Temperature dependence of Auger recombination in highly injected crystalline silicon

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PHYSICAL REVIEW B 15 NOVEMBER 1998-IVOLUME 58, NUMBER 19

Temperature dependence of Auger recombination in a multilayer narrow-band-gap superlattice

D.-J. Jang and Michael E. Flatte´Optical Science and Technology Center, Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 5224

C. H. GreinPhysics Department M/C 273, University of Illinois at Chicago, Chicago, Illinois 60607-7059

J. T. Olesberg, T. C. Hasenberg, and Thomas F. Boggess*Optical Science and Technology Center, Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 5224

~Received 2 March 1998; revised manuscript received 29 June 1998!

Temperature and density-dependent Auger recombination rates are determined for a four-layer broken-gapsuperlattice designed for suppression of both Auger recombination and intersubband absorption. The structureis intended as the active region of both optically pumped and diode lasers operating in the midwave infrared.Auger recombination and intersubband absorption are thought to be among the primary factors contributing tohigh-threshold current densities in such devices. Ultrafast time-resolved photoluminescence upconversion wasused to measure the Auger rates at lattice temperatures ranging from 50 to 300 K. Results are compared tocalculated rates using the temperature-dependent, nonparabolicK–p band structure and momentum-dependentmatrix elements. The calculations, which include umklapp processes in the superlattice growth direction, are inexcellent agreement with the experimental results. Comparison of these results with those obtained in othermid-IR semiconductor structures verifies Auger suppression. The measured temperature-dependent Auger re-combination rates, together with calculations of the gain, provide an upper bound for the characteristic tem-perature,T0581 K, for lasers utilizing this superlattice as an active region.@S0163-1829~98!01043-1#

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INTRODUCTION

Midwave infrared~MWIR, 2–5 mm! diode lasers havebeen extensively studied recently due to their potential apcation to remote sensing, pollution monitoring, and infrarcountermeasures. Significant progress has been made idevelopment of MWIR lasers, with much of the recentsearch in this spectral range focused on interband antimodevices utilizing a variety of quantum-well and superlattdesigns.1 The realization of commercial devices operatingor near room temperature, i.e., compatible with thermoetric cooling, has been elusive, however, particularly for tlonger wavelength MWIR lasers. This is in part a consquence of Auger recombination in the narrow-band-gaptive regions of these lasers. Auger recombination is a nodiative, density-dependent process that typically increastrongly with decreasing band-gap energy and increatemperature, thereby contributing to high threshold currdensities and low maximum operating temperatures in inband MWIR lasers.

As a result of the negative effects of Auger recombinaton interband MWIR semiconductor lasers and lonwavelength detectors, this process has received consideattention as efforts have been made both to understanimpact on laser performance and to design strategies fosuppression. Theoretical efforts have2–4 focused on the useof band-structure engineering~1! to modify the band-edgedensity of states through strain and quantum confinemen~astrategy similar to that used for near-IR semiconducto5!and ~2! to arrange superlattice minigaps to eliminate finstates for Auger transitions. An early success of this stratwas demonstrated by experiments using steady-state ph

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conductivity in longer wavelength~Eg;120– 140 meV!InAs/Ga12xInxSb type-II superlattices.6 These authorsshowed that such narrow-band-gap superlattices~variationsof which form the backbone of many current MWIR lasdesigns! can display Auger rates that are orders of magnitusmaller than those measured in Hg12xCdxTe samples withcomparable band gaps. The measured results were founbe within a factor of 3 of theoretical results for this structuSubsequent photoconductivity measurements at 77 andK on an InAs0.85Sb0.15/In0.87Al0.13As0.91Sb0.09 multiple quan-tum well [Eg(5 K)5343 meV# illustrated the importanceof final-state resonance for the Auger process.7 Auger ratesfor type-II antimonide quantum wells and superlattices wband gaps near 275 and 400 meV, respectively, havebeen extracted from optically pumped lasers by employmeasurements of the threshold pump intensity and calctions of the threshold carrier density.8,9 In both cases, Augersuppression relative to bulk materials was observed, andtemperature dependence of the Auger recombinationevaluated. Detailed theoretical calculations of the Augrates were not presented in Refs. 7–9.

