Strain-Compensated InGaAs Terahertz Quantum Cascade Lasers

Nov 9, 2016 - So far only a few papers have studied the material aspect of THz QCLs, and only two other material systems were successfully demonstrate...
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Strain-Compensated InGaAs Terahertz Quantum Cascade Lasers Keita Ohtani, Mattias Beck,* and Jérôme Faist* Institute for Quantum Electronics, ETH Zurich, Auguste-Piccard-Hof 1, 8093 Zurich, Switzerland ABSTRACT: Strain-compensated InGaAs/AlInGaAs terahertz quantum cascade lasers grown by molecular beam epitaxy are reported. A choice of a moderate amount of strain in the wells (−0.24%) and in the quaternary barriers (+1.07%) makes it possible to coherently grow an active region as thick as 10 μm. Lasers based on a four quantum well design emit at 3.3 THz with a maximum operation temperature of 149 K, which is among the highest temperatures of InGaAs-based THz quantum cascade lasers.

KEYWORDS: THz, quantum cascade laser, strain compensation, molecular beam epitaxy

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AlInGaAs. Compressively strained InGaAs wells with a higher indium (In) composition increase the optical gain coefficient due to the smaller effective mass.21 Tensile-strained AlInGaAs barriers with a lower aluminum (Al) composition decrease interface roughness scattering, which is predicted to deteriorate gain,23 due to a higher migration length of gallium (Ga) atoms on a grown surface, and alloy disorder scattering by a lower band gap of GaAs. A large optical gain coefficient generally decreases the threshold current density and increases the current density dynamic range, leading to an improvement in laser properties such as an optical output power and Tmax. However, it is a challenging task because the strain has to be balanced over the whole thickness of a THz QCL active region (typically 10 μm). Here we demonstrate that strain compensation can be successfully used for heterostructures exceeding 10 μm without relaxation and with individual strain up to 1%. The active region architecture is based on a four-QW scheme,9 while the thickness and composition of the active region are carefully determined by a strain compensation condition. The laser demonstrates a Tmax of 149 K, which is only 6 K less than the highest Tmax of its lattice-matched counterpart based on the three QWs,20 generally showing higher Tmax compared to four QWs.

erahertz (THz) quantum cascade lasers (QCLs) are compact and high optical power semiconductor-based light sources with a narrow line width.1,2 They are of great interest for spectroscopic applications such as astronomical THz heterodyne receivers.3,4 A drawback of the state-of-the-art THz QCLs is the low operation temperature. The maximum operating temperature (Tmax = 200 K)5 has not been improved since 2012, although a number of new design concepts were proposed. The current Tmax record is held by a three quantum well (QW) design based on the Al0.15Ga0.85As/GaAs material system.5 Most studies demonstrated THz QCLs based on new design schemes (e.g., the two-QW,6,7 four-QW,8,9 bound-tocontinuum,10 interlaced photon−phonon cascade,11 twophonon depopulation,12,13 and the scattering-assisted design14,15) using Al0.15Ga0.85As/GaAs, but none of them led to an improvement in Tmax. So far only a few papers have studied the material aspect of THz QCLs, and only two other material systems were successfully demonstrated: InGaAs-based16−18 and InAsbased19 material systems. A lattice-matched In0.53Ga0.47As/ In0.52Al0.48As THz QCL works up to ∼155 K,20 although a large optical gain coefficient is expected due to the smaller electron effective mass compared to that of the GaAs-based material system.21 The limitation is mainly due to the very thin barrier layers (0.6 nm) and the high alloy disorder scattering,22 which are attributed to the higher aluminum (Al) composition. Another approach to substitute the Al by antimony (Sb) benefited from the fact that thicker barriers can be used by the lower conduction band offset and demonstrated lasing up to 142 K.17 But this material combination suffers from Sb segregation during the growth, degrading the quality of the heterostructure interfaces. The InAs-based THz QCLs so far did not show lasing action without applying a strong magnetic field of 5 T.19 In this work we try to combine the advantages of the Al0.15Ga0.85As/GaAs-based material system having thick barriers and low alloy disorder scattering with those of an InGaAs-based material system having a low electron effective mass by fabricating strain-compensated structures based on InGaAs/ © XXXX American Chemical Society

