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07) 5282–5284www.elsevier.com/locate/matlet

Materials Letters 61 (20

Unusual changes observed in the photoluminescence of annealedInxGa1− xN/GaN quantum wells explained

Dipankar Biswas ⁎, Subindu Kumar, Tapas Das

Institute of Radio Physics and Electronics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India

Received 2 February 2007; accepted 12 April 2007Available online 19 April 2007

Abstract

InxGa1− xN/GaN heterostructures and quantum wells (QWs) are particularly important in the application of III–V nitride materials for lightemitting diodes and laser diodes. The photoluminescence (PL) emissions from InxGa1− xN/GaN QW structures have been reported, where, forsuccessive annealing operations, the PL peak suffers a primary red shift, followed by a blue shift. The observed phenomenon remains unexplainedbecause of its complexity. This paper is intended towards a proper explanation of the observed experimental results through suitable quantummechanical models and computations, whether the band gap of InN is 1.95 eV or 0.7 eV.© 2007 Elsevier B.V. All rights reserved.

Keywords: Nanomaterials; Semiconductors; Quantum wells; Annealing; Photoluminescence

1. Introduction

The ternary compound semiconductor InxGa1− xN is a highlysuccessful and promising material for carrier confinement andlight emission around the blue-green region [1]. High com-positional fluctuations of In are present, variations of the Incontent from about 20% to N60% have been reported [2,3].During growth of InxGa1− xN/GaN structures and after, due tohigh temperature thermal annealing, the parameters of thequantum well (QW) are likely to be changed, resulting inchanges in the optical properties [4,5].

Recently unusual PL results on annealing of InxGa1− xN/GaN QWs of 30 Å and 40 Å widths have been reported [3]. TheQWs were subjected to thermal annealing. Initially the PL peaksshift towards red and on further annealing at higher tempera-tures the peak shifts towards blue. It is worth noting that forInxGa1− xAs/GaAs and other III–V nanostructures, the PL peakshifts are reported to be monotonic on the blue side on annealing[6–8].

These extraordinary observations remain unexplained dueto its complex nature. The band offset ratios are not quite

⁎ Corresponding author.E-mail address: diiibiswas@yahoo.co.in (D. Biswas).

0167-577X/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.matlet.2007.04.052

established, strain changes the band offsets [9,10], and it involvesproblems ofmiscibility, alloy clustering, interdiffusion, etc. In thispaper we try to explain the experimental observations [3] the-oretically from physical and quantum mechanical concepts andcomputations.

2. Experimental and theoretical details

Fig. 1 shows the annealing induced changes of the PL peakas reported [3]. The 30 Å and 40 Å wide InxGa1− xN/GaN QWsamples were grown on sapphire substrates by metalorganicchemical vapor deposition (MOCVD) and the as grown sampleswere thermally annealed in a quartz tube furnace at 800, 850,and 900 °C in nitrogen for 30 min and PL measurements weremade at each step. The PL peak energy, initially on annealing at800 °C, decreases and it increases at higher annealingtemperatures. The high resolution transmission electron micro-scope (HRTEM) images [3] of the QWs indicate that in the asgrown samples the fluctuation of the well width is very wide.After annealing, a homogenization of indium composition andthe well width is shown along with some out diffusion.

The observed PL peak energy is the sum of the band gapenergy and the energies of the sub-bands of the QW from whichoptical transitions take place. During progressive annealing, the

Fig. 1. Variation of PL peak with annealing temperature.

Table 1Band offset parameters obtained in different studies

Band offset ratio Technique

38:62 Optical pumping30:70 X-ray photoemission spectroscopy62:38 Photoluminescence68:32 Calculation83:17 Calculation

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QWs of the conduction and valence bands gradually increase inwidth, and as In out diffuses due to the decrease of indium in theQW, the band gap of the well material increases. Thephenomenon is depicted pictorially by Vlaev and ContrerasSolorio [11]. Simultaneously a strong contesting secondphenomenon comes into picture. The energies of the sub-bands decrease sharply as the QWwidens. If the former is largerthere is a blue shift and if the latter is larger there is a red shift inthe PL spectrum. In the case of InxGa1− xN the change of theband gap, Eg, is not linear with change in the In mole fraction xas shown in Fig. 2. There is a strong bowing parameter ‘b’which deviates the curve from linearity and the slope of thecurve changes widely with the In mole fraction, x [12]. It isexpressed through the equation [1] as

Eg xð Þ ¼ xEg;InN þ 1� xð Þ Eg;GaN � bx 1� xð Þ ð1Þwhere x is the mole fraction of Indium, Eg(x) represents theband gap energy of InxGa1− xN, Eg,InN and Eg,GaN represent theband gap energies of the compounds InN and GaN which areconsidered to be 1.95 eV and 3.4 eV respectively. When x islarge the slope is small and as x decreases, the slope increasesand reaches the band gap energy of GaN, 3.4 eV. The change in

Fig. 2. Variation of the energy band gap in thewell, sumof the energy levels (e2+h4)and resultant PL peak with indium mole fraction (x) as annealing proceeds.

slope seems to play a major role in understanding the mentionedphenomenon.

