## Terahertz quantum cascade lasers operating up to ∼ 200 K with optimized oscillator strength and improved injection tunneling |

Optics Express, Vol. 20, Issue 4, pp. 3866-3876 (2012)

http://dx.doi.org/10.1364/OE.20.003866

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### Abstract

A new temperature performance record of 199.5 K for terahertz quantum cascade lasers is achieved by optimizing the lasing transition oscillator strength of the resonant phonon based three-well design. The optimum oscillator strength of 0.58 was found to be larger than that of the previous record (0.41) by Kumar et *al.* [Appl. Phys. Lett. 94, 131105 (2009)]. The choice of tunneling barrier thicknesses was determined with a simplified density matrix model, which converged towards higher tunneling coupling strengths than previously explored and nearly perfect alignment of the states across the injection and extraction barriers at the design electric field. At 8 K, the device showed a threshold current density of 1 kA/cm^{2}, with a peak output power of ∼ 38 mW, and lasing frequency blue-shifting from 2.6 THz to 2.85 THz with increasing bias. The wavelength blue-shifted to 3.22 THz closer to the maximum operating temperature of 199.5 K, which corresponds to ∼ 1.28*ħω*/*κ** _{B}*. The voltage dependence of laser frequency is related to the Stark effect of two intersubband transitions and is compared with the simulated gain spectra obtained by a Monte Carlo approach.

© 2012 OSA

## 1. Introduction

1. R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature **417**, 156–159 (2002). [CrossRef] [PubMed]

2. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express **13**, 3331–3339 (2005). [CrossRef] [PubMed]

10. A. Wacker, “Extraction-controlled quantum cascade lasers,” Appl. Phys. Lett. **97**, 081105 (2010). [CrossRef]

11. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “THz quantum cascade laser at *λ ≈* 100 *μ*m using metal waveguide for mode confinement,” Appl. Phys. Lett. **83**, 2124–2126 (2003). [CrossRef]

13. S. Fathololoumi, E. Dupont, S. G. Razavipour, S. R. Laframboise, G. Parent, Z. Wasilewski, H. C. Liu, and D. Ban, “On metal contacts of terahertz quantum-cascade lasers with a metal-metal waveguide,” Semicond. Sci. Technol. **26**, 105021 (2011). [CrossRef]

*al.*[3

3. H. Luo, S. R. Laframboise, Z. R. Wasilewski, and H. C. Liu, “Terahertz quantum cascade lasers based on a three-well active module,” Appl. Phys. Lett. **90**, 041112 (2007). [CrossRef]

5. S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum cascade lasers based on a diagonal design,” Appl. Phys. Lett. **94**, 131105 (2009). [CrossRef]

14. M. A. Belkin, Q. J. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron. **15**, 952–967 (2009). [CrossRef]

15. R. Terrazi and J. Faist, “A density matrix model of transport and radiation in quantum cascade lasers,” New J. Phys. **12**, 033045 (2010). [CrossRef]

17. E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density matrix model applied to three-well terahertz quantum cascade lsers,” Phys. Rev. B **81**, 205311 (2010). [CrossRef]

18. S. C. Lee and A. Wacker, “Nonequilibrium Greens function theory for transport and gain properties of quantum cascade structures,” Phys. Rev. B **66**, 245314 (2002). [CrossRef]

19. T. Kubis, C. Yeh, P. Vogl, A. Benz, G. Fasching, and C. Deutsch, “Theory of nonequilibrium quantum transport and energy dissipation in terahertz quantum cascade lasers,” Phys. Rev. B **79**, 195323 (2009). [CrossRef]

20. H. Callebaut, S. Kumar, B.S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett. **83**, 207–209 (2003). [CrossRef]

22. C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. **105**, 123102 (2009). [CrossRef]

16. S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B **80**, 245316 (2009). [CrossRef]

17. E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density matrix model applied to three-well terahertz quantum cascade lsers,” Phys. Rev. B **81**, 205311 (2010). [CrossRef]

