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PHYSICAL REVIEW B 85, 085203 (2012)
First-principles studies of the electronic properties of native
and substitutional anionicdefects in bulk iron pyrite
Jun Hu,1 Yanning Zhang,1 Matt Law,2 and Ruqian Wu1,*1Department
of Physics and Astronomy, University of California, Irvine,
California 92697-4575, USA
2Department of Chemistry and Department of Chemical Engineering
and Materials Science, University of California,Irvine, California
92697, USA
(Received 28 October 2011; revised manuscript received 22
December 2011; published 13 February 2012)
Systematic spin-polarized density functional theory calculations
were performed to investigate the formationenergies of native and
substitutional anionic point defects in iron pyrite (FeS2) and
their impact on bulk electronicstructure. A detailed analysis
indicates that neutral sulfur and iron vacancies do not act as
efficient donors oracceptors. We find that substitutional oxygen
does not induce gap states in pyrite and can actually passivate
gapstates created by sulfur vacancies. Most Group V and VII
impurities create mid-gap states and produce spinpolarization. In
particular, Cl and Br are shallow donors that introduce delocalized
spin-polarized electrons forpotential use in photovoltaic and
spintronics applications.
DOI: 10.1103/PhysRevB.85.085203 PACS number(s): 71.55.−i,
72.40.+w, 61.72.Bb, 75.50.Pp
I. INTRODUCTION
The development of highly photoactive earth-abundantmaterials is
critically urgent for both fundamental scienceand technological
applications.1,2 Iron pyrite (FeS2) is apromising photovoltaic
material because of its suitable bandgap (Eg = 0.95 eV), strong
light absorption (α > 105 cm−1for hν > 1.4 eV), long minority
carrier diffusion length (100–1000 nm), and essentially infinite
elemental abundance.3–8
Pyrite photoelectrochemical and solid-state Schottky solarcells
have shown large short-circuit current densities (30–42mA cm−2) and
quantum efficiencies as high as 90%.9,10The main obstacle for the
development of pyrite is its lowopen-circuit photovoltage (VOC),
which is typically only 0.3 eV), suchthat these native defects are
incapable of providing significantfree carrier densities in pyrite.
Oxygen substitution on sulfursites (OS) has a relatively small
formation energy in oxidizingconditions but does not induce gap
states in bulk pyrite, makingOS useful for passivating gap states
induced by sulfur vacanciesproduced in sulfur-lean growth or
annealing environments.Group V and VII dopants produce spin
polarization in pyritewith a magnetic moment of 1.0 μB per impurity
atom. Whilemost of the Group V and VII dopants induce only deep
defectlevels, ClS and BrS produce shallow donor or resonance
levelsthat may be useful for photovoltaic and spintronic
applications.
085203-11098-0121/2012/85(8)/085203(10) ©2012 American Physical
Society
http://dx.doi.org/10.1103/PhysRevB.85.085203
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JUN HU, YANNING ZHANG, MATT LAW, AND RUQIAN WU PHYSICAL REVIEW B
85, 085203 (2012)
u
R Γ X M R
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-2
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2
4
Ene
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-6 -4 -2 0 2 40
25
50GGA+UGGAHSE06
Energy (eV)
Den
sity
of
Sta
tes
(a) (b)
(c)
a
FIG. 1. (Color online) (a) The bulk unit cell of pyrite
FeS2.Violet (dark) and yellow (light) gray spheres represent Fe
andS atoms, respectively. The parameters a and u denote the
latticeconstant and the distance between the S atom and the walls
of thecubic box as indicated by the red arrows. (b) Band structure
and(c) density of states (in states/eV·cell) of perfect pyrite. The
valenceband maximum (VBM) has been set as reference energy. The
red/darkgray curves in (b) indicate the topmost valence band and
lowestconduction band, and the horizontal green dashed lines
indicate theVBM and conduction band minimum (CBM).
II. METHODS AND COMPUTATIONAL DETAILS
Spin-polarized density functional calculations were carriedout
with the Vienna ab initio simulation package (VASP)35,36
at the level of the generalized gradient approximation
(GGA)using the Perdew-Burke-Ernzerhof (PBE) functional.37 Weused
the projector augmented wave (PAW) method for thedescription of the
core-valence interaction.38,39 The energycutoff for the basis
expansion was set to 350 eV. As sketchedin Fig. 1(a), the pyrite
FeS2 structure belongs to the Pa3̄ spacegroup40 and adopts a
NaCl-like structure, with a face-centeredcubic sublattice of
diamagnetic Fe2+ ions and 〈111〉-orientedS-S dimers occupying the
anion positions. Each Fe ion has anoctahedral coordination to six S
ions, and each S ion has threeFe neighbors and one S neighbor. The
unit cell of the pyritestructure can be specified by two lattice
parameters: the latticeconstant a and the internal coordinate of S
from the face ofthe unit cell u, as indicated in Fig. 1(a). To
model individualpoint defects in pyrite, we used both 2 × 2 × 2
supercells with
96 atoms and 3 × 3 × 3 supercells with 324 atoms. A 7×7×7k-grid
mesh was used to sample the Brillouin zone.41 All atomswere fully
relaxed until the calculated force on each atom wassmaller than
0.01 eV/Å.