When 30 Å and 40 Å QWs are annealed, initially the rate ofdecrease of the sum of the energies of the electron and holelevels, with increase of the well width, is high, more than therate of increase of the band gap Eg. Thus the resulting PL energydecreases initially and after sufficient out diffusion of indiumafter a certain well width, Eg increases at a faster rate and the PLstarts increasing in energy.

For quantitative establishment of the above discussions, inconnection with the experimental results [3] theoretical computa-tions were made considering 32 Å and 40 Å InxGa1− xN/GaNQWs. Table 1 [4] shows the band offset ratios obtained throughdifferent experiments. The mole fraction of indium and the bandoffset ratios (ΔEC:ΔEV) were considered to be 0.7 [3,13] and55:45 [10] respectively. The effective masses are assumed to be0.2 m0 [1] for electrons and 1.56 m0 [13] for heavy holes. Theband gap Eg of InxGa1− xN has been calculated from Eq. (1).The experimental data [3] is taken at 77 K where the effect ispronounced.

The height of the QWof InxGa1− xNwith GaN is sufficient toaccommodate the second electron and fourth hole sub bands[13] with parameters mentioned. The electron and hole levelsfor the finite wells were calculated from the equation [14]:

En ¼ 2P2

P þ 1ð Þ2np2

� �2� 1

3 P þ 1ð Þ3np2

� �4� 27P � 8

180 P þ 1ð Þ6np2

� �6" #

ð2Þfor a well of finite height, where P=[√(2m⁎V0) /ħ](a / 2), is thewell strength parameter, V0 and a are the height and width ofthe well respectively and m⁎ is the effective mass of the carrierstaken into consideration. The out diffusion of indium and theremaining indium concentrations was estimated from Fick'sLaw of diffusion [7] as

C zð Þ ¼ C0

2erf

h� zLD

� �þ erf

hþ zLD

� �� �ð3Þ

where C0 is the initial In concentration, 2h is the well thickness,z is the distance in the growth direction with z=0 at well centerand LD=2√(Dt) is the diffusion length, where t is the annealtime and D is the diffusion coefficient.

3. Results and discussion

The results obtained are shown in Figs. 1, 2 and 3. In Fig. 2, theband gap energy of InxGa1− xN is plotted against the mole fraction x ofindium. When the QW is annealed the mole fraction (x) of In inside the

Fig. 3. Variations of the PL peak energy with annealing temperature for twodifferent band gaps of InN 1.95 eV and 0.7 eV.

5284 D. Biswas et al. / Materials Letters 61 (2007) 5282–5284

well changes, as the well broadens. The sum of the energies of thesecond electron level e2 and the fourth hole level h4 for the 32 Å, thebest fit, has also been plotted in Fig. 2 with change of indium molefraction (x). The resultant PL peak energy is shown in the same figure.It is to be noted that the slope of the band gap with mole fraction is lessthan the decrease in the sum of the energies (e2+h4) initially. Slope S4is greater than S3 and as annealing proceeds S4 becomes less than S1and red followed by blue shift. The theoretically obtained PL data forboth 32 Å and 40 Å QWs have been plotted in Fig. 1 with theexperimental curves. The average deviation is within 2%. We havepresented results of 32 Å, which gives the minimum error over the fourexperimental data points.

The unusual e2–h4 transitions are considered for the followingreasons. The 1–1 PL transitions for the 30 and 40 Å wells are of muchlower energies than the reported experimental values. It has beenclearly discussed [15–17] that a strong piezoelectric field is presentacross the InxGa1− xN/GaN QWs. There is a high degree of localizationof carriers [18] and the over lap of the electron and hole wave functionsdecreases a lot. In such a case direct optical recombination from thehigher sub-bands becomes more probable. Moreover the e2–h4transitions with the realistic value of all the parameters match theeight experimental data points of the QW within an average error of2%. This consistency emphasizes the e2–h4 transitions ruling outartifacts.

A large debate is going on regarding the band gap of InN. Someresearch groups claim the band gap to be 0.7 eV [19] but recently thisresult has been again contradicted by reports of which a few are beingsited [20–22]. We have carried out similar computations consideringthe band gap of InN to be 0.7 eV. The results are shown in Fig. 3. Theyare far away from the experimental values. The red blue shift can beobserved in wells of width as low as 22 Å in the place of 30 Å and 40 Åand the PL peak is far short in energy as shown in Fig. 3.

4. Conclusions

We have explained the observed unusual changes of the PLpeaks of InxGa1− xN/GaN QWs on annealing which have been

reported to be highly complex. Initially the PL peak energy islowered and as annealing proceeds the PL peak moves to higherenergies. On annealing, the electron and hole levels decrease inenergy as the effective well width increases. At the same time asthe indium out diffuses the band gap of the well materialincreases. These two opposing phenomena contest and de-termine the final PL peak position. Initially the former is largerthan the latter which produces a red shift of the PL peak, asannealing progresses and the In mole fraction drops, the latterbecomes greater than the former and the PL peak undergoes ablueshift.

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