Cluster size and composition variations in yellow and red light-emitting InGaN thinfilms upon thermal annealingShih-Wei Feng, Tsung-Yi Tang, Yen-Cheng Lu, Shi-Jiun Liu, En-Chiang Lin, C. C. Yang, Kung-Jen Ma, Ching-

Hsing Shen, L. C. Chen, K. H. Kim, J. Y. Lin, and H. X. Jiang Citation: Journal of Applied Physics 95, 5388 (2004); doi: 10.1063/1.1703828 View online: http://dx.doi.org/10.1063/1.1703828 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/95/10?ver=pdfcov Published by the AIP Publishing

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Cluster size and composition variations in yellow and red light-emittingInGaN thin films upon thermal annealing

Shih-Wei Feng,a) Tsung-Yi Tang, Yen-Cheng Lu, Shi-Jiun Liu, En-Chiang Lin,and C. C. Yangb)

Graduate Institute of Electro-Optical Engineering, Department of Electrical Engineering and GraduateInstitute of Electronics Engineering, National Taiwan University, 1, Roosevelt Road, Sec. 4, Taipei, Taiwan,Republic of China

Kung-Jen MaDepartment of Mechanical Engineering, Chung Hua University, Hsinchu, Taiwan, Republic of China

Ching-Hsing Shen and L. C. ChenCenter for Condensed Matter Sciences, National Taiwan University, Taipei, Taiwan, Republic of China

K. H. Kim, J. Y. Lin, and H. X. JiangDepartment of Physics, Kansas State University, Manhattan, Kansas 66506-2601

~Received 14 October 2003; accepted 17 February 2004!

We study thermal annealing effects on the size and composition variations of indium-aggregatedclusters in two InGaN thin films with photoluminescence~PL! in the yellow and red ranges. Themethods of investigation include optical measurement, nanoscale material analysis, and theoreticalcalculation. Such a study is important for determining the relation between the band gap and theaverage indium content of InGaN. In one of the samples, the major part of the PL spectrum is shiftedfrom the yellow band into the blue range upon thermal annealing. In the other sample, after thermalannealing, a broad spectrum covering the whole visible range is observed. Cathodo-luminescence~CL! spectra show that the spectral changes occur essentially in the photons emitted from theshallow layers of the InGaN films. Photon emission spectra from the deeper layers are essentiallyunaffected by thermal annealing. The spectral changes upon thermal annealing are mainly attributedto the general trend of cluster size reduction. This interpretation is supported by the CL, x-raydiffraction, and high-resolution transmission electron microscopy results. To obtain a basic physicspicture behind the spectral blue shift upon thermal annealing in the yellow emission sample, wetheoretically study the quantum-confinement effects of InGaN clusters based on a quantum boxmodel. The theoretical results can generally explain the large blue shift of PL spectral peak position.© 2004 American Institute of Physics.@DOI: 10.1063/1.1703828#

I. INTRODUCTION

Recently, the characteristics of InN have become thesubject of much attention. In particular, experimental datahave shown that the band gap of InN is around 0.75 eV,1,2

instead of the previously reported value 1.9 eV.3 Such a dra-matic change of InN band gap implies the need for carefulexamination of InGaN characteristics, particularly when theindium content is high. Also, the recently identified smallerband gap of InN implies that InGaN has the potential for anoptoelectronics application in a much broader spectral range.With the average indium contents of lower than 30%, InGaNcompounds have been widely used for the fabrications ofUV, blue, and green light-emitting devices. However, studieson the optical properties and nanostructures in such com-pounds of relatively higher indium contents~emitting yellow,red, or even longer-wavelength photons! were rarelyreported.1,4 Recently, indium aggregation in InGaN has been

observed~see the discussions below!. Such behavior impliesthat the reported InGaN band gaps may originate fromindium-rich clusters, and are due to quantum confinement.They cannot be used for describing the bulk material prop-erties of InGaN. The study on the indium aggregation phe-nomena, particularly when the average indium content ishigher than 30%, can help us understand the relation be-tween the InGaN band gap and its average indium content.

Due to the large lattice mismatch~11% in thec axis!between InN and GaN, their miscibility is quite low. In thissituation, indium aggregation and phase separation can occurin InGaN through the process of spinodal decomposition.5 Inthis process, the ‘‘up-hill’’ diffusion of indium atoms leads tothe formation of high-indium InGaN clusters such that thestrain energy can be released. Under certain conditions, thesizes of the clusters can be reduced to a few nanometers andstrong quantum confinement is generated. In other words,InGaN quantum dots~QDs! can be formed. With such clusterstructures, carriers can be localized in the potential minimafor effective radiative recombination.6–8 It is believed thatthe carrier localization mechanism is the key to the efficientphoton emission in such a compound of high defect density

a!Current address: Department of Applied Physics, National University ofKaohsiung, No. 700, Kaohsiung University Rd., Nan-Tzu Dist., 811,Kaohsiung, Taiwan, Republic of China.

