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The convergence of longitudinal excitons onto the Γ5 transverse exciton in GaN and the

thermal activation energy of longitudinal excitons

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2013 J. Phys.: Condens. Matter 25 335803

(http://iopscience.iop.org/0953-8984/25/33/335803)

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IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 25 (2013) 335803 (9pp) doi:10.1088/0953-8984/25/33/335803

The convergence of longitudinal excitonsonto the 05 transverse exciton in GaN andthe thermal activation energy oflongitudinal excitons

Amal Elgawadi, Gordon Gainer and Jerzy Krasinski

School of Electrical and Computer Engineering, Oklahoma State University, 202 Engineering South,Stillwater, Oklahoma 74078-5032, USA

E-mail: aelgaw01@hotmail.com (Amal Elgawadi)

Received 29 April 2013, in final form 5 July 2013Published 24 July 2013Online at stacks.iop.org/JPhysCM/25/335803

AbstractThe crystal orientation dependence of GaN excitons was investigated via thephotoluminescence (PL) technique. The PL emissions at a temperature of 10 K were obtainedfrom two experimental configurations where the emission K vector (the propagation vector)was either parallel (K ‖ c) or perpendicular (K ‖ c) to the crystal c-axis. Longitudinal,transverse and donor-bound excitons were observed in the two configurations. However, thelongitudinal excitons converged onto the transverse free exciton 05 in the K ⊥ c emission.This behavior was discussed in terms of electron screening due to the scattering of electronsmoving perpendicular to charged dislocation lines. Additionally, the thermal activation energyof the longitudinal excitons was calculated from the temperature dependent PL measurementscollected from the K ‖ c emission, and was found to be 5 to 6 times as high as the bindingenergy of the free excitons. This high energy was interpreted tentatively in view of the creationof polaritons in strong exciton–photon coupling regimes. These findings present fundamentalconcepts for applications such as vertical cavity surface-emitting lasers (VCSELs) andpolariton lasers.

(Some figures may appear in colour only in the online journal)

1. Introduction

Wide bandgap semiconductors have many applications inoptoelectronic and microelectronic devices, such as GaNbased light emitting diodes (LEDs), laser diodes (LDs),ultraviolet detectors, high temperature, high power andhigh frequency electronic devices [1–8]. With edge-emittingGaN-based lasers in commercial systems, attention isshifting to more demanding and rewarding emitters includingmicrocavity (MC)-based vertical cavity surface-emittinglasers (VCSELs) and polariton lasers. The impetus centerson applications such as high-speed/high-resolution laserprinting/scanning technology, lighting and new types ofcoherent but nearly threshold less optical sources [9].

III-nitrides are one of the most promising materials forpolariton devices with a wide range of applications such asGaN nanowire polariton lasers [10]. Polaritons are definedas the stable coupled mode eigenstates of excitons andphotons in a crystal [11]. The first room-temperature polaritonlaser with optical pumping was reported recently [12].Observation of spontaneous emission buildup in polaritonlasing emission is attributed to a Bose–Einstein condensateof cavity polaritons [9]. Recently optimized schemes ofelectrically pumped polariton lasers based on GaN MCs arediscussed in the literature [13]. Additionally, wide bandgapsemiconductor-based VCSELs based on polariton lasers wereproposed [14]. Tunable terahertz lasers expected to have

10953-8984/13/335803+09$33.00 c© 2013 IOP Publishing Ltd Printed in the UK & the USA

J. Phys.: Condens. Matter 25 (2013) 335803 A Elgawadi et al

wide areas of applications in many areas such as medicine,communication technologies and security.

However, because of the lack of suitable native substrates,GaN epilayers are usually grown on foreign substrates suchas Al2O3 (sapphire), SiC, and Si. Consequently, the epilayersexperience a considerable biaxial strain due to thermal andlattice mismatch. Among these foreign substrates, sapphireis especially attractive because of its low cost and largesize availability. The large difference between the latticeconstant of sapphire and that of GaN (∼14% for hexagonalsystem) and the great difference in their thermal expansioncoefficients give rise to mismatch strain [15]. This straingenerates dislocation and defects that have powerful effectson the optical and electrical properties of GaN epilayers.

