OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 3866–3876
« Show journal navigation

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

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  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 3866-3876 (2012)
http://dx.doi.org/10.1364/OE.20.003866


View Full Text Article

Acrobat PDF (1420 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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/cm2, 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 ∼ 1.28ħω/κB. 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

Nearly a decade after the first demonstration of terahertz quantum cascade lasers (THz QCL) [1

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]

], the quest for room temperature operation continues, through designing new lasing schemes with higher gain [2

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

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

], and lowering the waveguide loss [11

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

13

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]

]. So far among all existing designs, the three-well resonant phonon based THz QCLs, originally proposed by Luo et 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]

], have demonstrated the best temperature performance [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]

,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]

]. Several theoretical models have been employed to understand the details of charge transport and optical gain within THz QCLs, based on various approaches such as density matrix (DM) [15

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

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]

], non-equilibrium Green function [18

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

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]

], and Monte Carlo (MC) techniques [20

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

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

]. With a simplified DM model it has been found that the population inversion (Δρ) of three well resonant phonon based active regions is lowered by parasitic injection and extraction tunneling channels [16

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

, 17

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]

]. Kumar et 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 Tmax 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]

]. However, the gain of THz QCL depends on the product of population inversion and oscillator strength f (gisbf .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]

], through a MC approach. For frequencies above ∼ 3.5 THz, it was found that the diagonality of the lasing transition is beneficial between 150–200 K. Below ∼ 3.5 THz, the diagonality marginally improves population inversion at high temperatures and hence does not compensate for lowering of the oscillator strength.

2. Optimization of THz QCL by a density matrix model

The design process started by finding the lasing double wells with intersubband resonance at 15 meV, using GaAs/Al0.15Ga0.85As material system. Five different oscillator strengths within the lasing double-well, ful ≈ 0.25,0.30,0.35,0.41 and 0.47 at a design electric field of around 12 kV/cm, were selected [24

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,” Presented at Conference on Lasers and Electro-Optics, Baltimore, MD (2011).

]. 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

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]

], as well as in defining the linewidth and amplitude of the gain [17

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]

]. The optimization of the barrier thicknesses for each oscillator strength were performed using a simplified DM approach [17

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]

]. Despite its rather simple and fast computation process, the DM model provides essential design guidelines that include all the tunneling couplings and several scattering mechanisms. The tunneling coupling strengths between the four states are calculated using a tight-binding approach. The temperature, at which the gain coefficient of gisb ≃ 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 (gu for injection and le 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: gl and the wrong extraction: ue channels).

Fig. 1 a) Conduction band diagram of the designed THz QCL with ful = 0.475, in isolated-well picture at 12.2 kV/cm, b) Contour plot of gain spectra (unit of cm−1) for different electric fields at a lattice temperature of 10 K. The line with crosses represents the energy difference between upper (g) and lower (l) lasing states as a function of electric field. Doping level is 3 × 1010 cm−2.

Figure 1a depicts the isolated-well picture of the design with ful = 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 Eul = 15.1 meV, with the injector and extraction coupling of ħΩgu = 1.38 meV and ħΩle = 2.47 meV, respectively. The upper lasing state lifetime, set by LO phonon emission, is τul = 0.45 ps at kinetic energy ELO – Eul. 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 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.

]. The DM model predicts that the energy position of the gain peak is slightly higher than the energy difference between the upper and lower lasing states (Eul), 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

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]

]. This is believed to be due to the large coupling strength for the designed structure in the present work, which results in large frequency shift of the doublet transitions with respect of the bare transition Eu → El (see Fig. 8 of Ref. [17

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]

]).

Figure 2 shows the conduction band diagram and the square of extended wavefunctions of the design with ful = 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 f13 + f23 = 0.582, compared to ful = 0.475 calculated from the isolated-well picture. At this electric field, the 14 and 24 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 ue 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 zul, and further work is required to include interwell electron-light scattering.

Fig. 2 Conduction band diagram and squared moduli of wavefunctions of the optimized ful = 0.475 THz QCL at the design electric field of 12.2 kV/cm. It consists of three wells and three barriers with the layer thicknesses of 43/89/24.6/81.5/41/160 Å starting from injector barrier - the barriers are indicated in bold fonts.