b!Electronic mail: ccy@cc.ee.ntu.edu.tw

JOURNAL OF APPLIED PHYSICS VOLUME 95, NUMBER 10 15 MAY 2004

53880021-8979/2004/95(10)/5388/9/$22.00 © 2004 American Institute of Physics

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(;108 cm23). Typically, the process of indium aggregationand hence the effect of carrier localization become strongerwith increasing average indium content.5,9 The effect of car-rier localization has been regarded as one of the majormechanisms for the temperature-dependent S-shape variationof the photoluminescence~PL! spectral peak.2,10 Thetemperature-dependent behavior originates from the localiza-tion of thermalized carriers and hence a blue shift of PLspectral peak in a certain temperature range. On the otherhand, such an S-shape variation was also interpreted as theresult of quantum-confined Stark effect~QCSE! in anInGaN/GaN quantum well~QW! structure.11,12 QCSE origi-nates from the strain-induced piezoelectric field distributionin a QW. The tilted potential leads to a red shift of the effec-tive band gap. The existence of phonons at a relativelyhigher temperature can reduce the QCSE and generate ablue-shift trend.13,14 The combination of the basic red shift~phonon effect! and the blue shift results in the S-shape be-havior.

Post-growth thermal annealing can provide thermal en-ergy for atomic rearrangement such that a thermal equilib-rium state can be reached. It has been reported that post-growth thermal annealing could alter the sizes anddistributions of self-organized InAs QDs.15,16In our previousstudies, it was found that post-growth thermal annealing wasquite effective for changing the cluster structures and theirphoton emission properties in InGaN/GaN QW samples.17–19

This group has reported the formation of quasiregularquantum-dot-like structures from randomly distributedindium-aggregated clusters upon thermal annealing of anInGaN/GaN QW sample.17 The effects of thermal annealingin QW samples of different well widths have also beenstudied.18,19 It was discovered that under appropriate thermalannealing conditions, well-shaped QDs could be formedthrough spinodal decomposition in a narrow QW sample~well width ,3 nm!, leading to radiative efficiency improve-ment. However, in a sample of a relatively larger QW width~well width .3 nm!, QD formation or optical quality im-provement was not observed.19

Although indium aggregations through spinodal decom-position have been observed in InGaN/GaN QWs and thinfilms, their optical characteristics and nanostructures, par-ticularly when the average indium content is higher than30%, have not been well studied yet. Also, in such a sample,the effects of post-growth thermal annealing, which may fur-ther induce spinodal decomposition such that the equilibriumcondition can be reached, have never been reported. In thisarticle, we report the optical characteristics of two InGaNfilms with PL in the yellow and red ranges. In particular, thepost-growth thermal annealing effects are discussed. In oneof the samples, after thermal annealing, the PL spectral peakshifts from the yellow band into the blue range. This shift isparticularly clear for photons emitted from the shallow por-tion of the InGaN thin film. In the other sample of evenhigher average indium content~red emission!, the PL spec-trum broadens to cover almost the whole visible range uponthermal annealing. The spectral changes are mainly attrib-uted to the general trend of cluster shrinkage through spin-odal decomposition. In the process of spinodal decomposi-

tion, the increase of indium composition within a cluster andthe shrinkage of the cluster size may produce the counterac-tion between the red-shift and blue-shift trends. To determinethe dominating mechanism, we use a simple but reasonableInGaN quantum cube model and theoretically study thequantum-confinement effects in nanometer-scale InGaNcluster. The theoretically predicted trend of PL peak positioncan generally explain the large blue-shift trend in PL peakposition upon the thermal annealing process.

This paper is organized as follows: In Sec. II, samplestructures and experimental procedures are described. In Sec.III, optical characterization results, including PL, photolumi-nescence excitation~PLE!, and cathodo-luminescence~CL!,are reported. Also, the x-ray diffraction~XRD! patterns arepresented. In Sec. IV, theoretical results of band structurecalculations are discussed. Finally, discussions and conclu-sions are given in Sec. V.

II. SAMPLE PREPARATION AND EXPERIMENTALPROCEDURES

The two samples~designated as samples Y and R! usedin this study were grown in a low-pressure metal-organicchemical vapor deposition reactor. In each sample, a;1.5mm GaN epi-layer was deposited on ac-plane sapphire sub-strate with a 25 nm GaN buffer layer. The GaN epi-layergrowth was followed by the deposition of a slightly silicon-doped InGaN film with a thickness of;0.15mm. The aver-age indium contents were estimated slightly higher than 30%and 40% in samples Y and R, respectively, determined by theindium and gallium flow rates during crystal growth. Thesilicon doping concentration was 431017cm23. The growthtemperatures of the GaN buffer layer, GaN epi-layer, andInGaN layer were 550, 1050, and 710 °C, respectively. Ingrowing the GaN epi-layers and InGaN thin films, pressureof 325 torr was used. Trimethylgallium~TMGa! and trimeth-ylindium ~TMIn! were used as the precursors. The carriergases for growing InGaN and GaN were nitrogen and hydro-gen, respectively. High purity ammonia was used as the ac-tive nitrogen source. The GaN and InGaN growth rates were3.6 and 0.3mm/hr, respectively. Post-growth thermal anneal-ing was conducted at 800 °C for 30 min in ambient nitrogen.