III. RESULTS AND DISCUSSION
A. Structural and electronic properties of bulk iron pyrite
As a benchmark test for our approach and parameterization,we
first investigate the structural and electronic properties
ofperfect bulk pyrite. Regular GGA-PBE calculations
usuallyunderestimate the lattice constant and band gap of
pyritecrystals; some previous calculations even predicted a
metallicrather than a semiconducting state for bulk pyrite.42,43
Moresophisticated schemes such as the hybridized
exchange-correlation functional (HSE06)44 or Hubbard U
correction45
are therefore needed for reliable studies of pyrite systems.
Inthis work we examined both HSE06 and GGA+U schemesand found that
the latter, with U = 2 eV for Fe d-orbitals,is more appropriate for
the correct description of electronicproperties of bulk pyrite.
Our GGA+U calculations yield a nonmagnetic ground statefor the
bulk pyrite crystal, in agreement with experiment46 andprevious
density functional theory (DFT) calculations.19,47,48
As listed in Table I, the optimized lattice parameters, a =5.422
Å and u = 0.385, are very close to the experimentalvalues, a =
5.418 Å and u = 0.385.49,50 An indirect band gapof 1.02 eV was
obtained for bulk pyrite, as shown in Figs. 1(b)and 1(c). Similar
results were reported recently by Sun et al.(a = 5.424 Å and Eg =
1.03 eV).47 Experimental estimatesof the pyrite band gap vary from
0.73 to 1.2 eV, with∼0.95 eV the most widely accepted value.3,51–56
From curvesof density of states (DOS) in Fig. 1(c), one can see
that regularGGA calculation underestimates the band gap by 0.52
eV,whereas the HSE06 calculation overestimates the gap by1.67 eV
relative to the GGA+U result. This situation wasalso reported in
the previous literature.19,47 The band structurein Fig. 1(b) shows
that the valence band maximum (VBM)is close to the X-point and the
conduction band minimum(CBM) is at the �-point of the Brillouin
zone. We calculatedan isotropic electron effective mass of 0.49me
(me is the restmass of a free electron) at the CBM. This agrees
with theexperimental value (0.45me)49,53 but is larger than
previoustheoretical results, 0.35–0.37me.57,58 The effective mass
ofholes at the VBM is anisotropic and ranges from 1.23meto 1.98me,
comparable to the experimental estimates, 2.2 ±0.7me.4 Using these
effective masses, we obtained an intrinsiccarrier density ni of
2.7–3.8 × 1012 cm−3 at room temperature(300 K), with effective
electron and hole densities of statesNC = 2(2πme∗kBT /h2)3/2 = 8.6
× 1018 cm−3 and NV =
TABLE I. Properties of pyrite FeS2: lattice constant a (Å),
band gap Eg (eV), electron and hole effective masses m∗e and m∗h
(me), intrinsic
carrier density ni (×1012 cm−3), and effective electron and hole
densities of states NC and NV (×1019 cm−3). Values of ni , NC, and
NV areestimated at 300 K.
a Eg m∗e m
∗h ni NC NV
The. 5.42 1.02 0.49 1.23 − 1.98 2.7 – 3.8 0.9 3.4 − 7.0Exp.
5.4249,50 0.73 − 1.23,51,53,55 0.4549,53 2.2 ± 0.74 2.84 0.34 8.5 ±
54
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FIRST-PRINCIPLES STUDIES OF THE ELECTRONIC . . . PHYSICAL REVIEW
B 85, 085203 (2012)
2(2πmh∗kBT /h2)3/2 = 3.4–7.0 × 1019 cm−3, again close
toexperimental values.4 Wave function analysis reveals that theS-S
ppσ , ppπ , and ppπ∗ bands have energies below −1.5 eV;the valence
states between −1.0 eV and 0.0 eV have mostlythe Fe 3d-t2g
character, and the conduction states between1.02 eV and 4.2 eV are
composed primarily of Fe-eg andS-ppσ ∗ orbitals.
Following the Bader charge division scheme,59 we calcu-lated the
number of electrons on each atom in bulk pyrite,which results in
charge states of Fe and S atoms of +0.86e and−0.43e, respectively.
We will use these values as references inthe following discussions
regarding the charge redistributioninduced by native and nonnative
defects. Note that these valuesare smaller in magnitude than the
conventional oxidation statesof pyrite defined in inorganic
chemistry (Fe2+ and S1−), due tothe spatial division and the
partial covalent feature of the Fe-Sbonds. These values are
somewhat smaller than the chargesobtained using the Mulliken scheme
(+1.2e and −0.6e).43
B. Sulfur and iron vacancies
We considered various native defects in a 3 × 3 × 3 super-cell:
including single sulfur vacancy (VS), single iron vacancy(VFe),
interstitial sulfur (Si), sulfur-sulfur divacancy (VS-S),
andsulfur-iron divacancy (VFe-S). To quantitatively describe
theirenergetics, we calculated formation energies according to
�Hf = E(D) − E(FeS2) + �nDμD. (1)Here E(D) and E(FeS2) are total
energies of the pyritesupercell with and without defects,
respectively. μD andnD represent the chemical potential and number
of sulfuror iron atoms that are removed or added. To allow
directcomparison between iron and sulfur defects, we also assumedan
equilibrium growth/annealing condition with a constraint
2�μS + �μFe = �μFeS2 , (2)where �μS and �μFe are the deviations
of chemical potentialsof S and Fe relative to their elemental
phases (S8 and bulkFe), respectively. The calculated formation
enthalpy of pyrite,�μFeS2 , is −1.19 eV per FeS2 unit. Figure 2
gives results of�Hf as a function �μS in a range −0.6 eV < �μS
< 0.0 eV.Arrows in Fig. 2 mark positions of two typical
experimentalconditions that use H2S and S8 as the reservoirs of
sulfur.
