Spectroscopic ellipsometry studies of GaN films deposited by reactive rfsputtering of GaAs targetA. Biswas, D. Bhattacharyya, N. K. Sahoo, Brajesh S. Yadav, S. S. Major et al. Citation: J. Appl. Phys. 103, 083541 (2008); doi: 10.1063/1.2903443 View online: http://dx.doi.org/10.1063/1.2903443 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v103/i8 Published by the American Institute of Physics. Related ArticlesProperties of InxGa1−xN films in terahertz range Appl. Phys. Lett. 100, 071913 (2012) Thermal carrier emission and nonradiative recombinations in nonpolar (Al,Ga)N/GaN quantum wells grown onbulk GaN J. Appl. Phys. 111, 033517 (2012) Surface depletion mediated control of inter-sub-band absorption in GaAs/AlAs semiconductor quantum wellsystems Appl. Phys. Lett. 100, 051110 (2012) High-Q optomechanical GaAs nanomembranes Appl. Phys. Lett. 99, 243102 (2011) Mg-induced terahertz transparency of indium nitride films Appl. Phys. Lett. 99, 232117 (2011) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Spectroscopic ellipsometry studies of GaN films deposited by reactive rfsputtering of GaAs target

A. Biswas,1 D. Bhattacharyya,1,a� N. K. Sahoo,1 Brajesh S. Yadav,2 S. S. Major,2 andR. S. Srinivasa3

1Spectroscopy Division, Bhabha Atomic Research Centre, Mumbai 400 085, India2Department of Physics, Indian Institute of Technology Bombay, Mumbai 400 076, India3Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay,Mumbai 400 076, India

�Received 16 November 2007; accepted 29 January 2008; published online 25 April 2008�

GaN films have been deposited by reactive rf sputtering of GaAs target in 100% nitrogen ambienton quartz substrates at different substrate temperatures ranging from room temperature to 700 °C.A series of films, from arsenic-rich amorphous to nearly arsenic-free polycrystalline hexagonalGaN, has been obtained. The films have been characterized by phase modulated spectroscopicellipsometry to obtain the optical parameters, viz., fundamental band gap, refractive index, andextinction coefficient, and to understand their dependence on composition and microstructure. Ageneralized optical dispersion model has been used to carry out the ellipsometric analysis foramorphous and polycrystalline GaN films and the variation of the optical parameters of the films hasbeen studied as a function of substrate temperature. The refractive index values of polycrystallinefilms with preferred orientation of crystallites are slightly higher �2.2� compared to those foramorphous and randomly oriented films. The dominantly amorphous GaN film shows a band gap of3.47 eV, which decreases to 3.37 eV for the strongly c-axis oriented polycrystalline film due to thereduction in amorphous phase content with increase in substrate temperature. © 2008 AmericanInstitute of Physics. �DOI: 10.1063/1.2903443�

I. INTRODUCTION

The fabrication of GaN based light emitting diodes�LEDs� and laser diodes has been followed by a variety ofshort wavelength optoelectronic devices, such as solar blindphotodiodes, UV LEDs, and detectors.1–4 GaN has also re-ceived enormous attention due to its applications in whitelight sources,5 high frequency power transistors,6 high elec-tron mobility transistors,6 and spintronic devices.7 Devicequality epitaxial GaN films have usually been grown usingmetal organic chemical vapor deposition �MOCVD� or mo-lecular beam epitaxy �MBE� techniques.1,8 However, owingto their enormous application potential, there has recentlybeen increasing interest in polycrystalline GaN films grownby MBE,9–14 MOCVD,15–18 and sputtering.19–36

Polycrystalline,19 nanocrystalline,20 and amorphous37 GaNhave also shown good luminescence characteristics. Applica-tions of polycrystalline GaN films have been demonstrated inLEDs,38,39 white lighting,39 UV photodetectors,40 solarcells,41,42 thin film transistors,43,44 and field electronemitters,16,45 and suitability of GaN films for application inlarge area flat panel displays has also been explored.46 Thepotential of GaN films for these applications has thus driventhe search for low cost and low temperature deposition pro-cesses on low cost substrates.