PL measurements were carried out with the 325 nm lineof a 35 mW He–Cd laser for excitation. PLE experimentswere performed using a quasimonochromatic excitation lightsource from a xenon lamp dispersed with a monochromator.The PLE detection photon energy was set at the PL spectralpeak. The CL images were acquired using a Gatan monoCL3spectrometer in a JEOL JSM 6700F SEM system. The ki-netic energies of electrons for CL measurements ranged from3 to 15 keV with an electron beam current of 60–300 pA.The surface spatial resolution is about 100 nm. In addition,XRD measurements were carried out using CuK radiation,monochromated with the~111! reflection of Ge single crys-tal. The high-resolution transmission electron microscopy~HRTEM! investigations were performed using a PhilipsTECNAI F20 field-emission electron microscope with an ac-celerating voltage of 200 kV. All high-resolution micro-graphs were taken at the Scherzer defocus. The samples wereviewed along a@11–20# zone axis for bright-field images. To

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clearly show the compositional variations in InGaN alloy,digital micrograph 3.7.4 software was utilized to sharpen theboundaries between indium-rich clusters and the surroundingcompounds.

III. CHARACTERIZATION RESULTS

Figure 1 shows the PL and PLE spectra at 10 K of theas-grown and annealed samples Y. It is noted that PL spectralpeak of this sample has shifted from the yellow band~around2.2 eV! to the blue range~around 2.75 eV! after thermalannealing. The blue-emission contribution as a small side-lobe can also be observed in the PL spectrum of the as-grownsample. Usually, PL emission essentially originates from ashallow layer of the sample. Therefore, we can exclude thepossibility that the yellow-band emission comes from thedefects in GaN.20 The PLE spectrum of the as-grown sampleY shows multiple InGaN absorption peaks, corresponding tothe clusters of different geometries and compositions. TheStokes shift~SS! of the PL peak with respect to the PLEabsorption maximum~around 3.05 eV! is as large as about 1eV, indicating the strong indium composition fluctuationand/or strong QCSE. After thermal annealing, the spectralposition of the major absorption peak near 3.05 eV is un-changed. This energy level may correspond to the back-ground indium composition, on top of which higher indiumcompositions fluctuate, in the as-grown and annealedsamples. The distribution of the higher indium compositionfluctuation varied upon thermal annealing such that the PLspectrum blue-shifted and the SS became quite small~around200 meV!. However, it seems that the background indiumcomposition did not change upon thermal annealing.

Figure 2 shows the PL spectra of the as-grown and an-nealed samples R and the PLE spectrum of the as-grownsample R at 10 K. After thermal annealing, the luminescenceshows multiple-band emission including red, green, andblue, which may come from the contributions of InGaN clus-ters of different compositions and sizes. In other words, uponthermal annealing the nanostructures of part of the clusterswere changed to emit shorter-wavelength photons. The largeSS ~1.1 eV! of the as-grown sample R shows the strongerindium composition fluctuation and/or QCSE when com-pared with the as-grown sample Y. It is noted that after ther-mal annealing, photon emission from sample R became quite

dim such that the measurement of its PLE spectrum wasdifficult.

Figure 3 shows the typical CL images of the as-grown~a! and annealed~b! samples Y, both with the excitation of 3kV electrons. The 3 kV represents the electron accelerationvoltage and roughly corresponds to a penetration depth of 88nm. Therefore, only the shallow portions of the InGaN thinfilms are excited. The light spots of a few hundred nanom-eters in size in the CL image of the as-grown sample Y emitessentially yellow and relatively weaker blue photons. Theyare supposed to correspond to the indium-aggregated clus-ters. After thermal annealing, the CL image becomes blurred.Actually, the image in Fig. 3~b! consists of many tiny lightspots at the order of 100 nm in size, which is close to thespatial resolution of the used CL system. Those tiny lightspots essentially emit blue light. The generation of those tinylight spots implies that the cluster sizes in the InGaN filmmight be generally reduced upon thermal annealing, particu-larly in the shallow portion. Figure 4 shows the typical CLimages of the as-grown~a! and annealed~b! samples Y, both

FIG. 1. PL and PLE spectra at 10 K before and after thermal annealing ofsample Y. FIG. 2. PL and PLE spectra at 10 K before and after thermal annealing of

sample R.

