Increased coupling is observed in distributed-feedback quantum cascade lasers when placing a shallow second order grating between a continuous surface-plasmon layer and the active region. The combined effect of an air cladding and a metallic layer on the opposite sides of the waveguide increases the overlap with the grating region resulting in calculated coupling coefficients up to 100 cm-1. The waveguide design was implemented by Au thermo-compression bonding after grating formation and subsequent backside processing of ridges with air claddings. Lasers as short as 176 μm show single-mode behavior with a side-mode-suppression-ratio of 20 dB and thresholds (10 kA/cm2) as well as output powers (> 150 mW) close to Fabry-Pérot device performances are reached for 360 μm long devices.
© 2008 Optical Society of America
Quantum cascade lasers  (QCLs) are compact and powerful [2-4] semiconductor light sources in the mid-IR and THz region. Viable emission wavelengths cover a huge portion of the chemical fingerprint region making them interesting for spectroscopic and sensing applications . These in turn need tunable single-mode sources which are typically realized by either external cavity set-ups [6,7] or distributed feedback (DFB) lasers having a grating either on top , buried  or along the side [10,11] of a ridge waveguide. In the case of DFB lasers wavelength tunability is given via the change of refractive index with temperature. The relatively small tuning range can be increase by building DFB arrays with closely spaced emission wavelengths . By applying an additional bias current the device temperature can be influenced making a compact and continuously tunable source possible .
DFB gratings also enable surface emission. Since QCLs use intersubband transitions to generate light, the electric field is polarized perpendicular to the layers and surface emission is only possible with an adequate coupling mechanism. This can be provided by a second order DFB grating comprising both: single-mode and surface emission [14-17]. Since second order gratings typically have low coupling coefficients in the range of κ<10 cm-1 one has to provide a feedback length of L>1 mm in order to reach the critical coupling strength of κL=1 . This need of a large cavity which is an advantage when pushing towards high power output is limiting their usability e.g. as portable single-mode devices desiring low power consumption. Short cavities however need a stronger feedback. An interesting and new approach to this is to make use of the very high coupling in photonic crystals (PhCs) which was realized in a single-mode surface emitting PhC QCL . Very much the same way as for 2nd order DFBs, PhCs address single-mode operation and surface emission at once but allowing for compact device dimensions. However, since the PhC pattern has to penetrate the entire waveguide highly demanding etching techniques are necessary and the control of the air filling factor is crucial too.
In this paper we present the realization of a novel waveguide formed by a surface-plasmon and an air cladding having a DFB grating between the closed surface-plasmon layer and the active region. Its cavity length ranges in between a conventional DFB and a PhC laser since it increases the coupling strength for shallow gratings via an increased modal overlap with the grating. To prove the working principle we fabricated short 2nd order DFB lasers which show single-mode operation for cavities even shorter than 200 μm.
Although not shown in this publication the possibility of having a higher coupling strength than in the case of conventional waveguides allows fabricating 2D gratings of relatively small size. These shallow PhC structures could be used to decrease beam divergency in either direction, thus removing the need for complicated collimation optics allowing straight forward integration into sensitive gas sensing systems.
2. Waveguide design
The waveguide claddings are made up by a continuous surface-plasmon layer on one and air on the other side. This is realized by Au-Au thermo-compression bonding of the laser material on a GaAs template and processing the laser chip from the backside. The core of the waveguide consists of the active region (60 stages, 4.23 μm) and a 1 μm thick Al0.9Ga0.1As layer (doping: 4×1017 cm-3). The DFB grating is etched prior to the wafer bonding step into an Al0.9Ga0.1As buffer layer. In this way the grating is placed in between the metal layer and the active region (see Figs. 1, 3 or 4). The relatively large number of stages in the active region is due to a required minimum thickness for the waveguide core. A further reduction of waveguide thickness degrades laser performance due to increased losses in the metal layer. A doable way to reduce growth effort would be to partially remove the active region by GaAs spacer layers at both sides. Since the laser field is small at the sides population inversion is provided mainly in the center of the active region and laser performance is therefore expected to remain vastly unchanged.
Out-coupling of light takes place via the air cladding at the side opposite to the grating, similar as has been shown recently for a substrate emitting DFB QCL . This increases the slope efficiency of the laser since light that is otherwise lost by diffraction into the substrate will also be emitted via the device surface. For a more detailed explanation of the fabrication process and the exact layer sequence please refer to the fabrication section.