The inherent ability of sputtering to deposit large areathin films on a variety of substrates at relatively lower tem-perature opens up enormous opportunities for GaN. There

have been several early reports on the growth of GaN filmsby reactive sputtering of Ga target with nitrogen or nitrogen-argon mixture,21–23 though problems of reproducibility aris-ing out of the low melting temperature of gallium have beenreported.24 During the past few years, polycrystalline GaNfilms have been deposited by sputtering using Ga,25–28

GaN,29–34 or GaAs �Ref. 35� targets. Using the approach ofreactive sputtering of a GaAs target with 100% nitrogen, thecomposition and structure of GaN films grown on amor-phous quartz substrates have been recently studied.36 It hasbeen shown that the substrate temperature plays the mostcrucial role in controlling the composition and microstruc-ture of these films. In the present communication, a compre-hensive optical characterization of GaN films deposited onquartz substrates by this approach has been carried out byusing spectroscopic ellipsometry �SE�. By varying the sub-strate temperature, a series of films has been deposited, witha systematic variation in crystallinity from arsenic-rich amor-phous phase to practically arsenic-free, c-axis oriented poly-crystalline hexagonal GaN. These films have been character-ized by SE by using a generalized model of opticaldispersion for amorphous GaN �a-GaN� and crystalline GaN�c-GaN�.

SE is presently being used not only for the determinationof optical constants but also for a complete nondestructivedepth profiling of thin films and is being applied in wideareas of material science and solid state physics.47,48 Conven-tional ellipsometry suffers from the drawback of slow dataacquisition process and limited spectral range. However, the

a�Author to whom correspondence should be addressed. Electronic mail:dibyendu@barc.gov.in.

JOURNAL OF APPLIED PHYSICS 103, 083541 �2008�

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phase modulated SE technique employed in this study,49,51,52

offers fast and precise data acquisition over a large wave-length range.

Although several results of SE measurements have so farbeen reported on epitaxial or highly oriented GaN filmsgrown by MBE or MOCVD techniques,53,54 sputtered GaNfilms have mostly been studied by optical absorption mea-surements, with only few reports available on SEmeasurements.55,56

II. EXPERIMENTAL DETAILS

The films were deposited by rf magnetron reactive sput-tering of a 3 in. GaAs target with 100% nitrogen as sputter-ing cum reactive gas. A Hartley-oscillator-type rf power sup-ply �13.56 MHz� was used and the anode current was used tomonitor the rf power. A rf shielded heater was used to controlthe substrate temperature from room temperature to700 ��10� °C. Film deposition was preceded by evacuatingthe chamber to a base pressure of 1�10−6 mbar, which wasfollowed by presputtering with nitrogen at 8�10−3 mbar for5 min. The films were deposited at a nitrogen pressure of 8�10−3 mbar and flow rate of 25 SCCM �SCCM denotes cu-bic centimeter per minute at STP�. Atomic force microscopy�AFM� studies were carried out on the films in contact mode,with silicon nitride probes using Digital Instruments Nano-scope IV multimode Scanning Probe Microscope �SPM�.

Ellipsometric data for GaN films were measured in aspectroscopic phase modulated ellipsometer �modelUVISEL™ 460, ISA JOBIN-YVON SPEX� in the wave-length range of 300–1200 nm. In ellipsometry, the variationin the amplitude and the phase difference between the paral-lel �p� and perpendicular �s� components of the reflectedlight polarized with respect to the plane of incidence aremeasured. In general, reflection causes a change in the rela-tive phase of p and s waves and in the ratio of their ampli-tudes. The effect of reflection is measured by the two quan-tities, viz., � �which measures the amplitude ratio� and ��which measures the relative phase change�. These are givenby57

� =rp

rs= tan � exp�i�� , �1�

where rp and rs are the reflection coefficients for the p and scomponents of the waves, respectively. GaN films describedin this communication have been characterized by phasemodulated SE technique, in which the reflected light ismodulated by a photoelastic modulator at a frequency of50 kHz. The modulator is actually a fused silica bar, which issubjected to periodical stress induced by a piezoelectrictransducer. Due to its photoelastic property, the modulatorinduces a phase shift ��t� between the two eigenmodes. Themodulated intensity signal is detected and Fourier analyzedto generate the parameters of interest, viz., � and �.58 Theabove technique provides fast and accurate measurement of� and � over a large wavelength range. Taking into accountthe uncertainty in angular orientation of the optical compo-nents ��0.1° � of the SE, error in the calibration of the pho-toelastic modulator, nonlinearity of the photomultiplier de-

tector, and error in the calibration of the frequency responseof the detection system, the expected overall accuracy of themeasured � and � values is better than 0.5°.

