Gain in 1.3 μm materials: InGaNAs and InGaPAs semiconductor quantum-well lasersJ. Hader, S. W. Koch, J. V. Moloney, and E. P. O’Reilly Citation: Applied Physics Letters 77, 630 (2000); doi: 10.1063/1.127067 View online: http://dx.doi.org/10.1063/1.127067 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/77/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Unusual increase of the Auger recombination current in 1.3 μm GaInNAs quantum-well lasers under highpressure Appl. Phys. Lett. 82, 2335 (2003); 10.1063/1.1566468 The role of hole leakage in 1300-nm InGaAsN quantum-well lasers Appl. Phys. Lett. 82, 1500 (2003); 10.1063/1.1558218 Thermal characteristics of optical gain for GaInNAs quantum wells at 1.3 μm Appl. Phys. Lett. 79, 3038 (2001); 10.1063/1.1418022 Extraordinarily wide optical gain spectrum in 2.2–2.5 μm In(Al)GaAsSb/GaSb quantum-well ridge-waveguidelasers J. Appl. Phys. 90, 4281 (2001); 10.1063/1.1391421 Analysis of temperature dependence of the threshold current in 2.3–2.6 μm InGaAsSb/AlGaAsSb quantum-welllasers Appl. Phys. Lett. 74, 2743 (1999); 10.1063/1.124000

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Gain in 1.3 mm materials: InGaNAs and InGaPAs semiconductorquantum-well lasers

J. Hadera) and S. W. KochDepartment of Physics and Material Sciences Center, Philipps Universita¨t Marburg, Renthof 6,35032 Marburg, Germany

J. V. MoloneyArizona Center for Mathematical Sciences, University of Arizona, Tucson, Arizona 85721

E. P. O’ReillyDepartment of Physics, University of Surrey, Guildford, Surrey GU2 5XH, United Kingdom

~Received 11 January 2000; accepted for publication 6 June 2000!

The absorption and gain for an InGaNAs/GaAs quantum-well structure is calculated and comparedto that of a more conventional InGaAs/InGaPAs structure, both lasing in the 1.3mm range. Despitesignificant differences in the band structures, the gain value is comparable for high carrier densitiesin both structures and the transition energy at the gain maximum shows a similar blueshift withincreasing carrier density. For low and intermediate carrier densities, the calculated gain in theInGaPAs system is significantly lower and the bandwidth smaller than in the InGaNAs system.© 2000 American Institute of Physics.@S0003-6951~00!04431-4#

Recently, InyGa12yNxAs12x has been discovered to be avery promising material system. Replacing only a few per-cent of the arsenic atoms by nitrogen reduces the band gap inthese materials by up to several hundred meV.1,2 This opensthe possibility of optoelectronic devices based on GaAs atthe technologically important wavelengths of 1.3 and 1.5mm.3,4

The strong reduction of the band gap has been succes-fully described for bulk semiconductors in terms of an anti-crossing between the conduction band minimum of InGaAsand a resonant band of localized nitrogen defect states abovethe band edge.5–7 The hole bands are assumed to be undis-turbed by the nitrogen level.

In this letter we use ak•P Hamiltonian similar to the onepresented in Refs. 7 and 8 and a fully microscopic modelbased on the semiconductor Bloch equations of Refs. 9–12to calculate the gain and absorption characteristics of anInGaNAs/GaAs quantum-well~QW! structure. The resultsare compared with those for an InGaPAs-based QW structureto determine the signatures of theN-based system and itssimilarities and advantages as compared to the conventionalmaterial.

The QW band structure is calculated as described in Ref.13. The heterostructurek•P Hamiltonian is setup in realspace for the growth directionz andki space for the in-planemotion. After Fourier transformation intokz-space direct nu-merical diagonalization yields the subband energies. TheHamiltonian used includes two spin degenerate nitrogenbands in addition to the eight bands normally used~doublydegenerate electron, spin-split-off, heavy- and light-holebands!. The nitrogen bands are coupled only to the electronbands. The electron–nitrogen part of the Hamiltonian con-sists of two identical blocks~two, due to spin degeneracy! ofthe form:5,8

S E0~x,z!11/2s~z!k2 VNM~x,z!

