007) 4488–4491www.elsevier.com/locate/tsf

Thin Solid Films 515 (2

Band offsets of InXGa1−XN/GaN quantum wells reestimated

Dipankar Biswas ⁎, Subindu Kumar, Tapas Das

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

Available online 11 September 2006

Abstract

Recently InXGa1−XN/GaN heterostructures and quantum wells (QWs) have gained immense importance in the application of III–V nitridematerials. Reported values of the ratios of conduction band offset to valence band offset for InXGa1−XN/GaN QW structures, ΔEc:ΔEv, varywidely from 38:62 to 83:17. While trying to explain the unusual shifts in the photoluminescence (PL) spectra, obtained from InXGa1−XN/GaN QWstructures, it has been found that a band offset ratio, ΔEc:ΔEv=55:45, explains all the experimental data precisely. In this paper detailed theories,procedures, results and discussions to establish the newly estimated band offsets will be presented.© 2006 Elsevier B.V. All rights reserved.

Keywords: Quantum wells; InGaN; Photoluminescence

Fig. 1. An atomic-scale HRTEM image of the 800 °C annealed w20 sample with

1. Introduction

The heterojunction band offset is an important parameter forthe design of heterostructure based electronic and optoelectron-ic devices. The band offset is one of the parameters, whichgoverns carrier confinement in the heterostructures. The totalband discontinuity distributed over the conduction and valancebands as ΔEc and ΔEv, depends on the semiconductors and theamount of mismatch strain at the interface. The ratio ofΔEc:ΔEv is not constant for different heterointerfaces. Severalelectrical and optical measurements of band offsets are well-established [1–4]. The successful application of III–V nitridematerials for light emitting diodes (LEDs) and laser diodes(LDs) has initiated a big amount of research interest in this area.InXGa1−XN/GaN heterostructures and quantum wells (QWs) areespecially important since they are promising materials for theviolet–blue–green range.

The absence of lattice matched substrates and miscibilityproblems of InN and GaN make the growth of InXGa1−XN a verydifficult task. It often leads to wide composition fluctuations andphase separations in the alloy [5,6]. In spite of these problemsInXGa1−XN structures are gaining large importance for applica-tions. The ternary compound semiconductor InXGa1−XN has adirect band gap from 1.9 to 3.4 eV [7] at room temperature and

⁎ Corresponding author. Tel.: +91 33 2350 9115/9116; fax: +91 33 2351 5828.E-mail address: diiibiswas@yahoo.co.in (D. Biswas).

0040-6090/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.tsf.2006.07.139

extremely large heterojunction offsets, which makes the materialhighly successful and promising for light emission around the blueregion [8]. Usually InXGa1−XN/GaN QWs and multi-quantumwells (MQWs) are grown on sapphire substrates by metalorganicchemical vapor deposition (MOCVD). The high compositionalfluctuation of indium content and the wide variation of the thick-ness of QWs have been observed [9] because of alloy disorder,clustering and fluctuation of the well width. These play an impor-tant role in the final device. Despite the high dislocation density inGaN and InXGa1−XN grown on sapphire, surprisingly high light

nm-scale EDX measurements at five locations within a QD (indicated witharrows), corresponding to 54%, 42%, 32%, 28%, and 15% of indium from upperleft to lower right.

Fig. 2. Different shades indicate the local indium concentration of a InXGa1−XN/GaN QW sample.

Fig. 4. Gradual widening of the well width along with increasing band gap.

4489D. Biswas et al. / Thin Solid Films 515 (2007) 4488–4491

emission efficiency has been achieved in InXGa1−XN/GaN basedlight emitting devices [5,10,11].

The measurement of band offset of the InXGa1−XN/GaNheterostructures is a very complicated and difficult problem.The measurement has been carried out by various groups ofresearch workers. The band offset ratio, ΔEc:ΔEv has beenestimated to be 83:17, 68:32 from theoretical calculations[6,12], 62:38 by photoluminescence (PL) [13], 30:70 by X-rayphotoemission spectroscopy [14], 38:62 by optical pumping[15]. This unusual large range of estimated band offsets makes itamply clear that the measurement is complicated and needsdeeper understanding.

During the growth of the InXGa1−XN/GaN heterostructureQW and MQWs on sapphire substrates, as highlighted by Yi-Yin Chung et al. [16] and D. Gerthsen et al. [17], thecompositional fluctuations of the indium content is very largeand the fluctuations of the widths of the QWs are also verywide, as shown in Figs. 1 and 2 (Reproduced from [16,17]).These in turn lead to inhomogeneous strain fields in the

Fig. 3. Variation of PL peaks with temperature for 3 nm and 4 nm samples.

structure. These ultimately lead to a wide PL spectrum andmake the band offset measurement unusually complicated. Inthis paper we present new estimates of the band offsets forInXGa1−XN/GaN heterostructures and QWs by fitting someextraordinary PL results choosing suitable electron and holeeffective masses (me⁎ and mh⁎ respectively), bowing parameter,well width and indium concentration.

