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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 10172–10181
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Electronic temperatures of terahertz quantum cascade active regions with phonon scattering assisted injection and extraction scheme

Pietro Patimisco, Gaetano Scamarcio, Maria Vittoria Santacroce, Vincenzo Spagnolo, Miriam Serena Vitiello, Emmanuel Dupont, Sylvain R. Laframboise, Saeed Fathololoumi, Ghasem S. Razavipour, and Zbigniew Wasilewski  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 10172-10181 (2013)
http://dx.doi.org/10.1364/OE.21.010172


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Abstract

We measured the lattice and subband electronic temperatures of terahertz quantum cascade devices based on the optical phonon-scattering assisted active region scheme. While the electronic temperature of the injector state (j = 4) significantly increases by ΔT = Te4 – TL ~40 K, in analogy with the reported values in resonant phonon scheme (ΔT ~70-110 K), both the laser levels (j = 2,3) remain much colder with respect to the latter (by a factor of 3-5) and share the same electronic temperature of the ground level (j = 1). The electronic population ratio n2/n1 shows that the optical phonon scattering efficiently depopulates the lower laser level (j = 2) up to an electronic temperature Te ~180 K.

© 2013 OSA

1. Introduction

Terahertz quantum cascade lasers (QCLs) are the most promising solid state terahertz sources [1

1. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002). [CrossRef] [PubMed]

]. Significant performance improvement in terms of power [2

2. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42(2), 89–91 (2006). [CrossRef]

], wall-plug efficiency [3

3. M. S. Vitiello, G. Scamarcio, V. Spagnolo, S. S. Dhillon, and C. Sirtori, “Terahertz quantum cascade lasers with large wall-plug efficiency,” Appl. Phys. Lett. 90(19), 191115 (2007). [CrossRef]

], beam quality [4

4. M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009). [CrossRef]

], linewidth [5

5. M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012). [CrossRef]

] and wavelength tunability [6

6. J. Xu, J. M. Hensley, D. B. Fenner, R. P. Green, L. Mahler, A. Tredicucci, M. G. Allen, F. Beltram, H. E. Beere, and D. A. Ritchie, “Tunable terahertz quantum cascade lasers with an external cavity,” Appl. Phys. Lett. 91(12), 121104 (2007). [CrossRef]

] have been reported. However, their temperature performance, so far limited to heat sink temperatures TH < 200 K [7

7. 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/kB,” Nat. Phys. 7(2), 166–171 (2011). [CrossRef]

,8

8. 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(4), 3866–3876 (2012). [CrossRef] [PubMed]

], is still a key issue. Active regions based on the resonant tunneling scheme for the population of the upper laser level have so far shown a maximum operating temperature TH ~ħω/KB [7

7. 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/kB,” Nat. Phys. 7(2), 166–171 (2011). [CrossRef]

], where KB is the Boltzmann constant. For instance, the maximum operating temperature (~200 K) of the device reported in [8

8. 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(4), 3866–3876 (2012). [CrossRef] [PubMed]

] is about 1.28 ħω/KB. Designing the energy separation between the lower laser level and the ground state subband resonant to the LO-phonon energy (ELO) is very effective for the fast depopulation of the lower laser level (the so-called resonant phonon scheme). On the other hand, the use of scattering-assisted (SA) injection schemes, in which the energy difference between the injector state and the upper laser level is also close to ELO, is very promising for the attainment of terahertz laser action at TH > 200 K [7

7. 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/kB,” Nat. Phys. 7(2), 166–171 (2011). [CrossRef]

,9

9. E. Dupont, S. Fathololoumi, Z. R. Wasilewski, G. Aers, S. R. Laframboise, M. Lindskog, S. G. Razavipour, A. Wacker, D. Ban, and H. C. Liu, “A phonon scattering assisted injection and extraction based terahertz quantum cascade laser,” J. Appl. Phys. 111(7), 073111 (2012). [CrossRef]

,10

10. K. Fujita, M. Yamanishi, S. Furuta, K. Tanaka, T. Edamura, T. Kubis, and G. Klimeck, “Indirectly pumped 3.7 THz InGaAs/InAlAs quantum-cascade lasers grown by metal-organic vapor-phase epitaxy,” Opt. Express 20(18), 20647–20658 (2012). [CrossRef] [PubMed]

]. Recently, THz QCL devices based on phonon-SA active region scheme have been realized, showing lasing at 2.4 THz up to 152 K (~1.3 ħω/KB) in pulsed operation [11

11. S. G. Razavipour, E. Dupont, S. Fathololoumi, C. W. I. Chan, M. Lindskog, Z. R. Wasilewski, G. Aers, S. R. Laframboise, A. Wacker, Q. Hu, D. Ban, and H. C. Liu (unpublished).

] and at 1.8 THz to 163 K (~1.9 ħω/KB) [7

7. 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/kB,” Nat. Phys. 7(2), 166–171 (2011). [CrossRef]

].

