Download Ionization of High-Density Deep Donor Defect States Explains the

Supporting Information for
Ionization of High-Density Deep Donor Defect States Explains
the Low Photovoltage of Iron Pyrite Single Crystals
Miguel Cabán-Acevedo, Nicholas S. Kaiser, Caroline R. English, Dong Liang, Blaise J.
Thompson, Hong-En Chen, Kyle J. Czech, John C. Wright, Robert J. Hamers, and Song Jin*
Department of Chemistry, University of Wisconsin–Madison, 1101 University Avenue,
Madison, Wisconsin 53706, United States
AUTHOR EMAIL ADDRESS: [email protected]
I. EXPERIMENTAL METHODS
I.1 Chemical Vapor Transport (CVT) Growth of Iron Pyrite Single Crystals. A typical
pyrite crystal growth experiment consists of two steps: the synthesis of a high purity iron pyrite
precursor powder, and the growth of bulk single crystals by means of CVT. The iron pyrite
precursor was synthesize by heating high purity iron (99.998 %, VWR) and sulfur (99.999 %,
Materion) powder (1:2 weight ratio, respectively) in a sealed quartz ampoule at 600 ºC using a
single zone furnace, for a period of 5 – 7 days. The sulfur powder was added in excess to saturate
the ampoule atmosphere with sulfur gas and stabilize the formation of iron pyrite. A small
amount of iron (II) bromide (FeBr2, ~ 20 mg/1 g of iron pyrite) was added to enable a faster and
more complete reaction of the elemental iron with sulfur. Without the FeBr2, the reaction
S1
proceeded more slowly, which could be due to the tendency of iron to form passivated clumps.
During the reaction cool down, the FeBr2 and excess sulfur condensed at the cold end of the
ampoule, which was estimated to be at a temperature of ~ 450 – 500 ºC during the reaction.
Thus, when the furnace was cooled down naturally, the iron pyrite precursor powder could be
easily and cleanly recovered from the hot end of the ampule.
The synthetic iron pyrite precursor powder was then used to grow the square-faceted iron
pyrite single crystals by CVT using iron (II) chloride as the transporting agent (100 mg /1 g of
iron pyrite) in a sealed quartz ampule (14 mm inner diameter and 230 mm length), as shown in
Figure 1a in the main text. The CVT crystal growth was conducted for a period of 3 weeks in a
custom-built two zone tube furnace with a temperature gradient of 650–550 ºC for the precursor
and deposition zone, respectively.
I.2 Structural Characterization. The powder X-ray diffraction (PXRD) patterns for the
synthetic iron pyrite precursor powder and CVT-gown iron pyrite single crystal products were
collected on a Bruker D8 Advance Powder X-ray diffractometer using Cu Kα radiation. In the
case of the iron pyrite powder samples, borosilicate glass was used as the substrate for the PXRD
measurements and background subtraction was applied to the raw data. Confocal micro-Raman
spectra for the square-faceted pyrite single crystals were collected with a Horiba Jobin Yvan
LabRAM ARAMIS confocal microscope using a 200-µm aperture and a 532 nm laser source.
Optical measurements for the powder samples made from crushed pyrite single crystals were
performed using a Cary-5000 UV-Vis-NIR spectrophotometer equipped with an integration
sphere (Agilent Technologies).
I.3 Electrical Transport Measurements. Electrical devices for transport measurements were
carefully fabricated using CVT-grown iron pyrite single crystals with rectangular cuboid shape.
S2
Source-drain current contacts were made by sputtering Au on the two opposing facets along the
long axis. Before sputtering, the crystals were etched for 5 s using buffered HF (Buffered HF
Improved, Transene Inc.) to ensure ohmic contact. The voltage contacts were designed following
a Hall bar pattern and made by wire-bonding aluminum wires on a facet orthogonal to the axis of
current flow. The current and voltage contacts were tested and found to be ohmic. All electrical
measurements on iron pyrite single crystal devices were carried out in a Quantum Design
Physical Property Measurement System (PPMS-9T) combined with standard DC measurement
setup, using a Keithley 6221 as the current source and a Keithley 2182A as the voltmeter.
Temperature dependent resistivity and Hall measurements were performed using a constant
current of 5 µA for source-drain, and taken at discrete temperatures at which thermal equilibrium
was reached.