At the onset, we may exclude S-divacancy and interstitialsulfur,
since �Hf (VS-S) is larger than 4 eV, and �Hf (Si) iseven higher
(>8 eV, not shown in Fig. 2). On the contrary, Fe orS single
vacancy may have appreciable concentration in pyritesamples. �Hf
(VFe) is only 1.75 eV if S8 is the sulfur reservoir,and the lowest
value of �Hf (VS) is 2.36 eV under S-poorconditions (or,
equivalently, Fe-rich conditions). Interestingly,the formation of
the VFe-S pair might be as easy as VFe or VS,by removing either a S
atom around VFe with an energy costof 1.2 eV or an Fe atom around
VS with an energy cost of0.12 eV in the S-rich condition.
Therefore, we suppose thatVFe, VS, and VFe-S are the main native
defects in pyrite underequilibrium growth/annealing conditions.
Yu et al.19 and Sun et al.47 recently obtained
comparableformation energies of 3.5 eV and 3.0 eV for VS in the
S8environment, and they argued that equilibrium densities of
allnative defects should be insignificant for samples prepared
-0.6 -0.4 -0.2 0.01
2
3
4
5
6
VS
VS-S
VFe
VFe-S
μS (eV)
Δ
Δ
Hf (
eV)
S8H2S
FIG. 2. (Color online) Formation energies of native
defects,including VS, VS-S, VFe, and VFe-S as a function of sulfur
chemicalpotential (�μS = μS − μ0S, where μ0S is the sulfur chemical
potentialof its elemental phase, S8). The left and right boundaries
of sulfurchemical potential correspond to the so-called Fe-rich (Fe
bulk as thereservoir) and S-rich (S8 as the reservoir) conditions,
respectively.
at 2.00)may explain most if not all of these results. Evidence
forsulfur divacancies and vacancy clusters in pyrite by
positronannihilation spectroscopy has also been reported,16 but
thesestudies are in our view preliminary and far from conclusive.
Weconclude that the longstanding question of pyrite
stoichiometryremains unsettled. Of course, even if pyrite is
stoichiometricat the percent level, native defects that may be
present at partsper billion to parts per thousand could be
sufficient to dopepyrite films and dominate their electronic
properties.
085203-3
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JUN HU, YANNING ZHANG, MATT LAW, AND RUQIAN WU PHYSICAL REVIEW B
85, 085203 (2012)
(a) (b) (c)
FIG. 3. (Color online) Band structures of a 3 × 3 × 3
pyritesupercell with (a) VS, (b) VFe, or (c) VFe-S. The black solid
and reddashed lines in (b) and (c) represent majority- and
minority-spinbands, respectively. The VBM is set as the reference
energy for eachcase. The horizontal green dotted lines indicate the
correspondingFermi level of each case. The insets provide the
isosurfaces of singlestate charge densities (at 0.03 e/Å3) of the
defect states, indicatedby arrows. Violet (dark) and yellow (light)
spheres represent Fe andS atoms, respectively. The cross signs in
dotted circles denote thepositions of the missing S or Fe
atoms.
We now examine the impact of neutral VS, VFe, and VFe-Son the
electronic properties of pyrite. It remains debatablewhether S
vacancies produce gap states in bulk pyrite, eversince Birkholz et
al. reported that pyrite samples are sulfurdeficient up to 12
at.%.12 Although VS has received significantattention in the
literature, few studies have focused on VFeand VFe-S. From Fig. 3,
it can be seen that all three types ofvacancies produce defect
levels in the band gap and near theband edges. Although the
concentration of vacancies in ourcalculations is quite high (2.3 ×
1020 cm−3), the defect statesare nearly dispersionless and thus
their effect is well containedin the 3 × 3 × 3 supercell. The
presence of VS induces twodefect states in the band gap near the
valence band and aresonant state within the conduction band, 0.08
eV, 0.18 eV,and 1.21 eV relative to the VBM. From the single-state
charge-density plot in the left inset in Fig. 3(a), the gap state
at 0.18 eVhas mostly S-pz and Fe-t2g features around the S atom
nearestto VS and its three Fe neighbors. This state splits off
fromthe valence band because cleavage of the S-S dimer changesthe
charge distribution around the sulfur vacancy. The stateat 1.21 eV
distributes around the S and three Fe neighbors ofVS, mostly with
the S-pz and Fe-eg characters, as shown in theright inset of Fig.
3(a). The Bader charge state of the remainingS atom near VS becomes
−0.75e, almost double that of the Satom in the perfect bulk pyrite.
The Bader charge states of theother atoms, including the
neighboring Fe atoms of VS, remainessentially unchanged. Therefore,
the creation of VS convertsthe remaining S atom in the dimer to
S−2.