We present a study about the effect of the orientationof the strain-induced dislocations on the longitudinal excitonin GaN. Longitudinal excitons occur because of a strongcoupling between free excitons and photons. It is known thatGaN has a columnar, hexagonal growth structure [16]. Ifmore than one columnar structure direction is present, thenthe PL should reveal more than one mode of longitudinalexcitons. Hopfield et al [17] stated ‘it is expected that as thecrystal is rotated, the longitudinal line should converge on thetransverse one’. However, this was not observed in neitherHopfield et al work on CdS [17] nor Reynolds et al work onGaN [23].

In this paper, we report the convergence of the GaNlongitudinal excitons onto the transverse free exciton 05in the K ⊥ c emission configuration, which we believearen’t being reported in the literatures. Thus, the longitudinalexciton is crystal orientation dependent. This observation wasinterpreted in section 4 in terms of electron screening dueto the scattering of electrons moving perpendicular to straininduced charged dislocation lines. In addition, in section 3,we calculated the thermal activation energy of the GaNlongitudinal excitons from the temperature dependent PL thatwe believe aren’t reported in the literatures to the best ofour knowledge. The activation energies of two longitudinalexcitons were found to be 5–6 times as high as the freeexcitons binding energies. We discussed tentatively, thesehigh energies in view of the creation of polaritons in strongexciton–photon coupling regime. Strong-coupling effects [18]and polariton lasing [10, 19] are currently subjects of intenseresearch.

This paper is organized mainly as follows: after thisintroduction, section 2, the experimental procedure. Insection 3, we identified the excitons observed in the K ‖c PL emission via comparison to the results reported inthe literatures; the analysis of the obtained data using theVarshni equation and the thermal activation energies. Also, wereported the value of the estimated c-axis strain, εc, that wemeasured by two methods, high-resolution x-ray diffraction(HRXRD) and PL, for verification. The strain is explained inthe context of strain effects induced by the lattice mismatchbetween sapphire and GaN. The effect of the polarizabilityon the longitudinal excitons was investigated too. The highvalues of the thermal activation energies of the longitudinalexcitons were reported and interpreted tentatively in this

Figure 1. The sample geometry for photoluminescence (PL)measurements. The emission K vector is oriented toward thespectrometer slit.

section. In section 4, we show the results of the K ⊥ c PLemission mainly the convergence of the longitudinal excitonsinto the transverse free exciton 05 with interpretation in viewof electron screening. Finally we concluded.

2. Experimental procedure

The sample studied was 2 µm thick of undoped GaNlayer grown on c-plane sapphire by hydride vapor-phaseepitaxy technique (HVPE) followed by a much thinner40 nm undoped AlxGa1−xN layer where x = 0.15 asobtained by HRXRD technique. Photoluminescence (PL)measurements were carried out using the 3250 A lineof a cw HeCd laser. The sample was mounted in avariable-temperature angle-adjustable cryostat cooled bya closed-cycle helium refrigerator. The PL spectra wererecorded with a photomultiplier tube in conjunction witha 1 − m high-resolution double-grating spectrometer.The PL emissions were obtained from two experimentalconfigurations where the emission K vector (the propagationvector) was either parallel (K ‖ c) or perpendicular (K ⊥ c) tothe c-axis as seen in figure 1. The temperature dependent PLmeasurements were taken from the K ‖ c configuration only,while the K ⊥ c emission was just taken at temperature of10 K.

3. K ‖ c PL emission (designation of the excitons andstrain estimation)

The temperature dependent PL spectra (K ‖ c) are shownin figure 2. Here, two transverse free excitons 05 and 06dominate the spectra with transition energies of 3.490 eV and3.484 eV, respectively at temperature of 10 K. The separationbetween the two free excitons is 5.9 meV, in excellentagreement with Fang et al [20] report for a similar structure;Al0.15Ga0.85N/GaN heterostructure grown on (0001) sapphireby metal organic chemical vapor deposition (MOCVD). Theyreported photon energies of 3.492 eV and 3.486 eV for 05 and

2

J. Phys.: Condens. Matter 25 (2013) 335803 A Elgawadi et al

Figure 2. Photoluminescence spectra as a function of temperature.The spectra are displaced vertically for clarity. Sample geometrieswere K ‖ c. For clarity, the plots are displaced vertically.