FIG. 3. Typical CL images before~a! and after~b! thermal annealing ofsample Y with the excitation of 3 kV electron voltage.

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with the excitation of 15 kV electrons. The 15 kV accelerat-ing voltage roughly corresponds to the penetration depth of1300 nm, deep into the GaN layer beneath. The comparisonbetween Figs. 4~a! and 4~b! shows the same trend of tinylight spot generation upon thermal annealing as the case of 3kV-electron excitation. Also, compared with the 3 kV CLimage@see Fig. 3~a!#, the sizes of individual bright spots inthe 15 kV image are smaller. However, large bright areas~inthe dimension of micrometers!, consisting of many smallerspots, are formed. They are observed because a CL image isobtained by accumulating the luminescence along the depth.The same argument can be applied to the annealed sample Y.

Figure 5 shows the typical CL images of the as-grown~a! and annealed~b! samples R, both with the excitation of 3kV electrons. Compared with the CL image of the as-grownsample Y @see Fig. 3~a!#, that of the as-grown sample Rshows light spots of a larger variety in size. This observationis consistent with the speculation of the stronger indiumcomposition fluctuation in the as-grown sample R based onthe PLE results. After thermal annealing of sample R, the CLimage seems almost featureless. Nearly uniform tiny lightspots, with the sizes close to the spatial resolution of the CLsystem, are observed. Such an observation also implies thegeneral trend of cluster shrinkage upon thermal annealing.

Figures 6~a! and 6~b! show the CL spectra of the as-grown and annealed samples Y, respectively. In each sample,the 3, 5, 8, and 15 kV electron voltages roughly correspondto the penetration depths of 88, 210, 450, and 1300 nm,respectively. In the as-grown sample, luminescence mainlyin the yellow band is observed in a shallow layer~3 kVprobe!. With increasing electron voltage, not only the yellowband, but also the peak of blue luminescence~between 2.7and 2.85 eV! can be observed. Also, with 8 and 15 kV elec-tron excitations, the luminescence from the GaN layer

~around 3.4 eV! can be clearly seen. Hence, it is believed thatcertain nanostructures, existing in the deep portion of theInGaN film, can emit photons in the blue range. This result isconsistent with the side-lobe of the PL spectrum in the as-grown sample, as shown in Fig. 1. After thermal annealing,in the shallow layer of the InGaN film~3 kV probe!, onlyblue luminescence exists, that is again consistent with the PLmeasurement. With excitation of higher-energy electrons, theblue luminescence is enhanced and the GaN emission peakappears. Also, a broad yellow luminescence band is ob-served. This yellow luminescence is believed to originatefrom the defects in the GaN layer, instead of the clusterluminescence in the InGaN film. From the results describedabove, we speculate that after thermal annealing, the nano-structure of the shallow layer of the InGaN film has beenchanged into that similar to the structure resulting in blue

FIG. 4. Typical CL images before~a! and after~b! thermal annealing ofsample Y with the excitation of 15 kV electron voltage.

FIG. 5. Typical CL images before~a! and after~b! thermal annealing ofsample R with the excitation of 3 kV electron voltage.

FIG. 6. CL spectra with the excitations of 3, 5, 8, and 15 kV electronvoltages for the as-grown~a! and annealed~b! samples Y. All measurementswere performed at room temperature.

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luminescence in the deeper portion. Hence, the whole InGaNfilm emits blue light. The different nanostructures betweenthe shallow and deep portions in the as-grown InGaN filmcan be due to the fact that in growing the shallow portion, thehigh growth temperature had an effect of thermally annealingthe deep portion. The other possible reason for the differentnanostructures between the shallow and deep layers is theeffect of composition pulling in growing InGaN films.21,22 Inother words, the average indium content in the shallow layeris higher than that in the deep layer. Different average in-dium contents result in different aggregation structures andhence different photon emission spectra. In our study, it isfound that the deep-layer nanostructure does not seem tovary much upon thermal annealing. However, that in theshallow layer changes significantly.

Figures 7~a! and 7~b! show the CL spectra of the as-grown and annealed samples R, respectively, with differentelectron acceleration voltages. In the as-grown sample, onlyred luminescence is observed in a shallow layer~3 kVprobe!. With higher excitation voltages, not only the redband but also the broad visible range, particularly a smallpeak of blue luminescence~between 2.5 and 2.7 eV!, can beobserved. With increasing electron voltage, eventually theluminescence of the GaN layer appears. Hence, differentnanostructures exist at different depths of the InGaN film inthe as-grown sample R, leading to a broad spectrum of pho-ton emission. This result is also consistent with the long tailon the high-energy side of the PL spectrum in the as-grownsample, as shown in Fig. 2. After thermal annealing, broadCL spectra over the ranges of the visible and UV can alwaysbe observed with various excitation electron voltages@seeFig. 7~b!#, that is again consistent with the PL spectrum, asshown in Fig. 2. Such results confirm the hypothesis of ran-domly distributed cluster structures of different sizes andcompositions in the annealed sample R.