Interestingly, VFe triggers spin polarization, with a
sizeablemagnetic moment of 2.0 μB/cell. The distribution of
spinmoment is rather delocalized, with 0.06 μB on each S atomaround
VFe and 0.15 μB on each second-nearest-neighborFe atom. The large
spatial range of the spin polarizationaround VFe suggests potential
long-range magnetic ordering inFe-deficient pyrite, but more
studies are necessary to confirmthis possibility. The single-state
charge density plot in the inset
of Fig. 3(b) shows that the lowest unoccupied gap state in
theminority spin channel (0.57 eV above the VBM) consists ofthe pz
orbitals of the six sulfur atoms around VFe and thet2g orbitals of
the twelve Fe atoms adjacent to them. Thepronounced doubly
degenerate gap state in the majority-spinchannel 0.27 eV above the
VBM has a similar character but isoccupied. There are two other gap
states in the minority-spinchannel, approximately 0.21 eV and 0.31
eV above the VBM,and their counterparts in the majority-spin
channel are in theVB, manifesting the large exchange splitting for
Fe-t2g states.It appears that neutral VFe is neither a good donor
nor a goodacceptor since the impurity levels are far from both VB
andCB.
Similarly, VFe-S also induces a spin moment of 2.0 μB/cell,with
the spin density distribution in close analogy to that ofVFe. The
band structure in Fig. 3(c) shows several defect statesin the gap,
along with a few resonant states in CB. In particular,two pairs of
defect levels locate near the Fermi level: 0.33 eVand 0.40 eV above
VBM in the majority-spin channel and0.32 eV and 0.39 eV above VBM
in the minority-spin channel.The single-state charge density in the
inset in Fig. 3(c) for thedefect state near EF indicates it is
mainly from Fe-3d orbitals.The defect levels of VFe-S in the band
gap are all occupied, sothat neutral VFe-S defects are deep donors
in pyrite.
For the convenience of comparison, we extract the maindefect
levels of different vacancies from their band structuresand plot
them on top of the band gap of perfect pyrite inFig. 4. Sulfur
vacancies create states within the band gap, asoriginally proposed
in the qualitative ligand field theory modelof Birkholz et al.12
and developed by Bronold et al.13,15 Thelatter authors argue that
VS forms easily with a concentrationof 1020–1021 cm−3 and creates
mid-gap states that induce largethermionic-field emission currents
in the dark, leading to thelow VOC of pyrite electrochemical and
Schottky junctions.62
However, our calculations show that bulk VS creates gap
statesquite close to the VBM and hence is probably not
responsible
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Ene
rgy
(eV
)
VS VFe NS PS AsS FS BrSClSVFeS
Conduction band
Valence band
FIG. 4. (Color online) Kohn-Sham defect levels for a 3 × 3 ×
3supercell containing one vacancy or impurity with respect to
thevalence and conduction bands (shaded regions) of the perfect
bulkpyrite. Black and red (dark gray) lines denote defect levels in
themajority and minority spin channels, respectively. Thick lines
for VFedenote double degeneracy of defect states, and the rectangle
for BrSindicates a Br-induced resonant band. Dots represent the
electronoccupancy of the neutral defects.
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B 85, 085203 (2012)
TABLE II. Binding energies (Eb, in eV), induced spin moments (MS
, in μB), bond lengths (dI-S, in Å), and Bader charge states of
theimpurity-S dimers (QI and QS for impurity and S atoms,
respectively, in electron charge) for various substitutional
dopants in pyrite.
Impurity SS OS NS PS AsS FS ClS BrS
Eb −2.95 −3.11 −0.60 −2.49 −1.75 −3.56 −1.73 −0.97MS 0.00 0.00
1.00 1.00 1.00 1.00 1.00 0.81dI−S 2.16 1.73 1.74 2.15 2.26 2.59
2.56 2.56QI −0.43 −1.65 −1.07 +0.59 +0.68 −0.75 −0.51 −0.29QS −0.43
+0.62 −0.13 −1.37 −1.27 −0.55 −0.55 −0.55
for the low VOC of pyrite Schottky solar cells. Mechanisms
thatgreatly increase the concentration of VS, VFe, or VFe-S
(e.g.,non-equilibrium conditions, or lower defect formation
ener-gies near the crystal surface) would make the causal
connectionbetween vacancies and low VOC as advocated by Bronold et
al.more plausible. Theoretical studies of surface and
near-surfacedefects in pyrite are ongoing and will be reported
elsewhere.67
Of course, the electronic behavior of a defect state also
dependson its charge state or by the Fermi energy of the system.
Forexample, while neutral sulfur vacancies are very deep
donors,positively charged sulfur vacancies are likely to act as
shallowacceptors according to the energy diagram in Fig. 4.
Similarly,neutral VFe is a deep trap/recombination center for
carriers,whereas negatively charged VFe is a deep donor.