A critical understanding of the actual lattice temperature (TL) and the nature of the electronic distribution and particularly the individual j-th subband electronic temperatures (Tej) is crucial to validate theoretical models and to refine the design of THz QCL active regions with improved thermal performance [10

10. K. Fujita, M. Yamanishi, S. Furuta, K. Tanaka, T. Edamura, T. Kubis, and G. Klimeck, “Indirectly pumped 3.7 THz InGaAs/InAlAs quantum-cascade lasers grown by metal-organic vapor-phase epitaxy,” Opt. Express 20(18), 20647–20658 (2012). [CrossRef] [PubMed]

]. The temperature dependence of the physical parameters controlling the laser rate equations, i.e. intersubband transitions rates, the Debye screening length [12

12. R. Nelander and A. Wacker, “Temperature dependence of the gain profile for terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(8), 081102 (2008). [CrossRef]

] and the existence of hot-electron distributions have been neglected so far. Thermalized subband electron distributions characterized by the same electronic temperature in all subbands [9

9. E. Dupont, S. Fathololoumi, Z. R. Wasilewski, G. Aers, S. R. Laframboise, M. Lindskog, S. G. Razavipour, A. Wacker, D. Ban, and H. C. Liu, “A phonon scattering assisted injection and extraction based terahertz quantum cascade laser,” J. Appl. Phys. 111(7), 073111 (2012). [CrossRef]

] are typically assumed in theoretical models. However, microprobe band-to-band photoluminescence spectroscopy experiments demonstrated that in THz QCLs Tej > TL > TH [13

13. M. S. Vitiello, G. Scamarcio, V. Spagnolo, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Measurement of subband electronic temperatures and population inversion in THz quantum-cascade lasers,” Appl. Phys. Lett. 86(11), 111115 (2005). [CrossRef]

15

15. M. S. Vitiello, G. Scamarcio, V. Spagnolo, T. Losco, R. P. Green, A. Tredicucci, H. E. Beere, and D. A. Ritchie, “Electron-lattice coupling in bound-to-continuum THz quantum-cascade lasers,” Appl. Phys. Lett. 88(24), 241109 (2006). [CrossRef]

]. In addition, the combination of a resonant-tunneling injection and a resonant-phonon depopulation scheme, causes a strong increase of the upper laser level temperature by ΔT ~100 K [13

13. M. S. Vitiello, G. Scamarcio, V. Spagnolo, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Measurement of subband electronic temperatures and population inversion in THz quantum-cascade lasers,” Appl. Phys. Lett. 86(11), 111115 (2005). [CrossRef]

], while the ground-state temperature remains almost close to the lattice one.

In this work, we have compared the lattice temperatures and the subband electronic temperatures, in three GaAs/Al0.25Ga0.75As active regions structures based on the phonon scattering both for the population of the upper laser level and the depletion of the lower laser one. A hot electron distribution has been found in all investigated cases. However, a maximum electron heating Tej -TL ~40 K, much lower than the typical value reported for the QCLs based on the resonant phonon transitions only for the depopulation of the lower laser level, has been found.

2. Investigated samples

Three active region designs based on the phonon SA injection scheme have been investigated. Figure 1
Fig. 1 Calculated conduction (a-c) and valence (d-f) band structures (1 period) of the investigated GaAs/Al0.25Ga0.75As samples a (V0843), b (V0845) and c (V0962) under applied voltages per period / electric field of (67.1 mV / 18.6 kV/cm), (71.8 mV / 18.7 kV/cm), and (64.5 mV / 16.4 kV/cm), respectively. A 75% conduction-band offset, corresponding to a 0.275 eV barrier height, was used. Starting from the injection barrier, the layers thickness in (Å) are (from right to left) (a): 44/63/11/67/23/85/9/61, (b) 44/64/16/72/28/104/6/50, and (c) 35/48/8/39/9/72/27/86/5/66. The total number of periods are 276, 260 and 253 for samples (a), (b), and (c). The barriers are indicated in bold fonts. The underlined layers are doped. Samples (a) and (b) are center delta-doped with Si to a sheet density of n = 3.25∙1010 cm−2 and n = 3.46∙1010 cm−2, respectively. Sample (c) is conventionally doped to n = 1.5∙1017 cm−3 in the center 2 nm of the 4.8 nm quantum well.
shows the conduction and valence band structures of the three samples, while in Table 1

Table 1. The squared moduli of the overlap integrals |⟨ψj|ψk ⟩|2 between conduction (j) and valence (k) subband envelope functions are reported from top to bottom for sample (a), (b) and (c), respectively. This calculation is performed at the electric field values of Fig. 1. Bold values marks the transitions j → k with |⟨ψj|ψk ⟩|2 □ 0.2.

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are reported the squared moduli of the overlap integrals |⟨ψjk⟩|2 between conduction (j) and valence (k) subband envelope functions.

The laser emission frequencies measured at 10 K and close to threshold for QCLs having the same structures of sample (a), (b), and (c) are 2.8 THz, 2.4 THz, 2.45 THz and the maximum operating temperatures reached in pulsed mode are 138 K [9

9. E. Dupont, S. Fathololoumi, Z. R. Wasilewski, G. Aers, S. R. Laframboise, M. Lindskog, S. G. Razavipour, A. Wacker, D. Ban, and H. C. Liu, “A phonon scattering assisted injection and extraction based terahertz quantum cascade laser,” J. Appl. Phys. 111(7), 073111 (2012). [CrossRef]

], 128.5 K, 144 K, respectively.

