cu–ga–in thermodynamics: experimental study, modeling, and implications...

Cu–Ga–In thermodynamics: experimental study, modeling,and implications for photovoltaics

Christopher P. Muzzillo1 • Carelyn E. Campbell2 • Timothy J. Anderson1

Received: 18 September 2015 / Accepted: 6 December 2015 / Published online: 17 December 2015

� Springer Science+Business Media New York 2015

Abstract Both experimental measurements and assess-

ment of phase equilibria are reported in the Cu–Ga–In

material system, which is an important constituent in growth

of the thin film photovoltaic absorber Cu(In,Ga)Se2 (CIGS).

Characterization of four different alloys using inductively

coupled plasma atomic emission spectroscopy, X-ray

diffraction, scanning electron microscopy, energy dispersive

spectroscopy, differential thermal analysis, and differential

scanning calorimetry has been conducted, and high-tem-

perature equilibration studies have been performed on 2 of

those. The new data are qualitatively consistent with the

previous nonequilibrium thin film Cu–Ga–In observations.

A thermodynamic assessment of the ternary system has also

been performed using a CALPHAD approach after re-

assessing the Cu–In constituent. The model fits the ternary

data well in addition to the Cu–Ga, Cu–In, and Ga–In binary

data. Practical applications of the model to metal precursors

in a CIGS selenization process are discussed. Using the

assessed parameters, the model predicts that at temperatures

typically used in CIGS processes, Cu–Ga–In films should

undergo equilibrium phase transformations. Slight changes

in composition are found to determine whether or not these

transitions occur, and at what temperature. Equilibrated

precursor films are calculated to have high c-Cu9(Ga,In)4phase content, where reducing equilibration and c-

Cu9(Ga,In)4 formation have previously been found to

improve photovoltaic performance.

Introduction

The Cu–Ga–In material system has received recent attention

as a result of its use as an absorber in thin film photovoltaic

(PV) applications and could potentially be useful in lead-

free solder alloys as well [1, 2]. PV devices utilizing

Cu(InxGa1-x)Se2 (CIGS) absorber films have demonstrated

power conversion efficiencies up to 21.7 % [3]. CIGS is

often synthesized in a two-step selenization process begin-

ning with deposition of a metal precursor film and followed

by reaction with selenium and/or sulfur. In addition to the

potential low cost, this ‘selenization’ process has the

advantage of using established metal deposition techniques

to reduce complexity in the first step and thus simplify scale-

up. Device efficiencies obtained with selenization processes,

however, have lagged relative to the champion co-evapo-

rated films, due largely to nonoptimal cation distributions,

and poor adhesion and void accumulation at the rear inter-

face [4]. The phase constitution and spatial variations in the

composition of the Cu–Ga–In precursor film influence the

final cation distribution, void formation, and chalcogeniza-

tion reaction pathways. The thermochemistry and phase

equilibria of the Cu–Ga–In material system are, therefore, of

interest for both the design of ternary sputtering targets, as

well as understanding reactions during deposition of the

precursor film and the heating selenization process.

Knowledge of the material’s equilibrium behavior can assist

in the design of economical, robust processes for fabricating

quality CIGS PV absorbers.

As summarized in the modeling section, the thermody-

namic properties and phase equilibria of the constituent

& Christopher P. [email protected]

Timothy J. Anderson

[email protected]

1 Department of Chemical Engineering, University of Florida,

Gainesville, FL 32611, USA

2 National Institute of Standards and Technology,

Gaithersburg, MD 20874, USA

123

J Mater Sci (2016) 51:3362–3379

DOI 10.1007/s10853-015-9651-3

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binary systems have been experimentally investigated and

assessed extensively [5–57]. Very little experimental study,

however, has been carried out for the ternary system. Most

researchers studying Cu–Ga–In deposit thin film alloys

with overall compositions around Cu47Ga13In40 onto

unheated substrates. They typically contain the c-Cu9(Ga,In)4 and g-Cu16(Ga,In)9 ternary solid solutions as wellas solid elemental indium, while the Cu11In9 compound is

less frequently observed. The c and g phases exhibitextensive ternary solubility and, therefore, span much of

the phase diagram outside of the Ga-rich corner, which is

dominated by the liquid phase. No ternary compounds have

been reported. Common to most deposition processes is the

formation of In-rich nodules of mostly (In) atop a Cu- and

Ga-rich two-dimensional film consisting largely of c-Cu9(Ga,In)4. The subsequent chalcogenization of this c-Cu9(Ga,In)4 compound at the rear interface is often the

rate-limiting step in chalcopyrite film formation [58] and

has been suggested to be related to void formation [4].

The Cu–Ga–In ternary phase diagram was predicted

recently by combining Gibbs energy functions estimated

from assessments of the three binary systems [7]. The

prediction was consistent with the results of an equilibra-

tion study on a single Cu41Ga19In40 alloy [inductively

coupled plasma atomic emission spectroscopy (ICP-AES),

differential thermal analysis (DTA), and X-ray diffrac-

tometry (XRD)] [59]. At room temperature, the as-cast

alloy exhibited XRD peaks that were attributed to c-Cu9(Ga,In)4, Cu11In9, and (In). Thermal transitions at 429

and 926 K were attributed to c-Cu9(Ga,In)4 ? L $ c-Cu9(Ga,In)4 ? (In) and L $ c-Cu9(Ga,In)4 ? L transfor-mations, respectively. Additionally, a study of phase rela-

tions in Cu–Ga–In thin films on glass/Mo substrates was

reported by Purwins et al. [60]. The data therein may not be

at equilibrium because of (1) thin film stress, (2) possible

phase transitions during the slow cooling of samples, and

(3) possible substrate contamination (the type of glass was

not reported; soda-lime glass is often used for CIGS PV

substrates, from which Na usually accumulates in the film

up to *1 at.%). Despite these potential deviations fromtrue equilibrium, the study nevertheless presents stabilized

phase existence regions of particular importance to PV

device processing.

Experimental

Sample preparation and alloy annealing

A set of four alloy samples (A–D) was prepared for equi-

libration studies. Two of the alloy compositions were close

to that found in absorber precursors (molar ratios Cu/

(Ga ? In) * 1 and Ga/(Ga ? In) * 0.3). Sample A was

Cu-poor (Cu48Ga10In43) and sample B was Cu-rich (Cu55Ga18In27), where the Ga and Cu molar fractions were

chosen to span the range of interest for PV applications.

The other two samples were intended to better define the

three-phase region near very Cu-rich alloys (sample C:

Cu71Ga15In14 and sample D: Cu82Ga9In9). Alloys were

prepared by vacuum induction melting of pure Cu, Ga, and

In (99.999 % metals basis). The overall composition was

determined by ICP-AES (Table 1). The compositional

uniformity was also probed on pieces from three different

locations on the ingots. Differential scanning calorimetric

(DSC) or DTA measurements were performed on all

samples, and samples C and D were equilibrated at three

temperatures (591, 711, and 950 K). Pieces of the metal

alloy ingot were washed in heated trichloroethylene, ace-

tone, and methanol, followed by deionized (DI) water rinse

and N2 blow drying, and then loaded into fused quartz

ampoules with 2-mm-thick walls. The ampoule chamber

was evacuated and purged three times with 4 % H2 in N2(99.999 % minimum purity with\1 ppm O2 and H2O, and\0.5 ppm total hydrocarbons). Hydrogen was used toprevent formation of surface oxides during the long-time

equilibration anneal. The ampoules were sealed by soft-

ening the outer walls around their plugs with an oxygen

and acetylene torch, and slightly reduced pressure

(0.20–0.33 atm) in the ampoules was used to minimize

explosion hazards at high temperature.