Self-consistentcalculations for different charge states are needed
to explorethe effect of local charge on impurity levels, as were
done forseveral defected systems.68–70
C. The effect of substitutional oxygen (OS) impurities
Oxygen may be incorporated in pyrite samples duringgrowth and
annealing processes, and thus it is important toinvestigate the
electronic properties of O-doped pyrite. Theionic radius of oxygen
is slightly smaller than that of sulfur, andoxygen has a much
larger electronegativity (3.44 for O vs 2.58for S). Sun et al.
recently argued that substitutional oxygenimpurities can account
for the p-type doping that is nearlyalways observed for nominally
undoped pyrite thin films.70
However, the validity of some assumptions in their model
andanalysis, including the experimental growth conditions neededto
induce high oxygen concentrations, are questionable. Forexample,
many pyrite thin films that have been reported tobe p-type by
thermopower measurements were fabricatedin sulfur-rich, low-oxygen
conditions rather than the iron-rich, oxidizing conditions
emphasized by Sun et al.70 Theseconsiderations motivated us to
undertake a comprehensiveanalysis of the electronic effects of
substitutional oxygen (OS)in pyrite.
When one S is replaced by O in the 2 × 2 × 2
supercell(FeS1.97O0.03), the O-S dimer binds more tightly than the
S-Sdimer. The S-O bond length of 1.73 Å in O-doped pyrite
issignificantly smaller than the S-S bond length (2.16 Å) inbulk
pyrite. The Fe-O bond length, 2.32 Å, is neverthelessslightly
larger than the Fe-S bond length in bulk pyrite (2.27 Å).To
describe the strength of interaction for oxygen and
othersubstitutional anion impurities in pyrite (discussed later),
wedefine a binding energy:
Eb = E(IS) − E(VS) − μI , (3)
where E(IS) and E(VS) are the energies of pyrite with
asubstitutional impurity or VS in the supercell, and μI is
thechemical potential of the impurity atom. For simplicity, we
setμI in their standard states, e.g., O2 for oxygen, S8 for S, and
N2for nitrogen. Additional calculations are needed to determineμI
if other impurity sources are used. The calculated values ofEb are
given in Table II, where the result for S in a sulfur site(SS,
i.e., ideal pyrite) is listed for reference. One may easilyshow
that Eb for S is equal to −�Hf (VS) at S8, as in Fig. 2. It
isinteresting that Eb of oxygen is slightly larger by 0.16 eV
thanthat of sulfur. Although this value may change if
alternativereservoirs of oxygen are used, it is clear that OS binds
morestrongly than SS in pyrite. Therefore, OS can be effective
toheal VS defects of pyrite.
The effect of OS on the electronic properties of pyrite
isrevealed in the total and projected DOS and band structureplotted
in Figs. 5(a) and 5(b). We find that OS removes the gapstates
induced by VS and FeS2-xOx (x = 0.03 for a 2 × 2 × 2supercell with
one OS) appear to be an intrinsic semiconductor.This is
unsurprising given the identical valences and overallchemical
similarity of oxygen and sulfur. Although the S-Obond is shorter
than the S-S bond, the DOS curves of Fe andS atoms are not much
different from those of perfect bulkpyrite. The DOS curve of oxygen
is also very similar to thatof sulfur, except that its 2p band is
narrower [Fig. 5(a)]. Fromthe band structure in Fig. 5(b), we find
that the band gap ofthe hypothetical FeS1.97O0.03 crystal is about
1.06 eV, slightlylarger than that of pyrite itself. The VBM shifts
from nearthe X-point to near the �-point, as displayed in the inset
ofFig. 5(b), which means that FeS1.97O0.03 is also an indirect
gapsemiconductor. The effective electron and hole masses at theCBM
and VBM are estimated to be 0.54me and 2.05me, closeto the values
for perfect bulk pyrite. Interestingly, FeS1.99O0.01(a 3 × 3 × 3
supercell with one OS) has similar features,which implies that the
properties of FeS2-xOx compoundsare independent of oxygen
concentration lower than 3%.Therefore, incorporating a few percent
or less of O intopyrite samples may reduce the concentration of VS
andtheir accompanying gap states, thereby cleaning the gap
andimproving the carrier mobilities and lifetimes.
Bader charge analysis reveals that the O-S dimer is
stronglypolarized, with charge states of −1.65e and +0.62e on the
Oand S sites, respectively. To more clearly depict the
chargeredistribution caused by O substitution, we calculated
chargedensity difference, as shown in Fig. 5(c). It is obvious that
theO atom gains electrons from its neighboring Fe and S atoms.In
particular, the charge redistribution around the S atom inthe O-S
dimer is rather complex: the S atom gains electrons
085203-5
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0
100
200
300
400
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1
0
5
10
R Γ X M R
-6
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-2
0
2
4
0
1
Den
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of
Stat
es (
Stat
es/e
V c
ell)
Energy (eV
)
Total
Fe (Fe-S)Fe (Fe-O)
S (S-S)S (S-O)
O
(a) (b)
(c)
Energy (eV)
Γ-0.02
-0.01
0.00
FIG. 5. (Color online) Results for oxygen-doped
pyrite(FeS1.97O0.03). (a) Total and projected DOS. The notation in
paren-theses indicates the bonds to which the atoms belong. The VBM
isset as the energy reference. (b) Band structure. The reference
energyis the same as in (a). The red (dark gray) lines denote the
topmostvalence band and lowest conduction band. The inset is a
magnifiedview of valence bands near the VBM around the �-point and
they-axis unit is eV. (c) Charge density difference [�ρ = ρ(OS)
−ρ(VS-S) − ρ(O) − ρ(S)] viewed in the (110) plane. Note that
theatomic positions in reference systems were fixed as those in
O-dopedpyrite. The isosurfaces are at the values of ±0.03 e/Å3,
with blue(dark) and red (light) regions for charge gain and loss,
respectively.Violet (dark) and yellow (light) spheres represent Fe
and S atoms,respectively.
from its three neighboring Fe atoms and donates electrons tothe
O atom. The O-S dimer with a Bader charge of −1.03e isslightly more
negative than the S-S dimers with a Bader chargeof −0.86e.