*al.*proposed to make the lasing transition more diagonal in order to increase the upper lasing state lifetime and reduce the strength of undesired tunneling couplings, which leads to an improved population inversion at high temperatures. This strategy brought the maximum operating temperature T

_{max}to 186 K at 3.9 THz [5

5. S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum cascade lasers based on a diagonal design,” Appl. Phys. Lett. **94**, 131105 (2009). [CrossRef]

*f*(

*g*

*∝*

_{isb}*f*.Δρ), and hence low oscillator strength is expected to reduce the gain. The temperature dependence of population inversion, spectral bandwidth and gain for several degrees of diagonality and laser frequencies has been studied in Ref. [23

23. A. Mátyás, M. A. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett. **96**, 201110 (2010). [CrossRef]

_{max}of 199.5 K are presented. In Section 4 the electric field dependence of the laser spectra is discussed using a simple oscillator strength model and is further illustrated by MC simulations. We summarize our results in the last section.

## 2. Optimization of THz QCL by a density matrix model

_{0.15}Ga

_{0.85}As material system. Five different oscillator strengths within the lasing double-well, f

_{ul}≈ 0.25,0.30,0.35,0.41 and 0.47 at a design electric field of around 12 kV/cm, were selected [24]. Initially we assumed the lasing double-well (with

*l*: the lower and

*u*: the upper lasing states) is isolated from the upstream and downstream phonon wells. Each of the two phonon wells, shown in Fig. 1a, contains one injector (

*g*) and one extractor (

*e*) state. The injection and extraction barrier thicknesses play important roles in populating and depopulating the lasing levels [25

25. H. Luo, S. R. Laframboise, Z. R. Wasilewski, and H. C. Liu, “Effects of injector barrier on performance of terahertz quantum-cascade lasers,” IEEE Electron. Lett. **43**, 633–635 (2007). [CrossRef]

26. H. Luo, S. R. Laframboise, Z. R. Wasilewski, H. C. Liu, and J. C. Cao, “Effects of extraction barrier width on performance of terahertz quantum-cascade lasers,” IEEE Electron. Lett. **44**, 630–631 (2008). [CrossRef]

17. E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density matrix model applied to three-well terahertz quantum cascade lsers,” Phys. Rev. B **81**, 205311 (2010). [CrossRef]

**81**, 205311 (2010). [CrossRef]

_{isb}≃ 35 cm

^{−1}was maintained, was targeted to be maximized, without constraining the threshold current density. For each of the designs, several phonon well thicknesses were considered during the optimization process. This exercise converged towards rather thin injection and extraction barriers, and we found the pairs of states across these barriers (

*g*–

*u*for injection and

*l*–

*e*for extraction) are aligned at about the same electric field. The convergence of the model towards thinner barriers is mostly driven by the maximization of population inversion, but is constrained by the gain broadening that is induced by the tunneling couplings and the parasitic leakages (the wrong injection:

*g*→

*l*and the wrong extraction:

*u*→

*e*channels).

_{ul}= 0.475, the lasing double-well being isolated from upstream (injection) and downstream (extraction) phonon wells (this structure will be discussed for the rest of the paper). In this picture, at the design electric field of 12.2 kV/cm, the energy difference between the lasing states reads E

_{ul}= 15.1 meV, with the injector and extraction coupling of ħΩ

_{gu}= 1.38 meV and ħΩ

_{le}= 2.47 meV, respectively. The upper lasing state lifetime, set by LO phonon emission, is

*τ*

*= 0.45 ps at kinetic energy E*

_{ul}_{LO}– E

_{ul}. Figure 1b shows the DM calculation results of the gain spectra of the same design at different electric fields for a lattice temperature of 10 K [27

27. For the density matrix calculations, the electron temperature was chosen 90 K higher than lattice. Pure dephasing time constants of tunneling *τ*^{*} = 0.35 ps, and of optical intersubband transition