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DESIGNING STRUCTURE FOR STRAIN COMPENSATION In a first step, the condition for the strain compensation is derived: the equilibrium in-plane lattice constant a∥ = (awhwGw + abhbGb)/(hwGw + hbGb) is made to be equal to the lattice constant (asub) of the substrate. We take Gi (i = w, b referring to the well and the barrier) as the sheer modulus related to the elastic constant (=2(C11 + C12 − 2C122/C11)), ai is the equilibrium (unstrained) lattice constant, and hi is the total unstrained thickness of well and barrier layers over one period, respectively. The strain compensation condition over one period is thus expressed by24,25 Received: June 2, 2016

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Figure 1. (a) Computed well and barrier thickness ratio (hw/hb) as a function of the In composition of the InGaAs wells and the AlInGaAs barriers. Here an Al/Ga compositional ratio of 0.13 is selected. The white dashed and dashed dotted lines express the In composition having the maximum strain without generating dislocation. The black line represents the strain compensation condition for hw/hb = 3.95, which is typically used in the four-QW active region. The values of the elastic constants in the ref 26 are used. (b) Computed conduction band offset energy (ΔEc) as a function of In composition in the InGaAs wells and the AlInGaAs barriers. The black dotted line gives ΔEc ≈ 0.12 eV, while the black line shows the strain compensation condition for hw/hb = 3.95. The same Al/Ga compositional ratio as in Figure 1a is employed.

⎛ a − asub ⎞ ⎛ a − asub ⎞ Gw ⎜ w ⎟h w = − G b ⎜ b ⎟h b ⎝ asub ⎠ ⎝ asub ⎠

the white lines, ΔEc can be tuned in the range from 0.06 to 0.14 eV for a layer thickness ratio hw/hb = 3.95 (black line). The dashed black line represents ΔEc = 0.12 eV, the same value as the one used in GaAs/AlGaAs high-performance THz QCLs. For this work, In0.57Ga0.43As wells (compressive strain of −0.24%) and Al0.07In0.38Ga0.55As barriers (tensile strain of +1.07%) were selected, resulting in a ΔEc of 0.126 eV using eq 2.

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For an active region based on strain-compensated GaInAs/ AlInGaAs, In compositions in the InGaAs wells and the AlInGaAs barriers are determined by the ratio hw/hb of the total well and barrier thickness since the lattice mismatch between GaAs and AlAs is negligible. Figure 1a shows the computed hw/ hb as a function of In composition in the wells and the barriers. A compositional Al/Ga ratio of 0.13 is selected, which is about a quarter of the ratio used for our previous lattice-matched InGaAs/AlInGaAs THz QCLs.18 In InGaAs-based four-QW active regions, the thickest well layer is a phonon well, where electrons are extracted by resonant longitudinal-optical (LO) phonon scattering, with the typical thickness of 20−25 nm, whereas the thickest barrier is the injection barrier, with a thickness generally around 5.0 nm. On the basis of these values and to avoid exceeding the critical layer thickness, we restrict the maximum compressive strain to −0.5% for wells and the maximum tensile strain to +1.2% for barriers with respect to the lattice parameter of InP. Thus, hw/hb is restricted to the marked zone by the thick white straight lines shown in Figure 1a. The black line represents hw/hb = 3.95, which is a typical value of InGaAs THz QCLs based on the four-QW design.7 It also approximately fits a three-QW design5 because of the similar hw/hb value (≈4). Next the strain-induced shift of the conduction band edge is computed to obtain ΔEc, which is required for designing the subband structure. A hydrostatic component of the strain shifts the conduction band edge, while the shear component splits the valence band. Since the change in the conduction band edge energy (δEc) is expressed by δEc = ac(2ε∥ + ε⊥) where ac is the deformation potential, ε⊥ is the out-of-plane strain component, and ε∥ is the in-plane one, ΔEc is tuned by the strain as follows:24,25 ΔEc = ΔEc(unstrained) + δEc(barrier) − δEc(well)

