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Journal of Crystal Growth 310 (2008) 2987–2994

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Reaction kinetics of CuGaSe2 formation froma GaSe/CuSe bilayer precursor film

W.K. Kima, E.A. Payzantb, S. Kima, S.A. Speakmanb, O.D. Crisallea, T.J. Andersona,�

aDepartment of Chemical Engineering, University of Florida, 300 Weil Hall, P.O. Box 116550, Gainesville, FL 32611, USAbMetals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

Received 14 June 2007; received in revised form 3 December 2007; accepted 15 January 2008

Communicated by M.S. Goorsky

Available online 30 January 2008

Abstract

The reaction pathway and kinetics of CuGaSe2 formation were investigated by monitoring the phase evolution of temperature ramp

annealed or isothermally soaked bilayer glass/GaSe/CuSe precursor film using time-resolved, in situ high-temperature X-ray diffraction.

Bilayer GaSe/CuSe precursor films were deposited on alkali-free thin glass substrates in a migration-enhanced epitaxial deposition

system. The initial CuSe phase begins to transform to b-Cu2�xSe at around 230 1C, followed by CuGaSe2 formation accompanied by a

decrease in the b-Cu2�xSe peak intensity at around 260 1C. Both the parabolic and Avrami diffusion-controlled reaction models

represented the experimental data very well over the entire temperature range (280–370 1C) of the set of isothermal experiments with

estimated activation energies of 115(716) and 124(719) kJ/mol, respectively. Transmission electron microscopy–energy-dispersive

X-ray spectrometry (TEM–EDS) analysis suggests that CuGaSe2 forms at the interface of the initial GaSe and CuSe layers.

r 2008 Elsevier B.V. All rights reserved.

PACS: 61.10.Nz; 64.70.Kb; 68.55.Nq; 81.10.Jt; 81.15.Hi; 82.20.Pm

Keywords: A1. Growth models; A1. X-ray diffraction; B1. Copper gallium diselenide; B3. Solar cells

1. Introduction

The continuous improvement in the efficiency ofpolycrystalline thin-film Cu(InxGa1�x)Se2 (CIGS) solarcells achieved over the past several decades appears to beplateauing at the high value of 19.5% AM 1.5G [1]. Tosignificantly increase the cell efficiency, recent efforts havefocused on tandem structures that use the highly developedCu(In0.7Ga0.3)Se2 composition (Eg�1.2 eV) for the bottomcell. CuGaSe2 (CGS) is considered as a promising absorbermaterial for the top cell in a CIGS tandem structure [2–4],given its suitable band gap energy (1.68 eV), processcompatibility with a CIGS bottom cell, and completemiscibility of CIGS. Recently, a record cell efficiency of10.23% was reported for a surface-modified single-junction

e front matter r 2008 Elsevier B.V. All rights reserved.

rysgro.2008.01.034

ing author. Tel.: +1352 392 0946; fax: 1 352 392 9673.

ess: tim@ufl.edu (T.J. Anderson).

CGS solar cell [5]. Our previous device simulation resultsusing the AMPS-1D program suggest that it is possible toachieve a 25% (at AM 1.5G) conversion efficiency in aCIGS/CGS tandem cell with a double-graded band gapenergy CIGS bottom cell and a uniform band gap energyCGS top cell [6].There have been several experimental studies that

follow synthesis pathways in the CIS system and it isinteresting to review these results. Katsui and Iwata [7]investigated the reaction pathway for CIS formation fromglass/Cu/In/Se-stacked elemental layers by in situ high-temperature X-ray diffraction (XRD), suggesting thereaction path 2Cu+2In+4Se-Cu2Se+In2Se+2Se-2CuInSe2. Our group also used in situ high-temperatureXRD to track the reaction pathway and determine thekinetics of a-CIS formation from two different bilayerprecursors, InSe/CuSe [8] and In2Se3/CuSe [9], as well asselenization of a co-evaporated Cu and In metals [10]. The

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Fig. 1. Room-temperature XRD scans and TEM micrograph of as-grown

precursor films: (a) glass/GaSe monolayer, (b) glass/GaSe/CuSe bilayer.

