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Measurement of change in refractive index

in polymeric flexible substrates using

wide field interferometry and digitalfringe analysis

Gyanendra Singh and Dalip Singh Mehta*

Laser Applications and Holography Laboratory, Instrument Design Development Centre,

Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India

*Corresponding author: [email protected]

Received 17 July 2012; revised 15 October 2012; accepted 2 November 2012;posted 8 November 2012 (Doc. ID 172804); published 7 December 2012

Indium tin oxide coated polyethylene terephthalate (PET) polymeric films are widely used as substratesfor future optoelectronic devices, such as organic LEDs, organic thin film transistors, and organic solarcells. These PET substrates are thin, flexible, and rugged. But residual stresses are trapped in polymericsubstrates due to their manufacturing process, and this leads to the birefringence in flexible displays. Inthis paper we report the measurement of the change in refractive index of PET substrates using MachZehnder interferometry and the Fourier transform fringe analysis technique. Change in refractive indexwas observed by means of bending the PET substrate. This change in birefringence varies the opticalpath difference between the two arms of the interferometer, leading to the fringe shift. From the fringeshift the phase change was extracted as a function of bending, and the change in the refractive index wasdetermined experimentally for two wavelengths, i.e., red and green color lasers. We found that the value

of change in the refractive index of these substrates increases on bending of the substrates. 2012Optical Society of America

OCIS codes: 120.2650, 120.3180, 120.5050.

1. Introduction

Displays are now an integral part of our daily life, asthey are used in our homes, workplaces, vehicles,etc. [1]. Over the last few years display devices havebeen fabricated using liquid crystal technologies that

include twisted nematic LCDs [2], cholesteric LCDs[3], and polymer-dispersed liquid crystal displays [4].But all these displays are fabricated on glass sub-strates, which are breakable and bulky. Recentlythere has been great progress in fabricating displaydevices and many other optoelectronic devices ontoflexible substrates. Flexible electronics and photo-nics is the future concept for display applications.

Flexible substrates are being widely used for emis-sive displays including organic light-emitting diodes(OLEDs) [5], electroluminescent displays [6], field-emitting diodes [7], organic solar cells [8], and evenflexible plasma displays [9]. One of the most funda-mental requirements for flexible electronics is theavailability of a good substrate for device fabricationthat doesnt change its properties while bending. Themost important physical property of these polymericsubstrates is their flexibility in the complete operat-ing device. Other important properties are their low

volume, light weight, easy scalability in size, robust-ness, and low cost [10]. These polymeric substratesare made up of thin plastics substrates, like poly-ethylene terephthalate (PET), polycarbonate, andpolyethylene sulfone polyester films [11,12]. One ofthe major advantages of using polymer sheets as

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the substrate is that we can easily attain the desiredthickness and shape of the substrate by the stretch-ing process and mechanical stress [10]. But there is aproblem of birefringence related to polymeric sub-strates, which is the difference in the refractive indexin two orthogonal directions [13], which mightchange their optical properties during the operationof the devices. The birefringence in PET substratesoriginates during the fabrication process, in which

the mechanical stress causes the molecular reorien-tation of polymeric materials leading to structuralanisotropy and to birefringent optical propertiesi.e., the refractive indices in different directions[14]. Optical birefringence is a desired property inmany applications, like polymers of different typesand materials being used for the fabrication of linearand circular polarizers, pseudodepolarizers, andphase plates with tailored characteristics for work-ing at different spectral ranges [15,16]. Tuning ofthe polymer film can be done during the productionprocess, but the unwanted residual stress that re-mains inside the substrates degrades the opticalquality of the substrates [17]. Birefringence is always

present for plastic substrates because of the residualstress, while the bending of these substrates leads toan additional controllable birefringence due to theexternal applied stress. Further, during the opera-tion of optoelectronic devices fabricated on PETsubstrates, the temperature may change the bire-fringence. Therefore, it is important to study thechange in the refractive index by means of bendingthe substrates over the large area.

Birefringence studies of polymer substrateshave been done using various techniques, e.g.,Stchakovsky et al. presented polarimetric character-ization of optically anisotropic substrates by using

phase modulated spectroscopic ellipsometry as wellas liquid crystal Mueller matrix polarimetry [10].

Van Horn and Winter [18] determined the birefrin-gence and orientation in biaxially stretched polymerfilms and sheets using the conoscopic measurementtechnique. Medhat et al. [19] obtained fringesof equal tangential inclination by curve-inducedbirefringence in a Fortypan photographic plate.El-Dessouki et al. [20] used double-exposure specklephotography for measuring the birefringence of acurved sheet, and Russo [14] gave an alternativemethod for the determination of birefringence instretched polymeric substrates by determining the

phase difference using three different laser wave-lengths and a tilting compensator. Shabana andJaleel [21] studied the optical properties of highlybirefringent polymer films using different interfero-metric techniques. Among all the above-mentionedtechniques, optical interferometry is one of the bestmethods for the study of birefringence, as it can mostprecisely calculate the optical path difference overthe entire visible spectrum for which optical para-meters can be determined.

In this paper we report the study of the optical bi-refringence of a commercially available indium tin

oxide (ITO)-coated PET (ITO/PET) substrate usedin flexible electronics (photonics) by MachZehnderinterferometry (MZI). The change in refractive indexwas observed by means of bending of the PET sub-strate for two different monochromatic wavelengths(red and green lasers). Fourier transform fringe(FTF) analysis was used to reconstruct the phasemaps of the interferograms recorded at differentamounts of bending of the substrates. From this

phase change, the change in refractive index wascalculated. In the following section the theoreticalbackground is given, followed by experimentaldetails and results analysis.

2. Theoretical Background

The two-dimensional (2D) FTF analysis techniquehas been regarded as one of the best techniques,being fast and reliable for extracting the requiredphase information. Fourier fringe analysis hasundergone several modifications over time for im-proving the quality of result interpretation. Theinterference fringes recorded by CCD array are dis-

played on the computer screen. The equation for theintensity of fringes recorded by detector array is in adigitized form that can be expressed as a 2D sinusoi-dal intensity distribution Ix; y by the followingexpression [22,23]:

Ix; y IRx; y IOx; y

2IRx; y IOx; y

pcos 0x; y; (1)

where IRx; y and IOx; y are the intensities of lightcoming from the reference and object arms of theMZI, respectively, and 0x; y is the 2D phase distri-bution of the interferogram. In general, for the FTFanalysis a 2D fringe pattern can be expressed as

hx; y ax; y bx; y cos2fx; y x; y; (2)

where ax; y is the variation of background illumina-tion (irradiance variations arising from nonuniformlight reflection or transmission), bx; y is the ampli-tude modulation of the fringes, fx; y is the spatialcarrier frequency, and x; y is the phase of the in-terference fringes. The input fringe pattern givenin Eq. (2) can be rewritten in the following formfor the convenience of explanation [22]:

gx; y ax; y cx; y exp2if0

cx; y exp2if0; (3)

with

cx; y 1

2bx; y expix; y; (4)

where denotes the complex conjugate. Taking theFourier transform of Eq. (3) with respect to x, theexpression for the Fourier spectrum is shown below:

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Hfx; y Afx; y Cfx f0; y Cfx f0; y;

(5)

where the capital letters denote the Fourier spectra,f0 is the initial spatial carrier frequency, and fx is thespatial carrier frequency with a variable x. TheFourier spectra in Eq. (5) are separated by the carrierfrequencyf0. We make use of either of the two spectraon the carrier, say Cy; fx f0, and translate it by f0

on the frequency axis toward the origin to obtainCf0; y. Note that the unwanted background varia-tion ax; y has been filtered out in this stage.

By computing the inverse Fourier transform ofCf ; y with respect to f, we obtain Cx; y using fastFourier transform (FFT) again. The 2D phase map ofthe interferogram can be computed by using follow-ing expression:

x; y tan1

ImCx; y

ReCx; y

: (6)

From the phase maps corresponding to interfero-

grams recorded at different amounts of bending ofthe ITO/PET substrate, we can calculate change inphase, which is related to the corresponding changein refractive index of the ITO/PET substrate. Thechange in phase of interferograms with bendingcan be expressed by the following expression:

x; y 2

iOPD

2

inx; ydx; y; (7)

where n x; y is the change in refractive index ofthe ITO/PET substrate, which is a function of theamount of bending, i (i 1, 2 corresponding to

red and green colors, respectively) is the wavelengthof laser light, and dx; y is the geometrical thicknessof the PET substrate, which is constant. In Eq. (7),i and dx; y are known constants, and hence by mea-suring the phase difference with different amounts ofbending using Eq. (7), one can determine the changein the refractive index of the ITO/PET substrateusing the following expression:

nx; y i

2

x; y

dx; y

: (8)

The change in the refractive index is valuable for

determining the properties of ITO/PET substrates.As the refractive index is the fundamental propertyof the material, any change in it leads to a changein the final devices [OLEDs, organic thin film tran-sistors (OTFTs), and organic solar cells] fabricatedusing these substrates.

Figure 1 shows the schematic diagram of thevariation of the radius of curvature of an ITO/PETsubstrate on increasing the bending. The radius ofcurvature has been calculated by using simple trigo-nometry (Pythagorean theorem), and the relation isexpressed by

R 4F2 C2

8F: (9)

Here R, F, and C show the radius of curvature,out-of-plane displacement, and chord length, respec-

tively. The calculated radius of curvature for differ-ent amounts of bending of the PET substrate was5, 3, and 2.5 cm [24]. In order to determine the valueof radius of curvature R the distances C and F havebeen calculated.

An MZI was used for recording the fringes using theITO/PET substrate as a test plate. Two spatiallyseparated equivalent paths are present in the MZI,which is used for the measurement of the opticalphase shift. The optical path length is changed bymeans of introducing the test plate in one arm, calledthe object arm, of the interferometer. For constructiveinterference, the phase difference is an even multipleof, and for destructive interference, it is an odd mul-tiple of. The phase difference is given by Eq. (7).

Through bending, stress is applied to the ITO/PETsubstrate, which results an additional controlled bire-fringence along with the residual birefringence (due tothe manufacturing process) of the substrate. Thechange in curvature due to bending of the ITO/PETsubstrate is shown in Fig. 2, which depicts the pre-sence of two types of stresses, i.e., tension and com-pression stress toward the convex and concave sides

Fig. 1. Schematic diagram of the bending of the ITO/PETsubstrate.

Fig. 2. (Color online) Schematic diagram of the ITO/PET sub-strate in bending form, illuminated by the collimated monochro-matic (red or green) light.


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of the bending, respectively. The magnitude of thesestresses varies according to the thickness of the film.Uniform additional birefringence is present on thesubstrate due to the presence of these stresses [19].

The optic axis of the substrate changes according tothe bending curvature, and it always makes the tan-gent to the circle, as shown in Fig. 2. Therefore, theoptic axis is direction dependent rather than varyingin a straight line. As the stress applied to the sub-

strate increases due to bending, that leads to a de-crease in radius of curvature r. Without bending,the radius of curvature can be assumed to be r .

For a very thin substrate, the radius of curvaturefor both faces of the bended substrate can be consid-ered nearly equal. Under these circumstances the in-terference fringes are symmetrical around the axisOX. Then the distance of the fringes from both sideof the symmetric axis is the same and can be calledthe diameter of the fringe 2Z. From Fig. 2, the angleof incidence can be given by [19]

cos r d

r d

2

Z2p ; (10)

where Z is the distance between symmetric axis OXand the fringe, which is the radius of the fringe (PQ),and d is the thickness of the substrate. From RSQ,cos dl, where l is the thickness along the path ofincident light. Putting the value of cos in Eq. (10),we can get l dr dr d2 d212. Thechange in interference pattern occurs due to the var-iation of the value ofl. When the phase difference isan even multiple of2, the constructive interferencetakes place for which [19]

nl m ; (11)

where m is the integer order and is the fractionalorder of the interference fringes. Substituting the

value of l in Eq. (11), we get [19]

dr d

r d2 Z2

q m n: (12)

Since Z varies with angle , which is the angle be-tween the direction of the incidence beam and theradial direction, the relation between the order ofthe fringe and square of the radius, i.e., Z2, can begiven by

Z2 2r d2

dnm: (13)

More details about the derivation of Eq. (13) can befound in [19]. Equation (13) gives the linear relationbetween square of radius Z and order of the fringe,while the value of the change in refractive index(n) varies directly with the curvature (1r).Equation (13) is used for calculating the birefrin-gence of the ITO/PET substrate using fringes ofequal tangential inclination by Medhat et al. [19]and El-Dessouki et al. [20]. We have used the fullfield phase measurement method to determine thechange in n using Eq. (7). We compared our resultswith the theoretical model proposed by Medhat et al.

and El-Dessouki et al., and we found close agreementwith the theory.

3. Experimental Details

A birefringence study of the ITO/PET (surface resis-tivity is 35 sq, D is 5 mil, and transmittance is550 nm, >86%, product no. 639311, Sigma Aldrich,USA) substrate was done using the optical interfero-metric technique, for which an MZI was used, whichis shown in Fig. 3. A green diode pumped solid statelaser with a wavelength of 1 532 nm and a redHeNe laser with a wavelength of 2 632.8 nm,each with 10 mW of power, were mixed at a beam

splitter (BS). Both beams were passed through abeam expander (BE) and a spatial filter (P) unitsimultaneously. A collimating lens (CL) of focallength 24 cm, diameter 30 mm, was used to collimatethe beams. The collimated beams were then made

Fig. 3. (Color online) Schematic diagram of a MachZehnder interferometer used for the study of the ITO/PET substrate.


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incident on a beam splitter (BS1), and were allowedto pass through the aperture (A). The collimatedlight was divided into two beams by BS1 (5050),and the two resulting beams (the sample beamand the reference beam) were reflected by mirrorsM1 and M2, respectively. Two beams then passedthrough the second beam splitter BS2 (5050), andinterference fringes were observed and recorded bya color CCD camera interfaced with computer. TheITO/PET substrate used for the interferometricstudy was placed between one of the arms of theMZI, and interferograms were recorded for the differ-ent amounts of bending of the substrate.

The thickness of the ITO coated substrate is0.129 mm, which was measured by screw gaugeand also was obtained from the manufacturer. A pic-torial representation of the bending given to the PETfilm substrate is shown in Fig. 2. The experiment wascarried out by the following procedure. The ITO/PETsubstrate was placed in one arm of the MZI, and in-terferograms were recorded for different amounts ofbending of the PET substrate for dual wavelengths(1 532 nm and 2 632.8 nm). First a green laser

was switched on, and the ITO/PET without any bend-ing was placed in one of the arms of the MZI (asshown in Fig. 1) and the interference fringe was re-corded. The green laser was blocked and a red laserwas switched on, and the interferogram in the pre-sence of the ITO/PET substrate was recorded underidentical conditions as the sample. Bending wasapplied to the ITO/PET substrate, and the interfer-ograms for the green and red lasers were recordedsequentially by means of switching on one laser andblocking the other laser and vice versa. The bendingof the ITO/PET substrate was further increased andthe experiment was repeated, and interferograms for

the red and green lasers were recorded.4. Results and Discussion

Figures 4(a)4(d) show the interferograms recordedwhen the green laser was switched on with

increasing bending of the ITO/PET substrate.Figures 4(e)4(h) show similar results with the redlaser switched on with increasing bending of ITO/PET substrate. The interferograms were analyzedby the FTF analysis method, which we have dis-cussed in the theory section. First the 2D FFTof eachinterferogram was computed, and the first-orderspectrum of each was filtered out and inverse fastFourier transform (IFFT) was computed. A 2Dwrapped phase map of each interferogram was ob-tained, and the phase map was unwrapped using aMATLAB program. The pictorial representation forthe analysis of the interferograms is shown inFigs. 5(a)5(h), using the interferograms shown inFigs. 4(d) and 4(a), respectively, as examples. A simi-lar procedure was used for the phase map of rest ofthe interferograms. For the analysis of the interfer-ograms shown in Fig. 3, we have used the area, whichis subject to the maximum change in the fringeshape, having the dimensions 648 376 pixels. Asimilar procedure was followed for computing thephase map of a reference interferogram.

The unwrapped phase map of the object [Fig. 5(d)] is

subtracted from the reference phase map [Fig. 5(h)].Figure 6(a) shows the subtracted phase map. Fromthis phase map the change in the refractive index pro-file was calculated using Eq. (8), and the result isshown in Fig. 6(b). From this figure, it can be seen thatthe change in the refractive index is at its maximumat the center of the ITO/PET substrate. Analysis forall the interferograms shown in Fig. 4 has been doneby using the Fourier transform method for two wave-lengths. Figure 6 shows the analysis for the1 532 nm, where gray level images of the recordedinterferograms are used. In this study we have usedFig. 7(a) as the reference interferogram recorded with-

out bending of the ITO/PET substrate. The interfero-grams shown in Figs. 7(b)7(d) are recorded withbending of the ITO/PET substrate. The wrappedphase maps for the interferograms in Figs. 7(a)7(d)are shown in Figs. 7(e)7(h). The unwrapped phase

Fig. 4. (Coloronline) Optical interferograms recordedfor differentamountsof bending of theITO/PET substrateusingthe setup shown inFig. 3 for dual wavelengths.


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maps are calculated from the wrapped phase maps,shown in Figs. 7(e)7(h), using the MATLAB code.The reference unwrapped phase map is subtractedfrom the object phase maps one by one, and the calcu-lated phase difference is shown in Figs. 7(i)7(k).Figures 7(i)7(k) represent the phase difference forthe subtraction of the unwrapped phase mapcorresponding to the reference interferogram givenin Fig. 7(a) and the object interferograms shown inFigs. 7(b)7(d). Changes in the refractive index corre-sponding to the phase differences represented byFigs. 7(i)7(k) are shown below in Figs. 7(l)7(n),

which are calculated by using Eq. (8). The value forthe change in refractive index is given in Table 1.The same analysis was done for the interferograms re-corded using the red laser having wavelength2 632.8 nm, which is pictorially indicated in Fig. 8.

The change in the refractive index for the givenbending of the ITO/PET substrate is given in Table 1for both red and green wavelengths. We have noticedthat on increasing the bending of the substrate, thechange in refractive index also increasing. Thechange in refractive index is very close for the samebending given for the two wavelengths.

We know that plastics are made up of long chainsof molecules (hydrocarbons) known as polymers. Wehave bended the plastic substrate for our experi-ment, which is pictorially represented in Fig. 1. Thebend shown in Fig. 1 depicted that the ITO/PET sub-

strate from inside the curved surface is compressedand stretched from the outside. The cross section ofthe ITO/PET substrate remains unchanged duringbending, because when it compresses from the inside,the material expands sideways [25]. When the red

Fig. 5. (Color online) (a) Object interferograms; (e) reference interferograms; (b), (f) Fourier spectra; (c), (g) wrapped phase maps;(d), (h) unwrapped phase maps.

Fig. 6. (Color online) (a) Phase difference of unwrapped phase maps shown in Figs. 5(d) and 5(h) and (b) 2D change in refractive indexcalculated from phase difference.


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and green laser light passes through the ITO/PETsubstrates, we observe the phase change due tothe bending, which leads to the change in refractiveindex. The phase change caused by bending the sub-strate increases the optical path difference, and thisadditional path difference is added to the phase

change. Stress induced alignment (anisotropy) ofthe molecules that compose the PET substrate isanother reason behind this change in the refractiveindex. Stressing in an arbitrary direction leads to arandom orientation of the polymer molecule in thePET substrate, and the cumulative effect of theITO thin film due to the bending is also a reasonbehind the change in refractive index. The changein the refractive index is due to the strained polymerconfiguration, which causes the change in thebirefringence. However, the phase change is alsowavelength dependent. Birefringence is related todispersion, so the change in the refractive index ofthe PET substrate is related to the wavelength ofthe light passing through the sample.

Fig. 7. (Color online) Interferograms for wavelength 1 532 nm (a) without bending and (b)(d) with gradually increasing bending;(e)(h) the corresponding wrapped phase maps for the recorded interferograms (a)(d); (i)(k) the phase differences for the unwrappedphase maps with respect to the reference interferograms; (l)(n) the changes in refractive index corresponding to the phase differencesshown in (i)(k).