The main difference between the three structures is in the energies of the phonon-assisted transitions 43 and 21 (see Table 2

Table 2. Energies of relevant intersubband transitions of Fig. 1. E43 corresponds to the phonon scattering assisted injection; E32 is the laser transition energy; E21 is associated with the depletion of the lower laser level.

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) as compared with the LO phonon energy ELO = 36 meV.

A PdGeTiPtAu metallization process was used to fabricate top and bottom alloyed Ohmic contacts and In-Au wafer bonding technique was applied to transfer the epi-layers to a host GaAs n+. Mesa devices were fabricated by reactive-ion etching [16

16. 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(10), 105021 (2011). [CrossRef]

]. Electrical contacts are obtained by gold wire-bonding directly onto the top of the devices. The areas of devices (a), (b), and (c) are A = 70 μm × 170 μm, A = 75 μm × 170 μm, and A = 145 μm × 180 μm, respectively. The thickness of the active region is d = 10 μm for all samples.

Figure 2
Fig. 2 (a-c): the current density (J)-voltage per stage (V) characteristics of sample a, b, and c in continuous-wave (CW) operation and at the heat sink temperature TH = 50 K. Dashed lines are guides for eyes.
shows the voltage drop per stage (V) measured in continuous wave (CW) at TH = 50 K as a function of the current density (J). A first resonance, corresponding to 1’-3 (sample (a)) and 1’-2 (sample (b) and (c)) level alignment, can be observed at ~9 mV, ~25 mV, and ~17 mV, in sample (a), (b) and (c), respectively. At larger voltages, a negative differential resistance (NDR) region is evident in the range (27 mV - 60 mV), (30 mV - 65 mV), and (25 mV - 60 mV), in sample (a),(b) and (c) respectively. The flat monotonic increase of J at V > 64 mV, V > 67 mV, and V > 62 mV, in sample (a),(b), and (c), corresponds to the band alignment for tunnel injection into level 4, in good agreement with the calculations shown in Fig. 1.

3. Experimental setup

The lattice and electronic temperatures were extracted by analyzing microprobe band-to-band photoluminescence (PL) spectra, as a function of continuous current density and bias voltage. This technique has already proved successful for the investigation of mid-IR [17

17. V. Spagnolo, M. Troccoli, G. Scamarcio, C. Becker, G. Glastre, and C. Sirtori, “Thermal resistance and temperature characteristics of GaAs/Al0.33Ga0.67As quantum cascade lasers,” Appl. Phys. Lett. 78(9), 1177–1179 (2001). [CrossRef]

, 18

18. V. Spagnolo, G. Scamarcio, H. Page, and C. Sirtori, “Simultaneous measurement of the electronic and lattice temperatures in GaAs/Al0.45Ga0.55As quantum-cascade lasers: Influence on the optical performance,” Appl. Phys. Lett. 84(18), 3690 (2004). [CrossRef]

] and THz [13

13. M. S. Vitiello, G. Scamarcio, V. Spagnolo, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Measurement of subband electronic temperatures and population inversion in THz quantum-cascade lasers,” Appl. Phys. Lett. 86(11), 111115 (2005). [CrossRef]

15

15. M. S. Vitiello, G. Scamarcio, V. Spagnolo, T. Losco, R. P. Green, A. Tredicucci, H. E. Beere, and D. A. Ritchie, “Electron-lattice coupling in bound-to-continuum THz quantum-cascade lasers,” Appl. Phys. Lett. 88(24), 241109 (2006). [CrossRef]

, 19

19. M. S. Vitiello, G. Scamarcio, V. Spagnolo, C. Worrall, H. E. Beere, D. A. Ritchie, C. Sirtori, J. Alton, and S. Barbieri, “Subband electronic temperatures and electron-lattice energy relaxation in terahertz quantum cascade lasers with different conduction band offsets,” Appl. Phys. Lett. 89(13), 131114 (2006). [CrossRef]

, 20

20. G. Scamarcio, M. S. Vitiello, V. Spagnolo, S. Kumar, B. Williams, and Q. Hu, “Nanoscale heat transfer in quantum cascade lasers,” Physica E 40(6), 1780–1784 (2008). [CrossRef]

] QCLs. The PL signal was obtained by focusing the 647-nm line of a Kr+ laser directly onto the QCL front facet in an Airy disk of about ~2 μm diameter, by using an 80X long working distance achromatic microscope objective lens. The devices were mounted into a helium-flow micro-cryostat including a 0.5 mm quartz window. We simultaneously measured the temperature of the heat sink and device copper mount, by using a thermocouple and a calibrated Si-diode, respectively. In our experiment the copper mount temperature was kept at the constant value of TH = 50 K. The incident power density was kept below ~500 W/cm2, that caused a local laser-induced heating < 6 K. The estimated density of photogenerated carriers in the device is in the range 0.5-1 × 1015 cm−3, 1-2 orders of magnitude lower than the doping level in the active region. The laser excitation mostly provides the valence band holes needed to probe the electronic population via band-to-band radiative recombination.

