## Abstract

Strain-balanced In_{0.6}Ga_{0.4}As/Al_{0.56}In_{0.44}As quantum cascade lasers emitting at a wavelength of 7.1 μm are reported. The active region is based on a three-phonon-resonance quantum design with a low voltage defect of 120 meV at injection resonance. A maximum wall-plug efficiency of 19% is demonstrated in pulsed mode at 293 K. Continuous-wave output power of 1.4 W and wall-plug efficiency of 10% are measured at the same temperature, as well as 1.2 W of average power in uncooled operation. A model for backfilling of the lower laser level which takes into account the number of subbands in the injector is presented and applied to determine the optimum value of the voltage defect to maximize wall-plug efficiency at room temperature, which is found to be ~100 meV, in good agreement with experimental results.

© 2011 OSA

## 1. Introduction

The performance of room temperature infrared quantum cascade lasers (QCLs) has improved significantly in the past few years, which saw the demonstration of multi-watt continuous wave (cw) output power [1,2], pulsed mode wall-plug efficiency (WPE) of the order of 25% [2,3], and watt-level uncooled operation [4,5]. So far, most of these improvements have been realized in the mid-wave infrared (MWIR) spectral range, between 4 and 5 μm. QCL performance in the long-wave infrared (LWIR) range (7-12 μm), where principal applications are chemical sensing, is still significantly lower. The maximum pulsed WPE demonstrated in this spectral region is 11.5%, at a wavelength of 8.5 μm [6]. At a wavelength of ~7 μm [7–9], the maximum cw output power and wallplug efficiency at room temperature reported in the literature are 0.7 W and 5%, respectively [7]. In this letter, we report 7.1 μm QCLs with a pulsed WPE of 19% and cw output power and WPE of 1.4 W and 10%, respectively. A maximum average power of 1.2 W and a WPE of 12.5% at 1 W power level are demonstrated in uncooled operation.

The challenges in designing LWIR QCLs are critically different from those for MWIR QCLs. The WPE of the latter is mostly limited by carrier escape into the continuum and satellite valleys, which adversely affects the device internal efficiency [4,10]. The critical design parameters which influence the WPE of LWIR QCLs, on the other hand, are waveguide losses α_{w}, and the voltage defect Δ, defined as the energy difference between the lower laser level of one gain stage and the upper laser level of the next one, which, in this spectral range, is comparable to the photon energy. We address waveguide losses by growing a thick, low-doped dielectric waveguide. To optimize the voltage defect, we introduce a model for the backfilling of the lower laser level which, unlike the conventional model [11], takes into account the number of subbands in the injector. We show that the traditional model strongly overestimates backfilling at low voltage defect. Our model predicts an optimum voltage defect of ~100 meV for achieving maximum WPE at room temperature.

## 2. Laser design and fabrication

The active region of our QCL is based on a three-phonon-resonance design [12]. Each gain stage is composed of a five-quantum-well (QW) active region followed by a five-QW injector. The conduction band diagram of one gain stage under an applied electric field of 51 kV/cm is shown in Fig. 1
. Strain-balanced material compositions with ~0.5% strain were used in the active region to increase the conduction band offset to ~600 meV and hence improve carrier confinement. The use of similar strain has already been reported by several authors at this wavelength [7,8]. It is particularly important in our case because the upper laser level is higher in the quantum well, in our three-phonon-resonance design, than that in traditional two-phonon-resonance designs [7,8]. Our simulations show an energy difference Δ*E*
_{C4} of ~250 meV between the upper laser level and the continuum (see Fig. 1). The energy spacing between the upper laser level and the first state above it is Δ*E*
_{54} = 60 meV.

