Impact of ballistic electron transport on efficiency of InGaN based LEDs

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Impact of ballistic electron transport on efficiency of InGaN based LEDs
  Ballistic transport in InGaN-based LEDs: impact on efficiency This article has been downloaded from IOPscience. Please scroll down to see the full text article.2011 Semicond. Sci. Technol. 26 014022( details:IP Address: article was downloaded on 17/04/2012 at 16:10Please note that terms and conditions apply.View the table of contents for this issue, or go to the  journal homepage for more HomeSearchCollectionsJournalsAboutContact usMy IOPscience  IOP P UBLISHING  S EMICONDUCTOR  S CIENCE AND  T ECHNOLOGY Semicond. Sci. Technol.  26  (2011) 014022 (12pp)  doi:10.1088/0268-1242/26/1/014022 Ballistic transport in InGaN-based LEDs:impact on efficiency  ¨U ¨Ozg ¨ur 1 , X Ni 1 , X Li 1 , J Lee 1 , S Liu 1 , S Okur 1 , V Avrutin 1 ,A Matulionis 2 and H Morko¸c 1 1 Department of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond,VA 23284, USA 2 Semiconductor Physics Institute, Center for Physical Sciences and Technology, A. Goˇstauto 11,01108 Vilnius, LithuaniaE-mail: and Received 9 June 2010, in final form 22 September 2010Published 29 November 2010Online at Abstract Heterojunction light-emitting diodes (LEDs) based on the InGaN / GaN system have improvedconsiderably but still suffer from efficiency degradation at high injection levels which unlessovercome would aggravate LED lighting. Although Auger recombination has been proposedas the genesis of the efficiency degradation, it appears that the premise of electron overflowand non-uniform distribution of carriers in the active region being the immediate impedimentis gaining popularity. The lack of temperature sensitivity and sizeable impact of the barrierheight provided by an electron blocking layer and the electron cooling layer prior to electroninjection into the active region suggest that the new concept of hot electrons andballistic / quasi-ballistic transport be invoked to account for the electron overflow. The electronoverflow siphons off the electrons before they can participate in the recombination process. If the electrons are made to remain in the active region e.g. by cooling them prior to injectionand / or blocking the overflow by an electron blocking layer, they would have to eitherrecombine, radiatively or nonradiatively (e.g. Shockley–Read–Hall and Auger), or accumulatein the active region. The essence of the proposed overflow model is in good agreement withthe experimental electroluminescence data obtained for  m -plane and  c -plane LEDswith / without electron blocking layers and with / without staircase electron injectors.(Some figures in this article are in colour only in the electronic version) 1. Introduction Performance of InGaN-based light-emitting diodes (LEDs)has improved considerably to the point where they nowpenetrate outdoor general lighting applications and are poisedto penetrate indoor lighting applications as well. Lightingby LEDs is advantageous in terms of energy savings andlong operation lifetime. One pivotal issue surrounding theapplication of the InGaN LEDs for general lighting is thelack of retention of the electroluminescence (EL) efficiencyat high injection currents [1]. This manifests itself as theexternal quantum efficiency (EQE) reaching a peak valueat relatively small current densities, such as 50 A cm − 2 orlower, followed by a monotonic decrease even under low dutycycle short pulsed current operation [2]. It is essential for thephysical mechanisms behind this degradation in efficiency tobe understood and the problem mitigated. A fitting commentis that none of the above would have come into being if it werenot for the seminal pioneering work done on heterostructures[3–5]. The physical origin of the EL efficiency loss at highcurrents in InGaN LEDs is heretofore not clearly understoodand controversial, and thus the topic is open to furtherinvestigations. Carrier loss through nonradiative Augerrecombination at high injection currents has initially beenproposed for the efficiency degradation [6–8]. The Auger recombination coefficient deduced from a fit of the rateequation to the experimental photoluminescence (PL) datain an earlier effort is 1.4–2.0  ×  10 − 30 cm 6 s − 1 for quasi-bulk InGaN layers [6], but varies several orders of magnitude 0268-1242/11/014022+12$33.00  1  © 2011 IOP Publishing Ltd Printed in the UK & the USA  Semicond. Sci. Technol.  