The PL signal was transmitted through an holographic notch filter, dispersed using a 0.64 m monochromator equipped with a 600 lines/mm grating and detected with a Si charge coupled device cooled to 134 K. A spectral resolution of 0.2 meV is used. All experimental spectra were recorded by focusing the Kr+ laser spot on the cleaved side facet of the mesas, in the middle of the active region.

Preliminarily to the spectral analysis, the PL spectra have been corrected for the spectral response of the spectroscopic setup. The typical approach to determine the experimental response function is based on calibration procedure using radiation sources whose emission spectral lineshape are known, e.g. black body-like emitters. We have used as an internal standard the high energy portion of the luminescence spectra emitted from the thermalized two-dimensional electron gas of the investigated samples, without applied voltage. In fact, the corresponding lineshape is characterized by a simple exponential decay at increasing photon energy [21

21. J. Shah, Hot Carriers in Semiconductor Nanostructures: Physics and Applications (Academic, 1992).

]. Our approach has the advantage of inherently taking into account geometrical effect corrections that otherwise affect the calibrations based on the comparison with a standard light source [22

22. J. A. Gardecki and M. Maroncelli, “Set of secondary emission standards for calibration of the spectral responsivity in emission spectroscopy,” Appl. Spectrosc. 52(9), 1179–1189 (1998). [CrossRef]

].

4. Lattice and electronic temperatures

If a voltage is applied, the high energy conduction subbands start to be aligned and populated. The radiative recombination between populated conduction subbands and photogenerated holes gives origin to additional structure on the high energy side of the PL spectra, whose intensity is well reproduced by the following expression:
IPL(E)j=14k=14AjkEjk4|ψj|ψk|2(E)
(1)
where Ajk = nj ∙ pk; nj and pk are the populations of the conduction and valence subband. The lineshape function (E) is obtained joining a Lorentzian with a phenomenological broadening Γ(TL) on the low energy side and an exponential decay on the high energy side of the main peak, respectively:
(E)={A2πΓ(TL)(EEjk)2+Γ2(TL)       E<Ejk+ΔjBeE(1KBTej+me*mhh*  1KBThh)                      E>Ejk+Δj           
(2)
where Tej, Thh are the electron subband and heavy-hole temperatures, me* = 0.067 and mhh* = 0.51 are the electron and heavy-hole effective masses, Ejk is the j→k transition energy. The ratio A/B and Δj must been chosen to ensure the continuity between the two portions of. It is well accepted that the heavy hole temperature is close to the lattice one under moderate to high electric fields [21

21. J. Shah, Hot Carriers in Semiconductor Nanostructures: Physics and Applications (Academic, 1992).

] so that we assume Thh = TL. For the temperature dependence of the linewidth Γ(TL) we used:
Γ(TL)=Γ0+aTL+beωLOKBTL1
(3)
where Γ0 = 1.66 meV, a = 11.6 × 10−3 meV∕K and b = 15.6 meV [24

24. J. Martinez-Pastor, A. Vinattieri, L. Carraresi, M. Colocci, P. Roussignol, and G. Weimann, “Temperature dependence of exciton lifetimes in GaAs/AlxG1-xAs single quantum wells,” Phys. Rev. B 47(16), 10456–10460 (1993). [CrossRef]

].

An excellent reproduction of the photoluminescence spectra recorded under applied voltage was obtained by using Eqs. (1)(3), considering the j→k transitions having an overlap integral >˜ 0.2 (see the Table 2) and leaving only E13, Tej and Ajk as fitting parameters. The (Ejk - E13) energy differences are extracted from band structure calculations assuming temperature independence of the intersubband transitions. Figure 4
Fig. 4 (a-c): Representative photoluminescence spectra (blue lines) and best fit functions (dashed lines) of samples a-c under applied voltages per period / electric field of (64.3 mV / 17.8 kV/cm), (70.3 mV / 18.3 kV/cm), and (62.8 mV / 15.9 kV/cm), respectively. The heat sink temperature is TH = 50 K. The calculated individual contributions associated with relevant j → k transitions are also shown.
shows representative PL spectra and best fit curves for samples (a-c) corresponding to the band alignments of Fig. 1.

The main contributions to the PL spectra are due to transitions involving the conduction subbands j = 1 and j = 3, corresponding to the injection/extraction state and the higher laser level, respectively. This is qualitative in agreement with the expected higher populations of subbands j = 1 and j = 3, according to active region design [9

9. E. Dupont, S. Fathololoumi, Z. R. Wasilewski, G. Aers, S. R. Laframboise, M. Lindskog, S. G. Razavipour, A. Wacker, D. Ban, and H. C. Liu, “A phonon scattering assisted injection and extraction based terahertz quantum cascade laser,” J. Appl. Phys. 111(7), 073111 (2012). [CrossRef]

]. Analogously, PL contributions involving the conduction subbands j = 2 and j = 4, are considerably weaker. This is quantitatively supported by the detailed PL analysis, as discussed later. Note that, in the sample (b) the contribution of transitions involving the conduction subband j = 2 is negligible. This is due to the small overlap integral of j = 2 with valence subbands (see Table 1) and to its expected low population.