Table 1. Change in Refractive Index by Applied Bending to ITO/

PET Substrate for Dual Wavelength

S. No.Change in RefractiveIndex (1 532 nm)

Change in RefractiveIndex (2 632.8 nm)

1 G1-O 0.1531 103 R1-O 0.1334 10

3

2 G2-O 0.4387 103 R2-O 0.3485 10

3

3 G3-O 1.047 103 R3-O 0.876 10

3


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As ITO is an optically transparent film throughoutthe visible spectrum, the refractive index of thesefilms is modeled by the first-order Sellmeier disper-sion relation, where a, b, and 0 are constants [26]:

n2 1 a b22 20

: (14)

Under standard assumptions, the Sellmeier for-mula reduces to the Cauchy relation, where A andB are the constants for the given PET substrate [26]:

n A B2: (15)

The dispersion of the birefringent film is given bythe following equation, where n is the birefrin-gence at a long wavelength and C is a constant, while

absolute values ofn0 and ne are not required for thecalculation ofn [26]:

n ne no n C2: (16)

According to normal dispersion, by increasing thewavelength, the refractive index decreases. With theabove explanations, we can say that the change inthe refractive index is the phenomenon of both thebending of the ITO/PET substrate and the wavelengthof the laser light used for recording the interfero-grams, which leads to a change in the phase differenceand refractive index. We have observed that thechanges in the refractive index for two different wave-lengths increase with an increase in the bending of theITO/PET substrate. The order of change in the

Fig. 8. (Color online) Interferograms for wavelength 1 632.8 nm: (a) without bending and (b)(d) with gradually increasing bending;(e)(h) the corresponding wrapped phase maps for the recorded interferograms (a)(h); (i)(k) the phase differences for the unwrappedphase maps with respect to the reference interferograms; (l)(n) the changes in refractive index corresponding to the phase differencesshown in (i)(k).


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refractive index is nearly same for both wavelengths.This change in refractive index (birefringence) onbending the plastic substrates used for organic electro-nics and photonics may lead to further changes in var-ious electro-optical properties of the devices, such asconductivity, optical transmission, and the spectrumof light. The present study reported in this papermay give some insight into these properties.

The graph of changes in the refractive index for the

different bending curvatures of the PET substrate isplotted against the reciprocal of the radius of curva-ture, which is shown in Fig. 9. From the graph it isclear that the change in the refractive index is inver-sely proportional to the bending curvature applied tothe PET substrate. The change in the refractiveindex versus reciprocal of radius of curvature forthe green and red wavelengths is shown by the green(with squares) and red (with circles) curves, respec-tively. These results confirm the theoretical modelgiven in Section 2. Using the present method wecan determine the n at each pixel. Our method isbased on the measurement of the phase changedue to the change in the refractive index. Therefore,the accuracy of the determination of change in therefractive index depends on the phase measurement.

The error analysis is done by using Eq. (8), and themaximum error for calculating the value of n isgiven by

n

n

d

d; (17)

where , , and d are the error in the calculationfor wavelength of the light source, phase change bybending the substrate, and thickness of the PETfilm, respectively. The error in finding the value

of 102 nm, 1 102 rad, and d 1 103 mm. Error analysis is done for both greenand red wavelengths used for recording the interfer-

ogram. We have taken the average of and n forall the bending curvatures to calculate the maximumerror. For green and red wavelengths, the calculatedmaximum error is 4.29 106 and 3.589 106,respectively.

5. Conclusions

In conclusion, a commercially available ITO/PETsubstrate has been investigated for different

amounts of bending using a MZI and the Fourierfringe analysis technique. In this study we havefound that the refractive index of the PET substrateincreases with greater bending. This change of re-fractive index may lead to changes in other opticalproperties of the flexible substrate, such as the trans-mission, the spectrum profile of the light passingthrough it, and the conductivity of the devices thatare fabricated on this substrate. This study helpsus to signify the degree of bending that can beapplied to flexible substrate based devices so thattheir spectrum profile may not change drastically,as the emission spectrum is a very important para-meter of display devices such as OLEDs and OTFTs.

G. Singh is thankful to UGC [F.No. 10-2(5)/2007(i)-E.U.II], New Delhi, for financial assistance. Theauthors are also thankful to CSIR for financial grantno. 03(1147)/09/EMR-II.

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