_{ul}), below the design electric field. Figure 1b shows three separate peaks in the simulated contour plot, as opposed to a single peak gain in the structure discussed in the Ref. [17

**81**, 205311 (2010). [CrossRef]

_{u}→ E

_{l}(see Fig. 8 of Ref. [17

**81**, 205311 (2010). [CrossRef]

23. A. Mátyás, M. A. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett. **96**, 201110 (2010). [CrossRef]

^{−1}, T

_{max}of ∼ 170 K could be achieved for all the designs [28

28. S. Fathololoumi, E. Dupont, Z. R. Wasilewski, S. R. Laframboise, D. Ban, and H. C. Liu, “Effect of intermediate resonance on the performance of resonant phonon based terahertz quantum cascade laser,” Presented at 11th International Conference on Intersubband Transitions in Quantum Wells, Badesi, Italy (2011).

*μ*m thick active region and a sheet electron density of 3 × 10

^{10}cm

^{−2}per period using a 3D Si-doping within the middle 5 nm of the phonon well. The active region was sandwiched between 100 nm of 5 × 10

^{18}cm

^{−3}bottom n

^{+}GaAs and a top stack of 50 nm of 5 × 10

^{18}cm

^{−3}and 10 nm of low temperature grown 5 × 10

^{19}cm

^{−3}n

^{+}GaAs layers. Special emphasis was put on minimizing the drift of fluxes for Ga and Al during this long growth process. The X-ray diffraction rocking curve could be perfectly fitted with nominal parameters, with no extra broadening of satellites peaks, confirming the excellent stability of the growth rates (better than 0.5%) throughout the active region. The wafers were then processed into THz QCL structures with Au double metal waveguides. All devices have the following dimensions: ∼ 144

*μ*m wide ridges with ∼ 130

*μ*m wide top Ti/Au metallization forming a Schottky contact, and ∼ 1 mm long Fabry-Perot resonator. An In-Au wafer bonding technique was used [11

11. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “THz quantum cascade laser at *λ ≈* 100 *μ*m using metal waveguide for mode confinement,” Appl. Phys. Lett. **83**, 2124–2126 (2003). [CrossRef]

13. S. Fathololoumi, E. Dupont, S. G. Razavipour, S. R. Laframboise, G. Parent, Z. Wasilewski, H. C. Liu, and D. Ban, “On metal contacts of terahertz quantum-cascade lasers with a metal-metal waveguide,” Semicond. Sci. Technol. **26**, 105021 (2011). [CrossRef]

_{max}of 180 K observed from the device with f

_{ul}= 0.475. A module of this design consists of three wells and three barriers with the layer thicknesses of

**43**/89/

**24.6**/81.5/

**41**/160 Å starting from the injector barrier - the barriers are indicated in bold font.

_{ul}= 0.475, with large overlap of mixed states

*1*with

*2*and states

*3*with

*4*. This structure at 12.2 kV/cm results in a total oscillator strength between the lasing states of f

_{13}+ f

_{23}= 0.582, compared to f

_{ul}= 0.475 calculated from the isolated-well picture. At this electric field, the

*1*→

*4*and

*2*→

*4*transitions contribute marginally to the total oscillator strength. The increase of calculated oscillator strength with the extended wavefunctions as opposed to the isolated-well picture suggests non-negligible electron-light coupling between the upper lasing state,

*u*, and the extraction state,

*e*. Since there is a large population inversion between these two states, the transition

*u*→

*e*is expected to contribute positively to the gain. This particular DM model uses a basis of states from isolated lasing and phonon wells, meaning that the states

*u*and

*e*belong to two different Hamiltonians and are not orthogonal to each other. Therefore, in its present form, this DM model fails to accommodate dipole moments other than z

_{ul}, and further work is required to include interwell electron-light scattering.