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ACTIVE REGION STRUCTURE AND ITS MOLECULAR BEAM EPITAXIAL GROWTH The laser structure was grown on an Fe-doped InP (001) substrate by solid-source molecular beam epitaxy (MBE). To decrease In segregation, the growth temperature was 460 °C, which was lower than that of the lattice-matching quaternary THz QCL. It started with a 50 nm thick n-InGaAs bottom contact layer (n = 3.0 × 1018 cm−3), followed by 150 periods of the strained compensated InGaAs/AlInGaAs four-QW active region exhibiting hw/hb = 3.95. The total thickness of the active region is 11.3 μm. The growth was completed by a 50 nm thick n-InGaAs top contact layer (n = 2.15 × 1016 cm−3). Figure 2a shows the computed conduction band diagram of one period in the active region under an applied electric field (F) of 6.5 kV/ cm. As depicted in Figure 2b, the unstrained layer sequence hi of one period starting from the injection barrier (leftmost) is as follows (in nm): 5.2/13.1/2.0/13.5/3.6/11.3/4.4/22.1, where Al0.07In0.38Ga0.55As barriers are in bold, In0.57Ga0.43As wells are in Roman, and the underlined In0.57Ga0.43As phonon well was uniformly doped with Si to 2.15 × 1016 cm−3. Here the effective mass of 0.043m0 for the InGaAs wells and 0.056m0 for the AlInGaAs barriers27 were used. Laser action occurs between the labeled “E5” state and “E4” state. The energy separation (E54), dipole matrix element (z54), and normalized oscillator strength ( f ′54) are E54 = 11.6 meV, z54 = 6.7 nm, and f ′54 = 0.61. In the phonon well that was uniformly doped with Si to 2.15 × 1016 cm−3 to supply electrons, subpicosecond LO phonon scattering ensures efficient electron depopulation of the laser lower state. Figure 3a shows a high-resolution X-ray diffraction (XRD) spectrum recorded near the symmetric InP (004) Bragg reflection from the grown laser structure exhibiting satellite peaks up to 35th order. The full width of half-maximum (fwhm) of the satellite peaks is in the range of 20−30 arcsec,

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Figure 1b depicts ΔEc as a function of In composition in the wells and the barriers. The same compositional ratio (Al/Ga = 0.13) used in Figure 1a is employed, and the conduction to valence band offset ratio of 73:27 is assumed for the unstrained ΔEc.26 Within the allowed zone of In compositions marked by B

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Figure 2. (a) Conduction band diagram and relevant wave functions of one period of the active/injection layers applying the forward electric field of 6.5 kV/cm.The unstrained layer sequence hi of one period starting from the injection barrier (leftmost) is as follows: 5.2/ 13.1/2.0/13.5/3.6/11.3/4.4/22.1, where the Al0.07Ga0.55In0.38As barriers are in bold, the In0.57Ga0.43As wells are in Roman, and the underlined In0.57Ga0.43As layer is doped with Si to the sheet electron density of 4.75 × 1010 cm−2. (b) Layer sequence and schematic of the fabricated device.

Figure 3. (a) High-resolution symmetric (004) XRD spectrum from the laser structure. Many sharp satellite peaks were observed with fwhms of 20−30 arcsec, reflecting a high structural quality. (b) Asymmetric (−1−15) reciprocal space maps from the 0th order satellite peak of the laser structure (left) and the InP substrate peak of the calibration structure (right). Isointensity contours are plotted as wave vectors parallel (Qx, in-plane) and perpendicular (Qy) to the surface in linear scale (counts per second). The analyzer streak visible in both scans at 70 degrees clockwise from the in-plane axis is an experimental artifact caused by the finite size of the reciprocal space probe.