I.4 Surface Pretreatments of Iron Pyrite Single Crystals. Prior to surface photovoltage, UV
and X-ray photoelectron spectroscopy, Kelvin probe microscopy, electrochemical and
photoelectrochemical measurements, the {100}-faceted pyrite single crystals were cleaned by
chemical etching or electrochemical cleaning. The chemical etching was performed by
submerging a single crystal for 30 s in an acid solution mixture referred to as HNA, which
consists of hydrofluoric acid (HF, 48% in water, ≥99.99%, Sigma-Aldrich), nitric acid (HNO3,
70% in water, Sigma-Aldrich) and acetic acid (≥ 99.99%, Sigma-Aldrich) in a volume ratio of
1:2:1. The electrochemical cleaning (or H2SO4 polarization) was performed by sourcing a current
of -15 mA/cm2 through a pyrite single crystal electrode in 0.5 M sulfuric acid (H2SO4) for 3−5
min using a potentiostat (Bio-Logic SP-200) in a two electrode configuration with platinum (Pt)
as the counter electrode. Measurements were monitored through chronoamperometry to ensure
that a constant potential plateau was observed.
S3
I.5 Time-Resolved Surface Photovoltage (TR-SPV). SPV measurements for the {100}faceted iron pyrite single crystals were collected in a metal-insulator-semiconductor (MIS)
capacitor-like arrangement using a custom-made sample cell and a home-built instrumental setup
(Figure S1a). Indium-doped tin oxide (ITO) coated glass was used as a sense electrode, which
was separated from the pyrite single crystal electrode using a 127 µm Teflon spacer. The pyrite
single crystal electrode was connected to ground, and illuminated through the sense electrode
using a tunable laser (NT340, EKSPA, Inc., Vilnius, Lithuania) at ~ 0.1 mJ/pulse and ~ 3 ns
pulse duration. The response occurring upon sample illumination passed through a preamplifier
(Model TA2000B-3, ComTec GmbH, Oberhaching/München, Germany) with 50 Ω input and
output impedances, 1.5 GHz bandwidth, and 40x voltage gain. The SPV signal was recorded by
a digital oscilloscope (Model DSO9404A, Agilent, Inc., Santa Clara, CA) with a 50 Ω
impedance. The time-resolved photovoltage recorded by the oscilloscope was converted using
this information into a time-resolved photocurrent (Figure S2b). Then, by integrating the
photocurrent with respect to time the photoinjected charge per laser pulse at each photon energy,
as shown in Figure 3d,e in the main text was determined.
I.6 Ultrafast Reflective Pump-Probe Spectroscopy. Ultrafast pump-probe spectroscopy was
carried out on the {100}-faceted pyrite single crystals in a reflective geometry. An 800 nm (1.55
eV) pump and an 1190 nm (1.04 eV) probe were used, each with a 50 fs FWHM. Both beams
were brought in at 5º to surface normal, with ‘S’ polarization. The beam diameters at the sample
surface were 300 µm FWHM. The reflected probe beam was collected, and the difference signal
was measured by mechanically chopping the pump beam and isolating the corresponding change
in probe intensity via active background subtraction in a boxcar electronics module. The carrier
lifetimes were extracted by fitting the data to an exponetial of the form: + exp(/) .
S4
A power study was performed to verify the proportionality of the signal with respect to pump
power (Figure S2a, b). Beam diameters were 300 µm FWHM at the sample for both pump and
probe. We approximate that 8.5 µJ pump energy corresponds to ~1016 photons/cm2 per pump
pulse. In all cases the probe energy was at least four orders of magnitude lower than pump
energy, and had a negligable effect on the sample carrier density. The high resolution data shown
in Figure 4 of the main text was taken at 8.5 µJ. Additional reflective pump probe data were
collected for a polished natural pyrite crystal, from which similar lifetimes were obtained (Figure
S3c).