In the PL spectra of sample (b) at threshold for current injection are clearly visible additional bands due to heavy-hole (HH) and light-hole (LH) excitons bound to the j = 4 subband (see Fig. 4(b)). The intensity of these excitonic contributions rapidly decrease at larger power densities and become negligible when Te > 160. Similar excitonic transitions have been previously observed in bound-to-continuum THz QCLs [15

15. M. S. Vitiello, G. Scamarcio, V. Spagnolo, T. Losco, R. P. Green, A. Tredicucci, H. E. Beere, and D. A. Ritchie, “Electron-lattice coupling in bound-to-continuum THz quantum-cascade lasers,” Appl. Phys. Lett. 88(24), 241109 (2006). [CrossRef]

]. In addition, the HH-LH splitting (~17 meV) is in agreement with the value expected for a GaAs quantum well ~12 nm wide, similar to the extension of the j = 4 wavefunction (~14 nm). These bands are fitted with Lorentzian functions with a half width at half maximum of ~1.8 meV, typical of excitonic peaks [24

24. J. Martinez-Pastor, A. Vinattieri, L. Carraresi, M. Colocci, P. Roussignol, and G. Weimann, “Temperature dependence of exciton lifetimes in GaAs/AlxG1-xAs single quantum wells,” Phys. Rev. B 47(16), 10456–10460 (1993). [CrossRef]

]. Similar structure are barely visible in sample (c) at threshold for current injection and not present in the PL spectra of sample (a) due to the higher Te values that establish in this sample, as reported below.

Figure 5
Fig. 5 Mean lattice temperature (●) and electronic temperatures Te1,2,3 (■) and Te4 (▲) in the active region of sample (a), (b) and (c) measured as a function of the electrical power at a heat sink temperature TH = 50 K. Solid lines are linear fit to the data.
shows the lattice and electronic subband temperatures as a function of the electrical power density, as extracted from the fitting procedure. The temperature values in the NDR regions are not reported because of the uncertainty in the electric field homogeneity. Note that below band alignment for carrier injection into level j = 4 we determine only the active region lattice temperature (see Figs. 1(a)-1(c)).

From the data of Fig. 5 we extracted the normalized thermal resistance [14

14. M. S. Vitiello, G. Scamarcio, V. Spagnolo, J. Alton, S. Barbieri, C. Worrall, H. E. Beere, D. A. Ritchie, and C. Sirtori, “Thermal properties of THz quantum cascade lasers based on different optical waveguide configurations,” Appl. Phys. Lett. 89(2), 021111 (2006). [CrossRef]

] values RL*=RL·Ad where RL = dTL/dP is the device thermal resistance, and P is the electrical power. We found the values RL* = 6.86 K∙cm/W for sample (a), RL* = 7.11 K∙cm/W for sample (b), and RL* = 8.42 K∙cm/W for sample (c). These values are similar to those found in resonant-phonon active regions based on GaAs/Al0.15Ga0.85As material system and double-metal contacts [13

13. M. S. Vitiello, G. Scamarcio, V. Spagnolo, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Measurement of subband electronic temperatures and population inversion in THz quantum-cascade lasers,” Appl. Phys. Lett. 86(11), 111115 (2005). [CrossRef]

]. The larger RL* value measured for the sample (c) can be partly ascribed to the density of interfaces which is ~13% larger than samples (a), (b) [25

25. M. S. Vitiello, G. Scamarcio, and V. Spagnolo, “Temperature dependence of thermal conductivity and boundary resistance in thz quantum cascade lasers,” IEEE, J. Select. Topics in Quant. Electron. 14, 431–435 (2008).

].

5. Relative electronic populations

From the best fit values of Ajk associated with transitions involving the same valence subband k, it is possible to extract the nj /nm population ratios. It is particularly interesting to examine the ratio n2/n1 as extracted from the PL bands associated with the 1→3 and 2→3 transitions bands (see Fig. 4 (c)). Figure 6
Fig. 6 Relative population n2/n1 between the lower laser level (j = 2) and the extractor level (j = 1) for sample (c) (●). Relative population n2/n1 calculated assuming a thermal populations of the subbands j = 1 and j = 2 for sample (c) (■). The dashed curves are guides for the eye.
shows the ratio n2/n1 as a function of the electronic temperature for sample (c). These values are shown together with n2/n1 values calculated assuming a thermal occupancy of the subbands j = 1 and j = 2 following the Maxwell-Boltzmann thermal distribution, n2/n1=exp(E21/KBTe1), and using experimental electronic subband temperatures.