The QCLs active region and InP waveguide were grown by molecular beam epitaxy (MBE) on an n-doped InP substrate (3 **×** 10^{18} cm^{−3}) in a single growth step. The epitaxial layer sequence, starting from the substrate, was as follows: InP cladding layer (*n* = 1 **×** 10^{17} cm^{−3}, thickness 2.5 μm), InP cladding layer (3 **×** 10^{16} cm^{−3}, 2.5 μm), 45-stage strain-balanced In_{0.6}Ga_{0.4}As/Al_{0.56}In_{0.44}As active region (2.43 μm), InP cladding layer (3 **×** 10^{16} cm^{−3}, 2.5 μm), InP cladding layer (1 **×** 10^{17} cm^{−3}, 2.5 μm), InP plasmon layer (8 **×** 10^{18} cm^{−3}, 1.5 μm), and a heavily-doped InGaAs contact layer (0.2 μm). Waveguide simulations resulted in an optical confinement factor of 0.76 and waveguide losses of 0.65 cm^{−1} (not taking into account intersubband absorption in the active region) at a wavelength of 7.1 μm for 10 μm-wide lasers processed in buried heterostructure geometry. The voltage drop across the low doped InP cladding layers is estimated to be 28 mV/(kA/cm^{2}), assuming an electron mobility of 5000 cm^{2}V^{−1}s^{−1}.

The epi-wafer was processed into buried heterostructure lasers with active region width varying between 8 and 12 μm and cleaved into chips of 2 to 5.8 mm length, which were then mounted epi-side down on aluminum nitride submounts with gold-tin hard solder [13].

## 3. Laser characterization

#### 3.1 Low-duty-cycle pulsed operation

Low-duty-cycle pulsed testing was performed at chip-on-carrier level. Devices were pulsed at 10 kHz repetition rate with a pulse width of 500 ns and the output power was measured with a calibrated thermopile detector placed directly in front of the output facet. Peak output power (for two facets), voltage, and WPE as function of current of an uncoated 3 mm x 8 μm chip at a temperature of 293 K are shown in the main panel of Fig. 2
. The threshold and roll-over current densities are 1.45 and 5.38 kA/cm^{2}, respectively. The slope efficiency is 3.59 W/A, and the maximum WPE 18.9%. This is in excess of the room temperature wall-plug efficiency limit of 18% predicted by Faist at this wavelength, for a dephasing time of 70 fs [11]. To our knowledge, this is the first time that this limit, which, as stated in [11], should not be interpreted as a fundamental limit, is experimentally exceeded at any wavelength. By performing similar measurements for temperatures between 293 K and 348 K, we deduced characteristic temperatures of *T*
_{0} = 158 K and *T*
_{1} = 441 K for threshold current and slope efficiency, respectively. These values are comparable to those previously reported in the literature for high performance QCLs operating at similar wavelengths [7–9], indicating that the temperature dependence of the performance of our QCLs is not affected by the low voltage defect, in this temperature range. The maximum WPE is still 13.4% at 348 K.

The top panel of Fig. 2 shows the measured voltage defect Δ = V/*N*
_{p} – *h*ν, where V is the voltage drop across the entire structure, *N*
_{p} = 45 is the number of gain stages, and *h*ν = 175 meV is the photon energy, as a function of current. The voltage drop across the InP cladding layers (~0.1 V at *J* = 4 kA/cm^{2}) represents only ~1% of the total voltage and, therefore, was neglected in the voltage defect calculation. The voltage defect at threshold, maximum WPE, and roll-over is measured to be ~45, 95, and 120 meV, respectively.

Waveguide losses were estimated by measuring slope efficiency as a function of mirror losses for cavity lengths between 2 and 5.8 mm and performing the same analysis as in [4], resulting in α_{w} = 1.7 ± 0.2 cm^{−1}. The difference between the experimental value and waveguide simulations is attributed to sidewall roughness and non-resonant intersubband absorption in the active region, which were not taken into account in our simulations.

