Multiwatt long wavelength quantum cascade lasers based on high strain composition with 70% injection efficiency

Arkadiy Lyakh; Richard Maulini; Alexei Tsekoun; Rowel Go; C. Kumar N. Patel

doi:10.1364/OE.20.024272

1. Introduction

Driven by a strong demand from a number of commercial and defense applications, research on midwave infrared (MWIR) quantum cascade lasers (QCLs) emitting in the first atmospheric window (3.5-4.8µm) has resulted in a significant progress in laser performance over the last several years [1–4]. However, room temperature QCL characteristics could not be fully described by practical models, which did not rely on computation-intensive numerical simulations. Therefore, MWIR QCL development was mostly guided by general principles, often without a systematic analysis of relative contributions of different laser design parameters to overall laser performance.

While some success has been achieved in calculating threshold current density and its temperature dependence for MWIR QCLs [5], there is still a significant discrepancy between theoretical and experimental data for slope efficiency. In a simple model based on the rate equations, slope efficiency can be presented in the following form:

\frac{d P}{d I} \approx \frac{h υ}{q} N_{s} \frac{α_{m}}{α_{m} + α_{w}} \frac{1}{1 + \frac{τ_{3}}{τ_{4}}} η_{i}

where N_s is a number of cascade stages, α_m – mirror losses, α_w – waveguide losses, τ₄ – upper laser level lifetime, τ₃ – lower laser level lifetime, and η_i – injection efficiency that is usually determined by fitting results of Eq. (1) to experimental data. The fundamental reason why simple models do not adequately describe room temperature laser characteristics is that the injection efficiency term in Eq. (1) is a function of carrier leakage from the upper laser level, which is very difficult to fully take into account. As a consequence, unintentional changes in injection efficiency often mask expected results from changes in laser design. The best approach to experimentally study the injection efficiency would be first designing a structure with nearly ideal injection efficiency and then modifying the structure by changing, for example, band offset to study corresponding changes in injection efficiency in a controllable manner.

For MWIR QCLs, relatively large laser transition energy leads to a high position of the upper laser level, close to the top of the Γ-valley barriers and bottom of indirect-valleys quantum wells. As a consequence, it is difficult to entirely suppress carrier leakage through continuum states and indirect states in MWIR QCLs. In addition, it is difficult to separately evaluate individual contributions of the two types of carrier leakage. Situation is more favorable in the case of longwave infrared (LWIR) QCLs emitting in the second atmospheric window (8-12µm). Since laser transition energy is much smaller than in the MWIR region, it is easier to confine carriers in the upper laser level. Position of indirect valleys has a relatively weak dependence on material composition. Therefore, leakage through indirect states in LWIR QCLs is expected to be entirely suppressed for a wide range of band offsets. As a consequence, it is possible to independently study carrier leakage through Γ-states in LWIR QCLs by changing band offset.

LWIR QCLs, important for gas sensing and, potentially, free space communications, are traditionally designed and fabricated using the lattice matched AlInAs/InGaAs composition that has a relatively small band offset of 520meV. For emission wavelength of ~9µm, this band offset results in ~250meV energy spacing between the upper laser level and the continuum states located above the barriers, similar to that of MWIR QCLs. Therefore, band offset of the lattice matched composition is not sufficient for taking full advantage of smaller transition energy of LWIR QCLs for the purposes of suppressing carrier leakage from the upper laser state.

The main reason for using the lattice matched composition is that spontaneous emission linewidth of the laser transition is expected to increase with increase in band offset, i.e., with increase in strain, which, in turn, reduces optical gain. We experimentally showed recently, however, that highly strained QCL designs can have spontaneous emission linewidth similar to that of designs based on significantly lower strain composition [1]. Employment of high strain promises, therefore, a way of improving LWIR QCL performance.