2.1 Influence of the cladding layers on the coupling strength
The benefit of the design is its high modal overlap with the grating caused by the combined influence of the metallic and the air cladding. This is illustrated in Fig. 1, which shows the absolute value of the coupling strength |κ| calculated in 2D  for several variations on the waveguide. All of them have in common the same thickness for the active region (4.23 μm) and for the Al0.9Ga0.1As buffer layer (1 μm) as well as the same grating with a duty-cycle σ=0.5 and a depth of 700 nm. For a structure as fabricated with Au/air claddings we calculate |κ|=41.9 cm-1. If the top metal layer is replaced by air |κ| drops to 21.8 cm-1. Additionally replacing the lower air cladding by a plasmon-enhanced cladding, given via highly doped (2×1018 cm-3) GaAs, reduces the value to 11.5 cm-1. This behavior is understood by the fact that the metal attracts the optical mode and an increased fraction of the light is forced into the grating region. The stronger confinement provided by air instead of dielectric like claddings increases this effect. As a last variation a medium doped (4×1016 cm-3) GaAs core layer is placed in between the highly doped GaAs and the active region. This reduces the waveguide losses but yields a |κ| of only 2.5 cm-1. As a comparison we add values of a conventional waveguide optimized for a 2nd order DFB laser as used in Ref. . The according values are |κ|=7.7 cm-1 and α=13.6 cm-1. Cases B-D are of course no utilizable waveguides but are very well illustrating the influence of the cladding layers on the coupling strength and the transition to a standard waveguide for 2nd order DFB QCLs.
2.2 Influence of the duty-cycle on the coupling strength
Optimizing waveguide losses and coupling strength yields an ideal grating depth of 700 nm in a 1 μm thick Al0.9Ga0.1As layer (doping: 4×1017 cm-3). The dependence of the coupling strength on the grating duty-cycle σ was calculated as well the overall waveguide losses. The data is collected in Fig. 2(a). The main change which effects the waveguide properties is the rise of average refractive index in the grating region with increasing duty-cycle. This causes a larger portion of the mode to be located in the grating region, as can be seen comparing the waveguide modes shown in Fig. 2(b) that are calculated for σ=0.5 and 0.77 respectively. A higher modal overlap in turn increases the coupling strength until it reaches a maximum of |κ|≈100 cm-1 for a mark-space ratio of 0.77. For higher duty-cycles the increasing overlap is jeopardized by the fact that the perturbation of refractive index is getting smaller and |κ| decreases again. A large grating overlap is however also connected with increased absorption in the doped Al0.9Ga0.1As layer as well as at the semiconductor-metal interface, causing a steady increase in waveguide losses over duty-cycle. For the previously mentioned duty-cycle of 0.77 which maximizes the coupling we calculate α=54 cm-1 and Γ=0.97. To determine the origin of the waveguide losses a simulation with lower Al0.9Ga0.1As doping of 4×1016 cm-3 was carried out which results in waveguide losses of 12 cm-1 whereas coupling strength remains unchanged. A substantial fraction of the waveguide losses is therefore caused by free carrier losses in the doped Al0.9Ga0.1As layer (αAlAs≈42 cm-1). Future designs may preferably facilitate a GaAs layer instead of Al0.9Ga0.1As since doping, and hence waveguide losses, could be reduced significantly without sacrificing the electronic properties .
For the actually fabricated structure we decided for medium coupling strength where losses are within reasonable limits. The grating has a depth of 700 nm and a duty-cycle of σ=0.5. In this case we calculate a confinement of Γ=0.98, total losses of α=18.9 cm-1, and a coupling coefficient of κ=(41.7+3.7i) cm-1. This implies that a coupling of κL=1 is still provided by 250 μm short devices.
The sample was grown by solid source molecular beam epitaxy and contains 60 stages of a bound-to-continuum active region as presented in Ref. . Starting from the highly doped GaAs (100) substrate the layer sequence is as follows: a 200 nm Al0.48Ga0.52As etch stop layer followed by a 150 nm GaAs contact layer (1×1018 cm-3) and the active region (4.23 μm). After a low doped (4×1016 cm-3) 100 nm GaAs buffer layer a 1 μm thick Al0.9Ga0.1As layer is grown topped by the contact facilitating layers 30 nm GaAs (1×1018 cm-3) and 5 nm In0.53Ga0.47As (2×1019 cm-3).