While the characterization of Auger recombination usiphotoconductivity and optically pumped laser performanhave provided significant insight into this process in MWlaser materials,7–9 both of these techniques possess limitions. For example, the photoconductivity measurememust be performed on samples grown on a semi-insulasubstrate, leading to growth of the structures in Refs. 6 anon lattice-mismatched GaAs substrates. In addition, thmeasurements require Ohmic contacts, and quantitaanalysis using this technique relies on low-density measments of the carrier mobilities. Both the photoconductiv

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13 048 PRB 58D.-J. JANGet al.

and the optically pumped laser results also require knoedge of the absorption coefficient at the optical excitatwavelength. Moreover, the analysis assumes steady-statcitation, which could be compromised by multimode opetion of the excitation sources. The optically pumped laresults8,9 also can be influenced by factors related to thetical cavity. In addition, for these measurements, the Aurecombination cannot be uniquely isolated from other recobination processes.

Many of these limitations can be overcome using aoptical, device-independent, ultrafast techniquesapproaches that have been widely applied in the visiblenear IR, but less extensively in the MWIR due to both limited optical sources and limited interest in materials in tspectral region relative to the near IR. Such techniques othe advantage of injecting a well-defined~and potentiallywell-calibrated! carrier density that can be probed from ttime of injection through the time required for recombinatito be complete. In addition, ultrafast optical techniquescontactless and do not require semi-insulating substraThrough a combination of temporal resolution and variatof the optical excitation level, density-dependent recombition, such as Auger recombination, can be isolated reafrom Shockley-Read-Hall recombination. We have recenreported10 subpicosecond, time-resolved, differential tranmission measurements of Auger recombination at 300 K(Ga0.75In0.25Sb/InAs/Al0.20Ga0.80Sb superlattice multiplequantum well~MQW! with a band-gap energy of 330 meVThis structure is similar to those employed successfully ivariety of MWIR diode lasers.11 For these measurements thinitial optically injected carrier density was determined frothe optical excitation intensity and from the density depdence of the peak differential transmission measured. Nonificant Auger suppression was observed in this structurresult that is consistent with subsequent detailed analysthe band structure.4 We later used4,12 time-resolved differen-tial transmission to measure the 300 K Auger rates in ameV InAs/Ga0.60In0.40Sb/InAs/Al0.30Ga0.42In0.28As0.50Sb0.50superlattice, a structure similar to those successfutilized13 in optically pumped lasers operating at 5.2mm upto 185 K and at 3.7mm up to 300 K. This structure wadesigned specifically for suppression of Auger recombition and intersubband absorption, and a factor of 4 reducin the Auger rate was measured12 relative to InAs, a widerband-gap bulk semiconductor. This four-layer superlattwill be the subject of the temperature-dependent measments discussed below.

Here, we describe the application of an alternativetrafast, all-optical technique, i.e., time-resolved photolumnescence~PL! upconversion,14 to measurements of the temperature dependence of Auger recombination inaforementioned MWIR four-layer superlattice. Again, thtechnique is well established in the near IR but only sparsapplied in the MWIR.15–17 Advantages of this technique include the ability to readily extract the optically injected carier density18 and the carrier temperature19 from time-resolved PL spectra. Knowledge of the carrier densitycritical to any quantitative analysis of Auger recombinatioFurthermore, measurement of the carrier temperature iscial to the study of the temperature dependence of Aurecombination, since it is the carrier temperature that prim

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rily determines the Auger rate~although, as we show belowthe temperature dependence of the band structure canhave measurable effects!.

