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Engineering Solar Cell Absorbers by Exploring the Band
Alignment and Defect Disparity: The Case of Cu- andAg-Based Kesterite Compounds
Zhen-Kun Yuan, Shiyou Chen,* Hongjun Xiang, Xin-Gao Gong, Aron Walsh,
Ji-Sang Park, Ingrid Repins, and Su-Huai Wei

The development of kesterite Cu2ZnSn(S,Se)4 thin-film solar cells is currently
hindered by the large deficit of open-circuit voltage (Voc), which results fromthe easy formation of CuZn antisite acceptor defects. Suppressing the formation of CuZn defects, especially near the absorber/buffer interface, is thus
critical for the further improvement of kesterite solar cells. In this paper,
it is shown that there is a large disparity between the defects in Cu- andAg-based kesterite semiconductors, i.e., the CuZn or CuCd acceptor defects
have high concentration and are the dominant defects in Cu2ZnSn(S,Se)4or Cu2CdSnS4, but the AgZn acceptor has only a low concentration andthe dominant defects are donors in Ag2ZnSnS4. Therefore, the Cu-based
kesterites always show p-type conductivity, while the Ag-based kesterites
show either intrinsic or weak n-type conductivity. Based on this defectdisparity and calculated band alignment, it is proposed that the Voc limit of
the kesterite solar cells can be overcome by alloying Cu2ZnSn(S,Se)4 with
Ag2ZnSn(S,Se)4, and the composition-graded (Cu,Ag)2ZnSn(S,Se)4 alloys
should be ideal light-absorber materials for achieving higher efficiency
kesterite solar cells.

Z.-K. Yuan, Prof. H. Xiang, Prof. X.-G. Gong
Key Laboratory for Computational
Physical Sciences (MOE)State Key Laboratory of Surface Physics
and Department of Physics
Collaborative Innovation Centerof Advanced Microstructures
Fudan University
Shanghai 200433, China
Prof. S. Chen
Key Laboratory of Polar Materials and Devices (MOE)
East China Normal University
Shanghai 200241, China
E-mail: chensy@ee.ecnu.edu.cn
Prof. A. Walsh
Center for Sustainable Chemical Technologies
and Department of Chemistry
University of Bath
Bath BA2 7AY, UK
Dr. J.-S. Park, Dr. I. Repins, Dr. S.-H. Wei
National Renewable Energy Laboratory
Golden, CO 80401, USA

DOI: 10.1002/adfm.201502272

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1. Introduction

As the leading thin-film solar cell technology, CdTe and Cu(In,Ga)Se2 (CIGS)
solar cells have advanced to reach lightto-electricity conversion efficiencies over
20%, with annual production now in thegigawatt range.[1] However, as this volume
increases, the cost and scarcity of In andTe, as well as the toxicity of Cd, could
become major issues that may limit thewidespread utilization of CdTe and CIGS
photovoltaics. Therefore, the search andoptimization of alternative thin-film solar
cell materials is urgently needed. Quaternary I2–II–IV–VI4 (I = Cu, Ag, II = Zn, Cd,
IV = Si, Ge, Sn, VI = S, Se, Te)[2] chalcogenides form a large group of semiconductors with variable structural, optical, andelectrical properties.[3–7] Among them,
the kesterite semiconductors Cu2ZnSnS4
and Cu2ZnSnSe4 have recently emerged
as promising light-absorber materials forthin-film solar cells because of their close-to-optimal material
properties.[8–13] Furthermore, all their component elements areearth-abundant and nontoxic, so they are expected to be ideal
substitute for the currently commercialized CdTe and CIGS
absorbers.
Despite their good material properties such as suitable band
gap and high optical absorption, the increased number of elements in the quaternary compounds also results in a large
amount of native lattice defects.[14–20] In Cu2ZnSnS4 (similarly
Cu2ZnSnSe4), it was found that the CuZn antisite defects havea low formation energy and high concentration due to thesmall size and chemical difference between Cu and Zn,[15,19]
making the synthesized samples always show p-type conductivity.[21–25] When forming a p–n junction with the n-type CdS(buffer layer), the p-type Cu2ZnSnS4 (absorber layer) cannot
have an effective p-to-n type inversion near the p–n junction interface because high concentration of CuZn will form
at the interface and pin the Fermi level at the middle of theband gap.[15] Experimentally it was found that the surface of
Cu2ZnSnS4 is indeed p-type (without type inversion),[26] inagreement with the theoretical analysis. As a result, only asmall band bending can be induced in the absorber layer, as
shown in Figure 1a. Since the maximum Voc of the solar cell

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CuZn+SnZn, and 2CuZn+SnZn defect complexes, which can cause band gap and electrostatic potential fluctuations[36–43] and/or
the trapping and recombination of the carriers, thus further limiting the Voc.[30,37,44–47]
To suppress the CuZn related defects, Cupoor/Zn-rich growth conditions are required
to fabricate high-efficiency Cu2ZnSnS4-basedsolar cells.[48–52] Unfortunately, this approach
can cause the formation of secondary phasessuch as ZnS, too high concentrations of
Cu vacancies, and serious nonstoichiometry, which can also limit device performance.[51,53–60] Therefore, how to suppress
the formation of CuZn and related defects
imposes a great challenge to the further optimization of kesterite solar cells.
One of the possible approaches to suppress the formation of CuZn is to substitute
Cu or Zn in Cu2ZnSnS4 or Cu2ZnSnSe4 byatoms with different sizes, e.g., replacing
Zn by Cd to form Cu2CdSnS4 or replacing
Cu by Ag to form Ag2ZnSnS4. Considering
the large size mismatch between Cu andCd (Ag and Zn), we expect that CuCd in
Cu2CdSnS4 (AgZn in Ag2ZnSnS4) may havehigh formation energy, then these two semiconductors may have significantly different
defect properties from that in Cu2ZnSnS4
Figure 1. The band diagram of solar cells in the dark (left) and under illumination (right):
andthus the potential to overcome the Voca) the CdS/Cu2ZnSn(S,Se)4 solar cell with no type inversion (the Fermi level near the interbottleneck. Although this approach is inface is pinned at the middle of the band gap) and small band bending in the absorber layer,
principle simple, whether it is efficient isb) the CdS/Cu2ZnSn(S,Se)4 solar cell with a small Voc under the flat band condition, c) an ideal
absorber layer with type inversion (the Fermi level near the interface is close to the conduction
still a question. Previous experiments haveband) and a large band bending, and d) an ideal absorber layer with a large Voc under the flat shown that undoped Ag ZnSnS exhibits
2
4band condition. The band bending in the n-type CdS layer is not changed much under illumiintrinsic n-type conductivity,[61,62] however,nation because its absorption of visible light is weak and the concentration of the majority of
Cu2CdSnS4 retains p-type conductivity,[63–65]
electron carriers is not changed significantly by the photogenerated carriers. As we can see,similar to that of Cu2ZnSnS4. This is not
the maximum Voc under illumination is derived mostly from the band bending of the absorberfully in accordance with our expectation.
layer in the dark.[27–29]
Why the Cu2CdSnS4 samples are p-typewhile Ag2ZnSnS4 samples are n-type, andwhat defects are dominant in determining their electrical
under illumination (under the flat band condition, as shown in
conductivity? These questions are still open. A systematicalFigure 1b) is equal to the band bending of the absorber layer
study on the defects in these semiconductors is necessary
in dark,[27–29] the Fermi level pinning by CuZn defects (thusfor answering these questions and will also reveal whether
no type inversion) causes a large deficit of Voc. This intrinsic
the Voc limit can be overcome by the element-substitution
defect problem has hindered the further progress of Cu-based
kesterite solar cells, the record efficiency is only 12.7%,[30] still
approach. One recent study showed that the efficiency of
Cu2ZnSnS4 solar cell can be enhanced significantly frommuch lower than those of the CdTe and CIGS cells despite
they have similar band gaps. In contrast, the type inversion
5.30% to 9.24% through forming Cu2Zn1–xCdxSnS4 alloys(through forming n-type Cu-poor ordered vacancy compounds
as the absorber layer,[66] showing that the replacement ofor CdCu doping near the CdS/CIGS interface) and thus a large
Zn by Cd may have great potential for improving the device
performance.
band bending have been observed in CIGS solar cells,[28,31–35]
In this article, we have systematically investigated thewhich makes their maximum Voc much higher than that of the
intrinsic defects of Cu2CdSnS4 and Ag2ZnSnS4 based on the
Cu2ZnSn(S,Se)4 solar cells, as shown in Figure 1c,d. It is thus
critical to suppress the formation of CuZn and make the typedensity functional theory calculations and compared them withthose of Cu2ZnSnS4. Interestingly, we find that the CuCd antisite
inversion possible at the p–n junction interface if one intends
to overcome the Voc deficit of Cu2ZnSn(S,Se)4 solar cells.
related defects still have high concentration in Cu2CdSnS4 (similar to the case in Cu2ZnSnS4), making the samples intrinsically
The detrimental effect of the acceptor defect CuZn is further amplified because it can bind with donor defects such asp-type. In contrast, the formation of AgZn antisite defects is supZnCu and SnZn, forming high concentration of CuZn+ZnCu,pressed in Ag2ZnSnS4 with a lower equilibrium concentration