The measured ellipsometry spectra are then fitted withan appropriate theoretical model generated by assuming arealistic two-layer sample structure with a bulklike denselayer on the substrate and a top surface roughness layer. Thesurface roughness layer is modeled as a homogeneous mix-ture of 50% material and 50% void which is a usual practicein ellipsometric analysis of thin films.59 The effective dielec-tric constant of the surface roughness layer containing voidsis obtained using the Bruggeman effective medium approxi-mation �EMA�.59 The optical constants of the quartz sub-strates have been obtained from standard reference60 and ap-propriate dispersion relations for the optical constants ofGaN have been used for the layers. By assuming the abovesample structure, with trial thicknesses of the two layers andparameters of dispersion relation for the different layers asfitting parameters, the measured ellipsometric spectra are fit-ted by minimizing the squared difference ��2� between themeasured and calculated values of the ellipsometric param-eters �� and �� given by

�2 =1

�2N − P��i=1

N

���iexpt − �i

calc�2 + ��iexpt − �i

calc�2� , �2�

where N is the number of data points and P is the number ofmodel parameters. The maximum number of iteration al-lowed is 100 and the criterion for convergence used is ��2

=0.000 001.

III. RESULTS AND DISCUSSION

The GaN films discussed in the present communicationhave been deposited at substrate temperatures ranging fromroom temperature to 700 °C. The composition and micro-structure of these films were studied by x-ray fluorescencespectrometry, x-ray diffraction, transmission electron micros-copy �TEM�, and Raman spectroscopy. These results havebeen presented elsewhere36 and a summary of the importantresults is given below. Below the substrate temperature of300 °C, the sputtered films were predominantly amorphousand contained a large quantity of arsenic. The As /Ga ratiodecreased from �0.9 to �0.6 as the substrate temperaturewas changed from room temperature to 300 °C. The amor-phous phase consisted of GaN or GaAsN and some elemen-tal arsenic could also be present in these films. Above asubstrate temperature of 300 °C, a drastic decrease in thearsenic content of the films takes place, along with a clearindication of the appearance of the polycrystalline phase ofhexagonal GaN. The films deposited above 300 °C weredominantly polycrystalline GaN. The arsenic content of thefilms decreased to �1 at. % at substrate temperatures

500 °C. GaN crystallites exhibited a �101̄0� preferred ori-entation in films deposited at 300–350 °C, which changed to

�101̄1� preferred orientation �closer to random� in films de-posited in the range of 400–550 °C. The films deposited at

083541-2 Biswas et al. J. Appl. Phys. 103, 083541 �2008�

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600 and 700 °C, however, showed a strong �0002� orienta-tion of crystallites and contained negligible amount of ar-senic �0.5 at. % �.

In most of the SE analysis carried out so far on polycrys-talline or amorphous films of GaN or other III-V compoundsemiconductors,55,61 simplified analytical expressions pro-posed by Jellison, Jr. and Modine62 �Tauc–Lorentz model� orFerlauto et al.63 �Cody–Lorentz model� have been used.Here, we have used a generalized optical dispersion modelfor crystalline and amorphous materials proposed by Adachiet al.64 which is derived from the basic quantum mechanicalprinciple of absorption of light inside a material.

For the derivation of the dispersion relations for complexdielectric functions of crystalline semiconductors, Ninomiyaand Adachi65 had started with the following expression relat-ing the energy band structure and imaginary part of the com-plex dielectric function �taking into consideration momen-tum conservation in crystalline semiconductors�:

�2�E� =4e2�2

�2E2 � dk�Pcv�k��2��Ec�k� − Ev�k� − E� , �3�

where � is the combined density of states mass, the Dirac �function represents the joint spectral density of states be-tween the valence Ev�k� and the conduction band Ec�k�states differing by the energy E=�� of the incident light,Pcv�k� is the momentum matrix element between the valenceand the conduction band states, and the integration is per-formed over the first Brillouin zone.