VNM~x,z! EN~x,z!. D ~1!

Here,x denotes the nitrogen concentration, and 1/2sk2 is thequadratic conduction band dispersion term in the unper-turbed eight-band Hamiltonian. The energyE0(x,z) is givenby

E0~x,z!5H E0~z!21.55x eV, inside the well

E0~z!, outside the well, ~2!

whereE0(z) is the conduction band edge of the well/barriermaterial in the absence of nitrogen. The energy of the nitro-gen level is taken as

EN~x,z!5H 1.52 eV23.9x eV, inside the well

1.52 eV1Eb,N outside the well. ~3!

The height of the nitrogen barrier,Eb,N , has been tested tohave no significant influence on the resulting band structureand, especially, on the resulting gain and absorption. Weused a value ofEb,N50.22 eV. The coupling matrix elementVNM(x,z)52.4Ax eV for z inside the well and zeroelsewhere.7 Strain is included as described in Ref. 14.VNM

and EN are assumed independent ofk. The values of theseparameters were obtained by fitting to a range of experimen-tal transition energies. Although they have an uncertainity ofup to about 20%, the results we discuss below are of generalconsequence, independent of the precise values. We assumea valence band offset of 25% between InyGa12yNxAs12x andInyGa12yAs, i.e., 25% of the band gap reduction due to Eq.~1! is added to the valence band edge, and 75% to the con-duction band edge. Because the structure considered here hasdeep wells even in the absence of nitrogen, variation of theassumedN-related offset will not change the results signifi-cantly. However, experimental investigations suggest suchan offset.a!Electronic mail: jhader@acms.arizona.edu

APPLIED PHYSICS LETTERS VOLUME 77, NUMBER 5 31 JULY 2000

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With the single particle energies and wave functions ob-tained from thek•P calculation, the semiconductor Blochequations9,10,12 are setup and solved. Fourier transformationof the resulting polarization from time into frequency spaceyields the absorption and gain. Here, the incoherentelectron–electron and electron–phonon scattering processesare treated on a microscopic level. No phenomenological pa-rameters such as polarization dephasing times are needed.For conventional III–V and II–VI semiconductor systemssuch as InGaAs/AlGaAs or CdZnSe/MgZnSSe this methodhas been proven to give excellent agreement with experiment~see, e.g., Refs. 9, 11 and 15!.

We now compare the results for two structures. The firstis a 6 nm In0.3Ga0.7N0.02As0.98QW between 10 nm GaAsbarriers and Al0.1Ga0.9As cladding layers. The secondis a 6 nm In0.67Ga0.33P0.28As0.72 well between10 nm In0.90Ga0.10P0.78As0.22 barriers and InP cladding layers~barrier band gap 1.183 eV!. The compositions in the secondstructure are chosen so that all layers are lattice matched. Werefer to the first structure as the InGaNAs, and the second asthe InGaPAs structure.

Figure 1 shows the five lowest electron subbands andhighest hole subbands for the two structures. The lowesttransition energy is about the same in both cases~922 meVin InGaNAs, 933 meV in InGaPAs!. Adding nitrogen hasreduced the band gap by about 240 meV in the InGaNAscase. Both structures show pronounced conduction bandnonparabolicities. In InGaPAs this is due solely to the bandnonparabolicity present in the bulk eight-bandk•P Hamil-tonian used. In InGaNAs the anticrossing interaction with thenitrogen band drastically increases the nonparabolicities, es-pecially at band energies close to the nitrogen level. Thus,the effective mass as defined for very small in-plane momen-tum (ki,0.25 nm21) increases for the bands confined in thewell ~the lowest three! from me* 50.077m0 for the lowest to0.173m0 for the third confined band. The higher electronsubbands are unconfined and delocalized over the barrier re-gion. They do not interact strongly with the nitrogen states,and so have effective mass values determined primarily bythe barrier material. In the InGaPAs structure only one elec-tron subband is confined in the well.