3.2 Grating formation and bonding
The processing technique is similar to the fabrication of double-metal waveguides for THz QCLs , but in contrast to THz QCLs we do not use metal on both sides of the waveguide core. The laser chip is first bonded on a doped GaAs template which later acts as a carrier. The substrate on the laser chip side (on which the QCL was grown) is then removed via mechanical polishing and subsequent selective wet-etching. As a result only the epitaxial layers are Au-Au bonded onto the GaAs carrier. The particular benefit of this procedure is that it allows to “bury” a metallic layer below the epitaxy. The remaining processing steps (e.g.laser ridges, insulation layers and extended contact pads) are now carried out on the bare episide and are equal to standard laser fabrication.
The fabrication method also allows for the realization of the DFB design proposed in the previous section. Therefore the grating is structured into the laser chip prior to the bonding process. Hence, in the end it is situated between the active region and a continuous metal layer that acts as surface-plasmon cladding. The grating has a period of Λ=3.44 μm and was defined via UV contact lithography and lift off technique. The resulting metal stripes (Ti/Au 10/250 nm) are later providing the bonding area on the laser side. As a second step the grating was transferred into the 1 μm thick Al0.9Ga0.1As buffer layer where the metal stripes served as a hard mask in the reactive ion etching (RIE) process [Fig. 3(a)]. From scanning electron microscope (SEM) pictures we deduce a grating depth in Al0.9Ga0.1As of 700 nm with a duty-cycle of 0.5.
As illustrated in Fig. 3(b) the laser chip is then bonded grating down on a highly doped GaAs template (2×1018 cm-3). The template is unstructured and was previously covered with Ti/Au (10/500 nm). Bonding was carried out at a temperature of 330°C and a pressure of 940 N/cm2. These parameters ensure that no Au is squeezed into the grating.
For substrate removal [Fig. 3(c)] the sample was mechanically polished to a residual thickness of ~ 30 μm. The remaining GaAs was removed by selective wet-etching in H2O2:NH3 (20:1). Etching stops on a 200 nm thick Al0.48Ga0.52As etch stop layer which was then removed selectively in concentrated HF. Finally the uppermost bare epi-layer is a 150 nm thick highly doped layer that is used for contacting.
3.3 Final processing
As a result of the previous processing steps the epitaxial layers are now Au-Au bonded to a conducting GaAs carrier and the grating is located in the Al0.9Ga0.1As buffer layer between the active region and the Au bonding area.
In the next step laser ridges are fabricated. Facets and 30 μm wide ridges are formed by RIE in SiCl4/N2 . The etching process is carried out until the entire material is removed. As shown in the sketch in Fig. 4(c) the etch bottom exhibits the continuous metal layer previously deposited on the template and the metallic grating-stripes.
In a subsequent PCVD process 300 nm SiNx is deposited for electrical insulation. The insulation is opened on top of the ridges only, so that facets and sidewalls remain covered [Figs. 4(b) and 4(c)]. During this process SiNx bridges are building up on the etch bottom reaching from one Au grating stripe to the next. The grating can therefore be clearly seen in on the etch bottoms surrounding the laser ridge [Fig. 4(a)].
Extended Ti/Au (10/250 nm) contact pads are used for electrical contacting. In order to realize air claddings the contact pads were opened via lift off technique on top of the laser ridge. Current injection is taking place via two metal stripes along the laser ridge [14, 15] as shown in Figs. 4(a) and 4(b). The width of these air windows is 24 μm compared to 28 μm insulation opening and 30 μm ridge width.
Within this lift of process we also ensure that no Au is covering the end facets. They are therefore only covered with 300 nm SiNx which allows to keep the reflectivity low and suppresses Fabry-Pérot (FP) modes. The effect we are making use of to reduce facet reflectivity is the strong absorption of SiNx in the emission region of the laser. At a wavenumber of 990 cm-1 the refractive index of SiNx is nSiNx=1.317+1.024i  resulting in a transmission loss of αtrans=1.274×104 cm-1. With an experimentally deduced effective index of the waveguide mode nneff=2.94 we calculated a reflectivity of R=0.11 (T=0.34). The reflectivity (transmittivity) was calculated via summation over multiple reflections at the semiconductor-SiNx and SiNx-air interfaces including damping inside SiNx layer and phase retardation altered by the imaginary part of nSiNx at the interfaces.