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2. Results and Discussion
2.1. Defect Similarity between Cu-Based Cu2CdSnS4
and Cu2ZnSnS4
Since the size difference between Cu and Cd is large (the calculated Cu S and Cd S bond lengths in Cu2CdSnS4 are 2.32
and 2.56 Å, as shown in Table 1), we expected that the formation energy of the CuCd antisite may be high and the dominant
defect will be the shallow Cu vacancy VCu, similar to that in the
ternary CuInSe2 and CuGaSe2.[67,68] Surprisingly, our first-principles formation energies show a different picture. The CuCd
antisite defect still has a low formation energy, slightly higher
than CuZn in Cu2ZnSnS4 by about 0.2 eV, indicating that the formation energies of CuCd and CuZn antisite (more generally III in
I2-II-IV-VI4) may not be determined just by the size difference,in contrast to intuition. CuCd is still the lowest-energy acceptor
defect in Cu2CdSnS4, no matter what chemical potential conditions are considered, as shown in Figure 2. VCu has muchhigher formation energy (0.8–1.3 eV) than CuCd (0.3–0.6 eV),and all other acceptor and donor defects have higher formation
Table 1. Calculated bond length and defect formation energy of neutral
VI and III defects in Cu2ZnSnS4, Cu2CdSnS4, and Ag2ZnSnS4. Both thevalue when μCu = μCd = μZn = μ Ag = 0 and the largest value in the achievable chemical potential region are shown for comparison.
Bond length[Å]Formation energy[eV]

μCu = μCd = μZn = μ Ag = 0
Cu2ZnSnS4

Cu2CdSnS4

Ag2ZnSnS4

Maximum

Cu S

2.31

VCu

1.14[15]

VCu

Zn S

2.36

CuZn

1.41

CuZn 0.38[15]

Cu S

2.32

VCu

1.28

VCu

1.28

Cd S

2.56

CuCd

1.28

CuCd

0.59

Ag S

2.57

VAg

2.14

VAg

2.14

Zn S

2.36

AgZn

3.10

AgZn

1.80

Adv. Funct. Mater. 2015, 25, 6733–6743

1.14[15]

energies in their neutral charge state, so the dominance of theacceptor CuCd makes Cu2CdSnS4 show intrinsic p-type conductivity, similar to that in Cu2ZnSnS4 where CuZn is the dominant
defect.[15]If we compare the formation energy when μCu = μCd = 0,
the value of CuCd (1.28 eV) is actually equal to that of VCu. However, μCd is rather low, always lower than −0.9 eV because of
the easy formation of the binary CdS (as shown in Figure S1of the Supporting Information), which decreases the formation energy of CuCd according to Equation (1) and changes theenergy order of CuCd and VCu. Therefore, the constraint on the
Cd chemical potential by CdS plays an important role in thedominance of CuCd antisite.
The low formation energy of CuCd makes n-type doping of
Cu2CdSnS4 difficult because when the Fermi level increases,
the ionized CuCd acceptor defect can reduce its formationenergy to zero (see Figure 2a), thus forming spontaneously andlimiting the further increase of the Fermi level. In the kesterite
solar cells, there is a p–n heterojunction between the p-type
absorber layer (Cu2ZnSnS4 or Cu2CdSnS4) and the n-type
buffer layer (CdS). As shown in Figure 1, a p-to-n type inversion of the absorber layer is required near the junction interface so that a large band bending (as large as the band gap) can
be formed from the interior of the absorber layer to the junction interface. This band bending determines the open-circuit
voltage (Voc) of the solar cell. Because of the n-type doping difficulty (the Fermi level is pinned at the middle of the band gap),
the type inversion cannot be effectively achieved under equilibrium in Cu2ZnSnS4 or Cu2CdSnS4, so the band bending issmall and the Voc is severely limited to a small value, as shownin Figure 1b.
Furthermore, as a result of the low formation energy of
CuCd, defect complexes based on CuCd, such as the self-compensated antisite pair CuCd+CdCu, also have very low formationenergies. The value for CuCd+CdCu is only 0.21 eV/pair (seeFigure 2b), very close to the CuZn+ZnCu pair in Cu2ZnSnS4(0.20 eV/pair),[15,19] indicating that the Cu/Cd cation disorderis also common in Cu2CdSnS4. The formation of CuCd+CdCu
antisite pairs induces a small band gap shrinking (as shown in
Figure 3b), which can cause band gap fluctuations in different
area of the samples. Besides the CuCd+CdCu pair, the formationenergy of 2CuCd+SnCd is also low, about 0.43–0.65 eV, comparable with that of 2CuZn+SnZn clusters in Cu2ZnSnS4.[15] The
2CuCd+SnCd complexes induce more significant downshift ofthe conduction band and also the upshift of the valence band,so its high population causes more significant band gap fluctuation and also the trapping of the electron carriers, which also
leads to Voc deficit in devices.
Except for CuCd and VCu related defects, other donor andacceptor defects have high formation energies when they are
not ionized. The high concentration of CuCd defects makes the
samples p-type and shifts the Fermi level to close to the VBM,
3+
so the donor defects such as Cd +Cu , Sn 2+
Cd , and Sn Cu become ionized and decrease their formation energy to lower than 1.0 eV(according to Equation (1), and even to only 0.62, 0.55, and0.88 eV at the Sn-rich, Cu-poor, and Cd-poor condition (point P
in Figure S1, Supporting Information). This suggests that theseionized donor defects exist in p-type Cu2CdSnS4 samples. Fromthe calculated transition energy levels as shown in Figure 3a,© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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than three donor defects (ZnAg, SnZn antisites and S vacancies).
All the intrinsic point defects in Ag2ZnSnS4 have relatively highformation energy, so the samples show either poor or weakn-type conductivity. Based on the calculated valence band alignment, we explain the puzzling disparity in the defect properties of Cu- and Ag-based I2–II–IV–VI4 semiconductors, i.e.,
antisite defect formation is not solely determined by the size
difference of the elements; the easy formation of CuZn and
CuCd antisites in Cu-based compounds also results from thehigh valence band energy, determined by the Cu 3d level, while
the suppressed formation of AgZn in the Ag-based compounds
results from the lower valence band edge determined by Ag 4d.
Our results reveal a fundamental distinction between the defectphysics of the Cu- and Ag-based I2–II–IV–VI4 semiconductors,
based on which and calculated band alignment between Cuand Ag-based kesterites, we propose that forming compositionand band-graded (Cu1–xAgx)2ZnSn(S,Se)4 alloy absorber shouldhave great potential to overcome the Voc deficit and improve thesolar cell efficiency.