06, respectively, yielding a separation of 6.0 meV. 05 and 06were also observed in freestanding 200 µm thick GaN grownon sapphire by the HVPE technique [21, 22] and in ZnO [23].The analysis of the intensity variation with temperature ofthe excitons in this paper has been carried out using the wellknown thermal activation model [24–26]:

IPL(T) =IPL(T0)

1+∑n

i=1 αi exp(−Eai(T)kBT )

(1)

where IPL(T) is the PL intensity at temperature ofT K, IPL(T0) is the PL intensity at temperature of 0 K, αi areconstant(s) determined from the fitting of the equation to theexperimental data points, kB is Boltzmann’s constant, Eai(T)are the activation energy(s) of an exciton and n is the numberof thermal activation terms in the equation. In this paper, nequal 1 or 2.

Figure 3 shows the variation of the intensity of 05 and 06free excitons as a function of the temperature. Two differenttemperature regimes can be distinguished for each free excitonyielding two activation energies to satisfactory fit of the free

Figure 3. Arrhenius plots of the normalized integrated intensitiesversus the inverse of temperature for the transverse free excitons 05and 06, the donor-bound excitons D(05) and D(06), and thelongitudinal excitons Lx1,Lx2, and Lx3. The resulting data was fittedto the solid lines using equation (1) with two-channel model for05, 06,D(05) and D(06); one-channel model for Lx1,Lx2, and Lx3.Sample geometries were K ‖ c. For clarity, the plots are displacedvertically.

exciton data points to equation (1) with n = 2. At verylow temperatures, up to 15 K for 05 and 20 K for 06, theintensity remains constant with a low activation energies of5.68 meV for 05 and 6.0 meV for 06. Above these values, avery rapid quenching is observed, indicating the free excitonsdissociation with binding energies of 25.26 meV for 05 and24.0 meV for 06. The last two values are in the vicinity ofthe reported binding energies of 0V

7 and 0V9 (A and B free

excitons) [27] i.e. from 20 to 28 meV for A-exciton and from18 to 26 meV for B-exciton [21, 27].

From group theory arguments [28] 0V7 and 0V

9 transformto 0V

5 and 0V6 when the crystal field is modified by applied

magnetic field and/or strain [23, 29, 30]. The band gap energyis defined as the sum of the free exciton transition energyE05

PL = 3.490 eV and its binding energy E05B = 25.26 meV,

namely [31]

E(T=10 K)g (PL) = (E05(T=10 K)

PL + E05B ) eV. (2)

Therefore, the deduced bandgap for our GaN layer isE(T=10 K)

g (PL) = 3.515 26 eV at temperature 10 K. Theband gap for strain-free bulk GaN is 3.5 eV and 3.39 eVat temperatures of 1.6 K and 300 K, respectively. Clearly,in our epilayer the bandgap, E(T=10 K)

g (PL), is blue-shiftedapproximately 15.26 meV due to the significant mismatchbetween the lattice constants of the sapphire substrate andthe thin 2.0 µm GaN layer and the difference between theirthermal expansion coefficients. This indicates that the crystalis under high strain. Deviation of the free exciton energiesin thin GaN epilayers on sapphire from the values reportedfor strain-free ones was explained by the strain effect, Zhanget al [32] and Volm et al [31]. Volm et al [31] reportedfor GaN epilayers grown on sapphire; A-exciton energies of

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J. Phys.: Condens. Matter 25 (2013) 335803 A Elgawadi et al

3.4799 eV and 3.4962 eV for thicknesses 400 µm and 3.0 µmat temperature of 1.5 K, respectively. This shows that thestrain effect blue-shifted the photon energy of the A-exciton16.3 meV, as the thickness decreased. Likewise the B-excitonshowed blue-shift of 10 meV [31].

The strain-induced energy shift for the free A-excitonwas determined experimentally by Shikanai et al [33] forGaN epilayers with thicknesses of 0.004–10 µm grown byMOCVD on sapphire. They obtained the transition energiesof the A-exciton for the epilayers, Eepi

A , using photoreflectance

(PR) and PL at 10 K. EepiA was found to depend linearly on

the c-axis strain at the surface of the epilayer, εc, accordingto Eepi

A = (EBulkA + 15.4εc) eV = (3.478 + 15.4εc) eV, this

equation is the least-square fitting to the data they obtainedfrom their samples at 10 K. The value of EBulk