26  (2011) 014022 ¨U ¨Ozg¨ur  et al amongdifferentreports,10 − 27 –10 − 24 cm 6 s − 1 ,thelattergroupof figures being some three orders of magnitude or morehigher than the other reported values [6, 8–11]. Note that the Auger recombination coefficient decreases exponentiallywith the bandgap energy if the process involves transitionsacross the gap owing to a seminal contribution [12], whichis supported by a fully microscopic many body model [13].This suggests that the carrier losses due to the Auger effectin InGaN-based LEDs, particularly in those emitting atenergiesawayfromtheresonantconductionbandstatesituated2.5 eV above the bottom of the conduction band [8], wouldnot necessarily be dominant.There are also other experimental observations whichare not consistent with the Auger recombination proposal.For example, in below-the-barrier resonant photo excitationexperiments, in which the photons are absorbed only inthe InGaN active region with ensuing generation of   equal numberofcoolelectronsandholesfollowedbyeitherradiativeor nonradiative recombination only in the same region, theinternal quantum efficiency (IQE) degradation has not beennoted at photocarrier generation rates comparable to, if notbeyond, the electrical injection levels where the EL efficiencydegrades [14, 15]. Rather the IQE increases with optical generation and in fact reaches over 95% for carrier generationrates of 2  ×  10 18 cm − 3 , the density being dependent on theradiative recombination coefficient used. This would thensuggestthattheELefficiencydegradationisofelectricalnatureand that it is very likely to be related to carrier injection,transport and leakage processes.The above discussion narrows the choices to electronoverflow as being responsible in structures that are employedat the moment. It has been observed that a substantial ELefficiency reduction (by four to five times) occurs when anelectron blocking layer (EBL) is not employed, regardless of whether polar or non-polar surfaces of GaN are used [16]. InInGaNLEDs,whilenotbeingtheentirereasonatthisjuncture,relatively low hole injection (due to relatively low hole dopingof p-GaN) and / or poor hole transport inside the active region(due to large hole effective mass if quantum wells constitutethe active region) could exacerbate the electron overflow, aselectrons need accompanying holes in the active region forrecombination [15, 17]. Theoretical calculations also indicate that electron density in equilibrium with the lattice evenwell above the room temperature would not have a sufficientBoltzmann tail to surpass the barrier present for notableelectron spillover [18]. This further narrows the discussion inthat the non-equilibrium processes must be invoked to accountfor electron overflow. In this regard, this paper treats ballisticand quasi-ballistic electron transport across the InGaN activeregion as a substantial source for electron overflow and theassociated EL efficiency loss, as those electrons escape theradiative recombination in the active region. Evidence forballistic transport and the associated electron leakage has beenobtained from the temperature-dependent characteristics of InGaN LEDs and laser diodes [19–21]; however, ballistic electron transport has so far been included in the analysisof electronic devices only [1, 22]. Moreover, we demonstrate that an InGaN staircase electron injector (SEI, with a step-likeincreased In composition, each corresponding an energy stepequal to or greater than an LO phonon energy) on the n-sideof the active region reduces if not fully eliminates the ballisticand quasi-ballistic electron overflow. The SEI structure servesto cool the electrons and bring them into equilibrium with thelattice in the active region where their radiative recombinationwith holes takes place if the holes are present. Ultimately,though, holesmustbepresentforradiativerecombinationwithelectrons,andincreaseoftheholedensityisnaturallyexpectedto improve the efficiency in LEDs featuring designs to curbthe ballistic transport and thus the ensuing electron overflow.It should be noted that the concept of non-equilibriumhot electrons in the context of light emitters is non-conventional and represents a major departure from theproverbial treatments. One might then suggest that models,particularly the commercially available software packagesused to model the LEDs under discussion, which are voidof the treatment of hot electrons, would be off target. Weshould also point out that the hot electron transport discussedhere would also apply to semiconductor injection lasers. 2. Experimental procedures The investigated LED structures were grown on  m -plane ( 1 ¯100 )  GaN or  c -plane (0001) sapphire substrates in avertical low-pressure metalorganic chemical vapor deposition(MOCVD) system. In the case of   m -plane, the  ∼ 500  µ mthick   m -plane freestanding GaN substrates, sliced from boulesgrown in the  c -direction (produced at Kyma Technologies,Inc.) had a threading dislocation density of   < 5 × 10 6 cm − 2 andwereoff-cutby0.2 ◦ towardtheGaN a -axisand0.3 ◦ towardthe GaN  c -axis. The sapphire substrates were commerciallyobtained and not subjected to any special treatment prior togrowth. When grown on sapphire, templates on which theLED structure was grown consisted of a low-temperature GaNlayer, a high-temperature GaN layer followed by  in  s itu  SiN x deposition and an epitaxial laterally overgrown GaN layer[1, 23]. The LED structures contained a 6 nm undoped In 0 . 20 Ga 0 . 80 N (emitting at  λ peak   ∼ 440 nm) or In 0 . 15 Ga 0 . 85 Nactiveregion(emittingat λ peak  ∼ 410nm)witha3nmundopedIn 0 . 01 Ga 0 . 99 N top layer. Immediately beneath the active layer,a 60 nm Si-doped (2 × 10 18 cm − 3 ) In 0 . 01 Ga 0 . 99 N under-layerwas inserted for improved quality of the active region. Ininvestigations exploring the hot electron ballistic and quasi-ballistic transport across the active region [24] an  ∼ 10 nmEBL of p-Al x Ga 1 − x N (  x   =  15%, 8% or 0%) with varyingbarrier heights was deposited on top of the active layer. Instructures which aid to cool the electrons prior to the activeregion, an InGaN SEI, n-type doped with Si to an electrondensity of 2  ×  10 18 cm − 3 , was inserted under the InGaNactive region to thermalize the electrons [25]. The staircasestructure consists of three 5 nm InGaN layers (resulting in afour-step staircase) with In compositions of 3%, 6% and 10%,respectively, in the given order, as shown in figure 1, wherethe steps having potential energy drop by more than one LOphonon energy cause efficient electron thermalization. Forthe structures containing an SEI, a six-period In 0 . 01 Ga 0 . 99 N(7 nm) / In 0 . 06 Ga 0 . 94 N(3 nm) multiple quantum well (MQW) 2  Semicond. Sci. Technol.  26  (2011) 014022 ¨U ¨Ozg¨ur  et al c -sapphire or  m -plane GaN n -GaN n -GaNlow temp. GaNif on sapphireSiN  x   ELOif on sapphire Li g ht emission Ti/Al/Ni/A u Ni/A u  pad  p -GaNGZO or 5/5 nm Ni/A u  p -AlGaN EBLif neededSEIactive re g ion u nderlayer Energy E c  Figure 1.  Structures of LEDs used in the course of thisinvestigation. As indicated in section 2, some LEDs utilizedelectron blocking layers (EBLs) while some did not. Those that didnot, incorporated a staircase electron injector (SEI) to cool theelectrons before being injected into the active region. For improvingthe quality further, the  in situ  epitaxial lateral overgrowth (ELO)method as well as an In 0 . 01 Ga 0 . 99 N under-layer (beneath the activeregion) was incorporated. In some cases the InGaN under-layer wassubstituted by a superlattice of varying In composition(In 0 . 01 Ga 0 . 99 N / In 0 . 05 Ga 0 . 95 N). The right panel shows thecorresponding simplified flatband conduction band edge energydiagram. under-layer (instead of a 60 nm In 0 . 01 Ga 0 . 99 N structure, seefigure1),againn-doped,wasemployedpriortotheactivelayerunderneath the 12 nm thick In 0 . 01 Ga 0 . 99 N layer and the InGaNSEI to circumvent the quality degradation by the SEI layers.The final Mg-doped p-GaN layer was about 100 nm thick witha nominal hole density of 7  ×  10 17 cm − 3 . The p-layer wasactivated exsitu at950 ◦ CinN 2  atmospherefor1min. Insomesamples, this was followed by deposition of Ga-doped ZnO(GZO) (400 nm thick) for transparent conducting oxide bymolecular beam epitaxy in order to enhance current spreadingandreducethedifferential‘on’resistance[26, 27]. Aftermesa etching(250 µ mdiameter),Ti / Al / Ni / Au(30 / 100 / 40 / 50nm)metallization annealed at 800  ◦ C for 60 s was used for n-typeohmiccontacts. ANi / Au(5 / 5nm)semi-transparentp-contactmetal laminate was deposited for samples not utilizing GZO.This step was skipped for those which used GZO. Finally,50  µ m diameter Ni / Au (30 / 50 nm) contact pads weredeposited on part of the mesa tops for on-wafer ELmeasurements. Again, a schematic diagram elaborating thevarious structures used in the course of this study is shown infigure 1.The IQE was determined from excitation-power-dependent PL [28] measured at room temperature usinga frequency-doubled 80 MHz repetition rate femtosecondTi:sapphire laser. The excitation wavelength was 370–390 nm to ensure below the gap excitation and thus photo-excited electron–hole pair generation only in the InGaN activelayer to circumvent complexities involving carrier transportand skewed carrier injection which favor the electrons[14, 15]. On-wafer EL measurements were performed with pulsed current (1  µ s pulse width, 0.1% duty cycle) withoutany special means to enhance light extraction. The PL resultsshow that all LEDs in comparative studies have essentiallythe same IQE for the same injected carrier density [29]. It isinstructivetonotethatthe c -planeLEDstructuresexhibitIQEsashighas71%forsamplesnotfeaturing insitu ELO,andthosehavinggonethroughtheaforementioned insitu ELOexhibitedefficiencies up to 96% at injection levels corresponding to justabout 2 × 10 18 cm − 3 carrier density which is very respectableindeed. High IQEs reported here serve to refute any argumentthat reduced or the lack of efficiency loss at high injectionlevels is somehow related to low quality. 3. Theoretical and experimental data At the onset with no  a priori -predilection, the electronoverflow might have its origin in two possible routes:(i) thermionic emission of equilibrium electrons from thebottom of the active region over the barrier into the p-layer(the large band discontinuities preclude this process) and(ii) ballistic and quasi-ballistic transport of the injectedelectrons. The calculations discussed associated withthe thermionic emission process, immediately below, areconvincingly indicative of this process not being responsiblefor electron overflow. Below, following the discussion of thethermionic emission process, we will treat the hot electronmitigated electron overflow. 3.1. Electron overflow due to thermionic emission The simulations with Silvaco Atlas R  software forthe p-GaN / In 0 . 20 Ga 0 . 80 N / n-GaN LED without an EBLtake into account thermionic emission of equilibriumelectrons and tunneling within the Wentzel–Kramers–Brillouin approximation. The commonly accepted materialparameters were used for the In 0 . 20 Ga 0 . 80 N active layer:Shockley–Read–Hall (SRH) recombination coefficient of 1 × 10 7 s − 1 and spontaneous radiative recombination coefficientof 1  ×  10 − 11 cm 3 s − 1 . An Auger recombination coefficientof 1  ×  10 − 30 cm 6 s − 1 was assumed. For p-GaN, the SRHcoefficient of 1  ×  10 10 s − 1 (corresponding to a lifetime of 100 ps) was used. The conduction band offset    E  c  = 0.5 eV was taken to be 70% of the total band gap discontinuitybetween InGaN and p-GaN. The calculations show that evenat an uncharacteristically elevated junction temperature of 1000 K and at an unreasonably high current density of 1  × 10 4 A cm − 2 , the thermionic emission driven overflow electroncurrent into the p-GaN region due to electrons in thermalequilibrium with the lattice is only ∼ 11% of the total currentdensity. At the same current density of 1  ×  10 4 A cm − 2 ,the corresponding values are  ∼ 1% and  ∼ 0% for junctiontemperatures of 700 K and 500 K, respectively [18, 30]. Considering the large discrepancy for the Auger coefficient[6–8, 12], the calculated electron overflow values will be 0%, 3% and 36% for junction temperatures of 500, 700 and1000 K, respectively, if an Auger coefficient of 1  × 10 − 34 cm 6 s − 1 is assumed instead.The thermionic emission being inconsequential suggeststhat we must turn our attention to non-equilibrium electronsin the active region. The injected hot electrons can traversethe active layer by ballistic or quasi-ballistic transport, unless 3  Semicond. Sci. Technol.  26  (2011) 014022 ¨U ¨Ozg¨ur  et al 050010001500200025000510152025 w/o EBLAl 0.08 Ga 0.92 N EBLAl 0.15 Ga 0.85 N EBL Current density (A/cm 2 )    R  e   l  a   t   i  v  e   E   Q   E   (  a .  u   ) m-plane DH-LEDs ( λ  peak ∼ 440nm)6nm In 0.20 Ga 0.80 N active region 0 4 8 12 165001000150020002500    C  u  r  r  e  n   t   d  e  n  s   i   t  y   (   A  c  m   -   2    ) Voltage (V) Figure 2.  Relative EQE of   m -plane In 0 . 20 Ga 0 . 80 N LEDs withAl x Ga 1 −  x  N EBLs having Al compositions  x  = 15%, 8%, and 0%,measured under pulsed current, 1  µ s pulse width and 0.1% dutycycle. Emission wavelength is  λ peak  ∼ 440 nm. The inset shows thecurrent–voltage dependence for the LED with 15% Al in the EBL. blocked by an EBL, and recombine in the p-GaN regioninstead of the active region and do not contribute to lightemission at the desired wavelength. Below, we discuss ourfirst-order calculations of ballistic and quasi-ballistic transportof electrons through the active region and attempt to explainour data with varying barrier heights of the EBL layer in thisframework. 3.2. Electron overflow due to hot electron transport  To set the stage for us to segue into the calculation of hot electron-induced electron overflow, figure 2 displays theexperimental relative EQE as a function of the current densityfor three  m -plane LEDs with varying EBL barrier heights.Because the IQE is independent of the composition of theEBL barrier height (confirmed by resonant PL experiments),the observed difference in EQE can, therefore, be safelyassumed to srcinate from mechanisms having to do withcarrier injection and overflow rather than the quality variationamong the active regions of the samples tested. The EQE forthe m -planeLEDwith15%AlintheEBLshowsapronouncedpeak at approximately 80 A cm − 2 which proceeds to dropby  ∼ 45% with increasing current injection. A negligibleefficiency degradation ( ∼ 3–5%) is observed for the structurewithout an EBL (represented by 0% Al in the EBL) albeitits relative EQE is approximately three to five times lowerthan that with 15% Al EBL. Intermediate values for EQE andefficiency degradation ( ∼ 10%) are obtained for the LED with8% Al within the EBL.We assume that the LED with 15% Al EBL has negligibleelectron overflow at the current density of 80 A cm − 2 wherethe EQE peaks. Thus, in the LED without an EBL, lessthan one fifth of the overall current is contributing to the ELand approximately four fifths of the current passes the activeregion without contributing to light emission. After refutingthe thermionic emission route, in our opinion, we focus ourattention on hot electron transport as the cause for carrieroverflow. In the hot electron scenario, after the electrons areinjected from the n-GaN layer into the active region, they gainanadditionalkineticenergyequaltotheconductionbandoffsetbetween the n-GaN and the In 0 . 20 Ga 0 . 80 N active layers (   E  c , ∼ 0.5 eV). The hot electrons either undergo thermalization andlose their excess energy (mainly through their interaction withLO phonons [31]) or leave the active region. Let us considerthe electrons that experience ballistic motion (no scattering inthe active region) and quasi-ballistic motion (scattering eventswith LO phonons). Our calculations show that LEDs withoutan EBL suffer from serious electron overflow accounting for ∼ 67% of the total electron current under flatband conditionsfor a 6 nm thick active region. These spillover electrons arecomposed of both ballisticand quasi-ballisticelectrons, whereonly less than 1% of the injected electrons enter the p-GaNlayer after two scattering events. Therefore, the contributionof spillover electrons resulting from two or more scatteringevents can be ignored.The probability of the ballistic transport at a given energyis proportional to exp ( − t/τ  sc ) , where  t   is the transit timeand  τ  sc  is the electron–LO-phonon scattering time given by τ  sc  =  1 /( 1 /τ  abs  + 1 /τ  em ) , where  τ  abs  and  τ  em  are the LO-phonon absorption and emission times, respectively [24].If the acceleration and deceleration of the electrons by theelectrons in the active region are neglected, the percentage of the overflow electrons is then given by P  1  =   + ∞ max { 0 ,(φ EBL − qV) } f(E)N(E) exp  − L/v(E + E c )τ  sc  d E   + ∞ 0  f(E)N(E) d E, (1)where  E   depicts the excess electron energy with respect tothe bottom of the conduction band of the n-GaN layer,  L  is theactiveregionthickness(6nminourcase), V  isthenetpotentialdrop across the InGaN region,  φ EBL  is the barrier height of theEBL (i.e. the conduction band offset between the EBL andthe p-GaN, and is 0 for the LEDs without an EBL),  N  (  E  ) is theconduction-band density of states,  f  (  E  ) is the Fermi–Diracdistribution function,  v(E  +  E c )  =   2 (E  + 0 . 5 eV )/m e is the electron velocity with an initial energy of   E   plusthe gained energy due to the 0.5 eV band offset and  m e is the electron effective mass. For simplicity, we assumethat the electrons move only in the normal direction to thehetero-interface, which would insignificantly overestimate thespillover probability.In addition to fully ballistic electrons, quasi-ballisticelectrons undergoing a certain scattering event, such as oneLO phonon emission or one LO phonon absorption, can alsocontributetotheoverflow. Thetotalpercentageoftheoverflowelectrons that experience one scattering event is given by P  2  =    + ∞ 0 f(E)N(E) d E  − 1 ×    + ∞ max { 0 ,(φ EBL − qV  ± ¯ hω LO ) } f(E)N(E) ×    L 0 · 1 v(E  +  E c ) · τ  ph exp  − x/v(E  +  E c )τ  sc  ·  exp  − (L − x)/v(E  +  E c ∓ ¯ hω LO )τ  sc  · d x · d E,  (2) 4
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