_{ul}= 0.475 has very similar double and phonon wells, as the device reported by Belkin et

*al.*in Ref. [14

14. M. A. Belkin, Q. J. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron. **15**, 952–967 (2009). [CrossRef]

**51**/90/

**24**/81/

**46**/163 Å, which lased up to 174 K. The two structures mainly differ by thicker injection/extraction barriers in Belkin’s design that lead to smaller injection (ħΩ

_{inj}= 0.91 meV) and extraction (ħΩ

_{ext}= 1.89 meV) couplings. For Belkin’s structure, the states

*g*and

*u*are aligned at 11.8 kV/cm on the injection side, and the states

*l*and

*e*are aligned at 11.1 kV/cm on the extraction side. At the field of maximum gain, states

*1*and

*2*are perfectly mixed, whereas states

*3*and

*4*are localized in the double well and phonon well, respectively, reducing their overlap and hence the depopulation rate as compared to our design. Comparing the two structures using MC simulation reveals that the net scattering rate from level

*3*to

*4*is 6 % higher in our design. The increased injection anticrossing in our structure leads to reduced backscattering

*2*→

*1*and, therefore, higher net scattering from

*1*to

*2*by 8 %. The larger anticrossing facilitates a larger occupation of level

*2*and a less occupied level

*1*due to the quasi-Fermi distribution of electrons in the lowest states of the injector well. This is also confirmed by self-consistent MC simulations. Consequently in our design level

*2*populates more heavily, while it has also the highest oscillator strength with level

*3*, at the electric field of maximum gain. On the other hand, the anticrossing between levels

*g*and

*e*, around 8–9 kV/cm, is higher in our structure (0.97 meV) than that in Belkin’s (0.56 meV), which should result in a higher threshold current density in our device [5

5. S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum cascade lasers based on a diagonal design,” Appl. Phys. Lett. **94**, 131105 (2009). [CrossRef]

28. S. Fathololoumi, E. Dupont, Z. R. Wasilewski, S. R. Laframboise, D. Ban, and H. C. Liu, “Effect of intermediate resonance on the performance of resonant phonon based terahertz quantum cascade laser,” Presented at 11th International Conference on Intersubband Transitions in Quantum Wells, Badesi, Italy (2011).

## 3. Experimental results

_{max}for the optimized design requires further lowering the waveguide loss and improving heat dissipation. Hence a Cu-Cu based process with lower waveguide loss and better heat dissipation was employed. Moreover, the 100 nm thick top n

^{+}contact layer was removed for further lowering the waveguide loss, similar to the device with T

_{max}= 186 K reported in [5

**94**, 131105 (2009). [CrossRef]

_{3}PO

_{4}/H

_{2}O

_{2}/H

_{2}: 3/1/25) to etch through the entire thickness of the 10

*μ*m thick active region. The ridge waveguide of fabricated THz QCLs is ∼ 170

*μ*m wide. The substrate of the samples was thinned down to ∼ 150

*μ*m [29

29. S. Fathololoumi, D. Ban, H. Luo, E. Dupont, S. R. Laframboise, A. Boucherif, and H. C. Liu, “Thermal behavior investigation of terahertz quantum-cascade lasers,” IEEE J. Quantum Electron. **44**, 1139–1144 (2008). [CrossRef]

^{−4}). The device showed a T

_{max}of 199.5 K, while a peak output power of more than 6 mW could still be collected at 186 K - the previous T

_{max}record for THz QCLs. Higher duty cycle pulse would result in elevated active region temperature and hence reduces the measured T

_{max}[30

30. S. Fathololoumi, E. Dupont, D. Ban, M. Graf, S. R. Laframboise, Z. Wasilewski, and H. C. Liu, “Time-resolved thermal quenching of THz quantum cascade lasers,” IEEE J. Quantum Electron **46**, 396–404 (2010). [CrossRef]