Figure 8 shows the XRD patterns of the as-grownsamples Y and R. Besides the GaN peak~C!, the nearly pureInN peak~A!, and the InGaN distribution~B!, correspondingto indium composition fluctuation, clearly indicate strong in-dium aggregation processes in the samples. In these two and

all other InGaN samples previously studied by this group,the distribution B always terminates at around 2u533.2°,implying the solubility limit of InN in GaN at around 41%.This solubility limit is obtained based on a simple calculationof linear interpolation. It is noted that InGaN within a clusteris under compressive strain~affected by the surroundingInGaN of a lower indium composition!. In other words, thecalibrated indium composition based on the XRD measure-ment could be underestimated.

In the comparison between the as-grown samples Y andR, the broader distribution B and higher peak A in sample Ronce again confirm its stronger indium composition fluctua-tion. We have also compared the XRD patterns between theas-grown and annealed samples Y.23 After thermal annealingof the sample, the distribution B splits into two components.The low-indium component is attached to the GaN peak.This phenomenon may imply a larger contrast of indiumconcentration between a cluster and the surrounding region.The component attaching to the GaN peak is related to thecomposition of the region surrounding the formed clusters.

The InGaN cluster formation and InN solubility limit inGaN have important implications in the related studies. Re-cently, because of the interest in InN characteristics, the re-lation between material band gap and indium compositionhas been studied.1,2 In such a study, caution needs to be takenin the measurement of material band gap. Because of theclustering nature of InGaN, the emitted photons for band gapdetermination mainly come from clusters, which may bearthe quantum-confinement effect. In this situation, the cali-brated energies are actually not the bulk material band gaps.Also, with the aforementioned solubility limit, the nanostruc-tures of InGaN compounds of high average indium contentsneed to be carefully analyzed before one can determine theircorrect material band gaps.

Figures 9~a! and 9~b! show the HRTEM images of theas-gown and annealed samples Y, respectively. The arrowsshow the directions of crystal growth. The cluster domainstructures in both samples can be clearly seen. Although thedomain geometry in either sample is quite random, one stillcan observe that the domain size in the annealed sample Y isgenerally smaller than that of the as-grown sample. Duringthermal annealing, spinodal decomposition generally reducesthe cluster sizes in the case of our study. In this process, theindium content in an InGaN cluster is expected to increase.The increase of indium content is supposed to reduce theeffective band gap. However, the shrinkage of cluster size

FIG. 7. CL spectra with the excitations of 3, 5, 8, and 15 kV electronvoltages for the as-grown~a! and annealed~b! samples R. All measurementswere performed at room temperature.

FIG. 8. XRD patterns of the as-grown samples Y and R.

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should result in stronger quantum confinement and increasethe effective band gap. The counteraction between the twomechanisms actually led to the significant blue shift in thePL spectrum of sample Y. In the next section, we will use aquantum cube model to calculate the effective band gap of acluster with the experimental conditions taken into consider-ation. The aforementioned counteraction will be examined.

IV. THEORETICAL STUDY

To understand the blue-shift behaviors of the PL spectralpeak upon thermal annealing, we performed a theoreticalstudy by calculating the ground-state levels of a quantumbox based on a series-expansion model. In the calculations,we used certain experimental data of sample Y as input pa-rameters, including PL spectral peaks for the energy levels ofthe effective band gaps, PLE spectra and XRD patterns forthe estimates of indium compositions, and HRTEM imagesfor the sizes of indium-aggregated clusters.

In our calculations, the theory of a series expansionbased on the eigen-functions of infinity barrier for thediscrete-state wave functions is used.24,25The strain effect isincluded by evaluating the lattice mismatch between the in-dium compositions of a cluster and the surrounding com-pound. For simplicity, we neglect the effect of electron-holeCoulomb interaction. In other words, the exciton effect isignored. Although the exciton binding energy of GaN is quitelarge~;30 meV!, those of the InGaN compounds with highindium compositions in our samples are still unknown. Theexciton binding energy usually decreases with decreasingband gap. Although strong quantum confinement can en-

hance the exciton binding energy, it has been pointed out thatthe increase of effective band gap in energy discretization ismore important than the enhancement of exciton binding en-ergy in calculating the effective band gap of a QD.15 There-fore, in our model, it is reasonable to ignore the excitoneffect.

