Conceptual disadvantages of typical resonant phonon terahertz quantum cascade lasers THz-QCLs are analyzed. Alternative designs and their combination within a concrete device proposal are discussed to improve the QCL performance. The improvements are 1 indirect pumping of the upper laser level, 2 diagonal optical transitions, 3 complete electron thermalization, and 4 materials with low effective electron masses. The nonequilibrium Green’s function method is applied to predict stationary electron transport and optical gain. The proposed THz-QCL shows a higher optical gain, a lower threshold current, and a higher operation temperature. Alloy disorder scattering can worsen the QCL performance

Klimeck, Gerhard

Kubis, Tillmann

Mehrotra, Saumitra Raj

English

Tillmann Kubis

Saumitra Raj Mehrotra

Gerhard Klimeck

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Applied Physics Letters

Design concepts of terahertz quantum cascade lasers: Proposal for terahertz laser efficiency improvements

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Purdue UniversityPurdue e-PubsBirck and NCN Publications Birck Nanotechnology Center12-28-2010Design Concepts of Terahertz Quantum Cascadelasers: Proposal for Terahertz Laser EfficiencyImprovementsTillmann KubisNCN, Purdue UniversitySaumitra Raj MehrotraNCN, Purdue UniversityGerhard KlimeckNCN, Purdue University, gekco@purdue.eduFollow this and additional works at: http://docs.lib.purdue.edu/nanopubPart of the Electrical and Electronics CommonsThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Kubis, Tillmann; Mehrotra, Saumitra Raj; and Klimeck, Gerhard, "Design Concepts of Terahertz Quantum Cascade lasers: Proposalfor Terahertz Laser Efficiency Improvements" (2010). Birck and NCN Publications. Paper 723.http://dx.doi.org/10.1063/1.3524197Design concepts of terahertz quantum cascade lasers: Proposal forterahertz laser efficiency improvementsTillmann Kubis,a Saumitra Raj Mehrotra, and Gerhard KlimeckNetwork for Computational Nanotechnology, Birk Nanotechnology Center, School of Electrical andComputer Engineering, Purdue University, West Lafayette, Indiana 47907, USAReceived 24 September 2010; accepted 11 November 2010; published online 28 December 2010Conceptual disadvantages of typical resonant phonon terahertz quantum cascade lasers THz-QCLsare analyzed. Alternative designs and their combination within a concrete device proposal arediscussed to improve the QCL performance. The improvements are 1 indirect pumping of theupper laser level, 2 diagonal optical transitions, 3 complete electron thermalization, and 4materials with low effective electron masses. The nonequilibrium Green’s function method isapplied to predict stationary electron transport and optical gain. The proposed THz-QCL shows ahigher optical gain, a lower threshold current, and a higher operation temperature. Alloy disorderscattering can worsen the QCL performance.© 2010 American Institute of Physics. doi:10.1063/1.3524197A wide range of scientific and commercial applicationsrequires high power and coherent terahertz sources since thecharacteristic excitation lines of many molecules lie withinthe terahertz spectral region.1–3 Terahertz quantum cascadelasers THz-QCLs are promising candidates to supply in-tense coherent terahertz light. Since the realization of THz-QCLs by Koehler et al.,4 the performance of these lasers hasbeen significantly improved, but their operation is still lim-ited to cryogenic temperatures.To increase the maximum operating temperature and toincrease the output power, several disadvantages of the com-monly used resonant phonon THz-QCL design are analyzed.Subsequently, alternative design concepts and their combina-tion within an efficient THz-QCL are presented. Finally, thecalculated data of a concrete example of the proposed designconcept are presented. Although the various parameters ofthis proposed QCL have not been optimized, this exampleshows a much higher optical gain and a higher operatingtemperature.The mechanisms that are responsible for optical gain in atypical resonant phonon THz-QCL can be deduced from Fig.1a. It depicts a schematic of the conduction band profileand the resonant states at an applied electric field close tothreshold. The upper laser level labeled 4 is aligned withthe injector state 5 in the leftmost source-sided quantum welland therefore gets filled by resonant tunneling. The spatialoverlap of the lower laser level 3 with the upper one is verylarge to guarantee a large oscillator strength of the opticaltransition. The lower laser level 3 gets efficiently emptied bytwo mechanisms. State 3 is aligned with state 2 of the right-most well, which allows its coherent depletion by tunneling.Second, the energy difference between this state and the low-est resonant state 1 matches the energy of an LO-phonon,which leads to an additional depletion by the resonant emis-sion of LO-phonons. The alignment of the resonant