Chemical deposition of bismuth selenide thin films using N,N-dimethylselenourea

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Semicond. Sci. Technol. 12 (1997) 645–653. Printed in the UK PII: S0268-1242(97)76578-7

Chemical deposition of bismuthselenide thin films usingN ,N -dimethylselenourea

V M Garc ıa†, M T S Nair†, P K Nair † and R A Zingaro ‡

† Laboratorio de Energıa Solar, IIM, Universidad Nacional Autonoma de Mexico,Temixco-62580, Morelos, Mexico‡ Department of Chemistry, Texas A&M University, College Station,TX 77843-3255, USA

Received 23 July 1996, in final form 11 November 1996, accepted for publication17 January 1997

Abstract. Good quality thin films of bismuth selenide of thickness up to 0.28 µmwere deposited from solutions containing bismuth nitrate, triethanolamine andN ,N -dimethylselenourea maintained at temperatures ranging from roomtemperature to 40 ◦C. X-ray diffraction patterns of the samples annealed at 200 ◦Cin air match the standard pattern of hexagonal Bi2Se3 (paraguanajuatite, JCPDS33-0214). The films exhibit strong optical absorption corresponding to a bandgap ofabout 1.7–1.41 eV in the as-prepared films. These values decrease to about1.57–1.06 eV upon annealing the films at 200 ◦C for 1 h in nitrogen. As-deposited,the films show high sheet resistance (∼1012 � �−1) in the dark. Annealing thefilms in air or in nitrogen enhances the dark current by about seven orders ofmagnitude; the resulting dark conductivity is about 10 �−1 cm−1. Thisenhancement in conductivity results from improved crystallinity as well as frompartial loss of selenium.

1. Introduction

Solid solutions of bismuth selenide with bismuth tellurideare well known thermoelectric cooling materials. Thisprompted investigations on preparation of crystals of solidsolutions of Bi2Te3–Bi2Se3 and their alloys. Their structure,composition, mechanical and electrical properties [1, 2] andthe influence of gravity on the crystallization process andelectrical properties [3] have been previously reported.Thin films of bismuth selenide have been prepared bychemical bath deposition [4, 5] and the molecular jet [6]methods. In chemical bath deposition, the authors [4, 5]used sodium selenosulphate, Na2SeSO3, as the sourceof selenide in a bath containing bismuth nitrate andtriethanolamine. From the electronic absorption spectraof these films, two absorption edges, one at 3500 nmcorresponding to a bandgap of 0.354 eV and another at1200 nm corresponding to a bandgap of 1.03 eV, have beenreported for the films [5]. Based on its bandgap value of0.354 eV, the authors have suggested application of Bi2Se3

thin films as photographic films in infrared photography [5].The chemical bath deposition technique is known to

yield good quality thin films with easily reproducibleproperties in the case of thin films of metal chalcogenides.We have already reported the chemical deposition ofthin films of CdSe [7, 8], ZnSe [9], CuSe [9] andPbSe [10] from solutions containing soluble complexes of

the corresponding metal ions andN ,N -dimethylselenourea.The present work describes a similar procedure fordepositing thin films of bismuth selenide on glasssubstrates using a bath containing solutions of bismuth(III),triethanolamine andN ,N -dimethylselenourea. The effectof annealing the films in air and nitrogen on the structural,optical and electrical properties of the films is presented.The issue of the optical bandgap is discussed and possibleapplications of the films are considered.

2. Experimental details

2.1. Materials

Baker-analysed reagent-grade bismuth nitrate penta-hydrate (Bi(NO3)3·5H2O) and triethanolamine (TEA,N(CH2CH2OH)3), anhydrous sodium sulphite(Na2SO3) ofanalytical reagent quality from Productos Quımicos Mon-terrey, andN ,N -dimethylselenourea((CH3)2NCSeNH2)

prepared in our laboratory following the method reportedearlier [11] were used in the deposition of the bismuthselenide thin films. Corning glass microscope slides of26 mm× 76 mm× 1 mm were used as substrates. Thesubstrates were cleaned well using detergent and water anddried prior to film deposition.

0268-1242/97/050645+09$19.50 c© 1997 IOP Publishing Ltd 645

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2.2. Deposition of the thin films

A solution of approximately 0.5 M bismuth nitrate wasprepared by dissolving 24.25 g of Bi(NO3)3 ·5H2O in65 ml of 3.7 M TEA and making the volume to 100 mlwith deionized water in a standard volumetric flask.The deposition bath was prepared in a 100 ml beakerby the sequential addition (under stirring) of 7 ml ofthe bismuth solution, 7 ml of 3.7 M TEA, 20 ml of0.066 M solution ofN ,N -dimethylselenourea preparedfreshly in 0.01 M Na2SO3 and 56 ml of deionized water.Thus the total concentration of the constituents of thefreshly constituted bath may be described approximatelyas: Bi(III), 0.035 mol l−1; triethanolamine, 0.42 mol l−1;N ,N -dimethylselenourea, 0.013 mol l−1; and sodiumsulphite, 0.002 mol l−1. The cleaned glass substrateswere placed in the bath against the wall of the beaker.This was covered with a larger beaker kept inverted. Thedepositions were allowed to proceed without stirring fordifferent durations at room temperature (22–26◦C) as wellas at 30◦C, 34◦C and 40◦C. A temperature-controlled ovenwas used for this purpose. At the end of the deposition,the substrates were removed from the bath and washedwell with deionized water and dried. Both sides of theglass substrates were coated with thin films. The substratesurface facing the wall of the beaker during the depositionwas coated with a specularly reflective uniform thin film.This film was retained for all the measurements. Thecoating on the surface of the substrate facing the interior ofthe bath exhibited a mosaic appearance due to precipitatesettling on the growing thin film surface. This film wasremoved by a cotton swab moistened with dilute HCl. AnAlfa Step 100 unit (Tencor Inc., CA, USA) was used tomeasure the film thickness.

2.3. Characterization of the films

The optical transmittance and the near-normal specular re-flectance spectra of the films were recorded on a ShimadzuUV-3101PC UV–VIS–NIR scanning spectrophotometer.The light beams were incident from the film side. Thereference was air while recording the transmittance spec-tra and a front aluminized mirror in the case of reflectancespectra. X-ray diffraction (XRD) patterns of the films wererecorded on a Siemens D 500 machine with CuKα radia-tion. X-ray fluorescence spectra were recorded on selectedsamples in a Siemens SRS 303 spectrometer. Electricalconductivity measurements were done using a Keithley 230programmable voltage source coupled with a 619 electrom-eter/multimeter and an XT personal computer. The electri-cal contacts to the film surface were made through a pair ofsilver paint electrodes of 5 mm length printed at a separa-tion of 5 mm. For the photocurrent response measurementsthe samples were illuminated with a tungsten–halogen lampproducing an intensity of 2 kW m−2 over the plane of thesample. The applied bias was 10 V. The samples wereallowed to reach the steady-state dark current and subse-quently the photocurrent response curves were recorded for20 s in the dark, 20 s under illumination and for 20 s afterthe illumination was shut off.

3. Results and discussion

3.1. Film growth

The basic principles involved in the chemical bathdeposition of metal chalcogenides have been discussedin earlier papers [12–15]. In the present case, theformation of Bi2Se3 in the bath involves the hydrolysisof dimethylselenourea which releases selenide ions into thebath:

[(CH3)2NCSeNH2] +OH−→(CH3)2NCN+H2O+ HSe−

HSe− +OH− → H2O+ Se2−

and the dissociation of triethanolaminebismuth(III) complexions which releases bismuth ions:

[Bi(TEA)n]3+ → Bi3+ + nTEA.

These ions can now condense on an ion-by-ion basis toproduce thin film on the glass substrate and over the wallof the beaker. The ions also condense and settle down asprecipitate in the bath. The overall chemical equation forthe formation of bismuth selenide in the present bath canbe stated as:

2[Bi(TEA)]3+ + 3[(CH3)2NCSeNH2] + 6OH−

→ 3[(CH3)2NCONH2] + Bi2Se3+ 3H2O+ 2TEA.

In chemical bath deposition, the formation ofa thin film on a substrate takes place through anucleation process followed by a growth phase until aterminal thickness is reached [15, 16]. The choice ofN ,N -dimethylselenourea as a source of selenide ions in anaqueous medium was made after a careful study of varioussubstituted selenoureas, selenazolones and selenazoles [11].N ,N -dimethylselenourea was found to be the most stableagainst decomposition into elemental selenium. Theuse of sodium sulphite in the chemical bath containingdimethylselenourea further inhibits the oxidation of selenideto selenium, as discussed in [10]. Thus we expect the filmsdeposited by the present technique to be devoid of elementalselenium.

Figure 1 shows the increase in thickness of the bismuthselenide thin films as a function of duration of depositionat room temperature (22–26◦C), 30◦C, 34◦C and 40◦C.The rate of deposition increases with the bath temperature.This is expected because of the increase in concentrationsof Bi(III) and Se2− ions in the bath due to enhanceddissociations of the metal complex ion as well as ofN ,N -dimethylselenourea in solution at higher temperatures.Such behaviour is very common in the chemical bathdeposition of metal chalcogenide thin films [15, 16].

3.2. Structure and composition of the films

Figure 2 shows the XRD patterns of the films, as-preparedand after they were annealed in air for 1 h at 200◦C. TheXRD profile of the glass substrate, which is typical ofamorphous glass, is also given. The as-prepared film showslittle crystallinity—the XRD profile is not distinct from thatof the glass substrate. Well defined peaks corresponding to

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Chemical deposition of Bi2Se3 thin films

Figure 1. Variation of Bi2Se3 thin film thickness as afunction of the duration of deposition at different bathtemperatures: room temperature (22–26 ◦C), 30 ◦C, 34 ◦Cand 40 ◦C.

the thin film are absent in the XRD pattern. However,the crystallinity of the film improves upon annealing andXRD peaks appear superimposed on the XRD profile ofthe glass substrate. This XRD pattern matches well thestandard pattern of Bi2Se3 mineral paraguanajuatite (JCPDS33-0214) which possesses hexagonal layer structure withalternating layers of Bi and Se. The crystallographic datafor this structure of bismuth selenide have been cited asa = 0.41396 nm andc = 2.8636 nm. The XRD resultstherefore establish that the films deposited by the presenttechnique possess this structure and hence a compositionBi2Se3.

The grain size of the crystallites (mean crystallitediameter,D) in the annealed film was calculated usingScherrer’s equation [17]:D = 0.9λ/β cosθ , whereλ isthe wavelength of the x-ray (0.154 06 nm in the presentcase),β is the full width in radians at half maximum ofthe peak andθ is the Bragg angle of the x-ray diffractionpeak. Calculation made on the (015) peak at 2θ = 29.48◦

(θ = 14.74◦) in figure 2 gave a value of 12 nm for thecrystallite diameter. A close value, 11 nm, was fromthe (006) peak at 2θ = 18.44◦. The conversion ofthe as-deposited amorphous thin films to crystalline filmswith well defined crystal structure and grain size in therange of 10–20 nm is a behaviour shared by chemicallydeposited bismuth sulphide thin films as well [18, 19].In the latter case, annealing the as-deposited amorphousbismuth sulphide thin films at 200◦C leads to crystallizationinto a structure corresponding to that of the mineral samplebismuthinite with composition Bi2S3.

Figure 2. CuKα XRD patterns of bismuth selenide thinfilms, as-prepared and air annealed for 1 h at 200 ◦C alongwith the XRD profile of the glass substrate and thestandard XRD powder pattern (JCPDS 33-0214) of Bi2Se3(paraguanajuatite).

3.3. Optical transmittance and reflectance spectra

The optical transmittance and reflectance spectra of thebismuth selenide films of three different thicknesses,recorded in the wavelength range of 200 to 2500 nm,are given in figure 3. These curves exhibit superimposedoptical interference patterns in the case of thicker films.The quality of the films is attested to by the fact thatthe sum of the percentage reflectance and transmittancein the long-wavelength region, away from the absorptionedge, adds up to almost 100. In the figure we have alsoincluded transmittance curves corrected for the reflectionlosses. The reflectance of the films vary dependingon the film thickness. It is more than 40% at certainwavelength ranges. The transmittance corrected for thereflectance losses (Tcorr) may be expressed to a firstapproximation asTcorr(%) = 100T (%)/(100− R(%)) forany wavelength. This correction modifies the transmittancecurves considerably and the characteristic optical absorptionof the semiconductor material emerges. The correctedtransmittance curves will be used for the calculation of theoptical bandgap of the material of the film.