By introducing the concept of joint density of states atthe critical points �CPs� and using the analytical expressionsfor different CPs, expressions for the imaginary part of thedielectric constants ��2� at different CPs can be obtainedfrom Eq. �3� and then using the Kramers–Kronig relation, anexpression for the real part of the dielectric function ��1�,and hence for the complete dielectric function ���, can begenerated over the whole spectral range.

According to the above formalism, the expression for thetotal dielectric function ��E� corresponding to the E0 andE0+�0 transitions is obtained as

��E� = AE0−1.5 f��0� + 1

2 �E0/�E0 + �0��3/2f��s0� �4�

with

f��0� = �0−2�2 − �1 + �0�0.5 − �1 − �0�0.5� ,

f��s0� = �s0−2�2 − �1 + �s0�0.5 − �1 − �s0�0.5� ,

�0 = �E + i��/E0,

�s0 = �E + i��/�E0 + �0� ,

where A and � are, respectively, the strength and broadeningparameters of the E0 and E0+�0 transitions.

As described by Ninomiya and Adachi,65 the complexfrequency-dependent dielectric constant ��E� is given by

��E� = �� + �0�E� + �0x�E� , �5�

where �� is the high frequency component of the dielectricconstant and �0�E� is the contribution of E0 band gap to the

complex frequency-dependent dielectric constant and isgiven by Eq. �4�.

The term �0x�E� in Eq. �5� is the excitonic contribution atE0 and E0+�0 CPs arising due to the Coulomb-like interac-tion between the electrons and holes and is given by

�0x�E� = �n=1

�A0x

n3 � 1

E0 − �G0/n2� − E − i�

+1

2� 1

E0 + �0 − �G0/n2� − E − i� � , �6�

where A0x is the exciton strength parameter and G0 is theexciton binding energy.

Similar expressions can be derived for the variation ofthe dielectric functions near the other CPs also �i.e., at E1 ,E2

gaps, etc.�.Adachi and co-workers have used their model over a

large number of II-VI and III-V semiconductor compoundsand binary alloys.66–68 According to Adachi et al.,64 theabove expressions for the real and imaginary parts of thedielectric constants of a crystalline semiconductor can beused for its amorphous counterpart with different values forCP energies and broadening parameters. The dielectric func-tion �2�E� of an amorphous material shows a relatively fea-tureless spectrum with one broad peak centered near the E1

CP �two-dimensional M0-type� peak of the correspondingcrystalline material. According to Adachi et al.,64 since theshort range coordination in the structures of amorphous ma-terials is preserved, the local coordination of the structureand the values of the first-nearest-neighbor distance, coordi-nation number, or binding energy remain more or less thesame in the amorphous and crystalline phases though thesharp structure in the optical dispersion is absent in the amor-phous phase because of the nonexistence of long range order.If the short range order in the amorphous state is similar tothat in the corresponding crystal, one can expect the elec-tronic and phonon density of states to show some similarity,and thus the density of states in the amorphous state wouldbe a broadened version of that of the crystalline state. Thisidea was confirmed by fitting the experimentally measured��E� spectrum of amorphous Si to the model dielectric func-tion �MDF� proposed by Adachi et al.64 for crystalline Siwith different CP and broadening parameters. Subsequently,the model was also used to describe the optical dispersionfunction of amorphous GaAs.69 Tripura Sundari70 has alsofollowed the CP based approach to describe the commonoptical dispersion function of crystalline and amorphous Si,and thus the estimated amorphization of crystalline Si by ionirradiation. For GaN also, as has been observed by Budde etal.71 by extended x-ray-absorption fine structure measure-ments with synchrotron radiation, the first-nearest-neighborcoordination is similar for a- and c-GaN, and thus the gen-eralized MDF model of Adachi et al.64 discussed aboveshould be applicable.