states aswell as the electric field at threshold are chosen such that thepotential drop per period eth equals the sum of the energyof one emitted photon E and the energy of one LO-phonon ELO.There are several issues with this design concept thatintrinsically lower the overall device performance:Coherent filling. The alignment of the injector state 5with the upper laser level 4 allows for a delocalization of theupper laser level beyond the area of the lower laser level 3.This reduces the oscillator strength as well as the lifetime ofelectrons in the upper laser level. In addition, multibarriertunneling across a complete QCL period becomes morelikely if the upper laser level is not confined well enough.5Direct laser transition. The large spatial overlap of theupper 4 and lower 3 laser level significantly increases theprobability of nonluminescent transitions. Accordingly, it hasbeen shown in previous work that the optical gain of thiskind of THz-QCL is dramatically reduced by the electronscattering on rough interfaces.6 Scattering on rough inter-faces suggests to increase the laser frequency: a larger energyseparation between the laser levels increases the scatteredin-plane momentum and thereby reduces the scatteringprobability.7,8 However, the thermally activated LO-phononemission of electrons in the upper laser level is another im-portant degradation mechanism.9 The LO-phonon emissionsuggests a smaller laser frequency: the larger the energy dif-ference between the laser levels 3 and 4 is, the more elec-trons meet the minimum energy requirement for the phononemission and the smaller is the scattered in-plane momen-tum. The conflict of both effects limits the improvement op-tions in typical THz-QCLs.Incomplete thermalization. Typical THz-QCLs are de-signed such that the potential drop per period at thresholdbias equals the sum of the emitted photon energy and theenergy of one LO-phonon. On the average, however, mostelectrons pass THz-QCL periods without emitting light.6 Ithas been shown in previous work that electrons that pass aperiod without emitting a photon get heated up with respectto their in-plane distribution.6 When these electrons are ther-malized in subsequent periods, the population inversion issignificantly reduced. The resulting overall optical gain canbe lowered by almost a factor of 2.6aElectronic mail: tkubis@purdue.edu.APPLIED PHYSICS LETTERS 97, 261106 20100003-6951/2010/9726/261106/3/$30.00 © 2010 American Institute of Physics97, 261106-1Downloaded 15 Jun 2011 to 128.46.94.26. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsMaterial properties. It is very common to use unstrainedAl0.15Ga0.85As /GaAs quantum well heterostructures for reso-nant phonon THz-QCLs. Meanwhile, it is known that theoptical gain is proportional to 1 /m3/2, with the effectiveelectron mass m.10 Therefore, designing the THz-QCLsbased on materials with lower effective electron masses canlead to a higher optical gain.These issues are solved in a THz-QCL design proposedin the next paragraphs. The mechanisms that lead to occupa-tion inversion and optical gain in this design are depicted inFig. 1b with a schematic of the conduction band profile andthe resonant states at an applied electric field close to thresh-old. The upper laser level 4 is filled by electrons of the in-jector state 5 that resonantly emit an LO-phonon. The lowerlaser level 3 is spatially separated from the upper laser levelforcing the optical transition to be diagonal. The lowest levelof the collector well 1 is exactly one LO-phonon energybelow the upper laser level 4. This guarantees that most ofthe electrons i.e., the nonluminescent ones are thermalizedin each QCL period. Compared to the conventional resonantphonon design of Fig. 1a, this concept has several advan-tages:Indirect pumping. The upper laser level is well confinedwithin a single quantum well. This reduces the chance ofcoherent leakage to the next QCL stage. In addition, thenumber of rough interfaces that can influence the upperstate lifetime is reduced. As has been shown in previouswork, just indirect pumping alone can increase the peak gainby a factor of approximately 3.9 Recent experimental andtheoretical works confirm that indirect pumping can improvethe device performance.11,12Diagonal transitions. Nonluminescent transitions be-tween the laser levels are suppressed because the spatialoverlap is much smaller than in the typical design. Pleasenote that the optical transition is proportional to the transitiondipole element, which has a different spatial characteristicthan nonluminescent transitions. Previous work has demon-strated that the optical gain of a diagonal transition is muchless sensitive to scattering on rough interfaces than directtransitions.13 It is worth to note that the THz-QCL with atemperature limit of 186 K utilizes diagonal opticaltransitions.14 Once the nonluminescent elastic transitions aresuppressed, the energy difference