The temperature dependence of the Auger process isticularly relevant to diode laser design, since lasers desigfor Auger suppression at one temperature may not be omized at another,20 and the temperature dependenceMWIR quantum wells and superlattices may not displaytrends that one might anticipate from simple models.21 It iswell known that in near-IR band-gapbulk materials the Au-ger rate increases strongly with increasing temperature.18 Fornear-IR band-gapquantum wells, however, the Auger ratehas been found to depend only weakly on temperature, leing some investigators to conclude that phonon-assistedger recombination dominates in these structures.18,22 Othershave concluded that band-to-band Auger recombinationdominates,23 but electrostatic band-profile deformation influences the band-edge populations in a manner that decrethe temperature dependence of the Auger rate. The tempture dependence of Auger recombination in somebulkMWIR III-V semiconductors is more complicated thannear-IR materials. This is a consequence of the proximitythe spin-orbit split-off band energyD0 to that of the funda-mental gapEg in narrow-band-gap semiconductors, suchInAs and related alloys. The split-off band can thereby pvide resonant states for hole-hole Auger processes. Sincetemperature dependences ofEg andD0 are generally differ-ent, the Auger resonance energy may move relative toband-gap energy, and, therefore, the Auger rate may incror decrease with temperature.7 Similar arguments can bemade with respect to subbands in MQW’s and minibandssuperlattices, potentially leading to unexpected temperadependence to the recombination in such structures. Forample, the Auger coefficient in a 275-meV bangap InAs/Ga0.69In0.31Sb/InAs/AlSb type-II MQW was foundto increase with temperature modestly in a monotomanner.8 On the other hand, the Auger coefficient wfound9 to saturate with temperature in a 400 meInAs/GaSb/Ga0.75In0.25Sb/GaSb superlattice designed withvalence-band Auger resonance in the middle of a minigFurthermore, the Auger coefficient was found to actually dcrease with temperature above;180 K in a similar superlat-tice designed with a heavy-hole-1 to heavy-hole-3 Augresonance.24 Such widely varying results indicate the impotance of understanding the temperature dependence oAuger process in structures designed for MWIR lasers.

We will present both experimental and theoretical anases of the temperature dependence of Auger recombinain a 310 meV, strain-balanced, broken-gap superlatticesigned for suppression of Auger recombination and intersband absorption at room temperature. Time-resolved MWPL upconversion was used to measure carrier recombinarates, and results are presented for lattice temperatures ring from 50 to 300 K. We obtain excellent agreement btween measured and calculated Auger rates, which are foto increase monotonically with lattice temperature and crier density. The PL upconversion technique readily providthe carrier temperature, and we discuss the impact ofcarriers on our analysis. Finally, the temperature dependeof the Auger rate is used, together with estimates of threold carrier density, to place an upper bound on the empir

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PRB 58 13 049TEMPERATURE DEPENDENCE OF AUGER . . .

temperature parameterT0 for lasers incorporating this structure as an active region.

SAMPLE STRUCTURE

The sample of interest for these studies was groby molecular-beam epitaxy~MBE! on a nominallyundoped GaSb substrate. It is comprised of 40 periof an InAs ~15 Å!/Ga0.60In0.40Sb ~25 Å!/InAs ~15 Å!/Al 0.30Ga0.42In0.28As0.50Sb0.50 ~39 Å! superlattice bounded b1000 Å layers of Al0.30Ga0.42In0.28As0.27Sb0.73. The structureis capped with 100 Å of GaSb to prevent oxidation of thecontaining quinternary alloy. The superlattice is not intetionally doped and, although not determined specificallythis sample, background carrier densities in similar structugrown in the same MBE system are typically in the lo1015 cm23 range. As shown in Fig. 1, under continuowave excitation the sample exhibits strong room-temperaPL, from which a band gap of 310 meV~4 mm! is obtained.

The band-edge energies of the bulk constituents osingle period of the superlattice, shown in Fig. 2, illustra

FIG. 1. Time-integrated photoluminescence at 300 Kcontinuous-wave excitation.

FIG. 2. Band-edge diagram for a single period of the narroband-gap superlattice. The solid, long-dashed, and short-dalines represent the conduction, heavy-hole, and light-hole bbands, respectively. The energy of the superlattice conduction-valence-band edges are shown on the right edge of the figure.

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the complicated type-II band alignments in this structuThe full nonparabolic band structure with momentumdependent matrix elements is obtained from a superlatK–p formalism similar to that applied previously to twocomponent superlattices2,25 but modified to allow for an ar-bitrary number of layers in a unit cell.4 The results of thiscalculation are shown in Fig. 3 for some of the lattice teperatures relevant to the experimental studies. Inparameters26 to the calculation are limited to the energy leels, matrix elements, and effective masses of the bulk cstituents, and valence-band offsets between layers. Asin Fig. 3, the band-gap energy clearly decreases with incring temperature, although the changes in dispersion ofvarious bands are rather subtle. Nevertheless,temperature-dependent band gap results in a temperaturpendence of the Auger and intersubband resonances. Thexplicitly accounted for in our theoretical model of the Ager recombination and is borne out in our measurementthe temperature dependence of the Auger rates.