High-temperature samples (950 K) were annealed for a

period of approximately 1 week, while the lower temper-

ature samples (591 and 711 K) were annealed for 3 weeks.

These durations were chosen to be slightly longer than

those reported for Cu–Ga and Cu–In alloy equilibration

[34, 44]. The sealed ampoules were placed at the center of

a resistively heated tube furnace with temperature con-

trolled to within approximately ±1 K. After equilibration,

the ampoules were dropped from the furnace directly into

icy brine to quench the high-temperature equilibrium

states. A filed powder of sample C equilibrated at 591 K

was additionally annealed at 600 ± 10 K for 10 min under

4 % H2 in N2 and then cooled quickly to room temperature

to relieve micro-strain for subsequent collection of high-

resolution XRD patterns. Bulk samples were filed and then

polished using lapping film with 0.3 lm Al2O3 particles.Polished surfaces were then swabbed with an etchant of

67 vol.% ethyl alcohol and 33 vol.% aqueous solution

[19 wt.% ferric chloride (FeCl3) and 6 wt.% hydrochloric

acid (HCl) in DI water].

Alloy characterization

Compositions were measured by ICP-AES on a Perkin

Elmer Optima 3200RL system, after dissolving the alloys

in nitric acid and calibrating with plasma standard solutions

J Mater Sci (2016) 51:3362–3379 3363

123

obtained from Alfa Aesar. Phase and structure analysis was

performed by XRD using a PANalytical PRO powder

diffractometer and Cu Ka radiation generated at 45 kV and

40 mA. DTA was performed on a Mettler–Toledo ther-

mogravimetric analysis (TGA)/SDTA 851 system under

pure N2 flow (no greater than 200 ppm O2 impurity). Quick

scans were first acquired from room temperature to 1273 K

for sample C and 1373 K for sample D at a ramp rate of

10 K/min, followed by scans in temperature regions of

interest at a ramp rate of 5 K/min. Thermograms of empty

alumina crucibles were subtracted from each scan. Peak

onset temperatures did not change within the accuracy of

the technique (estimated ±1 K) in the ramp rate range

(5–10 K/min). DSC scans were taken with a Netzsch

Instrument STA 449C using alumina-lined platinum pans

with a purified (gettering furnace to\10-10 ppm oxygen)Ar purge flow. Heating and cooling scans were performed

twice at 10 K/min from room temperature to 1423 K. The

phase distributions and composition were determined using

a field-emission gun scanning electron microscope (FE-

SEM) and energy dispersive X-ray spectroscopy (EDS),

respectively, on a JEOL 6335F FE-SEM at 15.0 kV fila-

ment tension. Both secondary electron (SE) and backscat-

tered electron (BSE) micrographs were captured to better

distinguish phases.

Experimental results

The compositions of the ingots are summarized in Table 1,

as determined by ICP-AES. Overall ingot composition data

from EDS are not presented, but satisfactory agreement

between the two techniques was observed. No evidence of

oxidation for any sample was found by EDS or XRD.

XRD

The crystalline phases of equilibrated alloys C and D were

identified at room temperature by powder XRD, with

example patterns shown in Fig. 1. The XRD pattern of

sample C equilibrated at 711 K (Fig. 1) was very similar to

sample C at 591 and 950 K, as well as sample D at 950 K.

The pattern of sample D equilibrated at 711 K (Fig. 1) was

very similar to sample D at 591 K. Assigning the peaks

unambiguously to particular phases is challenging in this

system, as the candidate intermetallic phases have multiple

overlapping peaks that can shift with alloy composition.

Also, the g-Cu16In9 binary phase field is known to exhibitsuperstructure ordering, although neither standard powder

XRD patterns nor unambiguous structures have been

published for all the phasoid regions [49]. XRD was first

performed on the bulk samples, so phase fraction specifi-

cation is complicated by the possible presence of texture as

well as peak shifts due to probable misalignment and long-

range stresses. Bulk sample XRD scans revealed more

peaks that were narrower and more intense, and thus were

used to help identify phases. XRD scans on filed powders

had substantially more disorder, yielding broader, and less

intense peaks, but more reliable peak positions and relative

intensities, and so were used to measure lattice constants

and phase fractions (summarized in Table 2). The com-

position of c-Cu9(Ga,In)4 was on the Cu-rich side, so itsstructure was taken to be that of the c1-Cu9Ga4 phase withCu69Ga31 composition determined by Mizutani et al. [40].

The published diffraction pattern of quenched, high-tem-

perature c-Cu9In4 permitted linear interpolation of thecubic lattice constant to be related to group III

Table 1 Composition of alloys,as determined by ICP-AES

Sample Nominal composition Composition (at.%)

Cu Ga In

Kim et al. [59] Cu41Ga19In40 40.72 19.44 39.84

A Cu48Ga10In43 47.6 9.5 42.9

B Cu55Ga18In27 54.5 18.2 27.3

C Cu71Ga15In14 71.2 ± 2.3 15.0 ± 1.0 13.9 ± 1.5

D Cu82Ga9In9 81.6 ± 2.5 9.4 ± 1.0 9.0 ± 1.5

Fig. 1 XRD patterns for samples C and D (Cu71Ga15In14 andCu82Ga9In9, respectively) bulk samples annealed at 711 K with

according crystalline phase assignments. Reference powder diffrac-

tion patterns were calculated from the known structures and site

occupancies for a-(Cu), c-Cu9(Ga,In)4 [40], and d-Cu7In3 [36],respectively

3364 J Mater Sci (2016) 51:3362–3379

123

composition. Lattice parameter variation due to Cu/

(Ga ? In), or Cu/III, compositional change is assumed to

be negligible relative to that of In/III changes. The d-Cu7In3 structure [36], or powder diffraction file (PDF) #

01-073-8028, and experimental diffraction pattern [32], or

PDF# 03-065-2249, have been published. Lattice parame-

ters of the a-fcc(A1)-(Cu) phase with up to 10.4 at.% Inand separately 20.0 at.% Ga have also been published [45,

53]. Lattice constants exhibit a linear relationship with

group III composition for both systems. Although solubil-

ity of both Ga and In in a-(Cu) has not been studiedexperimentally, a linear combination of the 2 separate

lattice parameter-composition functions has been used to

arrive at an approximate anticipated lattice parameter for a

particular ternary composition. In this way, a latticeparameters have been calculated from EDS compositional

information and compared with those measured by XRD in

Table 2.

SEM/EDS

Example SE and BSE micrographs of the samples etched in

FeCl3:HCl:H2O after annealing at 950 K are shown in

Fig. 2. The differential etching contrasted the phases to

reveal the microstructure. The etching process also

revealed surface scratches due to imperfect polishing. In all

cases, both SE and BSE images revealed two phases, with

the darker-appearing region the major phase in sample D

and the minor phase in sample C. Multiple spot EDS

measurements acquired for each phase in all samples

indicated that the darker phase had a composition that

corresponded to a-(Cu), while the lighter phase corre-sponded to either c-Cu9(Ga,In)4 or separately d-Cu7In3,depending on the sample (see Table 2). Overall sample

compositions were measured using EDS with a beam raster

area much larger than individual phase domains, and these

were commensurate with ICP-AES results. Overall EDS

composition was combined with individual phase compo-

sition to obtain estimates for phase fractions in each sample

(see Table 2). Although EDS and XRD lattice parameter

measurements have relatively low precision, rough agree-

ment between the two drastically different characterization

techniques is presented in Table 2 to strengthen the phase

constitution and composition conclusions.

