Pivotal role of ballistic and quasi-ballistic electrons on LED efficiency

Superlattices and Microstructures 48 (2010) 133–153

Contents lists available at ScienceDirect

Superlattices and Microstructures

journal homepage: www.elsevier.com/locate/superlattices

Review

Pivotal role of ballistic and quasi-ballistic electrons onLED efficiencyX. Ni ∗, X. Li, J. Lee, S. Liu, V. Avrutin, A. Matulionis 1, Ü. Özgür, H. MorkoçDepartment of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA

a r t i c l e i n f o

Article history:Received 21 April 2010Accepted 11 May 2010Available online 8 June 2010

Keywords:Light emitting diodes (LEDs)MOCVDInGaNElectroluminescence (EL)Efficiency

a b s t r a c t

Significant progress in the power conversion efficiency andbrightness of InGaN-based light emitting diodes (LEDs) has pavedthe way for these devices to be considered for LED lighting. In thisrealm, however, the efficiency must be retained at high injectionlevels in order to generate the lumens required. Unfortunately,LEDs undergo a monotonic efficiency degradation starting atcurrent densities even lower than 50 A/cm2 which would hinderLED insertion into the general lightingmarket. The physical originsfor the loss of efficiency retention are at present a topic of intensedebate given its enormous implications. This paper reviews thecurrent status of the field regarding the mechanisms that havebeen put forward as being responsible for the loss of efficiency,such as Auger recombination, electron overflow (spillover), currentcrowding, asymmetric injection of electrons and holes, and poortransport of holes through the active region, the last one beingapplicable to multiple quantum well designs. While the Augerrecombination received early attention, increasing number ofresearchers seem to think otherwise at the moment in that italone (if any) cannot explain the progressively worsening lossof efficiency reduction as the InN mole fraction is increased.Increasing number of reports seems to suggest that the electronoverflow is one of the major causes of efficiency degradation.The physical driving force for this is likely to be the relativelypoor hole concentration and transport, and skewed injectionfavoring electrons owing to their relatively high concentration.Most intriguingly there is recent experimental convincing evidence

∗ Corresponding address: Department of Electrical Engineering, Virginia Commonwealth University, 601WestMain St. Room343, Richmond, VA 23284, USA. Tel.: +1 804 827 7010.E-mail addresses: [email protected] (X. Ni), [email protected] (H. Morkoç).

1 Permanent address: Semiconductor Physics Institute, ‘‘Puslaidininkiu Fizikos Institutas’’, Vilnius, Lithuania.

0749-6036/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.spmi.2010.05.009

134 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

to suggest that quasi-ballistic electrons in the active region, whichare not able to thermalize within the residence time and possiblylongitudinal optical phonon lifetime, contribute to the carrieroverflow which would require an entirely new thought process inthe realm of LEDs.

© 2010 Elsevier Ltd. All rights reserved.

Contents

1. Introduction.................................................................................................................................................... 1342. Auger recombination ..................................................................................................................................... 1353. Electron overflow........................................................................................................................................... 1374. Other possible sources of efficiency loss in InGaN LEDs ............................................................................. 1385. Performance and efficiency loss studies ofm-plane InGaN LEDs ............................................................... 1396. Effect of EBL on EL efficiency in LEDs withm-plane and c-plane orientations.......................................... 1417. Effect of ballistic electrons on the LED efficiency ........................................................................................ 1438. Conclusions..................................................................................................................................................... 151

Acknowledgements........................................................................................................................................ 152References....................................................................................................................................................... 152

1. Introduction

Lighting constitutes more than 20% of the total US electricity consumption, a similar percentagein the European Union, and an even higher percentile in many developing countries [1]. Powergeneration needed for lighting contributes approximately 1900 Mt CO2 per year (equivalent to 70%of the emissions from the world’s light passenger vehicles) according to the International EnergyAgency (IEA) [2]. Compared to conventional lighting technology, light emitting diode (LED) lightingoffers great promise as an energy-efficient, environment-friendly and affordable source of reasonablycolor-balanced white light owing to highly efficient LEDs. The performance of InGaN LEDs eitheras direct source of light generation and or pump source for relevant dyes is front and central togeneral lighting applications. Over the past two decades, the performance of InGaN-based LEDs hasimproved significantly and LEDs are nowbeing put to use in applications such as general lighting (bothindoors and outdoors), backlight for flat displays including flat panel energy-efficient TVs, where highelectroluminescence (EL) is required which necessitate high injection current levels. Unfortunately,the InGaN-based LEDs suffer from loss of efficiency at high injection levels needed, which has beendubbed as the ‘‘efficiency droop’’ [3]. This manifests itself as the external quantum efficiency (EQE)reaching its peak value at current densities even lower than 50 A/cm2 and monotonically decreasingfrom there on with further increase in current [4]. Despite substantial progress on the performancefront, the physical origin of the efficiency drop in InGaN LEDs is not understood with sufficientclarity as of yet and is open to further investigations, a prerequisite for the remedies to be foundand implemented. Among the various causes proposed for the observed efficiency degradation areAuger recombination [5], current roll-off resulting from phonon-assisted tunneling through defectsites [6], poor hole injection [7–9], polarization field [10,11], and junction heating [12], as well ascurrent crowding and related contact degradation. Junction heating can bemitigated by increasing theefficiency and employment of packages capable of removing the dissipated heat very efficiently, bothof which are the subject of vigorous developmental efforts in industry. For the purpose of determiningany role of junction heating pulsed measurements with low duty cycle are typically employed.Despite being considered rather consistently by some as the origin of efficiency degradation in

InGaN LEDs, the intrinsic Auger losses in wide bandgap semiconductors involving just the conductionband and the valence band are expected to be relatively small [13–16], as verified by fullymicroscopicmany-bodymodels [17], but there are somenewnuanceswhichwill be discussed below. The availabledata in aggregate appear to suggest that the Auger recombination alone (if any)might not be dominantas the observed efficiency droop depends on structural details of the active region, beyond the electronconcentration.

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 135

Complicating the matters or clarifying them some depending on one’s point of view further is theabsence of the efficiency loss in photo-excitation experiments where carriers are photo-generateddirectly and only in the active region evenwith generation rates orders ofmagnitude larger than thoseencountered in high electrical injection levels [10,18]. This instead suggests that the electron spillover(or overflow) caused by unequal carrier injection (lower number of holes), poor hole transport,and very intriguingly by quasi-ballistic electron transport in electrical injection could be the mainmechanisms responsible for the observed loss of efficiency. To reiterate, the term ‘‘spillover electrons’’refers to the electrons which escape the active region without participating in any recombinationprocess, radiative and non-radiative alike, and end up recombining in the p-GaN region or makeit to the p-contact if the minority carrier lifetime in that region permits it. In fact, by employingp-type doped barriers [18,19] or by using a lightly n-type doped GaN injection layer just below theInGaN multiple quantum wells (MQWs) on the n side, intended to bring electron and hole injectionto comparable levels [18], better efficiency retention and higher optical power output have alreadybeen demonstrated. In concord with the above discussion, reducing the barrier widths (i.e. the totaleffective barrier height)within theMQWregions has also been shown tomitigate the loss of efficiencyat high injection [20].In the present manuscript, the current understanding regarding the efficiency degradation in

InGaN LEDs will be reviewed critically along with our understanding of the problem. Processes suchas Auger recombination, carrier spillover (or overflow, leakage), skewed carrier injection due todissimilar carrier concentrations on the n- and p-type GaN, and somewhat impeded transport ofholes, which are heavy, through the LED active region are discussed. In addition, in order to reveal thepresence or the absence of any relationship between the electron spillover and polarization-inducedelectric field, the performance of the non-polar (11̄00) m-plane InGaN LEDs will also be discussed. Itwill be shown that the electron spillover is also the dominantmechanism for the LEDs in this non-polarorientation as well, even though the spillover might seem at first sight to be less serious as comparedto the case of c-plane LEDs due to relatively higher achievable p-type doping and smaller effectivehole mass inm-plane.Intriguingly and representing a major deviation from LED narrative is that the cumulative data

obtained in our laboratory suggest that the spillover is affected mainly by quasi-ballistic electrons inthe active region which do not thermalize easily, escape recombination altogether, and end up on thep-side of the junctionwhen they presumably recombine. The concept is completely foreign to the LEDlexicon andunless proper active regions designed to cool or thermalize the electrons are implemented,it would hamper LED performance. Designs assuring electron thermalization will be shown to exhibitno dependence on the presence or absence of electron blocking layers which suggests also that thestrikingly new concept of ballistic and quasi-ballistic hot electrons seem to be in effect.

2. Auger recombination

Let us now discuss the processes commonly attributed to causing efficiency degradation. Carrierloss due to Auger recombination, which is non-radiative in nature, has been proposed early on asthe origin of the efficiency drop [5,21]. Auger recombination is a three-carrier process such as CCCH(conduction band→ conduction band and conduction band→ heavy-hole valence band transitions),which depicts the process inwhich an electron gains the energy given off by another electron droppingto the valence band. Naturally both the energy and momentum must be conserved and as one cansurmise the energy given off when dropping to the valence band does not lead to a radiative process.The aforementioned one together with those depicted by nomenclatures CHHS (conduction band→heavy-hole valence band and spin–orbit split-off band→ heavy-hole valence band transitions) andCHHL (conduction band→ heavy-hole valence band and light-hole band→ heavy-hole valence bandtransitions) represent the intrinsic Auger processes. There are also other intrinsic processes whichinclude phonons and extrinsic varieties involving defects [22]. To reiterate, the CCCH process couldbe visualized as scattering involving two electrons, with one being knocked down from conductionband to the valence band and the other being scattered to a higher energy state in the conductionband. The latter would eventually thermalize down to the bottom of the conduction band, releasingthe excess energy as heat to the crystal lattice. The CHHS and CHHL processes could be viewed as

136 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

collisions of two holes within the heavy-hole band, with one excited to the conduction band and theother sent deeper to either the split-off valence band or the light-hole valence band, all obeying themomentum and energy conservation. Since the Auger processes depend on carrier collisions, Augerrecombination rate highly depends on the carrier density, and thus gains more relevance at highinjection current levels for optoelectronic devices. It also strongly depends on the bandgap energy (Eg )and temperature (T ) [22]. For a semiconductor with a conduction band effective mass smaller thanthe valence band effective mass, the lifetime is determined by electron–electron collisions, namelyelectron recombination with a hole followed by another electron excitation to a higher energy whilethe entire process having to conserve the energy and momentum.The net Auger recombination rate can be expressed as: [3]

UAuger = Cn[n(pn− n2i )] + Cp[n(pn− n2i )] (1)

where Cn and Cp represent the Auger recombination coefficients for electrons and holes, respectively,p and n are the hole and electron concentrations given by p = p0+∆p, n = n0+∆n, ni is the intrinsiccarrier concentration. Here ∆p and ∆n represent the excess hole and electron concentrations whichare equal to each other when equal injection takes place such as in optical excitation. The first termin Eq. (1) is due to the CCCH Auger processes and the second term is due to the CHHS process. Thisequation is valid only under non-degenerate conditions since Boltzmann approximation is employedfor the derivation of the equation. For degenerate semiconductors, Eq. (1) overestimates the Augerrecombination rate. SinceGaN is nominally n-type (p0 � n0) and at high injection∆p� n0,∆p� p0,the above expression could be simplified to

UAuger = Cnpn2 + Cpp2n. (2)

In the case where ∆n = ∆p � n0, the electron and hole concentrations can be assumed equalleading to the Auger rate being Cnn3+Cpn3, which represents a third power dependence on the carrierconcentrations.The Auger coefficient deduced through a rate equation fit to photoluminescence (PL) data in an

earlier effort is 1.4–2.0 × 10−30 cm6/s for quasi-bulk InGaN layers [5]. A recent calculation basedon the first-principle density-functional and many-body theory reported the Auger recombinationcoefficient to be as large as 2 × 10−30 cm6/s [23]. It must be noted, however, that this coefficientis said to result from the upper conduction band which would be in resonance for LEDs emittingat 2.5 eV. In this case, the Auger coefficient due to the aforementioned resonance should drop offprecipitously on either side of the corresponding wavelength. In the absence of this resonance, thedirect Auger recombination coefficient decreases exponentially with increasing bandgap energy andthe carrier loss due to Auger effect is expected to be very small in InGaN if we were to use the sizeof the forbidden gap alone [13]. Further credence to a small Auger coefficient is provided by fullymicroscopic many-body models [17]. If inherent and intrinsic Auger recombination were to be solelyresponsible for the efficiency degradation, one would surmise that it would have prevented laseraction in InGaN, which requires high injection levels, which is not the case. The vexing phonon-assisted and extrinsic Auger recombination, however, could be examined to determine whether thisphenomenon could be in play here. To make matters more complex, through fitting the EL efficiencydata from commercial LEDs to the rate equation, which includes Auger recombination in addition tothe Shockley–Read–Hall (SRH) recombination and bimolecular radiative recombination, Ryu et al. [24]found unreasonably large Auger recombination coefficients in the range of 10−27–10−24 cm6s−1whenthe non-radiative lifetime τSRH is assumed to be between 5 and 50 ns. The deduced Auger coefficientsare at least three orders ofmagnitude larger, if notmore, than the other reported valueswhich are alsoextracted from the efficiency dependence on injection [5,23,25,26]. The wide variation, in fact some 6orders ofmagnitude,might signal that the Auger recombination alone if any is not sufficient to explainthe efficiency drop in InGaN LEDs. Furthermore, the extraction of the Auger coefficient assumes thatthe A, B, and C coefficients used to calculate the carrier loss rate in conjunction with the followingequation

dndt= An+ Bn2 + Cn3 (3)

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 137

do not depend on the electron concentration (injection levels) and also valid for any electronconcentrations. The conditions under which Eq. (3) would hold can be found in Ref. [3]. We shouldunderscore that in below the barrier resonant photo-excitation experiments (photons absorbed onlyin the quantum wells with ensuing generation of equal number of electrons and holes followed byeither radiative or non-radiative recombination only) the efficiency degradation has not been detectedat carrier generation rates comparable to electrical injection where efficiency degradation has beenobserved (confirmed in our experiments as well) which indicates that efficiency degradation mightbe related to the carrier injection, transport, and leakage processes [10,18]. As mentioned above,aggravating the situation is the omission of the potential effects such as injection dependence of non-radiative processes.

3. Electron overflow

Let us now turn our attention to another often proposed mechanism, namely the electronoverflow. Evidencewhich is increasing in time appears to suggest that electron overflow (or spillover)represents the prominent cause of efficiency degradation at high injection currents. In an effort tomake thepoint that 3rd order polynomial fitting to the observed efficiency vs. injection current densitymay not solely be reprehensive of a particular physical phenomenon Li et al. [27] performed fitting ofthe LED EL efficiency as a function of injection current with a modified recombination rate equationat steady state where the Auger recombination term is replaced by a empirical current spillover term,albeit with injection independent coefficients, as follows:

(J − Jspillover)/qd = An+ Bn2 + Cn3Jspillover/qt (4)

where d is the active region thickness, and t is the thickness within which the spillover current couldbe assumed to be linear. Note that the volume density of the electron concentration is used here. Anempirical dependence of the spillover current on the injection current is chosen as Jspillover = kJbwith k and b being fitting parameters, and t = d is chosen. If one was to entirely neglect theAuger process, a good fit to the data can be obtained for the particular LEDs tested with n3 likedependence of the leakage current [28]. While n3 dependence is the same as that of the Auger processin this particular case, other power dependencies such as n2, which make the case against the Augerrecombination, have been reported as well implying the current overflow is structure dependent. Thepower dependence of the carrier overflow term on the carrier density as high as 4.8 has been reportedfor InGaN light emitters [29]. For reference, a power dependency of as high as 5.5 has been reportedfor InGaAsP light emitters where the barrier height due to the push towards green is very small andelectrons leak out of the quantum well (QW) before recombining [30].The suggestion that electron spillover is in part caused by impeded transport of holes, which are

heavy is supported byour EL efficiency data obtained in LEDswith coupledquantumwells inwhich theefficiency degradation is reduced [20]. To probe the effect of hole transport through the MQW region,the LEDs so investigated featured InGaN barrier thicknesses in the range of 3–12 nm (encompassingcoupled and uncoupled quantum wells) and emit at ∼400–410 nm. The EL data (under short pulseddrive current, 1 µs, 0.1% duty cycle) obtained for coupled quantum wells with 3 nm InGaN barriersshow that the extent of the efficiency drop has been reduced to ∼5% for current densities up to2000 A cm−2, as compared to ∼45% of drop for the LED with 12 nm InGaN barriers (uncoupled) inthe same current range. This again is consistent with the above discussion regarding the poor holeinjection and transport model.Barring technological issues such as the layer quality, etc., replacing the MQW active region

with a double-heterostructure (DH) LED would be desirable so as to not impede the hole transportin the active region. In this context, experiments with DH structures having 6 and 12 nm thickIn0.15Ga0.85N active regions have been undertaken. As shown in Fig. 1 the two DH LEDs with 6 or 12nm In0.15Ga0.85N active region have relatively much smaller EQE droop (∼9% for 6 nm DH–LED,∼7%for 12 nm DH–LED) when compared to the MQW–LED with 6 pairs of 12 nm In0.01Ga0.99N barriersand 2 nm In0.15Ga0.85N quantum wells (∼42%), representing uncoupled quantum wells, when thecurrent density is increased up to 1800 A cm−2. The 6 nm DH–LED has the highest EQE among thethree LEDs at higher current densities (>380 A cm−2), which is approximately 60% larger than that

138 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

Fig. 1. Relative EQE values under pulsed injection current (1 µs, 0.1% duty cycle) for a 6 nm In0.15Ga0.85N DH–LED,12 nm In0.15Ga0.85N DH–LED and an MQW–LED with 12 nm In0.01Ga0.99N barriers and 2 nm In0.15Ga0.85N QWs grown on ac-plane sapphire. All samples were grown on 60 nm In0.01Ga0.99N underlying layers for improved active layer quality.

of the MQW–LED with 12 nm In0.01Ga0.99N barriers at a current density of ∼1800 A cm−2 due to amuch better retention of the EQE. However, at current densities below 380 A cm−2, the EQE of the6 nm DH–LED is lower than that of the MQW–LED with 12 nm barriers. This could be attributed torelatively higher carrier densities in the MQW active region as compared to that in the 6 nm DH at aparticular current density (most likely only a few of the QWswhich are situated near the p-side in theMQW–LED, where the majority of holes are, contribute to the EL intensity), which in turn results ingreater radiative recombination rate relative to the non-radiative recombination rate. Moreover, theEQE of the 6 nm DH–LED is ∼40% stronger than that from the 12 nm DH–LED, very likely due to thedegraded InGaN material quality with the increase of its thickness [21]. It is evident that the DH–LEDis a promising structure to reduce the efficiency droop. However, the thickness of the active region ofthe DH–LED should be optimized in order to strike a balance between the volume of active region andmaterial quality which is highly related to InGaN thickness.

4. Other possible sources of efficiency loss in InGaN LEDs

Besides the electron overflow and Auger recombination, the efficiency droop has also beenattributed to carrier de-localization from In-rich clusters inside the active region at high injectionlevels [31]. According to this model, at relatively low currents the carriers are localized in the In-richclusters, which are purported to be free of defects and thus the non-radiative recombinationcomponent is negligible, which results in a relatively high internal quantum efficiency (IQE) ofthe LEDs. At high current levels, the clusters are saturated with localized carriers, and pathwaysto additional non-radiative recombination centers become available, thereby the IQE is degradedat high current levels. However, it has been shown by others who had prepared samples formicroanalysis without causing beam damage that the In composition within the active region isquite homogeneous [32]. Moreover, it is generally observed experimentally that low-defect-densityLEDs show a more pronounced efficiency peak at relatively low injection levels followed by amore pronounced efficiency loss [33]. This obviously goes counter to the above-mentioned ‘‘carrierlocalization’’ model. We should be reminded that the overall goal is to achieve and retain a highefficiency at all injection levels.Another cause of efficiency loss has its genesis in the detrimental effect of current crowding.

In some LEDs where a lateral contact configuration is employed, either for n- or the p-side, thecurrent density is distributed non-uniformly across the device area. It is concentrated near the edgesof the thicker metal around the mesa and decreases exponentially with distance from the mesaedge [3]. While this is more detrimental in the p-layer due to its large resistance, the n- or p-layercontact configuration, depending on regular or flip-chip mount, also contributes and must be takeninto consideration. In LEDs not using the flip-chip technology, meaning the p-layer is on the top

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 139

and through which the light is extracted, the current is denser near the metal electrodes whosedistribution and geometry must be optimized with current crowding in mind.The current concentrated near the metal grid/contacts can result in efficiency degradation due

to locally increased injection levels which results in local heating which in turn results in a highercurrent, a detrimental positive feedback. The particulars of current crowding in lateral contacts,although an age old problem in many devices including bipolar transistors, have been discussed inthe context of nitride-based LEDs in numerous papers, see, e.g., Ref. [34]. In addition to the contactconfiguration, a proper choice of p-contact material is also critical for relieving the current crowdingeffect, thereby reducing the extent of the efficiency degradation as supported by our comparativestudies of LED structures which employed a highly conductive Ga-doped ZnO (GZO) layer [35] and asemi-transparent Ni/Au as p-contact materials. The GZO p-contact was grown by molecular beamepitaxy on an MQW–LED sample which was in turn grown on c-plane sapphire with 6-period2 nm In0.15Ga0.85N wells and 12 nm In0.01Ga0.99N barriers. The relatively thick barriers employedwere to allow efficiency degradation so that a comparative analysis of the efficiency loss can bemade.For comparison, semi-transparent Ni/Au (5 nm/5 nm) p-contact was used on another piece of thesame LED wafer as a reference sample. The results show that in addition to nearly doubling the lightextraction due to improved transmittance of GZO andmore uniform light emission over the thinNi/Aucontact, the extent of the efficiency degradation was also reduced from ∼37% for the LED with thinNi/Au contact to∼27% for the one with GZO contact in tests up to current levels of 3500 A cm−2 [36].The reduced efficiency drop in the GZO case is attributable tominimization if not the total eliminationof the current crowding effect. Note that a muchmore uniform emission intensity distribution at highcurrent levels is achieved for the LED with GZO contact layer as compared to the case with thin Ni/Aucontact which exhibited non-uniform light emission at high injection levels.Last but not least, junction Joule heating effect on LED efficiency deserves a close attention as it

has also been proposed to contribute to the InGaN LED efficiency drop, indicating the obvious needfor optimal heat removal [37]. The junction heating issue is very important due to several reasons.First, it affects the internal quantum efficiency due to enhanced non-radiative processes including theSRH recombination [28]. Second, excessive junction heatingwould also degrade the contacts and con-tact/semiconductor interfaces, which would manifest itself as an increased series resistance, therebydegrading efficiency as well as the power conversion efficiency. At high currents, the dominant heatsource is from Joule heating of the p-type GaN and p-contact, having a dependence of I2R. Additionalheat may also come from an increased non-radiative recombination due to the layer degradation athigh operating currents and low photon extraction efficiency. The aforementioned discussion goessomewhat counter to that proposed by Kim et al. [10] which stated that the junction heating onlyreduce the overall efficiency of the LEDs, but not the cause of the efficiency drop. According to ourmeasured EL data, at high injection levels thermally induced drop is observed even at 1% duty cycleas judged from the fact that the drop can be partially eliminated by employing 0.1% duty cycle.

5. Performance and efficiency loss studies ofm-plane InGaN LEDs

As mentioned above, polarization field induced along the polar direction has been cited as a causeor the main cause of efficiency degradation in InGaN LEDs. In order to clarify any correlation betweenefficiency droop and polarization-induced electric field and or the extent of it, we have undertakenan investigation of the m-plane LEDs and their EL efficiency degradation behavior. In addition to thelack of polarization-induced field, the non-polar m-plane GaN, on which InGaN/GaN LED material isgrown, has been predicted to have a few advantages such as lower valence band density of states,shallower acceptor level and thus higher hole concentration. It is well known that, in the c-orientedGaN films, the internal spontaneous and strain-induced piezoelectric polarizations produce a strongelectric field. This results in the spatial separation of electron and hole wavefunctions in QWs usedin LEDs and laser diodes (LDs), thereby reducing the quantum efficiency, particularly at low injectionlevels [38,39]. The polarization-induced electric field also causes a red shift in LEDs and makes theemission wavelength dependent on injection current, blue shifting with increasing injection, unlessvery thin quantumwells are employed. By employing non-polar orientations, namelym-plane [40,41]or a-plane GaN, [42,43] this problem could be circumvented. As noted above,m-plane GaN is reported

140 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

to be well suited for optoelectronic applications in that it is predicted to have a lower valence banddensity of states, reduced valence band effective mass (thus smaller acceptor binding energy), andlarger optical matrix elements relative to its c-plane counterpart, which would bode well for LEDsand LDs on this orientation [44]. The above-mentioned reduced hole effectivemasswould also help toobtain a relatively high hole concentration [45,46]. This in turn would increase hole injection into therecombination medium and thus increase the radiative recombination rate as well as increasing thehole concentration inwells farther away from the p–n junction. In this regard, the use of non-polar ori-entations would assuage carrier spillover and help in the efficiency retention at high injection levels.In measurements in one set of our experiments, which should be termed as preliminary,m-plane

InGaN LEDs were shown to have some advantages, which might be inherent if the predictions areaccurate, over its c-plane cousin in terms of the IQE [47]. The IQE values were extracted from theexcitation dependent PL studies with resonant excitation at room temperature using a frequency-doubled 80 MHz repetition rate femtosecond Ti:Sapphire laser. The excitation laser wavelength was370 nm whose energy is below the bandgap of the quantum barriers and top GaN, but higher thanthat of the wells. In this scenario, the photo-excited electron–hole pairs are generated only withinthe quantum wells where they are forced to recombine either radiatively or non-radiatively. Thisapproach avoids optical carrier generation in the barriers and also allows bypassing the carrierinjection effects in electrical injection cases which cause efficiency droop in the EL case [10,18]. Interms of some details of efficiency determination, we have used a procedure similar to that describedin Ref. [48] to measure the IQE with the power dependent PL. In our model we assume a steady stateand high injection case in which the total generation rate (G) is equal to the total recombinationrate (R) the latter of which includes the Shockley–Read–Hall non-radiative recombination (An),bimolecular radiative recombination (Bn2), and Auger recombination (Cn3), if any, terms, where nrepresents the carrier concentration. One should note that any dependence of the A, B, C constantson the excitation level is neglected at this point. The measured PL intensity could be representedas IPL = ηcBn2, where IPL is the integrated PL intensity, ηc is a factor that includes the escapeefficiency of photons as well as their collection efficiency by the optics/detector. Fortunately, thisfactor remains constant during a given measurement. The caveat is that it could vary from sampleto sample even though attempts are made to keep the collection geometry the same. This variabilitydoes not, however, affect the values of the efficiencies reported here.From the above discussion it follows that the total generation rate at steady state and high injection

levels can be related, in a modified form, to the A, B, and C parameters as:

G =A√ηcB

√IPL +

1ηcIPL +

C(ηcB)3/2

(√IPL)3/2. (5)

The generation rate, G, can also be independently calculated from the excitation laser power, asdescribed in Ref. [48], provided that the absorption and reflection coefficients are known accurately,as:

G = Plaser(1− R)α/(Aspothυ) (6)

where Plaser is the laser power, R is the Fresnel reflectivity at the sample surface, α is the absorptioncoefficient of the quantumwells at the laser emissionwavelength, hυ is the photon energy from laser,Aspot is the area of the laser spot. By fitting the calculated generation rate as a function of the squareroot of integrated PL intensity

√IPL, the three coefficients for each term in Eq. (5) can be obtained, from

which the IQE = Bn2/G = (IPL/ηc)/G values are subsequently calculated. Taking the most commonlyreported value for the B coefficient, one can also obtain A and C recombination parameters. However,it should be mentioned here that the IQE value so determined does not depend on the assumed valueof the B parameter (1 × 10−11 cm3 s−1 used here, which is the most commonly reported value), butonly the corresponding electron concentration depends on the choice of the B coefficient.The IQE values extracted from the excitation dependent PLmethod form-plane and c-plane InGaN

layers are shown in Fig. 2. The two LEDs for which the data were obtained have the same structure:6-period 2 nm In0.14Ga0.86N quantum wells with 12 nm In0.01Ga0.99N barriers, and a 60 nmSi-doped (2×1018 cm−3) In0.01Ga0.99Nunderlayer just beneath the active region for improved quality.

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 141

Fig. 2. Extracted IQE values for the m- and c-plane LEDs on bulk GaN substrates using excitation intensity dependent PLmeasurements. The two LEDs have the same structure: 6-period 2 nm In0.14Ga0.86N quantum wells with 12 nm In0.01Ga0.99Nbarriers. During the calculation of carrier concentrations for the samples, the B coefficient was assumed to be 1×10−11 cm3s−1 .

A ∼10 nm p-Al0.15Ga0.85N electron blocking layer (EBL) was deposited on top of the active quantumwell region. During the calculation of the carrier concentrations for the samples under investigation,as noted above, the B coefficient was assumed to be 1 × 10−11 cm3 s−1. At relatively high carrierconcentrations, the IQE values of the m-plane LEDs are ∼30% higher than those of their c-planecounterparts measured in our laboratory in one set of experiments. At the highest excitation power,the IQE values are 80% and 60% for them-plane and c-plane LEDs, respectively.In terms of the EL performance, the m-plane LED shows higher EL intensity and better efficiency

retention with increasing current injection. The EL measurements were carried out for bothm-planeand c-plane LED samples onwafer-formwithout any special treatment to enhance light extraction andeffortswere undertaken to assure the same photon collection geometry from sample to sample duringmeasurements. The light intensity vs. current characteristics were measured under pulsed injectioncurrent (1 µs, 0.1% duty cycle) in order to minimize, if not totally eliminate, the heating effect on LEDefficiency.Fig. 3 shows the integrated EL intensity and relative EQE as a function of the injection current

density for the two LEDs investigated. The m-plane LED shows negligible efficiency loss, i.e. almostfull retention of its efficiency up to 2500 A cm−2, which represents the highest current density underwhich the experiments were conducted. Quantitatively speaking, only 5% loss in efficiency for the LEDonm-plane as compared to∼25% for that on c-plane freestanding GaN having the same structure wasnoted.The above observation is consistent with the premise of relatively high hole concentration in

m-plane that would provide higher hole concentrations in the recombination region and reducethe electron spillover (or overflow) and thereby mitigate the efficiency loss. Furthermore, as alsoevident from Fig. 3, at relatively low injection levels the EL intensity for the m-plane LED increasesmore rapidly than that for the c-plane LED, reaching its peak value at ∼140 A cm−2 compared to∼400 A cm−2 for the c-plane LED, which is indicative of a relatively small Shockley–Reed–Hall non-radiative recombination coefficient for the m-plane variety. Among several devices tested for bothorientations, the m-plane LED EQE values are consistently higher by ∼35%. This difference is evenhigher at higher injection levels due to better efficiency retention than those of the c-plane LEDswhich is consistent with the IQE results obtained from the intensity dependent PL measurements.The variation from device to device for each orientation was less than 10%.

6. Effect of EBL on EL efficiency in LEDs withm-plane and c-plane orientations

As discussed above, if the electron overflow/spillover plays a major role in the efficiencydegradation in InGaN LEDs, one would then wonder about the genesis of this overflow. To reiterate,

142 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

Fig. 3. (a) Integrated EL intensity and (b) relative external quantum efficiency of the m-plane LED on freestanding GaN andthe reference LED on c-plane bulk GaN as a function of pulsed injection current density (1 µs, 0.1% duty cycle). Both sampleshave the same device structure (MQW active region with 2 nm In0.14Ga0.86N quantum wells, 12 nm In0.01Ga0.99N barriers, andp-Al0.15Ga0.85N electron blocking layers).

Kim et al. [10] suggested that the polarization-induced electric field in the active region and the EBLcauses the electron overflow to the p-GaN layer. If this is indeed the case, then the non-polar LEDswould lessen if not eliminate the said electron overflow. In this regard, we investigated the LED ELintensity (relative external quantum efficiency as well) as a function of current density for LEDs onc-plane GaN, which is polar and possesses polarization-induced field, and on (11̄00)m-plane GaN,which is non-polar, and therefore, free of polarization-induced field. For added inquisition one caninsert or not insert EBLs in both varieties to interrogate the extent of the role or the lack of polarization-induced electric field on the carrier spillover.The IQE values extracted from the excitation dependent PL method for the m-plane and c-plane

InGaN MQW LEDs are shown in Fig. 4. First, the IQE values, determined from resonant opticalmeasurements, of c-plane LEDs with and without an EBL layer are very similar in the entire rangeof photo-generated carrier concentrations up to 1.0× 1018 cm−3 (assuming B = 1× 10−11 cm3 s−1),where a value of ∼50% is reached. This similarity in the IQE values is a result of the fact that theresonant carrier excitation causes electron–hole pair generation only in the quantum wells of theactive regionwhich is alsowhere they undergo radiative andnon-radiative recombination. Second, forthe twom-plane LEDs, themaindifference in termsof IQE is that the onewithout EBL exhibits a smallernon-radiative SRH recombination, manifested by a steeper increase with increasing carrier density.This is most likely attributable to the variation in the material quality of the two structures, arisingpossibly from the variations in the quality of them-plane bulk substrates. However, this variation willnot affect the nature of our discussion as we will show below. Third, the IQE values of the m-planeLEDs are ∼40% higher in general than those of their c-plane counterparts at relatively high carrierconcentrations, reaching slightly above 85% for the structure without the EBL and a comparable valueof ∼80% for the one with EBL at steady state carrier concentrations of 7 × 1017 and 1 × 1018 cm−3,respectively. The higher IQE in them-plane variety might probably be due to relatively larger opticalmatrix elements predicted form-plane compared to c-plane of GaN [49].Fig. 5 illustrates that the LEDs without EBL, show 4–5 times lower EL intensity under the same

current levels as compared to those with EBLs in both c-plane [Fig. 5(a)] andm-plane cases [Fig. 5(b)].Excitation power dependent PL measurements discussed above showed that the LEDs with and

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 143

Fig. 4. Extracted IQE values of c- and m-plane LEDs with and without EBL vs. the induced carrier concentration calculatedfrom the resonant PL measurements using excitation power dependence. All LEDs have the same structure: 6-period2 nm In0.14Ga0.86N quantum wells with 12 nm In0.01Ga0.99N barriers either with or without the 10 nm p-Al0.15Ga0.85N EBL. Forthe calculation of carrier concentrations, the radiative recombination coefficient B was assumed to be 1 × 10−11 cm3s−1.λ ∼400–410 nm.

without EBL have essentially the same IQE values under optical excitation (for m-plane, the onewithout EBL is even slightly higher possibly due to the variation of substrates), even though underelectrical injection the former ones have higher EL intensity. These results suggest that the lowerEL intensity for the LEDs without EBL is related to carrier injection (i.e. more electron overflow forthe LEDs without EBL), which would not apply under resonant optical excitation since equal numberof holes and electrons are generated solely inside the quantum wells and no carrier transport isinvolved in the process. Although it has been suggested that the polarization-induced band bendingin the InGaN and EBL regions of the c-plane LEDs results in a reduced effective barrier of the EBL[10], thereby causing more electron overflow in c-plane orientation as compared to that in m-plane,polarization field in the polar structures is already screened at high injection, and substantial carrierspillover in both orientations w/o EBL implies that the polarization charge is not the major factorresponsible for the loss of efficiency observed particularly at high injection levels [Fig. 5(b)]. It shouldalso be mentioned that the m-plane variety with EBL did not show any discernable loss of efficiencyup to a maximum current density of 2400 A cm−2 while that on c-plane showed a reduction by∼20%, indicating better ability of efficiency retention for the LED in the m-plane orientation. Thefact that the m-plane LED with EBL shows no notable efficiency degradation seems to imply thatAuger recombination at these injection levels is not of major importance, at least in the structureinvestigated.

7. Effect of ballistic electrons on the LED efficiency

The discussion provided above point in the direction of electron overflow (or spillover) causing asubstantial EL efficiency reduction for LEDs where no EBL are employed both in polar and m-planenon-polar orientations [50]. Because the barriers in between the active region and surroundingregions, including the p-side, are very large, in the vicinity of 0.5 eV and larger depending on theInN mole fraction, it would be nearly impossible for the thermalized carrier to escape the activeregion. In fact, the Boltzmann tail in energy even at an elevated lattice temperature for equilibriumelectrons does notmake it near the top of the barrier for any discernable electron escape. The situationwould change in favor of this escape in the case of an electric field across the active regions, buteven then the escape probability for thermalized and equilibrium carriers would be unlikely unlesselectron densities in excess of 1019 cm−3 are injected in which case a small fraction of electrons couldescape the active region without recombining [28]. This, together with the observation that the lackof EBL in both c- and m-plane devices allows nearly 80% of the electrons to escape the active regionaltogether, suggests that non-equilibrium carriers, hot electrons, be considered. In this framework,

144 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

Fig. 5. Relative EQE for (a) c-plane LEDs on c-plane sapphire and (b) m-plane LEDs on bulk m-GaN with and without EBLmeasured under pulsed current (1 µs, 0.1% duty cycle). With the exception of the EBL, all the LEDs have the same structure:MQWswith 6 periods of 2 nm In0.14Ga0.86Nwells and 12 nm In0.01Ga0.99N barriers (thick barriers are chosen to allow efficiencyloss at high currents). All of the LEDs used for this particular study have an emission wavelength of ∼400–410 nm. For bothc-plane andm-plane varieties the EL intensity from the LEDswith EBLs is higher by 4–5 times than that from the respective LEDswithout EBLs. Them-plane LEDwith EBL shows almost negligible efficiency droop (∼5%) up to a current density of 2250 A cm−2 ,compared to∼40% droop for the c-plane LED with EBL.

the electrons injected from the n-side into the active region with relatively small bandgap gain largekinetic energy. If the transit time is shorter than scattering time, inverse of scattering rate, for some orlarge number of electrons, those electrons would ballistically traverse across the active region to thep-region without participating in the recombination process. It is also possible for some electrons toundergo scattering with LO phonons which end up in phonon emission and other electrons to absorbphonons. If the scattering angles are small, it is possible that even some of the electrons participatingin phonon emission and absorption could make it across the active layer without recombination. Inthe discussion that follows, we are going to refer to those electrons not suffering any scattering asballistic electrons and those suffering collisions but ending up traversing across the active layer intothe p-layer without recombination as quasi-ballistic electrons [51].The LED structures investigated for probing the physics associatedwith ballistic and quasi-ballistic

electrons were grown on freestanding m-plane (11̄00)GaN substrates in a vertical low-pressuremetalorganic chemical vapor deposition (MOCVD) system. The structures contained a 6 nm undopedactive region of In0.20Ga0.80N (emission wavelength, λ ∼ 440 nm) with a 3 nm undoped In0.01Ga0.99Ntop layer. A p-AlxGa1−xN electron blocking layer (EBL) of thickness ∼10 nm was deposited on top ofthe active layer. Three LED structures with EBL compositions of x = 15%, 8%, and 0% were preparedfor this purpose.Fig. 6 shows the relative external quantum efficiency (EQE) as a function of the injection current

density for the m-plane LEDs with 15% Al EBL, 8% Al EBL and no EBL showing a progressive decreasein the external quantum efficiency (EQE) as the Al mole fraction in the EBL decreases with the endpoint of having no EBL. This is in contrast to the all optical IQE measurements showing all three LEDstructures essentially having the same IQE (IQE of 50%–56% at a carrier density of 1 × 1018 cm−3

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 145

Fig. 6. Relative EQE of m-plane LEDs with varying Al composition (15%, 8%, 0%) in the EBL. The LEDs were measured underpulsed current, 1 µs pulse width and 0.1% duty cycle. The LEDs were grown on freestanding m-plane (11̄00) GaN substrates,and their active regions are composed of 6 nm thick In0.20Ga0.80N (corresponding emission wavelength, λ ∼ 440 nm).

under the assumption that the radiative recombination coefficient B is 1 × 10−11 cm3 s−1). Thissuggests that the observed dependence of EL intensity on the particulars of EBL has its origin in thecarrier injection and overflow rather than the dispersion in the active region quality. The EQE forthe m-plane LED with 15% Al in EBL shows a pronounced peak at approximately 80 A cm−2 (opensquares), and the efficiency drops by ∼45% with increasing current injection up to 2400 A cm−2. Anegligible efficiency loss (∼3%–5%) is observed for the structure without EBL (i.e., for 0% Al in EBL) athigh injection; moreover, its relative EQE is∼3–5 times lower (solid circles) than that with 15% Al inthe EBL. Intermediate values for EQE and efficiency drop (∼10%) are obtained for the LED with 8% Alwithin EBL (open circles).The above-mentioned observations are consistent with electron overflow (Fig. 6) which may

originate from: (i) thermionic emission of equilibrium electrons from the bottom of the active regionover the barrier into the p-layer (which we ruled out and will show it not to be important dueto large band discontinuity), (ii) ballistic and quasi-ballistic transport of the injected electrons thatdo not thermalize inside the active region. Using Silvaco Atlas r©software for the LED without theEBL and assuming complete thermalization, the thermionic emission and any tunneling within theWentzel–Kramers–Brillouin (WKB) approximation was computed. Using the commonly acceptedmaterials parameters [51] it was found that at an elevated junction temperature of 200 °C, thethermionic emission related overflow electron current is only ∼5 A cm−2 as compared with a totalcurrent density of 104 A cm−2. This supports the premise that the overflow does not result fromthe thermionic emission and that it is very likely that substantial proportion of electrons are notsufficiently thermalized inside the active region and end up traversing the active region ballisticallyand or quasi-ballistically.Within the framework of ballistic and quasi-ballistic electrons, our calculations show that ∼62%

of the total electron current does not participate in light production in the LED without an EBL layer.The thermalized electrons in the n-GaN layer gain additional kinetic energy once injected into the6 nm In0.20Ga0.80N active region, equal to the conduction band offset between n-GaN and In0.20Ga0.80N(∆Ec, ∼ 0.5 eV in this case). These hot electrons would either undergo thermalization and lose theirexcess energy mainly through their interaction with LO phonons [52] or avoid thermalization andleave the InGaN region. Our calculation includes the electrons which experience (i) no scattering inthe active region represented by ballistic motion, (ii) one scattering event, either LO phonon emissionor absorption, and two scattering events (4 types of combinations of two scattering mechanisms:phonon emission and absorption). The mechanisms involving a combination of phonon emission andthen absorption, which lead to carrier transit across the active region to the p-side, are representedby quasi-ballistic motion. To a first extent one can assume low angle scattering in that the directionof motion of the electrons before and after scattering remains the same, which would overestimate

146 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

the quasi-ballistic contribution. Doing so, however, simplifies the theoretical treatment considerablyand allows a first-order view as to the inner workings of electron transport and recombination. Theelectrons undergoing two scattering events and contributing to overflow make less than 1% of thetotal injected electrons and can be neglected.The probability of the ballistic transport at a given energy is proportional to exp(−t/τsc), where t is

the transit time, and τsc is the electron–LO-phonon scattering time given by τsc = 1/(1/τabs+1/τem),where τabs and τem are the phonon absorption and emission time, respectively. The percentage ofoverflow electrons is then given by

p1 =

∫+∞

max{0,(φEBL−qV )}f (E)N(E) exp

(−L/v(E)τsc

)dE∫

+∞

0 f (E)N(E)dE(7)

where E is the electron excess energy with respect to the bottom of the conduction band of n-GaN, Lis the active region width (6 nm in our case), V is the potential drop across the InGaN region,me is theelectron effective mass, φEBL is the barrier height of EBL in terms of eV (i.e. ∆Ec between the EBL andthe GaN), N(E) is the conduction band density of states, f (E) is the Fermi–Dirac distribution function,and v(E) =

√2 (E + 0.5 eV) /me is the electron velocity with an initial energy of E plus the gained

energy due to the 0.5 eV band offset between the n-GaN and the InGaN active region. For simplicity, aselucidated above, we assume that the electrons move only in the normal direction to the heterointer-face, whichwould overestimate the probability but insignificantly. As for the quasi-ballistic electrons,the total percentage of the overflow electrons that suffer one scattering event is given by:

p2 =

∫+∞

max{0,(φEBL−qV±h̄ωph)}f (E)N(E)

∫ L0 exp

(−x/v(E)τsc

)·

1v(E)·τph

· exp(−(L−x)/v(E∓h̄ωph)

τsc

)· dx · dE∫

+∞

0 f (E)N(E)dE

(8)

where+h̄ωph and τph = τem, are for phonon emission (−h̄ωph and τph = τabs are for phonon absorp-tion). ‘‘+h̄ωph’’ in the low end of the integration range for the phonon emission case represents thatthe electrons that are able to spill over to the p-region after one phonon emission shall have additionalh̄ωph energy to lose during scattering. Eq. (8) takes into account energy conservation and the proba-bilities for an electron to reach position x without being scattered, to be scattered near x, and to exitthe active region without being scattered between x and L. The integration over dx and dE accountsfor all possible paths and all such suitable electrons. In a similar way, the percentage of the overflowelectrons is expressed for the case of two scattering events, but the contribution of these electrons isnegligible.Fig. 7(a) shows the calculated percentile electron current overflow as a function of the EBL barrier

height assuming flat band conditions in and near the active region. A phonon emission time (τem),a phonon absorption time (τabs), and a phonon scattering time (τsc) of 0.01 ps, 0.1 ps, and 0.009 ps,respectively, have been used for the calculation [53]. For the LED without EBL (i.e. 0% Al in EBL), asignificant portion (∼62%) of the electrons overflow, while almost no electron overflow occurs whenan EBL with 15% Al is inserted, which are reasonably consistent with experiments (Fig. 6) which showthat approximately 4/5 of the current for the LED without EBL is the overflow current whereas only1/5 of the electron current is captured by the InGaN active region. While the assumption of transitnormal to the interfaces would overestimate electron overflow, the assumption of flat band wouldhave the opposite effect. Therefore, the agreement between the experiments and theory is consideredto be good at this stage.Fig. 7(b) shows the calculated percentile of electron overflow as a function of the applied forward

voltage with different EBLs. Noted that in this ideal scenario, 0.5 V of the applied voltage droppingacross the active region corresponds to the flat band conditions, and higher applied voltages wouldlower the effective EBL barrier height and thus the overflow current would increase with the appliedvoltage.When the applied voltage is increased from 0.5 to 0.67 V causing an increase in the net poten-tial drop across the well increasing from 0 to 0.17 V [(∼2h̄ωph/e)], the overflow electron current in-creases from 62% to 93%with no EBL (a 40% increase), while an increase from 0% to 41% is observed forthe LED with 15% Al in EBL. It should be noted that during calculation we assumed a constant phonon

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 147

Fig. 7. (a) Calculated ratio of overflow electron current to total current as a function of EBL barrier height (φEBL) assuming flatband conditions in the active region (i.e. 0 V net potential drop across the InGaN active region after the applied external voltagecompensates the built-in potential, which is ∼0.5 V). The calculation takes into account ballistic electrons (undergoing nophonon scattering) and quasi-ballistic electrons (undergoing one phonon scattering event: one phonon emission or absorption,those undergoing 2 or more phonon scattering events have less than 1% contribution). (b) Calculated ratio of overflow electroncurrent to total current as a function of the applied voltage (forward direction) across the InGaN active region for LEDs withthree types of EBLs: w/ 0% Al, 8% Al and 15% Al. It should be noted that 0.5 V applied voltage corresponds to the flat band caseand higher applied voltages could lower the effective EBL barrier height.

scattering rate with the increase of current. To be strictly correct, however, this has been reported notto be the case [53]. Therefore, with the increase of injection current and thus the accumulation of elec-trons and also non-equilibrium LO phonons in the active region, the electron–LO–phonon scatteringwill be increased (thereby the electron overflowwould be less). So our calculationwould overestimatethe dependence of electron overflow on applied voltage (or current). For a more in depth discussionof the calculations and assumptions therein, see reference by Ni et al. [54].To interrogate further, to dispel any possible doubt, that the hot electrons play the role outlined

above, one can simply conduct experiments in structures wherein the electrons are forced to coolwhile being injected into the active region. This can be accomplished by replacing the abrupt barrierwith a graded or a step graded one, the latter will be referred to as the staircase. In the staircasecase, each step or the pair of steps needs to be equal to or larger than the LO phonon energy to allow

148 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

Fig. 8. Schematic for the two m-plane LEDs with InGaN staircase electron injector (SEI) structures before the active regions,one with a 10 nm EBL with 15% Al, and the other without any EBL in the p-region. InGaN-based MQW underlayer is employedbefore the InGaN SEI structure to improve the material quality in the active region.

the electrons to scatter and transfer their energy to LO phonons. We now show that by employingan InGaN staircase structure as an electron injector the ballistic and quasi-ballistic processes can beeliminated, which would pave the way to thermalization of electrons in the active region. Likewise,we show that incorporation of such a staircase electron injector (SEI) as an ‘‘electron cooler’’ on then-side has substantially reduced the overflow electrons responsible for the efficiency loss of LEDsfabricated on non-polarm-plane GaN, evenwhen no EBL is employed. The LED structures investigatedin this segment of the work were also grown on freestanding m-plane (11̄00)GaN substrates ina vertical low-pressure MOCVD system. The ∼500 µm-thick m-plane freestanding GaN templateswere provided by Kyma Technologies, Inc., similar to what we stated in the cases without the SEI.Two m-plane InGaN LEDs were investigated (see Fig. 8 for the device schematics); one having a10 nm p-Al0.15Ga0.85N EBL, while the other without any EBL layer. Their active regions are composedof a single undoped 6 nm In0.2Ga0.8N layer followed by a 3 nm thick undoped In0.01Ga0.99N barrier.Distinguishing this segment from the earlier ones is the presence of an InGaN SEI structure before theInGaN active region for the purpose of thermalizing the electrons, naturally for both types of LEDs.The SEI structure consists of three 5 nm InGaN layers (resulting in a four-step staircase, or a 3-layerSEI) with In compositions of 3%, 6% and 10%, respectively, in the given order, as shown in Fig. 8, wherethe pairs of steps having potential energy drop by more than one LO phonon energy contribute toelectron thermalization. The InN compositions in the SEIwere chosen for technological reasons relatedto the growth procedure, and especially the first pairs of SEI layers are expected to act as a singlelayer supporting electron cooling via LO phonon emission. To ensure that the radiative efficiency ofthe active region in both LED structure is nearly the same so as to not be a skewing factor, IQE wasextracted from excitation power dependent PL as described above. The two double heterojunction(DH) LEDs under investigation have essentially the same IQE under the same carrier density (IQE of50%–55% at a carrier density of 1 × 1018 cm−3 under the assumption of a radiative recombinationcoefficient B of 1 × 10−11 cm3 s−1). On-wafer EL measurements were then performed using pulsedcurrent (1 µs, 0.1% duty cycle) without any special means to enhance light extraction.Fig. 9 shows the relative EQE of the two m-plane 3-layer SEI DH LEDs, one with and the other

without EBL. As can be easily gleaned from the data, the LED with the EBL has essentially the samerelative EQE value (i.e. EL intensity) as the one without EBL under the same current density for theentire range of current densities investigated. This is un-mistakenly different from that observed inLEDs without the SEI ‘‘electron cooler’’ structure, where the EL intensity from the LED without EBLis 4–5 times lower than that from the one with EBL. It is, therefore, reasonable to suggest that byemploying the InGaN SEI structure before the active region, the electron overflow due to ballistic andquasi-ballistic electron transport across the active region is substantially reduced or eliminated,whichhas resulted in the similar EL performance for the DH LEDs with and without the EBL [55].In order to quantitatively account for the reduction of electron overflow by employing InGaN-

based SEI structures, we performed first-order calculations of the electron overflow for the LEDs withand without SEI (both without EBL) under different applied forward voltages across the active region.

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 149

Fig. 9. Relative EQE of twom-plane staircase LEDs with andwithout EBLs, respectively. The LEDs weremeasured under pulsedcurrent of 1 s duration with 0.1% duty cycle. The LEDs were grown on freestandingm-plane (11̄100) GaN substrates, and theiractive regions are composed of 6 nm single In0.20Ga0.80N layers (∼440 nm peak emission wavelength).

The approach taken is very similar to that for the abrupt barrier LEDs wherein the composition of the10nmEBL layer is varied. Again, for simplicity, let us consider a 1-layer SEI (one In0.10Ga0.90Nstep layerbefore the In0.20Ga0.80N). A SEI with higher number of steps, as in experiments, will not change thenature of this discussion.We treat the SEI region as having a total thickness of 15 nm,which is the sameas the total thickness of the 3-layer SEI region of the LEDs investigated experimentally. To reiterate,the probability of a ballistic transit (i.e. no scattering) has a dependence, exp(−t/τsc), where t is thetransit time, and τsc is the electron–LO-phonon scattering time given by τsc = 1/(1/τabs + 1/τem).The percentage of overflow electrons due to ballistic electrons is then calculated as described indetail in Ref. [54], but to suffice, their probability to traverse the SEI and the active region withoutrecombination is expressed as:

p0 =

∫+∞

max{0,(φEBL−qV )}f (E)N(E) · exp

(−d1/v1(E)τsc

)· exp

(−d2/v2(E)τsc

)dE∫

+∞

0 f (E)N(E)dE(9)

where E is the excess electron energy with respect to the bottom of the conduction band ofn-GaN, depicting the initial situation before carrier injection, d1 = 15 nm and d2 = 6 nm arethe thicknesses for the SEI region (In0.10Ga0.90N), and the active region, respectively, and v1(E) =√2(E + 0.25 eV)/me and v2(E) =

√2(E + 0.5 eV)/me are the electron velocities for the SEI region

(In0.10Ga0.90N), and the active region, respectively. The term V represents the net potential drop acrossthe well (determined by a combination of the applied voltage, and the built-in voltage along withthe charge density in the region), φEBL is the EBL barrier height (i.e. ∆Ec between the EBL and theGaN) which is 0 in this case as there is no EBL layer employed, me is the electron effective mass,N(E) is the conduction band density of states, and f (E) is the Fermi–Dirac distribution function. Theenergies, 0.25 and 0.5 eV in the velocity expressions represent the excess energy gained by electronsfrom the conduction band discontinuities upon injection to the In0.10Ga0.90N staircase layer and theIn0.20Ga0.80N active layer, respectively. For simplicity, we assume that the electrons move in thenormal direction to the heterointerfaces which at the first sight suggest an overestimation. However,this assumption will not have a significant effect on the estimated probability.In calculating the percentage of the overflow current due to the electrons that experience only

one scattering event, we considered four different cases encompassing only one phonon emission orabsorption in each of the SEI and the active regions. Among the processes, the probability of only one

150 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

Fig. 10. Calculated (overflow electron current/total electron current) as a function of applied forward voltage across the InGaNactive region (6 nm In0.20Ga0.80N) for the LEDwithout staircase andwithout EBL, and the LEDwith 1-layer InGaN staircase (oneIn0.10Ga0.90N step layer before the active region) and without EBL. Symbols represent the calculated values and solid lines areguides to the eye. The inset shows the schematics for the LED with and without (dashed line) the staircase. It should be notedthat 0.5 V corresponds to a flat band case where the applied external voltage compensates the built-in potential within theactive region. For simplicity, a 1-layer staircase (one In0.10Ga0.90N step layer) was employed for the calculations.

phonon emission in the SEI region is given by:

p11 =

∫+∞

max{0,(ϕEBL−qV+h̄ωph )}f (E)N(E)

∫ d10 exp

(−x/v1 (E)τsc

)·

1v1 (E)·τem

·exp

(−(d1−x)/v1 (E−h̄ωph )

τsc

)·exp

(−d2 /v2 (E−h̄ωph )

τsc

)·dx·dE∫

+∞

0 f (E)N(E)dE

(10)

where τm is the phonon emission time, and h̄ωph is the phonon energy. Eq. (10) takes into account theprobabilities for a suitable electron (with E ≥ h̄ωph) to reach the position x (0 ≤ x ≤ d1 = 15 nm)without being scattered, to emit a phonon near x, and to exit the active regionwithout being scatteredbetween points x and d2. The integration over dx and dE accounts for all possible paths and all suitableelectrons within the realm of processes discussed above. The probability of only one phonon emissionin the active region is given by:

p12 =

∫+∞

max{0,(φEBL−qV+h̄ωph )}f (E)N(E)

∫ d10 exp

(−d1 /v1 (E)τsc

)·exp

(−(x−d1 )/v2 (E)

τsc

)·

1v2 (E)·τem

·exp

(−(d1+d2−x)/v2 (E−h̄ωph )

τsc

)·dx·dE∫

+∞

0 f (E)N(E)dE.

(11)

Similarly, we can obtain the probabilities for one phonon absorption events. These single scatteringevents account for∼10% of the overall electron overflow. The contribution of two scattering events tothe overflow electrons was also considered, but was found to be negligible (<1%). The total electronoverflow amount is obtained by summing the electron overflow due to both ballistic electrons (noscattering) and quasi-ballistic electrons (one scattering-like event) for LEDs with and without the SEIstructure.Fig. 10 shows the calculated percentile overflow electron current, namely the overflow electron

current divided by the total current for two DH LEDs without EBL representing the cases of withand without the SEI structure. Phonon emission, absorption, and scattering times of τem = 10 fs,τabs = 100 fs, and τsc = 9 fs, respectively, have been used for the calculations [56]. The sensitivity ofthe calculated overflow amount is tested by varying the τsc value from 8 to 16 fs, in which case theoverflow due to ballistic electrons for the staircase LED is increased from 4% to 18%. However, since allof the calculations use the same values for the above parameters, the validity of our discussion is notaffected. As mentioned previously, the calculated probabilities for the overflow by the electrons that

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 151

undergo two scattering events are negligible (≤1%). Therefore,most of these electrons are thermalizedin the active region. For a flat band DH case, the portion of the applied voltage needed to compensatethat due to the built-in voltage across the active region for this condition is 0.5 V which correspondsto 0.8MV/cm. For this bias condition, a significant portion (∼62%) of the total electron current is theoverflow electron current for the LED without a staircase and without EBL. However, for the LED witha 1-layer SEI, and also without EBL, the electron overflow is substantially reduced to∼8%.The results suggest that by employing a SEI structure the electrons are allowed to havemore transit

time due to reduced velocity owing to relatively small kinetic energy that they gain from a reducedband discontinuity, during which they could be thermalized by interacting with LO phonons. Thisfeature alone is very effective in substantially decreasing the electron overflow current. Obviously,more layers in the SEI (3 layers have been used for the LEDs discussed above) provide more freedomfor designing the optimal SEI. Particularly at high bias, more layers may be beneficial for efficientlycooling down the electrons. Note that each step barrier height needs to be equal to or larger than theLO phonon energy in the applicable material.To recap the experimental data presented heretofore, essentially the same EL performance

observed for the two DH LEDs with and without EBL when the SEI is employed before the activeregion is consistent with the above described calculations based on the premise of the ballistic andquasi-ballistic hot electrons as in the case with no SEI. The employment of the SEI structure nearlyeliminates the ballistic and quasi-ballistic electrons traversing the LED active regions.We should notealso that the electron overflow solely due to equilibrium thermionic emission is negligible (<1% evenfor the LEDwithout EBL) under the assumption that all the injected electrons are thermalized down tothe bottom of the InGaN active region (data not shown here). This conclusion holds for any reasonablejunction temperature that might be experienced by an LED even in extremely high injection levels.This means that the overflow current, not necessarily the experimentally observed efficiency loss athigher current, would be nearly junction temperature independent as the main process contributingto overflow is that due to ballistic and quasi-ballistic hot electrons. Also to be noted is that regardlessof whether the EBL is employed in a LED with the SEI does not make any discernable difference interms of the EL efficiency, and therefore, the electron overflow. The SEI electron cooler at the n-sideis a better solution than inserting an EBL as EBLs impede the hole injection to a certain degree (whichdepends on the Al composition used for the EBL and also the hole concentration that can be attained)due to the valence band offset between the EBL and p-GaN (∼0.08 eV for the case of EBL with 15% Al).

8. Conclusions

GaN-based InGaN LEDs are serious contenders for general lighting applications. They are alreadyknown to the general public in many ways than one and as LED lighting for general illumination.However, for this to come to fruition fully with the highest possible power conversion efficienciesin hand, the quantum efficiency loss at high injection currents must be overcome. As reviewed inthis paper, the loss of efficiency retention at high injection levels has so far been attributed to manyphenomenawhich include Auger recombination, carrier overflow, large effectivemass of holes whichalso provide an impediment to hole transport across the MQW region used, relatively low holeconcentration in the p-layer (particularly in relation to the electron concentration on the n-side),defects, and current crowding effects. In our investigations we used LEDs prepared on non-polarm-plane GaN, which eliminates the polarization charge and thus the field induced by it. To go withthe experiments, we developed a theoretical framework in which electrons injected into the activeregion do not thermalize fully and take part in the recombination processes and that substantialportion of them, particularly when electron blocking layers with sufficiently large barriers are notemployed, traverse the active region ballistically (without experiencing any scattering) and quasi-ballistically (suffering scattering with optical phonons, by e.g. emitting and absorbing optical LOphonons). Our calculations also indicate that thermionic emission is of no discernable consequence, asthe Boltzmann tail of equilibrium electrons cannot overcome the energy barriers present. This meansthat the overflow process would not be dependent of any reasonable junction temperature, whichmight be experienced during LED operation. However, this does not rule out any experimentallyobserved efficiency loss caused by processes such as current crowding and contact degradation.

152 X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153

The theoretical framework proposed is consistent with the experimental data that the ballistic andquasi-ballistic electrons play an important role in electron overflow (or spillover) in InGaN LEDs,which has resulted in a substantially reduced EL intensity for the LEDs without any electron blockinglayer (EBL). Further support for the proposed framework comes from experiments wherein theelectrons are allowed to cool and thermalizewith the use of a staircase electron injector (SEI) on n-GaNside of the active region. These staircase electron injector structures show no discernable dependenceon the presence or the absence of EBLs. Specifically, in order to thermalize these hot electrons andthereby to reduce the efficiency loss caused by electron overflow, InGaN SEI structures (with graduallyincreased In composition) were employed prior to the active region, which has resulted in essentiallythe same EL performance for the LEDs with and without EBL. Lack of any EBL is beneficial in that anybarrier presented to hole injection and transit is eliminated. Our calculation confirms that the insertionof a staircase injector structure is beneficial for a better electron thermalization and a reduced electronoverflow.

Acknowledgements

The work at VCU was supported by a grant from the National Science Foundation and AirForce Office of Scientific Research under the program monitor Dr. K. Reinhardt, and that at theSemiconductor Physics Institute, ‘‘Puslaidininkiu Fizikos Institutas (PFI)’’ was supported by AFOSRunder the Window on Science program AFMC (ITO–TEL-037).

References

[1] US Lighting Market Characterization, vol. I, National Lighting Inventory and Energy Consumption Estimates, USDepartment of Energy, 2002, Navigant Consulting, Inc., Washington, DC [Online]. Available at:http://apps1.eere.energy.gov/buildings/publications/pdfs/corporate/lmc_vol1_appendices.pdf.

[2] International Energy Agency, Light’s labours lost: policies for energy-efficient lighting, in support of the G8 plan of action,2006, p. 558.

[3] H. Morkoç, Handbook of Nitride Semiconductors and Devices, Volume 3, Wiley-VCH, 2008.[4] M.R. Krames, O.B. Shchekin, R. Mueller-Mach, G.O. Mueller, L. Zhou, G. Harbers, M.G. Craford, J. Display Tech. 3 (2007) 160.[5] Y.C. Shen, G.O. Mueller, S. Watanabe, N.F. Gardner, A. Munkholm, M.R. Krames, Appl. Phys. Lett. 91 (2007) 141101.[6] B. Monemar, B.E. Sernelius, Appl. Phys. Lett. 91 (2007) 181103.[7] I.V. Rozhansky, D.A. Zakheim, Semiconductors 40 (2006) 839.[8] I.V. Rozhansky, D.A. Zakheim, Phys. Status Solidi A 204 (2007) 227.[9] I.A. Pope, P.M. Smowton, P. Blood, J.D. Thomson, M.J. Kappers, C.J. Humphreys, Appl. Phys. Lett. 82 (2003) 2755.[10] M. Kim, M.F. Schubert, Q. Dai, J.K. Kim, E.F. Schubert, J. Piprek, Y. Park, Appl. Phys. Lett. 91 (2007) 183507.[11] M.F. Schubert, J. Xu, J.K. Kim, E.F. Schubert, M.H. Kim, S. Yoon, S.M. Lee, C. Sone, T. Sakong, Y. Park, Apl. Phys. Lett. 93 (2008)

041102.[12] A.A. Efremov, N.I. Bochkareva, R.I. Gorbunov, D.A. Larinovich, Yu.T. Rebane, D.V. Tarkhin, Yu.G. Shreter, Semiconductors

40 (2006) 605.[13] A.R. Beattie, P.T. Landsberg, Proc. R. Soc. Lond. A. 249 (1958) 16.[14] A.R. Beattie, P.T. Landsberg, Proc. R. Soc. Lond. A. 258 (1960) 486.[15] P.T. Landsberg, Proc. R. Soc. Lond. A. 331 (1972) 103.[16] P.T. Landsberg, M.J. Adams, Proc. R. Soc. Lond. A. 334 (1973) 523.[17] J. Hader, J.V. Moloney, B. Pasenow, S.W. Koch, M. Sabathil, N. Linder, S. Lutgen, Appl. Phys. Lett. 92 (2008) 261103.[18] J. Xie, X. Ni, Q. Fan, R. Shimada, Ü. Özgür, H. Morkoç, Appl. Phys. Lett. 93 (2008) 121107.[19] S.-H. Han, C.-Y. Cho, S.-J. Lee, T.-Y. Park, T.-H. Kim, S.H. Park, S.W. Kang, J.W. Kim, Y.C. Kim, S.-J. Park, Appl. Phys. Lett. 96

(2010) 051113.[20] X. Ni, Q. Fan, R. Shimada, Ü. Özgür, H. Morkoç, Appl. Phys. Lett. 93 (2008) 171113.[21] N.F. Gardner, G.O. Müller, Y.C. Shen, G. Chen, S. Watanabe, W. Götz, M.R. Krames, Appl. Phys. Lett. 91 (2007) 243506.[22] J.I. Pankove, Optical Processes in Semiconductors, Prentice Hall, Englewood Cliffs, NJ, 1971.[23] K.T. Delaney, P. Rinke, C.G. Van de Walle, Appl. Phys. Lett. 94 (2009) 191109.[24] H. Ryu, H. Kim, J. Shim, Appl. Phys. Lett. 95 (2009) 081114.[25] G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Götz, F. Steranka, Phys. Status Solidi A 205 (2008)

1086.[26] K.A. Bulashevich, S.Y. Karpov, Phys. Status Solidi C 5 (2008) 2066.[27] X. Li, H. Liu, X. Ni, Ü. Özgür, H. Morkoç, Superlattices Microstruct. 47 (2010) 118.[28] Ü. Özgür, H. Liu, X. Li, X. Ni, H.Morkoç, Proc. of IEEE on Challenges andOpportunities in GaN and ZnODevices andMaterials,

Proc. of IEEE (2010) (special issue) (in press).[29] P.G. Eliseev, Appl. Phys. Lett. 75 (1999) 3838.[30] C.B. Su, J. Schafer, J. Manning, R. Olshansky, Electron. Lett. 18 (1982) 1108.[31] S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Matushita, T. Mukai, J. Nitride Semicond. Res. 4S1 (1999) G1.1.[32] M.J. Galtrey, R.A. Oliver, M.J. Kappers, C.J. Humphreys, D.J. Stokes, P.H. Clifton, A. Cerezo, Appl. Phys. Lett. 90 (2007) 061903.

X. Ni et al. / Superlattices and Microstructures 48 (2010) 133–153 153

[33] M.F. Schubert, S. Chhajed, J.K. Kim, E.F. Schubert, D.D. Koleske, M.H. Crawford, S.R. Lee, A.J. Fischer, G. Thaler, M.A. Banas,Appl. Phys. Lett. 91 (2007) 231114.

[34] X. Guo, E.F. Schubert, Appl. Phys. Lett. 78 (2001) 3337.[35] H.Y. Liu, V. Avrutin, N. Izyumskaya, M.A. Reshchikov, Ü. Özgür, H. Morkoç, Phys. Status Solidi Rapid Lett. 4 (2010) 70.[36] X. Li, H.Y. Liu, S. Liu, X. Ni, M. Wu, V. Avrutin, N. Izyumskaya, Ü. Özgür, H. Morkoç, Phys. Status Solidi A, unpublished.[37] A.A. Efremov, N.I. Bochkareva, R.I. Gorbunov, D.A. Larinovich, Yu.T. Rebane, D.V. Tarkhin, Yu.G. Shreter, Semiconductors

40 (2006) 605.[38] R. Langer, J. Simon, V. Ortiz, N.T. Pelekanos, A. Barski, R. Andre, M. Godlewski, Appl. Phys. Lett. 74 (1999) 3827.[39] T. Deguchi, K. Sekiguchi, A. Nakamura, T. Sota, R. Matsuo, S. Chichibu, S. Nakamura, Japan. J. Appl. Phys. 38 (1999) L914.[40] Y.J. Sun, O. Brandt, S. Cronenberg, S. Dhar, H.T. Grahn, K.H. Ploog, P. Waltereit, J.S. Speck, Phys. Rev. B 67 (2003) 041306.[41] P. Waltereit, O. Brandt, A. Trampert, H.T. Grahn, J. Menniger, M. Ramsteiner, M. Reiche, K.H. Ploog, Nature 406 (2000) 865.[42] H.M. Ng, Appl. Phys. Lett. 80 (2002) 4369.[43] M.D. Craven, S.H. Lim, F. Wu, J.S. Speck, S.P. DenBaars, Appl. Phys. Lett. 81 (2002) 469.[44] A. Niwa, T. Ohtoshi, T. Kuroda, Appl. Phys. Lett. 70 (1997) 2159.[45] M. McLaurin, T.E. Mates, F. Wu, J.S. Speck, J. Appl. Phys. 100 (2006) 063707.[46] M. McLaurin, J.S. Speck, Phys. Status Solidi (RRL) 3 (2007) 110.[47] X. Ni, J. Lee, M. Wu, X. Li, R. Shimada, Ü. Özgür, A.A. Baski, H. Morkoç, T. Paskova, G. Mulholland, K.R. Evans, Appl. Phys.

Lett. 95 (2009) 101106.[48] Q. Dai, M.F. Schubert, M.H. Kim, J.K. Kim, E.F. Schubert, D.D. Koleske, M.H. Crawford, S.R. Lee, A.J. Fischer, G. Thaler,

M.A. Banas, Appl. Phys. Lett. 94 (2009) 111109.[49] A. Niwa, T. Ohtoshi, T. Kuroda, Appl. Phys. Lett. 70 (1997) 2159.[50] J. Lee, X. Li, X. Ni, Ü. Özgür, H. Morkoç, T. Paskova, G. Mulholland, K.R. Evans, Appl. Phys. Lett. 95 (2009) 201113.[51] X. Ni, X. Li, J. Lee, S. Liu, Ü. Özgür, H. Morkoç, A. Matulionis, T. Paskova, G. Mulholland, K.R. Evans, Phys. Status Solidi. RRL,

unpublished.[52] K.T. Tsen, R.P. Joshi, D.K. Ferry, A. Botchkarev, B. Sverdlov, A. Salvador, H. Morkoç, Appl. Phys. Lett. 68 (1996) 2990.[53] J. Liberis, I. Matulionienë, A. Matulionis, M. Ramonas, L.F. Eastman, Hot phonons in high-power microwave HEMT and

FET channels, in: Ho-Young Cha (Ed.), Advanced Semiconductor Materials and Devices Research: III-Nitrides and SiC,Transworld Research Network, 2009.

[54] X. Ni, X. Li, J. Lee, S. Liu, V. Avrutin, Ü. Özgür, H. Morkoç, A. Matulionis, J. Appl. Phys., unpublished.[55] X. Ni, X. Li, J. Lee, S. Liu, Ü. Özgür, H. Morkoç, A. Matulionis, T. Paskova, G. Mulholland, K.R. Evans, IEEE Photon. Technol.

Lett., unpublished.[56] J. Liberis, I. Matulionienë, A. Matulionis, M. Ramonas, L.F. Eastman, in: Ho-Young Cha (Ed.), Advanced Semiconductor

Materials and Devices Research: III-Nitrides and SiC, Transword Research Network, Kerala, India, 2009, pp. 203–257.