Because of the higher effective masses in the InGaNAssystem one might have expected stronger absorption in this

system. However, as shown in Fig. 2, the absorption at lowcarrier densities is higher for InGaPAs than for InGaNAs.The dominant reason for this is that the coupling between theconduction band and nitrogen band~which is responsible forthe higher effective masses!, also leads to strong mixing be-tween the conduction band and nitrogen band states. Theconduction band edge of InGaAs then gets an admixture ofnitrogen character.7 The overlap between this admixture andthe valence band states is zero, thus reducing the overallabsorption value. Also, the mixing between different valencebands has a very pronounced effect in the InGaPAs structure,as can be seen from the strong nonparabolicity of the highestbands. Due to this mixing many transitions become partiallyallowed that would be symmetry forbidden in the absence ofthis coupling and corresponding excitonic resonances appearin the spectrum. Finally, the density of states is higher nearthe valence band maximum in the InGaPAs structure, as canbe seen from the dispersion of and small energy separationbetween the three highest valence subbands. This also leadsto higher absorption. At about 1.1 eV, the InGaNAs structureshows a very pronouncede2 –hh2 transition. Its high oscil-lator strength arises because bothe2 and hh2 have largezone center effective masses, as well as both having astrongly nonparabolic band dispersion. The peak slightly be-low this transition is thee1 –lh1 exciton. In the InGaPAsstructure thee2 –hh2 transition is very weak, since the sec-ond electron state is already unconfined in the well, whereasthe hole state is not. The corresponding overlap is thereforesmall.

Figure 3 shows that the transparency carrier density islower, and the differential gain above transparency initiallyhigher in the InGaNAs system, while the gain bandwidth isalso initially smaller in the InGaPAs structure. This arisesbecause the asymmetry between the conduction and valenceband edge effective masses is stronger in the InGaPAs thanin the InGaNAs structure.16 At higher densities, the carriersspread over a wider energy range and the differences be-tween the band edge density of states become less important.

FIG. 1. The five highest hole subbands~left! and lowest electron subbands~right! in the InGaN As/GaAs~solid lines! and InGaAs/InGaPAs structures~dashed lines!.

FIG. 2. Absorption and gain for a 6 nm In0.3Ga0.7N0.02As0.98 well ~solidlines! and a 6 nm In0.67Ga0.33P0.28As0.72 well ~dashed lines! for sheet carrierdensities~from top to bottom! of 0.25, 1.0, 2.5, 5.0, and 10.031012 cm22.

631Appl. Phys. Lett., Vol. 77, No. 5, 31 July 2000 Hader et al.

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For the highest densities shown, the gain then tends to thesame value in both structures and the gain bandwidths be-come similar. The shift of the peak gain energy with increas-ing carrier density is about the same in both structures.

In conclusion, we have shown that InGaNAs QW struc-tures show very promising gain characteristics around 1.3mm. For low to intermediate carrier densities, the materialgain amplitudes and bandwidths are larger than in lattice-matched InGaPAs structures, although the difference will beless pronounced when compared with strained InGaPAsstructures.17 At high densities the InGaNAs and InGaPAsgain characteristics are similar. Since both the conductionand valence band wells are deeper in the InGaNAs structure,the spill out of carriers from the well into barrier statesshould be reduced compared to conventional InP-based 1.3mm lasers. Usually, reduced spill out also implies higherstability of a semiconductor laser. Another factor favoringthe new material system is that the calculated difference be-tween the material gain in InGaNAs and in InGaPAs be-comes even more pronounced when the modal gain is con-

sidered. This is because the confinement factor is higher inGaAs based than in InP-based materials, due to the greaterrefractive index contrast achievable in the former materials.Overall, the calculated gain characteristics of a 1.3mmInGaNAs QW structure confirm the potential of this newmaterial for application in GaAs-based optoelectronic sys-tems.

The authors thank P. Klar and W. Heimbrodt for infor-mative discussions concerning the valence band offset inInGaNAs/InGaAs. This work was supported by the U.S. AirForce Office of Scientific Research under Contract Nos.AFOSR-F49620-97-1-0002 and AFOSR-F49620-98-1-0227,by the Deutsche Forschungsgemeinschaft~Germany!through the Leibniz program and through the Max-PlanckResearch Program, and by the Engineering and Physical Sci-ences Research Council~UK!.

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FIG. 3. Enlarged view of the gain region of Fig. 2.

632 Appl. Phys. Lett., Vol. 77, No. 5, 31 July 2000 Hader et al.

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