DTA/DSC

The significant peaks from DTA scans for samples C and

D are presented in Fig. 3. The scan in this figure for

sample D only covered the temperature range 675 to

1060 K. A single phase transition was detected for sample

C by DTA, with its onset at 990 K. This peak also dis-

plays a possible shoulder which ends at 1044 K. Two

peaks were observed for sample D, with onset tempera-

tures of 913 K and 1002 K. The 913 K transition is cor-

roborated by XRD scans showing a change from a ? dfor sample D equilibrated at 711 K to a ? c when equi-librated at 950 K. Example DSC heating curves for

samples A and B are presented in Figs. 4 and 5, respec-

tively. When scans were repeated substantial variability

(*20 K) was observed in the cooling curve peaks, andthis was taken to be the result of supercooling, as there

was little change in the repeated heating curve peaks.

Heating curve peak onsets were therefore taken to cor-

respond to phase transitions listed in Table 3. Both sam-

ple A and B display transitions at *428 K and highertemperatures. For comparison, a DTA scan of a sample

with Cu content (Cu41Ga19In40) lower than samples A–D

from Kim et al. is reproduced in Fig. 6 [59]. Due to the

ambiguity of assigning onset temperatures to the high-

temperature peaks of Cu41Ga19In40 [59], sample A, and

sample B calculated enthalpy curves have been overlaid

for comparison in Figs. 4, 5, 6. The phase transitions

which are predicted to correspond to these heat effects are

discussed in section ‘‘Cu–Ga–In Assessment,’’ and com-

pared with calculations in Table 3.

Table 2 Comparison of phases and their composition and extent asdetected from XRD and SEM/EDS measurements at three equili-

bration temperatures

SEM/EDS XRD

Sample C 591 K 18 % a; 82 % c

a… a = 3.690 Åc… In/III = 57 %

8 % a; 92 % c

c… In/III = 48 %

Sample D 591 K 40 % a; 60 % d

a… a = 3.677 Å61 % a; 39 % d

a… a = 3.670 ÅSample C 711 K 21% a; 79 % c

a… a = 3.657 Åc… In/III = 61 %

21 % a; 79 % c

a… a = 3.663 Åc… In/III = 52 %

Sample D 711 K 64 % a; 36 % d

a… a = 3.649 Å57 % a; 43 % d

a… a = 3.666 ÅSample C 950 K 24 % a; 76 % c

a… a = 3.722 Åc… In/III = 54 %

6 % a; 94 % c

c… In/III = 43 %

Sample D 950 K 45 % a; 55 % c

a… a = 3.678 Åc… In/III = 74 %

18 % a; 82 % c

a… a = 3.686 Åc… In/III = 58 %

EDS phase amounts were estimated by combining overall composi-

tion with those of individual phases. Lattice constants were calculated

assuming linear composition dependence. XRD phase amounts were

estimated from relative peak areas

J Mater Sci (2016) 51:3362–3379 3365

123

Thermodynamic assessment

Thermodynamic literature

The three constituent binary systems have previously been

assessed. The recent Cu–Ga assessment by Li et al. [34]

has been used here with almost no modification; the only

additional data considered being the new structural infor-

mation for the c1-Cu9Ga4 compound [40]. The Ga-Inassessment by Anderson and Ansara has been used here

without modification [5]. The subsequent Ga-In assessment

by Reddy and Hajra introduces 2 more parameters in a less-

common composition- and temperature-dependent excess

Fig. 2 Scanning electron micrographs at 92000 magnification of samples equilibrated at 950 K, with a-(Cu) and c-Cu9(Ga,In)4 phases labeled.a SE image and b BSE image of sample C. c SE image and d BSE image of sample D

Fig. 3 DTA heating curves for samples C and D, with peak onsettemperatures indicated

Fig. 4 DSC heating curve (left axis) and calculated system enthalpy(right axis) for sample A, where mol refers to the chemical formula

3366 J Mater Sci (2016) 51:3362–3379

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Gibbs energy function to marginally reduce residual error

for selected data [50], relative to the prior assessment, and

so has not been used. Two phase models (Cu11In9 and

liquid) from the recent Cu–In assessment by Cao et al. have

been used here without modification [11]. The re-assess-

ment of the Cu–In binary system reported in this work

considered the extensive equilibrium experimental data [6–

10, 12, 13, 15–19, 21, 22, 24–26, 28–33, 35, 36, 39, 41–44,

46–49, 51–53, 55–57], as well as several previous ther-

modynamic assessments [11, 20, 27, 37, 38, 54]. The newly

reported Cu10In7 phase has not been presently included in

the model because no previous experimental reports have

documented it, apparently due to pronounced kinetic bar-

riers to its formation (requiring 9 mo of equilibration to

surmount) [46]. A ternary Cu–Ga–In CALPHAD model

has previously been fitted to the data of Purwins et al. and

Kim et al. [59, 60], although the optimized parameters

were not included in the report. The data from this work,

Purwins et al. [60] and Kim et al. [59] were considered in

the Cu–Ga–In optimization.

Thermodynamic models

Pure elements

The pure solid �GfccCu ,�GortGa, and

�GtetIn are taken as the a-fcc(A1)-(Cu), orthorhombic-Ga, and tetragonal(A6)-(In)-

condensed phase reference Gibbs energy functions relative

to the respective standard elemental reference enthalpies

published by Dinsdale [61]. The pure element liquid phases

and lattice stabilities have also been taken from Dinsdale.

Gas-phase species of Cu, Cu2, Ga, Ga2, In, and In2 are

included in the database, and their models are taken from

the Scientific Group Thermodata Europe (SGTE) 1994

substance database. The standard elemental reference

functions have the following form.

�Giu ¼ Gui � HSERi¼ aþ b � T þ c � T � ln T þ d � T2 þ e � T3 þ f � T�1

þ g � T4 þ h � T5 þ . . .ð1Þ

Here G, �, u, i, H, SER, a–h, and T represent Gibbsenergy, use of a standard elemental reference, phase

structure, component, enthalpy, standard elemental refer-

ence (298.15 K at 1 bar), estimated coefficients, and

absolute temperature, respectively. The coefficients are

typically fitted to experimental data and can be directly

related to heat capacity and entropy.

Stoichiometric compounds

The expressions and estimated parameters for the Gibbs

energy of Cu778Ga222 and CuGa2 suggested by Li et al.

were used without further modification [34]. The Cu11In9phase model and parameters of Cao et al. were used [11]. It

has been established that the d-Cu7In3 and g-LT-Cu16In9phases exist over *1 at.% compositional ranges [23, 54].However, to base the models for these phases on their

structures and to produce more reliable extrapolations [62],

it was necessary to model them as line compounds.

Enthalpy data for d-Cu7In3 [7] (Fig. 7), as well as invariantreaction compositions and temperatures (Table 4), were

used to optimize the parameters for d-Cu7In3 and g-LT-Cu16In9 listed in Table 5. The models use the following

formalism.

�GCumIIIn ¼ GCumIIIn � m � HSERCu � n � HSERIII ¼ aþ b � Tð2Þ

Here III has been used to represent either Ga or In, and

the stoichiometric coefficients are m and n. The optimized

Fig. 6 DTA cooling curve (left axis) [59] and calculated systementhalpy (right axis) for the Cu41Ga19In40 alloy, where mol refers to

the chemical formula

Fig. 5 DSC heating curve (left axis) and calculated system enthalpy(right axis) for sample B, where mol refers to the chemical formula

J Mater Sci (2016) 51:3362–3379 3367

123

coefficients, a and b, are the enthalpy and negative entropy

of formation, respectively.