Our results show that the electronic population ratios n2/n1 remains below the value corresponding to the thermal occupancy due to the quasi-resonant optical phonon scattering. This process efficiently depopulates the lower laser level (j = 2) up to an electronic temperature Te ~180 K. However, at larger Te the ratio n2/n1 starts to increase with a rate comparable with the thermal activation one, thereby hindering the population inversion between the laser levels j = 3 and j = 2. Similar results are found for sample (a).

6. Conclusion

We have measured and compared the electronic and lattice temperatures of three QCL active region structures based on the phonon-scattering assisted injection and extraction by means of microprobe band-to-band photoluminescence. A non-equilibrium hot electron distribution have been found. Differently from resonant phonon scheme where electrons are directly injected into the upper laser level, causing a large extra heating with respect to the lattice [13

13. M. S. Vitiello, G. Scamarcio, V. Spagnolo, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Measurement of subband electronic temperatures and population inversion in THz quantum-cascade lasers,” Appl. Phys. Lett. 86(11), 111115 (2005). [CrossRef]

, 26

26. M. S. Vitiello, G. Scamarcio, J. Faist, G. Scalari, C. Walther, E. H. Beere, and D. A. Ritchie, “Probing quantum efficiency by laser-induced hot-electron cooling,” Appl. Phys. Lett. 94(2), 021115 (2009). [CrossRef]

], in the investigated phonon-SA injection and extraction scheme both laser levels remain much colder and share the same electronic temperature of the extractor level. The relative n2/n1 subbands electron population ratios shows an efficient lower laser level depletion at low electronic temperatures, whereas at temperatures larger than Te ~180 K the ratio n2/n1 starts to increase with a rate comparable with the thermal activation one.

Acknowledgments

We gratefully acknowledge G. Palazzo for useful discussions on the spectral calibration analysis. This work is partially supported by Italian research projects: PON01_02238 and PON02_00675. The co-authors from Canada acknowledges D. Ban and H.C. Liu for their support and useful discussions on the design. M.S.V. acknowledges financial support of the Italian Ministry of Education, University, and Research (MIUR) through the program “FIRB-Futuro in Ricerca 2010” RBFR10LULP “Fundamental research on terahertz photonic devices”.

References and links

1.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002). [CrossRef] [PubMed]

2.

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42(2), 89–91 (2006). [CrossRef]

3.

M. S. Vitiello, G. Scamarcio, V. Spagnolo, S. S. Dhillon, and C. Sirtori, “Terahertz quantum cascade lasers with large wall-plug efficiency,” Appl. Phys. Lett. 90(19), 191115 (2007). [CrossRef]

4.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009). [CrossRef]

5.

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012). [CrossRef]

6.

J. Xu, J. M. Hensley, D. B. Fenner, R. P. Green, L. Mahler, A. Tredicucci, M. G. Allen, F. Beltram, H. E. Beere, and D. A. Ritchie, “Tunable terahertz quantum cascade lasers with an external cavity,” Appl. Phys. Lett. 91(12), 121104 (2007). [CrossRef]

7.

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/kB,” Nat. Phys. 7(2), 166–171 (2011). [CrossRef]

8.

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(4), 3866–3876 (2012). [CrossRef] [PubMed]

9.

E. Dupont, S. Fathololoumi, Z. R. Wasilewski, G. Aers, S. R. Laframboise, M. Lindskog, S. G. Razavipour, A. Wacker, D. Ban, and H. C. Liu, “A phonon scattering assisted injection and extraction based terahertz quantum cascade laser,” J. Appl. Phys. 111(7), 073111 (2012). [CrossRef]

10.

K. Fujita, M. Yamanishi, S. Furuta, K. Tanaka, T. Edamura, T. Kubis, and G. Klimeck, “Indirectly pumped 3.7 THz InGaAs/InAlAs quantum-cascade lasers grown by metal-organic vapor-phase epitaxy,” Opt. Express 20(18), 20647–20658 (2012). [CrossRef] [PubMed]

11.

S. G. Razavipour, E. Dupont, S. Fathololoumi, C. W. I. Chan, M. Lindskog, Z. R. Wasilewski, G. Aers, S. R. Laframboise, A. Wacker, Q. Hu, D. Ban, and H. C. Liu (unpublished).

12.

R. Nelander and A. Wacker, “Temperature dependence of the gain profile for terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(8), 081102 (2008). [CrossRef]

13.

M. S. Vitiello, G. Scamarcio, V. Spagnolo, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Measurement of subband electronic temperatures and population inversion in THz quantum-cascade lasers,” Appl. Phys. Lett. 86(11), 111115 (2005). [CrossRef]

14.

M. S. Vitiello, G. Scamarcio, V. Spagnolo, J. Alton, S. Barbieri, C. Worrall, H. E. Beere, D. A. Ritchie, and C. Sirtori, “Thermal properties of THz quantum cascade lasers based on different optical waveguide configurations,” Appl. Phys. Lett. 89(2), 021111 (2006). [CrossRef]

15.

M. S. Vitiello, G. Scamarcio, V. Spagnolo, T. Losco, R. P. Green, A. Tredicucci, H. E. Beere, and D. A. Ritchie, “Electron-lattice coupling in bound-to-continuum THz quantum-cascade lasers,” Appl. Phys. Lett. 88(24), 241109 (2006). [CrossRef]

16.