A = 3.478 eVfor bulk GaN at 2 K was obtained by Monemar et al [34].However, Monemar et al [35] and Dingle et al [36] wereobtained EBulk

A = 3.4751 eV at 1.6 K and EBulkA = 3.474 eV

at 2 K, respectively. We used the relation with the averagevalue, EBulk

A (average) = 3.4759 eV, of the reported EBulkA in

the three indicated references to approximately estimate thec-axis strain at the surface of our epilayer, εPL(T=10 K)

c , usingthe PL data at temperature of 10 K. That is

E(05) = (EBulkA (average)+ 15.4εPL(T=10 K)

c ) eV

= (3.4759+ 15.4εPL(T=10 K)c ) eV, (3)

where εc = (c − c0)/c0; c0 and c are the lattice parametersfor the strain-free bulk GaN and strained GaN epilayerrespectively. Accordingly, the strain at the surface of our2 µm thick GaN epilayer on sapphire determined by the PL isε

PL(T=10 K)c = 9.29 × 10−4 at temperature of 10 K. From the

HDXRD measurements, we obtained the c-axis strain of theepilayer, εHDXRD(T=RT)

c = 7.72 × 10−4 at room temperature,compared to 8.82 × 10−4, obtained for 3.3 µm thick GaNepilayer grown on sapphire by Zhang et al [32]. We would liketo emphasize that we calculated εPL(T=10 K)

c optically from theexciton energies measured at 10 K while εHDXRD(T=RT)

c wefound via the HRXRD was determined at room temperature.However, additional strain emerging from further cooling to10 K is expected [32]. This extra strain can be deduced fromexisting thermal expansion coefficient (CTE) measurementsbetween RT and 10 K. Following the method detailed in [32],it is expected therefore that HDXRD measurements wouldyield εHDXRD(T=10 K)

c = 9.26 × 10−4 at 10 K, in excellentagreement with the our PL estimation of the c-axis strain atthe surface, εPL(T=10 K)

c = 9.29 × 10−4. The variation in thebandgap of GaN at 10 K as a function of the biaxial stress canbe expressed by [32]

E(T=10 K)g (εc) = EBulk

g + bgεPL(T=10 K)c

= [3.5+ (14.2)× (9.29× 10−4)] eV (4)

where the value of bg = 14.2 eV is the potential deformationof the bandgap obtained for GaN at temperature of4 K [32]. Using equation (4) we approximately estimatedE(T=10 K)

g (εc) = 3.513 eV, in good agreement with value of

E(T=10 K)g (PL) = 3.515 26 eV we obtained using equation (2).

Also, two shoulders were seen in figure 2 at transitionenergies below that of 06. They collapsed at faster ratethan the free excitons as the temperature increases. Thisbehavior including the position, separation and intensityrelative to 06 are comparable to those reported in [20, 21, 23]for donor-bound excitons. The two shoulders identified astwo donor-bound excitons D(05) and D(06) associated withthe free excitons 05 and 06, respectively, since highertemperatures free bound excitons thus creating free excitonsand free donors [37].

The former located 12.4 and 6.5 meV below 05 and 06respectively at photon energy of 3.478 eV. Figure 3 shows a fitfor the Arrhenius plots of integrated PL intensity for D(05) asa function of the temperature following the equation (1) withn = 2. The thermally activated dissociation of a bound exciton(BX) involves two activation energies [25]. The higher is itsbinding energy Ea1(T) = EBX

B from which we can define theassociated free exciton while the lower is the bound excitonlocalization energy Ea2(T) = EBX

Loc. Where BX in our case arethe donor-bound excitons D(05) and D(06). Accordingly, thefitting gave ED(05)

Loc = 4.4 ± 0.14 meV and ED(05)B = 14.0 ±

0.2 meV for 05. The later is in excellent agreement with theseparation between 05 and D(05) transition energy, 13.6 meV,which proves that 05 is the associated free exciton to thedonor-bound exciton D(05) i.e. D(05)→ 05 + D1.