between the laser levelscan be reduced in order to suppress the probability for ther-mally activated LO-phonon emission of electrons in the up-per laser level.Complete thermalization. The energy balance of theQCL in Fig. 1b is neglecting the photon energy. In this way,it is guaranteed that the majority of electrons, i.e., those thatare not emitting light, are thermalized within each period.Therefore, nonperiodic effects, which have shown to signifi-cantly worsen the QCL performance, are efficientlysuppressed.6,15Low effective mass. The combination of In0.53Ga0.47Asand GaAs0.51Sb0.49 layers instead of the commonly usedAl0.15Ga0.85As /GaAs material system has the advantage oflower effective electron masses. This material system hasrecently been shown to yield optical intersubbandtransitions.16All these suggestions have been combined into a con-crete In0.53Ga0.47As /GaAs0.51Sb0.49 QCL device design.Starting from the leftmost barrier in Fig. 1b, one period ofthe indirect-pumped QCL sequence was taken as 2.7/9/1.8/20.7/2.7/15.3/2.7/18.9 nm. The bold and regular numbersrepresent GaAs0.51Sb0.49 and In0.53Ga0.47As layers, respec-tively. The underlined 9-nm-thick quantum well is the onlyn-doped region at the level of 2.041016 cm−3. We haveapplied the nonequilibrium Green’s function NEGF methodon the stationary charge transport and the linear optical re-sponse of this QCL. Thereby, the QCL is considered as anopen quantum device with multiquantum well leads. Elec-trons within each lead are distributed according to Fermidistributions. Therefore, all electrons enter the QCL devicein equilibrium distributions and nonequilibrium electronsthat leave the device are thermalized within the leads. Inco-herent scattering of electrons on optical and acousticphonons, charged impurities, rough interfaces, and randomalloy disorder is included. The electron-electron interactionin the Hartree approximation is taken into account. Pleaserefer to Ref. 6 for implementation details. Figure 2 shows thespectral function Az ,E at zero in-plane momentum of theproposed QCL resulting from this NEGF calculation. Reso-nant states correspond with peaks of Az ,E. We have as-sumed an LO-phonon energy of 34 meV in the composedmaterial system and designed the potential drop at thresholdbias commensurable with this LO-phonon energy. The alloyscattering potential VTB is estimated from empirical tight-binding parameters to be 0.493 eV for In0.53Ga0.47As and0.36 eV for GaAs0.51Sb0.49.17–19 All remaining material pa-rameters are taken from Ref. 10. The calculated emissionenergy of the present laser is 10 meV. Figure 3 compares thecalculated peak gain as a function of the lattice temperatureFIG. 1. Color online Schematics of the conduction band black and theresonant states thick of a typical resonant phonon THz-QCL a and thepresently proposed design concept b at threshold voltage th. Arrows de-pict emitted photons white and phonons black. The potential drop eth inthe typical design a equals the energy of one photon and one phonon. Inthe proposed design b, it is equal to the energy of two phonons.FIG. 2. Color online Calculated conduction band profile line and contourplot of the energy and spatially resolved spectral function Az ,E at vanish-ing in-plane momentum in the proposed QCL at the threshold bias voltageof 68 mV per period and a lattice temperature of 100 K. The zero in energymarks the chemical potential of the source.261106-2 Kubis, Mehrotra, and Klimeck Appl. Phys. Lett. 97, 261106 2010Downloaded 15 Jun 2011 to 128.46.94.26. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsin the present QCL to the conventional THz-QCL of Ref. 20with the same effective doping density per period. The pro-posed design yields a higher optical gain for all temperaturesand has an about 20 K higher maximum operation devicetemperature. Note that the high threshold current of the con-ventional design heats the QCL by 20–50 K above the heatsink temperature.21,22 It is also worth to mention that thethreshold current density of the proposed design at 40 Klattice temperature is 0.13 kA /cm2. This is approximatelyfour times smaller than in the conventional design of thesame effective doping and temperature.20 Rough interfacesreduce the optical gain of the proposed design by only about40% instead of 90% in the old design and tend to stabilizethe carrier transport. In particular, the calculations predict ahigher current density if the QCL is grown with the source-sided barrier interfaces being rough and the opposite inter-faces being smooth. The implemented alloy scattering poten-tial in In0.53Ga0.47As agrees with experimental findings.23However, some authors use the conduction band differenceof the binary alloys VCB instead about 1 eV forIn0.53Ga0.47As and 0.1 eV for GaAs0.51Sb0.49. Figure 3 showsthe influence of the alloy disorder scattering on the proposedQCL. At low temperatures, the filling of the upper laser leveland the optical