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(10), 105021 (2011). [CrossRef]

17.

V. Spagnolo, M. Troccoli, G. Scamarcio, C. Becker, G. Glastre, and C. Sirtori, “Thermal resistance and temperature characteristics of GaAs/Al0.33Ga0.67As quantum cascade lasers,” Appl. Phys. Lett. 78(9), 1177–1179 (2001). [CrossRef]

18.

V. Spagnolo, G. Scamarcio, H. Page, and C. Sirtori, “Simultaneous measurement of the electronic and lattice temperatures in GaAs/Al0.45Ga0.55As quantum-cascade lasers: Influence on the optical performance,” Appl. Phys. Lett. 84(18), 3690 (2004). [CrossRef]

19.

M. S. Vitiello, G. Scamarcio, V. Spagnolo, C. Worrall, H. E. Beere, D. A. Ritchie, C. Sirtori, J. Alton, and S. Barbieri, “Subband electronic temperatures and electron-lattice energy relaxation in terahertz quantum cascade lasers with different conduction band offsets,” Appl. Phys. Lett. 89(13), 131114 (2006). [CrossRef]

20.

G. Scamarcio, M. S. Vitiello, V. Spagnolo, S. Kumar, B. Williams, and Q. Hu, “Nanoscale heat transfer in quantum cascade lasers,” Physica E 40(6), 1780–1784 (2008). [CrossRef]

21.

J. Shah, Hot Carriers in Semiconductor Nanostructures: Physics and Applications (Academic, 1992).

22.

J. A. Gardecki and M. Maroncelli, “Set of secondary emission standards for calibration of the spectral responsivity in emission spectroscopy,” Appl. Spectrosc. 52(9), 1179–1189 (1998). [CrossRef]

23.

V. Spagnolo, G. Scamarcio, D. Marano, M. Troccoli, F. Capasso, C. Gmachl, A. M. Sergent, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, H. Page, C. Becker, and C. Sirtori, “Thermal characteristics of quantum-cascade lasers by micro-probe optical spectroscopy,” IEE Proc., Optoelectron. 150(4), 298–305 (2003). [CrossRef]

24.

J. Martinez-Pastor, A. Vinattieri, L. Carraresi, M. Colocci, P. Roussignol, and G. Weimann, “Temperature dependence of exciton lifetimes in GaAs/AlxG1-xAs single quantum wells,” Phys. Rev. B 47(16), 10456–10460 (1993). [CrossRef]

25.

M. S. Vitiello, G. Scamarcio, and V. Spagnolo, “Temperature dependence of thermal conductivity and boundary resistance in thz quantum cascade lasers,” IEEE, J. Select. Topics in Quant. Electron. 14, 431–435 (2008).

26.

M. S. Vitiello, G. Scamarcio, J. Faist, G. Scalari, C. Walther, E. H. Beere, and D. A. Ritchie, “Probing quantum efficiency by laser-induced hot-electron cooling,” Appl. Phys. Lett. 94(2), 021115 (2009). [CrossRef]

OCIS Codes
(250.5230) Optoelectronics : Photoluminescence
(140.5965) Lasers and laser optics : Semiconductor lasers, quantum cascade

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: February 19, 2013
Revised Manuscript: March 22, 2013
Manuscript Accepted: March 22, 2013
Published: April 16, 2013

Citation
Pietro Patimisco, Gaetano Scamarcio, Maria Vittoria Santacroce, Vincenzo Spagnolo, Miriam Serena Vitiello, Emmanuel Dupont, Sylvain R. Laframboise, Saeed Fathololoumi, Ghasem S. Razavipour, and Zbigniew Wasilewski, "Electronic temperatures of terahertz quantum cascade active regions with phonon scattering assisted injection and extraction scheme," Opt. Express 21, 10172-10181 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-10172