2. Laser design

The 9μm non-resonant extraction active region design presented here was based on a strain-balanced In_0.58Ga_0.42As/Al₀.₆₄In_0.36As composition (0.36% strain in quantum wells and −1.10% in barriers). A conduction band diagram of two gain stages of the new design is shown in Fig. 1 . Radiative transition is between levels 4 and 3. Energy spacing E₅₄ was designed to be approximately 60meV. Energy spacing between the upper laser level and top of the direct barriers, E_C4, was increased up to 430meV. Calculated laser transition matrix element, upper and lower laser lifetimes for this design were 2.44nm, 1.22ps and 0.25ps, respectively. Carrier lifetimes were calculated taking into account only interaction with longitudinal optical phonons and assuming T = 298K. Targeted sheet carrier density for active region doping was 1.5·10¹¹ cm⁻².

Fig. 1 Band diagram of a quantum cascade laser structure based on In_0.58Ga_0.42As/Al₀.₆₄In_0.36As composition and designed using non-resonant extraction principle for light emission at 9 μm.

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The optical waveguide was designed to achieve low free-carrier optical losses by keeping the doping level low (2·10¹⁶cm⁻³) in the 3µm cladding layers adjacent to the 45-stage active region design described above. The rest of the waveguide structure consists of 4µm (top) and 2µm (bottom) low doped (5·10¹⁶cm⁻³) InP layers and a highly doped (8·10¹⁸cm⁻³) 1µm plasmon layer, which helps to decouple the optical mode from the lossy metal top contact. This waveguide design resulted in calculated free-carrier waveguide losses of α_fc = 1.1cm⁻¹ and optical mode overlap factor with the active region, Γ, of 52%. Loss contribution from free carriers in the active region was ignored in these calculations.

The 45-stage quantum cascade laser active region, along with the waveguide and contact layers was grown by molecular beam epitaxy on a low doped (2·10¹⁷ cm⁻³) InP substrate. The wafer was then processed into a buried heterostructure geometry and cleaved into individual laser chips and into round mesas for electroluminescence measurements. The laser chips were mounted epi-side down on AlN/SiC composite submounts [1] for pulsed and CW characterization. Pulsed testing was performed with 500 ns pulses and 0.5% duty cycle and CW operation was controlled with a thermo-electrical cooler.

3. Experimental data

Electroluminescence (EL) data measured at room temperature for a round mesa in the vicinity of threshold voltage and roll over voltage are shown in Fig. 2(a) . EL peak is centered at 9.1µm at threshold and 8.7µm at roll over. Figure 2(b) summarizes EL full width at half maximum (FWHM) dependence on bias. EL is relatively wide at threshold since several radiative transitions contribute to gain. It quickly narrows down at higher bias as a single transition becomes dominant, reaching approximately 14meV at roll over. The narrow EL spectrum at roll over confirms our previous results published in Ref. 1 demonstrating that EL FWHM comparable to that of lattice matched material can be achieved for highly strained compositions.

Fig. 2 (a) Electroluminescence spectra of a round mesa at threshold and roll-over voltages (298K); (b) Dependence of electroluminescence linewidth on voltage.

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Figure 3 shows a comparison between pulsed and CW total optical power from both facets vs. current (LI) and voltage vs. current (IV) characteristics at 293 K for an uncoated 3 mm by 10 µm laser. Threshold current density, slope efficiency, maximum WPE and maximum optical power from both facets in pulsed and CW modes at 293K were measured to be 2.1 and 2.5 kA/cm², 2.8 and 2.1 W/A, 16 and 10%, and 4.4 and 2.0 W, respectively. Both optical power and efficiency in pulsed/CW mode are the highest values reported at this wavelength and exceed the best previously reported result by over factor of two [6]. Figure 3 inset shows that pulsed laser spectrum taken at maximum current was centered close to 9.2 µm.

Fig. 3 Comparison between pulsed and CW total optical power vs current and voltage vs current characteristics measured at 293K for an uncoated 3mm by 10µm laser mounted epi-down on a AlN/SiC composite submount. Inset shows pulsed laser spectrum taken at maximum current.

