transport3131. I. Bhattacharya, C. W. I. Chan, and Q. Hu, “ Effects of stimulated emission on transport in terahertz quantum cascade lasers based on diagonal designs,” Appl. Phys. Lett. 100, 011108 (2012). https://doi.org/10.1063/1.3675452 and is sought after in this manuscript. The simulated gain vs temperature using NEGF is shown in Fig. 2(b) for these designs. The maximum operating temperature Tmax can be inferred from Fig. 2(b), at which the gain decreases to the total cavity loss of ∼20 cm−1.3232. D. Burghoff, T. Yu. Kao, D. Ban, A. W. M. Lee, Q. Hu, and J. Reno, “ A terahertz pulse emitter monolithically integrated with a quantum cascade laser,” Appl. Phys. Lett. 98, 061112 (2011). https://doi.org/10.1063/1.3553021 This was corroborated by the temperature performance of G652 with Tmax ≈ 250 K.1616. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “ High-power portable terahertz laser systems,” Nat. Photonics. 15, 16–20 (2021). https://doi.org/10.1038/s41566-020-00707-5 Further details on the optimization scheme can be found in the supplementary material. A summary of growth parameters, the maximum operating temperature, and maximum and threshold current densities are summarized in Table I.

TABLE I. The layer sequence starts from the injection barrier. Bold denotes barriers separating GaAs quantum wells. The phonon well is indicated by parentheses, and the red ink indicates the doped region. The volume doping n3D is defined relative to that of G652 (1.5 × 1017 cm−3) and represented as n3DG652 in the table. Here, x represents the aluminum fraction in the barriers. The number of modules is chosen for ∼10 μm of an active region.

Labelx (±0.003 )Tmax (±0.1 k)Jth20K−JmaxTmax (±20  A/cm2)Layer sequence (Å) (±.5 Å)DopingVB12810.252321600–265038.4, 69.7, 24.2, (27,25,93)n3DG652G8130.32601350–260032.7, 70.4, 20.8, (57,30.57)n3DG652G9300.352591450–270030.4, 72.5,19.1, (59,28,59)1.2 n3DG652G9020.352602050–335030.6 73.0, 19.0, (56,35,55)1.2 n3DG652G9380.352611750–285028.8, 74.5, 17.6, (30,30,90)n3DG652A 25% Al barrier composition was used in VB1281 to reduce the impact of IFR scattering. As shown in Fig. 2(b), the NEGF simulations predict a similar gain in VB1281 compared to G652 with a Tmax = 250 K.1616. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “ High-power portable terahertz laser systems,” Nat. Photonics. 15, 16–20 (2021). https://doi.org/10.1038/s41566-020-00707-5 The Tmax = 232 K was achieved for this structure, the highest reported for designs based on 25% barriers (previously 210 K2121. L. Bosco, M. Franckié, G. Scalari, M. Beck, A. Wacker, and J. Faist, “ Thermoelectrically cooled THz quantum cascade laser operating up to 210 K,” Appl. Phys. Lett. 115, 010601 (2019). https://doi.org/10.1063/1.5110305) Since no drop of Jmax−T was observed in VB1281 (suggesting a tunneling transport regime), some improvements in Tmax may still be possible using a higher ζ. However, as shown in Fig. 2(c), a higher rate of increase in Jth−T in VB1281 was measured as compared to G652. This higher rate suggests thermal leakage to parasitic channels is more severe in 25% Al barriers and could explain the overestimation of gain in NEGF simulations.In design that utilize 30% aluminum barriers, the Tmax for G813 was improved to 260 K, aligning with recent theoretical predictions made by concurrent studies using a different implementation of the NEGF method.2323. V. Rindert, E. Önder, and A. Wacker, “ Analysis of high-performing terahertz quantum cascade lasers,” Phys. Rev. Appl. 18(4), L041001 (2022). https://doi.org/10.1103/PhysRevApplied.18.L041001 Despite the superior operating temperature in G813, a higher rate of increase in Jth−T is observed compared to G652, as shown in Fig. 2(c). Based on the anticrossing plot in Fig. 2(a) and the simulated subband population for G813 using the NEGF simulations shown in Fig. S7(d) of the supplementary material, there are no apparent leakage channels introduced compared to G652. Additionally, the regrowth of G813 exhibited the same behavior, indicating that growth problems can be ruled out. One possible explanation for the higher rate of increase in Jth−T could be the |ln⟩→|p2,n+1⟩ alignment. Further explorations are required to shed more light on the impact of this transport channel on the behavior of Jth−T. Though not shown here, the Jmax−T of G813 showed a negligible decrease with temperature, suggesting that the transport is tunneling limited and further reduction in injection barrier thickness and lower ful (a higher ζ) are worth pursuing. The details of this design labeled as VA1186-B are presented in the supplementary material. Another direction to improve the Tmax of G813 is through doping scheme optimization, as explained in detail in the supplementary material.In designs with 35% barriers, a similar temperature performance was measured in G930 as compared to G813, which is consistent with the NEGF simulations shown in Fig. 2(b). However, as shown in Fig. 2(c), the rate of increase in Jth with temperature is reduced in G930 compared to G813 and G652. This implies a higher suppression of thermal leakages. However, since G930 has a higher barrier composition, the IFR scattering rate might have been understated in our model for this barrier composition. Motivated by the simulated improvement of approximately 10 K in Tmax, a design designated as G902 was explored. This design has an identical structure to G930, but with higher doping achieved through the same volume doping density (n3D) and an expansion of the doped region by 1.2 times. However, even though G902 benefited from a higher growth quality compared to G930, no additional improvement was observed. The lack of gain improvement in G902 may be due to an underestimation of broadening caused by imp and e–e scattering in the simulation model. In G902, the measured Jmax decreased from 3400 to 3350 A/cm2 from 10 to 260 K suggesting the onset of a lifetime limited transport. As a result, further increase in ζ in this design was not pursued.As discussed in the supplementary material, designs with a wider phonon-well have a higher value of the figure of merit fulτLO