Probing scattering mechanisms with symmetric quantum cascade lasers

A unique feature of quantum cascade lasers is their unipolar transport. We exploit this feature and designed nominally symmetric active regions for terahertz quantum cascade lasers, which should yield equal performance with either bias polarity. However, symmetric devices realized in the InGaAs/GaAsSb material system exhibit a strongly polaritydependent performance due to different elastic scattering rates, which makes them an ideal tool to study their importance. In the case of an InGaAs/GaAsSb heterostructure, the enhanced interface asymmetry can even lead to undirectionally working devices, although the nominal band structure is symmetric. The results are also a direct experimental proof that interface roughness scattering has a major impact on transport/lasing performance. 2012 Optical Society of America OCIS codes: (000.0000) General; (000.2700) General science. References and links 1. B. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517 (2007). 2. F. Capasso, “High-performance midinfrared quantum cascade lasers”, Opt. Eng. 49, 111102 (2010). 3. C. Gmachl, A. Tredicucci, D. L. Sivco, A. L. Hutchinson, F. Capasso, and A. Y. Cho, “Bidirectional semiconductor laser”, Science 286, 749 (1999). 4. L. Lever, N. M. Hinchcliffe, S. P. Khanna, P. Dean, Z. Ikonic, C. A. Evans, A. G. Davies, P. Harrison, E. H. Linfield, and R. W. Kelsall, “Terahertz ambipolar dual-wavelength quantum cascade laser”, Opt. Express 17, 19926 (2009). 5. T. Kubis, C. Yeh, P. Vogl, A. Benz, G. Fasching, and C. Deutsch, “Theory of nonequilibrium quantum transport and energy dissipation in terahertz quantum cascade lasers”, Phys. Rev. B 79, 195323 (2009). 6. R. Nelander and A. Wacker, “Temperature dependence of gain profile for terahertz quantum cascade lasers”, Appl. Phys. Lett. 92, 081102 (2008). 7. C. Jirauschek and Paolo Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers”, J. Appl. Phys. 105, 123102 (2009). 8. A. Bismuto, R. Terazzi, M. Beck, and J. Faist, “Influence of the growth temperature on the performance of strain-balanced quantum cascade lasers”, Appl. Phys. Lett. 98, 091105 (2011). 9. Y. Chiu, Y. Dikmelik, P. Q. Liu, N. L. Aung, J. B. Khurgin, and C. F. Gmachl, “Importance of interface roughness induced intersubband scattering in mid-infrared quantum cascade lasers”, Appl. Phys. Lett. 101, 171117 (2012). 10. M. P. Semtsiv, Y. Flores, M. Chashnikova, G. Monastyrskyi, and W. T. Masselink, “Low-threshold intersubband laser based on interface-scattering-rate engineering”, Appl. Phys. Lett. 100, 163502 (2012). 11. P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers”, Nat. Photonics 4, 95 (2010). 12. S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. C. Liu, “Terahertz quantum cascade lasers operating up to 200 K with optimized oscillator strength and improved injection tunneling”, Opt. Express 20, 3866 (2012). 13. H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, “Terahertz quantum-cascade lasers based on a three-well active module”, Appl. Phys. Lett. 90, 041112 (2007). 14. C. Deutsch, A. Benz, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, T. Kubis, P. Vogl, G. Strasser, and K. Unterrainer, “Terahertz quantum cascade lasers based on type II InGaAs/GaAsSb/InP”, Appl. Phys. Lett. 97, 261110 (2010). 15. M. Nobile, H. Detz, E. Mujagic, A. M. Andrews, P. Klang, W. Schrenk, and G. Strasser, “Midinfrared intersubband absorption in InGaAs/GaAsSb multiple quantum wells”, Appl. Phys. Lett. 95, 041102 (2009). 16. R. M. Feenstra, D. A. Collins, D. Z.-Y. Ting, M. W. Wang, and T. C. McGill, “Interface roughness and asymmetry in InAs/GaSb superlattices studied by scanning tunneling microscopy”, Phys. Rev. Lett. 72, 2749 (1994). 17. T. Unuma, T. Takahashi, T. Noda, M. Yoshita, H. Sakaki, M. Baba, and H. Akiyama, “Effects of interface roughness and phonon scattering on intersubband absorption linewidth in a GaAs quantum well”, Appl. Phys. Lett. 78, 3448 (2001). 18. T. Ando, A. B. Fowler, and F. Stern, “Electronic properties of two-dimensional systems”, Rev. Mod. Phys. 54, 437 (1982). 19. C. Deutsch, APL published soon