revealing a high structural quality and stable fluxes during the growth. The broadening of the satellite peaks can be explained by a slight indium drift of −0.2% over the last 50 periods of the 11 h growth. The period thickness of the active region can be calculated from the angular spacing between the satellite peaks and was 0.6% thicker than the designed value (75.6 nm instead 75.2 nm). Because the InP substrate peak vanishes in the 0th order satellite peak of the 11 μm thick structure, the total net strain can only be estimated but is better than ±0.015% given by the total width of the 0th order peak. Using an analyzer in front of the detector, high-resolution triple-axis space maps were recorded near the asymmetric (−1−15) Bragg reflection from the 0th order superlattice peak of the laser structure (in Figure 3b, left) and compared to the InP substrate peak of a calibration structure (in Figure 3b, right) with identical design but only 25 periods. The slight composition drift in the laser structure is clearly visible in the out-of-plane direction (Qy). The in-plane broadening (along Qx) of the 0th order superlattice peak is comparable to that of the InP substrate, indicating a fully strained heterostructure with negligible inplane strain relaxation. The calibration sample features a slight overall −0.04% compressive strain, and the 0th order superlattice peaks appears in the lower part of the right map in Figure 3b. Room-temperature Hall measurements on the free-standing active region glued on a highly resistive Si substrate gave an electron concentration of n = 8.1 × 1015 cm−3, which is almost

the same as that (n = 9.0 × 1015 cm−3) of the lattice-matching quaternary THz QCL.18 Those numbers are higher than the doped Si concentration (6.3 × 1015 cm−3) in the active region probably due to residual electrons in the epitaxial layers. These facts imply that a lower growth temperature together with a higher In composition in the present sample does not increase the residual electron concentration in the active region. The room-temperature electron mobility was 1.0 × 104 cm2/(V·s), which is close to the value of the bulk InGaAs electron mobility at a similar electron concentration.28

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LASER CHARACTERISTICS RESULTS AND DISCUSSION Figure 4a shows light peak output and voltage versus current characteristics of the ridge laser device processed with a double metal Cu waveguide. To decrease waveguide loss, the bottom and top contact layers were removed by wet chemical etching. The ridge width of the laser device was 200 μm wide, and the cavity length was 1.25 mm long. Lasing was observed with a threshold current density (Jth) of 0.8 kA/cm2. It is higher than Jth (=0.6 kA/cm2) of the lattice matching quaternary THz QCL probably due to larger coupling energies by the smaller ΔEc than that of the lattice matching one (=0.14 eV);18 Jth could be limited by a prealignment current determined by couplings to the laser lower states and the extraction state in the phonon C

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Figure 4. (a) Light output and voltage versus current characteristics applyied at forward bias voltage. Current pulses of 100 ns wide with a repetition frequency of 450 Hz were used, and the output power was recorded by a calibrated Si bolometer. (b) Jth as a function of temperature. T0 = 94 K was obtained by fitting Jth from 110 to 149 K using an empirical equation of Jth = J0 exp(T/T0). (c) Light output and voltage versus current characteristics of the same device at the reverse bias voltage. (d) Emission spectra measured at both bias polarities (T = 10 K).

Figure 5. (a) Current density−voltage curve at 10 K obtained from another laser device with the n-InGaAs bottom contact layer. The device size is 200 μm × 1.25 mm. (b) Computed conduction band diagram with the relevant wave functions in one period under the reverse electric field of F = 7.7 kV/cm corresponding to the laser threshold, and (c) F = 8.9 kV/cm, which is just before the appearance of the NDR. (d) Computed electron population of each state as a function of F. A density matrix method taking into account the electron kinetic energy balance was used.31

range defined as (Jmax − Jth)/Jmax where Jmax expresses the maximum current was 50% at 10 K. The maximum operation

well. The device emitted at 3.3 THz and delivered a light peak output power of 14 mW at 10 K. The current density dynamic D