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An important aspect of the LIV curves shown in Fig. 3 is their behavior at bias values above LI curve roll over. The pulsed LI curve shows a very abrupt decrease in optical power, while the pulsed IV curve shows a sharp increase in differential resistance. This behavior in the vicinity of the roll-over condition demonstrates that carrier tunneling from the injector to the active region states other than the upper laser level is suppressed. In other words, these results indicate improved injection efficiency for the upper laser level.

4. Discussion on capability of a simple model based on rate equations to predict room temperature laser characteristics

Injection efficiency term, as well as waveguide losses and material gain, can be extracted from dependence of laser slope efficiency and threshold current density on cavity length [7]. Formula for threshold current density in this case should take into account transparency current density J_tr, as follows [7].

J_{t h} = J_{t r} + \frac{α_{m} + α_{w}}{Γ g}

where g is the differential gain. The largest contribution to transparency current is carrier backfilling of the lower laser level. This approach may have limited accuracy when slope efficiency has strong dependence on applied voltage in the entire dynamic range, as suggested in Ref. 5. However, for this design pulsed slope efficiency was constant close to threshold for all tested lasers, which justified employment of this method in this work.

A linear fit for inverse slope efficiency vs. cavity length data is shown in Fig. 4(a) . Injection efficiency term calculated from the data was equal to 70%, a significant improvement over the value of 50% that we measured for one of our best 4.6 µm structures with the same E₅₄ ≈60meV [8, 9]. We attribute this improvement to larger E_C4 achieved in the active region design. Measured injection efficiency was also larger than 60% reported in Ref. 10, its highest value reported for QCLs.

Fig. 4 Dependence of slope efficiency (a) and threshold current density (b) on cavity length. The two linear fits resulted in the following set of parameters: η_i = 70%, α_w = 1.6cm⁻¹, g = 14cm/kA, and J_tr = 1.3kA/cm².

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Waveguide losses obtained from the linear fit in Fig. 4(a) were equal to 1.6 cm⁻¹. As discussed above, free carrier losses in the bulk waveguide layers (not taking into account losses originating from the active region) were calculated to be 1.1 cm⁻¹. Therefore, combined contribution from all the other components of waveguide losses that are often difficult to calculate a priori, such as sidewall scattering and intersubband/free-carrier losses in the active region, is 0.5 cm⁻¹, less than 10% of the total losses for an uncoated 3 mm laser. This is an important result showing that laser slope efficiency for this structure can be well predicted taking into account only free carrier absorption in bulk waveguide layers that is well studied and easy to calculate.

Transparency current density and differential gain obtained from the linear fit to the data for threshold current density dependence on inverse laser cavity length (Fig. 4(b)) were found to be 1.3 kA/cm² and 14 cm/kA, respectively.

Differential gain gets clamped at its threshold value. EL data in Fig. 2(a) demonstrate that several radiative transitions contribute to gain at threshold. This observation is consistent with band diagram simulation in the vicinity of threshold that shows that there are three radiative transitions from the upper laser level with large matrix elements (1.61nm, 1.58nm, and 0.74nm) separated by approximately 10meV (levels 3, 2, and one of injector levels). To account for the multiple closely spaced transitions, formula for differential gain should take the following form:

g (λ) = \frac{4 π e}{ε_{0} n λ L_{p}} η_{i} τ_{4} (1 - \frac{τ_{3}}{τ_{43}}) \sum^{​} \frac{z_{4 f}^{2} (\frac{γ_{4 f}}{2})}{{(E_{4 f} - h ν)}^{2} + {(\frac{γ_{4 f}}{2})}^{2}}

where L_p is active region stage length equal to 45nm for this structure, z_4f and γ_4f – matrix element and EL FWHM of a radiative transition from the upper laser level 4 to a final state f. Summation in Eq. (3) is done over all final states contributing to gain. Since individual linewidths for each of the involved transitions could not be measured separately, we used γ_4f measured at 11V, i.e. 18meV. 11V was the closest voltage to threshold whose EL was defined by a single transition. Under this assumption, differential gain calculated using Eq. (3) was found to be 16 cm/kA, close to the measured value of 14 cm/kA.