Introduction
The emission wavelength of quantum cascade lasers (QCLs), currently ranging from the midinfrared to the terahertz (THz) spectral region (3-300 µm) [1,2], can be engineered by designing subband levels in a semiconductor heterostructure.This unique feature is accomplished by band structure engineering.A second unique feature of QCLs is their unipolarity, which allows the realization of bidirectional devices [3,4].In this work, we demonstrate how such bidirectional devices can be used to gain a deeper understanding of elastic scattering in a QCL.
The carrier transport in QCLs is still a controversially discussed subject and simulations are especially contradictory for active regions used in THz QCLs.While longitudinal optical (LO) phonon scattering is known to be crucial in mid-infrared and, at elevated temperatures, in THz QCLs, the influence of elastic scattering mechanisms is not well understood.Low temperature transport in THz QCLs is a complex interplay of coherent tunneling, elastic scattering and LO phonon scattering.However, which elastic scattering mechanisms are dominant and which are negligible is disputed.Theoretical modeling has been focusing on interface roughness, impurity and electron-electron scattering [5][6][7].Even for the very mature mid-infrared QCL technology, the recent focus of research into elastic scattering due to interface roughness gained considerable device improvements [8][9][10][11].THz QCL performance is expected to be even more susceptible to elastic scattering since the optical transition energy is well below the LO phonon energy.The knowledge of the origin and influence of scattering mechanisms is going to be important in the race for higher operating temperatures, as they decrease/broaden the optical gain.Currently, the only successful strategy towards higher operating temperatures is to increase the optical gain by careful design optimizations [12], avoiding elastic scattering could be the next step.The experimental challenge lies in the direct observation of the influence of a certain scattering mechanism in QCLs.For this purpose we exploit the unipolar carrier transport feature of QCLs.Combined with a high degree of freedom due to band structure engineering, one can design bidirectional dual wavelength or nominally symmetric active regions.An early work on mid-infrared QCLs was focused on dual wavelength operation with either bias polarity and a symmetric active region was merely demonstrated as a proof of principle [3].

Symmetric active regions
Motivated by nonequilibrium Green's function calculations performed on asymmetrically rough interfaces [13], we designed a series of three symmetric THz QCL active regions based on the three-well phonon depletion scheme in the InGaAs/GaAsSb material system [14,15].The band structures are modeled with an effective mass 1D Schrödinger solver and the material parameters used are from [16], Nobile et al.The active region of the initial design (sample 1), biased with either polarity, is shown in Fig. 1(a) and 1(c).Samples 2 and 3 are improved versions of sample 1 and the modifications are described in Section 4 and Fig. 2. In theory, the bias polarity makes no difference and should result in equal device performance.However, the two sides of the GaAsSb barrier are not symmetric due to the actual growth of the sample.This effect of asymmetric interface qualities is known to be pronounced in the 6.1 Å material family, when different group V materials like As and Sb are used in the growth of the semiconductor heterostructure [17].The same effect is also found in the presented material system, InGaAs/GaAsSb latticed matched to InP.A high-resolution cross-sectional TEM picture of the 3 nm GaAsSb barrier, shown in from the well to barrier material in the conduction band during growth (from InGaAs to GaAsSb in this case) and vice versa for the inverted.The interface asymmetry with respect to the growth direction is also sketched in the band structures, where the rough lines indicate the inverted interfaces.By applying a bias, the nominally symmetric band structure becomes asymmetric and depending on the polarity, the wave functions are either pushed to the rougher or smoother interfaces, i.e. the subband levels exhibit a different value of probability at the position of the two interfaces.The consequence is different scattering rates and lifetimes between the two operating directions.The interface roughness scattering rate has to be split into two parts, accounting for the difference in step height 1 2 , Δ Δ and correlation length 1 2 , Λ Λ between the normal and inverted interface (Fig. 1(b)) [9,18,19]: Here, m* is the effective electron mass, δU is the conduction band offset, 2 2  , i f ψ ψ are the probabilities of the initial and final subband at the position z inv , z norm of the respective interfaces and q if is the absolute value of the 2D scattering vector.The evaluation of the two sums in Eq. ( 1) for the upper to lower laser level scattering rate for positive bias and vice versa for negative (the sums are evaluated for sample 1 and at an electric field of 8.4 kV/cm).
Thus an interface asymmetry leads to different upper level lifetimes, τ 4 -and τ 4 + , for the two bias polarities.