The superlattice has been designed to suppress Augecombination and intersubband absorption at 300 K. Thisaccomplished through the reduction of the valence-baedge density of states and through the elimination of stanear zone center that are one band-gap energy abovelowest conduction subband edge and below the highestlence subband edge at a lattice temperature of 300 K.design very effectively reduces intersubband absorption300 K for photon energies near that of the band gap.4 Inaddition, the light uppermost heavy-hole band leads to ladifferential gain in lasers based on such active regions.4 Thisin turn should result in low threshold current densities ahence, low Auger rates at carrier densities appropriatedevice operation. On the other hand, a detailed study ofband-structure dependence of the Auger rate in this strucindicates that the final-state optimization results in onabout a factor of 2 suppression of the Auger rate at 300 K27

Considerably more suppression can be obtained throfinal-state optimization at lower temperatures, but a modcation of the superlattice design is required.

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FIG. 3. Band structures along the in-plane direction (ki) andgrowth direction (k') for lattice temperatures of 50, 100, 150, 26and 300 K. The band edges are indicated by the solid horizolines and the zone-center Auger resonance energies are indicatthe horizontal dashed lines.

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EXPERIMENTAL RESULTS

Time-resolved PL upconversion was used to investigthe density and temperature dependence of the recombtion in this superlattice. The MWIR PL, excited in thsample by an intense 140 fs, 843 nm pulse from a Kerr-lmode-locked Ti:sapphire laser, was mixed with a portionthe same Ti:sapphire laser pulse in a potassium titanyl arate crystal oriented for phase-matched sum-frequencyeration. The intensity of the measured upconverted signaproportional to that of the PL emitted from the sample. Teporal resolution is obtained in the measurement by adjusthe relative delay between the pulse that excites the PLthe pulse that is used for the upconversion process. Speresolution is realized by adjusting the phase-matching anand, simultaneously, a monochromator through whichupconverted signal passes. Details of the experimental shave been described previously.16

PL decay curves for lattice temperatures of 50, 100, 1175, 200, 230, 260, and 300 K were measured for a ranginitial carrier densities. Representative curves are showFig. 4 for four lattice temperatures. The decay rate of theclearly increases both with increasing lattice temperatureincreasing initial carrier density. We attribute the fast decoccurring within a few hundred picoseconds at high cardensities to Auger recombination and the slower featurelonger delays to Shockley-Read-Hall recombination. Thassertions are justified in the analysis discussed below.

The initial carrier densities, which are crucial in determing Auger rates, were calibrated by comparing selectedperimental time-resolved PL spectra with those calculabased on the band structures shown in Fig. 3. For these msurements, the time delay between the pulse used to ethe sample and that used for the upconversion processfixed at 10 ps and the entire PL spectrum was measured.carrier temperature was extracted from the high-energyof the spectrum and used in calculations of the PL for a raof carrier densities. As illustrated in Fig. 5, the calculatedspectra were then compared to the experimental spectryield the carrier density. Note that these results are plotteda semilogarithmic scale to illustrate the exponential ene

FIG. 4. Time-resolved photoluminescence measured nearband-gap energy for lattice temperatures of 50, 100, 150, and 2and initial carrier densities of~from the top! 1.731018, 1.131018,5.731017, 2.831017, and 1.431017 cm23.