The design with ful = 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 (ħΩinj = 0.91 meV) and extraction (ħΩext = 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 21 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

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

Additional improvement of the Tmax 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 Tmax = 186 K reported in [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]

]. A Cu-Cu based double metal waveguide for the THz QCLs was fabricated, using Cu-Cu wafer bonding and standard photolithography. A bottom and top metal stacks of Ta/Cu (10/600 nm) and Ta/Cu/Ti/Au (10/300/20/150 nm) were used, respectively, for the contacts. Wet etching was performed (H3PO4/H2O2/H2 : 3/1/25) to etch through the entire thickness of the 10 μm thick active region. The ridge waveguide of fabricated THz QCLs is ∼ 170 μm wide. The substrate of the samples was thinned down to ∼ 150 μm [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]

] and then cleaved into laser bars with a 1.8 mm long Fabry-Perot resonator. The laser bars were then gold plated on the back side, indium soldered (epilayer side up) on a copper package and then mounted in a closed-cycle cryostat for measurements.

Fig. 3 Collected THz light (optical output power) versus current density at different heat sink temperatures, for the THz QCL with ful = 0.475. For comparison, the thicker and thinner lines are the LI curves of the Cu-Cu (lased up to 199.5 K, 170 × 1800 μm2 in dimension) and Au-Au (lased up to 180 K, 144 × 1000 μm2 in dimension) devices, respectively. Since the two devices are not measured in the same optical setup, the waveguide loss difference can not be estimated from the external differential efficiencies. The curves with a horizontal left arrow are the voltage-current density characteristics of the Cu-Cu based laser without (w/o) the top n+ layer at 8 K and of the Au-Au-based laser with (w/) this layer at 9 K and 180 K. The insets show the spectra of the Cu-Cu based lasing device, at 8 K and 199.5 K, and the threshold current density versus temperature for two devices.

4. Analysis of lasing frequency

The lower-left inset to Fig. 3 shows the spectra of the Cu-Cu lasing device at 8 K and 199.5 K. At 199.5 K, the laser showed a single mode emission at 3.22 THz, corresponding to Tmax ∼ 1.28ħω/κB. 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 (1 to 4) and their respective oscillator strength. One can see the transitions 13 and 23 dominate over the other two around the design electric field (12.2 kV/cm). They exchange their oscillator strength around 11.8 kV/cm, 13 being stronger below this electric field. The other transitions, 14 and 24, 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]

]. This interference effect is not included in our DM model, since it only considers one dipole moment (between the two states of the double well, zul). 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 14 transition is the strongest transition in the DM picture (see Fig. 8a in Ref. [17

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]

]). Instead, the measured laser frequency is closer to the energy of 13 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

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]

]. At this field, we read from Fig. 4 E13 ≡ 2.4 THz, a value close to the observed laser frequency, 2.7 THz.

Fig. 4 Energy spacing between various extended wavefunctions in the designed THz QCL. The width of each curve at each point represents the corresponding oscillator strengths.

At high temperatures, lasing occurs at high electric fields; for instance at 180 K the peak power occurs at 13.45 V (Fig. 3), corresponding to an electric field of ∼12.7 kV/cm by assuming the same 0.8 V Schottky barrier. At this electric field, both the 13 and 23 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: E13 ≡ 3.71 THz and E23 ≡ 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 E23. 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.

Fig. 5 Spectra of the lasing device at various current densities at 10 K (a to d), 150 K (e and f), and 199.5 K (g), along with the comparison with the calculated gain spectra using MC simulation. The corresponding measured current density along with the simulated bias values are indicated within each plot, assuming 0.8 V Schottky voltage drop across the top contact. Plots (a) to (f) show the laser spectra for the Au-Au device with the top n+ GaAs contact layer (Tmax = 180 K); plot (g) shows the laser spectra for the Cu-Cu device (Tmax = 199.5 K). The vertical scales for all plots are the same.