Figure 4 shows the effect of annealing the films inair or nitrogen on the optical transmittance and reflectancespectra. Here again, the corrected transmittance spectra isgiven. Comparison of the corrected transmittance curves ofthe as-prepared and annealed films of thickness 0.15µm orhigher, suggests a shift in the absorption edge towards thelonger wavelength upon annealing.

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Figure 3. Optical transmittance (T %) and reflectance (R%) spectra of the as-prepared Bi2Se3 thin films of three differentthicknesses: 0.09 µm, 0.15 µm and 0.25 µm. The optical transmittance data corrected for reflection losses (Tcorr) and T + Rdata for one of the samples are also given.

3.4. Evaluation of optical bandgap

Figure 5 shows the plots ofα2 versushν of representativefilms, whereα is the absorption coefficient andhν thephoton energy. These values were computed from thecorrected optical transmittance curves illustrated in figures 3and 4. The absorption coefficient is calculated at anywavelength (and hence at the corresponding photon energy)using the relationα = (1/d) ln(100/Tcorr(%)), where dis the film thickness. Extrapolation of the straight linepart in each of the plots to the abscissa gives a valuefor the direct bandgap. Optical bandgap values distinctfrom that of the bulk crystalline material are known toexist in polycrystalline thin films. The variation is ascribedto very small crystallites constituting a thin film whichresults in the quantum confinement of charge carriers inthe crystallites. The resultant effect is an increase inthe bandgap in thin films, as compared with its value in

bulk crystalline material, when crystallite size is typicallyless than 10 nm [20]. In a thin film, the crystallitesize depends on the specific technique of deposition andthe annealing conditions. For example, in the case ofchemically deposited CdSe thin films, optical bandgaps inthe range of 1.7 eV to 2.4 eV have been reported, dependingon the deposition conditions [21].

In the case of the bismuth selenide thin film of 0.09µmthickness, the as-prepared film in figure 5 indicates a directbandgap of 1.70 eV. When annealed in nitrogen at 200◦Cfor 1 h, this value drops to 1.57 eV. In the case of thickersamples (0.15µm, 0.18µm and 0.25µm), the as-preparedfilms indicate a direct bandgap of about 1.41 eV. Whenannealed at 200◦C for 1 h in air or nitrogen the valuedrops to 1.08–1.06 eV. For the sake of clarity, only the plotfor the film of 0.15 µm thickness is given to represent thethicker films. The shift in the absorption edge toward longer

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Chemical deposition of Bi2Se3 thin films

Figure 4. Optical transmittance (T %), reflectance (R%) and Tcorr(%) spectra of the films of figure 3 recorded after annealingin air or nitrogen at 200 ◦C for 1 h each.

wavelength upon annealing the chemically deposited thinfilms is associated with an improvement in the crystallinityof the films [18, 19]. In the present case the improvementin the crystallinity of the films upon annealing is evidencedin the XRD pattern in figure 2.

In the literature, Bi2Se3 is reported as a semiconduc-tor material with a direct bandgap. Two different valuesfor the minimum energy gap are reported for bulk Bi2Se3:0.35 eV [22] and 0.16 eV [23]. In the case of chemically de-posited thin films of Bi2Se3, the presence of two absorptionedges has been reported [4, 5]: one at 3500 nm correspond-ing to 0.354 eV and the other at 1200 nm corresponding to1.03 eV. The latter value is close to what is obtained for theannealed films (of thickness>0.15µm) reported here. Fig-ure 5 establishes that this value is that of a direct bandgapassociated with the strong optical absorption in the film.

Figure 3 shows that very little optical absorption takesplace at wavelengths above 1500 nm (or a photon energy of

less than 0.83 eV) in any of the films. The optical absorp-tion is not significant at such wavelengths in the case of an-nealed films (figure 4). Particularly notable is the near-zerooptical absorption at wavelengths above 850 nm (photon en-ergy less than about 1.5 eV) in the case of as-prepared or an-nealed films of thickness 0.09µm. Figure 6 shows the plotsof α2 andα1/2 versushν, evaluated from the corrected opti-cal transmittance curves represented in figure 4 for the low-energy region (0.5–0.8 eV). Data for thicker films which arenot given in figure 4 (for the sake of clarity) are includedin figure 6. A straight line fit is possible over the entirelow-energy spectral region in the case of theα1/2 versushν plots for the films of different thicknesses. This indi-cates that the very low optical absorption may be related toan indirect bandgap with energy in the 0.2–0.35 eV range.The presence of direct bandgaps at energies of 0.16 eVor 0.34 eV reported by other researchers [5, 22, 23] is notevident in the case of the present films.