W.K. Kim et al. / Journal of Crystal Growth 310 (2008) 2987–29942988

results of the bilayer precursor studies showed direct routesto CIS formation without producing any intermediatephases as expressed by the reactions CuSe+InSe-CuInSe2 [8], and CuSe+1

2In2Se3-CuInSe2+12Se [9]. Dur-

ing the selenization of the Cu–In metal precursor, theformation of CuSe and its transformation to CuSe2, andthen to CuInSe2 were observed [10].

Using DTA, Purwins et al. [11] also studied the reactionkinetics of CIS formation from single and multiple (2, 4and 6 sequences) InSe/CuSe bilayer precursors and alsoobserved the reaction pathway. Similar to our results, theoverall kinetics of CIS formation could be modeled by aone-dimensional diffusion-controlled reaction, and theinitial nucleation reaction at the interface of InSe andCuSe was only observed for four and six alternating InSe/CuSe bilayer precursors, presumably due to the increasedinterfacial area that gave sufficient CIS to be detectable.

These combined studies [8–11] show that for CIS thepathway is dependent on the precursor structure. Theresults are also consistent with a one-dimensional diffu-sion-controlled reaction, and the detailed kinetic para-meters depend on the precursor structure.

The reaction kinetics of CGS formation have beenreported by Purwins et al. [11] for the reaction Cu2Se+Ga2Se3-CuGaSe2 using thermal analysis of Ga2Se3/Cu2Sebilayer, and by our group for selenization of an alloy ofCu–Ga metal precursor [12]. The in situ investigation ofCGS formation by selenization of the Cu–Ga metalprecursor clearly showed formation of the intermediate-phase CuSe followed by transformation to CGS. The datafrom both studies were well described by diffusion-controlled reaction mechanisms with similar values ofactivation energy (i.e., 129–148 kJ/mol for Cu2Se/Ga2Se3and 109(77) kJ/mol for selenization of Cu–Ga).

Comparing the reported results for CIS with those forCGS, the most rapid route to CIS formation is directsynthesis with the InSe/CuSe binary couple (CuSe+InSe-CuInSe2) for temperature o265 1C [8]. In this paper, thereaction pathway and kinetics for direct formation ofCuGaSe2 from a GaSe/CuSe stacked bilayer are studiedusing in situ time-resolved, high-temperature XRD(HTXRD).

It is also noted that only two investigations of the phasediagram of CuGaSe2 [13,14] have been reported. Thepseudo-binary Cu2Se–Ga2Se3 phase diagram was investi-gated by Palatnik and Belova [13] and Mikkelsen [14].Based on the interpretation of numerous DTA and XRDdata, Palatnik and Belova [13] reported three solid solutionsin the range from 40 to 100mol% Ga2Se3 includingchalcopyrite CuGaSe2 (50–65mol% Ga2Se3), CuGa3Se5or CuGa5Se8 (71–89mol% Ga2Se3), and Ga2Se3-basedsolid solution (91–100mol% Ga2Se3). A later determina-tion of the pseudo-binary Cu2Se–Ga2Se3 phase diagram byMikkelsen [14] gave a considerably different result. Thisstudy evidenced two ternary solid solutions at the twobinary edges and only one ternary chalcopyrite CuGaSe2phase in the range 50–58mol% Ga2Se3.

2. Experimental procedure

2.1. Precursor preparation

Precursor films were prepared using a migration-enhancedepitaxial deposition system in which effusion cells areemployed to generate molecular-beam fluxes of elementalsources in a high-vacuum chamber (10�7–10�8Torr). Theflux from each cell is sensed for Cu using electron impactemission spectroscopy, and for Ga and Se by measurementof the film-composition run-to-run. The flux is then adjustedat the beginning of each run by changing the temperature asdetermined from previous flux calibration experiments. Moredetailed descriptions of the deposition technique andexperimental apparatus are provided elsewhere [8,9,15].Bilayer GaSe/CuSe precursor films were deposited on

sodium-free (alkali level o0.3%) borosilicate glass sub-strates (Corning ]7059). Thin glass substrates with athickness of 0.4 (70.127)mm were selected to minimizethe temperature difference and response time between thePt/Rh heater strip and the precursor film in the HTXRDfurnace used for subsequent characterization. The pre-cursors were fabricated by depositing an amorphous GaSefilm onto glass substrates at a substrate temperature of�250 1C, followed by deposition of a crystalline CuSe filmon the as-grown GaSe layer at a lower substratetemperature of �150 1C to minimize the potential reactionbetween the GaSe and CuSe precursor layers. Thethickness of each layer (�300 nm) was measured by TEMas shown in the cross-sectional image inserted into Fig. 1.The atomic composition was measured by inductivelycoupled plasma optical emission spectroscopy (ICP-OES),yielding the atomic ratios [Cu]/[Ga]�1.02 and [Se]/[Metal]�0.97. As shown in the cross-sectional TEM micrographinserted in Fig. 1, the interfaces between the substrateand the GaSe and between GaSe and CuSe are planar,while the top surface is faceted and rough. The XRDanalysis is consistent with the presence of an amorphous

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GaSe/polycrystalline CuSe bilayer structure, and shows nonoticeable pre-reaction between the two layers during thefilm deposition. The polycrystalline CuSe layer is highlytextured in the /0 0 1S direction.

2.2. Time-resolved, in situ high-temperature X-ray

diffraction

The high-temperature X-ray diffractometer used for thisstudy included a Scintag PAD X vertical y/y goniometer, achamber furnace (Buehler HDK 2.3), and an mBraunlinear position-sensitive detector (LPSD). The LPSDcollects the XRD data simultaneously over a 101 2ywindow (e.g., from 241 to 341 when centered at 291), anddramatically shortens the data collection time to permit in

situ time-resolved studies of phase transformations, crystal-lization, and grain growth. Precursor samples weremounted on the heater strip using carbon or silver paintto improve the thermal contact between the precursor andheater strip. The heater temperature was measured by atype-S thermocouple, which was welded onto the bottomof the Pt/Rh strip heater, and controlled by a PIDtemperature controller. The precursor surface temperaturewas calibrated from a determination of the lattice expan-sion of silver powder, dispersed on an identical thin glasssubstrate to quantify the thermal offset between theheater strip and sample surface over the full temperaturerange of interest [8–10,13]. The HTXRD furnace waspurged by He flowing at 100 sccm and the oxygen contentof the outlet gas as measured by an oxygen analyzer waso0.1 ppm.

Fig. 2. In situ XRD scans during temperature ramp ann

Temperature step-ramp annealing was first performed tosurvey the phase evolution of the samples and to establish asuitable isothermal annealing temperature range. Theglass/GaSe/CuSe bilayer sample was first heated to150 1C at a rate of 30 1C/min. The ramp heating was thenceased to collect the XRD data. The temperature was thenramped by a 10 1C increment at 30 1C/min, followed bydata collection at constant temperature. This sequence ofstep heating in 10 1C increments and XRD data collectionwas repeated over the temperature range 150–350 1C in aflowing He atmosphere. To cover the required 2y range of20–541, four individual sub-ranges centered at the PSD 2ysettings of 251, 331, 411 and 491 were scanned taking a totalof �1min. At each data collection temperature, four full-range scans were taken to provide an averaging effect. Thestep-ramp heating thus consisted of a �20 s ramp heatfollowed by a �4min isothermal data collection sequence.It is noted that all full scans are shown in the plot.The result of the step-ramp anneal suggested the

temperature range (280–370 1C) for a set of isothermalexperiments for quantitative analysis. The temperaturerange (280–370 1C) was selected so that the total isothermalholding time was much longer (i.e., several hours) than anindividual scan time (�35 s). It is pointed out that anindividual scan time (�35 s) during the isothermal anneal-ing experiments was longer than that (�15 s) used for thestep-ramp annealing to ensure higher reflection intensityand thus more accurate quantitative analysis. A three-stepheating protocol was used to minimize heating timewithout temperature overshooting. Initially, the tempera-ture was rapidly ramped at a rate of 300 1C/min to a value

ealing (30 1C/min) of the glass/GaSe/CuSe sample.