With the exciton effect ignored, the equations for theelectron and hole wave functions can be decoupled. Thewave function solutions of electron and hole can be ex-pressed as the series expansions of the complete sets ofortho-normal eigen-functions, with properly chosen coeffi-cients, of a quantum box with the assumption that the barrierpotential is infinitely high. With the barrier of infinite height,the amplitudes of the eigen-functions decay to zero at thebox boundaries. However, with the finite barrier height in thereal situation, wave functions extend into the barrier to acertain distance. To include the wave function penetrationinto the barrier, we choose the dimensions of the infinity-barrier quantum box to be twice those of the real quantumbox, following an empirical conclusion.25 This choice of theempirical factor can slightly influence the numerical results.However, the key physics is unaffected. After certain deriva-tions, we can obtain a matrix eigen-problem, which is to besolved numerically. Ten terms are considered in the afore-mentioned series expansion for each dimension.

In general, with compressive strain in the quantum-confined region, the conduction-band and valence-bandedges are shifted upward and downward, respectively. Thestrain-induced band structure modification of a quantum dotcan be expressed with a product of strain components by adeformation potential.15 With hydrostatic strains, the straineffects of the conduction band are decoupled from those ofthe valence band. In the following, we assume that strain iszero outside the quantum box and is compressive inside, asdepicted in Fig. 10. In this situation, at theG point, theconduction- and valence-band edges are modified by the en-ergy shifts dEc and dEv , respectively.15 In Fig. 10,En

c (Env) (n50,1,2,...,) represent the discrete energy levels in

the conduction~valence! band. They are to be obtained bynumerically solving the aforementioned matrix eigen-problem. Also,Eg is the material band gap of the InGaNcompound inside the quantum box.

Table I lists the physical parameters used in our calcula-tions. We use an edition of the band-gap energy forInxGa12xN as given in Ref. 1. The band-edge discontinuity

FIG. 9. HRTEM images of the as-grown~a! and annealed~b! samples Y.The arrows show the crystal growth directions.

FIG. 10. Schematic drawing of the band structure of a quantum cube withsizeL.

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~band offset! ratio for the conduction and valence bands isassumed to be 0.67:0.33.27 We calculate the parameters ofInxGa12xN, other than material band gap energy, with thelinear interpolation formula.

In our numerical calculations, we consider a quantumcube with the dimensionL. Also, the indium composition ofthe barrier is fixed at 8%. This percentage is determined withthe major absorption peak of the PLE spectra~around 3.05eV! of the as-grown and annealed samples Y, as shown inFig. 1. With Eg(x)53.05 eV, we can obtainx50.08. Thiscomposition is consistent with the attached side-lobe~around2u534.4°! of the GaN peak in the XRD pattern of the an-nealed sample Y.23

Figure 11 showsE0c values as functions of indium com-

position for several quantum cube sizes. With the same cubesize, theE0

c value increases with the indium compositioninside the cube. As indium composition increases, thesmaller electron effective mass of InGaN results in the in-creasing trend ofE0

c although the material band gap de-creases. In addition, with the same composition inside thequantum cube, the variation ofE0

c is more sensitive to thechange of cube size as indium composition increases. Thesmaller electron effective mass of InGaN with a higher in-dium composition can also explain this trend. It is noted thata bound state may not exist in the quantum cube if the com-position contrast or the cube size is too small.13 Figure 12shows theE0

v values as functions of cube indium composi-tion for several cube sizes. Their general trends are the same

as those of the electron. Figure 13 shows hydrostatic-strain-induced energy shiftsdEc and dEv as functions of the in-dium composition in the cube for the conduction and valencebands. As indium composition increases, the lattice mis-match between the cube and barrier becomes larger andhence the strain effect is enhanced.

With the calculation results based on the quantum cubemodel, we are ready to compare the theoretical predictionswith the experimental data. As shown in Fig. 14, we plot theelectron transition energies, corresponding to the transitionbetween the ground electron state and the ground heavy-holestate, versus the indium composition in the cube for severalcube sizes. These transition energies, denoted byEPL , isdefined as

EPL[E0c1dEc1Eg1dEv1E0

v . ~1!

At low temperatures, optically excited electrons and holesrelax to individual ground states before recombination.Therefore, we can assume that the measured PL spectralpeak corresponds to the energyEPL . In Fig. 14, the dashedcurve represents the material band gap of InxGa12xN insidethe cube. With the same cube size, the difference betweenEPL and the material band gap becomes larger as indiumcomposition increases. Comparing with the experimentaldata, we plot two horizontal lines in Fig. 14 to indicate thePL spectral peaks of the as-grown and annealed samples Y.From the HRTEM images, one can assume 10 nm for theindium-aggregated cluster size in the as-grown sample Y and2–4 nm in the annealed sample Y. The assumptions lead tothe conclusion that the indium compositions in the cube arearound 45% before annealing and around 55% after anneal-ing, with the two points connected by the arrow in Fig. 14.

FIG. 13. Hydrostatic strain-induced energy shiftsdEc anddEv as functionsof the indium composition in the quantum cube.

TABLE I. Material parameters of GaN and InN used for calculations.