The second shoulder is 10.4, 16.9 and 22.8 meV belowD(05), 05 and 06 respectively at transition energy 3.467 eVas seen in figure 2. This shoulder is corresponding to thedonor-bound exciton D(06) associated with 06. The fittingobtained by equation (1) with n = 2 is shown in figure 3.The fitting gave ED(06)

Loc = 9.84 ± 0.02 meV and ED(06)B =

16.43 meV. The binding energy obtained for this shoulderis in an excellent agreement with the separation between thisshoulder and 06, 16.9 meV. This is an indication that this peakis another donor-bound exciton, D(06), associated with 06 i.e.D(06)→ 06+D2. It is worth noting that the large differencebetween the localization energies, ED(05)

Loc = 4.4 ± 0.14 meV

and ED(06)Loc = 9.84 ± 0.02 meV is evidence that the two

shoulders did not originate from the same source i.e. they arefor two donor-bound excitons [25].

Generally, epitaxial layers of GaN contain a highdensity of dislocations, due to the absence of a suitablelattice-matched substrate for epitaxial growth. The occurrenceof two defect-induced donor states indicates the existence ofthreading dislocations (TDs) caused by the GaN/sapphire lat-tice mismatch and unintended doping [38]. High dislocationdensity is generated at the GaN/sapphire interface [39–44].The density of dislocations decreases with increasing the filmthickness [45]. These dislocations are predominantly orientedparallel to the c-axis of the material [46]. In principle, thestrain distribution associated with the dislocations may alsobe expected to have a pronounced influence through thepiezoelectric effect, which is known to be strong in the nitridematerials [47]. As the temperature increases the donor-boundexcitons dissociated to donors and free excitons thusgenerating free carriers that screen the piezoelectric-inducedpolarization hence reducing the polarizability, which wouldreduce the longitudinal–transverse separation.

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J. Phys.: Condens. Matter 25 (2013) 335803 A Elgawadi et al

The temperature dependent PL spectra showed also threeshoulders at higher energies than the transverse excitons asseen in figure 2. We believe they are longitudinal excitonsdenoted Lx1,Lx2 and Lx3 at photon energies of 3.497 eV,3.506 eV, and 3.516 eV, respectively. The separations betweenthe longitudinal excitons and 05 in the same order areapproximately 6.9 meV, 15.7 meV and 25.8 meV. Thesevalues are in the vicinity of the values reported in [20]for the similar structure, where the transition energies were3.492 eV for 05 and 3.505 eV for the only longitudinal excitonthey observed, at temperature of 10 K, giving separation of13.0 meV. The formation of three longitudinal-mode excitonsin our sample is associated with the existence of threecolumns or hexagonal grains having different orientations dueto GaN/substrate lattice mismatch [21, 22].

Arrhenius plots of integrated PL intensity for the threelongitudinal excitons as a function of the temperature areshown in figure 3 following equation (1) with one-channelthermal activation term (n = 1). The fitting provided thermalactivation energies: ELx1

a (T) = 153 ± 7 meV,ELx2a (T) =

107 ± 4 meV and ELx3a (T) = 11.8 ± 1 meV. Clearly,

ELx1a and ELx2

a are approximately 5–6 times as high as thebinding energies of 05 and 06 which indicate that theseexcitons aren’t free excitons. To the best of our knowledgethere are no reports for the activation energy of III-nitrideslongitudinal excitons. However, a tentative interpretation ofthe very high ELx1

a and ELx2a in view of strongly coupled

semiconductors is following. In strongly polar materials suchas GaN and ZnO, transverse free exciton 05 couples stronglywith photons to form polaritons, Morkoc [48–50]. In otherwords, the usual transverse 05-exciton dispersion, Eex =

Eex,0+h2k2ex/2mex, will mix with the dispersion of the photon,

Ephoton = hckphoton, to produce two new dispersion curvesknown as the upper polariton branch (longitudinal exciton)and the lower polariton branch, Morko [48] and Voos [51].The longitudinal exciton energy is therefore defined as theenergy of the interacting exciton and photon [52].

The minimum energy splitting between the upper and thelower polariton branches is known as Rabi splitting (�). �and the longitudinal exciton thermal activation energy wererelated to each other in a strong exciton–photon coupledorganic semiconductor J-aggregate regime [53] where anArrhenius thermal activation energy of 25 meV was found tobe corresponding to a tuned � = 25 meV. This indicates thattuning Rabi splitting could affect the light–matter interactioni.e. influence the strength of exciton–photon coupling.The longitudinal exciton activation energies we obtainedELx1

a (T) = 153 ± 7 meV and ELx2a (T) = 107 ± 4 meV

are in the vicinity of the reported giant � of III-nitride rangedfrom 50 to 125 meV depending on the structure [54–56]. Thisindicates that our sample is subject to a strong exciton–photoncoupling. Thorough assessment of the correlation among Rabisplitting, longitudinal activation energy and exciton–photoncoupling is beyond the scope of this study and would be asubject for future comprehensive investigation.