13. S. Fathololoumi, E. Dupont, S. G. Razavipour, S. R. Laframboise, G. Parent, Z. Wasilewski, H. C. Liu, and D. Ban, “On metal contacts of terahertz quantum-cascade lasers with a metal-metal waveguide,” Semicond. Sci. Technol. **26**, 105021 (2011). [CrossRef]

^{−1}(from 24 to 19.4 cm

^{−1}) by employing the Cu-Cu waveguide and removing the top contact n

^{+}, and hence explains the 19 K improvement in the T

_{max}. This is fairly consistent with previous observations on several four-well resonant phonon QCLs at similar frequency [31]. Similarly, the MC simulations (at 12.8 kV/cm) showed a degradation of ∼ 5.2 cm

^{−1}on the gain at 3.22 THz, when temperature increased from 180 K to 199.5 K; this is in good agreement with the estimated change of cavity loss (∼ 5.6 cm

^{−1}: 4.6 cm

^{−1}from the waveguide loss and 1 cm

^{−1}from the mirror loss). For a fair comparison, one cannot exclude the effect of process variation (for instance the ridge etching process) between the Au-Au device (fabricated at NRC) and Cu-Cu device (fabricated at MIT), on the improvement of T

_{max}. At low temperatures (below 120 K), both waveguides show very similar threshold current densities but a discrepancy appears above 120 K (see inset of Fig. 3), suggesting that the waveguide loss increases faster with temperature for the Au-Au device. Furthermore, a Au-Au based device (∼ 170

*μ*m wide and 1.98 mm long) without the top n

^{+}layer was fabricated and a T

_{max}of 195 K was recorded [32, 33

33. The waveguide loss of 22.1 cm^{−1} was calculated for the Au-Au device without the top n^{+} layer (∼ 170 *μ*m wide and 1.98 mm long). The estimated cavity loss is, therefore, reduced for ∼ 3 cm^{−}^{1} (1.9 cm^{−}^{1} from the waveguide loss and 1.1 cm^{−}^{1} from the mirror loss), as compared to the estimated cavity loss of the Au-Au device with the top n^{+} layer (∼ 144 *μ*m wide and 1 mm long), lasing up to 180 K. The MC simulations at 12.8 kV/cm and 3.22 THz showed a gain reduction of ∼ 4 cm^{−}^{1}.

## 4. Analysis of lasing frequency

*T*

*∼ 1.28*

_{max}*ħω*/

*κ*

*. At 8 K and close to maximum power, the device lases at 2.75 THz, which is closer to the value predicted by solving the Schrödinger equation along several periods as what was done for Fig. 2. Figure 4 shows the energy spacing between all four extended energy states (*

_{B}*1*to

*4*) and their respective oscillator strength. One can see the transitions

*1*→

*3*and

*2*→

*3*dominate over the other two around the design electric field (12.2 kV/cm). They exchange their oscillator strength around 11.8 kV/cm,

*1*→

*3*being stronger below this electric field. The other transitions,

*1*→

*4*and

*2*→

*4*, are not very optically active, which can be explained by a destructive quantum interference between dipole moments [34

34. J. Faist, F. Capasso, A. L. Hutchinson, L. Pfeiffer, and K. W. West, “Suppression of optical absorption by electric-field-induced quantum interference in coupled potential wells,” Phys. Rev. Lett. **71**, 3573–3576 (1993). [CrossRef] [PubMed]

_{ul}). Below the design electric field, the gain peak frequency predicted by the DM model (Fig. 1b) is overestimated compared to the measured lasing frequency, as the

*1*→

*4*transition is the strongest transition in the DM picture (see Fig. 8a in Ref. [17

**81**, 205311 (2010). [CrossRef]

*1*→

*3*transition, which has the highest oscillator strength below 11.8 kV/cm. From data taken from the Au-Au device, with the top n

^{+}contact layer, one knows the lasing threshold occurs at ∼ 11 V, which corresponds to an electric field of 10.2 kV/cm after subtracting the extra 0.8 V due to the top Schottky contact [13

**26**, 105021 (2011). [CrossRef]

_{13}≡ 2.4 THz, a value close to the observed laser frequency, 2.7 THz.