#### 3.2 Continuous-wave operation

For thermoelectrically-cooled cw operation, thermistors were mounted ~0.5 mm away from the QCL chips on the AlN submounts [13]. Chips-on carriers were then mounted in hermetically-sealed butterfly-type packages containing a thermoelectric cooler (TEC) and collimating optics. The back facet was high-reflection (HR) coated to provide single-ended emission, and the front facet was partially anti-reflection (AR) coated to maximize WPE [4]. The partial AR coating was designed to produce the same mirror losses α_{m} as for a 1.5 mm-long HR/uncoated chip, i.e. α_{m} = 4.3 cm^{−1}, which for a 4 mm-long device requires a reflectivity of ~3%. Cw output power, voltage, and WPE as function of current of a 4 mm **×** 8 μm laser at a temperature of 293 K are shown in Fig. 3
. Data were corrected for the lens collection efficiency which is equal to 0.9. A threshold current density of 2.12 kA/cm^{2}, slope efficiency of 2.81 W/A, maximum power of 1.38 W and maximum WPE of 10.0% are measured at this temperature. The inset in Fig. 3 shows the laser spectrum in cw mode at 293 K at a current of 1.12 A. The spectrum is centered at 7.14 μm under these operating conditions. The significant increase in threshold current and decrease in slope efficiency and WPE observed between pulsed and cw modes indicates that the doping level is too high for optimum cw operation. This is also confirmed by the fact that the power roll-over in cw operation occurs at a current density of ~3.9 kA/cm^{2}, which is ~30% lower than in pulsed mode. Cw performance will be improved by regrowing the structure with a lower active region doping.

A beam picture of the packaged QCL is shown in Fig. 4
. The picture was taken with a pyroelectric camera placed 2 m away from the laser, without additional optics. The laser was operated in cw mode at 293 K at a current of 1.12 A, corresponding to an output power level of 1.06 W (not corrected for the lens collection efficiency). A zeroth order beam profile is observed along both axes (TM_{00}). The measured divergence half-angles at 1/*e*
^{2} of the collimated beam are 1.6 mrad and 1.5 mrad along the horizontal (x) and vertical (y) axes, respectively.

#### 3.3 High-duty-cycle uncooled operation

Chips were also tested in high-duty-cycle uncooled operation [4,5]. In this case, chips-on-carrier were mounted in hermetically-sealed packages containing a heat spreader and collimating optics, but no TEC. A thermistor was mounted close to the chip for temperature monitoring. Larger chip dimensions of 5.8 mm x 12 μm were chosen to improve heat dissipation [5]. Devices were HR/AR coated. An AR coating reflectivity of 0.7% was chosen, in order to obtain the same value of mirror losses as for cw operation. Measured average power as a function of duty cycle of such a device operated at a heatsink temperature of 293 K is shown in the top of Fig. 5 . The laser was operated at 12.3 V and 2.3 A with 500 ns pulses. Data were corrected for the lens collection efficiency. The maximum average power is 1.18 W at a duty cycle of 42.5%. WPE as a function of output power is shown in the bottom of Fig. 5. The WPE is equal to 14.5% and 12.5% at 0.5 W and 1 W average power levels, respectively. Since these lasers do not contain a TEC, the efficiency of the overall laser system is roughly equal to that of the laser, making them appealing for battery-operated portable and handheld LWIR applications.

## 4. Backfilling model

As discussed in the introduction, one of the critical design parameters, which influence QCL WPE in the LWIR, is the voltage defect Δ. Faist [11] and Howard [14] predict optimal voltage defects of 150 meV and 175 meV, respectively, for room temperature operation. Both of these models described backfilling of the lower laser level as *n*
_{therm} = *n*
_{s} exp(-Δ/*kT*), where *n*
_{s} is the sheet carrier density per gain stage. This implicitly assumes a constant density of states in the injector, i.e. an injector consisting of a single subband. Here we introduce a more refined model, which takes into account the number of subbands in the injector.