Regarding the third longitudinal exciton energy ofELx3

a (T) = 11.8 meV, when it added to its transition energy,

3.5158 eV, the sum is 3.5276 eV which is much higher thanE(T=10 K)

g (PL) = 3.515 26 eV and E(T=10 K)g (εc) = 3.513 eV

which we calculated from equations (2) and (4), respectively.That indicates that this peak isn’t for a free exciton. However,the lower value of ELx3

a (T) = 11.8 meV relative to ELx1a and

ELx2a is consistent to the fact that Lx3 vanished at much lower

temperature (T > 80 K) than that of Lx1 and Lx2 (T > 150 K).The photon energies of the free excitons as functions of

the temperatures are shown in figure 4(a) together with thefittings to the Varshni’s equation [57],

EPL(T) = EPL(T0)− βT2/(γ − T) (5)

where EPL(T) is the photon energy at temperature of T Kand EPL(T0) is the transition energy at temperature of 0 K.β and γ are Varshni temperature parameters. The parametersextracted from the fitting to equation (5) are β = (8.0± 1.0)×10−5 eV K−1 for both 05 and 06, γ = 115 ± 9 K for 05, andγ = 240± 48 K for 06. Reynolds et al [22] have examined thelongitudinal excitons. They concluded that the longitudinalexciton transitions shift to lower energies with increasingtemperature at faster rate than do other exciton transitions,since the strain and accordingly the polarizability has sometemperature dependence. The splitting between the transverse(05) and longitudinal excitons (Lx) is given by [58–61].

ELxPL(T)− E05

PL(T) = E05PL(T)[4πP(T)/D] (6)

where ELxPL(T) is the photon energy of the longitudinal exciton

as a function of the temperature T,E05PL(T) is the photon

energy of the free exciton 05 as a function of the temperatureT,P(T) is the polarizability as a function of the temperatureT , and D is the dielectric constant, which varies between 5.15and 5.73 depending on the author [21]. The polarizability asa function of the temperature calculated using equation (6)with D = 5.15 is shown in figure 4(b). The values of thepolarizability we obtained vary from 1.2 × 10−3 to 6.0 ×10−3 compared to the values reported for GaN (1.16 × 10−3

and 2.2 × 10−3) [21, 61], CdS (14 × 10−3) [52] and ZnO(7.7× 10−3) [52]. Clearly, the polarizability decreased as thetemperature increased. The solid lines shown in figure 4(b)are the linear fits of the experimental data which haveapproximately the same slopes ∼10−6 K−1.

A longitudinal exciton therefore has two factorscontributing to its energy shift with increasing temperature:(1) the red-shift in the band gap, which observed in otherexcitons transitions and (2) the decrease in the polarizability.That explain why the longitudinal excitons red-shifted atfaster rate than the free excitons with increasing temperature,Reynolds et al [22]. They matched the energy shift of thelongitudinal excitons with a linear and a quadratic temperaturedependent to the Varshni equation as follows:

EPL(T) = EPL(T0)− βT2/(γ − T)

− [γ1T + γ2T2] × 10−3 (7)

where the parameters β = (8.0 ± 1.0) × 10−5 eV K−1 andγ = 115 ± 9 K are the same as those used for 05 whichindicates the association of the longitudinal excitons with 05.

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J. Phys.: Condens. Matter 25 (2013) 335803 A Elgawadi et al

Figure 4. (a) Temperature dependence of the photon energy positions of the transverse free excitons, 05 and 06, and the longitudinalexcitons Lx1,Lx2, and Lx3. The dots are plots of experimental data, while the solid lines are fits to these data using equation (5) for 05 and06, and equation (7) Lx1,Lx2, and Lx3. (b) Temperature dependence of the polarizability of Lx1,Lx2, and Lx3. The dots are the polarizabilitycalculated using equation (6), whilst the solid lines are the linear fits. Sample geometries were K ‖ c.