Figures 1�a�–1�c� show the experimental spectra of �and � for three representative GaN films deposited at sub-strate temperatures of 200, 400, and 700 °C, respectively,over the wavelength range of 300–1200 nm, along with thebest-fit theoretical simulations. The theoretical simulations

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have been carried out by using the dispersion model of Ada-chi et al. given by Eqs. �4� and �6� for the dispersion of theoptical constants of GaN. Because of the limited range ofmeasured data, in the present analysis, the contribution to��E� from the fundamental transition at E0 has only beenassumed and the spin-orbit splitting factor ��0� has been as-sumed to be zero.54 As has been discussed earlier, the sampledeposited at 200 °C is predominantly amorphous, the filmdeposited at 400 °C is polycrystalline film with small grains,while the film deposited at 700 °C has large grains withstrong �0002� orientation. The quality of the ellipsometricfitting shown in Figs. 1�a�–1�c� shows the suitability of themodel of Adachi et al. in describing the optical dispersion ofboth amorphous and crystalline samples.

As mentioned in the previous section, the best fits in allthe above cases are obtained with a two-layer model assum-ing a bulklike dense layer on the substrate and a top surfaceroughness layer with 50% void. Miyazaki et al.56 have alsofound that a two-layer sample structure is required to fit theellipsometric spectra of rf sputtered GaN films in which thebulk GaN layer had a void fraction of 4%, while the surfacelayer had a void fraction of 70%. A similar observation hasalso been made by Yan et al.53 who used variable angle SE

measurements on MBE grown hexagonal GaN films, wheresurface layers were found to contain up to 41% void. Thethicknesses of the bulklike and surface layers of all the filmsdeposited at different substrate temperatures, ranging fromroom temperature to 700 °C, including the above threesamples are shown in Table I. Figure 2�a� shows the variationof the percentage fraction of surface layer thickness over thetotal thickness of the film as a function of substrate tempera-ture, which shows that the fraction varies between 0% and5%.

As mentioned above, the composition and microstruc-ture of these films critically depend on the substratetemperature.36 Since the surface morphology of the films hasdirect relevance to the analysis of ellipsometric data, it hasbeen independently investigated by AFM and typical AFMimages are shown in Fig. 3. The films deposited up to asubstrate temperature of 300 °C, which were dominantlyamorphous, show smooth and uniform surface features oflateral size of 25�5 nm and surface roughness of �2 nm.Nearly similar features were seen for the films deposited upto a substrate temperature of 400 °C, but for higher substratetemperatures, the films exhibited a significantly different sur-face morphology. The film deposited at 500 °C shows an

FIG. 1. Experimental � and � vswavelength along with best-fit theoret-ical curves for representative GaNfilms deposited at substrate tempera-tures of �a� 200 °C, �b� 400 °C, and�c� 700 °C: ������ experimentaldata; �—� theoretical spectrum.

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increase in surface roughness as well as the size of surfacefeatures, which also tend to become asymmetric in shape.With increase in substrate temperature to 550 °C, a drasticchange in the shape of surface features is clearly seen, whichbecome elongated and needlelike. With further increase insubstrate temperature up to 700 °C, the lateral size of thesurface features continues to increase, but the asymmetry inshape remains to some extent. It must be mentioned here thatthe lateral surface features seen in Fig. 3 may not representindividual crystallites, since transmission electron micros-copy �TEM� studies36 have shown that the films depositedbelow 300 °C were dominantly amorphous and those depos-

ited above 300 °C were polycrystalline with crystallite sizein the range of 8–16 nm. In contrast, the size of the lateralfeatures seen from the AFM images varies from �30 nm towell above 100 nm, indicating that these surface featuresrepresent agglomerates of crystallites. However, the increasein overall size of surface features is possibly related to in-crease in crystallite size and thus correlates well with TEMstudies.36 It is interesting to note that the drastic change insurface morphological features with substrate temperature,seen in the AFM images, is associated with the significantchange in the growth rate of the films above 300 °C thattakes place concurrently with the efficient removal of arsenicfrom the growing film and the onset of polycrystallinity.36

The correlation between the surface morphological featuresand the microstructure of the films, particularly crystalliteorientation, is a noticeable and interesting feature but willnot be discussed in detail here.