Solution phases

A simple ideal-substitutional-solution model (ideal gas)

has been used for the gas phase [63]. An ionic two-sub-

lattice liquid model has been used with the metal ion

species (Cu?1, Ga?3, and In?3) mixing on the cation

sublattice and only vacancies (Va) on a second sublattice

[64]. This model has been chosen so that anion species may

be readily added for a Cu–Ga–In–Se database. Since there

are no anions in the present material system, the ionic two-

sublattice model is mathematically equivalent to a substi-

tutional solution (also known as Redlich–Kister, or R–K

model [65]), the only difference being the ionized species

in place of the neutral atoms. The liquid parameters were

therefore taken from the previous assessments of Li et al.

for Cu–Ga [34], Cao et al. for Cu–In [11], and Anderson

and Ansara for Ga-In [5]. As the respective assessments

have achieved excellent fits to extensive liquid component

activity measurements, the binary liquid parameters were

not modified, and no ternary parameters were added.

Equilibrium calculations for the ternary system extrapolate

the binary R–K series parameters using the symmetric

Muggianu method [63]. The R–K formalism is as follows:

Gu ¼X

i

xi �� Gui þ R � T �X

i

xi � ln xi

þX

i

X

j[ ixi � xj �

X

m

mLui;j � xi � xj

� �m ð3Þ

mLui;j ¼ aþ b � T ð4Þ

Here R, m, and L represent the gas constant, parameterorder, and mixing parameter, respectively. For m only up to0, the R–K model simplifies to an ideal-substitutional-so-

lution model, and for m only up to 1, it simplifies to asubregular-solution model [63].

The f, c2-Cu9Ga4 and c3-Cu9Ga4 subregular-solutionmodels of Li et al. were used without further modification,

Table 3 Comparison of Cu–Ga–In experimental thermal

analyses and calculated phase

transitions

Sample Experimental Calculated

Peak range (K) Transformation Temperature (K)

Cu41Ga19In40 [59]

Cu4322Ga1844In3834

890–949 L $ c 885.8–924.2L $ c ? L 885.8–891.2

425–455 L $ c ? (In) 374.8–407.5A

Cu476Ga95In429

860–946 L $ g 904.0–933.4L $ g ? L 904.0–912.2L $ c ? g ? L 904.0

428 L $ c ? g ? (In) 427.7B

Cu55Ga18In27

825.9–1018.8 L $ c 825.9–1001.4L $ c ? L 904.2c ? L $ g 825.9

427.3 L $ c ? g ? (In) 427.7C

Cu711Ga150In139

990–1044 L $ c 990.4–1048.9L $ a ? c 990.4–1014.4

D

Cu844Ga65In91

1002–1027 L $ a 945.6–1176.7L $ a ? c 945.6–946.2

913–939 c $ a ? d 912.7–917.3

Compositions in italics were used in the calculations

Fig. 7 Enthalpy of formation of the Cu7In3 alloy as a function oftemperature, with reference state at 298 K, where mol refers to the

chemical formula. The line is calculated and the circles are

experimental data [7]

3368 J Mater Sci (2016) 51:3362–3379

123

as they only exist on the Cu–Ga binary tie-line at equi-

librium [34]. Here the ternary c-Cu9(Ga,In)4 phase is takento be separate from c2-Cu9Ga4 and c3-Cu9Ga4. The high-temperature disordered c0-Cu9Ga4 phase has been identi-fied experimentally by the observation of DSC transitions.

However, it has been presently omitted because its relation

to the c-Cu9(Ga,In)4 and c-Cu9In4 compounds (as distinct

from the c1-Cu9Ga4 compound’s relation to them) isunclear. The substitutional-regular-solution model taken

from Anderson and Ansara has been employed for the

tetragonal(A6)-(In), or (In), solid phase, which incorpo-

rates Ga but not Cu.

An R–K formalism has been used for both the a, orfcc(A1)-(Cu), phase and the b, or bcc(A2)-Cu4(Ga,In),

Table 4 Comparison ofexperimentally measured and

calculated invariant reactions in

the binary Cu–In system

Cooling reaction Respective phase’s composition (at.% In) T (K) Reference

a ? L $ b 9.5 20.8 18.3 988 [57]10.05 20.9 18.05 983 [21]

7.5 20.0 19.0 984.5 [8]

7.5 19.5 18.8 976.4 This work

L $ c 29.1 29.1 – 958.2 [57]29.56 29.56 955.5 [51]

29.4 29.4 957.3 [8]

30.3 30.3 957.5 This work

L $ b ? c 25.8 23.8 27.2 952 [57]– 24.5 – 949 [21]

26.0 22.0 28.5 952.2 [8]

26.9 24.4 28.9 953.8 This work

c ? L $ g-HT 31.2 35.2 32.7 944 [57]32.0 35.6 33.3 943.4 [8]

- 35.4 33.0 940 [23]

31.9 37.4 35.2 944.5 This work

c $ d 29.5 29.5 – 904.2 [57]29.8 29.8 905.4 [8]

30.0 30.0 917.7 This work

c $ d ? g-HT 30.8 30.5 32.7 888 [57]32.0 30.6 33.3 891.0 [8]

– – 33.4 887 [23]

31.8 30.0 35.1 896.3 This work

c $ b ? d 27.9 22.1 28.2 889 [57]27.7 21.8 28.9 890 [51]

– 22.0 29.0 893.3 [8]

26.8 21.3 30.0 885.4 This work

b $ a ? d 20.0 11.63 28.7 847 [57]20.15 10.90 – 847 [21]

19.0 – 29.0 849.7 [8]

– 10.90 – 848 [43]

– 10.85 – 848 [24]

19.6 9.3 30.0 847.1 This work

d ? g-HT $ g-LT 32.0 35.0 34.5 661.8 [8]30.0 36.3 36.0 652.8 This work

g-HT ? L $ Cu11In9 36.4 97.0 45.0 579.0 [8]38.6 95.9 45.0 574.3 This work

g-HT $ g-LT ? Cu11In9 – – – 549.8 [8]38.5 36.0 45.0 554.7 This work

L $ Cu11In9 ? (In) – – 100.0 428.7 [8]99.3 45.0 100.0 426.3 This work

J Mater Sci (2016) 51:3362–3379 3369

123

Table 5 Optimized Gibbsenergy expression parameters,

where mol refers to the

chemical formula

Phase T range (K) Parameters (J/mol)

a-fcc(A1)-(Cu,In) 298–3000 �GaCu ¼� GfccCu � HSERCu�GaIn ¼� GfccIn � HSERIn0LaCu;In ¼ �22452:5439 þ 39:4052846 � T1LaCu;In ¼ �35850:2348 � 9:1642906 � T2LaCu;In ¼ 62576:0783 � 39:7753474 � T

b-bcc(A2)-Cu4In 298–3000 �GbCu ¼� GbccCu � HSERCu�GbIn ¼� GbccIn � HSERIn0L

bCu;In ¼ �3632:122 þ 0:4448 � T

1LbCu;In ¼ �47128:413 � 0:6313 � T

2LbCu;In ¼ 13753:699 þ 11:2268 � T

d-Cu7In3 298–3000 �GdCu7In3 � 0:7 �� GfccCu � 0:3 �� GtetIn ¼ �7991:308 þ 1:1703 � T

c-Cu9In4 298–3000 �GcCu:Cu:Cu:Cu:In � 12 �� GfccCu �� GtetIn ¼ 0

�GcCu:Va:Cu:Cu:In � 11 �� GfccCu �� GtetIn ¼ 0�GcCu:Cu:Cu:In:In � 9 �� GfccCu � 4 �� GtetIn ¼ �62519:633 � 11:0002 � T�GcCu:Cu:In:Cu:In � 9 �� GfccCu � 4 �� GtetIn ¼ 0�GcCu:Va:Cu:In:In � 8 �� GfccCu � 4 �� GtetIn ¼ �80900 � 3 � T�GcCu:Va:In:Cu:In � 8 �� GfccCu � 4 �� GtetIn ¼ 0�GcCu:Cu:In:In:In � 6 �� GfccCu � 7 �� GtetIn ¼ 0�GcCu:Va:In:In:In � 5 �� GfccCu � 7 �� GtetIn ¼ 0