*1*→

*3*and

*2*→

*3*transitions contribute to the gain. The peak gain frequency is, therefore, increased. At 199.5 K, the measured frequency (3.22 THz) is between the computed energy spacings at 12.7 kV/cm: E

_{13}≡ 3.71 THz and E

_{23}≡ 3.02 THz, the latter transition being more intense according to the oscillator strength picture. Considering the uncertainty in electric field due to the Schottky contact, the laser frequency at high temperature agrees well with E

_{23}. This exercise of oscillator strength calculation between levels

*1*to

*4*indicates that the MC approach, which uses the extended states and considers all the broadening and population inversion between levels

*1*to

*4*, is probably better suited to predict the laser frequency than the present simplified DM model. Therefore to predict the laser frequency at different temperatures and biases, an MC based approach is employed.

^{+}layer, at different biases and temperatures. For all temperatures, the spectra show a consistent blue (Stark) shift at higher biases. The highest lasing frequency is measured close to the T

_{max}, as at this temperature no NDR is observed and hence high biases are achievable. The device with the top n

^{+}layer provides us with rather accurate voltage measurement and hence the voltage across the active region can be estimated by considering the 0.8 V Schottky voltage drop across the top contact [13

**26**, 105021 (2011). [CrossRef]

22. C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. **105**, 123102 (2009). [CrossRef]

22. C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. **105**, 123102 (2009). [CrossRef]

*1*→

*3*and

*2*→

*3*transitions. Therefore, the frequency position of the peak gain becomes very sensitive to the electric field, which along with the waveguide loss frequency dependence sets the lasing frequency at 3.22 THz. At T

_{max}, the MC model predicts a peak–gain or equivalently a waveguide loss of 37.5 cm

^{−1}, a value that is consistent with a previous measurement by cavity frequency pulling [35

35. L. A. Dunbar, R. Houdré, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, “Small optical volume terahertz emitting microdisk quantum cascade lasers,” Appl. Phys. Lett. **90**, 141114 (2007). [CrossRef]

37. A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys. **110**, 013108 (2011). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

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14. | M. A. Belkin, Q. J. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron. |

15. | R. Terrazi and J. Faist, “A density matrix model of transport and radiation in quantum cascade lasers,” New J. Phys. |

16. | S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B |

17. | E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density matrix model applied to three-well terahertz quantum cascade lsers,” Phys. Rev. B |

18. | S. C. Lee and A. Wacker, “Nonequilibrium Greens function theory for transport and gain properties of quantum cascade structures,” Phys. Rev. B |

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21. | H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. |

22. | C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. |

23. | A. Mátyás, M. A. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett. |

24. | S. Fathololoumi, E. Dupont, S.R. Laframboise, Z. R. Wasilewski, D. Ban, and H. Liu, “Design of laser transition oscillator strength for THz quantum cascade lasers,” |

25. | H. Luo, S. R. Laframboise, Z. R. Wasilewski, and H. C. Liu, “Effects of injector barrier on performance of terahertz quantum-cascade lasers,” IEEE Electron. Lett. |

26. | H. Luo, S. R. Laframboise, Z. R. Wasilewski, H. C. Liu, and J. C. Cao, “Effects of extraction barrier width on performance of terahertz quantum-cascade lasers,” IEEE Electron. Lett. |

27. | For the density matrix calculations, the electron temperature was chosen 90 K higher than lattice. Pure dephasing time constants of tunneling |

28. | S. Fathololoumi, E. Dupont, Z. R. Wasilewski, S. R. Laframboise, D. Ban, and H. C. Liu, “Effect of intermediate resonance on the performance of resonant phonon based terahertz quantum cascade laser,” Presented at 11th International Conference on Intersubband Transitions in Quantum Wells, Badesi, Italy (2011). |