In our work, the three longitudinal excitons shifted to lowerenergies with increasing temperature at faster rate than thefree excitons transitions as seen in figure 4, in agreementwith Reynolds et al [22] observation. This proves that thesepeaks are for longitudinal excitons. The parameters γ1 =

−2.16 ± 0.0357 eV K−1 and γ2 = 0.515 ± 0.0027 eV K−1

are the same for the three longitudinal excitons, in consistentwith the constant rate of the decrease in their polarizabilitieswith temperatures, as seen in figure 4(b). This shows that theeffect of the polarizability on the red-shift of the longitudinalexcitons is higher than that of the free excitons.

4. K ⊥ c PL emission (convergence of Lxs onto 05)

Hopfield et al [17] stated ‘it is expected that as the crystalis rotated the longitudinal line should converge on thetransverse line’. This was not observed in neither Hopfieldet al work on CdS [17] nor Reynolds et al work on GaN [23].They attributed this behavior to the rapid broadening of thelongitudinal line as the crystal rotated. In our work, foremission K ⊥ c, all longitudinal excitons disappeared and thehighest energy line (the longitudinal line in case of K ‖ c) wasred-shifted as seen in figure 5. Furthermore, 05 and D(05)

are red-shifted so that the transition energies are 3.489 eV for05 and approximately 3.477 eV for D(05) i.e. the red-shiftwas 1.0 meV for 05 and approximately 0.7 meV for D(05).Therefore, the transition energy separation between the two

transverse excitons, 05 and 06, was reduced to 5.1 meVinstead of 5.9 meV in the case of the K ‖ c emission.Insignificant energy shift for 06 and D(06) were observed asseen in figure 5. In addition, the oscillator strength of 05 washigher than that of 06 in the case of K ‖ c emission; however,it was lower in the case of K ⊥ c emission at the sametemperature of 10 K. These observations indicate that thelongitudinal excitons have energies and oscillator strengthsdepend on the direction of propagation and they are stronglycoupled to the transverse free exciton 05.

These behaviors are somehow analogous to Reynoldset al [21] observations for a 200 µm thick freestandingGaN layer, which was originally grown on c-plane sapphireby HVPE. They excited the crystal simultaneously with aHeCd (3250 A) laser which excites electrons across thegap and with an argon-ion laser (Ar+) 5145 A that had avariable pump power, in the range of milliwatts, which excitedadditional electrons thus reduced the exciton polarizability,as they reported. This reduced the longitudinal–transverseexciton separation i.e. the longitudinal excitons were red-shifted to lower energies toward the transverse excitons. Thered-shift was increasing with increasing the (Ar+) laser powerintensity i.e. the longitudinal exciton was converging onto thetransverse exciton. Further, there was no energy shift of theother excitons.

The large lattice mismatch of GaN epitaxy depositedon sapphire substrate leads to high dislocation densityfrom 108 cm−2 [62, 63] to 1011 cm−2 [64]. Dislocations

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J. Phys.: Condens. Matter 25 (2013) 335803 A Elgawadi et al

Figure 5. The PL emission from the two experimental configurations, K ‖ c and K ⊥ c, at temperature of 10 K. The lower part shows theconvergence of the longitudinal excitons (Lxs) onto the transverse free exciton 05. The upper part zooms on the free excitons. It illustratesthe red-shift of 05 in the case of K ⊥ c emission. It shows also that the oscillator strength of 05 was higher than that of 06 in the case ofK ‖ c emission; however, it was lower in the case of K ⊥ c emission at the same temperature of 10 K.

originate at the film/substrate interface [39–41] where theirdensity decreases with increasing the film thickness [45].Transmission electron microscopy (TEM) has shown highdensity of screw dislocation near the substrate–bufferinterface in addition to high edge dislocation densitieswith edge dislocation lines threading extended from thesubstrate–buffer interface to the epilayer surface [40]. Inepitaxial GaN films, edge dislocation density is higher thanthe screw dislocation density [62]. The highly dislocatedwurtzite crystal can be described as hexagonal columns orprisms rotated relatively to each other by a small angle,with inserted atomic planes to fill the space between twocolumns [65] as illustrated in [22]. TEM investigations, etchpit counts, and planar electron micrograph reveal isolatedsingle dislocation lines rather than dislocation arrays. Inaverage, there is only one TD line per prism [65].