5. Conclusion

Acknowledgments

The authors would like to acknowledge support from Natural Science and Engineering Research Council (NSERC) of Canada, from Canadian Foundation of Innovation (CFI) and from the Ontario Research Fund (ORF). HCL thanks funding by the National Major Basic Research Program (2011CB925603) and the Shanghai Municipal Major Basic Research Program (09DJ1400102). The work at MIT is supported by NASA and NSF.

References and links

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]

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]

4.

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express 16, 3242–3248 (2008). [CrossRef] [PubMed]

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]

6.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-THz quantum cascade laser operating significantly above the temperature of ħω/κB,” Nat. Phys. 7, 166–171 (2011). [CrossRef]

7.

R. W. Adams, K. Vijayraghavan, Q. J. Wang, J. Fan, F. Capasso, S. P. Khanna, A. G. Davies, E. H. Linfield, and M. A. Belkin, “GaAs/Al0.15Ga0.85As terahertz quantum cascade lasers with double-phonon resonant depopulation operating up to 172 K,” Appl. Phys. Lett. 97, 131111 (2010). [CrossRef]

8.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “Two-well terahertz quantum-cascade laser with direct intrawellphonon depopulation,” Appl. Phys. Lett. 95, 141110 (2009). [CrossRef]

9.

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 8, 8043–8052 (2010). [CrossRef]

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 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003). [CrossRef]

12.

Q. Hu, B. S. Williams, S. Kumar, H. Callebaut, S. Kohen, and J. L. Reno, “Resonant-phonon-assisted THz quantum-cascade lasers with metal–metal waveguides,” Semicond. Sci. Technol. 20, S228–S236 (2005). [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]

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]

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]

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]

21.

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005). [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]

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]

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,” Presented at Conference on Lasers and Electro-Optics, Baltimore, MD (2011).

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]

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 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.

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. 44, 1139–1144 (2008). [CrossRef]

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]

31.

S. Kumar, “Development of terahertz quantum-cascade lasers,” Massachusetts Institute of Technology163–166 (2007).

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−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 cm1 (1.9 cm1 from the waveguide loss and 1.1 cm1 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 cm1.

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]

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]

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 79, 165322 (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]

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 42, 2628 (2010). [CrossRef]

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


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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,” Nature417, 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. Express13, 3331–3339 (2005). [CrossRef] [PubMed]
  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]
  4. M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express16, 3242–3248 (2008). [CrossRef] [PubMed]
  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]
  6. S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-THz quantum cascade laser operating significantly above the temperature of ħω/κB,” Nat. Phys.7, 166–171 (2011). [CrossRef]
  7. R. W. Adams, K. Vijayraghavan, Q. J. Wang, J. Fan, F. Capasso, S. P. Khanna, A. G. Davies, E. H. Linfield, and M. A. Belkin, “GaAs/Al0.15Ga0.85As terahertz quantum cascade lasers with double-phonon resonant depopulation operating up to 172 K,” Appl. Phys. Lett.97, 131111 (2010). [CrossRef]
  8. S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “Two-well terahertz quantum-cascade laser with direct intrawellphonon depopulation,” Appl. Phys. Lett.95, 141110 (2009). [CrossRef]
  9. 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. Express8, 8043–8052 (2010). [CrossRef]
  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 μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003). [CrossRef]
  12. Q. Hu, B. S. Williams, S. Kumar, H. Callebaut, S. Kohen, and J. L. Reno, “Resonant-phonon-assisted THz quantum-cascade lasers with metal–metal waveguides,” Semicond. Sci. Technol.20, S228–S236 (2005). [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]
  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]
  16. S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B80, 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. B81, 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. B66, 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. B79, 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]
  21. H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys.98, 104505 (2005). [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]
  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]
  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,” Presented at Conference on Lasers and Electro-Optics, Baltimore, MD (2011).
  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]
  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 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.
  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.44, 1139–1144 (2008). [CrossRef]
  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 Electron46, 396–404 (2010). [CrossRef]
  31. S. Kumar, “Development of terahertz quantum-cascade lasers,” Massachusetts Institute of Technology163–166 (2007).
  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−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.
  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]
  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]
  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. B79, 165322 (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]
  38. 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited