Bimberg, IEEE (1997), InGaAs-GaAs Quantum-dot Lasers

196 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 3, NO. 2, APRIL 1997

InGaAs–GaAs Quantum-Dot LasersD. Bimberg, N. Kirstaedter, N. N. Ledentsov, Zh. I. Alferov, P. S. Kop’ev, and V. M. Ustinov

Abstract—Quantum-dot (QD) lasers provide superior lasingcharacteristics compared to quantum-well (QW) and QW wirelasers due to their delta like density of states. Record thresholdcurrent densities of 40 A�cm�2 at 77 K and of 62 A�cm�2 at300 K are obtained while a characteristic temperature of 385K is maintained up to 300 K. The internal quantum efficiencyapproaches values of�80%. Currently, operating QD lasers showbroad-gain spectra with full-width at half-maximum (FWHM) upto �50 meV, ultrahigh material gain of �105 cm�1, differentialgain of �10�13 cm2 and strong nonlinear gain effects with again compression coefficient of�10�16 cm3. The modulationbandwidth is limited by nonlinear gain effects but can be in-creased by careful choice of the energy difference between QDand barrier states. The linewidth enhancement factor is�0.5.The InGaAs–GaAs QD emission can be tuned between 0.95�mand 1.37 �m at 300 K.

Index Terms— Characteristic temperature, gain, linewidthenhancemant factor, quantum-dot gain, semiconductor lasers,threshold current density.

I. INTRODUCTION

SEMICONDUCTOR lasers having as active medium anuniform array of quantum dots (QD’s) are expected to ex-

hibit properties superior to three-dimensional (3-D), quantum-well (QW) and QW wire lasers [1]–[3]. Due to the threedimensional confinement of carriers in a quantum dot with asize below or equal to the exciton Bohr radius the densityof states becomes a delta function [4]. Consequently, notemperature dependent broadening of the gain function ispossible if the sublevel splitting is sufficiently large. QD laserswith such an atomic like density of states are expected to showultra low-threshold current densities, ultrahigh temperature sta-bility of threshold current, ultrahigh differential gain increased,cutoff frequency and chirpfree operation under direct currentmodulation. Potential device applications therefore range fromhigh-power semiconductor lasers to high-speed light sourcesfor fiber-based data transmission.

Practical realization of the fundamental advantages of QDlasers was proposed to be hampered both by a theoreticallypredicted othogonality of electron- and hole-wave function inQD’s leading to a very small radiative recombination probalityand by carrier capture delayed by more than nanosecondsdue to the “phonon bottleneck.” Both effects together werepredicted to lead to zero quantum efficiency for dots of stillmacroscopic dimensions (100 nm) [5]. Recent numericalcalculations [6] of electron, hole and exciton wavefunctionsfor actual InAs–GaAs QD levels on the other hand did not

Manuscript received December 3, 1996.D. Bimberg and N. Kirstaedter are with Technical University-Berlin, 10623

Berlin, Germany.N. N. Ledentsov, Zh. I. Alferov, P. S. Kop’ev, and V. M. Ustinov are with

the Ioffe Physical-Technical Institute, 194021, St. Petersburg, Russia.Publisher Item Identifier S 1077-260X(97)04525-5.

confirm the complete wavefunction orthogonality of groundand excited states. In addition multiphonon relaxation allowsefficient carrier capture [7] and experiments presented in detailbelow yield luminescence decay times of 2 ns for allowedtransitions and carrier capture times of 20 ps.

Consideration of the actual statistical nature of carriercapture into realistic dots having excited states and of theimportance of the weak or vanishing thermal coupling betweenadjacent QD’s lead recently to considerable revision of theoriginal predictions for gain, threshold and chirp [8], [9].

In the last decade two different approaches have beenexplored to fabricate quantum dots. The first one originallydeveloped for quantum-wire lasers uses different variationsof patterning techniques either prior to growth for selectivegrowth or after growth (e.g., chemical etching with followingovergrowth). Using patterning techniques InGaAs–InGaAsPQD lasers were successfully realized, but they still show highthreshold current density of 7.6 kAcm at 77 K [10]. Thesecond approach simply uses strain induced self-organizationof InGaAs–GaAs quantum dots [11], [12] on low indexsubstrates yielding threshold current densities as low as60A cm at room temperature [13]. Self-organization is alsovery successfully applied to the growth of InP on GaInP [14]and GaSb [15] or InSb [16] on (100)-GaAs resulting in theformation of 3-D-islands. Growth of InGaAs on (311)B-GaAs[17] shows formation of dots with a disk like shape. Theirdiameter of 60 nm is however comparatively large and no largeimpact of quantum effects could be yet demonstrated. Sincethe first presentation of a QD injection laser [11] based on self-organized dots as gain medium large efforts were undertakento decrease the threshold current density to its ultimate limitdetermined by the transparency condition of the dot states. Forthis purpose one has to increase the internal efficiency andthe carrier capture rate into the dots which present the mostserious performance limitations for QD lasers. Since 1994 thethreshold density has beeen indeed decreased byorders ofmagnitude as visualized in Table I. The threshold will soonapproach the limit given by the actual dot size distribution(see Section III on threshold characteristics) and there will benow additional strong focus on other fundamental propertiesof QD lasers like the temperature and excitation dependenceof the gain spectra and the modulation characteristics.

II. REALIZATION OF QD LASERS

A schematic view of the band structure of a typical QDlaser is presented in Fig. 1. The ideal QD laser consists of a3-D-array of dots with equal size and shape surrounded by ahigher bandgap material which confines the injected carriers.The whole structure is embedded in an optical waveguideconsisting of lower and upper cladding layers.

1077–260X/97$10.00 1997 IEEE

BIMBERG et al.: InGaAs–GaAs QUANTUM-DOT LASERS 197

TABLE IHISTORY OFMAJOR STEPS IN THEDECREASE OFTHRESHOLDCURRENT DENSITY OF QD LASERS. THESECOND COLUMN LISTS THEDOT (QD) AND BARRIER MATERIAL,

THE NUMBER OF QUANTUM DOT LAYERS (DOT LAYERS) GROWN ON TOP OF EACH OTHER, THE TYPE OF DOT FORMATION (FORMATION), THE SIZE OF THE DOT

BASELENGTH (DOT SIZE), THE DOT GROWTH TEMPERATURE(Tgrowth), THE AREA DOT DENSITY (DOT DENSITY) AND THE GROWTH REACTOR TYPE (REACTOR). THE

THIRD COLUMN LISTS THE THRESHOLD AT VARIOUS TEMPERATURES AND THEFOURTH COLUMN THE CORRESPONDINGLASING WAVELENGTH AND THE TYPE OF THE

LASING TRANSITION. WL I NDICATES LASING TRANSITION VIA WETTING LAYER STATES, QD� VIA EXCITED QUANTUM DOT STATES AND QD VIA QD GROUND STATE

Fig. 1. Schematic bandstructure of a quantum dot laser with self-organizeddots under forward bias. A 3-D-array of dots vertically aligned along thegrowth direction which is formed during the growth of multiple QD layers isillustrated schematically. Typically the dot area density in the (100)-plane is4 � 1010 cm�2 and the dot size distribution is around 10%. The distancebetween the dot layers is 5 nm and the real dot density in the recombinationvolume with a thickness of 200 nm is 6� 1015 cm�3 for three QD layers.

Spontaneous formation of QD’s for currently operating QDlasers (see Table I) was successfully demonstrated at growthtemperatures between 460C and 550 C. The QD’s areformed using a Stranski–Krastanov growth mode. The arealdot densities range between 210 cm [19] and 1 10cm [4] with a typical size distribution of 10% [22]. Thelow-dot density causes several problems concerning thresholdand gain that will be described in the following section.

If the cladding layer and the GaAs QD barrier are alsogrown at the same low temperature as the active dot layersthey are a possible source for current leakage and nonradiativerecombination. The QD’s show intermixing with the surround-ing barrier material if temperatures of 700C are used to growhigh-quality cladding layers.

The limited dot areal density sets an upper value for theQD modal gain. The modal gain can be increased by stacking

Fig. 2. Modal gain spectrum of a single layer of quantum dots obtained afterdeposition of nominally 2ML of InAs derived from single pass amplification.The transition energies of the QD ground state and excited states and the WLare marked.

several layers of QD’s upon each other [23]. Using thisapproach ground state lasing [13] at room temperature hasbeen demonstrated.

The relaxation rate might actually exceed values of 10electrons/s permitting a modulation bandwidth up to 200 GHz[24] if the energy difference between barrier and dot states iscarefully tailored.

III. GAIN OF SELF-ORGANIZED QD LASERS

Some of the most important properties which stronglyinfluence the threshold current density and modulation band-width of a semiconductor laser are the material gain and thedifferential material gain. The material gain of a QD laser canbe derived from the complex susceptibilityof an ensembleof atoms interacting with a time-dependent electromagnetic


field. In case the dots show only one electron and one holelevel the susceptibility is as follows:

(1)

and are proportional to the absorption (materialgain) and the refractive index, respectively. is the photonenergy, the dot transition energy, the Bloch matrixelement and the QD electron hole wavefunction overlapintegral. The phase coherence time accounts for allmechanisms which cause a loss of coherence between the pho-ton field and the QD exciton. According to (1) the lineshape ofthe gain is Lorentzian and its width is determined by the phasecoherence time. In the case of self-organized dots the transitionenergies of different dots are not identical due to size orshape fluctuations. Thus the gain function is inhomogenouslybroadened and one can define a function so that theprobability of a dot having its emission energy betweenand is . is normalized such that theprobability of finding a dot emission within an infinite energyrange becomes unity. If is multiplied with the idealdot density of a 3-D-dot array in the recombination volumeone gets the density of states for an inhomogenouslybroadened dot ensemble. The ideal dot density is the numberof dots per volume where the number of dots is chosen as thetotal recombination volume divided by the dot volume .

(2)The factor of 2 in (2) accounts for the spin degeneracy.is the maximum of the dot distribution. The width of theGaussian is given by . By combining (1) and (2), onegets the material gain for an inhomogenously broadeneddot ensemble.

(3a)

(3b)

(3c)

The Fermi functions determine the occupation probabilityof the single dot states by electrons and holes. If the minimumspectral distance between transitions from two different dotsis much smaller than the single dot emission line width(determined by the phase coherence time) the gain spectrum of(3) is determined by the density of states of the dot ensemble.Since the total number of dots in the recombination volume ofa typical ridge-waveguide laser exceeds a value of10 the -function gain spectrum of a single dot transition (demonstratedby Grundmannet al. [4]) transforms to a broad gain spectrumas shown in Fig. 2 for QD’s formed after the deposition oftwo monolayer (ML) InAs.

Due to the lateral separation of the dots carriers in differentdots are thermally coupled only via wetting layer (WL) andGaAs barrier states [23]. The coupling between dots and the

(a)

(b)

Fig. 3. (a) Material gain spectra as a function of excitation density rangingfrom 20–250 A�cm�2 for an ensemble of InAs dots having a base length of 7nm and a size distribution of 13%. The WL is assumed to be a�0.5-nm-thicksingle QW. The inset shows the peak material gain(gmat) at �1.28 eV andthe differential material gain(dgmat=dN) as a funcion of current density. (b)Arrhenius plot of WL- and QD electroluminescence (EL) well below thresholdcurrent density proving thermal equilibrium of carriers between QD and WLstates.

WL is directly proved by the intensity ratio of QD and WLelectroluminescence (EL) at different temperatures and con-stant injection level which follows an Arrhenius dependence[see Fig. 3(b)]. The temperature dependence of the intensityratio can be used to derive an activation energy of the QDexciton to the WL of 25 meV.

Based on the structural parameters of the laser, the lumines-cence spectra and the transition energies of ground and excitedstates one can derive the material gain spectra according to(3). Since the Bloch matrix element and the overlap integralare not exactly known for the case of a QD laser one has tocalibrate the gain spectra [22] to absolute values by using thewell known equilibrium value of the absorption coefficient ofbulk GaAs.

The derivation of the material gain versus current densityin Fig. 3(a) is based on the experimentally determined decaytime of carriers in the recombination volume (see Fig. 1)in order to calculate the carrier density in that volume fromthe injection current density [25].

(4)


Here, is the thickness of the recombination volume (seeFig. 1), is a factor which accounts for the different volumesoccupied by QD, WL, and GaAs [22], is the density ofstates, is the Fermi function and the electron charge.

The modal and material gain spectra in Figs. 2 and 3 areasymmetric due to the contribution of excited QD states al-ready at comparatively low excitation in agreement with recenttheoretical predictions [8]. The overlapping gain functions ofground and excited states enhance the material gain to a valueof 9 10 cm at 250 A cm in the single layer QDlaser investigated here. This value is one order of magnitudelarger than for a 8 nm In Ga As–GaAs single QW laser[22] and in agreement with the prediction of Asada et al. [2].

The current density for the onset of gain saturationshown in Fig. 3(a) is much larger than the value estimatedfrom the laser rate equation [26] in the case that all carriersare confined to the QD states.

(5)

Here, is the dot area density and is the exciton decaytime of the InAs QD’s. The factor of three accounts forone ground state and two excited states. From (5) the gainsaturation level is 19 Acm for a dot area density of 410 cm and a QD decay time of 2 ns [22]. This saturationlevel is exceeded in real QD laser structures by one order ofmagnitude. In the next section it will be shown that currentleakage due to the population of barrier states (WL, GaAs) andnonradiative recombination in our yet nonoptimized structurescan explain the delayed saturation level.

IV. THRESHOLD CHARACTERISTICS

From the gain versus current density relation and the lasingcondition one can easily calculate the threshold (transparency)current density by

(6a)

(6b)

Here, is the fraction of the current density in-jected into QD’s and contributing to radiative recombination,

is the fraction of the current density from the bar-riers contributing to radiative recombination andthe fraction of the current density contributing to the leakagecurrent at threshold (transparency). is the sum of internalloss and mirror losses [see (10)]. Although the maximummaterial gain of the QD ensemble reaches a value of 10cmaccording to (3) the confinement factordefined as

(7)

is rather low for a single layer QD laser. Here denotesthe number of dots in the recombination volume (definedin Fig. 1), is the integral over the laser volume ofthe electric field vector of the optical mode which isnormalized to unity at its maximum value. Using a typical dot

Fig. 4. Threshold current density (solid line) as a function of the dot density.The calculation is done for a typical laser structure shown in Fig. 1 with anactive layer thickness of 200 nm and total loss of 8 cm�1. The thresholdcurrent densities for single and triple QD layer lasers are marked. Thetransparency current density is also shown (dashed line). The dashed areamarks the forbidden region due to gain saturation.

lateral coverage of 2% in the (100)-plane (dot areal densityof 4 10 cm , dot base length 7 nm) and the QDexciton volume 80 nm [22] the confinement factorfor a single layer dot laser structure is estimated to be110 . Thus for a maximum material gain of 10 cm atypical single-layer QD laser structure is expected to have amodal gain of 10 cm in agreement with our experimentalresults. This value is just sufficient for laser action in longcavity lasers. Short cavity lasers require a higher dot volumedensity. A way to overcome this limitation is the introductionof multiple layers of dots [23], [13].

The maximum material gain is calculated from thesteady state rate equation with the radiative current density

(assuming that all injected carriers are 100% confinedto the dots and no leakage current exists) and the populationinversion factor :

(8a)

-

-

(8b)

(8c)

Here, - is the dot density and is the density of QDexcitons calculated from the steady-state rate equation usingthe QD carrier decay time and the thickness of therecombination volume (see Fig. 1). Using (8) and the lasercondition [see (6)] one can calculate the threshold currentdensity as a function of the dot density (Fig. 4) assumingadditionally that only one energy level exists for electronsand holes.

For a total loss of 8 cm (e.g., for a long laser cavity of2 mm and an internal loss of3 cm ) the threshold currentdensity for a single-layer QD laser structure with a gain widthof 50 meV and a QD carrier decay time of 2 ns is as lowas 2 Acm . Thus, even for a QD laser with typical dot sizedistribution of 10% and dot areal density of 4 10 cmthe minimum threshold current density neglecting any current


Fig. 5. (a) Temperature dependence of threshold current density for asingle layer QD laser. The largeT0 between 50 K and 100 K reveals thetemperature independent peak gain of the QD ensemble. (b) Above 100-Kbarrier population and nonradiative centers decrease the decay time of carriersin the QD ground state. The integrated electroluminescence (EL) intensity ofQD, WL barrier and GaAs barrier at threshold unambiguously indicates theonset of current leakage above 100 K resulting in the decrease ofT0.

leakage can reach values more than one order of magnitudelower than in high quality QW lasers which exhibit lowestthreshold current densities of 50 Acm at 300 K [27].

From (8), we see that for longer decay times (i.e., loweroscillator strength) which are expected for dots with sizesmaller or equal to the exciton Bohr the transparency currentfurther decreases. But simultaneously the reduced oscillatorstrength reduces the maximum gain, thus, increasing thethreshold current to maintain the threshold gain. Note that thetransparency current is proportional to the dot volume densityand also to the number of dot layers if the carriers in theQD’s are not thermally coupled.

A. Temperature Dependence of Threshold and Loss Mechanism

A nonequilibrium distribution of carriers between all dotsin a dot ensemble should prohibit thermal broadening of thegain spectrum. If this condition is strictly fullfilled the peakgain should remain constant as a function of temperatureat constant injection level. Therefore the phenomenologicaldescription of the threshold temperature dependence accordingto the following equation results in an infinite characteristictemperature .

(9)

The first observation of an enhancement ofdue to carrierconfinement was reported by Arakawa et al. [1] for bulklasers placed in a magnetic field. A dramatic increase offor a true single layer QD laser up to 425 K is shown inFig. 5. Unfortunately in this structure the breakdown of thenonequilibrium carrier distribution and the temperature depen-dent current leakage reduces the value ofat temperaturesabove 100 K.

Fig. 6. Threshold current density as a function of temperature for a single dotlayer laser structure. The dots are placed in a 16-nm—wide GaAs–AlGaAsQW to reduce the escape probability of QD excitons into the barrier. ThisenhancesT0 up to 385 K while maintaining a low threshold current densityof �400 A�cm�2 at 300 K.

It was discussed in the last section that for this laser structurethe carriers in the dots are thermally coupled to the WL andthe GaAs barrier. Since the activation energy of a QD exciton(confined to a 7-nm InAs–GaAs dot) is only25 meV (seeFig. 3) one can expect two loss mechanisms:

First of all, with increasing temperature the injected carriersstart to populate the barrier states thus increasing the injectioncurrent to maintain the threshold gain of the QD laser. Sec-ondly nonradiative recombination in the barrier might lead tocurrent leakage. This leakage current is related to the quality ofthe barrier layer (in particular the low temperature GaAs) anddoes not present a principal limitation of the threshold current.

It has been shown [28] that higher growth temperatures ofthe cladding layers and optimization of the dot size (leading toan increase of the activation energy) shifts the onset of currentleakage to 220 K with an ultrahigh of 530 K between 80 Kand 220 K. Another way to decrease the leakage current is toplace the dot layers in a GaAs–AlGaAs QW, thus, drasticallydecreasing the escape probability of carriers from the dots (seeFig. 6). With this approach the onset of current leakage hasbeen increased up to room temperature while maintaining ahigh of 385 K between 80 K and 300 K [29].

An other important factor characterizing the laser quality isthe differential internal efficiency of the laser. This valuecan be derived from the dependence of the external differentialquantum efficiency on mirror losses according to

(10a)

(10b)

Here, is the laser facet reflectivity, the cavity length,and the internal loss of the laser. The differential internalefficiency of the single-layer QD laser is about 40%. This valuewas improved to 50% by introducing multilayer QD structures(see Fig. 7). Values of 70% for a InGa As–GaAs QD laserand of 81% for a In Ga As–GaAs QD laser were recentlyreported by Mirinet al. [19] and Ustinovet al. [30]. Thesevalues are not much lower than the recently reported recordinternal efficiency of QW lasers of 99% [31].

The more typical internal efficiency around 50% of currentQD lasers demonstrates that the difference between the cal-


(a)

(b)

Fig. 7. (a) The threshold density versus mirror losses yields a transparencycurrent density below 20 A�cm�2 and demonstrates clearly gain saturation forsmall cavity lengths. (b) External differential efficiency for single and multiplelayer QD laser as a function of mirror losses. The internal efficiency obtainedfor a stack of ten QD layers is about 50% at 300 K.

culated threshold current density of2 A cm (see Fig. 4)for an quasi-ideal QD laser (with no leakage current and oneelectron and one hole state) and the measured value of100A cm for a single layer QD laser having both a total loss of 8cm is still connected to current leakage. On the other handthe transparency current density for a single layer QD lasershown in Fig. 7 is below 20 Acm indicating that indeedultralow threshold current densities are feasible.

V. SPECTRAL CHARACTERISTICS

The emission of QD lasers consisting of a dot ensemblewith only one energy state for electrons and holes is expectedto occur at the maximum of the PL emission and should notshow any energy shift with injection current. In the case ofreal structures emission from both ground and excited statesis often observed. Thus the line shape of the gain spectrum isno longer independent of the injection level causing a strongblueshift of the laser emission with injection current. Sucha blueshift is demonstrated in Fig. 8. Obviously excited QDstates provide higher modal gain here. Upon complete QD gainsaturation the laser emission jumps to the WL state which hasa much higher modal gain due to the larger confinement factor.

One of the most interesting features of a QD laser isits potential to produce longitudinal single-mode operationwhen the gain spectrum is more narrow than the longitudinal

Fig. 8. (a) Blueshift of the QD emission due to state filling. Each spectrumis marked with the corresponding laser cavity length. For short cavity lasersthe QD gain is completely saturated and the emission jumps to WL states. (b)Light current characteristic of a six-fold layer QD laser with a 400-�m-longand 5-�m-wide laser cavity showing single-mode operation just above thethreshold.

mode spacing defined by the laser cavity length. None ofthe currently existing QD lasers exhibit a gain width below1 meV, which is necessary to fullfill this condition for stripegeometry lasers with a typical laser cavity length of0.5 mm.For vertical-cavity surface-emitting lasers (VCSEL) there is amuch larger chance to obtain single-mode lasing.

The full-width at half-maximum (FWHM) of the QD PLranges from 33 meV [20] to 50 meV [22] which is suffi-ciently narrow for VCSEL’s to show single-mode operation.Nevertheless the experiment on Fabry–Perot lasers show anunexpected single-mode operation just above the threshold(see Fig. 8). For QW lasers it is well known that they canswitch to one single mode at injection levels far above thresh-old despite their broad-gain spectra. Two possible mechanismmight be responsible for the single-mode operation reportedhere. Due to inhomogenities of the dot distribution the gainspectra may have local minima near the main gain maximum.This effect will effectively increase the threshold of other lon-gitudinal modes near the main emission mode. Consequentlythe first suppressed mode will start lasing only at higherinjection levels. In addition dots of different sizes might havedifferent carrier capture times. Thus under stimulated emissionconditions only dots that are rapidly refilled contribute.

The wavelength of the laser emission from QD states can betuned by varying the InGa As composition and by varyingthe size of the dots. With this approach the QD PL emissioncould be tuned between 0.95 and 1.37m at 300 K [29]. Thus


Fig. 9. Electroluminescence spectra (solid line) for an InAs QD laser with afivefold stacked dot layer at 1.05 times the threshold current density at 293 K.The inset shows the pulsed light current characteristic. The photoluminescencespectra (dotted line) at 293 K indicates that laser emission is due to the QDstates. WL and GaAs transitions are also marked.

the first optical transmission window of glass fibers is alreadycovered by emission from QD’s grown on GaAs substrate.Using InSb instead of InAs 1.5-m emission is possible. Itwas shown by several groups that InGa As QD lasersin the composition range of 0.3 1 can be grown byMBE [23], [13] but growth by MOCVD was thought to bemore complicated because of the different growth kinetics ascompared to MBE [32]. Recently, we discovered a MOCVDgrowth window for InAs–GaAs QD’s and demonstrated athree-layer InAs–GaAs QD laser. The threshold at 77 K isas low as 21 Acm and lasing occurs via the QD groundstate (see Fig. 9). The threshold current density increases to320 kA cm at 293 K and the laser emission is red shiftedby 45 meV going from 77 K to 293 K which is only slightlyless than the InAs bandgap change [21].

If the ground state gain is enhanced by the existence of sev-eral QD layers, the laser operates far away from ground stategain saturation and all higher lying energy levels, especiallythe excited states are well below the transparency condition.Therefore lasing occurs in this case via the ground state andan increase of temperature does not increase the occupation ofthe excited states above the transparency level. Then the QDlaser emission should follow the bandgap change of the dotmaterial with temperature.

VI. DYNAMIC PROPERTIES ANDMODULATION BANDWIDTH

The time behavior of the ground state and excited state QDluminescence after short pulse excitation is shown in Fig. 10.The monoexponential decay of the ground state luminescenceintensity over more than one order of magnitude provesthe excitonic nature of the QD recombination. We do notobserve any dependence of the ground state decay time onthe excitation density. But the decay time reduces from 2.5 nsdown to 1 ns by decreasing the GaAs barrier width from 5nm to 1.5 nm between adjacent QD layers. This result maybe explained by a higher oscillator strength [20] and a largergain of the excited QD states compared to the ground staterecombination (see Fig. 10). Additionally the luminescencedecay time spectrally integrated over the QD, WL, and GaAsbarrier emission decreases with excitation density because

(a)

(b)

Fig. 10. (a) Time resolved spectra of the QD ground state and excited stateluminescence integrated over 5 meV spectral bandwidth for a single dot layerwith dots grown by nominally 2ML InAs deposition. The inset shows thecorresponding spectra of the QD structure where the energetic position ofthe QD ground (1) and excited (2) state as well as the peak energy of QDand WL luminescence are marked. (b) Time behavior of the integrated QDluminescence (scattered graph) of a threefold stacked dot layer with dotsgrown by nominally 2ML InAs deposition and a GaAs barrier width of 1.5nm between adjacent dot layers. The excitiation puls has a full width halfmaximum of 38 ps and an energy of 1.7 eV. The solid line shows a fit using(11). The inset demonstrates the dependence of the QD ground state decaytime on excitation density for a single dot layer (uncoupled) and a twofoldstacked dot layer (coupled) with a 1.5-nm-thick GaAs barrier of dots grownby nominally 2ML InAs deposition.

of the enhanced oscillator strength of the excited QD statesand the bimolecular recombination kinetics of WL and GaAsbarrier states [25].

From the streak camera recording of the spectrally inte-grated QD luminescence after short pulse excitation we deducethe rise time and the decay times of the ground(excited) state QD PL using a convolution of the QD PL signal

[according (11)] [33] and of the excitation puls:

(11)

One gets a rise time for the QD luminescence of 2010 pswhich is almost the same as the rise time of 13 ps for theexciation pulse indicating that the QD PL rise time can belower than 20 ps. The fast rise time of the QD luminescenceafter barrier excitation is attributed to fast capture of carriersfrom the barrier into the QD’s. Therefore, the spontaneousrecombination lifetime of several nanoseconds is at leastmore than two oders of magnitude longer than the carriercapture into the QD’s. Thus, the phonon bottleneck problemas described in the introduction may be overcome in self-organized QD structures.

The orders of magnitude larger differential gain of QDlasers should lead to an increased modulation bandwidth.Small-signal analysis of standard rate equations yields an


(a)

(b)

Fig. 11. (a) Relaxation oscillation frequency!R of a QD laser as a functionof the square root of pulse power in the laser cavity for two different cavitylengths. The excitation was done by a square pulse of 5-ns length and rise-timebelow 100 ps. The ridge waveguide laser structure (ridge 5�m) consists ofa six-fold stacked QD layer (GaAs barrier width 5 nm) with dots grownby nominall 2ML InAs deposition. (b) Calculated modulation bandwidth fordifferent relaxation oscillation frequencies and capture times according to (12)using the parameters given in Fig. 11(a).

approximation of the modulation bandwidth defined as the 3-dB value of the ratio of photon density and current density

[34]:

(12a)

(12b)

(12c)

(12d)

Here, is the modulation frequency, the QD capturetime, the QD carrier decay time, the photon round-trip time in the laser cavity, the differentialmaterial gain, the confinement factor, the group velocityin the laser, the gain compression coefficient, the photondensity in the laser cavity at the bias level, the ratio ofQD capture and emission time, the proportionality constantbetween the damping factorand the square of the relaxationoscillation frequency . By measuring the relaxation oscil-lation frequency as a function of the photon density (i.e., thepower in the laser cavity) one can determine experimentally

Fig. 12. (a) Differential gaing0 and differential refractive indexn0

realfor a

quasi-ideal QD ensemble with a symmetric gain curve and only one energylevel for electrons and holes. (b) Calculated linewidth enhancement factor�

for the quasi-ideal QD ensemble and the experimentally reported single-layerQD ensemble with an asymmetric gain spectrum shown in Fig. 3.

the differential gain and the gain compression coefficientwhich is equal to the inverse of the saturation photon densitycoefficient in the laser resonator. From these values the

-factor is obtained. If and remain linear functions ofpower the maximum modulation bandwidth is given by

.The carrier density used for the calculation of the

differential gain in Fig. 11 is related to the recombinationvolume defined by the lower and upper cladding layer of thelaser structure (see Fig. 1). The experimental dependence ofthe relaxation oscillation frequency on pulse power shows adeviation from the expected proportionality [see (12)] to thesquare root of optical pulse power indicating the onset ofgain compression at a power level of50 mW. The gaincompression coefficient has a minimum of 4 10 cmat 90 K equivalent to a power saturation coefficient of100mW in the laser cavity. The gain compression coefficient ismore than one order of magnitude higher than typical values( cm ) in InGaAs–InGaAlAs QW lasers [35]. Thedifferential gain of 2 10 cm obtained from the fitaccording to (12) is close to the value derived in the previoussection from the QD parameters.

Since the gain compression is closely correlated to thecapture time of carriers into the dots the physical origin ofthe enhanced gain compression in QD laser structures may beconnected to the slower relaxation rate into the QD’s. Thismechanism reduces the modulation bandwidth even when thedifferential gain is as high as shown in Fig. 3. The measured

-factor of 0.38 ns (corresponding to a maximum modulationbandwidth of 23 GHz) is a factor of 2–3 higher than best valuesreported for InGaAs QW [34] lasers at 100 K indicating thatthe modulation bandwidth is lower in present QD lasers thanin QW lasers.