Accordingly, three Fe atoms near OS have higherBader charges
(+0.95e) compared to other Fe atoms (+0.86e).Overall, the impact of
OS on the electronic properties of pyriteis rather local. We
reiterate that the conventional viewpointof inorganic
chemistry—which labels ions only with integercharge states (e.g.,
Fe2+ and S1−)—is unrealistic because ofthe strong covalent nature
of bonding in perfect and O-dopedpyrite. Although a similar charge
difference was found bySun et al.,70 it is improper to claim, as
these authors did, thatOS is an acceptor based only on the assumed
charge state ofsubstitutional O (O2−). The DOS and band structure
in Fig. 5clearly show no gap state induced by a neutral OS.
D. Doping with Group V elements
To use pyrite in photovoltaic applications, it is crucial
tocontrol carrier concentrations and diffusion lengths
throughdoping. Several groups have reported that substitution
ofphosphorus or arsenic for sulfur yields p-type conduction
inpyrite, but the results for carrier concentration and mobilityare
rather scattered.21–23 Here, we investigate the effects of NS,PS,
and AsS impurities in order to understand the challengesinvolved in
p-type doping with Group V elements. From
Table II we can see that both NS and AsS are
energeticallyunfavorable because their binding energies are much
smallerthan SS in bulk pyrite. In contrast, the binding energy ofPS
is only 0.5 eV smaller than SS, which implies that Phas a
reasonable probability to be incorporated into pyrite.This is
expected based on the similar atomic sizes andelectronegativity of
P and S. Note that the values of Eb can beincreased if less stable
impurity sources are used. Therefore, Nand As may still be doped in
pyrite with more reactive impuritysources. We find that NS, PS, and
AsS all make pyrite magneticwith a spin moment of 1.0 μB per
impurity atom. The magneticproperties will be further discussed in
detail.
Similar to the O-doping case, the N-S dimer has a very shortbond
(1.74 Å) when N replaces S atom in pyrite. The chargestates of N
and S are −1.07e and −0.13e, respectively. Thisindicates that the
N-S bond is also polarized due to the chargetransfer from S to N.
The charge state of Fe atoms near Sremain nearly unchanged
(∼+0.86e), whereas Fe atoms nearNS lose more electrons to N and
their Bader charge becomes+0.98e. Obviously, the N-S dimer attracts
more electrons fromFe than does the S-S dimer. In the DOS plots in
Fig. 6(a), onecan see that nitrogen substitution produces several
pronouncedside peaks near the VBM, mainly from the Fe-t2g states.
Inaddition, it is clear that the DOS is spin-polarized, with
alocalized gap state at 0.7 eV above the VBM in the minority-spin
channel (also see Fig. 4). As seen in the inset of Fig. 6(a),this
gap state features mainly the t2g orbitals of the six Featoms
around the N-S dimer and the 2p orbitals of N and S.
FIG. 6. (Color online) Total DOS of a 2 × 2 × 2 pyrite
supercellwith a single (a) NS, (b) PS, and (c) AsS dopant,
corresponding to adefect concentration of 7.8 × 1020 cm−3. The
vertical dashed lineindicates the Femi energy. The positive and
negative DOS indicatemajority and minority spin channels,
respectively. The inset in (a)shows the isosurfaces (at 0.01 e/Å3)
of the single-state charge densityof the defect state induced by NS
in the minority spin channel at 0.7 eVabove the VBM. Similar
features were found for gap states of PS andAsS.
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Since N has one fewer valence electron than S, NS is expectedto
be an acceptor in pyrite, but the acceptor level is about0.7 eV
above the VBM [Fig. 6(a)] and cannot ionize efficientlyat room
temperature. In this sense, neutral NS centers areextremely
inefficient dopants. NS also reduces the local pointgroup symmetry
of the neighboring Fe atoms from Oh to C4v;the t2g states regroup
to e-states (dxz and dyz) and b2-state (dxy)(here the z-axis is
along the Fe-N bond).71 As a result of chargeredistribution and
lattice distortion, the b2 state becomes vacantin the minority-spin
channel.
PS and AsS are also deep acceptors in pyrite. As shown inFigs.
6(b) and 6(c), the DOS features are very similar to thoseof NS, but
their acceptor levels shift closer to the VBM (0.31 eVand 0.44 eV,
respectively, as shown in Fig. 4). Therefore,heavily P- and
As-doped pyrite is expected to be weaklyp-type at 300 K via thermal
excitation of electrons to thesedeep acceptor levels (ionization
efficiency of 10−5–10−8). Itis interesting that the carrier should
be 100% spin-polarizedsince the acceptor level in the minority-spin
channel onlyexchange electrons with states in VB with the same
spin.This feature could be very useful for spintronics
applicationsif the magnetic ordering is sustained at room
temperature.Studies of magnetic properties of pyrite samples with
largeconcentrations of PS are desired to test these
predictions.
Due to the very similar atomic sizes and electronegativitiesof P
and S, the valence band is almost unaffected by PS exceptthat the
b2 state splits off. The bond length of the P-S dimerin P-doped
pyrite is almost the same as that of S-S dimer(2.15 Å vs 2.16 Å),
which indeed indicates minimal localstructural change.
Surprisingly, the charge states of P and Satoms are +0.59e and
−1.37e, respectively. This suggests astrong charge polarization in
the vicinity of the P-S dimer, butin the opposite way compared to
the OS and NS cases. Thebond length of the As-S dimer in As-doped
pyrite is 2.26 Å,and the charge states of the As and S atoms are
+0.68e and−1.27e, respectively. This sizeable structural distortion
causesthe upward shift of the AsS gap state compared to that of
PS.
Overall, the density of holes in N-, P-, and As-doped
pyriteshould be rather low near room temperature, with
Boltzmannfactors for thermal excitation ranging from 10−5 (for PS)
to10−12 (for NS). Other complex processes such as the formationof
defect clusters and the activity of other impurities mayeasily
produce larger carrier densities.21,22 This may explainthe
scattered results of Hall measurements for p-type pyritesamples
containing P and As.21–23
E. Doping with Group VII elements
Finally, we discuss the effect of the substitutional
halogenimpurities FS, ClS, and BrS in pyrite. Experimentally,
substan-tial concentrations of halogen atoms may exist in pyrite
crystalsfabricated by chemical vapor transport (CVT) or
chemicalvapor deposition (CVD) when halogen transport agents
(e.g.,Br2) or precursors (e.g., FeCl3) are used. We find that
FS,ClS, and BrS all lead to large structural distortions in
pyrite,with S-F, S-Cl, and S-Br bond lengths of 2.59 Å, 2.56 Å,
and2.56 Å, respectively, about 18% longer than the S-S bond inbulk
pyrite. Such a large bond length implies that the S-F, S-Cl,and
S-Br dimers are actually broken. The binding energieslisted in
Table II indicate that FS binds very strongly to its
neighboring Fe atoms, with an energy gain of 0.61 eV per Fatom
relative to SS. Therefore, F may easily replace S if F2 gasis used
as the impurity source and S8 is the sulfur reservoir. Thebinding
energy of ClS (Eb = −1.73 eV) is 1.22 eV smaller thanSS, meaning
that substitution of each Cl for S costs 1.22 eVwhen Cl2 is used as
the source. The binding energy of BrS isonly −0.97 eV, so that
substitution of Br for S costs 1.98 eV peratom. We emphasize again
that the energies needed to form FS,ClS, or BrS (or indeed any
impurity) depend strongly on boththe impurity source and sulfur
sink. For instance, taking thecommonly used Cl source of FeCl3 as
reference, the bindingenergy is only −0.70 eV, which implies that
the equilibriumClS concentration should be very low when this
source is used.Therefore, searching for chemically reactive doping
sourcesis essential to achieve appreciable impurity concentrations
inpyrite (as well as other semiconductors).
We now analyze the total and partial DOS plots of FS-and
ClS-containing pyrite in order to understand the electroniceffects
of halogen impurities. It can be seen from Figs. 7(a)–7(c) that FS
induces a state about 0.5 eV above the VBM in themajority-spin
channel, which makes neutral FS a deep donor inpyrite. Since the
distance between F and S atoms is 2.59 Å, theF-S interaction is
weakened whereas the p-d hybridizationbetween F or S and their
neighboring Fe atoms becomesstronger (dS-Fe = 2.27 Å and dF-Fe =
2.22 Å). This gives rise toa localized state in the band gap as
well as resonant states in thevalence and conduction bands, as
shown in Figs. 7(a)–7(c). Anet spin moment of 1.0 μB per atom is
produced since F adds anextra electron to the system. Intriguingly,
the spin polarizationis rather delocalized, distributed mainly
around the S atomadjacent to F (MS = 0.24μB) and the three Fe
neighbors of S(MFe = 0.27 μB/Fe). The charge states of the F and S
atomsare −0.75e and −0.55e, respectively. This indicates that the2p
shell of the F atom is almost completely filled and the Satom near
F also gains more electrons than other S atoms.
-200
0
200
-10
0
10
-6 -4 -2 0 2 4-4
0
4
-6 -4 -2 0 2 4
FS ClS
Fe (Fe-S)Fe (Fe-F)
Fe (Fe-S)Fe (Fe-Cl)
S (S-F)F (S-F)
S (S-Cl)Cl (S-Cl)
Energy (eV) Energy (eV)
(a)
(b)
(c)
(d)
(e)
(f)
EF EF
Den
sity
of
Stat
es (
Stat
es/e
V c
ell)
FIG. 7. (Color online) Total and projected DOS of a 2 × 2 ×
2pyrite supercell with a single FS (a)–(c) or ClS (d)–(f) defect.
Therespective VBM is set as the energy reference for both cases.
Thevertical dashed lines indicate the Femi energy. The positive
andnegative values of the DOS denote majority and minority
spinchannels, respectively.