I.7 X-ray Photoelectron Spectroscopy (XPS). High-resolution angle resolved XPS
measurements for S2p were taken using a Thermo Al Kα XPS with a 180° double focusing
hemispherical analyzer and 128-channel detector (60° angular acceptance), which under
effective operating conditions had an analyzer resolution of 0.8 eV. High resolution XPS
measurements of S2p peak at a 90° source-to-analyzer angle and 45° take-off (emission) angle
were taken on a custom-built XPS system (Phi Electronics, Eden Prairie, MN) with a model 10610 Al Kα X-ray source (1486.6 eV photon energy) and a model 10-420 toroidal
monochromator. A model 10-360 hemispherical analyzer with a 16-channel detector array was
used (4° angular acceptance), which under effective operating conditions had an analyzer
resolution of 0.4 eV. All X-ray photoelectron spectra were shifted so that the adventitious carbon
C1s peak was at 284.8 eV; this allowed the comparison of peak positioning among samples and
XPS instruments. To account for the spin-orbit coupling of sulfur 2p peaks into S2p3/2 and S2p1//2
components, all peaks were fitted using doublets with a 1:0.5 (3/2p:1/2p) area ratio, 1.18 eV
apart, and with the same FWHM, unless otherwise stated.
S5
I.8 Ultraviolet Photoelectron Spectroscopy (UPS). Ultraviolet photoelectron spectroscopy
(UPS) was performed on a custom-built system (Phi Electronics Inc., Eden Prairie, MN)
equipped with a model 10-360 hemispherical analyzer. A He I (21.2 eV photon energy)
discharge lamp served as the UV light source. Spectra were collected with an electron take-off
(emission) angle of 0° from the sample surface normal and an analyzer resolution of 0.09 eV. A
bias was applied to the samples during the measurement in order to overcome the vacuum level
of the analyzer. The Fermi level was determined by collecting an UP spectrum of platinum and
fitting the platinum valence band maximum (VBM) to a Fermi function. For the UPS data
reported, all spectra were shifted so that the Fermi level fell at 0 eV. To determine the VBM of
the iron pyrite single crystals, the low-binding energy edge of the UP spectrum was fit to a line
and the x-axis intercept taken as the VBM. To determine sample work function, the high-binding
energy edge of the UP spectrum was first fit to a line and the x-axis intercept taken as the highbinding energy cutoff (HBEC). The HBEC was then subtracted from the photon energy (21.2
eV) in order to determine the sample work function.
I.9 Kelvin Probe Force Microscopy (KFM). KFM and topographic measurements were
performed simultaneously using an Agilent 5500 AFM equipped with KFM capabilities. The
measurements were taken in intermittent contact mode while employing an amplitude
modulation feedback loop for KFM data collection. KFM measures the contact potential
difference (CPD) between a metallized AFM tip and a sample. Since CPD = (tip work function)
– (sample work function), proper tip calibration allows direct access to the work function of a
sample. A new, platinized Si AFM cantilever (Mikromasch HQ:NSC18/Pt) was calibrated by
measuring a ZYA grade HOPG (Ted Pella, Inc.) that was freshly cleaved via the Scotch tape
method. Immediately following calibration, CPD measurements were acquired for 10 pyrite
S6
single crystals that were previously HNA etched or electrochemically cleaned, then rinsed with
18 MΩ • cm nanopure deionized water, and then dried in a vacuum desorption chamber (pressure
< 5 µtorr, room temperature) overnight.
Measurements were completed on three different
locations for each crystal. Note that both the calibration and sample KFM measurements were
performed in a sealed environmental control chamber (Agilent N9441A) that had been purged
with ultrahigh purity argon for 5 min. Purging was performed each time a new sample was
introduced into the chamber or after 1 hour passed.
I.10 Photoelectrochemical Measurements. The iron pyrite photoelectrodes were fabricated
by mounting a {100}-faceted single crystal to a glass tubes using insulating epoxy. Ga-In
eutectic (≥ 99.99%, Sigma-Aldrich) was used as the back-contact, which was then attached to a
Cu wire using silver paint (Ted Pella). Prior to measurements, all electrodes were
electrochemically cleaned as described above in Section I.4. The photoelectrochemical J-V
curves of the {100}-faceted iron pyrite photoelectrodes were measured using a Bio-Logic SP200 potentiostat in a two-electrode configuration using platinum (Pt) mesh as counter electrode,
under simulated 1 Sun irradiation (100 mW/cm2) supplied by a 1 kW Xe short arc lamp solar
simulator (Newport Corp., Model 91191; AM 1.5G filter). The light intensity was calibrated
using a silicon photodiode (Thorlabs) to generate a photocurrent equal to that at 100 mW/cm2
light intensity. Two types of electrolytes were employed for photoelectrochemical
measurements:
Aqueous: The chemicals used in this section and the non-aqueous electrolyte section were
received from Sigma-Aldrich and used without further purifications unless otherwise stated.