g-HT-Cu16In9 298–3000 �Gg�HTCu:Cu:In � 2 �� GfccCu �� GtetIn ¼ �19569:83 � 0:9607 � T�Gg�HTCu:Va:In �� GfccCu �� GtetIn ¼ �7199 þ 0:14 � T0L

g�HTCu:Cu;Va:In ¼ �17436 þ 26:453 � T

g-LT-Cu16In9 298–3000 �Gg�LTCu16In9 � 0:64 �� GfccCu � 0:36 �� GtetIn ¼ �8173:8 þ 1:38 � T

a-fcc(A1)-(Cu,Ga,In) 298–3000 0LaGa;In ¼ 7369b-bcc(A2)-Cu4(Ga,In) 298–3000 0LbGa;In ¼ 150000d-Cu7(Ga,In)3 �GdCu:Ga � 0:7 �� GfccCu � 0:3 �� GortGa ¼

�GdCu:In � 0:7 �� GfccCu � 0:3 �� GtetIn ¼�7991:308 þ 1:1703 � T

1LdCu:Ga;In ¼ 17:04 � Tc-Cu9(Ga,In)4 298–3000 �GcCu:Cu:Cu:Ga:In � 9 �� GfccCu � 3 �� GortGa �� GtetIn ¼

�GcCu:Cu:Cu:Ga:Ga � 9 �� GfccCu � 4 �� GortGa ¼� 166571:3935 � 46:786919 � T�GcCu:Va:Cu:Ga:In � 8 �� GfccCu � 3 �� GortGa �� GtetIn ¼�GcCu:Cu:Cu:Ga:Ga � 9 �� GfccCu � 4 �� GortGa ¼� 166571:3935 � 46:786919 � T

0LcCu:Va:Cu:Ga;In:In ¼ 10:94 � T

1LcCu:Va:Cu:Ga;In:In ¼ 13100

g-HT-Cu16(Ga,In)9 298–3000 �Gg�HTCu:Cu:Ga � 2 �� GfccCu �� GortGa ¼�Gg�HTCu:Cu:In � 2 �� GfccCu �� GtetIn ¼ �19569:83 � 0:9607 � T�Gg�HTCu:Va:Ga �� GfccCu �� GortGa ¼ �17199 � 14:142 � T ¼�Gg�HTCu:Va:In �� GfccCu �� GtetIn � 10000 � 14:282 � T0L

g�HTCu:Cu;Va:Ga ¼ �17436 þ 26:453 � T ¼

0Lg�HTCu:Cu;Va:In � 120 þ 0:5 � T

0Lg�HTCu:Cu:Ga;In ¼ �99950 þ 100 � T

1Lg�HTCu:Va:Ga;In ¼ �12400 þ 101:8 � T

3370 J Mater Sci (2016) 51:3362–3379

123

phase [65]. While the previous Cu–Ga–In assessment

employed a sublattice model for b with Cu0.73(Cu,Ga,In,Va)0.14(Ga,In)0.13, the R–K model based on the

structure was used in this work to allow more realistic

extrapolations and to employ sublattices suitable for dif-

fusion modeling. Binary a and b parameters were takenfrom Li et al. for Cu–Ga and used without modification.

Modifications were made to both a binary Cu–In parame-ters taken from Cao et al. and to b binary Cu–In parameterstaken from Hertz et al. [20]. A single ternary mixing

parameter was added to the b description to destabilize andprevent ternary solubility, which has not been observed

experimentally (Table 5). Also, a single ternary mixing

parameter was added to the a phase to destabilize andprevent its appearance in the Ga-In binary tie-line.

The optimized parameters of the binary c1-Cu9Ga4phase were taken from Li et al. although the sublattice was

slightly modified. The new Cu5(Cu,Va)(Cu,Ga)3(Cu,Ga)3-

Ga sublattice is based on the site occupancies published by

Mizutani et al. [40], and it is more suitable for extrapola-

tion and diffusion modeling than the previous assessment’s

Cu0.654(Cu,Ga,In,Va)0.115(Ga,In)0.231 model [59]. The

analogous sublattice model was also optimized for the c-Cu9In4 phase in the Cu–In binary description to fit exper-

imental enthalpy data (Fig. 7) and to slightly improve

phase boundaries (see Fig. 8). The ternary c-Cu9(Ga,In)4(or simply c) description combines the c1-Cu9Ga4 and c-Cu9In4 binary parameters into a single phase along with

two new ternary c end-members to fit experimental solu-bility data (Table 5). These end-members were included to

extend the single-phase c region to encompass the 623 KCu659Ga218In123 datum of Purwins et al. [60]. Specifically,

the Cu5(Va)(Cu)3(Ga)3(In) and Cu5(Cu)(Cu)3(Ga)3(In)

end-member parameters were used directly from the binary

Cu5(Va)(Cu)3(Ga)3Ga and Cu5(Cu)(Cu)3(Ga)3Ga end-

members, respectively, after appropriately replacing �GortGa

with �GtetIn . The two new ternary c mixing parameters wereadded to pin the boundary between the two-phase c ? Land 3-phase c ? g ? L regions observed in the 623 Kisotherm (here g refers to the ternary g-Cu16(Ga,In)9 forbrevity) [60]. Those data are not technically equilibrated,

but they are qualitatively corroborated by the experimental

phase transitions observed in the neighboring Cu41Ga19In40and sample B alloys. The g phase was not observed byXRD in the Cu41Ga19In40 alloy [59], which is in agreement

with the boundary drawn by Purwins et al. [60]. On the

other hand, sample B’s DSC curve displays a low-tem-

perature peak (corresponding to L $ c ? g ? (In) inTable 3), a possible shoulder around 826 K (corresponding

to c ? L $ g), which is then followed by a broad thermalarrest up to 1018.8 K (L $ c in Table 3). These threetransitions in sample B compared with the two transitions

and lack of g observation in Cu41Ga19In40 indicate that thethin film 623 K isotherm boundary approaches that of

equilibrium (see phase diagram in Fig. 9). The1L

cCu:Va:Cu:Ga;In:In mixing parameter also extends the single-

phase c region to Ga-poor compositions as temperature isincreased. This was experimentally observed, as less Ga

content was found in the c phase in sample C at 711 K thanfor 591 K. Stabilization of the c phase at these more Ga-poor compositions additionally at lower temperatures was

avoided because it was found to narrow the two-phase

a ? d region and lower the c $ d transition temperature,pushing both further away from experimental observation.

No Ga solubility was observed by EDS or by XRD peak

shifts in the d-Cu7(Ga,In)3 phase in sample D equilibrated at591 and 711 K. However, a Cu0.7(Ga)0.3 end-member with

parameters equal to those of Cu0.7(In)0.3, along with a single

first-order mixing parameter were added to its model

Fig. 8 Close-up of the calculated Cu–In phase diagram with overlaidexperimental data

Fig. 9 Calculated Cu–Ga–In 623 K isotherm with overlaid experi-mental data [59, 60]

J Mater Sci (2016) 51:3362–3379 3371

123

(Table 5). This single new parameter allowed the a ? d2-phase region to more closely approach the composition of

sample D (Fig. 9), and it enabled the accurate prediction of

the c $ a ? d transition temperature at 913.0 K (Table 3).The g phase field is centered at the Cu16In9 (Cu0.64In0.36)

composition in the binary Cu–In phase diagram and con-

sists of at least 5 equilibrium phases [23]. These phases

span the range of approximately 33.0–38.0 at.% In [23,

51], depending on temperature. The exact nature of these

phases’ stability and equilibrium boundaries is unsolved;

however, it is clear that they are all based on a simple P63/

mmc substructure [35]. Like the previous Cu–In thermo-

dynamic assessments, only an ordered low-temperature (g-LT-Cu16In9) phase and a disordered high-temperature (g-HT-Cu16In9) phase have been considered [11, 37, 38].