The values of surface roughness of the films deposited atdifferent substrate temperatures have been obtained from theAFM images and are plotted in Fig. 2�b�. The experimentalerror in the measurement of surface roughness was found tovary between 3% and 5%. The error was smaller for the filmsdeposited below 300 °C. It can be seen that the correlationbetween the fractional thickness of the surface layer and themeasured surface roughness of the films is extremely goodover the entire range of substrate temperature studied. Thisjustifies the two-layer model used for the analysis of ellip-sometry data. It may be mentioned that Koh et al.72 have alsoshown by real time AFM and SE analysis of Plasma-enhanced Chemical Vapour Deposition �PECVD� growna-Si1−xCx :H films that the thickness of the surface roughnesslayer obtained from the ellipsometric analysis gives a realis-tic estimation of the surface roughness of the films. It is thusinferred from Figs. 2�a� and 2�b� that the steady increase infractional thickness of the surface layer with substrate tem-perature manifests the increase in surface roughness of thefilms, as the structure of the films changes from amorphousto polycrystalline with oriented crystallites. However, thefilms deposited at high temperatures �600–700 °C� show a

TABLE I. Best-fit sample structure and best-fit parameters of the dispersion relation as obtained from ellipso-metric analysis of the GaN films deposited at different substrate temperatures.

Substratetemperature

�°C�

Thickness ofbulk layer

��

Thickness ofsurface

roughness layer�� ��

E0

�eV��0

�eV�A0

�eV3/2�A0x

�eV�G0

�eV�

Roomtemperature

8363 38 1.13 3.34 0.359 48.83 0.015 0.405

200 7681 35 1.27 3.39 0.209 52.41 0.003 0.478300 5326 32 1.13 3.47 0.198 52.57 0.011 0.313350 4174 43 2.16 3.44 0.145 45.38 0.017 0.341400 4043 81 2.26 3.43 0.144 44.62 0.015 0.305450 3578 97 2.27 3.42 0.121 40.27 0.007 0.371500 7987 191 2.29 3.41 0.077 38.44 0.007 0.309550 6294 232 2.32 3.39 0.065 37.39 0.006 0.317600 3873 183 2.60 3.38 0.080 38.86 0.014 0.173700 7222 168 2.34 3.37 0.064 42.29 0.011 0.157

FIG. 2. Variation in �a� fraction of the surface layer thickness obtained fromellipsometric analysis and �b� surface roughness measured from AFM im-ages of the films with substrate temperature.

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small decrease in surface roughness, which is attributed tothe increase in lateral size of surface features, as seen fromthe AFM images.

The best-fit values of the parameters of the dispersionmodel for all the films are also shown in Table I. It is foundthat the parameters are of the same order of magnitude asthose obtained by Kawashima et al. in their SE analysis ofMOCVD grown hexagonal GaN films.54 It may be notedfrom Table I that the broadening parameter of the fundamen-tal transition ��� decreases continuously as the substrate tem-perature is increased for the GaN films manifesting the in-crease in crystallinity of the films with increase in substratetemperature. The variation in refractive index �n� and extinc-tion coefficient �k� in the wavelength range of 300–1200 nm

generated by the best-fit parameters of the dispersion modelare shown in Fig. 4 for the films deposited at 200, 400, and700 °C. Yan et al.53 and Kawashima et al.54 have showed asimilar variation in refractive index for MOCVD and MBEgrown epitaxial hexagonal GaN films measured by SE,though their values of refractive index at higher wavelengthswere slightly larger than those of the rf sputtered polycrys-talline GaN films discussed in the present work.

The refractive index �n� values at 1200 nm for all thefilms are plotted in Fig. 5 as a function of the substrate tem-perature. The amorphous films with high arsenic contentshow a small increase in n from 2.05 to 2.1 as the substratetemperature approaches 300 °C. With increase in substratetemperature to 350 °C, a jump is seen in the refractive index

FIG. 3. �Color online� AFM images of films deposited at different substrate temperatures �as indicated in the figure�.

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value to �2.2, beyond which it again decreases to �2.1 inthe substrate temperature range of 450–550 °C. Finally, thefilms deposited at substrate temperatures of 600 and 700 °Cagain show stable refractive index values of �2.2. The fluc-tuation in refractive index with substrate temperature showsan interesting correspondence with the dependence of growth

rate on substrate temperature, which has also been plottedagainst substrate temperature in the same figure. As men-tioned above, the variations in growth rate with substratetemperature above 300 °C have been attributed to changes inthe nature of crystallite orientation of polycrystalline GaN

films.36 The films having strong �101̄0� preferred orientation�substrate temperature �350 °C� or �0002� preferred orien-tation �substrate temperature �550 °C� exhibit a slightlylarger value of refractive index, �2.2, which is close to thevalues of 2.25 and −2.3 reported for epitaxially grown GaNfilms.53,54,73,74 Miyazaki et al.56 have also found that the re-fractive index of the polycrystalline GaN films prepared byreactive sputtering of metallic Ga is slightly less than thecorresponding value for epitaxial GaN film deposited byMOCVD. The lower values of refractive index in the presentcase for films deposited in the substrate temperature range of400–550 °C, however, is due to variation in crystallite ori-entation or near random orientation of crystallites in theabove films.