Measured transparency current density for the new structure accounts for more than 50% of the threshold current density. It should be, therefore, considered as one of the most important characteristics in laser design. In the rate equation model, transparency current J_tr can be written as:

J_{t r} = \frac{e}{η_{i} τ_{4} (1 - τ_{3} / τ_{43})} \cdot n_{3, t h e r m}

where n_3,therm is the thermal backfilling of the lower laser level. In the following calculations we use the injector model presented in Ref. 11. With a few generally valid approximations, the backfilling term in this model can be expressed as:

n_{3, t h e r m} = n_{s} e^{- \frac{Δ_{i n j}}{2 k T}} \frac{\sinh (\frac{Δ_{i n j}}{2 N_{i n j} k T})}{\sinh (\frac{(N_{i n j} + 1) Δ_{i n j}}{2 N_{i n j} k T})}

where n_s is the sheet carrier density per gain stage in the active region, Δ_inj is the energy difference between the lower laser level and the ground state of the injector (equal in our case to 93 meV at threshold), and N_inj = 6 is the number of injector states. Since doping calibration for strained layers may not be accurate, we deduced n_s from the measured pulsed roll-over current density J_max, by fitting the experimental value to the theoretical value calculated using the density matrix approach [12]:

J_{\max} = e n_{s} \frac{2 Ω^{2} τ_{⊥}}{1 + 4 Ω^{2} τ_{4} τ_{⊥}},

where the injector splitting is

2 ℏ Ω

= 7 meV, and the in-plane relaxation time

τ_{⊥} = ℏ / γ_{43}

= 95 fs is estimated from measured electroluminescence linewidth at roll over. This procedure resulted in a sheet carrier density n_s = 5.7·10¹¹ cm⁻². For this value of carrier density, calculated transparency current density equals 1.4 kA/cm², in a very good agreement with its measured value of 1.3 kA/cm². It is important to point out that employment of the traditionally used formula for back filling that neglects step-like density of states for the injector with quantized energy levels [13] results in J_tr = 2.9 kA/cm², in poor agreement with the experimental data. While the latter approximation may be valid at low temperatures, Eq. (5) should be used for higher accuracy at room temperature.

In the calculations for transparency current we assumed that the electronic temperature is equal to the lattice temperature. Terazzi and Faist have shown in Reference [14] that this electron–lattice thermalization hypothesis accurately describes experimental QCL characteristics at room temperature. The data presented in Fig. 4(a) and 4(b) were acquired in pulsed operation with a short pulse width of 500 ns and a low duty cycle of 0.5%. Therefore self-heating of the QCL active region could be neglected and the lattice temperature was taken to be equal to the heatsink temperature, i.e. 293K.

The fact that the experimentally found value for injection efficiency gave accurate prediction both for differential gain and transparency current shows that results presented here are self consistent. In the calculations above we used experimental data for EL FWHM and sheet carrier density. However, these experimental data can now be used to calibrate the process of growing new designs in the same reactor. This will allow calculating both quantities a priori. The only parameter in the model that still cannot be predicted is the injection efficiency term. As mentioned above, the best starting point to study this term would be a LWIR QCL structure with nearly ideal injection efficiency. A systematic study based on modifications of this structure would allow the development of a practical, semi-empirical model for injection efficiency. We believe that the goal of reaching injection efficiency close to 100% is realistic. Other than the use of large band offset (high strain), the present LWIR structure was not optimized for the highest injection efficiency and, therefore, can be improved further. Carrier leakage through the parasitic energy level 5 located above the upper laser level and direct carrier injection to the lower laser level can be addressed first.

6. Conclusion

In conclusion, we have presented experimental data on 9 µm QCLs with active region design based on a high strain composition. Record-high pulsed and CW WPE of 16% and 10% and optical power of 4.4W and 2.0W, respectively, were demonstrated at 293 K for an uncoated 3mm by 10µm laser mounted epi side down on AlN/SiC composite submounts. Very good correspondence was demonstrated between experimental data for all laser characteristics and a refined model based on rate equations using measured 70% injection efficiency.