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dependence of the tail of the spectrum. The slope ofhigh-energy tail is primarily indicative of the carrier temperature, while for a reasonably cool distribution the overwidth of the spectrum is largely controlled by the carridensity as a consequence of band filling. In fitting the sptrum, we fix the band-gap energy at the low-density vaobtained from continuous wave PL~band-gap renormalization is insignificant at the densities of interest in this lowmass semiconductor!, use the carrier temperature obtainfrom the high-energy portion of the spectrum, and thenjust only the carrier density to obtain a best fit to the daThe PL observed below the band edge is present at all dsities indicating that it is a consequence of band tailinThese data are ignored in the fits. We assume in the calations that within 10 ps after optical excitation the initialhot carriers diffuse across the thin superlattice and areformly distributed in the growth direction at the time of thmeasurement. Since the experimental arrangement ensthat only the emission from the central portion of the excitregion of the sample is upconverted, transverse variationthe density are ignored. Shown in Fig. 5 are theoreticalsults for three values of the carrier density, illustrating ththis procedure is sensitive to variations in density of appromately 620%. This process was repeated for various teperatures and excitation conditions. We conclude from tprocess and from knowledge of our optical excitation intesity that, over the range of our experimental conditions,sentially all of the incident photons transmitted through tsemiconductor surface produce carriers that are confinethe superlattice, nominally independent of lattice temperatand excitation level. Hence, for this structure, the initial crier density is readily determined from the incident photflux.

DISCUSSION

The data in Fig. 4 are converted to density dependratesR(n) using

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FIG. 5. Semilogarithmic plot of calculated~lines! and measured~circles! time-resolved~10 ps after excitation! photoluminescencefor an excitation fluence of 8mJ/cm2, a lattice temperature of 260K, and a carrier temperature of 300 K. Calculated PL for carrdensities of 4.531017 ~dash-dot-dotted line!, 5.731017 ~solid line!,and 7.031017 cm23 ~dashed line! are indicated.

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where I PL is the intensity of the PL and the derivatives areadily obtained from Fig. 4. Specifically,dIPL /dt is ob-tained directly from Fig. 4 anddIPL /dn is obtained from afunctional fit to the peak PL signals measured at each etation level. This procedure is illustrated in Fig. 6, whereshow the fit and the normalized PL as a function of carrdensity for the 260 K data, measured at a fixed time denear the peak of the data shown in Fig. 4.R(n) is interpretedas the sum of radiative and nonradiative rates. Phoreabsorption28 is not considered here because of the smexcitation beam size~50 mm, thin active region~0.375mm!,low band-edge absorption coefficient~approximately 2000cm21), and relatively small radiative rate~never larger than10% of the total recombination rate!. Here, we are interestein primarily the nonradiative recombination rate. To obtathis for each density, we subtract fromR(n) the calculatedradiative rate, a quantity that is readily determined fromband structure and matrix elements and is essentially innificant relative to Shockley-Read-Hall and Auger recomnation in this structure.

This procedure yields the nonradiative rates as a funcof density as shown in Fig. 7 for the same lattice tempetures and initial carrier densities as depicted in Fig. 4. Nthat the data shown in Fig. 7 originate, in essence, entifrom experiment, with theory invoked only to account for tminor effect of radiative recombination and to calibrate tinitial carrier density. The intercepts in these plots yield tShockley-Read-Hall rates, which correspond to lifetimesall cases of about 2 ns. This value is within the 2–4 ns ratypical of antimonide structures grown in this MBE systeand is within a factor of 5 of the best MBE-grown anmonide structures studied in our laboratory. The specificgin of this density-independent recombination is not knowbut may be associated with antisite defects in the quinternlayers and/or interface states. Since the radiative ratebeen removed from the results of Fig. 7, deviations fromzero slope are a consequence of Auger recombination.data clearly illustrate an Auger rate that increases unifor

FIG. 6. Peak PL intensity as a function of carrier density folattice temperature of 260 K. The curve represents a smooth ftional fit to the data from which the partial derivativedIPL /dn isobtained and used in the evaluation of the recombination rateR(n).

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with both increasing carrier density and increasing tempeture. We find that, over much of the density range of interethe density dependence of the Auger rate is subquadwith carrier density12 as a consequence of degeneracyboth the conduction and valence bands. The effects of deeracy have been confirmed through detailed investigationthe density dependence of the recombination, and the rewill be discussed elsewhere.29 The temperature dependencof the Auger process is seen more clearly in Fig. 8, whereplot the Auger rate as a function of lattice temperatureseveral different carrier densities.