4 Results and Discussion
4.1 Measurement setup
Laser chips with cavities of different lengths where In soldered on a copper plate, wire bonded and mounted to a liquid N2(LN2) flow cryostat. The lasers were operated in pulsed mode with a repetition rate of 5 kHz and a pulse-width of 100 ns. Output power was recorded with a thermoelectric DTGS detector. Far fields were taken in a distance of 10.4 cm with a LN2 cooled HgCdTe (MCT) detector (250×250 μm2) and spectra were recorded with a fourier-transform IR spectrometer in free running mode. For spectral measurements again a LN2 cooled MCT detector was used but the pulse-width was reduced to 20 ns and repetition rate was increased to 40 kHz.
4.2 Lasing threshold and output power
Light-current and voltage-current characteristics of devices 360μm long and 30 μm wide are presented in Fig. 5. The threshold current of 1.1 A at 78 K corresponds to a current density of 10 kA/cm2. This marks a comparably good result since FP lasers with cleaved facets containing a similar active region embedded in a double plasmon-enhanced waveguide  with a length of L≈1.5 mm have typical threshold current densities of 7 kA/cm2. The increase in threshold current density is dedicated to the increase of total losses of the laser cavity. The referenced laser has waveguide losses of 15 cm-1 compared to 19 cm-1 for the presented structure. Additionally the losses via the end facets have to be considered. Since the laser field amplitude is non-zero at both ends of the cavity (especially for |κ|L≈1) light can escape via the facets. In case of two cavities with an equal |κ|L product higher threshold current densities are expected for the shorter laser . This is discussed in Ref.  for the case of zero reflectivity. For the actual structure we calculate R=0.11 due to the absorbing SiNx layers and we therefore expect a strong influence on the threshold current density.
The increased total cavity losses also influence the slope efficiency. Light collected from the surface has a slope efficiency of 120 mW/A whereas the mentioned comparable lasers  exhibit a value around 160 mW/A per facet. Both values are corrected for slope efficiency. The devices worked in single-mode at a wavenumber of 987.3 cm-1 as shown in the inset of Fig. 5. This corresponds to an effective refractive index of neff=2.944, which is close to the value 3.016 estimated from our simulations.
Room temperature operation was not achieved with these devices which we mostly dedicate to the optical, thermal and electrical properties of the Al0.9Ga0.1As grating buffer. Apart from the reduced area provided for heat transfer through the grating thermal management is sacrificed by the Al0.9Ga0.1As grating-buffer layer which has low thermal conductivity and, due to high electric resistivity [28, 29] generates additional heat. In order to achieve room temperature performance with GaAs-based devices one would replace the (relatively high doped) Al0.9Ga0.1As grating buffer with (low doped) GaAs. This improves thermal properties due to the higher thermal conductivity  and lower electric resistivity of GaAs and decreases waveguide loss due to lower free carrier absorption. InP being a potential buffer layer when working in the InP-based material system, would have a similar impact.
Additionally the better overall performance represented by lower thresholds and superior temperature performance for InP-based QCLs promises a substantial improvement for the presented DFB concept. An optimization via the grating duty-cycle does not seem promising. As can be seen from Fig. 2(b) higher losses and coupling strengths are expected for high duty-cycles. Also heat transfer from the active region into the GaAs template is expected to increase with duty-cycle. Hence, thermal and single-mode performance can be optimized simultaneously but are on the cost of waveguide losses.
4.2 Single mode performance
Temperature behavior of the emission wavelength as well as far fields exhibit typical DFB characteristics as will be discussed in the following for a 176 μm long device. These shorter cavities were created by cleaving existing devices, hence only one of the two facets has low reflectivity. The other, with a typical reflectivity of R=0.27 was used to characterize the laser also concerning its facet emission. Spectra recorded from the facet instead of the surface ensure that modes not being resonant with the DFB grating are also collected with the same collection efficiency as the resonant mode since the entire output is emitted normal to the facet. Surface emission of non-resonant modes in contrast takes place under a detuning dependent angle to the surface normal and may - in the worst case - not appear in the spectrum. Figure 6 shows single-mode spectra at a driving current density of 17 kA/cm2 collected from the facet. Single-mode operation with a side-mode-suppression-ratio (SMSR) of 20 dB is still provided with such lasers. The emitted wavenumber of 988.6 cm-1 (neff=2.940) is slightly blue-shifted with respect to the 360 μm long devices which can be explained by the difference in cavity length and/or different phase shifts at the arbitrarily positioned end facets. Temperature depending measurements where carried out in steps of 10 K showing the continuous tuning of the DFB mode with a slope of dν/dT=- 0.0384 cm-1K-1. Threshold currents of 176 μm long devices ranged around 800 mA (15 kA/cm2) for LN2 temperatures. For cavities slightly shorter than this (L=156 μm) the FP modes reach threshold earlier than the DFB modes and no single-mode operation was observed.