The variation of fundamental transition energy �E0� orthe band-gap value obtained from ellipsometric analysis isplotted as a function of substrate temperature in Fig. 6�a�. Itis found that the band gap initially increases with substratetemperature and exhibits the largest value �3.47 eV� for thefilm deposited at a substrate temperature of 300 °C. Withfurther increase in substrate temperature, the band gap de-creases in a systematic fashion and the band-gap value of3.37 eV for the film deposited at a substrate temperature of700 °C matches very well with the standard value for hex-agonal GaN �3.38 eV�.54

As has been discussed above, the films deposited up to asubstrate temperature �300 °C are amorphous in nature and

FIG. 4. Dispersion of refractive index and extinction coefficient with wave-length for the GaN films deposited at substrate temperatures of 200, 400,and 700 °C as obtained from the best-fit parameters of the dispersionrelation.

FIG. 5. Variation in refractive index values at 1200 nm and growth rate�nm/h� of the films with substrate temperature �the lines are drawn for guid-ance and are not best fits�.

FIG. 6. Variation in �a� band gap and �b� ratio of amorphous to crystallinephases of the GaN films as a function substrate temperature.

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contain significant quantity of arsenic, which may be in oneor more forms, such as a-GaN and elemental As and/oramorphous GaAsN. The smaller band gap of these films isattributed to the presence of arsenic, since amorphousGaAsN is known to have a smaller band gap than pureGaN.75 The increase in the measured band gap of the amor-phous films with initial increase in substrate temperature isattributed to the reduction in their arsenic content. Large dis-crepancies exist in literature regarding the band-gap valuesof a-GaN films. Bittar et al.76 have reported a band gap of3.1 eV for a-GaN films deposited by ion-assisted thermalevaporation of Ga under N2 ambient, while Kang andIngram77 have reported a band gap of 2.5 eV for a-GaNfilms prepared by ion-assisted reactive evaporation. How-ever, Khosman and Kordesch55 have reported a value of3.44 eV for a-GaN films obtained by reactive rf sputtering ofGa target. Knox-Davies et al.27 and Miyazaki et al.20 havereported band-gap values as high as 3.64 and 3.7 eV for theira-GaN films deposited by rf sputtering of Ga targets undermixed ambient of Ar2, N2, and H2. The largest band-gapvalue of 3.47 eV, which was obtained in the present case forthe film deposited at 300 °C, is thus attributed to its domi-nantly amorphous nature, though it could still be affected bythe presence of arsenic in the film.

As mentioned earlier, the arsenic content of the filmsdeposited above the substrate temperature of 300 °C is sig-nificantly low �1–5 at. % � and the films are predominantlypolycrystalline GaN. It is seen from Fig. 6�a� that with in-crease in substrate temperature above 300 °C, the band gapmonotonically decreases from the value of 3.47 eV to nearlythe value of 3.37 eV for the GaN film deposited at 700 °C.This variation in the band gap has been explained by assum-ing the presence of amorphous phase in polycrystalline GaNfilms deposited above 300 °C which monotonically de-creases with increase in substrate temperature. This conjec-ture has been substantiated by the following analysis.