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Figure 2. The calculated formation energy change of defects in Cu2CdSnS4 a) as a function of the Fermi level at the chemical potential point P andb) as a function of the elemental chemical potentials. The chemical potential points P–Q–M–N–G are shown in Figure S1 (Supporting Information),and μCu = 0 , μCd = −0.69 eV, and μSn = −0.29 eV at the point A. The Fermi level is assumed to be at the VBM (p-type conditions), and therefore, alldonor defects are ionized in panel (b).

the donor level of CdCu is shallow, while those of SnCu and SnCd
are deep in the gap and thus may act as electron-hole recombination centers. This is also similar to the deep-level donors
SnCu and SnZn in Cu2ZnSnS4.[15] The calculated acceptor levelof CuCd is 0.13 eV above the valence band, relatively deeper
than that of VCu (0.01 eV).
Given the relatively deep level of the dominant acceptor
defect CuCd as well as the existence of detrimental deep-level
donor defects and defect complexes, the Cu2CdSnS4 solar cell
performance should be limited. In order to suppress the formation of CuCd and the detrimental donor defects and defect complexes, and also to increase the shallow acceptor VCu, Cu-poor,
Sn-poor, but Cd-rich growth conditions are necessary. However, too Cd-rich condition also causes the existence of CdS,
which should be avoided. Similar bottleneck effect exists alsoin Cu2ZnSnS4, where Zn-rich condition is required to suppress

detrimental defects but it also causes the formation of ZnS secondary phase.[51,53–60]
Based on the above discussion, the main features of thedefect properties of Cu2CdSnS4 and Cu2ZnSnS4 are very
similar. Since the formation energies of deep-level donors areeven lower in Cu2CdSnS4, we predict that the developmentof high-efficiency Cu2CdSnS4 solar cells is more challenging.
Indeed, the achieved efficiency of Cu2CdSnS4-based solar cells
is currently much lower than that of Cu2ZnSnS4-based solar
cells.[64,69] After we finished the current work, we noticed amore recent study which shows that the solar cells based on
Cu2Zn1–xCdxSnS4 alloys with appropriate Zn/Cd ratio have an
efficiency up to 9.24%, while the efficiency is decreased when
the Cd content is high,[66] which can be understood according
to our finding that high concentration of deep-level defects(recombination centers) exist in pure Cu2CdSnS4.

Figure 3. a) The transition energy levels of intrinsic point defects in the band gap of Cu2CdSnS4, and b) the band edge shift caused by the low-energy
defect complexes. The GGA/DFT band gap is corrected to the experimental value of 1.38 eV. The band edge shift is calculated assuming one defectcomplex in a 64-atom supercell.

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energy (0.20 eV/pair) of CuZn+ZnCu in
Cu2ZnSnS4,[15,19] the formation energy of
AgZn+ZnAg is high (0.52 eV/pair), and thatof 2AgZn+SnZn is even higher (above 3 eV,
so it is not shown in Figure 5). Other defectcomplexes including VAg+ZnAg, ZnSn+SnZn,
AgZn+Agi, VZn+SnZn, and 2VAg+SnZn haveformation energies in the range 0.6–1.4 eV,
showing that the existence of defect complexes is also possible in Ag2ZnSnS4, but
their concentration and the influence (trapping of carriers) are much smaller than thosein Cu2ZnSnS4.
The increase of AgZn formation energy
also changes the dominant defect inAg2ZnSnS4. As shown in Figure 5, theacceptor AgZn has the lowest formationenergy among all the acceptor and donor
defects only near the chemical potential
Figure 4. The calculated formation energy change as a function of the Fermi level for possible point M, while the donor defects VS, SnZn,
acceptor and donor defects in Ag2ZnSnS4. Two chemical potential points in Figure S1 (Sup- and ZnAg become the dominant defects at
porting Information) a) M and b) P are considered. The slope shows the charge state of ionized other chemical potential points. This candefects (following Equation (1)), e.g., positive slope means ionized donor while negative slope be seen more clearly in Figure 4, where themeans ionized acceptor defects. The GGA/DFT band gap is corrected to the experimental
formation energy change of the neutral andvalue of 2.01 eV.
ionized defects as a function of the Fermi
level is plotted. At the chemical potential
point M (Zn-poor, S-rich), the acceptor AgZn has a formation
2.2. Defect Disparity between Ag-Based Ag2ZnSnS4
and Cu-Based Cu2ZnSnS4
energy slightly lower than those of the donors SnZn, VS, andZnAg when they are charged neutral. When they are ionized,
Unlike Cu2CdSnS4, we find the defect behavior of Ag2ZnSnS4
their competition will determine the Fermi level of the samples
at around 1.0 eV, just in the middle of the band gap. Due tois remarkably different from that of Cu2ZnSnS4. As shown inthe compensation of the acceptor and donor defects, the carrier
Figure 4, the formation energy of AgZn antisite increases toconcentration of the samples will be low and thus the electricalabove 1.5 eV, much higher than that of CuZn in Cu2ZnSnS4 andconductivity will be very poor. At the chemical potential point P
CuCd in Cu2CdSnS4, in accordance with our expectation that the(Zn-rich, Sn-rich, and S-poor), the donor defects have lower forlarge difference between Ag and Zn may increase the formamation energy than the acceptor ones, so the sample will showtion energy of their antisite. When the chemical potentials of
n-type conductivity. However, the formation of the acceptor
the elements are zero ( μ Ag = μZn = 0), the formation energy ofAgZn becomes spontaneous and compensates the electron carAgZn is even larger, 3.10 eV, as shown in Table 1. Due to thecompetition from ZnS, the Zn chemical potential is limited
riers as the Fermi level approaches the conduction band (highly
to lower than −1.3 eV (shown in Figure S1 of the Supportingn-type), which limits the concentration of electron carriers.
Information), which decreases the AgZn formation energy by
According to Figure 4b, we estimate that the Fermi level of theundoped Ag2ZnSnS4 samples is located at 0.8 eV below the
1.3 eV. Comparing the formation energy of AgZn in Ag2ZnSnS4,
CuZn in Cu2ZnSnS4, and CuCd in Cu2CdSnS4 when the chemCBM (the cross point of ZnAg and AgZn lines) under equilibical potentials are zero (see Table 1), the value of AgZn isrium growth condition, so the conductivity is still poor despite
the n-type character. At other chemical potential points such as
much larger than that of CuZn (1.41 eV) and CuCd (1.28 eV).
A, the n-type conductivity increases slightly because the energy
This cannot be fully explained by the size mismatch because
difference between the neutral ZnAg and AgZn increases, but
the bond length difference between Ag S and Zn S is evensmaller than that between Cu S and Cd S, but the formation
the increase is not large.
Considering all of the representative chemical potenenergy of AgZn is much larger than that of CuCd. One possible
tial points, we can predict that the electrical conductivity ofreason is that it costs larger strain energy to replace one small
undoped Ag2ZnSnS4 is always poor, i.e., either intrinsic or
cation (Zn) by one large cation (Ag) than replace one large
cation (Cd) by one small cation (Cu), but this is not enough to
weakly n-type with low electron carrier concentration. This is
explain the large energy difference around 1.2 eV between AgZn
dramatically different from the situation in Cu2ZnSnS4 andand CuCd. Therefore, other factors should play an important
Cu2CdSnS4 where only p-type conductivity is possible and therole in the high formation energy of AgZn antisite, which will
n-type doping is impossible because of the spontaneous compensation of the acceptor defects (CuZn and CuCd antisites).
be discussed in Section 3.3.
Our prediction is in agreement with available experimental
Since the AgZn antisite has a high formation energy, theobservations that i) only n-type Ag2ZnSnS4 samples have beenformation of related defect complexes such as AgZn+ZnAg and
2AgZn+SnZn is also suppressed. Compared to the low formation
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conduction band, respectively. Therefore,
their contribution to the n-type conductivity
is small. Instead, their high concentration
facilitates the recombination of electron andhole, which imposes a serious limitation on
the application of Ag2ZnSnS4 as the photovoltaic and photocatalytic semiconductors.[71–73]