29. | S. Fathololoumi, D. Ban, H. Luo, E. Dupont, S. R. Laframboise, A. Boucherif, and H. C. Liu, “Thermal behavior investigation of terahertz quantum-cascade lasers,” IEEE J. Quantum Electron. |

30. | S. Fathololoumi, E. Dupont, D. Ban, M. Graf, S. R. Laframboise, Z. Wasilewski, and H. C. Liu, “Time-resolved thermal quenching of THz quantum cascade lasers,” IEEE J. Quantum Electron |

31. | S. Kumar, “Development of terahertz quantum-cascade lasers,” |

32. | C. W. I. Chan, S. Fathololoumi, E. Dupont, Z. R. Wasilewski, S. R. Laframboise, D. Ban, Q. Hu, and H. C. Liu, “A terahertz quantum cascade laser operating up to 193 K,” Presented at 11th International Conference on Intersubband Transitions in Quantum Wells, Badesi, Italy (2011). |

33. | The waveguide loss of 22.1 cm |

34. | J. Faist, F. Capasso, A. L. Hutchinson, L. Pfeiffer, and K. W. West, “Suppression of optical absorption by electric-field-induced quantum interference in coupled potential wells,” Phys. Rev. Lett. |

35. | L. A. Dunbar, R. Houdré, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, “Small optical volume terahertz emitting microdisk quantum cascade lasers,” Appl. Phys. Lett. |

36. | C. Weber, A. Wacker, and A. Knorr, “Density-matrix theory of the optical dynamics and transport in quantum cascade structures: the role of coherence,” Phys. Rev. B |

37. | A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys. |

38. | A. Mátyás, T. Kubis, P. Lugli, and C. Jirauschek, “Comparison between semiclassical and full quantum transport analysis of THz quantum cascade lasers,” Physica E |

**OCIS Codes**

(140.5965) Lasers and laser optics : Semiconductor lasers, quantum cascade

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: November 21, 2011

Revised Manuscript: January 17, 2012

Manuscript Accepted: January 18, 2012

Published: February 1, 2012

**Citation**

S. Fathololoumi, E. Dupont, C.W.I. Chan, Z.R. Wasilewski, S.R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. C. Liu, "Terahertz quantum cascade lasers operating up to ∼ 200 K with optimized oscillator strength and improved injection tunneling," Opt. Express **20**, 3866-3876 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3866