Far fields of devices working in single-mode show a double-lobed pattern with small higher order peaks. This is expected for index coupled DFB lasers and therefore corroborates the correctness of our simulations that yield a coupling coefficient being dominated by its real part. The origin of the double lobed far field is that the near field has maxima of opposite phase at both ends of the cavity . Due to this phase difference of 180° the far field has a center node and the separation of the two main maxima correlates with cavity length. The far fields shown in Fig. 7 were collected from the surface of the 360 μm and 176 μm long devices discussed above. The main maxima are separated by ±1° and ±2° respectively, being in good agreement with the device dimensions. The asymmetry in the maxima of the main lobes is attributed to the arbitrary position of the end mirrors to the grating.
To summarize we have used thermo-compression bonding and backside processing to form a novel surface-plasmon/air waveguide that significantly enhances the coupling coefficient of a second order DFB QCL. We have presented lasers as short as 176 μm exhibiting single-mode operation and 360 μm long devices already showed comparably good performance in terms of lasing threshold and output power. The presented waveguide concept promises an increase in resonator design freedom including the realization of compact 2D grating structures as well as an expansion to QCLs based on different material systems. Both is in the scope of our future work.
The authors acknowledge the support by the EU-TRN Project POISE, the Austrian FWF project ADLIS, the “Gesellschaft für Mikro- und Nanoelektronik” GMe, and the PLATON project within the Austrian NANO Initiative. One of us (G. S.) also acknowledges support through the New York state award NYSTAR.
References and links
2. M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295, 301–305 (2002). [CrossRef] [PubMed]
3. A. Evans, S. R. Darvish, S. Slivken, J. Nguyen, Y. Bai, and M. Razeghi, “Buried heterostructure quantum cascade lasers with high continuous-wave wall plug efficiency,” Appl. Phys. Lett. 91, 071101 (2007). [CrossRef]
4. C. Pflügl, L. Diehl, A. Tsekoun, R. Go, C. K. N. Patel, X. Wang, J. Fan, T. Tanbun-Ek, and F. Capasso, “Room-temperature continuous-wave operation of long wavelength (λ=9.5 l μm) MOVPE-grown quantum cascade lasers,” Electron. Lett. 43, 19 (2007).
5. A. A. Kosterev and F. K. Tittel, “Chemical Sensors based on Quantum Cascade Lasers,” IEEE J. Quantum Electron. 38, 582–591 (2002). [CrossRef]
6. G. P. Luo, C. Peng, H. Q. Le, S. S. Pei, W.-Y. Hwang, B. Ishaug, J. Um, J. N. Baillargeon, and C.-H. Lin, “Grating-tuned external-cavity quantum-cascade semiconductor lasers,” Appl. Phys. Lett. 78, 2834–2836 (2001). [CrossRef]
7. R. Maulini, A. Mohan, M. Giovannini, J. Faist, and E. Gini, “External cavity quantum-cascade laser tunable from 8.2 to 10.4 μm using a gain element with a heterogeneous cascade,” Appl. Phys. Lett. 88, 201113 (2006). [CrossRef]
8. J. Faist, C. Gmachl, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “Distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 70, 2670–2672 (1997). [CrossRef]
9. S. R. Darvish, S. Slivken, A. Evans, J. S. Yu, and M. Razeghi, “Room-temperature, high-power, and continuous-wave operation of distributed-feedback quantum-cascade lasers at λ~9.6 μm,” Appl. Phys. Lett. 88, 201114 (2006). [CrossRef]
10. S. Golka, C. Pflügl, W. Schrenk, and G. Strasser, “Quantum cascade lasers with lateral double-sided distributed feedback grating,” Appl. Phys. Lett. 86, 111103 (2005). [CrossRef]