2.3. Influence of Band Edge Position on
Defect Formation
As discussed above, the most important feature in the defect properties of Cu- and Agbased I2–II–IV–VI4 semiconductors is that
the CuCd antisite related defects have low
formation energy thus high concentration in
Cu2CdSnS4, while the AgZn antisite related
defects have high formation energy thus low
concentration in Ag2ZnSnS4. This is in conFigure 5. The calculated formation energy change as a function of the elemental chemical trast to our earlier expectation that the large
potentials (growth conditions) for low-energy defects and defect complexes in Ag2ZnSnS4. The
size difference will suppress the formation ofchemical potential points P–Q–M–N–G are shown in Figure S1 (Supporting Information), andboth CuCd and AgZn, indicating that there areμ Ag = 0 , μZn = −1.30 eV, and μSn = −0.59 eV at the point A.
other factors influencing the formation of theantisite defects.
One possible factor is the energy of the valence and conwe know,[61,70] and ii) the highest electron concentration measduction bands. Figure 7a shows the calculated band alignment
ured so far is lower than 1014 cm−3 in Ag2ZnSnS4 samples.[61]of the Cu2CdSnS4, Cu2ZnSnS4, and Ag2ZnSnS4. The valenceThis situation may be changed if suitable extrinsic dopants canbe introduced. According to Figure 4, the formation energy ofband edge of Ag2ZnSnS4 is lower (by 0.74 eV) than those of
AgZn decreases to zero only when the Fermi level is close to
Cu2CdSnS4 and Cu2ZnSnS4. The low valence band edge posithe CBM (the Fermi level is almost not pinned by AgZn), sotion indicates that the binding energy of the valence electrons
is high, and thus it will cost more energy to create a hole in
the Fermi level can be shifted up to close to the CBM if high(take an electron away from) the system. Because the formaconcentration of extrinsic n-type dopants such as CdAg can betion of acceptor defects such as CuCd, CuZn, and AgZn creates
introduced to the Ag2ZnSnS4 samples, then a high concentration of electron carriers and good n-type conductivity could bea hole near the valence band edge, the low valence band edge
achieved.
of Ag2ZnSnS4 increases the formation energy of AgZn. The
In Figure 6, the calculated transition energy levels of defects
valence band edge positions of Cu2CdSnS4 and Cu2ZnSnS4 areare plotted. AgZn has an acceptor level at 0.2 eV above the VBM,
comparably high, so the formation energies of CuCd and CuZn
which is deeper than CuZn and CuCd. Among the low-energy
are both low, despite the fact that the size difference between
Cu and Cd is much larger than between Cu and Zn. The infludonor defects, ZnAg has a relatively shallow level, so it plays anence of the band edge position exists not only for the antisite
important role in determining the n-type conductivity. In condefects but also for other defects. For example, the Ag vacancy
trast, both VS and SnZn have deep donor levels. Their ε (0/2+)(VAg) in Ag2ZnSnS4 has a much higher formation energy thantransition levels are calculated at 0.88 and 0.51 eV below the

Figure 6. a) The transition energy levels of intrinsic point defects in the band gap of Ag2ZnSnS4 and b) the band edge shift caused by the low-energy
defect complexes. The GGA/DFT gap is corrected to the experimental value of 2.01 eV. The band edge shift is calculated assuming one defect complex
in a 64-atom supercell.

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Figure 7. a) Calculated band alignment between Cu2CdSnS4, Cu2ZnSnS4, Ag2ZnSnS4, CuInSe2, CuGaSe2 , and CdS; b,c) total and partial electronic
density of states (DOS) of Cu2CdSnS4 and Ag2ZnSnS4. The calculation methods are described in ref. [74]. The dashed line shows the Fermi energy(p)pinning level Epinfor p-type doping.

Cu vacancy (VCu) in Cu2CdSnS4 and Cu2ZnSnS4, as shown in
Figures 2 and 5.
It should be noted that the large formation energy of AgZn
is determined not only by the low valence band edge position.
This can be seen clearly in the large formation energy difference (around 1.4 eV, see Figure 5 and Figure 7 of Chen et al.[15])between AgZn in Ag2ZnSnS4 and CuZn in Cu2ZnSnS4, which ismuch larger than the difference of valence band edge positions(0.74 eV shown in Figure 7). Therefore, the larger formationenergy of AgZn is contributed not only by the lower valenceband but also by the larger strain energy cost (estimated to beabout 0.66 eV) caused by the larger size difference between
Ag and Zn than that between Cu and Zn. Since the formation energy of CuCd is just slightly (by about 0.2 eV) higher
than CuZn, and the difference is almost equal to the valenceband offset between Cu2CdSnS4 and Cu2ZnSnS4 (0.15 eV), thestrain energy cost in the formation of CuCd should be small
despite the large size difference between Cu and Cd. This canbe understood considering that it costs smaller strain energy
to replace one large cation (Cd) by one small cation (Cu) thanreplace one small cation (Zn) by one large cation (Ag). With thesame argument, we can understand why the formation energyof the donor antisite defect CdCu (large replaces small) is 0.6 eVlarger than that of ZnAg (small replaces large) although theirconduction band edge positions are comparable.
All the acceptor defects have high formation energies in
Ag2ZnSnS4 due to the low valence band edge position, so theintrinsic defects cannot give rise to p-type conductivity. Furthermore, even if we intentionally introduce extrinsic dopants,
the doping sites that produce acceptor levels will also havehigher formation energies than the sites producing donor
levels. Therefore, a p-type doping difficulty always exists forsemiconductors such as Ag2ZnSnS4. This is known as the(p)“doping limit rule.”[67,75] A p-type doping limit level E pin(shownby the green dashed line in Figure 7) was proposed in theprevious studies about the ternary chalcogenides CuGaSe2
and CuInSe2,[75–77] which have similar crystal and electronic