2. Experimental and theoretical details

In a first set of experiments carried out by Yi-Yin Chunget al. [16], the MQWs of InXGa1−XN/GaN were grown onsapphire substrates with MOCVD. The well widths of thesamples were 3 nm and 4 nm. The as grown samples werethermally annealed in a quartz tube furnace at different tem-

Fig. 5. Variation of energy band gap with indium mole fraction x in InXGa1−XNfor different bowing parameters: (a) b=1.0, (b) b=2.6, (c) b=3.2, (d) variable bvalues, (e) and (f) linear relationship between energies and x values for0bxb0.4.

Fig. 6. Variation of PL peak energies (eV) with transition in quantum well ofwidth 2.6 nm for: (a) experimental [8], (b) b=1.4, me

⁎=0.2m0, mh⁎=1.56m0,

x=0.8, Ec:Ev=38: 62, (c) b=1.4, me⁎=0.2m0, mh

⁎=1.56m0, x=0.8, Ec:Ev=55:45, (d) b=1.0, me

⁎=0.11m0, mh⁎=1.56m0, x=1.0, Ec:Ev=38: 62, (e) b=1.0,

me⁎=0.11m0, mh

⁎=1.56m0, x=1.0, Ec:Ev=55: 45.

4490 D. Biswas et al. / Thin Solid Films 515 (2007) 4488–4491

peratures ranging from 800 °C to 900 °C in N2 ambient for30 min. The PL spectral peak variations with temperatures ofthe two samples at various thermal annealing conditions areshown in Fig. 3 (solid line).

The shift of the PL peak on annealing is rather unusual.Instead of shifting monotonically, the PL peaks undergo aprimary red shift, which is followed by a blue shift as shownin Fig. 3. The nature of annealing and interdiffusion of theelements of the III group are shown in Fig. 4. As annealingproceeds, the band gap of the well material changes and thewell widens so that there are changes in the transition levels inthe well [18]. When the changes of the band gap of the wellmaterial with mole fraction include bowing parameter, asshown in Fig. 5 (Reproduced from [7]), a result like Fig. 3 isanticipated.

In a second set of experiments carried out by Chii-ChangChen [9], InXGa1−XN/GaN MQW structures were grown bylow pressure MOCVD on sapphire substrates. The InGaNwells were 3 nm thick with barriers being 10 nm. Thesamples were optically excited from N2 laser (wavelength,337 nm). The PL spectra were obtained at low powerexcitation and the optical pumping spectra were recorded atdifferent excitation power densities (0.7 MW/cm2 to7.1 MW/cm2). The PL peaks obtained for differenttransitions are labeled in Table 1.

For the first set of experiments, the residual concentration ofindium in the QW on successive annealing was found fromFick's law as [19]:

CðzÞ ¼ C0

2erf

h−zLD

� �þ erf

hþ zLD

� �� �ð1Þ

where C0 is the initial In concentration, 2h is the wellthickness, z is the distance in the growth direction with z=0 atwell center and LD=2√(Dt) is the diffusion length, where t isthe anneal time and D is the diffusion coefficient. The energyband gap Eg of InXGa1−XN was calculated from the equation[8]:

EgðxÞ ¼ ð1−xÞEg;GaN þ xEg;InN−bxð1−xÞ ð2Þ

where, x is the mole fraction of indium, Eg,GaN and Eg,InN arethe energy band gaps of GaN and InN respectively, and b isthe bowing parameter. The energy levels of the finite

Table 1Comparison of the PL peaks [8] and calculated interband transition energies

Interband transition energyE conduction band–valance band

Calculated interbandtransition energy

Peak position inoptical-pumping spectra

E2c–4v 2.99 2.88E1c–5v 2.82 2.74E2c–2v 2.69 2.55E1c–3v 2.43 2.36E1c–1v 2.22 2.14

rectangular QW of different depths and widths were calculatedfrom the formula [20] outlined below:

En ¼ 2P2

ðP þ 1Þ2

� nk2

� �2−

1

3ðP þ 1Þ3nk2

� �4−

27P−8180ðP þ 1Þ6

nk2

� �6" #

ð3Þ

Here P ¼ ð ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m⁎V0= h̄

p Þa=2, V0 and a are the height andwidth of the well respectively and m⁎ is the effective mass ofthe carrier taken into consideration. The parameters chosen forcalculations to fit the PL data of two sets of experiments wereme⁎=0.2m0 [21], mh⁎=1.56m0 [9] and b=1.4. As outlined bythe authors [9,16], for the first set of experiments, the initialindium mole fraction, x, was considered to be 0.7, while in thesecond case, x was taken to be 0.8. The ratio of the band offsetwas varied to make a common best fit to the two sets ofexperiments.

3. Results

The results for the theoretical fit for the first set ofexperiments with the band offset ratio ΔEc:ΔEv=55:45 areshown in Fig. 3. The results for the second set of experimentsare shown in Fig. 6. The experimental data was previouslyfitted [9] with an indium mole fraction ≥80%, correspondingto a band gap of 2.0 eV without any bowing parameter. Thisrequires the indium concentration to be close to 100%, whichis rather unusual for the InGaN material grown as discussedearlier. Moreover, the InXGa1−XN layer with indium concen-tration around 80% without any bowing parameter produces aband gap of 2.2 eV.