The calculated direct band-to-band Auger rates are ashown in Fig. 8. These were obtained from Fermi golderule calculations based on the nonparabolic band strucwith momentum-dependent matrix elements. Transition mtrix elements are evaluated using a statically screened Clomb interaction and first-orderK–p perturbation theory forthe wave-function overlaps. The implementation is simi

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FIG. 7. Nonradiative recombination rates at lattice temperatuof 50, 100, 150, and 260 K obtained from the data in Fig. 4 usdensity calibrations such as that shown in Fig. 5 and the approdescribed in the text.

FIG. 8. Measured~filled symbols! and calculated~open con-nected symbols! Auger rates as a function of temperature for initidensities of 531017 ~triangles!, 1031017 ~squares!, and 1331017 cm23 ~circles!.

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to that reported previously,30 but modified to include Um-klapp processes in the growth direction.29 This intrinsic phe-nomenon characterizes scattering processes that involveciprocal lattice vector.31 While these processes have littimpact on Auger recombination in bulk narrow-gasemiconductors32 that have large reciprocal lattice vectorthey can play a significant role in superlattices. Zone foldin such structures greatly reduces the Brillouin-zone widththe growth direction~by more than an order of magnitudeour superlattice! making Umklapp processes more probabCalculations indicate that these processes contribute appmately half of the total Auger rate in this structure. Umklaprocesses involving a reciprocal lattice vector larger th5(2p/D), whereD is the superlattice period of 94 Å, arnegligible. We find that,with no adjustable parameters, thetheory successfully predicts both the density dependencethe temperature dependence of the Auger process as wethe absolute rate. The latter, however, must be placedcontext with the roughly 10% systematic and random errothe data and the 20% uncertainty in carrier density.

We have discussed the temperature dependence oAuger process in terms of the lattice temperature. WhileAuger process depends on thelattice temperature throughthe temperature dependence of the band structure, it willdepend on the occupation of the bands as determined bycarrier temperature. For our measurements, carriers arejected with roughly an electron volt of excess energy. Ustime-resolved PL, we find that most of the cooling of tinitially hot carrier distribution occurs within 10 ps, a timscale for which recombination is not significant. On the othhand, for high initial carrier densities we have observsomewhat elevated carrier temperatures that persist for mhundreds of picoseconds. This behavior is illustrated in F9, where we show the measured carrier temperaturefunction of time after excitation for a lattice temperature150 K and an initial carrier density of 5.731017 cm23. Al-though we have not completed a detailed analysis ofpersistent heating, it may be due in part to Auger recomnation itself, which supplies roughly the band-gap energythe carrier distribution for each Auger event. Auger-induc

FIG. 9. Time dependence of the carrier temperature obtafrom time-resolved photoluminescence for a lattice temperatur150 K and an initial carrier density of 5.731017 cm23. The insetshows an expanded view of the initial carrier cooling. The dindicate that the carrier distribution remains warmer than the latfor hundreds of picoseconds.

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carrier heating has been observed in wider band-gap sttures with much lower Auger rates.33 We use measurementsuch as those shown in Fig. 9 to obtain an average catemperature over time delays ranging from 10 ps to 1 nseach of our Auger measurements. These temperatures, ware shown on the upper axis of Fig. 8, are used in the calations of the Auger rates.

An important observation is that the average carrier teperature is essentially identical for the two highest latttemperatures. On the other hand, the measured and clated Auger rates are significantly different for these twlattice temperatures. This clearly indicates that the Aurate has been modified strictly by the dependence of the bstructure on the lattice temperature. Specifically, detaanalysis of the states involved in the Auger process revthat at a lattice temperature of 260 K, most of the final hstates are in the fourth valence subband, whereas at 30they are in the third valence subband. This behavior, wharises from the slight decrease inEg as the temperature iincreased from 260 to 300 K, is illustrated in Fig. 10 whewe show the electron~filled circles! and hole~open circles!states for;99% of the Auger transitions for lattice tempertures of 260 and 300 K, and for a carrier temperature of 3K. This figure clearly indicates that electrons near the Auresonance in the valence bands~indicated by the dashed line!are more likely to participate in Auger transitions for a lattitemperature of 300 K compared to the case of a lattice tperature of 260 K. This implies that either a near-zone-cenelectron in the lowest conduction subband or a near-zocenter hole in the highest valence subband~or both! is morelikely to participate in an Auger scattering process in tformer case. Since the Fermi occupation factor is highestnear-zone-center particles, we therefore expect a signifiincrease in the Auger rate as the lattice temperature increfrom 260 to 300 K, as calculated and observed.