Adv. Funct. Mater. 2015, 25, 6733–6743

structure to Cu2CdSnS4, Cu2ZnSnS4, and Ag2ZnSnS4. Whenthe valence band edge is lower than this limit level, it is difficult to produce a high concentration of hole carriers and shift
the Fermi level to below this level, no matter through the formation of intrinsic acceptor defects or doping of extrinsic elements.[34] The valence band edge of Ag2ZnSnS4 is about 0.7 eVlower than this level, so the high formation energy and low
concentration of intrinsic acceptor defects (including AgZn)in Ag2ZnSnS4 are consistent with this doping limit rule. The
valence band edges of Cu2CdSnS4, Cu2ZnSnS4, CuGaSe2, andCuInSe2 are above or close to this level, so their Fermi levelcan be shifted to close to the valence band edge, i.e., high concentration of hole carriers (from ionized CuZn, CuCd, or VCu)
and good p-type conductivity can be achieved in these semiconductors, in good agreement with the previous experimental
observation.[21–25,63–65]
Since the band energy has direct influence on the defectformation, its control becomes important for tuning thedefect and electrical properties of the semiconductors. To control the band edge positions, we need to know the componentof the band edge states, which can be seen in the calculatedpartial and total density of states as shown in Figure 7. The
top part of the valence bands of Cu2CdSnS4 (Ag2ZnSnS4)
are composed of the hybridized states of the Cu 3d (Ag 4d)
and S 3p orbitals, while the contribution from Zn and Sn
orbitals is small, similar to the situation in Cu2ZnSnS4.[78,79]
One obvious difference is that the high Ag 4d peaks are 4 eV
below VBM, while the Cu 3d peaks are much higher, around
2 eV below the VBM. This results from the atomic energy
level difference of Ag 4d and Cu 3d orbitals (the Ag 4d atomic
levels are 2.3 eV lower than Cu 3d levels[5,85], so the hybridized
states of the Ag 4d orbitals are lower in the valence band. The
VBM consists of hybridized states of the Cu 3d (Ag 4d) andS 3p orbitals, so the lower Ag 4d atomic level also explains
the lower valence band edge position of Ag2ZnSnS4. Furthermore, the Ag S bond is longer than Cu S bond, so the p–dhybridization is weaker between Ag and S than between Cu© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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and S, which also contributes to the lower valence band edge
position of Ag2ZnSnS4.
According to this mechanism, the formation energies of theacceptor defects should also be high and thus the p-type doping
should be difficult in other Ag S or Ag Se compounds withsimilar valence band component (Ag 4d and S 3p or Se 4p
hybridized states). Interestingly, experiments showed that mostof the synthesized Ag2S, Ag2Se, AgInS2, AgInSe2, and Ag2ZnSnSe4 samples show intrinsic n-type conductivity and theirp-type doping is difficult,[81–90] in agreement with our prediction based on the atomic levels.

2.4. Strategy to Increase Voc of Kesterite Solar Cells
Due to the significantly increased formation energy of AgZnantisite, the Voc bottleneck of Cu2ZnSnS4 solar cells causedby the spontaneous formation of CuZn antisite defects at theinterface (as mentioned in Section 1 and also shown schematically in Figure 8) can be largely avoided if it is replaced
by Ag2ZnSnS4. However, since Ag2ZnSnS4 has poor electricalconductivity and defect levels are relatively deep, the solar cell
performance should be limited if pure Ag2ZnSnS4 is used as
the absorber layer.
Thus, one possible strategy to increase Voc of Cu2ZnSnS4
solar cells is to form (Cu1–xAgx)2ZnSnS4 alloys, in which theantisite acceptor defects are expected to have higher formation energy, so a large band bending can be achieved nearthe (Cu1–xAgx)2ZnSnS4/CdS junction interface, and thus theVoc can be increased. There exists an optimal value for the Ag

Figure 8. Schematic plot of the p–n junction interface between the n-type
CdS buffer layer and p-type absorber layer: Cu2ZnSn(S,Se)4 with high concentration of CuZn antisite defects limiting Voc (top) and compositiongraded (Cu1–xAgx)2ZnSn(S,Se)4 free of Voc-limiting defects (bottom). Notethat CuZn is everywhere inside the Cu2ZnSn(S,Se)4 absorber layer, however, its concentration is extremely high near the p–n junction interface
because the Fermi level shifts up to a higher level (as shown in Figure 1a)and thus the formation energy of CuZn decreases to a small value. Whena high composition of Ag is alloyed into (Cu1–xAgx)2ZnSn(S,Se)4 near theinterface, the formation of CuZn is suppressed.

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composition parameter x because too high Ag composition cani) reduce the good p-type conductivity in the absorber region too
much and even change it to n-type, ii) create more recombination center defects, and because iii) the band gap increases
from the optimal value 1.5 eV to a larger one (2.01 eV whenx = 1), causing the efficiency drop.
Since high efficiency of the kesterite solar cells was usuallybased on the Cu2ZnSnSe4[8,91] or Cu2ZnSn(S,Se)4[9] alloys withhigh Se composition, we may apply the similar strategy to them,forming (Cu1–xAgx)2ZnSnSe4 and (Cu1–xAgx)2ZnSn(S,Se)4
alloys. According to the discussion in Section 3.3, the antisite
acceptor defects also have high formation energies in the selenides, so the Voc can be increased too. Furthermore, Cu2ZnSnSe4 has a small band gap of 1.0 eV while Ag2ZnSnSe4 has alarger gap, so the alloying will increase the band gap to closer
to the optimal value, which makes the efficiency improvement
more obvious in the alloys of the selenides than in the alloys ofthe sulfides.
Besides forming composition-uniform alloys, an even better
choice to improve the Voc and efficiency would be forming composition-graded (Cu1–xAgx)2ZnSn(S,Se)4 alloys as the absorberlayer with low Ag concentration in the back and higher Ag concentration in the region close to the (Cu1–xAgx)2ZnSn(S,Se)4/
CdS junction interface, as shown in Figure 8. This is because
in the interior of the absorber layer good p-type conductivity
and less recombination-center defects are needed, which canbe achieved by pure Cu2ZnSn(S,Se)4 or (Cu1–xAgx)2ZnSn(S,Se)4
alloy with low Ag concentration; however, close to absorber/buffer layer interface, suppressing the formation of CuZnantisites is needed to make a p-to-n type inversion possible near
the interface and thus to improve Voc, which can be achieved byadding more and more Ag to the region when it is more andmore close to the junction. In this way the negative effect of
the Ag alloying is avoided, and meanwhile the type inversion
becomes possible near the interface, which should improve the
Voc and the efficiency significantly, as shown in Figure 1. Moreover, there are two extra advantages: i) the higher band gap near
the front can improve the light absorption and ii) the type-IIband alignment between Cu2ZnSn(S,Se)4 and Ag2ZnSn(S,Se)4(shown in Figure 7a for sulfides, where the CBM of Ag2ZnSnS4
is slightly lower than that of Cu2ZnSnS4, and the VBM of
Ag2ZnSnS4 is significantly lower than that of Cu2ZnSnS4)
makes both the valence and conduction bands have a downward slope from the back contact to the p–n junction interface, which can facilitate the electron-hole separation and thus
reduce carrier recombination in this system. Therefore, a solar
cell with composition-graded (Cu1–xAgx)2ZnSn(S,Se)4 alloy as
the absorber layer should have great potential to improve the
Voc and efficiency.
With this composition-graded (Cu1–xAgx)2ZnSn(S,Se)4 alloy
as the absorber layer, it is not necessary to dope the nearinterface region with high Ag composition to highly n-type
or form a buried p–n junction inside the absorber layer
between the regions with high Cu composition (p-type) andhigh Ag composition (n-type). If the near-interface region is
intrinsic or weakly n-type (with the Fermi level near the middleof band gap), a p–n junction will be formed between the(Cu1–xAgx)2ZnSn(S,Se)4 absorber layer and n-type CdS, and alarge band bending will be produced inside the absorber layer© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Adv. Funct. Mater. 2015, 25, 6733–6743

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3. Conclusions
We show that the valence band edge energy has important
influence on the formation of the acceptor defects including the
III antisites in the Cu- and Ag-based I2–II–IV–VI4 quaternary
semiconductors. Since the valence band edges of Cu2ZnSnS4
and Cu2CdSnS4 are high, the CuZn and CuCd antisites and therelated defect complexes have high equilibrium concentrations,contributing to the high intrinsic p-type conductivity but also to
the limited Voc of the solar cells based on these systems, as havebeen experimentally observed. Since the valence band edge aswell as the conduction band edge of Ag2ZnSnS4 are much lower
than those of Cu2ZnSnS4, the formation energy of the acceptor
defect AgZn becomes higher than those of three donor defects(ZnAg, SnZn, and VS), which makes Ag2ZnSnS4 n-type althoughwith low electron carrier concentration. Similar disparity in thedefect properties and electrical conductivity are expected to exist
also in other Cu- and Ag-based quaternary, ternary, and binary
chalcogenide semiconductors, which are supported by the available experiments. Our study reveals an important disparity
between the defect properties of Cu- and Ag-based I2–II–IV–VI4
semiconductors. Based on this disparity, we propose a strategy
to overcome the Voc bottleneck and increase the efficiency of
the kesterite solar cells through forming a composition-graded(Cu1–xAgx)2ZnSn(S,Se)4 alloy absorber.

4. Experimental Section
To predict what kinds of defects are dominant in Cu2CdSnS4 andAg2ZnSnS4, we calculated the formation energy ΔH f of a series ofpossible point defects
ΔH f (α , q) = E (α , q ) − E(host) + ∑ ni (E i + μ i )+ q[ε VBM(host) + E F ](1)

where α represents the defect and q is its charge state. As Equation (1)shows, ΔH f is a function of the element chemical potential E i + μ i(describing the richness or partial pressure of elements in the synthesis
atmosphere), and also a function of the Fermi level ε VBM(host) + E F
when it is charged (q is not zero). In the element chemical potential
E i + μ i , E i is the reference and set to the total energy of the pure phaseof the element i, e.g., face-centered-cubic Cu and Ag, hexagonal-closepacked Cd crystals, α-Sn, and α-S (S8). μ i = 0 represents the limit
where the element is so rich that the pure elemental phase will start toform. Since the quaternary semiconductor can be synthesized only in acertain atmosphere, μ i of the component elements is limited in a range,
which are given in Figure S1 (Supporting Information). The Fermi levelis referenced to the energy level of valence band maximum (VBM) of thehost ε VBM(host) , so E F = 0 means that the Fermi level is at the VBM

Adv. Funct. Mater. 2015, 25, 6733–6743

level, and E F = Eg means that the Fermi level is at the conduction band
minimum (CBM).
The formation energy of point defects can be calculated using a
supercell model in which one defect α is placed at the center of thesupercell.[92] E(host) is the total energy of the host supercell free of
defects, and E(α , q) is that of the defect-containing supercell. ni is thenumber of atoms removed from the supercell to the external reservoir
when the defect is formed, e.g., ni = +1 (−1) if one atom is removed
from (added to) the supercell. For a defect α , when its formationenergy for two different charge states q1 and q2 are equal at a certain
Fermi level, we define that Fermi level as its transition energy level ε(α , q1/ q2 ). Therefore the transition energy levels can be derived when
the formation energies of defects with different charge states arecalculated. More details about the defect calculation models are given
in refs. [14,15].
The total energy and electronic eigenvalues in Equation (1) arecalculated using density function theory methods as implemented inthe Vienna Ab-initio Simulation Package (VASP).[93] The generalized
gradient approximation (GGA) to the exchange correlation functionalis used as formulated by Perdew–Burke–Ernzerhof (PBE).[94] The GGA
calculations usually overestimate the VBM level and underestimate
the CBM level (thus underestimate the band gap), which causes thecalculated formation energies of the acceptor and donor defect also
underestimated, so a band edge correction is needed, as discussed
in detail by Lany and Zunger.[95] In the current study, both the VBM
overestimation and the CBM underestimation (ΔVBM = 0.50 eV,
ΔCBM = 0.88 eV for Cu2CdSnS4, and ΔVBM = 1.17 eV, ΔCBM = 0.40 eV for
Ag2ZnSnS4, determined according to the PBE+U and G0W0 calculations)are corrected through adding ΔVBM (ΔCBM) to the calculated formationenergy of acceptor (donor) defects, following the same procedure asthat used in the study of CuGaSe2 and CuInSe2.[34] After the correction,
the calculated formation energies[15] are consistent with those fromthe hybrid functional calculations[16] for the Cu2ZnSnS4 defects. The
formation energies of the dominant acceptor and donor defects (CuCdand CdCu in Cu2CdSnS4, and AgZn and ZnAg in Ag2ZnSnS4) which
determine the p-type or n-type conductivity are also calculated using the
hybrid functional (HSE06). As shown in the supporting information, theresults are close to those from the PBE calculation (after the band edge
correction), so the conclusion of our current study is not influenced by
the specific functionals that we used. For defects with deep levels (VSn,CuSn, SnCd, SnCu, VS, Cdi, AgSn, SnAg, SnZn), the GGA calculation tends
to predict shallower transition energy levels, so we adapted a simple
correction scheme through adding the dispersion difference between
valence (conduction) band and acceptor (donor) defect band, which
was found to give results more consistent with those from the hybrid
functional calculations for deep level defects in Cu2ZnSnS4.[15,16]
The projector augmented-wave pseudopotentials[96] and an energy
cutoff of 300 eV were used in all cases. A 2 × 2 × 2 k-point mesh isused for the Brillouin zone integration of the 64-atom supercell. Test
calculations showed that the results are well converged, i.e., the error
is less than 0.03 eV with respect to the energy cutoff and the k-pointmesh (test results with energy cutoff up to 500 eV and k-point mesh
up to 4 × 4 × 4 are shown in the Supporting Information) and theerror is 0.1 eV with respect to the supercell size according to both test
calculations by us with supercells as large as 512 atoms and by Han
et al with supercells as large as 1728 atoms.[16] It should be noted thatno correction is performed for the Coulomb interaction error of charged
defects, so a larger error (0.1–0.2 eV) is possible for multivalent point
defects, which is tolerable for the qualitative analysis in the present
study.

FULL PAPER(with the Fermi level shifted up to close to CBM in the nearinterface region, as shown in Figure 1c), so a large Voc can stillbe achieved.
Since Ag is an expensive element, we should point out
that there may be other elements that can also be alloyed into
Cu2ZnSn(S,Se)4 and have similar function to the compositiongraded (Cu1–xAgx)2ZnSn(S,Se)4 alloy, then the cost can be
reduced. Our current study may inspire the further theoreticaland experimental study to find alternative cheap elements to
replace Ag.

Acknowledgements
The work at Fudan was supported by the Special Funds for Major
State Basic Research, National Natural Science Foundation of China(NSFC), International collaboration project, Program for Professor ofSpecial Appointment (Eastern Scholar), and Fok Ying Tung Education© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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Foundation. S.C. is supported by NSFC under Grant No. 91233121
and Shanghai Rising-Star Program (14QA1401500). The work at Bathis supported by the Royal Society and the EPSRC (Grant nos. EP/
K016288/1 and EP/L017792/1). The work at NREL was funded by the U.S.
Department of Energy (DOE), under Contract No. DE-AC36-08GO28308.
Received: June 3, 2015
Revised: August 30, 2015
Published online: October 19, 2015

[1] M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, Prog.
Photovoltaics 2015, 23, 1.
[2] C. Wang, S. Chen, J.-H. Yang, L. Lang, H.-J. Xiang, X.-G. Gong,
A. Walsh, S.-H. Wei, Chem. Mater. 2014, 26, 3411.
[3] C. H. L. Goodman, J. Phys. Chem. Solids 1958, 6, 305.
[4] F.-J. Fan, L. Wu, S.-H. Yu, Energy Environ. Sci. 2014, 7, 190.
[5] S. Chen, X. Gong, A. Walsh, S.-H. Wei, Phys. Rev. B 2009, 79,
165211.
[6] G. M. Ford, Q. Guo, R. Agrawal, H. W. Hillhouse, Chem. Mater.
2011, 23, 2626.
[7] S. Levcenco, D. Dumcenco, Y. Huang, E. Arushanov, V. Tezlevan,
K. Tiong, C. Du, J. Appl. Phys. 2010, 108, 073508.
[8] I. Repins, C. Beall, N. Vora, C. DeHart, D. Kuciauskas, P. Dippo,
B. To, J. Mann, W.-C. Hsu, A. Goodrich, R. Noufi, Sol. Energy Mater.
Sol. Cells 2012, 101, 154.
[9] W. Wang, M. T. Winkler, O. Gunawan, T. Gokmen, T. K. Todorov,Y. Zhu, D. B. Mitzi, Adv. Energy Mater. 2014, 4, 1301465.
[10] F. Liu, K. Sun, W. Li, C. Yan, H. Cui, L. Jiang, X. Hao, M. A. Green,Appl. Phys. Lett. 2014, 104, 051105.
[11] H. Katagiri, K. Saitoh, T. Washio, H. Shinohara, T. Kurumadani,
S. Miyajima, Sol. Energy Mater. Sol. Cells 2001, 65, 141.
[12] B. Shin, Y. Zhu, N. A. Bojarczuk, S. J. Chey, S. Guha, Appl. Phys. Lett.
2012, 101, 053903.
[13] H. Zhou, W.-C. Hsu, H.-S. Duan, B. Bob, W. Yang, T.-B. Song,
C.-J. Hsu, Y. Yang, Energy Environ. Sci. 2013, 6, 2822.
[14] S. Chen, J.-H. Yang, X. Gong, A. Walsh, S.-H. Wei, Phys. Rev. B 2010,
81, 245204.
[15] S. Chen, A. Walsh, X.-G. Gong, S.-H. Wei, Adv. Mater. 2013, 25,
1522.
[16] D. Han, Y. Y. Sun, J. Bang, Y. Y. Zhang, H. B. Sun, X. B. Li,
S. B. Zhang, Phys. Rev. B 2013, 87, 155206.
[17] K. Biswas, S. Lany, A. Zunger, Appl. Phys. Lett. 2010, 96, 201902.
[18] M. Grossberg, J. Krustok, J. Raudoja, T. Raadik, Appl. Phys. Lett.
2012, 101, 102102.
[19] S. Chen, X. Gong, A. Walsh, S.-H. Wei, Appl. Phys. Lett. 2010, 96,021902.
[20] S. Levcenko, V. E. Tezlevan, E. Arushanov, S. Schorr, T. Unold, Phys.
Rev. B 2012, 86, 045206.
[21] N. Nakayama, K. Ito, Appl. Surf. Sci. 1996, 92, 171.
[22] J. J. Scragg, P. J. Dale, L. M. Peter, G. Zoppi, I. Forbes, Phys. Status
Solidi B 2008, 245, 1772.
[23] K. Ramasamy, M. A. Malik, P. O’Brien, Chem. Commun. 2012, 48, 5703.
[24] M. Suryawanshi, G. Agawane, S. Bhosale, S. Shin, P. Patil, J. Kim,
A. Moholkar, Mater. Sci. Technol. 2013, 28, 98.
[25] A. Moholkar, S. Shinde, G. Agawane, S. Jo, K. Rajpure, P. Patil,
C. Bhosale, J. Kim, J. Alloys Compd. 2012, 544, 145.
[26] M. Bär, B.-A. Schubert, B. Marsen, R. G. Wilks, S. Pookpanratana,
M. Blum, S. Krause, T. Unold, W. Yang, L. Weinhardt, C. Heske,
H.-W. Schock, Appl. Phys. Lett. 2011, 99, 222105.
[27] P. Würfel, in Physics of Solar Cells, Wiley-VCH, Weinheim, Germany
2007, Ch. 6.
[28] A. Chirilǎ, S. Buecheler, F. Pianezzi, P. Bloesch, C. Gretener,
A. R. Uhl, C. Fella, L. Kranz, J. Perrenoud, S. Seyrling, R. Verma,

6742

wileyonlinelibrary.com

S. Nishiwaki, Y. E. Romanyuk, G. Bilger, A. N. Tiwari, Nat. Mater.
2011, 10, 857.
[29] U. Rau, H. W. Schock, Appl. Phys. A 1999, 69, 131.
[30] J. Kim, H. Hiroi, T. K. Todorov, O. Gunawan, M. Kuwahara,
T. Gokmen, D. Nair, M. Hopstaken, B. Shin, Y. S. Lee, W. Wang,
H. Sugimoto, D. B. Mitzi, Adv. Mater. 2014, 26, 7427.
[31] M. Graetzel, R. A. J. Janssen, D. B. Mitzi, E. H. Sargent, Nature
2012, 488, 304.
[32] R. Klenk, Thin Solid Films 2001, 387, 135.
[33] D. Liao, A. Rockett, J. Appl. Phys. 2003, 93, 9380.
[34] C. Persson, Y. J. Zhao, S. Lany, A. Zunger, Phys. Rev. B 2005, 72,
035211.
[35] F. Pianezzi, P. Reinhard, A. Chirila, B. Bissig, S. Nishiwaki,
S. Buecheler, A. N. Tiwari, Phys. Chem. Chem. Phys. 2014, 16, 8843.
[36] J. P. Leitão, N. M. Santos, P. A. Fernandes, P. M. P. Salomé,A. F. da Cunha, J. C. González, G. M. Ribeiro, F. M. Matinaga, Phys.
Rev. B 2011, 84, 024120.
[37] T. Gokmen, O. Gunawan, T. K. Todorov, D. B. Mitzi, Appl. Phys. Lett.
2013, 103, 103506.
[38] T. Gershon, B. Shin, N. Bojarczuk, T. Gokmen, S. Lu, S. Guha,
J. Appl. Phys. 2013, 114, 154905.
[39] M. J. Romero, H. Du, G. Teeter, Y. Yan, M. M. Al-Jassim, Phys. Rev.
B 2011, 84, 165324.
[40] M. Grossberg, J. Krustok, J. Raudoja, K. Timmo, M. Altosaar,
T. Raadik, Thin Solid Films 2011, 519, 7403.
[41] B. G. Mendis, M. D. Shannon, M. C. J. Goodman, J. D. Major,
A. A. Taylor, D. P. Halliday, K. Durose, J. Phys.: Conf. Ser. 2013, 471,
012014.
[42] J. P. Teixeira, R. A. Sousa, M. G. Sousa, A. F. da Cunha,
P. A. Fernandes, P. M. P. Salomé, J. C. González, J. P. Leitão, Appl.
Phys. Lett. 2014, 105, 163901.
[43] L. Yin, G. Cheng, Y. Feng, Z. Li, C. Yang, X. Xiao, RSC Adv. 2015, 5,40369.
[44] M. E. Erkan, V. Chawla, I. Repins, M. A. Scarpulla, Sol. Energy Mater.
Sol. Cells 2015, 136, 78.
[45] T. Gershon, Y. S. Lee, R. Mankad, O. Gunawan, T. Gokmen,
D. Bishop, B. McCandless, S. Guha, Appl. Phys. Lett. 2015, 106,
123905.
[46] O. Gunawan, T. Gokmen, B. S. Shin, S. Guha, in 38th IEEE Photovoltaic Specialists Conf., IEEE, Austin, TX, USA 2012, 003001.
[47] S. M. Pawar, B. S. Pawar, K. V. Gurav, D. W. Bae, S. H. Kwon,
S. S. Kolekar, J. H. Kim, Jpn. J. Appl. Phys. 2012, 51, 10NC27.
[48] H. Katagiri, K. Jimbo, W. S. Maw, K. Oishi, M. Yamazaki, H. Araki,
A. Takeuchi, Thin Solid Films 2009, 517, 2455.
[49] T. K. Todorov, K. B. Reuter, D. B. Mitzi, Adv. Mater. 2010, 22, E156.
[50] K. Wang, O. Gunawan, T. Todorov, B. Shin, S. J. Chey,
N. A. Bojarczuk, D. Mitzi, S. Guha, Appl. Phys. Lett. 2010, 97,
143508.
[51] B. Shin, O. Gunawan, Y. Zhu, N. A. Bojarczuk, S. J. Chey, S. Guha,
Prog. Photovoltaics 2013, 21, 72.
[52] A. D. Collord, H. W. Hillhouse, Chem. Mater. 2015, 27, 1855.
[53] W. Li, J. Chen, C. Yan, X. Hao, J. Alloys Compd. 2015, 632, 178.
[54] T. Washio, H. Nozaki, T. Fukano, T. Motohiro, K. Jimbo, H. Katagiri,
J. Appl. Phys. 2011, 110, 074511.
[55] M. Courel, O. Vigil-Galán, D. Jiménez-Olarte, M. Espíndola-Rodríguez,
E. Saucedo, J. Appl. Phys. 2014, 116, 134503.
[56] Y. Zhao, W. Tao, J. Liu, A. Wei, Mater. Lett. 2015, 148, 63.
[57] C. J. Hages, N. J. Carter, R. Agrawal, T. Unold, J. Appl. Phys. 2014,
115, 234504.
[58] B. G. Mendis, M. C. Goodman, J. D. Major, A. A. Taylor, K. Durose,
D. P. Halliday, J. Appl. Phys. 2012, 112, 124508.
[59] J. J. Scragg, T. Ericson, T. Kubart, M. Edoff, C. Platzer-Björkman,
Chem. Mater. 2011, 23, 4625.
[60] P. Bras, J. Sterner, C. Platzer-Björkman, Thin Solid Films 2015, 582,
233.

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Adv. Funct. Mater. 2015, 25, 6733–6743

www.afm-journal.de
www.MaterialsViews.com

Adv. Funct. Mater. 2015, 25, 6733–6743[78] S. Chen, X. Gong, A. Walsh, S.-H. Wei, Appl. Phys. Lett. 2009, 94,
041903.
[79] J. Paier, R. Asahi, A. Nagoya, G. Kresse, Phys. Rev. B 2009, 79,115126.
[80] J. Jaffe, A. Zunger, Phys. Rev. B 1983, 28, 5822.
[81] J. Jang, K. Cho, S. H. Lee, S. Kim, Mater. Lett. 2008, 62, 1438.
[82] B. Tell, J. Shay, H. Kasper, J. Appl. Phys. 1972, 43, 2469.
[83] P. P. Ramesh, O. M. Hussain, S. Uthanna, B. S. Naidu, P. J. Reddy,
Mater. Lett. 1998, 34, 217.
[84] H. P. Geserich, W. Suppanz, Phys. Status Solidi B 1969, 35, 381.
[85] S. S. Dhumure, C. D. Lokhande, Thin Solid Films 1994, 240, 1.
[86] Y. Ueno, Y. Hattori, M. Ito, T. Sugiura, H. Minoura, Sol. Energy
Mater. Sol. Cells 1992, 26, 229.
[87] H. M. Pathan, P. V. Salunkhe, B. R. Sankapal, C. D. Lokhande,
Mater. Chem. Phys. 2001, 72, 105.
[88] K. Hattori, K. Akamatsu, N. Kamegashira, J. Appl. Phys. 1992, 71,3414.
[89] M. Ferhat, J. Nagao, J. Appl. Phys. 2000, 88, 813.
[90] K. Wei, G. S. Nolas, ACS Appl. Mater. Interfaces 2015, 7, 9752.
[91] Y. S. Lee, T. Gershon, O. Gunawan, T. K. Todorov, T. Gokmen,
Y. Virgus, S. Guha, Adv. Energy Mater. 2015, 5, 1401372.
[92] S.-H. Wei, Comput. Mater. Sci. 2004, 30, 337.
[93] G. Kresse, J. Furthmuller, Phys. Rev. B 1996, 54, 11169.
[94] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77,3865.
[95] S. Lany, A. Zunger, Phys. Rev. B 2008, 78, 235104.
[96] G. Kresse, D. Joubert, Phys. Rev. B 1999, 59, 1758.

© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

wileyonlinelibrary.com

FULL PAPER[61] L. Y. Yeh, K. W. Cheng, Thin Solid Films 2014, 558, 289.
[62] T. Sasamura, T. Osaki, T. Kameyama, T. Shibayama, A. Kudo,
S. Kuwabata, T. Torimoto, Chem. Lett. 2012, 41, 1009.
[63] K. Ito, T. Nakazawa, Jpn. J. Appl. Phys., Part 1 1988, 27, 2094.
[64] W. G. Zhao, G. Wang, Q. W. Tian, L. J. Huang, S. Gao, D. C. Pan,
Sol. Energy Mater. Sol. Cells 2015, 133, 15.
[65] S. Wagner, P. M. Bridenbaugh, J. Cryst. Growth 1977, 39, 151.
[66] Z. Su, J. M. R. Tan, X. Li, X. Zeng, S. K. Batabyal, L. H. Wong, Adv.
Energy Mater. 2015, DOI: 10.1002/aenm.201500682.
[67] S. B. Zhang, S.-H. Wei, A. Zunger, H. Katayama-Yoshida, Phys. Rev.
B 1998, 57, 9642.
[68] J. Pohl, K. Albe, Phys. Rev. B 2013, 87, 245203.
[69] K. Timmo, M. Kauk-Kuusik, M. Altosaar, J. Raudoja, M. Pilvet,
T. Raadik, T. Varema, I. Leinemann, in Proc. 28th European Photovoltaic Solar Energy Conf. and Exhibition (Eds: A. Mine, A. Jager-Waldau,
P. Helm), EU PVSEC, Paris, France 2013, 2385.
[70] I. Tsuji, Y. Shimodaira, H. Kato, H. Kobayashi, A. Kudo, Chem.
Mater. 2010, 22, 1402.
[71] K. Li, B. Chai, T. Y. Peng, J. Mao, L. Zan, RSC Adv. 2013, 3, 253.
[72] K. Zhang, L. Guo, Catal. Sci. Technol. 2013, 3, 1672.
[73] K. Iwashina, A. Iwase, Y. H. Ng, R. Amal, A. Kudo, J. Am. Chem. Soc.
2014, 137, 604.
[74] S.-H. Wei, A. Zunger, J. Appl. Phys. 1995, 78, 3846.
[75] Y. Yan, S.-H. Wei, Phys. Status Solidi B 2008, 245, 641.
[76] S. B. Zhang, S.-H. Wei, A. Zunger, J. Appl. Phys. 1998, 83, 3192.
[77] Y. F. Yan, J. B. Li, S.-H. Wei, M. M. Al-Jassim, Phys. Rev. Lett. 2007,
98, 135506.

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