The dislocation lines are associated with traps alongthe dislocation lines [65–67]. Empty traps are electricallyneutral while each filled trap carries one electronic charge.

The negatively charged lines act as Coulomb scatteringcenters. Many techniques such as scanning capacitancemicroscopy [68], electron holography [69] and positronspectroscopy [70] proved that edge dislocation is negativelycharged. Therefore, electron traveling parallel to thedislocations is unaffected by the scattering at the chargeddislocation lines due to the repulsive potential aroundthe charged dislocation lines, Weimann et al [65]. Theyconcluded: ‘vertical devices are unaffected by the scatteringof electrons at the TD lines due to the repulsive bandbending around dislocations and the directional dependenceof dislocation scattering. This may explain the observedperformance of LEDs and LDs even in the presence of highdislocation densities of GaN grown on sapphire or SiC’.However, the TDs cause current leakage under reverse biasfor p–n junction devices such as field-effect transistors [71]and high-electron-mobility transistors [72]. Look et al [73]developed a charged dislocation line scattering theory, whichpointed out that the scattering due to dislocation line

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J. Phys.: Condens. Matter 25 (2013) 335803 A Elgawadi et al

charges is two-dimensional, that is only electrons movingperpendicular to the dislocation lines will be scattered.

We believe that the appearance of the longitudinalexcitons in the K ‖ c emission is due to electrons transferparallel to the dislocation lines. These electrons do notscatter at the charged dislocation line according to Looket al [73]. Therefore, a number of electron–hole pairsis generated, sufficient to create high rate of radiativerecombination as indicated by the high oscillator strengthof the transverse free excitons, 05. Accordingly, sufficientinteraction between 05 and photons are present, whichformed the associated longitudinal excitons observed in theK ‖ c emission configuration. On the other hand, the red-shiftof the 05 and the highest photon energy line in case ofK ⊥ c emission (longitudinal excitons in the case of K ‖ cemission) and the weakness in the oscillator strength of 05are indications of electronic screening. The screening of thefree electrons is due to the scattering of the electrons movingperpendicular to the charged dislocation lines [21, 23, 73].The electronic screening for K ⊥ c emission led to a muchweaker interaction between the 05 and the photons than inthe case of K ‖ c emission, which we believe led to theconvergence of the longitudinal line onto the transverse.

5. Conclusion

We investigated the crystal orientation dependence of GaNexcitons by means of PL technique. At temperature of 10 K,the PL measurements were taken at two different sampleconfigurations, K ‖ c and K ⊥ c emissions. Transverse freeexcitons and donor-bound excitons were observed in the twoconfigurations while the longitudinal excitons were observedfrom K ‖ c emission only, in other words the longitudinalexcitons converged onto the transverse free exciton 05 in theK ⊥ c PL emission as expected by Hopfield et al [17]. Thisobservation was interpreted in terms of electron screeningdue to the scattering of electrons moving perpendicular tocharged dislocation lines. Additionally, we calculated theactivation energy of the GaN longitudinal excitons from thetemperature dependent PL. We found the activation energyof the longitudinal excitons approximately 5–6 times ashigh as the binding energy of the free excitons. The highactivation energies of the longitudinal excitons were discussedtentatively in the view of polaritons in strong exciton–photoncoupling regime. Also, the estimated c-axis strain, εc, usingHDXRD and PL techniques were reported, which explainedin the framework of the strain effects induced by the latticemismatch between sapphire and GaN. In addition, the effect ofthe polarizability was investigated, which was found to havemore influence on the longitudinal excitons than on the freeexcitons.

With edge-emitting GaN-based lasers commerciallyavailable, attention is shifting to more demanding andrewarding emitters. These include MC-based VCSELs andpolariton lasers. This report presents many fundamentalconcepts for such applications. Collecting K ‖ c emission(surface emission) minimize the electron screening, thusleading to strong exciton–photon coupling and therefore the

occurrence of the longitudinal excitons. The observation ofmore than one longitudinal exciton is associated with theexistence of more than one columnar growth orientation thatdifferent angles with respect to the c-axis. On the otherhand, the large activation energy of longitudinal excitonsin GaN would lead to high resistance to electron screeningfor polariton devices and performance stability at hightemperatures, some of the basic requirements to realizepolariton lasers at high temperature. More investigations aresubject to future research.

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