References and links

1. A. Lyakh, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “Tapered 4.7 μm quantum cascade lasers with highly strained active region composition delivering over 4.5 watts of continuous wave optical power,” Opt. Express 20(4), 4382–4388 (2012). [CrossRef] [PubMed]

2. Y. Bai, N. Bandyopadhyay, S. Tsao, S. Slivken, and M. Razeghi, “Room temperature quantum cascade lasers with 27% wall plug efficiency,” Appl. Phys. Lett. 98(18), 181102 (2011). [CrossRef]

3. A. Lyakh, R. Maulini, A. Tsekoun, R. Go, S. Von der Porten, C. Pflugl, L. Diehl, F. Capasso, and C. K. N. Patel, “High-performance continuous-wave room temperature 4.0-µm quantum cascade lasers with single-facet optical emission exceeding 2 W,” Proc. Natl. Acad. Sci. U.S.A. 107, 18801 (2010).

4. N. Bandyopadhyay, Y. Bai, B. Gokden, A. Myzaferi, S. Tsao, S. Slivken, and M. Razeghi, “Watt level performance of quantum cascade lasers in room temperature continuous wave operation at λ~3.76 µm,” Appl. Phys. Lett. 97(13), 131117 (2010). [CrossRef]

5. D. Botez, S. Kumar, J. C. Shin, L. J. Mawst, I. Vurgaftman, and J. R. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97(7), 071101 (2010). [CrossRef]

6. M. Troccoli, X. Wang, and J. Fan, “Quantum cascade lasers: high-power emission and single-mode operation in the long-waveinfrared (λ>6 µm),” Opt. Eng. 49(11), 111106 (2010). [CrossRef]

7. M. Razeghi, “High-perfomance InP-based Mid-IR quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 15(3), 941–951 (2009). [CrossRef]

8. R. Maulini, A. Lyakh, A. Tsekoun, R. Go, C. Pflugl, L. Diehl, F. Capasso, and C. K. N. Patel, “High power thermoelectrically cooled and uncooled quantum cascade lasers with optimized reflectivity facet coating,” Appl. Phys. Lett. 95(15), 151112 (2009). [CrossRef]

9. A. Lyakh, R. Maulini, A. Tsekoun, R. Go, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, and C. K. N. Patel, “3 W continuous-wave room temperature single-facet emission from quantum cascade lasers based on nonresonant extraction design approach,” Appl. Phys. Lett. 95(14), 141113 (2009). [CrossRef]

10. Y. Bai, S. Slivken, S. R. Darvish, and M. Razeghi, “Very high wall plug efficiency of quantum cascade lasers,” Proc. of SPIE vol. 7608, 76080F (2010)

11. R. Maulini, A. Lyakh, A. Tsekoun, and C. K. N. Patel, “λ~7.1 μm quantum cascade lasers with 19% wall-plug efficiency at room temperature,” Opt. Express 19(18), 17203–17211 (2011). [CrossRef] [PubMed]

12. C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34(9), 1722–1729 (1998). [CrossRef]

13. J. Faist, C. Sirtori, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “High-power long-wavelength (λ~11.5 µm) quantum cascade lasers operating above room temperature,” IEEE Photon. Technol. Lett. 10(8), 1100–1102 (1998). [CrossRef]

14. R. Terazzi and J. Faist, “A density matrix model of transport and radiation in quantum cascade lasers,” New J. Phys. 12(3), 033045 (2010). [CrossRef]

Multiwatt long wavelength quantum cascade lasers based on high strain composition with 70% injection efficiency

Abstract

1. Introduction

2. Laser design

3. Experimental data

4. Discussion on capability of a simple model based on rate equations to predict room temperature laser characteristics

6. Conclusion

References and links

Cited By

Figures (4)

Equations (6)

Optics Express