VII. CHIRP

Potential applications of a QD laser as directly modulatedlight source for data transmission via glass fibers requires


minimum chirp. The chirp is determined from the shift ofthe wavelength a laser exhibits during current modulation. Thephysical origin of this shift is related to the coupling of the realand imaginary part of the complex susceptibility in the lasermedium [see (1)]. A gain (imaginary part of the susceptibility)variation due to a change of the injection level changes therefractive index (real part of the susceptibility) which modifiesthe phase of the optical mode in the laser cavity. The couplingstrength between real and imaginary parts is defined by thelinewidth enhancement factor which is defined as follows:

(13)

Here, is the carrier density, are the real andimaginary parts of the complex refractive index, is thevelocity of light in vacuum, is the photon energy, thematerial gain, the differential gain, and the differentialrefractive index.

The linewidth enhancement factor can be calculated fromthe gain spectrum via the Kramers–Kronig (KK) relation.In the case of a QD laser with a dot ensemble showing aperfect Gaussian energy distribution and only one energy levelfor electrons and for holes the gain spectrum is perfectlysymmetric around the peak gain energy. In this case, thedifferential gain is also symmetric to the peak gain energyposition where lasing occurs. Thus the differential refractiveindex change computed via the KK relation is exactly zeroat the lasing energy (i.e., peak gain position). Therefore thelinewidth enhancement factor is zero at the lasing energyand QD lasers with a quasi ideally distributed (symmetric)ensemble of QD’s exhibit chirpfree operation. This propertyis shown in Fig. 12.

In the case of real QD lasers the contribution of excitedstates might cause a non symmetric gain curve (see Fig. 3)which increases the linewidth enhancement factor dependingon excitation level to about 0.5. This value is considerablylower than values of 1–2 [36], which are considered as beingvery good for QW laser structures.

VIII. C ONCLUSION

We have described lasing characteristics of (InGa)As QDlasers. Already the first preliminary results indicate that mostof the laser key parameters are significantly improved ascompared to QW lasers due to the introduction of QD’s asan active medium. The single layer QD structures exhibit anultrahigh material gain of 10cm only limited by the dotsize distribution. A threshold density of 2 A cm for alaser structure with a QD ensemble having a gain width of

50 meV and no current leakage is predicted. The thresholdcurrent density of currently operating lasers is as low as 40A cm at 77 K and 62 Acm at 300 K while a of 385K is obtained up to room temperature.

The main current leakage is connected to barrier populationand nonradiative loss in the barrier. Both effects can besuppressed in the future by growth optimization and careful

bandgap engineering of the laser structure. The QD emissionwavelength can be tuned up to 1.5m, which is importantfor fiber-optic communication. The linewidth enhancementfactor of currently operating laser is reduced due to a nearlysymmetric gain spectrum to a value of 0.5, which is a factorof 3 better than in current QW lasers.

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D. Bimberg (M’92) was born in Schrozberg, Ger-many, on July 10, 1942. He received the Diplomain physics and the Ph.D. degree from the GoetheUniversity, Frankfurt, Germany, in 1968 and 1971,respectively.

From 1972 to 1979, he was a Senior Scientist withthe Max Planck Institute for Solid State Research.From 1979 to 1981, he was an Associate Professorwith the Department of Electrical Engineering, Uni-versity of Aachen, Aachen, Germany. He presentlyholds the Chair of Applied Solid State Physics at

the Technical University of Berlin, Berlin, Germany. He authored more than300 papers, patents, and books. His research interests include the physicsof microstructures and microstructures devices, integrated optics, high-speedmodulation of semiconductor lasers, and transition metals in III–V materials.

N. Kirstaedter was born in Berlin, Germany, in1964. He received the M.S. and the Ph.D. degreesin physics from the Technical University of Berlin,Germany, in 1990 and 1996, respectively.

He is presently working on fabrication, character-ization, and modeling of QD lasers.

N. N. Ledentsov, photograph and biography not available at the time ofpublication.

Zh. I. Alferov , photograph and biography not available at the time ofpublication.

P. S. Kop’ev, photograph and biography not available at the time ofpublication.

V. M. Ustinov, photograph and biography not available at the time ofpublication.

Bimberg, IEEE (1997), InGaAs-GaAs Quantum-dot Lasers

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