4491D. Biswas et al. / Thin Solid Films 515 (2007) 4488–4491

4. Discussions and conclusions

The determination of the band offsets of InXGa1−XN/GaNQWs is quite a complicated proposal because of the facts thatthe indium concentration and the well width vary widely andthere is a propensity of QDs being formed inside the QW. All ofthese lead to wide PL spectra. The peak of the PL spectra ofsuch QWs on annealing and interdiffusion, undergo an unusualred shift followed by a blue shift. This could be explainedthrough quantum mechanical calculations using Fick's law ofinterdiffusion, a suitable bowing parameter and a band offset forthe best fit.

The different interband transition energies of the optical pumpspectra as obtained by strong optical pumping of a InXGa1−XN/GaN QWon sapphire were computed theoretically with the sameparameters varying the band offset for the best fit. The piezo-electric field has been considered as in Chii-ChangChen et al. [9].From the two sets of best agreements between experiment andtheory, the band offsets are determined to be ΔEc:ΔEv=55:45.

References

[1] F. Capasso, G. Margaritondo (Eds.), Heterojunction Band Discontinuity:Physics and device Application, Elsevier, Amsterdam, 1987.

[2] N. Debber, D. Biswas, P. Bhattacharya, Phys. Rev., B 40 (1989) 1058.[3] D. Biswas, N. Debber, P. Bhattacharya, Appl. Phys. Lett. 56 (1990) 833.[4] Dipankar Biswas, Satyajit Chakrabarti, Sudipto Dasgupta, Sudakshina

Kundu, Resmi Dutta, Phys. Status Solidi, B Basic Res.1 236 (2003) 55.

[5] H.W. Shim, R.J. Choi, S.M. Jeong, Le Van Vinh, C.-H. Hong, E.-K. Suh,H.J. Lee, Y.-W. Kim, Y.G. Hwang, Appl. Phys. Lett. 81 (2002) 3552.

[6] Chii-Chang Chen, Kun-Long Hsieh, Gou-Chung Chi, Chang-ChengChuo, Jen-Inn Chyi, Chin-An Chang, J. Appl. Phys. 89 (2001) 5465.

[7] Bernard Gil (Ed.), Low-Dimensional Nitride Semiconductors, OxfordUniversity press, New York, 2002, p. 234.

[8] Shuji Nakamura, Takashi Mukai, Masayuki Senoh, Shin-ichi Nagahama,Naruhito Iwasa, J. Appl. Phys. 74 (1993) 3911.

[9] Chii-Chang Chen, Hui-Wen Chuang, Gou-Chung Chi, Chang-Cheng Chuo,Jen-Inn Chyi, Appl. Phys. Lett. 77 (2000) 3758.

[10] S. Nakamura,M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T.Matsushita,Y. Sugimoto, H. Kiyoku, Appl. Phys. Lett. 69 (1996) 4056.

[11] I. Akasaki, S. Sota, H. Sakai, T. Tanaka, M. Koike, H. Amano, Electron.Lett. 32 (1996) 1105.

[12] C.G. Van de Walle, J. Neugebauer, Appl. Phys. Lett. 70 (1997) 2577.[13] S.-H. Wei, A. Zunger, Appl. Phys. Lett. 69 (1996) 2719.[14] Ch. Manz, M. Kunzer, H. Obloh, A. Ramakrishnan, U. Kaufmann,

Appl. Phys. Lett. 74 (1999) 3993.[15] G. Martin, A. Botchkarev, A. Rockett, H. Morkoç, Appl. Phys. Lett. 68

(1996) 2541.[16] Yi-Yin Chung, Yen-Sheng Lin, Shih-Wei Feng, Yung-Chen Cheng,

En-Chiang Lin, C.C. Yang, Kung-Jen Ma, Cheng Hsu, Hui-Wen Chuang,Cheng-Ta Kuo, Jian-Shihn Tsang, J. Appl. Phys. 93 (2003) 9693.

[17] D. Gerthsen, B. Neubauer, A. Rosenauer, T. Stephan, H. Kalt, O. Scho¨n,M. Heuken, Appl. Phys. Lett. 79 (2001) 2552.

[18] Dipankar Biswas, Tapas Das, Subindu Kumar, Abstract Proceedings of theSeventh International Conference on Optoelectronics, Fiber Optics andPhotonics, Cochin, India, December 9–11, 2004, p. 337, OMD 6.3.

[19] W.P. Gillin, D.J. Dunstan, K.P. Homewood, L.K. Howard, B.J. Sealy,J. Appl. Phys. 73 (1993) 3782.

[20] David L. Aronstein, C.R. Stroud Jr., Am. J. Phys. 68 (2000) 943.[21] Jun-jie Shi, Zi-zhao Gan, J. Appl. Phys. 94 (2003) 407.