The present calculation of the Auger rates does not

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FIG. 10. Band structure of the superlattice indicating the baedge~short-dashed lines! and the valence-band zone-center Augresonance energies~dashed lines! for lattice temperatures of 260and 300 K and a carrier temperature of 300 K. The filled~open!circles represent electron~hole! states associated with;99% of thehole Auger transitions at 260 K and 300 K for a carrier density5.731017 cm23. The states are plotted as a function of in-plamomentum,ki ~Å21!, only; hence, states not lying directly oa subband possess a growth direction momentum compok' ~Å21).

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clude phonon-assisted Auger recombination, which ispected to be rather insensitive to temperature variations.the other hand, the calculation indicates that, in this strture, the rate associated with direct Auger processescreases modestly with temperature, a trend accuratelyflected in the data. Although phonon-assisted transitionscertainly present, the agreement between the magnitude,sity dependence, and temperature dependence of thesured rates and those calculated based purely on direct Atransitions suggests that phonon-assisted Auger transido not significantly impact the nonradiative recombinationthis structure.

The calculated band structure can be used, together wband-filling model and calculations of the intersubbandsorption, to obtain the temperature-dependent gain specfor this superlattice. This, combined with the measuShockley-Read-Hall and temperature-dependent Auger racan be used to estimate the temperature-dependent threcurrent densityJth(T) per active layer width for lasers utilizing the superlattice for an active region. For an assumed tcavity loss of 100 cm21, we obtain aJth(300 K) of 16kA cm2 mm21. As shown in Fig. 11, a semilogarithmic ploof Jth as a function of temperature is well approximated bstraight line, and the inverse slope of ln(Jth) yields the em-pirical characteristic temperatureT0581 K. We attribute thisrelatively high characteristic temperature to the suppresof Auger recombination and intersubband absorption instructure throughout this temperature range. We note, hever, that thisT0 is based solely on material properties. Sinother temperature-dependent loss mechanisms maypresent in an actual laser, thisT0 can be taken only as aupper limit ~if Shockley-Read-Hall recombination remainsmall!. Nevertheless, such a material parameter is a usfigure of merit for a laser gain medium.

FIG. 11. Calculated threshold current density~filled circles! as afunction of lattice temperature for a laser that uses the multilasuperlattice as an active region. In obtaining this result, a totalof 100 cm21 was assumed, the measured temperature-depenrecombination rates and the calculated threshold carrier denswere used. The slope of the resulting data, indicated by the sline, yieldsT0581 K, which represents an upper bound to the chacteristic temperature.

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SUMMARY AND CONCLUSIONS

In summary, we have measured and calculated Aurates for a 4-mm band-gap type-II superlattice designed fsuppression of Auger recombination and intersubbandsorption at room temperature. The calculated Auger rawhich include superlattice Umklapp processes, weretained using Fermi’s golden rule for the transition rates athe full temperature-dependent, nonparabolic band structUmklapp processes, which provide roughly half of the toAuger rate, are found to be necessary to describe the exmental results. The experimental Auger rates were demined from time-resolved PL upconversion as a functionoptically injected carrier density and lattice temperature. Wfind excellent agreement between measured and calcurates for direct Auger transitions at all temperatures andrier densities, which suggests that phonon-assisted Auprocesses do not contribute significantly to the overall nradiative recombination rate.