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Figure 5. Plots of α2 versus hν in the region of high opticalabsorption of two of the samples of figures 3 and 4computed from Tcorr(%) values.

We also consider that the weak optical absorption inthe low-energy region of the transmittance spectra may berelated to diffuse scattering losses from the film surface.Such scattering will depend on the roughness of thesurface [24]. Figure 7 shows the plot of logA versuslogλ, whereA is the extinction of the transmitted beam(due to scattering losses from the surfaces and absorptionin the medium),A = 1− (Tcorr/100). It is seen that thedata fit a straight line in the log–log plot, i.e. they obey arelation of the type,A = constant× λ−n. This is typicalof many scattering mechanisms. Rayleigh scattering, whichapplies to particles of size less than the incident wavelength,is characterized byn = 4, and for intermediate cases,n = 2 [24]. In figure 7,n has values 1.9 to 4.3 illustratingthat the extinction data in the low-energy region may alsofit into specific scattering mechanisms. Further work isrequired to establish the extinction processes and confirmwhether the weak extinction observed in the low-energyregion of the films should be associated with an indirectoptical bandgap or whether it results from scattering losses,or both.

We wish to point out that most of the publishedresults on the optical properties of bismuth selenide[25–27] are based on optical reflectance on single crystalsof Bi2Se3 with relatively high electrical conductivities(103 �−1 cm−1). These results cannot be readily correlatedwith the present work. In the case of thin filmsprepared by vacuum techniques of the same range ofelectrical conductivities, the optical properties have notbeen discussed [28, 29].

3.5. Electrical properties

Figure 8 shows the photocurrent response curves of the thinfilms as a function of thickness of the bismuth selenide thinfilms, as-prepared and after having been annealed for 1 heach in air or nitrogen at 200◦C. The as-prepared samplesare seen to be very resistive—showing sheet resistancesof 8.8 × 1012–2.1 × 1011 � �−1 in the dark. Underillumination, the corresponding values are 1.3 × 1011–1.2×1010 � �−1; the resistance being lower at higher filmthicknesses. The highest photocurrent-to-dark current ratio(70) is obtained for the thinnest of the samples (0.09µm)—a result similar to what was reported for bismuth sulphidethin films [30].

After annealing in air, the films show a systematicincrease in the dark current with film thickness, even thoughsuch an effect was not obvious in the case of the as-preparedfilms. Annealing in a nitrogen atmosphere increases thedark current of the samples by about an order of magnitudecompared with the samples annealed in air. The increase inthe current is due to the improvement in the crystallinity ofthe films, which would increase the charge carrier mobility.Annealing in a nitrogen atmosphere inhibits incorporationof oxygen in the grain boundaries and hence furtherenhances the mobility [31]. The photosensitivity is hardlynoticed in the case of the thicker samples, which acquirehigh electrical conductivities, of about 10�−1 cm−1. Thecarrier type in the annealed films was tested by the hotprobe method and the material was found to be n-type.Again, similar behaviour has been reported in the case ofchemically deposited bismuth sulphide thin films [18].

The XRF spectra of the as-prepared and annealed filmsshown in figure 9 suggests that the drastic increase in theelectrical conductivity of the annealed films may also bedue to a loss of selenium—a process which would makethe films bismuth rich on an atomic scale and hence makethem n-type. The ratio of the area under the XRF peak ofbismuth Lα1 (λ = 0.11439 nm, 2θ = 47.36◦) and of thecombined XRF peaks of selenium Kα1 (λ = 0.11048 nm,2θ = 45.65◦) and Kα2 (λ = 0.11088 nm, 2θ = 45.83◦)in the as-prepared film (full curve) was considered tocorrespond to the atomic ratio of a stochiometric Bi2Se3

material, i.e. 2/3 = 0.67. This indicated a ratio of thesensitivity factors for the bismuth peak and the combinedselenium peaks of 0.5. The ratio of the area under thecorresponding peaks of the annealed film was multiplied bythe factor 0.5 to estimate the atomic ratio of bismuth andselenium in the annealed film. This indicated a value 0.98,suggesting a notably higher atomic percentage of bismuthin the annealed film. The annealing at a higher temperature,300◦C, for 1 h was done in order to produce a more notableeffect than is possible under annealing at 200◦C.