Fabrication and experimental setup
The active region designs are grown with a Riber 32 on InP with a substrate temperature of 470-480°C.Both group V species are supplied from valved-cracker sources, which allow presetting the fluxes for reliable lattice-matching throughout the growth.Due to the large number of interfaces, switching is done immediately by shutter operations only [20].Symmetric InGaAs contact layers doped to 7 × 10 18 cm −3 are grown bottom and top.The total active region thickness is ≈10 µm (170 periods).The 10/1000 nm Ti/Au metal layers are deposited on the sample wafers and on n + GaAs host substrates.After wafer bonding using a thermo-compression method, the original substrate is removed by mechanical polishing and selective wet etching.Standard lithography is used to define the top contact/waveguide and is followed by metallization of 10/500 nm Ti/Au.Subsequently, ridges are dry-etched with an inductively coupled plasma reactive ion etcher using an SiCl 4 :Ar chemistry.The top contact is protected by an additional SiN or Ni layer and, which acts as an etch mask.Unlike commonly used wet-etching, dry-etching also guarantees vertical sidewalls and a symmetric geometry of the device.Typical device dimensions are 0.5-1 mm by 40-90 µm.
The fabricated devices are indium soldered on a copper submount, wire-bonded and mounted on the cold finger of a helium flow cryostat.Light emission is collected using an off-axis parabolic mirror, sent through an FTIR spectrometer and detected with a DTGS detector.Absolute power values are measured with a calibrated thermopile detector (Dexter 6M) under vacuum conditions, mounted at a distance of 5-10 mm from the laser facet inside the cryostat.The detector element has a diameter of 6 mm.Light-current-voltage (LIV) curves and spectra are recorded in pulsed mode, with a pulse duration of 200 ns and up to 4% duty cycles (200 kHz repetition rate).

Experimental results and discussion
Figure 2(a) summarizes the design parameters and major differences between the three tested samples.The bidirectional LIV characteristic of sample 1 is shown Fig. 2(b).Although the active region design, as well as contacts and device geometry, is completely symmetric, lasing is just observed with negative top bias polarity with a threshold current density of 0.62 kA/cm 2 .In this case, the electron transport occurs in growth direction and electrons "see" the normal, sharper interfaces, resulting in a decreased interface roughness scattering compared to the opposite polarity.The enhanced interface roughness scattering with positive bias causes increased leakage beyond 4 V.More important though, the upper level lifetime τ 4 + is also dramatically decreased and the optical gain cannot overcome the waveguide losses.Lasing with negative bias is observed up to a maximum temperature of 105 K.
By redesigning the subband level alignment and energy separation of level 1 and 2 for resonant depletion, sample 2 also shows lasing for positive polarity, presented in Fig. 2(c).However, the IV asymmetry remains basically unchanged with a higher leakage current and hence higher threshold for positive polarity.The threshold bias is almost identical for both polarities ( -0.5 , which underlines the importance of the alignment of subbands and also indicates symmetric contact properties.Again, the reduced optical output power reflects the decreased upper level lifetime τ 4 + .For a more significant comparison of the polarity-dependent performance, we characterized four devices.The average values and their negative/positive bias ratio, including standard deviation, are summed up in Table 1.Sample 2 exhibits a 43% reduced threshold, a 238% higher output power and a 20% higher operating temperature for negative polarity.The peculiar kinks, visible in the negative polarity IV of sample 1 and 2, vary from device to device and can be attributed to the formation of high field domains in the active region..86 ± 0.28 Four devices of sample 2 and 3 have been measured for a meaningful comparison between the two operating directions.Sample 1 only works with negative bias.The average values for threshold current density J th , maximum operating temperature T max and the ratio of them are listed.Please note that for the statistics the negative/positive ratio is calculated separately for every single device.Peak optical output power P peak is only provided as a ratio since the absolute values strongly depend on the device dimensions and collection efficiency.The standard deviation is also provided for the ratios and shows that the difference is not within the error bars.J th and P peak have been measured at 5K.The purpose of sample 3 is to study the influence of a thinner injection/extraction barrier on the performance for both bias polarities.Figure 2(d) shows the LIV characteristics of sample 3. The IV exhibits a less pronounced asymmetry and the threshold current difference is reduced to -19%.Thinner barriers give stronger tunneling coupling, which means that coherent transport plays a more dominant role compared to elastic scattering in this structure.The change of the barrier width from 3 nm to 2.8 nm in sample 3 yields an anticrossing energy of 3 meV, compared to 2.2 and 2.5 meV, respectively.However, the difference for the upper level lifetimes τ 4 -and τ 4 + remains unaffected and causes a similar negative/positive ratio of the output power ( + 286% for negative polarity) compared to sample 2. Sample 3 shows the best temperature performance of 134 K for negative polarity, 32% higher than for positive polarity.
The results prove that rough interfaces, even if they are only present on one side of the barrier, play a major role in the transport and performance of THz QCLs, confirming theoretical predictions of non-equilibrium Green's function calculations by Kubis et al. [5,13].Results of such calculations on symmetric active region designs are in good qualitative agreement with the experimental findings of this paper.Accurate transport simulations would require precise input parameters, such as step height and correlation length, of the normal and inverted interface.However, we can estimate whether realistic interface roughness parameters [5][6][7][8][9] lead to a reasonable lifetime ratio - ), fitting the threshold ratios rather well.
Figure 3 illustrates the positive and negative polarity spectra of a representative device of sample 2, recorded at the maximum output power.The spectra are relatively broadband, which is attributed to the generally rougher interfaces compared to GaAs/AlGaAs [22].More interesting though is the similarity of the recorded spectra.It indicates that the subband structure and alignment are symmetric for the both bias polarities, resulting in the same emission frequency.