GaN InN

Lattice constant~Å!a

a 3.189 3.545c 5.185 5.703Effective massb m5(mim'

2 )1/3

Electron mass along thec-axis mi

perpendicular to thec-axis m'

0.19m0 0.11m0

0.17m0 0.1m0

1.76m0 1.56m0

Heavy hole mass along thec-axis mi

perpendicular to thec-axis m'

(m0 : free electron mass!

1.69m0 1.68m0

Hydrostatic deformation potential~eV!a

Conduction-bandac 6 3Valence-bandav 0.8 0.5

aReference 26.bReference 27.

FIG. 11. Electron energy shifts (E0c) as functions of the indium composition

in the quantum cube for several quantum cube sizes.

FIG. 12. Heavy hole energy shifts (E0v) as functions of the indium compo-

sition in the quantum cube for several quantum cube sizes.

5394 J. Appl. Phys., Vol. 95, No. 10, 15 May 2004 Feng et al.

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The results of 45% indium composition before annealingand 55% composition after annealing seem to contradict thesolubility limit calibrated from the XRD measurements. Sev-eral possible explanations are given as follows:~1! as dis-cussed in Sec. III, the solubility of 41% indium from XRDmeasurements is underestimated;~2! it is noted that in thereal situation, the cluster interfaces are not as sharp as thoseof the assumed quantum cube in the theoretical calculations.Hence, the strains built in the QDs are expected to be weakerthan the theoretical predictions. Therefore, the data curves inFig. 14 are lower than those as shown. In other words, theindium compositions in the samples before and after thermalannealing can be lower than those described above; and~3!from the optical measurements, such as PLE, the QCSE canbe significantly released after thermal annealing. Hence, theblue shift after annealing may not be completely due to theshrinkage of clusters. Although it is uncertain, the quantumdot may not be as small as 2 nm in size. The effect of QCSErelaxation deserves further investigation.

V. DISCUSSIONS AND CONCLUSIONS

Because of the relatively higher thermal annealing tem-perature~800 °C!, compared with the InGaN growth tem-perature~710 °C!, desorption of InN from the InGaN layercould occur during thermal annealing. Such a process couldreduce the indium content and shrink the cluster size in theshallow layer of a sample. However, we speculate that thisprocess is a minor one because based on the theoretical re-sults in the last section, the indium composition in a clusterneeds to be increased such that the significant PL blue shiftafter thermal annealing in sample Y can be well explained.

In summary, we have studied the indium aggregationphenomena in two InGaN thin films with PL in the yellowand red ranges and their variations upon post-growth thermalannealing through optical measurements, material analyses,and theoretical calculations. The Stokes shifts of the PLspectral peaks with respect to the major PLE absorptionpeaks in the as-grown samples could be as large as 1 eV,indicating the strong indium composition fluctuations and/orstrong QCSEs. In one of the samples, the major part of PLspectrum was shifted from the yellow band into the bluerange upon thermal annealing. In the other sample, after ther-mal annealing, a broad spectrum covering the whole visiblerange was observed. CL spectra showed that the spectralchanges occurred essentially in the photons emitted from the

shallow layers of the InGaN films. Photon emission spectrafrom the deeper layers were essentially unaffected by ther-mal annealing. The spectral changes upon thermal annealingwere mainly attributed to the general trend of cluster sizereduction. The interpretation was supported by the CL, XRD,and HRTEM results. To obtain a basic physics picture behindthe spectral blue shift upon thermal annealing in the yellowemission sample, we theoretically studied the quantum con-finement effects of the InGaN clusters based on a quantumcube model. The theoretical results generally explained wellthe large blue shift in PL spectral peak position.

ACKNOWLEDGMENTS

This research was supported by National Science Coun-cil, The Republic of China, under Grant Nos. NSC 92-2210-M-002-006 and NSC 92-2215-E-002-010, and by the U.S.Air Force under Contract No. AOARD-02-4052.

1J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager III, E. E. Haller, Hai Lu, andWilliam J. Schaff, Appl. Phys. Lett.80, 4741~2002!.

2T. Matsuoka, H. Okamoto, M. Nakao, H. Harima, and E. Kurimoto, Appl.Phys. Lett.81, 1246~2002!.

3K. L. Westra, R. P. W. Lawson, and M. J. Brett, J. Vac. Sci. Technol. A6,1730 ~1988!.

4F. B. Naranjo, M. A. Sa´nchez-Garcı´a, F. Calle, E. Calleja, B. Jenichen, andK. H. Ploog, Appl. Phys. Lett.80, 231 ~2002!.

5Y. S. Lin, K. J. Ma, C. Hsu, S. W. Feng, Y. C. Cheng, C. C. Liao, C. C.Yang, C. C. Chou, C. M. Lee, and J. I. Chyi, Appl. Phys. Lett.77, 2988~2000!.