11. K. Kennedy, A. B. Krysa, J. S. Roberts, K. M. Groom, R. A. Hogg, D. G. Revin, L. R. Wilson, and J. W. Cockburn, “High performance InP-based quantum cascade distributed feedback lasers with deeply etched lateral gratings,” Appl. Phys. Lett. 89, 201117 (2006). [CrossRef]
12. A. Wittmann, M. Giovannini, J. Faist, L. Hvozdara, S. Blaser, D. Hofstetter, and E. Gini, “Room temperature, continuous wave operation of distributed feedback quantum cascade lasers with widely spaced operation frequencies,” Appl. Phys. Lett. 89, 141116 (2006). [CrossRef]
13. B. G. Lee, M. A. Belkin, R. Audet, J. MacArthur, L. Diehl, C. Pflügl, F. Capasso, D. C. Oakley, D. Chapman, A. Napoleone, D. Bour, S. Corzine, G. Höfler, and J. Faist, “Widely tunable single-mode quantum cascade laser source for mid-infrared spectroscopy,” Appl. Phys. Lett. 91, 231101 (2007). [CrossRef]
14. D. Hofstetter, J. Faist, M. Beck, and U. Oesterle, “Surface-emitting 10.1 μm quantum-cascade distributed feedback lasers,” Appl. Phys. Lett. 75, 3769–3771 (1999). [CrossRef]
15. V. Moreau, M. Bahriz, R. Colombelli, R. Perahia, O. Painter, L. R. Wilson, and A. B. Krysa, “Demonstration of air-guided quantum cascade lasers without top claddings,” Opt. Express 15, 14861–14869 (2007). [CrossRef] [PubMed]
16. W. Schrenk, N. Finger, S. Gianordoli, L. Hvozdara, G. Strasser, and E. Gornik, “Surface-emitting distributed feedback quantum-cascade lasers,” Appl. Phys. Lett. 77, 2086–2088 (2000). [CrossRef]
17. C. Pflügl, M. Austerer, W. Schrenk, S. Golka, G. Strasser, R. P. Green, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, “Single-mode surface-emitting quantum-cascade lasers,” Appl. Phys. Lett. 86, 211102 (2005). [CrossRef]
18. H. Kogelnik and C. V. Shank, “Coupled-Wave Theory of Distributed Feedback Lasers,” J. Appl. Phys. 43, 2327–2335 (1972). [CrossRef]
19. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. I. Sivco, A. Y. Cho, and F. Capasso, “Quantum Cascade Surface-Emitting Photonic Crystal Laser,” Science 302, 1374–1377 (2003). [CrossRef] [PubMed]
20. A. Lyakha, P. Zory, M. D’Souza, D. Botez, and D. Bour, “Substrate-emitting, distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 91, 181116 (2006). [CrossRef]
21. N. Finger, W. Schrenk, and E, Gornik, “Analysis of TM-Polarized DFB Laser Structures with Metal Surface Gratings,” IEEE J. Quantum Electron. 36, 780–786 (2000). [CrossRef]
. C. Pflügl, W. Schrenk, S. Anders, G. Strasser, C. Becker, C. Sirtori, Y. Bonetti, and A. Muller, “Hightemperature performance of GaAs-based bound-to-continuum quantum-cascade lasers,” Appl. Phys. Lett. 83, 4698–4700 (2003). [CrossRef]
23. C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlxGa1-xAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998). [CrossRef]
24. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003). [CrossRef]
25. S. Golka, S. Schartner, W. Schrenk, and G. Strasser, “Low bias reactive ion etching of GaAs with a SiCl4/N2/O2 time-multiplexed process,” J. Vac. Sci. Technol. B 25(3), 839–844 (2007). [CrossRef]
26. M. Klanjšek, Gunde, and M. Maček, “Infrared Optical Constants and Dielectric Response Functions of Silicon Nitride,” Phys. Status Solidi. A 183, 439–449 (2001). [CrossRef]
27. M. A. Afromowitz, “Thermal conductivity of Ga1-xAlxAs alloys,” J. Appl. Phys. 44, 1292–1294 (1972). [CrossRef]
28. A. K. Saxena, “Electron mobility in Ga1-xAlxAs alloys”Phys. Rev. B 24, 3295–3302 (1981). [CrossRef]
29. N. Chand, T. Henderson, J. Klem, W. T. Masselink, R. Fischer, Y. Chang, and H. Morkoc, “Comprehensive study of Si-dopedAlxGa1-xAs (x=0 to 1): Theory and experiments,” Phys. Rev. B 30, 4484–4492 (1984).
30. R. J. Noll and S. H. Macomber, “Analysis of grating surface emitting lasers,” IEEE J. Quantum Electron. 26, 456–466 (1990). [CrossRef]