We assume that the injector states are equally spaced by Δ*E*
_{inj} = Δ /*N*
_{inj}, where *N*
_{inj} is the number of injector subbands ( = numbers of subbands below the lower laser level, per gain stage). This is a good approximation of a typical energy level distribution in a QCL injector (see Fig. 1) and it has the advantages that it does not require to know the exact positions of the levels and that it introduces only one additional parameter (*N*
_{inj}) compared to the traditional model. Neglecting non-parabolicity, the two-dimensional density of states can be written as:

*D*

_{0}is the density of states of one subband and

*θ*is the Heaviside step function. Assuming, as in the conventional model, a thermal distribution in the injector, the carrier density per unit energy and area iswhere

*f*(

*E*) is the Fermi-Dirac distribution and $Z={\displaystyle {\int}_{0}^{\infty}D(E)f(E)dE}$ is the partition function. Due to the low carrier density in QCLs,

*f*(

*E*) can be approximated by the Boltzmann distribution exp(-

*E*/

*kT*). The lower laser level backfilling is calculated as:

*N*

_{inj}+ 1) factor accounts for the degeneracy of the energy states due to the presence of multiple subbands. Calculations can be performed analytically in the case of the Boltzmann distribution, resulting in the following formula for backfilling:

In the limit Δ >> 2*N*
_{inj}
*kT*, our formula tends towards the single-subband approximation: *n*
_{therm} ≈*n*
_{s} exp(-Δ/*kT*), because only the lowest injector subband is significantly populated. However, this limit does not correspond to a practical case at room temperature. At *T* = 300 K, for instance, it corresponds to Δ >> 400 meV.

*n*
_{therm}/*n*
_{s} as a function of Δ at *T* = 300 K obtained with this model and with the usual approximation are plotted in the inset in Fig. 6
. Comparing the two, we find that, for the design presented in this paper in which *N*
_{inj} = 8, the single-subband approximation overestimates the backfilling by factors of ~2, 2.5, and 4 for Δ = 150, 100, and 50 meV, respectively.

We now apply our model to determine the voltage defect, which maximizes WPE at room temperature. The WPE as a function of Δ is plotted in Fig. 6 for *N*
_{inj} = 8, using the same numerical parameters as in [11]. The maximum WPE is reached for Δ ~100 meV, which is significantly lower than the values given in [11] and [14]. This is in good agreement with our experimentally observed maximum WPE of 19% for Δ ~95 meV. The maximum WPE of 27% at 4.9 μm reported by Bai et al. in [2] was also obtained at Δ ~100 meV. The single-subband model, on the other hand predicts that lasing is not possible for Δ < 65 meV, which is in contradiction with our experimental results presented in Fig. 2.

Our model reveals a dependence of backfilling on the number of subbands in the injector, with a noticeable decrease of *n*
_{therm} with increasing *N*
_{inj}. For a typical *N*
_{inj} of 8, this translates into a significant reduction of the optimum value of Δ, which results in an increased WPE, especially in the LWIR, where the photon energy is comparable to the voltage defect, and in the very long-wave infrared (VLWIR, λ > 12 μm), where the photon energy is smaller than the voltage defect. Quantitatively, a voltage defect reduction from 150 meV to 100 meV corresponds to a relative increase in voltage efficiency of 18% at 7 μm, 22% at 10 μm, and 25% at 12 μm. This is in contrast to the model of [11] in which the number of injector states only influences the WPE indirectly via the transport time. We believe that this is one of the reasons why the various attempts of increasing QCL WPE by shortening the injector, in order to decrease the transport time, reported in the literature (see for instance [15] and [16]) did not work as expected: shortening the injector resulted in an increased backfilling at room temperature.

## 5. Conclusion

In conclusion, we report 7.1 μm QCLs with strain-balanced active region and low voltage defect. The maximum WPE is 19% in pulsed mode at room temperature. This is the first report of a WPE higher than the Faist limit (for a dephasing of 70 fs). Output power of nearly 1.4 W and WPE of 10% were measured in cw mode, at 293 K. We believe that cw WPE can be further increased for the same active region design by reducing the doping level. Average output power of nearly 1.2 W and WPE in excess of 10% were measured from uncooled lasers. Finally, we have presented a model for backfilling of the lower laser level and have given a new design rule for the voltage defect, which according to our calculations is ~100 meV for maximum WPE at room temperature, in agreement with our experimental results. Based on the experimental and theoretical results presented here, we conclude that the WPE predictions for the LWIR spectral range [11] have been underestimated thus far and should be revised.

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