6Y. Narukawa, Y. Kawakami, S. Fujita, S. Fujita, and S. Nakamura, Phys.Rev. B55, R1938~1997!.

7S. F. Chichibu, K. Wada, J. Mu¨llhauser, O. Brandt, K. H. Ploog, T. Mi-zutani, A. Setoguchi, R. Nakai, M. Sugiyama, H. Nakanishi, K. Korii, T.Deguchi, T. Sota, and S. Nakamura, Appl. Phys. Lett.76, 1671~2000!.

8Y. Narukawa, Y. Kawakami, S. Fujita, and S. Nakamura, Phys. Rev. B59,10 283~1999!.

9C. C. Liao, S. W. Feng, C. C. Yang, Y. S. Lin, K. J. Ma, C. C. Chuo, C. M.Lee, and J. I. Chyi, Appl. Phys. Lett.76, 318 ~2000!.

10Y. H. Cho, G. H. Gainer, A. J. Fischer, J. J. Song, S. Keller, U. K. Mishra,and S. P. DenBarrs, Appl. Phys. Lett.73, 1370~1998!.

11S. F. Chichibu, A. C. Abare, M. S. Minsky, S. Keller, S. B. Fleischer, J. E.Bowers, E. Hu, U. K. Mishra, L. A. Coldren, S. P. DenBaars, and T. Sota,Appl. Phys. Lett.73, 2006~1998!.

12E. Berkowicz, D. Gershoni, G. Bahir, E. Lakin, D. Shilo, E. Zolotoyabko,A. C. Abare, S. P. Denbaars, and L. A. Coldren, Phys. Rev. B61, 10 994~2000!.

13P. Perlin, Ch. Kisielowski, V. Iota, B. A. Weinstein, L. Mattos, N. A.Shapiro, J. Kruger, E. R. Weber, and J. Yang, Appl. Phys. Lett.73, 2778~1998!.

14P. Riblet, H. Hirayama, A. Kinoshita, A. Hirata, T. Sugano, and Y. Aoyagi,Appl. Phys. Lett.75, 2241~1999!.

15D. Bimberg, M. Grundmann, and N. N. Ledentsov,Quantum Dot Hetero-structures~Wiely, England, 1999!.

16T. M. Hsu, Y. S. Lan, W.-H. Chang, N. T. Yeh, and J.-I. Chyi, Appl. Phys.Lett. 76, 691 ~2000!.

17Y. S. Lin, K. J. Ma, C. Hsu, Y. Y. Chung, C. W. Liu, S. W. Feng, Y. C.Cheng, M. H. Mao, C. C. Yang, H. W. Chuang, C. T. Kuo, J. S. Tsang, andT. E. Weirich, Appl. Phys. Lett.80, 2571~2002!.

18L. T. Romano, M. D. McCluskey, B. S. Krusor, D. P. Bour, C. Chua, S.Brennan, and K. M. Yu, J. Cryst. Growth189Õ190, 33 ~1998!.

19Y. Y. Chung, Y. S. Lin, S. W. Feng, Y. C. Cheng, E. C. Lin, C. C. Yang, K.J. Ma, C. Hsu, H. W. Chuang, C. T. Kuo, and J. S. Tsang, J. Appl. Phys.93, 9693~2003!.

20D. Vanderbilt and L. K. Wickham, Mater. Res. Soc. Symp. Proc.202, 555~1991!.

21S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, C. Trager-Cowan,F. Sweeney, and E. Alves, Phys. Rev. B64, 205 311~2001!.

FIG. 14. Electron transition energies (EPL) as functions of the indium com-position in the quantum cube for several quantum cube sizes.

5395J. Appl. Phys., Vol. 95, No. 10, 15 May 2004 Feng et al.

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129.118.248.40 On: Mon, 03 Mar 2014 01:54:43

22M. Hao, H. Ishikawa, T. Egawa, C. L. Shao, and T. Jimbo, Appl. Phys.Lett. 82, 4702~2003!.

23S. W. Feng, E. C. Lin, T. Y. Tang, Y. C. Cheng, H. C. Wang, C. C. Yang,K. J. Ma, C. H. Shen, L. C. Chen, K. H. Kim, J. Y. Lin, and H. X. Jiang,Appl. Phys. Lett.83, 3906~2003!.

24H. Gotoh, H. Ando, T. Takagahara, H. Kamada, A. Chavez-Pirson, and J.Temmyo, Jpn. J. Appl. Phys., Part 136, 4202~1997!.

25S. Gangopadhyay and B. R. Nag, Nanotechnology8, 14 ~1997!.26Y. C. Yeo, T. C. Chong, and M. F. Li, J. Appl. Phys.83, 1429~1998!.27S. L. Chung, IEEE J. Sel. Top. Quantum Electron.32, 1791~1996!.

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