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temperature (Tmax) was 149 K, which is among the highest Tmax of the InGaAs-based THz QCLs.17,29 Figure 4b displays Jth as a function of temperature. The observed characteristic temperature (T0 = 94 K) of Jth was comparable to that (=90 K) obtained from a 3 THz GaAs four-QW QCL, implying that T0 seems to be independent of the material used.9 Although a relatively larger current density dynamic range was observed, Tmax (=149 K) was lower due to the smaller T0 compared to that (T0 ≈ 160 K) of the state-of-the-art high-performance THz QCLs.30,31 T0 would be mainly determined by two phenomena: lifetime of the laser upper state and thermal carrier backfilling to the laser lower state. The former mechanism would be more relevant in this temperature range. As depicted in Figure 2a, our active layer has three lower states (E2, E3, and E4) and one laser upper state (E5) to facilitate electron depopulation to E1, which forms the three different intersubband transitions (E52, E53, and E54) from the laser upper state (E5). Although the dipole matrix elements of E52 and E53 are designed to be small compared to that of the laser transition (E54), the presence of the additional lower states of E2 and E3 increases the thermally activated LO phonon scattering rate from E5 due to the larger transition energy of E52 and E53 (which are 4 and 8 meV larger than E54). In fact, another four-QW design having only two lower states in the active layer22 shows weaker temperature dependence of the laser upper state lifetime; the computed lifetime ratio (τ5 (=0.9 ps at 150 K)/τ5 (=1.8 ps at 90 K) = 0.50) of the laser upper state at the two different temperatures (90 and 150 K) is 19% larger than that of our present structure (τ5 (=1.4 ps at 150 K)/τ5 (=3.4 ps at 90 K) = 0.42), although it has a larger normalized oscillator strength ( f ′ = 0.86). This situation increases the electron populations in the laser lower states with temperature, hence degrading T0. The argument is qualitatively consistent with the experimentally observed T0 (=130 K),12 which is higher than ours (T0 = 94 K). Thus, employing active structures such as three QWs where two lower states are used in the active layer5,30,31 should improve temperature performance of the strained compensated InGaAs THz QCLs. As shown in Figure 4c, we also observed lasing by applying a reverse bias voltage even though an asymmetric electron potential profile was used in the active region. At the reverse bias, Jth was 1.0 kA/cm2 at 10 K with an output power of 7.5 mW. Tmax was 112 K. The current density dynamic range was 32% for the reverse bias, which is smaller than that for the forward bias (50%). Figure 4d depicts laser emission spectra in both directions. The emission energy (13.9 meV) at the reverse bias was slightly higher than that (13.8 meV) measured at the forward bias. In order to investigate which intersubband transition shows laser action at the reverse bias, we measured a transport curve of other devices with the n-InGaAs bottom contact layer since the high voltage drop (seen in Figure 4c) by Schottky contact made it difficult to analyze. On the J−F transport curve in Figure 5a, the plateau feature around F = 4.5 kV/cm was observed, which was attributed to the parasitic current channel where the ground state in the phonon well pumps to the lower states in the following period.30,31 After pumping this channel, the current reaches Jth at F ≈ 7.7 kV/cm and then the laser action stops around F ≈ 8.9 kV/cm due to the negative differential resistance (NDR). In this electric field range we found that there are three possible intersubband transitions (E54, E43, and E42) that could lase as depicted by the arrows in Figure 5b and c. To identify it, the electron population distribution in one period of the structure is

computed by a density matrix formula taking into account the electron kinetic energy balance.32 Figure 5d shows the electron population of the relevant states as a function of F. By pumping E5 above F > 4.0 kV/cm, the electron population between E4 and E5 starts to be first inverted due to the short lifetime of E4 by coupling to the excited state (E3) in the phonon well. The electrons at E2 tend to stay until F ≈ 6.0 kV/cm due to the slow extraction rate, preventing the formation of the population inversion between E2 and E4. Although the population inversion between E3 and E4 is achieved above F = 6.5 kV/ cm, the computed peak gain is not large enough due to the gain broadening by the short lifetime (≈0.4 ps) of E3. As a consequence, the transition of E45 exhibits much larger gain compared to those of E43 and E42, indicating that lasing at the reverse bias is attributed to the intersubband transition of E54. At F ≈ 7.7 kV/cm, corresponding to the laser threshold, the emission energy (E54) is computed to be 17.5 meV, which is higher than the experiment (13.9 meV). This could probably be due to a strong wave function coupling via the thin injection barrier (4.5 nm) at the reverse bias voltage: a strong injector coupling broadens the gain spectra, making it difficult to predict the laser emission frequency.33 The lower Tmax at the reverse bias could be attributed to the smaller current density dynamic range by the higher Jth. To improve the laser performance, an interesting design would be a structure simply making the third well (from the injection barrier) thickness thinner (for example, thinning down to 9.6 nm) to increase E54 enough to emit the LO phonon. Thus, the scattering-assisted carrier injection, which is predicted to improve laser performance,14,15,34,35 would be possible at a reverse bias, while the conventional resonant tunneling injection is employed at a forward bias voltage.