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20 1C below the set-point temperature, and then at a rate of200 1C/min to a value 10 1C below the set-point tempera-ture. Finally, the temperature was ramped to the set-pointat a rate of 100 1C/min, and then maintained at set-pointtemperature to monitor the phase evolution of theisothermal reaction. To complete the reaction, the tem-perature was elevated to 500 1C until only the CuGaSe2phase remained and the corresponding (1 1 2) reflectionintensity remained constant (�12min). The 2y scan range(24–341) for the isothermal experiments allowed the majorpeaks of the reactant, intermediate, and product (i.e., CuSe(0 0 6), Cu2�xSe (1 1 1), and CuGaSe2 (1 1 2)) to be followedwhile requiring only a single 101 2y scan.

3. Results and discussion

3.1. High-temperature XRD results

The X-ray reflection data collected during the prelimin-ary temperature-ramp annealing experiments, as shown in

Fig. 3. In situ time-resolved XRD scans during isothermal annealing of the gl

340 and 370 1C).

Fig. 2, demonstrate that the initial CuSe phase begins to betransformed to b-Cu2�xSe at around 230 1C, and CuGaSe2formation is initiated with the decrease of b-Cu2�xSe peakat around 260 1C. A selenium precursor phase(Tm ¼ 221 1C) released from CuSe by its transformationto Cu2�xSe likely reacts with the initially amorphous GaSe,which is the only stable phase to form a selenium-richGa–Se compound, which is most likely Ga2Se3 in theGa–Se binary system [16]. Since no peaks corresponding toGa–Se compounds were apparent in the XRD patternshown in Fig. 2, the Ga–Se precursor film is eitheramorphous or contains too small amount of crystallinematerial to be detected by the PSD set at low resolution. Itis noted that the fully reacted film contains only stoichio-metric CuGaSe2 form within the detection limit of XRD.Furthermore, as shown in Fig. 2, CuSe fully converts toCu2�xSe before the onset of detectable CuGaSe2 forma-tion. As predicted by Cu2Se–Ga2Se3 pseudo-binary phasediagram suggested by Mikkelsen [14], Cu2�xSe and Ga2Se3(or Se-rich Ga–Se compound) directly form CGS. The

ass/GaSe/CuSe precursor structure at selected temperatures (i.e., 280, 300,

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Fig. 4. Fractional reaction (a) with respect to time (t) at selected

isothermal temperatures.

Fig. 5. Parabolic rate model plot and corresponding Arrhenius plot for

the parabolic rate constant.

W.K. Kim et al. / Journal of Crystal Growth 310 (2008) 2987–2994 2991

expected interfacial reaction pathway leading to theformation of CGS is

2CuSe! Cu2�xSeþ Se at �230 1C; (1)

Cu2�xSeþ Seþ 2Ga2Se ðamorphousÞ

! 2CuGaSe2 at �260 1C: (2)

As shown in Fig. 2, it is interesting to note that thepreferred orientation of crystal grains, i.e., CuSe(0 0 6),Cu2�xSe(1 1 1) and CGS(1 1 2) contains the same close-packed plane, even though the unit cell structures aredifferent, i.e., CuSe:hexagonal, Cu2�xSe:cubic and CGS:tetragonal.

Fig. 3 displays the time-resolved XRD data collected forthe film isothermally reacted at a set of differenttemperatures. The comparison between the isothermalplots at four different temperatures clearly illustrates thatthe reaction rate increases with temperature and follows adeceleratory reaction pattern. To obtain the fractionalreaction (a), which is defined as the fraction of reactioncompleted at time t, the integrated intensities of theproduct CuGaSe2 (1 1 2) peaks were obtained by peakfitting of the diffraction data using JADE [17], and werenormalized assuming that the reactants were completelytransformed to crystalline CuGaSe2 after the final soak at500 1C, and that the texture of the CuGaSe2 did notappreciably change during the heating process.

It is reported that the preferred orientation of CIS isrelated to the substrate material, precursor orientation, andprocess conditions [18,19]. Contreras et al. [18], however,reported that the (1 1 2) preferred orientation is alwaysobtained for CIS deposited onto amorphous substrates,such as bare soda lime glass (SLG) and Corning 7059 glass,regardless of growth conditions, while the (220/204)preferred orientation is observed for CIS on Mo-coatedSLG substrate for certain deposition conditions. Thesestudies suggest that there is likely no significant change inthe texture of the CGS formed from the glass/GaSe/CuSeprecursor structure during the annealing.

As shown in Fig. 4, a plot of the fractional reaction (a)with respect to time at different isothermal temperaturesdemonstrates that CuGaSe2 formation follows the decel-eratory reaction trend, which is consistent with diffusion-controlled reaction kinetics.

3.2. Kinetic analysis

The reaction kinetics in terms of activation energy (Ea),kinetic constant (k) and reaction order (n) were investi-gated by employing two conventional diffusion-controlledreaction models, i.e., parabolic rate and Avrami models,along with the Arrhenius equation. It has been shown thatthese methods yield satisfactory fits to relevant experi-mental data such as CuInSe2 formation from InSe/CuSe [8]and In2Se3/CuSe [9] bilayer precursors, and selenization ofCu–In [10] and Cu–Ga [11] metallic precursors.

The reaction kinetics of the parabolic model [20] aredescribed by

a2 ¼ kptþ C, (3)

where kp is the parabolic rate constant and C is a constantdetermined by the initial condition. Fig. 5 shows the plot ofa2 vs. t for the isothermal reaction of the precursor films atset-point temperatures in the range 280–370 1C. The insetin this figure shows the corresponding Arrhenius plot,which yields a value of Ea ¼ 115(716) kJ/mol. Theextracted parabolic kinetic constants (kp) are summarizedin Table 1.Considering the initial condition, i.e., a (t ¼ 0) 6¼0 as

evidenced by Fig. 4, a modified Avrami expression [12] issuggested

lnð� lnð1� aÞÞ ¼ n lnðtþ t�Þ þ n ln k, (4)

where t* is the time constant which satisfies the initialcondition at a given temperature. The resulting Avramimodel plot yields a satisfactory fit with the estimatedkinetic parameters summarized in Table 1, as compared

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Table 1

Estimated kinetic parameters for CuGaSe2 formation from glass/GaSe/CuSe bilayer precursor films

Temperature (1C) Parabolic model Modified Avrami model

kp� 103 (s�1) n k� 103 (s�1) t* (s)

280 0.050 (78.02� 10�4) 0.70 (77.4� 10�3) 0.129 (71.20� 10�4) 0a

300 0.237 (72.92� 10�3) 0.69 (79.1� 10�3) 0.693 (78.71� 10�4) 75.0

340 0.623 (72.38� 10�2) 0.73 (71.3� 10�2) 1.74 (73.47� 10�3) 49.2

370 2.22 (72.32� 10�1) 0.68 (72.2� 10�2) 7.97 (74.53� 10�2) 24.6

kp and k: apparent kinetic constants.

n: Avrami exponents.

t*: time constant for modified Avrami model.aExperimentally determined since no pre-reaction was observed for this run (i.e., a (t ¼ 0) ¼ 0).

Fig. 6. Fractional reaction (a) with respect to time (t+t*) and modified

Avrami model plot at selected isothermal temperatures (Symbols:

experiments, solid line: Avrami model prediction.).

Fig. 7. Modified Avrami model plot and corresponding Arrhenius plot for

the Avrami kinetic constant.

W.K. Kim et al. / Journal of Crystal Growth 310 (2008) 2987–29942992

with the experimental data in Figs. 6 and 7. More completedescriptions of the modified Avrami model is presentedelsewhere [12].

The kinetic analyses using both reaction models suggestthat the formation of CuGaSe2 in glass/GaSe/CuSe bilayerprecursor films is consistent with a reaction that is limitedby a one-dimensional diffusion of a reactant. The resultingAvrami exponents (0.68–0.73) suggest that nucleationoccurs rapidly and thus the nucleation time is negligible.This is consistent with the suggestion that nucleation andsubsequent growth have occurred before the start of theisothermal experiment, i.e., t ¼ 0. Formation of nuclei andtheir growth either in the deposition process or during theheating step are consistent with rapid nucleation asestimated by n ffi0.5.

From the Arrhenius plot shown in the inset of Fig. 7, it isseen that the apparent activation energy is 124 (719) kJ/mol,which is in good agreement with the value of 115 (716)kJ/molobtained via the parabolic rate model analysis. Theseactivation energies for CGS formation are larger than thevalue of 65–66 kJ/mol [8] obtained by parabolic andAvrami model analyses for a-CIS formation from glass/InSe/CuSe stacked bilayer precursor having a structureanalogous to the glass/GaSe/CuSe used in this study. It isnoticeable that a similar activation energy of 109 (77) kJ/mol was obtained using a modified Avrami model for CGSformation from selenization of glass/Mo/Cu–Ga precursorin our previous report [12]. The reaction paths andactivation energies of CIS and CGS formation fromdifferent precursor structures are summarized in Table 2.It is noteworthy that the Avrami model provides asatisfactory fit when an amorphous/crystalline bilayerprecursor structure is tested (e.g., GaSe/CuSe and InSe/CuSe [8]), but not for a crystalline/crystalline bilayerprecursor (e.g., In2Se3/CuSe [9]). The parabolic growthmodel, however, describes well both the amorphous/crystalline and crystalline/crystalline bilayer precursorstructures.

Recently, Purwins et al. [11] reported the formation ofCuGaSe2 from a stacked bilayer Ga2Se3/Cu2Se followed anucleation and growth model with an activation energy inthe range 129–148 kJ/mol, which is almost identical to our

result (124719 kJ/mol) for CGS formation from GaSe/CuSe, extracted from a Kissinger analysis of differentialscanning calorimetric data.

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3.3. Transmission electron microscopy–energy-dispersive

X-ray spectrometry (TEM–EDS) analysis

To support the HTXRD results on reaction pathwayand kinetics of CGS formation, a TEM–EDS analysisof an as-grown precursor and a 300 1C-annealed sample

Table 2

Summary of reaction pathways and activation energies of CuInSe2 and CuGa

Precursor Reaction path

InSe/CuSe -CIS

In2Se3/CuSe -CIS+Se (evaporated)

GaSe/CuSe -GaSe (amorphous)+12Cu2�xSe+

12Se-CGS

Selenization

Cu–In+nSe (vapor) -CuSe+In+nSe (vapor)-CuSe2+In+nSe

Cu–Ga+nSe (vapor) -CuSe+Ga+nSe (vapor)-CGS

Fig. 8. TEM-EDS analysis on (a) as-grown glass/GaSe/CuSe

was performed using a JEOL JEM 2010 F scanningtransmission electron microscope. First, the glass/GaSe/CuSe precursor was isothermally soaked on the Pt/Rhstrip heater at 300 1C for 30min in flowing He, andthen quenched by turning off the heater power and increa-sing the He flow rate. The as-grown precursor and

Se2 formation from different precursor structures

Ea (kJ/mol) Ref.