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### References

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- S. Fathololoumi, E. Dupont, S. G. Razavipour, S. R. Laframboise, G. Parent, Z. Wasilewski, H. C. Liu, and D. Ban, “On metal contacts of terahertz quantum-cascade lasers with a metal-metal waveguide,” Semicond. Sci. Technol.26, 105021 (2011). [CrossRef]
- M. A. Belkin, Q. J. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15, 952–967 (2009). [CrossRef]
- R. Terrazi and J. Faist, “A density matrix model of transport and radiation in quantum cascade lasers,” New J. Phys.12, 033045 (2010). [CrossRef]
- S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B80, 245316 (2009). [CrossRef]
- E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density matrix model applied to three-well terahertz quantum cascade lsers,” Phys. Rev. B81, 205311 (2010). [CrossRef]
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- H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys.98, 104505 (2005). [CrossRef]
- C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys.105, 123102 (2009). [CrossRef]
- A. Mátyás, M. A. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett.96, 201110 (2010). [CrossRef]
- S. Fathololoumi, E. Dupont, S.R. Laframboise, Z. R. Wasilewski, D. Ban, and H. Liu, “Design of laser transition oscillator strength for THz quantum cascade lasers,” Presented at Conference on Lasers and Electro-Optics, Baltimore, MD (2011).
- H. Luo, S. R. Laframboise, Z. R. Wasilewski, and H. C. Liu, “Effects of injector barrier on performance of terahertz quantum-cascade lasers,” IEEE Electron. Lett.43, 633–635 (2007). [CrossRef]
- H. Luo, S. R. Laframboise, Z. R. Wasilewski, H. C. Liu, and J. C. Cao, “Effects of extraction barrier width on performance of terahertz quantum-cascade lasers,” IEEE Electron. Lett.44, 630–631 (2008). [CrossRef]
- For the density matrix calculations, the electron temperature was chosen 90 K higher than lattice. Pure dephasing time constants of tunneling τ* = 0.35 ps, and of optical intersubband transition τul*=1.1 ps were used. Intrawell intersubband scatterings by LO phonon, e-impurities and interface roughness were considered. The momentum dependance of scattering is averaged over the assumed Maxwell-Boltzmann distribution of carriers in the sub-bands.
- S. Fathololoumi, E. Dupont, Z. R. Wasilewski, S. R. Laframboise, D. Ban, and H. C. Liu, “Effect of intermediate resonance on the performance of resonant phonon based terahertz quantum cascade laser,” Presented at 11th International Conference on Intersubband Transitions in Quantum Wells, Badesi, Italy (2011).
- S. Fathololoumi, D. Ban, H. Luo, E. Dupont, S. R. Laframboise, A. Boucherif, and H. C. Liu, “Thermal behavior investigation of terahertz quantum-cascade lasers,” IEEE J. Quantum Electron.44, 1139–1144 (2008). [CrossRef]
- S. Fathololoumi, E. Dupont, D. Ban, M. Graf, S. R. Laframboise, Z. Wasilewski, and H. C. Liu, “Time-resolved thermal quenching of THz quantum cascade lasers,” IEEE J. Quantum Electron46, 396–404 (2010). [CrossRef]
- S. Kumar, “Development of terahertz quantum-cascade lasers,” Massachusetts Institute of Technology163–166 (2007).
- C. W. I. Chan, S. Fathololoumi, E. Dupont, Z. R. Wasilewski, S. R. Laframboise, D. Ban, Q. Hu, and H. C. Liu, “A terahertz quantum cascade laser operating up to 193 K,” Presented at 11th International Conference on Intersubband Transitions in Quantum Wells, Badesi, Italy (2011).
- The waveguide loss of 22.1 cm−1 was calculated for the Au-Au device without the top n+ layer (∼ 170 μm wide and 1.98 mm long). The estimated cavity loss is, therefore, reduced for ∼ 3 cm−1 (1.9 cm−1 from the waveguide loss and 1.1 cm−1 from the mirror loss), as compared to the estimated cavity loss of the Au-Au device with the top n+ layer (∼ 144 μm wide and 1 mm long), lasing up to 180 K. The MC simulations at 12.8 kV/cm and 3.22 THz showed a gain reduction of ∼ 4 cm−1.
- J. Faist, F. Capasso, A. L. Hutchinson, L. Pfeiffer, and K. W. West, “Suppression of optical absorption by electric-field-induced quantum interference in coupled potential wells,” Phys. Rev. Lett.71, 3573–3576 (1993). [CrossRef] [PubMed]
- L. A. Dunbar, R. Houdré, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, “Small optical volume terahertz emitting microdisk quantum cascade lasers,” Appl. Phys. Lett.90, 141114 (2007). [CrossRef]
- C. Weber, A. Wacker, and A. Knorr, “Density-matrix theory of the optical dynamics and transport in quantum cascade structures: the role of coherence,” Phys. Rev. B79, 165322 (2007). [CrossRef]
- A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys.110, 013108 (2011). [CrossRef]
- A. Mátyás, T. Kubis, P. Lugli, and C. Jirauschek, “Comparison between semiclassical and full quantum transport analysis of THz quantum cascade lasers,” Physica E42, 2628 (2010). [CrossRef]

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