XRD patterns indicate ternary solubility in a P63/mmc

structure [60], and ternary solubility in LT superstructures

has been documented [14, 58, 66–69]. Samples A and B,

however, display no thermal transition that could corre-

spond to g-HT-Cu16(Ga,In)9 $ g-LT-Cu16(Ga,In)9.Therefore, only g-HT is extended to Cu–Ga–In. An g-HTmodel similar to that used by Kao et al. was employed,

except the energetically unfavorable VaIn was not allowed

[27]. The following sublattice model has been used for the

g-Cu16(Ga,In)9 phase.�Gg ¼ y00Cu � y000Ga ��G

gCu:Cu:Ga þ y000In ��G

gCu:Cu:In

� �

þ y00Va � y000Ga ��GgCu:Va:Ga þ y000In ��G

gCu:Va:In

� �

þR �T � y00Cu � lny00Cu þ y00Va � lny00Va þ y000Ga � lny000Ga þ y000In � lny000In� �

þ y00Cu �y00Va � y000Ga � 0LgCu:Cu;Va:Ga þ y000In � 0L

gCu:Cu;Va:In

� �

þ y00Cu �y000Ga �y000In � 0LgCu:Cu:Ga;In

þ y00Va �y000Ga �y000In � 1LgCu:Va:Ga;In � y000Ga � y000In

� �

ð5Þ

The first two terms are the surface of reference end-

members, the third term is the configurational entropy, and

the final terms are the excess Gibbs energies. The

Cu0.545(Cu,Ga,In,Va)0.122(Ga,In)0.333 model used in the

previous Cu–Ga–In assessment was exchanged in favor of

the structure-based Cu(Cu,Va)(Ga,In), which again is

expected to yield more accurate extrapolations.

As the Cu–Ga binary system contains no analogous

phase, its parameters were taken to be equal to those

optimized for Cu–In, only with �GortGa replacing�GtetIn . These

2 binary phase descriptions were combined for the ternary

g description. The single Cu–In binary mixing parameterwas unchanged and entered as a Cu–Ga binary mixing

parameter. Two new temperature-dependent ternary mix-

ing parameters were added to complete the optimization

(Table 5). The 0LgCu:Cu:Ga;In parameter dominates stability in

the Cu-rich corner. Stabilizing too much at lower

temperature was found to further narrow the two-phase

a ? d (d refers to d-Cu7(Ga,In)3) region, contrary toexperimental evidence. Moderate stabilization was neces-

sary to increase the c $ a ? d transition temperaturecloser to the experimental value for sample D. Destabi-

lization of this parameter at high temperature was neces-

sary to match the experimental g solidus and liquiduscurves for samples A and B. The asymmetric 1L

gCu:Va:Ga;In

parameter was needed to destabilize g at Ga-rich compo-sitions. This parameter also determines the boundary

between the two-phase g ? L and three-phase c ? g ? Lregions, determined experimentally in the thin film 623 K

isotherm. Its destabilization at high temperature was also

necessary to match experimentally determined g solidusand liquidus temperatures in samples A and B. A total of

11 terms were added or modified in the assessment of the

ternary system, not including those used to prevent for-

mation of a and b in the Ga-In binary system.

Results and discussion

Thermodynamic calculations and parameter optimizations

were performed with global Gibbs energy minimization

software (Thermo-Calc and Pandat). The calculated binary

phase diagrams are presented in Figs. 10, 11, 12.

Cu–In assessment

As can be seen from Fig. 8, the calculated g-HT high-temperature phase boundary does not sufficiently extend to

the Cu-rich compositions to fit experimental measure-

ments. However, improved fit to enthalpy measurements

Fig. 10 Cu–Ga phase diagram calculated with the model used in thepresent work, from Li et al. [34]

3372 J Mater Sci (2016) 51:3362–3379

123

(Table 6; Fig. 7) with a sublattice that is based on the real

structure was obtained, which is better suited for ternary

extrapolation and diffusivity modeling. The phase bound-

aries of the a-(Cu,In), b-Cu4In, and c-Cu9In4 have all beenimproved slightly (Fig. 8). The calculated invariant reac-

tions are in line with the previous measurements and

assessments (see Table 4). Overall fit to enthalpy data has

been improved for the re-assessed phases (see Table 6).

Cu–Ga–In assessment

As can be seen from the calculated isotherm in Fig. 9,

satisfactory fit to the data has been obtained. The thin film

single-phase c datum at Cu659Ga218In123 composition [60]is actually predicted to contain two phases at equilibrium:

89 % c and 11 % g. It is postulated that either lack ofaccuracy in the composition measurement technique (the

technique is not reported) or the minor phase amounts in

the already thin film were not sufficient to produce a dis-

cernible XRD signal. A composition of Cu671Ga212In117,

which probably lies within the error of the composition

measurement technique, does lie in the calculated single-

phase c region. The average composition of sample Ddetermined by ICP places it in the calculated three-phase

a ? c ? d region at 623 K. However, if the composition isshifted to Cu8198Ga895In907 (which falls well within the

error margin of the experimental technique), the model

predicts it to fall in the two-phase a ? d region, inagreement with experiment.

The phases identified by XRD for each sample were the

same as those predicted by the thermodynamic model. The

only crystalline phases observed in samples C and D were

a, d, and c. The XRD pattern for Cu41Ga19In40 displayed cand (In) peaks as well as peaks which were attributed to

Cu11In9 [59], but due to peak overlap with c, the presenceof Cu11In9 in that alloy is considered uncertain in the

present work. The model has also been optimized against

thermal analysis scans at the five compositions shown in

Fig. 9. Better agreement was found when calculations used

compositions which were slightly different from the as-

measured values (see Tables 1, 3). The phase transitions

observed with thermal analyses are predicted adequately by

the model (Figs. 3, 4, 5, 6; Table 3). Notably, the largest

deviations of the calculated transitions from experiment

coincide with peaks which have ambiguous onsets. In these

cases, calculated system enthalpies have been overlaid on

experimental thermal scans to assist in the comparison

(Figs. 4, 5). The Cu41Ga19In40 alloy displayed a thermal

event with onset at 425 K, which is not predicted well by

the model, and which is very similar to the 427.7 K

eutectic L $ c ? g ? (In) transition temperature. Thismay be evidence that at lower temperatures, the c com-pound’s (c-Cu9(Ga,In)4; c1-Cu9Ga4; c2-Cu9Ga4; c3-Cu9Ga4) stability extends the three phase c ? g ? (In) regionto a more Ga-rich composition than predicted by the

model. Further experimental evidence would be needed to

substantiate this possibility. Overall, good binary system

fits have been retained, while re-assessment of the Cu–In

binary system has enabled appropriate ternary extrapola-

tions. The few added ternary parameters were necessary to

match experiments, and good fit was obtained.