3.6. Applications of the films

The above results show that the chemically depositedbismuth sulphide thin films reported here possess strongoptical absorption corresponding to a direct bandgap inthe 1.7–1.06 eV region. Annealed thin films of thickness>0.15 µm indicate a bandgap of nearly 1.06 eV, whichin solar cells should result in conversion efficiencies up

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Chemical deposition of Bi2Se3 thin films

Figure 6. Plots of α2 and α1/2 versus hν for the region of low optical absorption of various samples annealed in air ornitrogen at 200 ◦C for 1 h each computed from Tcorr (%) values represented in figure 4.

to 21% according to Prince-Loferski analyses [32]. Theelectrical conductivity (n-type) of the chemically depositedbismuth selenide thin films may be modified using post-deposition treatments such as nitrogen annealing for makingthem suitable for integration into solar cell structures.

Recent work on chemically deposited CuS filmson Bi2S3 films has indicated the formation of a newcompound, Cu3BiS3, with crystal structure correspondingto the mineral sample wittichenite [19, 33]. Witticheniteis a mineral sample obtained from Wittichen mine inGermany [34]. The formation of the thin film materialof this composition was achieved by depositing a coppersulphide thin film on a bismuth sulphide thin film andsubjecting the stack to annealing at 280◦C for about 1 h.This leads to interfacial diffusion of the atoms—a processalso previously reported in chemically deposited PbS–CuSand ZnS–CuS stacks [35]. The solid state reaction hasbeen suggested as: 6CuS+ Bi2S3→ 2Cu3BiS3+ 3S↑. Weconsider that the same reaction may be extended to Bi2Se3–CuSe stacks as well, in which the Bi2Se3 film is depositedby the present method and the CuSe film is deposited asreported in [9]. The formation of the compound Cu3BiSe3

in the bulk form has been reported previously [36], whichindicates the feasibility of this approach. This material

is expected to be of p-type conductivity, due to copperdeficiency. It may also be electrochemically stable indevice configuration because of the inhibition of copper(Cu+) diffusion through the material by Bi3+—in a similarmanner as achieved in the case of CuInSe2—a provenabsorber material for thin film solar cells [37].

4. Conclusions

In this paper we have reported a method for producinggood quality bismuth selenide thin films from a chemicalbath containingN ,N -dimethylselenourea as the source ofselenide ions. The as-prepared samples have a structurewhich is mainly amorphous, having a high sheet resistancewhich decreases with the increase in thickness. As-prepared, the films are nearly intrinsic. We report thatthe air and nitrogen annealing process at 200◦C increasesthe dark conductivity by many orders of magnitude, whicharises from an enhancement of the crystallinity of thematerial indicated by the XRD pattern matching JCPDS33-0214 of paraguanajuatite, and loss of Se from the film.Both these processes transform the as-prepared materialinto a conductive state, having an n-type conductivity of

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Figure 7. Plots of log of the extinction coefficient (A)versus log of wavelength (λ) of the representative annealedthin films.

Figure 8. Photocurrent response curves of Bi2Se3 thinfilms of different thicknesses recorded for samples:as-prepared (A, 0.09 µm; B, 0.15 µm; C, 0.18 µm;D, 0.25 µm); annealed in air (A1–D1); and annealed innitrogen (A2–D2) with an applied bias of 10 V across 5 mm.

about 10�−1 cm−1. This may open up various possibilitiesfor the application of these films prepared by the chemicaldeposition technique.

Figure 9. X-ray fluorescence spectra of the as-prepared(full curves) and air annealed (300 ◦C, 1 h) Bi2Se3 thin films.The plots show only the Kα1 (λ = 0.110 48 nm, 2θ = 45.65◦)and the Kα2 (λ = 0.110 88 nm, 2θ = 45.83◦) peaks for Seand the Lα1 (λ = 0.114 39 nm, 2θ = 47.36◦) peak for Bi,which are the strongest peaks for these elements.

Acknowledgments

The authors are grateful to Leticia Banos of IIM, UNAMfor recording the XRD and XRF patterns and to CONACYT(Mexico) and DGAPA (UNAM-Mexico) for financialsupport. We also acknowledge the financial support givento one of us (VMG) by the Universidad Autonoma deZacatecas, Mexico.

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