In the subsequent analysis, it has been assumed that thefilm deposited at 250 °C is completely amorphous, whilethat deposited at 700 °C is completely polycrystalline GaN.The dispersion of optical constants obtained by fitting of theellipsometric data of GaN films deposited at 250 °C hasbeen assumed to be the dispersion relation for �a-GaN�,while the dispersion of optical constants for GaN film depos-ited at 700 °C has been assumed to be the dispersion relationfor �c-GaN�. The ellipsometric data for all the other filmshave been fitted by assuming these films to be mixtures ofa-GaN and c-GaN and the Bruggemann EMA model hasbeen used to determine the effective dispersion constant ofthe film. By fitting the ellipsometric data in this manner, therelative fraction �ratio� of a-GaN and that of c-GaN havebeen determined for all the films deposited above 300 °C.The ratio of amorphous to crystalline phase present in thefilms as obtained by the above method is plotted as a func-tion of substrate temperature in Fig. 6�b�. It is found that thecrystalline phase begins to appear in the films deposited atsubstrate temperature of 300 °C, while the films deposited at600 °C and above are completely polycrystalline in nature.

Finally, the refractive index at 1200 nm and the band-gap values of the films deposited above 300 °C are plotted in

Figs. 7�a� and 7�b� as a function of the fractional amorphouscontent �i.e., ratio of amorphous to crystalline phases� of thesamples which is more relevant to material properties. Thecorrespondence between the amorphous content of the filmsand the measured band gap given in Fig. 7�b� clearly showsthat the above conjecture is justified and the decrease in bandgap of the films deposited at substrate temperatures above300 °C can be attributed to the removal of the amorphousphase from polycrystalline GaN films at higher substratetemperatures. However, as can be seen from Fig. 7�a�, therefractive index values do not monotonically increase withthe decrease in amorphous content of the films and are alsosensitive to the degree of orientation of the polycrystallinefilms, because the presence of crystallites with different ori-entations leads to lower refractive index values for films de-posited at substrate temperatures in the range of400–550 °C.

IV. CONCLUSION

SE measurements have been carried out on GaN filmsdeposited by reactive rf sputtering of GaAs target in 100%nitrogen ambient at different substrate temperatures rangingfrom room temperature to 700 °C. With increase in substratetemperature, the structure of the films changes from arsenic-rich amorphous to nearly arsenic-free oriented polycrystal-line hexagonal GaN. A generalized dispersion model for op-tical constants proposed by Adachi et al. for crystalline andamorphous materials has been used for ellipsometric analysisof the films. Best fits have been obtained for all the filmswith a two-layer sample structure consisting of a bulklikelayer on the substrate and a surface roughness layer on top,

FIG. 7. Variation in �a� refractive index at 1200 nm and �b� band gap of thefilms as a function of amorphous fraction.

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having a void fraction of 50%. It is found that the thicknessof the surface layer increases with the increase in substratetemperature and correlates very well with the surface rough-ness of the films measured from the AFM images. From thebest-fit parameters of the dispersion model, refractive index,extinction coefficient, and band-gap values have been calcu-lated for all the films. The refractive index of the films isrelatively lower for the amorphous films deposited below300 °C. The fluctuation in refractive index of films depositedabove 300 °C with substrate temperature correlates wellwith the dependence of their growth rate on substrate tem-perature, which has been earlier36 attributed to change inpreferred orientation of crystallites. Polycrystalline GaN

films with �101̄0� and �0002� oriented crystallites show re-fractive index value of 2.2 at 1200 nm, which is slightlylower than the reported values of 2.25–2.3 for epitaxiallygrown GaN films. The increase in band gap of the films withinitial increase in substrate temperature correlates well withthe earlier reported36 observation of reduction in arsenic con-tent in the films with increase in substrate temperature. Thelargest band-gap value of 3.47 eV for the film deposited at300 °C is attributed to the dominating presence of a-GaNphase in the film. Above 300 °C, the band gap monotoni-cally decreases with increase in substrate temperature and thenearly arsenic-free GaN film deposited at 700 °C exhibits aband gap of 3.37 eV, close to the reported value for hexago-nal GaN. The decrease in band gap with increase in substratetemperature is attributed to the reduction in amorphous con-tent of GaN films with increase in substrate temperature.

ACKNOWLEDGMENTS

The financial support for this work received from theBoard of Research in Nuclear Sciences, Department ofAtomic Energy, Government of India, is gratefully acknowl-edged. The authors also wish to thank Dr. S. C. Sabharwal,Head, Spectroscopy Division, Bhabha Atomic Research Cen-tre, for his encouragement during this work. FIST �Physics�-IRCC central SPM Facility of IIT Bombay is acknowledgedfor providing the facilities for AFM measurements.

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