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CONCLUSION

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AUTHOR INFORMATION

We have reported the design, MBE growth, and laser characteristics of a strained compensated InGaAs THz QCL with quaternary AlInGaAs barriers. A moderate choice of the strain in the wells and the barriers together with their thickness has allowed coherently growing a quite thick active region over 10 μm. Lasing at 3.3 THz was observed with Jth = 0.8 kA/cm2 up to a temperature of Tmax = 149 K. We have also observed lasing with Jth = 1.0 kA/cm2 at 10 K at the reverse bias voltage, although an asymmetric electron potential is used in the active region. Although the maximum operation temperature is slightly lower (≈6 K) than the record one of the InGaAsbased THz QCLs,20 the result demonstrates the potential of the strained material and is an encouraging and important step toward aluminum-free InGaAs/InGaAs or GaAs/InGaAs THz QCL structures based on InP. Aluminum-free structures would not only benefit from the above-mentioned advantages but also facilitate the fabrication of photonic crystal THz QCLs or even active regions with lateral quantum confinement.

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest. E

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(17) Deutsch, C.; Krall, M.; Brandstetter, M.; Detz, H.; Andrews, A. M.; Klang, P.; Schrenk, W.; Strasser, G.; Unterrainer, K. High performance InGaAs/GaAsSb terahertz quantum cascade lasers operating up to 142 K. Appl. Phys. Lett. 2012, 101, 211117. (18) Ohtani, K.; Beck, M.; Scalari, G.; Faist, J. Terahertz quantum cascade lasers based on quaternary AlInGaAs barrier. Appl. Phys. Lett. 2013, 103, 041103. (19) Brandstetter, M.; Kainz, M. A.; Zederbauer, T.; Krall, M.; Schönhuber, S.; Detz, H.; Schrenk, W.; Andrews, A. M.; Strasser, G.; Unterrainer, K. InAs based terahertz quantum cacade lasers. Appl. Phys. Lett. 2016, 108, 011109. (20) Krall, M.; Kainz, M. A.; Brandstetter, M.; Deutsch, C.; Schönhuber, S.; MacFarland, D. C.; Zederbauer, T.; Detz, H.; Andrews, A. M.; Schrenk, W.; Strasser, G.; Unterrainer, K. High performance InGaAs-based Terahertz Quantum Cascacde Lasers. International Quantum Cascade Lasers School and Workshop, 2016, Sept 4−9, Cambridge, United Kingdom. (21) Benveniste, E.; Vasanelli, A.; Delteil, A.; Devenson, J.; Teissier, R.; Baranov, A.; Andrews, A. M.; Strasser, G.; Sagnes, I.; Sirtori, C. Influence of the material parameters on quantum cascade devices. Appl. Phys. Lett. 2008, 93, 131108. (22) Vasanelli, A.; Leuliet, A.; Sirtori, C.; Wade, A.; Fedorov, G.; Smirnov, D.; Bastard, G.; Vinter, B.; Giovannini, M.; Faist, J. Role of elastic scattering mechanisms in GaInAs/AlInAs quantum cascade lasers. Appl. Phys. Lett. 2006, 89, 172120. (23) Franckié, M.; Winge, D. O.; Wolf, J.; Liverini, V.; Dupont, E.; Trinité, V.; Faist, J.; Wacker, A. Impact of interface roughness distributions on the operation of quantum cascade lasers. Opt. Express 2015, 23, 5201−5212. (24) Van de Walle, C. G. Band lineups and deformation potentials in the model-solid theory. Phys. Rev. B: Condens. Matter Mater. Phys. 1989, 39, 1871−1883. (25) Faist, J. Quantum Cascade Lasers; Oxford University Press: Oxford, 2013; pp 202−203. (26) Sugiyama, Y.; Inata, T.; Fujii, T.; Nakata, Y.; Muto, S.; Hiyamizu, S. Conduction band edge discontinuity of In0.52Ga0.48As/ In0.52(Ga1‑xAlx)0.48As (0 ≤ x ≤ 1) heterostructure. Jpn. J. Appl. Phys. 1986, 25, L648−650. (27) Vurgaftman, I.; Meyer, J. R.; Ram-Mohan, R. L. Band parameters for III-V compound semiconductors and their alloys. J. Appl. Phys. 2001, 89, 5815−5875. (28) Chattopadhyay, D.; Sutradhar, S. K.; Ng, B. R. Electron transport in direct-gap III-V ternary alloys. J. Phys. C: Solid State Phys. 1981, 14, 891. (29) Valmorra, F.; Scalari, G.; Ohtani, K.; Beck, M.; Faist, J. InGaAs/ AlInGaAs THz quantum cascade lasers operating up to 195 K in strong magnetic field. New J. Phys. 2015, 17, 023050. (30) Kumar, S.; Hu, Q.; Reno, J. R. 186 K operation of terahertz quantum-cascade lasers based on a diagonal design. Appl. Phys. Lett. 2009, 94, 131105. (31) Fathololoumi, S.; Dupont, E.; Wasilewski, Z. R.; Chan, C. W. I.; Razavipour, S. G.; Laframboise, S. R.; Huang, S.; Hu, Q.; Ban, D.; Liu, H. C. Effect of oscillator strength and intermediate resonance on the performance of resonant phonon-based terahertz quantum cascade lasers. J. Appl. Phys. 2013, 113, 113109. (32) Terazzi, R.; Faist, J. A density matrix model of transport and radiation in quantum cascade lasers. New J. Phys. 2010, 12, 033045. (33) Dupont, E.; Fathololoumi, S.; Liu, H. C. Simplified densitymatrix model applied to three-well terahertz quantum cascade lasers. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 205311. (34) Scamarcio, G.; Troccoli, M.; Capasso, F.; Hutchinson, A.; Sivco, D.; Cho, A. High peak power (2.2W) superlattice quantum cascade laser. Electron. Lett. 2001, 37, 295−296. (35) Wacker, A. Extraction-controlled quantum cascade lasers. Appl. Phys. Lett. 2010, 97, 081105.

ACKNOWLEDGMENTS The authors would like to thank Dr. Federico Valmorra for fruitful discussions. This work was supported by ETH Zurich with the FIRST cleanroom facility and carried out within ETH Zurich Research Grant ETH-24-13-2 and the collaborative research council 956 (SFB956), funded by Deutsche Forschungsgemeinschaft (DFG).

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REFERENCES

(1) Köhler, R.; Tredicucci, A.; Beltram, F.; Beere, H. E.; Linfield, E. H.; Davies, A. G.; Ritchie, D. A.; Iotti, R. C.; Rossi, F. Terahertz semiconductor-heterostructure laser. Nature 2002, 417, 156−159. (2) Rochat, M.; Ajili, L.; Willenberg, H.; Faist, J.; Beere, H. E.; Davies, G.; Linfield, E.; Ritchie, D. A. Low-threshold terahertz quantum-cascade laser. Appl. Phys. Lett. 2002, 81, 1381−1383. (3) Gao, J. R.; Hovenie, J. N.; Yang, Z. Q.; Baselmans, J. J. A.; Baryshev, A.; Hajenius, M.; Klapwijk, T. M.; Adam, A. J. L.; Klaassen, T. O.; Williams, B. S.; Kumar, S.; Hu, Q.; Reno, J. L. THz heterodyne receiver based on a quantum cascade laser and a superconducting bolometer. Appl. Phys. Lett. 2005, 86, 244104. (4) Richter, H.; Wienold, M.; Schrottke, L.; Biermann, K.; Grahn, H. T.; Hübers, H. − W. 4.7-THz local oscillator for the GREAT heterodyne spectrometer on SOFIA. IEEE Trans. Terahertz Sci. Technol. 2015, 5, 539−545. (5) Fathololoumi, S.; Dupont, E.; Wasilewski, Z. R.; Chan, C. W. I.; Wasilewski, Z. R.; Laframboise, S. R.; Huang, S.; Ban, D.; Mátyás, A.; Jirauschek, C.; Hu, Q.; Liu, H. C. Terahertz quantum cascade lasers operating up to ≈ 200 K with optimized oscillator strength and improved injection tunneling. Opt. Express 2012, 20, 3866−3876. (6) Kumar, S.; Chan, C. W. I.; Hu, Q.; Reno, J. L. Two-well terahertz quantum cascade laser with direct intrawell-phonon depopulation. Appl. Phys. Lett. 2009, 95, 141110. (7) Scalari, G.; Amanti, M. I.; Walther, C.; Terazzi, R.; Beck, M.; Faist, J. Broadband THz lasing from a photon-phonon quantum cascade structure. Opt. Express 2010, 18, 8043−8052. (8) Williams, B. S.; Kumar, S.; Hu, Q. Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous wave mode. Opt. Express 2005, 13, 3331−3339. (9) Amanti, M.; Scalari, G.; Terazzi, R.; Fischer, M.; Beck, M.; Faist, J.; Rudra, A.; Gallo, P.; Kapon, E. Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/ injection stage. New J. Phys. 2009, 11, 125022. (10) Scalari, G.; Ajilli, L.; Faist, J.; Beere, H.; Linfield, E.; Ritchie, D. A.; Davis, A. G. Far-infrared (λ ≈ 87 μm) bound-to-continuum quantum cascade lasers operating up to 90 K. Appl. Phys. Lett. 2003, 82, 3165−3167. (11) Köhler, R.; Tredicucci, A.; Mauro, C.; Beltram, F.; Beere, H. E.; Linfield, E. H.; Davies, A. G.; Ritchie, D. A. Terahertz quantumcascade lasers based on an interlaced photon-phonon cascade. Appl. Phys. Lett. 2004, 84, 1266−1268. (12) Williams, B. S.; Kumar, S.; Qin, Q.; Hu, Q.; Reno, J. L. Terahertz quantum cascade lasers with double-resonant-phonon depopulation. Appl. Phys. Lett. 2006, 88, 261101. (13) Adams, R. W.; Vijayraghavan, K.; Wang, Q. J.; Fan, J.; Capasso, F.; Khanna, S. P.; Davies, A. G.; Linfield, E. H.; Belkin, M. A. GaAs/ Al0.15Ga0.85As terahertz quantum cascade lasers with double-phonon resonant depopulation operating up to 172 K. Appl. Phys. Lett. 2010, 97, 131111. (14) Yamanishi, M.; Fujita, K.; Edamura, T.; Kan, H. Indirect pump scheme for quantum cascade lasers: dynamics of electron-transport and very high T0-values. Opt. Express 2008, 16, 20748−20758. (15) Kumar, S.; Chan, C. W. I.; Hu, Q.; Reno, J. L. A 1.8-THz quantum cascade laser operating significantly above the temperature of ω/kB. Nat. Phys. 2011, 7, 166−171. (16) Fischer, M.; Scalari, G.; Celebi, K.; Amanti, M.; Walther, Ch.; Beck, M.; Faist, J. Scattering processes in terahertz quantum cascade lasers. Appl. Phys. Lett. 2010, 97, 221114. F

DOI: 10.1021/acsphotonics.6b00376 ACS Photonics XXXX, XXX, XXX−XXX