Practical applications

The thermodynamic model may be used as a guide for

choosing promising Cu–Ga–In precursors for selenization

Fig. 11 Cu–In phase diagram calculated with the optimized model

Fig. 12 Ga-In phase diagram calculated with the model used in thepresent work, from Anderson and Ansara [5]

J Mater Sci (2016) 51:3362–3379 3373

123

processes. For metal precursors sputtered onto Mo sub-

strates, the formation of a Cu- and Ga-rich matrix with In-

rich nodules on top is usually observed [4, 58, 70–73].

Examples of various deposition methods that affect this

morphological segregation are sequential sputtering of a

Cu0.8Ga0.2/In bilayer [73], sequential in situ sputtering of

350 ultrathin-stacked layers of Cu0.8Ga0.2 and pure In [4,

70], sputtering from single ternary targets of varying

compositions [72, 74–76], or simultaneously co-sputtering

onto the same substrate from dual targets [77]. Similar

results are obtained by co-deposition from effusion sources

onto unheated substrates in the cases of CuGa/CuIn

bilayers, Cu/Ga/In layers repeated four times, and the same

repeated eight times [73]. The overall film compositions for

these examples fall between 0.8\Cu/III\ 1.0 and0.2\Ga/III\ 0.3 [4, 70, 72, 73, 75–77]. The lack ofdependence on deposition sequence suggests that the

observed phase segregation is correlated with overall film

composition more than it is correlated with local compo-

sitional modulations. Calculations for Cu/III = 0.9 and Ga/

III = 0.3 at room temperature predict an equilibrated Cu–

Ga–In system to contain c, g, and (In) with indium molefractions of 0.08, 0.23, and 1.00, respectively. It is

speculated that sputtered and co-deposited films may tend

toward equilibrium segregation of the two major phases

(Cu–Ga-rich c and In-rich (In)) due to natural heating ofthe substrate induced by sputtered particle bombardment or

energetic evaporant arrival, depending on the process.

Liquid indium is known to have a significantly lower sur-

face free energy than both liquid gallium and copper for all

temperatures [78]. Liquid alloys containing mostly indium

are expected to have surface tensions approaching that of

pure indium. Therefore, the surface segregation of In-rich

nodules may be related to the liquid phase, while its rela-

tion to any solid phases remains unknown.

Calculations indicate that overall cation compositions

that are reasonably close to those of record efficiency CIGS

cannot avoid (In) and In-rich liquid phases in equilibrated

metal precursors below and above 428 K, respectively.

Figure 13 shows phase fractions of systems as a function of

temperature with Cu/III = 0.9 at different Ga/III. As can

be seen, the g phase is avoided at all temperatures for Ga/III = 0.4 (more precisely, for all Ga/III C 0.34). Similarly,

the c phase can be avoided at all temperatures for all Ga/III B 0.14. The c phase typically segregates toward the rearcontact in the as-deposited metal precursors and also

Table 6 Comparison of experimental, previous assessments’ calculated, and the present assessment’s calculated standard formation enthalpiesin the binary Cu–In system, with pure solid fcc(A1)-Cu and pure solid tetragonal(A6)-In reference states, and mol refers to the chemical formula

Exp. phase T (K) Mole fraction of In Experimental DH (J/mol) Previous calc. DH (J/mol) Present calc. DH (J/mol)

b 903 0.2086 -431 [25] -976 [27], -48 [20], -1330 [37] -1017

b 903 0.2194 -2423 [25] -976 [27], -1487 [37] -1099

b 941 0.2086 -464 [25] -949 [27], -1330 [37] -1017

c 903 0.3116 -6100 [25] -5667 [37] -6454 (-5958)

c 941 0.2995 -3310 [25] -5147 [37] -5519

c 941 0.3 -4424 [26] -6734 [27] -5532

c 941 0.3087 -3874 [25] -4218 [20], -5542 [37] -5749

c 941 0.3116 -6088 [25] -5667 [37] -5818

g-HT 723 0.338 -8000 [30] -6573 [27] -7444 (-7134)

g-HT 723 0.352 -7548 [55] -7267 [37] -7242 (-7134)

g-HT 723 0.358 -7780 [55] -7110 [27] -7156 (-7134)

g-HT 723 0.365 -7700 [55] -7185 [27] -7193

g-HT 723 0.375 -7700 [30] -7132 [27] -7245

g-HT 723 0.377 -7470 [55] -7132 [27] -7229 (-7247)

g-HT 723 0.39 -7531 [30], -7382 [55] -6839 [27], -6540 [20] -6936 (-7247)

g-HT 773 0.352 -7550 [55] -6933 [27], -7055 [20] -7174 (-7097)

g-HT 773 0.358 -7450 [55] -7074 [27], -7417 [37] -7114

g-HT 773 0.365 -7420 [55] -7096 [27], -7504 [37] -7193

g-HT 773 0.375 -7264 [55] -7463 [37] -7172 (-7238)

g-HT 773 0.377 -7470 [55] -7048 [27] -7122 (-7238)

g-HT 903 0.3431 -6636 [26] -6477 [27], -5837 [20], -6915 [37] -6762 (-7000)

g-HT 903 0.3476 -6402 [26] -6591 [27], -5916 [20], -7113 [37] -6896 (-7000)

For conditions in two phase regions, calculated equilibrium system values are listed first followed by metastable single-phase values in

parenthesis

3374 J Mater Sci (2016) 51:3362–3379

123

during the selenization, reducing the reaction rate and

ultimately relating to the void formation at the back contact

that may increase the series resistance [4, 58, 71, 72].

Notably, an overall metal precursor composition of Cu/

III = 0.9 and Ga/III = 0.14 in practice would probably

still not avoid these phenomena, because the preferential

reaction of In with Se during initial selenization is likely to

enrich the rear interface to Ga/III[ 0.14. It is thereforeimpractical to avoid c formation in equilibrated metalprecursors with compositions of interest for high-efficiency

PV devices. However, it may be possible to avoid equili-

bration—a previous report found that as-deposited Cu/Ga/

In films exhibited reduced c content relative to CuGa/Infilms [79], while equilibration (by annealing) caused both

films to form similar amounts of c. As less c formation wasassociated with better PV performance in that study, low

energy precursor processes may be advantageous.

The undesired formation of voids at the rear interface

may also be related to the nearly ubiquitous agglomeration

of indium at the surface. As the agglomeration forms

nodules, it is also likely a source of lateral nonuniformity.

Assuming either of these phenomena is a result of In-rich

liquid, the fraction of overall indium in the system which is

present in the liquid would give a measure of the likelihood

of In surface agglomeration. The model predicts that no

Ga/III precursor compositions or temperatures can avoid a

significant equilibrium amount of liquid In, with the

exception of Ga/III approaching unity (that is, composi-

tions which are presently of diminished interest for high-

efficiency PV).

Calculated isopleths at three different constant Ga/III are

shown in Fig. 14. At lower processing temperatures (such

as those reached by an unheated substrate during

sputtering), the equilibrium phases change from

CuGa2 ? c ? (In) to c ? (In) to c ? g ? (In) withincreasing Cu/III or decreasing Ga/III. The

c ? L $ CuGa2 ? (In) invariant reaction occurs at374.8 K, and the L $ c ? g ? (In) eutectic reactionoccurs at 427.7 K; both these transitions shift to greater Cu/

III with increasing Ga/III. This is a 50 �C change in initialliquid formation temperature which is caused by small

compositional changes.