As discussed in more detail in Ref. 12, the 300 K Augcoefficient of 2.9310227 cm6/s measured at low densitiesinthe present structure is roughly a factor of 4 smaller thanof InAs,34 even though the band gap of this bulk semicoductor is 50 meV wider. The coefficient is also nearlyfactor of 3 smaller than that measured in~Ga0.75In0.25Sb/InAs/Al0.2Ga0.8Sb superlattice MQW with a20-meV-wider band gap.10 On the other hand, the Augecoefficient measured at 300 K in our 310-meV band-gapperlattice is only;30% smaller than that obtained in a 27meV band-gap InAs/Ga0.69In0.31Sb/InAs/AlSb type-II MQW~Ref. 8!. While such comparisons are necessary to attempdetermine the success of Auger suppression in a given sture, we caution that a simple comparison of coefficientsnot adequate. We clearly observe saturation of the Aucoefficient in our structure12 as a consequence of degeneraThis saturation results in a high-density Auger rate thatbe well below that expected assuming a simple quadrcarrier-density dependence for the rate. Saturation of theger coefficient was not observed in the structure studiedRef. 10, and saturationcannotbe quantified using the technique of Refs. 8 and 9. In addition, caution must be usedcomparing Auger rates in various types of structures~bulk,quantum well, and superlattice! as carrier-density conventions vary. For example, in a superlattice it is reasonableuse a carrier density averaged over the superlattice period~aswe have done in the present analysis!, but three-dimensionadensities in isolated quantum wells are usually determibased on the width of the well. In the latter case, sheet dsities and two-dimensional Auger coefficients are often usIn either case, however, density variations along the grodirection will exist leading to a degree of ambiguity in thAuger coefficient.

We have used the measured temperature-dependencombination rates and the calculated gain in the structurextract an upper bound on the characteristic temperaturT0581 K for a laser based on this material. We presenhave no direct experimental measure forT0 for a laser uti-lizing this specific design as an active region. However, aT0of 37 K was obtained in a much longer wavelength~5.2 mm!optically pumped laser based on a similar superlattice de

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and a 3.7mm superlattice device has lased up to 300 K.13 AT0 of 81 K for a MWIR laser, while lower than state-of-theart near-IR lasers, would be exceptional if experimentarealizable for a MWIR laser. We emphasize again, howevthat as long as the Shockley-Read-Hall recombinationmains small this should be considered as an upper limitT0, since other temperature-dependent loss mechan~e.g., carrier leakage! will exist in an actual device.

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ACKNOWLEDGMENTS

This research was supported in part by the United StaAir Force, Air Force Material Command, Air Force ResearcLaboratory, Kirtland AFB New Mexico 87117-5777~Con-tract No. F29601-97-C-0041! and the National ScienceFoundation~Grant Nos. ECS-9406680 and ECS-9707799!.

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*Also at the Department of Electrical and Computer EngineerinUniversity of Iowa, Iowa City, Iowa 52242. Electronic [email protected]

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3M. E. Flatte, C. H. Grein, H. Ehrenreich, R. H. Miles, and HCruz, J. Appl. Phys.78, 4552~1995!; C. H. Grein, P. M. Young,and H. Ehrenreich,ibid. 76, 1940~1994!.

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5See, e.g., E. Yablonovich and E. O. Kane, J. Lightwave Techn6, 1292~1988!; E. P. O’Reilly and A. R. Adams, IEEE J. Quantum Electron.30, 366 ~1994!.

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11T. C. Hasenberg, R. H. Miles, A. R. Kost, and L. West, IEEEQuantum Electron.33, 1403~1997!.

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14J. Shah, IEEE J. Quantum Electron.24, 276 ~1988!.15D. von der Linde and R. Lambrich, Phys. Rev. Lett.42, 1090

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23Shunji Seki, Wayne W. Lui, and Kiyoyuki Yokoyama, Appl.Phys. Lett.66, 3093~1995!.

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26O. Madelung, inSemiconductors, Group IV Elements and III-VCompounds, edited by K.-H. Helluege and O. Madelung,Landolt-Bornstein, New Series, Group III, Vol. 17, Pt. a~Springer-Verlag, Berlin, 1982!.

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30C. H. Grein, P. M. Young, M. E. Flatte´, and H. Ehrenreich, J.Appl. Phys.78, 7143~1995!.

31R. Peierls, Ann. Phys.~Leipzig! 12, 154 ~1932!.32S. Brand and R. A. Abram, J. Phys. C17, 571 ~1984!.33See, e.g., H. Lobentanzer, W. Stolz, J. Nagle, and K. Ploog, Phys

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Temperature dependence of Auger recombination in highly injected crystalline silicon