Conclusion
In this work we demonstrated the potential of symmetric quantum cascade lasers to study the influence of elastic scattering on the device performance.Due to their unipolarity, QCLs can be designed in a way to operate under both polarities.The only difference is the transport direction with respect to the growth direction.The material system InGaAs/GaAsSb exhibits a pronounced interface asymmetry and is therefore ideal to investigate the role of interface roughness scattering in QCLs.Inverted interfaces exhibit an increased roughness and cause a stronger influence of interface roughness scattering when electrons are incident on them.We compared the performance of three symmetric samples with different design parameters.One sample shows the most outstanding situation of only unidirectional lasing.The other two samples can be operated in both directions but with significant performance degradation with positive bias.We observe up to 43% lower threshold current densities, 286% higher optical output power and 34% higher maximum operating temperature for negative polarity.
The results show that the growth order of a QCL sample, which then defines the applied bias polarity, can significantly affect the device performance.So far, the growth order of QCLs was believed to have no influence on performance [3,4,23].The interface asymmetry in InGaAs/GaAsSb heterostructures defines a favorite operating direction for THz QCLs [22].To our knowledge, there are no other unipolar intersubband devices (e.g.resonant tunneling diodes, quantum well infrared photodetectors), which suffer from interface asymmetry and hence require to be grown in a certain order.
Due to their sensitivity to interface roughness scattering, symmetric THz QCLs could also serve as a test structure to evaluate and improve interface qualities and interface engineering recipes.In addition, they could also be used as a benchmark for testing transport models since scattering mechanisms can be increased or decreased by simply switching the bias polarity.

# 4 -Fig. 1 .
Fig. 1.Nominally symmetric active region of a terahertz quantum cascade laser biased with either bias polarity.The symmetry is broken by the different quality of the normal and inverted interfaces with respect to the growth direction.The inverted interfaces are sketched as a rough line in the band structure.(a) Positive top bias polarity results in an electron flow incident on the inverted interfaces.(b) The cross-sectional TEM picture confirms the interface asymmetry in the InGaAs/GaAsSb material system and the enhanced roughness of the inverted interface.(c) Negative polarity reverses the current flow and electrons are moving against the normal interfaces.The influence of interface roughness scattering can therefore be studied by simply switching between the bias polarities.

Fig. 1 (
b), reveals the increased roughness of the inverted interface.The expression normal and inverted are commonly used in 2DEG structures for the two kind of interfaces, where the normal interface describes the switching #180918 -$15.00USD Received 11 Dec 2012; revised 14 Feb 2013; accepted 14 Feb 2013; published 14 Mar 2013 (C) 2013 OSA

Fig. 2 .
Fig. 2. Comparison of the different active region designs and light-current-voltage characteristics of each sample measured with both operating polarities.(a) The layer sequence of sample 1 is 3.0/14.0/1.0/14.0/3.0/2.0/22.0/2.0 nm.For sample 2 the layer sequence is modified to 3.0/13.3/1.0/13.3/3.0/2.0/18.8/2.0 nm, which results in a better depletion of the lower laser level due to optimized subband alignment and energy separation (E 21 ).Sample 3 employs thinner injection/extraction barriers for stronger tunneling coupling.The layer sequence is 2.8/13.0/0.9/13.0/2.8/1.9/20.5/1.9 nm.GaAsSb barriers are in bold fonts.The Si doping density is 1 × 10 16 cm −3 in the underlined sections.(b) Sample 1 only shows lasing for negative polarity.(c) Sample 2 works with both bias polarities but exhibits a significant transport and performance difference.(d) Thinner barriers in sample 3 enhance the tunneling coupling and reduce the threshold difference.

4 4 /=
τ τ + of the upper laser levels as observed in our measurements.In a first approximation (unity injection efficiency, negligible lower level lifetime τ 3 , equal broadening of the optical transtition - ) of rate equations[21], the upper level lifetime is inversely proportional to the threshold current, which is -

#Fig. 3 .
Fig.3.Normalized spectra of sample 2 recorded in both bias polarities at the maximum optical output power and at 5 K.The main lasing modes are observed in both spectra.It indicates that the spectral position of the gain is not influenced by the applied polarity and the resulting subband level alignment/spacing is identical.