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References

  1. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002). [CrossRef] [PubMed]
  2. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett.42(2), 89–91 (2006). [CrossRef]
  3. M. S. Vitiello, G. Scamarcio, V. Spagnolo, S. S. Dhillon, and C. Sirtori, “Terahertz quantum cascade lasers with large wall-plug efficiency,” Appl. Phys. Lett.90(19), 191115 (2007). [CrossRef]
  4. M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics3(10), 586–590 (2009). [CrossRef]
  5. M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012). [CrossRef]
  6. J. Xu, J. M. Hensley, D. B. Fenner, R. P. Green, L. Mahler, A. Tredicucci, M. G. Allen, F. Beltram, H. E. Beere, and D. A. Ritchie, “Tunable terahertz quantum cascade lasers with an external cavity,” Appl. Phys. Lett.91(12), 121104 (2007). [CrossRef]
  7. 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/kB,” Nat. Phys.7(2), 166–171 (2011). [CrossRef]
  8. 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. Express20(4), 3866–3876 (2012). [CrossRef] [PubMed]
  9. E. Dupont, S. Fathololoumi, Z. R. Wasilewski, G. Aers, S. R. Laframboise, M. Lindskog, S. G. Razavipour, A. Wacker, D. Ban, and H. C. Liu, “A phonon scattering assisted injection and extraction based terahertz quantum cascade laser,” J. Appl. Phys.111(7), 073111 (2012). [CrossRef]
  10. K. Fujita, M. Yamanishi, S. Furuta, K. Tanaka, T. Edamura, T. Kubis, and G. Klimeck, “Indirectly pumped 3.7 THz InGaAs/InAlAs quantum-cascade lasers grown by metal-organic vapor-phase epitaxy,” Opt. Express20(18), 20647–20658 (2012). [CrossRef] [PubMed]
  11. S. G. Razavipour, E. Dupont, S. Fathololoumi, C. W. I. Chan, M. Lindskog, Z. R. Wasilewski, G. Aers, S. R. Laframboise, A. Wacker, Q. Hu, D. Ban, and H. C. Liu (unpublished).
  12. R. Nelander and A. Wacker, “Temperature dependence of the gain profile for terahertz quantum cascade lasers,” Appl. Phys. Lett.92(8), 081102 (2008). [CrossRef]
  13. M. S. Vitiello, G. Scamarcio, V. Spagnolo, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Measurement of subband electronic temperatures and population inversion in THz quantum-cascade lasers,” Appl. Phys. Lett.86(11), 111115 (2005). [CrossRef]
  14. M. S. Vitiello, G. Scamarcio, V. Spagnolo, J. Alton, S. Barbieri, C. Worrall, H. E. Beere, D. A. Ritchie, and C. Sirtori, “Thermal properties of THz quantum cascade lasers based on different optical waveguide configurations,” Appl. Phys. Lett.89(2), 021111 (2006). [CrossRef]
  15. M. S. Vitiello, G. Scamarcio, V. Spagnolo, T. Losco, R. P. Green, A. Tredicucci, H. E. Beere, and D. A. Ritchie, “Electron-lattice coupling in bound-to-continuum THz quantum-cascade lasers,” Appl. Phys. Lett.88(24), 241109 (2006). [CrossRef]
  16. 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(10), 105021 (2011). [CrossRef]
  17. V. Spagnolo, M. Troccoli, G. Scamarcio, C. Becker, G. Glastre, and C. Sirtori, “Thermal resistance and temperature characteristics of GaAs/Al0.33Ga0.67As quantum cascade lasers,” Appl. Phys. Lett.78(9), 1177–1179 (2001). [CrossRef]
  18. V. Spagnolo, G. Scamarcio, H. Page, and C. Sirtori, “Simultaneous measurement of the electronic and lattice temperatures in GaAs/Al0.45Ga0.55As quantum-cascade lasers: Influence on the optical performance,” Appl. Phys. Lett.84(18), 3690 (2004). [CrossRef]
  19. M. S. Vitiello, G. Scamarcio, V. Spagnolo, C. Worrall, H. E. Beere, D. A. Ritchie, C. Sirtori, J. Alton, and S. Barbieri, “Subband electronic temperatures and electron-lattice energy relaxation in terahertz quantum cascade lasers with different conduction band offsets,” Appl. Phys. Lett.89(13), 131114 (2006). [CrossRef]
  20. G. Scamarcio, M. S. Vitiello, V. Spagnolo, S. Kumar, B. Williams, and Q. Hu, “Nanoscale heat transfer in quantum cascade lasers,” Physica E40(6), 1780–1784 (2008). [CrossRef]
  21. J. Shah, Hot Carriers in Semiconductor Nanostructures: Physics and Applications (Academic, 1992).
  22. J. A. Gardecki and M. Maroncelli, “Set of secondary emission standards for calibration of the spectral responsivity in emission spectroscopy,” Appl. Spectrosc.52(9), 1179–1189 (1998). [CrossRef]
  23. V. Spagnolo, G. Scamarcio, D. Marano, M. Troccoli, F. Capasso, C. Gmachl, A. M. Sergent, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, H. Page, C. Becker, and C. Sirtori, “Thermal characteristics of quantum-cascade lasers by micro-probe optical spectroscopy,” IEE Proc., Optoelectron.150(4), 298–305 (2003). [CrossRef]
  24. J. Martinez-Pastor, A. Vinattieri, L. Carraresi, M. Colocci, P. Roussignol, and G. Weimann, “Temperature dependence of exciton lifetimes in GaAs/AlxG1-xAs single quantum wells,” Phys. Rev. B47(16), 10456–10460 (1993). [CrossRef]
  25. M. S. Vitiello, G. Scamarcio, and V. Spagnolo, “Temperature dependence of thermal conductivity and boundary resistance in thz quantum cascade lasers,” IEEE, J. Select. Topics in Quant. Electron.14, 431–435 (2008).
  26. M. S. Vitiello, G. Scamarcio, J. Faist, G. Scalari, C. Walther, E. H. Beere, and D. A. Ritchie, “Probing quantum efficiency by laser-induced hot-electron cooling,” Appl. Phys. Lett.94(2), 021115 (2009). [CrossRef]

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