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JUN HU, YANNING ZHANG, MATT LAW, AND RUQIAN WU PHYSICAL REVIEW B
85, 085203 (2012)
0 1 20
0.2
0.4
Cl Concentration (%)2x2x2 3x3x3
Δ (eV
)
3x3x3 2x2x2
R Γ X M R-0.5
0.0
0.5
1.0
1.5
2.0
R Γ X M R
Ene
rgy
(eV
)
EF
R Γ X M R
EF
Δ
(b)
(a)
FIG. 8. (Color online) (a) Band structures of pyrite with a
singleClS impurity in a 2 × 2 × 2 supercell (left) and 3 × 3 × 3
supercell(right). The solid black and dotted red (dark gray) lines
denotethe majority- and minority-spin states, respectively. The
horizontaldashed lines give the Fermi energy for each case. The
inset shows thespin density of FeS1.97Cl0.03, with the violet
(dark) and yellow (light)spheres representing Fe, S, and Cl atoms,
respectively. (b) Left andmiddle panels: sketches of the
hybridization between the conductionband of pyrite (solid black
line) and the atomic level of Cl (solidred/dark gray line) in 2 × 2
× 2 and 3 × 3 × 3 supercells, respectively.Right panel: the
separation between ClS impurity level and CBM inthe majority-spin
channel as a function of Cl concentration.
Accordingly, the charge states of the Fe atoms adjacent to theF
and S atoms are +0.91e and +0.98e, respectively.
From Figs. 7(d)–7(f), we can see that ClS induces gap statesnear
the CBM in both majority- and minority-spin channels.Due to the
large size of Cl, the gap states are broad. From theband structure
for the 2 × 2 × 2 supercell in the left panelin Fig. 8(a), one can
see a new dispersive band with anenergy ranging from 0.5 eV to 0.8
eV in the majority-spinchannel. Clearly, Cl-induced states strongly
hybridize with theconduction states of pyrite, and thus one should
actually viewthis system (one ClS in a 2 × 2 × 2 supercell) as a
chemicalcompound with a formula of FeS1.97Cl0.03. Furthermore,
twoClS bands are partially occupied in both spin channels, andhence
this heavily doped pyrite is metallic. Nevertheless, asdisplayed in
the right panel in Fig. 8(a), the ClS band in themajority-spin
channel becomes rather flat except in the vicinityof the �-point in
the 3 × 3 × 3 supercell (FeS1.99Cl0.01) that hasa ClS density of
2.3 × 1020 cm−3.
The formation of ClS bands can be simply understood bythe
hybridization of the atomic level of Cl and the conductionband of
pyrite, as depicted in Fig. 8(b). This opens theconduction band of
perfect pyrite and forms two new bands.The bandwidth of the lower
new band, denoted as �, isthe separation between ClS level and CBM.
If we assume alinear dependence of � on the ClS concentration, we
find that� approaches zero at the low ClS concentration limit.
Theposition of the ClS level should be right under the CBM
intypical samples that have Cl concentration of 1016–1018cm−3.
ClS impurities hence act as shallow donors and provideefficient
n-type doping in pyrite.
ClS induces a magnetic moment of 0.996 μB and 1.000 μBin the 2 ×
2 × 2 and 3 × 3 × 3 supercells, respectively. Asdisplayed in the
inset in Fig. 8(a), the spin density mainlydistributes around the
Cl-S dimer and its neighboring Fe atoms.The spin moments of Cl and
S in the Cl-S dimer are 0.06 μBand 0.22 μB, respectively, while Fe
atoms near the Cl or S atompossess 0.03 μB and 0.15 μB. Unlike
FS-containing pyrite, thecharge states of Cl and S are −0.51e and
−0.55e, respectively.The charge states of Fe atoms (+0.89e) near Cl
and S arenot significantly different from perfect pyrite, even
though ClSbrings in an additional electron that is loosely bounded
aroundthe impurity.
The features of Br-doped pyrite (or more exactly theFeS2-xBrx
compound) are very similar to the Cl-doped case.Nevertheless, the
mixed bands are somewhat broader due tothe larger spatial extent of
Br p-orbitals. The defect level ofBrS is hard to trace in
FeS1.97Br0.03 but still shows as a broadresonance above CBM with a
width of 0.12 eV in FeS1.99Br0.01,as depicted by a rectangle in
Fig. 4. The reliable determinationof Br level at low concentration
hence needs calculationswith 4 × 4 × 4 or larger supercell, which
are arduous even onparallel computers at this stage. We believe
that the Br-dopinglevel is close to CBM at low concentration and it
shouldproduce n-type pyrite, as does Cl.
IV. CONCLUSIONS
In summary, the properties of native point defects
andsubstitutional anion impurities in iron pyrite were studied
usingspin-polarized DFT calculations. Our results indicate that
thecommonly held notion that sulfur vacancies are donors and
ironvacancies are acceptors may be incorrect because these
nativedefects, when neutral, induce localized and deep gap states
thatcannot easily contribute free carriers near room
temperature.The large formation energies of these defects under
typicalexperimental growth conditions imply very low
equilibriumconcentrations (
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FIRST-PRINCIPLES STUDIES OF THE ELECTRONIC . . . PHYSICAL REVIEW
B 85, 085203 (2012)
ACKNOWLEDGMENTS
We thank the NSF SOLAR Program (Award CHE-1035218) and the UCI
School of Physical Sciences Center
for Solar Energy for support of this work. Calculations
wereperformed on parallel computers at NERSC and at
NSFsupercomputer centers.
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