gain is slightly improved by alloy disorderscattering. Once this level filling gets saturated by high dis-order potentials V or at high temperatures by enhanced pho-non scattering at about 175 K in Fig. 3, alloy disorderscattering preferably supports nonradiative losses and re-duces the optical gain.In conclusion, several conceptual disadvantages of com-mon resonant phonon THz-QCLs have been discussed. Al-ternative concepts have been presented that avoid all of thesedisadvantages and result in THz-QCLs with improved laserperformance. A concrete THz-QCL that combines all alter-native design concepts has been proposed. NonequilibriumGreen’s function calculations of this proposed QCL showsignificantly higher optical gain, a higher maximum tempera-ture, and an approximately four times lower threshold cur-rent density than in a comparable conventional THz-QCL. Itis shown that a strong alloy disorder scattering can worsenthe optical output performance.This work has been supported by the Austrian ScientificFund FWF Grant No. SFB-IRON and the National ScienceFoundation NSF Grant Nos. OCI-0749140, EEC-0228390,and ECCS-0701612. Computational resources of nano-HUB.org are gratefully acknowledged.1J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshev, M.Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, B. S. Williams,S. Kumar, Q. Hu, and J. L. Reno, Appl. Phys. Lett. 86, 244104 2005.2H.-W. Hübers, S. G. Pavlov, H. Richter, A. D. Semenov, L. Mahler, A.Tredicucci, H. E. Beere, and D. A. Ritchie, Appl. Phys. Lett. 89, 0611152006.3A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno,Appl. Phys. Lett. 89, 141125 2006.4R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G.Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, Nature London 417, 1562002.5T. Kubis and P. Vogl, Laser Phys. 19, 762 2009.6T. Kubis, C. Yeh, P. Vogl, A. Benz, G. Fasching, and C. Deutsch, Phys.Rev. B 79, 195323 2009.7R. Lake, G. Klimeck, R. C. Bowen, and D. Jovanovic, J. Appl. Phys. 81,7845 1997.8B. K. Ridley, Quantum Processes in Semiconductors Oxford, New York,1982.9H. Yasuda, T. Kubis, P. Vogl, N. Sekine, I. Hosako, and K. Hirakawa,Appl. Phys. Lett. 94, 151109 2009.10E. Benveniste, A. Vasanelli, A. Delteil, J. Devenson, R. Teissier, A. Bara-nov, A. M. Andrews, G. Strasser, I. Sagnes, and C. Sirtori, Appl. Phys.Lett. 93, 131108 2008.11A. Wacker, Appl. Phys. Lett. 97, 081105 2010.12S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, Conference on Lasersand Electro-Optics (CLEO) and the Quantum Electronics and Laser Sci-ence Conference (QELS) Optical Society of America, Washington, D.C.,2010, Paper No. CThU1.13T. Kubis, Quantum Transport in Semiconductor Nanodevices, edited by G.Abstreiter, M. C. Amann, M. Stutzmann, and P. Vogl Verein zurFörderung des Walter Schottky Instituts der Technischen UniversitätMünchen e.V., Garching, 2009, http://nanohub.org/resources/8612.14S. Kumar, Q. Hu, and J. L. Reno, Appl. Phys. Lett. 94, 131105 2009.15T. Kubis and P. Vogl, J. Phys.: Conf. Ser. 193, 012063 2009.16M. Nobile, H. Detz, E. Mujagić, A. M. Andrews, P. Klang, W. Schrenk,and G. Strasser, Appl. Phys. Lett. 95, 041102 2009.17T. B. Boykin, G. Klimeck, R. C. Bowen, and F. Oyafuso, Phys. Rev. B 66,125207 2002.18G. Hegde and G. Klimeck, unpublished parameters; G. Klimeck, R. C.Bowen, T. B. Boykin, C. Salazar-Lazaro, T. A. Cwik, and A. Stoica,Superlattices Microstruct. 27, 77 2000.19S. Krishnamurthy, A. Sher, and A.-B. Chen, Appl. Phys. Lett. 47, 1601985.20A. M. Andrews, A. Benz, C. Deutsch, G. Fasching, K. Unterrainer, P.Klang, W. Schrenk, and G. Strasser, Mater. Sci. Eng., B 147, 152 2008.21H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, Appl.Phys. Lett. 83, 207 2003.22M. S. Vitiello, G. Scarmacio, V. Spagnolo, B. S. Williams, S. Kumar, andQ. Hu, Appl. Phys. Lett. 86, 111115 2005.23P. K. Basu and B. R. Nag, Appl. Phys. Lett. 43, 689 1983.FIG. 3. Color online Calculated peak optical gain as a function of thelattice temperature. The conventional resonant phonon QCL of Ref. 20diamonds exhibits a smaller optical gain than the presently proposed de-sign spheres for all temperatures when the alloy scattering potentials VTBare estimated from tight binding calculations VTB. The triangles show theresults of the proposed QCL with the approximate alloy scattering potentialsVCB due to conduction band differences of the binary alloys. The squaresdepict the proposed gain without alloy scattering. Lines are meant to guidethe eye.261106-3 Kubis, Mehrotra, and Klimeck Appl. Phys. Lett. 97, 261106 2010Downloaded 15 Jun 2011 to 128.46.94.26. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Design Concepts of Terahertz Quantum Cascade lasers: Proposal for Terahertz Laser Efficiency Improvements

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Design Concepts of Terahertz Quantum Cascade lasers: Proposal for Terahertz Laser Efficiency Improvements

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