Avrami Parabolic

66 65 [8]

N/A 16275 [9]

124719 115716 This work

(vapor)-CIS 124719 100714 [10]

10977 N/A [12]

precursor and (b) sample annealed at 300 1C, for 30min.

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300 1C-annealed samples were coated by carbon to obtainbetter electrical conductivity and thus better image resolu-tion during TEM analysis. The TEM samples wereprepared using an FEI Strata DB 235 focused ion beam(FIB). It is noted that an Au-grid instead of theconventional Cu-grid was used to hold TEM samples toprevent the Cu-grid from interfering with the EDS analysisfor Cu concentration.

The TEM images along with EDS line scan results arecompared in Fig. 8. A bilayer structure of as-grownglass/GaSe/CuSe precursor is clearly illustrated by TEMimage and EDS scan results in Fig. 8(a). Interestingly, theEDS gallium concentration profile shows a small tail onthe topside of the CuSe layer, which is attributed to thediffraction by the gallium ion used in the FIB system.The TEM image and EDS line scan results of the300 1C-annealed sample shown in Fig. 8(b) demonstratethat CuGaSe2 forms at the interface between the GaSe andCuSe layers, which explicitly supports the primary assump-tion of a parabolic growth model. According to the plot offractional reactions with respect to time at 300 1C shown inFig. 4, the glass/GaSe/CuSe film isothermally annealed at300 1C for 30min is expected to yield around 0.7 offractional reaction, which is pictorially evidenced by theTEM image in Fig. 8(b). There is, however, non-uniformityin the Ga concentration within the CGS layer, while theconcentration of Cu and Se is consistent over the entireCGS region. This may be qualitatively explained by a lowervalue of diffusivity of Ga than that of Cu into CGS thatyields a Cu-rich CGS at the top part of CGS and a Ga-richCGS at the bottom part of CGS layer.

4. Conclusions

The reaction pathway and kinetics of polycrystallineCuGaSe2 formation from glass/GaSe/CuSe bilayer pre-cursor films were investigated using time-resolved, in-situ

high-temperature XRD. The qualitative reaction pathwayobservation during the temperature ramp annealingevidenced that the initial CuSe phase begins to betransformed to b-Cu2�xSe at approximately 230 1C,followed by CuGaSe2 formation initiated at around260 1C, which is described as the reaction Cu2�xSe+2GaSe+Se-2CuGaSe2. Quantitative kinetic analysis oftime-resolved XRD data obtained during isothermalsoaking fits both the parabolic rate and modified Avramimodels, which suggests that CuGaSe2 formation from abilayer glass/GaSe/CuSe precursor should be described bya one-dimensional diffusion-controlled reaction. The acti-vation energy of this reaction, 115 (716) kJ/mol (parabolicrate model) or 124 (719) kJ/mol (modified Avrami model),is much higher than that found for a-CIS obtained by thesame type of experiments, but very close to that reportedfor CGS formation from selenization of Cu–Ga andGa2Se3/Cu2Se. The TEM-EDS analysis supports theprimary assumption of the parabolic growth model thatCuGaSe2 forms at the interface of GaSe and CuSe layers.

Acknowledgments

The authors gratefully acknowledge the financial sup-port of DOE/NREL High-Performance PhotovoltaicProgram, under Subcontract no. XAT-4-33624-15. Theauthors also appreciate sponsorship, in part, by theAssistant Secretary for Energy Efficiency and RenewableEnergy, Office of FreedomCAR and Vehicle Technologies,as part of the High Temperature Materials LaboratoryUser Program, Oak Ridge National Laboratory, managedby UT-Battelle, LLC, for the US Department of Energyunder Contract no. DE-AC05-00OR22725. The authorsthank Ryan Acher and Ryan Kaczynski for supporting theprecursor preparation, Dr. Gerald R. Bourne for preparingthe TEM samples, and Kerry Siebein for TEM-EDSanalysis at the University of Florida’s Major AnalyticalInstrumentation Center.

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