The calculated ternary isotherms at 423, 823, and 1023 K

are in Figs. 15, 16, and 17, respectively. As can be seen by

visual inspection of the isotherms, compositions with Cu/

III & 0.9 and Ga/III & 0.3 (In & 37; Ga & 16 at.%)

Fig. 15 Calculated Cu–Ga–In 423 K isotherm. Bold lines indicatebinary tie-line phase existence regions

Fig. 14 Calculated Cu–Ga–In isopleths, or vertical sections atconstant Ga/III = 0.25 (light-gray solid lines), 0.30 (dark-gray

dashed lines), and 0.35 (black-short dashed lines)

Fig. 13 Calculated phase fractions of g (red) and c (blue) at constantCu/III = 0.9 and Ga/III = 0.2 (solid lines), Ga/III = 0.3 (dashed

lines), and Ga/III = 0.4 (dotted line) as a function of temperature

J Mater Sci (2016) 51:3362–3379 3375

123

exist quite near to or overlapping phase boundaries from low

temperature up to the liquidus temperature (Figs. 15, 16,

17). Generally speaking, the In-poor c and In-rich (In)phases predominate, while the g phase with moderate Incontent is calculated to be present in smaller amounts. The

CuGa2 phase also appears at low Cu/III and/or high Ga/III

(see also Fig. 14), in agreement with its experimental

observation in Cu437Ga388In175 films [80]. The L $ CuGa2,L $ (In), and L $ g equilibrium transitions all occurwithin typical processing temperature ranges (\873 K), andthe product liquid phase is always very In-rich (see tie-lines

in Fig. 9). The likely presence of In-enriched liquid may

relate to enhanced In mobility in the early stages of a sel-

enization temperature ramp. Enhanced In mobility may

permit rapid diffusion to the surface, where it selenizes first,

in excellent agreement with a recent in situ XRD study of

Cu–Ga–In selenization [81].

At later stages of chalcogenization, however, a possible

intermetallic phase transition at around 773 K has been

hypothesized based on observance of a step increase for

incorporation of Ga into chalcogenide phase(s), and there-

fore apparent Ga mobility [71]. A subsequent study found a

step increase in the extent of reaction of Ga with S at around

803–813 K in a selenization process [82]. There are only

three possible explanations for the observed jump in reaction

extent with only slightly increasing temperature: (1) the

thermodynamic-limited case where temperature changes the

Gibbs energy of reaction, (2) the diffusion-limited case

where temperature probably causes a phase change to greatly

increase Ga mobility, and (3) the reaction kinetic-limited

case where temperature causes a change in activation

energy. The first two cases are most likely because the

reaction of gases with condensed phases is usually diffusion

limited, and thermodynamics determines the favorability of

competing reaction pathways. The Ga-S thermodynamic

system has not been assessed to the authors’ knowledge, so

Gibbs energy calculations for the Cu–Ga–In–S system

cannot presently be performed for the thermodynamic-lim-

ited case. The diffusion-limited case, though, would quali-

tatively agree with the Cu–Ga–In model. Assuming the back

of the films are effectively still chalcogen free and have Cu/

III & 0.9 and Ga/III & 0.3 [82], the c ? L $ c ? g ? Ltransition can be expected to occur around 773–813 K,

depending on precise Cu/III and Ga/III. This precise com-

position dependence could also explain why the step in

reaction extent with temperature was originally observed at

773 K [71] and subsequently observed at 803–813 K [82].

Importantly, the c ? L $ c ? g ? L transition tempera-ture shown in Fig. 14 is calculated to vary greatly with only

slight changes in both Cu/III and Ga/III composition. For

example, changing overall Cu composition by ± 0.5 at.%

about Cu/III = 0.9 at a constant Ga/III = 0.3 changes the

c ? L $ c ? g ? L transition temperature from 708 to801 K. Furthermore, changing overall Ga composition

by ± 0.5 at.% about Ga/III = 0.3 at a constant Cu/III = 0.9

changes the temperature from 822 to 695 K. As the sel-

enization process is most likely condensed phase diffusion

limited, and diffusion through liquids is usually orders of

magnitude faster than through solids, the anticipated variance

in L $ g transition temperature could have drastic reactionrate implications. If film composition of all cations is not

controlled to better than the ambitious target of ±0.5 at.%,

then significant reaction rate inhomogeneity can be expected.

This is evidence that the equilibrium reaction pathways fol-

lowed for metal precursors commonly used in selenization



3376 J Mater Sci (2016) 51:3362–3379

123

processes are inherently non-robust, that is, highly sensitive to

slight compositional changes which approach the detection

limits of typical measurement techniques.

The vapor pressures of all metal species were calculated

for an equimolar mixture of Cu–Ga–In (Fig. 18). A system

of Cu0.9Ga0.3In0.7 has very similar calculated vapor pres-

sures. The vapor pressures vary greatly, with PIn[ 10PGa[ 100 PCu[ 100 PIn2 at typical processing tempera-tures. As temperature increases, the In partial pressure

increases more rapidly than that of Se (not shown). How-

ever, only in the case of extreme processing temperatures

would the In vapor pressure be relevant (e.g., at 680 �C(950 K) In is just five orders of magnitude lower than

weighted Se partial pressure). While some studies found

material loss of In/Ga by evaporation to be an issue during

selenization [83], a subsequent report attributed the appar-

ent material loss to a characterization artifact [84]. The

equilibrium vapor pressures indicate that while cation

material loss by pure element evaporation should indeed be

negligible, material loss by metal selenide molecule evap-

oration could nevertheless be important. Specifically, the

vapor pressure of In2Se at processing temperatures is

greater than In by an order of magnitude [85], or substan-

tially more [86–88]. Similarly, the vapor pressure of Ga2Se

at processing temperatures is greater than Ga [85, 89]. It is

therefore likely that In and Ga loss occurs by In2Se and

Ga2Se formation and evaporation during selenization.

Conclusions

Equilibrium in the Cu–Ga–In material system has been

studied. High-temperature equilibration experiments have

been performed that map the ternary phase diagram at two

different compositions and at three temperatures, as well as

thermal analysis for five compositions. A Cu–Ga–In ther-

modynamic model has been assessed that fits the equilib-

rium data and nonequilibrium thin film observations

reasonably well, which may indicate that typical precursor

films approach equilibrium. With the model and thermo-

dynamic calculation software, calculations may be per-

formed to predict thermodynamic reaction pathways. This

could be quite useful in the development of metal precursor

films for selenization processing of CIGS PV absorbers.

Specifically, at typical compositions and processing tem-

peratures, metal precursor films are expected to undergo a

phase transition that is highly sensitive to slight composi-

tion changes. Small compositional fluctuations could

therefore cause lateral nonuniformity in chalcogenized

absorbers. Equilibrated films are calculated to have high ccontent. Reducing film equilibration could therefore reduce

c formation, which has been shown experimentally, andwas associated with better PV performance [79]. Extension

of the model to diffusivity modeling could further assist in

understanding selenization reaction pathways.

Acknowledgements The authors gratefully acknowledge fundingfrom the U.S. Department of Energy under FPACE contract DE-

EE0005407. The authors would like to thank GE for graciously

providing bulk alloys and performing DSC, and Thermo-Calc Soft-

ware and CompuTherm LLC for providing software. This study was

funded by Department of Energy FPACE grant DE-EE0005407.

Compliance with ethical standards

Conflict of interest The authors declare that they have no conflictof interest.

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Cu--Ga--In thermodynamics: experimental study, modeling, and implications for photovoltaicsAbstractIntroductionExperimentalSample preparation and alloy annealingAlloy characterization

Experimental resultsXRDSEM/EDSDTA/DSC

Thermodynamic assessmentThermodynamic literatureThermodynamic modelsPure elementsStoichiometric compoundsSolution phases

Results and discussionCu--In assessmentCu--Ga--In assessmentPractical applications

ConclusionsAcknowledgementsReferences

cu–ga–in thermodynamics: experimental study, modeling, and implications...

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