Deionized water was obtained from a Barnstead Nanopure system with a resistivity of ρH2O ≥
18.0 MΩ • cm. Sulfuric acid (ACS reagent), potassium sulfate (K2SO4, ≥ 99%), and various
S7
chemicals as redox couples: hydroid iodic acid (HI, 57% in water, destabilized, 99.999%),
calcium iodide (CaI2, 99%), iodine (I2, ≥ 99.8%), potassium ferricyanide (K3[Fe(CN)6], 99%),
potassium ferrocyanide (K4[Fe(CN)6] • 3H2O, 98−102%), hexaammineruthenium (II)/(III)
chloride (Ru(NH3)6Cl3, 98% / Ru(NH3)6Cl2, 99.9%) and iron (II)/(III) sulfate (FeSO4 • 7H2O,
99% / Fe2(SO4)3, 97%), were mixed in appropriate ratios to make the electrolyte solutions. The
redox couple iron (II)/(III) phenanthroline (Fe(phen)32+/3+) was prepared by ligation of the
respective iron sulfate with 1,10-phenanthroline (≥ 99%) in 1 M sulfuric acid. The standard
reduction potentials of the redox couples were experimentally determined using Pt wire as the
working electrode and Hg/HgSO4 as the reference electrode. All redox potential reported in the
main text were converted to the normal hydrogen electrode (NHE) scale.
Non-Aqueous: The acetonitrile (99.8% anhydrous) used in the non-aqueous electrochemical
measurements was vacuum distilled using calcium hydride (Acros Organics) as the drying agent.
Ferrocene (Fc, 99%, Strem), ferrocenium tetraflouroborate (Fc[BF4], technical grade), and 1-1’dimethylferrocene
(DFc,
pentamethylcobaltocene
95%)
were
(CoCp2*)
used
were
as
received.
purified
by
Cobaltocene
sublimation.
(CoCp2)
and
Cobaltocene
hexaflourophosphate (CoCp2[PF6], 98%) and pentamethylcobaltocene hexaflourophosphate
(CoCp2*[PF6], 98%) were recrystallized from a hot ethanol/acetone mixture and dried under
vacuum. Dimethylferrocenium (DFc+) was generated in-situ via electrochemical oxidation of
DFc.
The
supporting
electrolyte
tetrabutylammonium
perchlorate
(TBAP,
≥
99%,
electrochemical analysis grade) was used as received. The standard reduction potentials of the
redox couples were experimentally determined using Pt wire as the working electrode and a
home-built electrode composed of Ag/0.01M AgClO4 with 0.1 M TBAP/acetonitrile filling
solution as the reference electrode. The Ag/0.01M AgClO4 reference electrode was prepared and
S8
calibrated against Fc0/+ on a daily basis, then all of the redox potentials were reported relative to
the NHE scale. All non-aqueous J-V measurements were taken using a custom-made sealable 4neck glass cell with vertical ports for the working electrode and Si photodiode, for in situ light
intensity calibration. The electrochemical cell was assembled in an argon-filled glove box using
compression Teflon fittings to preserve an air-tight sealed inert atmosphere. Then, the
electrochemical cell was taken outside and measured.
I.11 Electrochemical Impedance Spectroscopy. Electrochemical impedance spectroscopy
(EIS) were performed using a Bio-Logic SP-200 potentiostat in a three-electrode configuration
with a Pt mesh as counter electrode and a home-built Ag/0.01 M AgClO4 reference electrode.
The electrolyte used was 0.1 M tetrabutylammonium perchlorate (TBAP, ≥ 99%,
electrochemical analysis grade) solution in acetonitrile (vacuum distilled as previously stated),
which was also used as the filling solution for the reference electrode. The EIS measurements
were taken using a single sine wave with an amplitude of 10 mV, which was scanned in the
frequency range of 5 MHz to 1Hz. The waiting time between frequencies was 0.10 period and
each individual frequency data point is the average of three measurements. The cell DC bias was
scanned between -0.5 V to 1.5 V vs Ag/0.01M AgClO4 for a total of 180 potential steps which
were taken in succession after the completion of a frequency sweep. The fitting results for the
proposed circuit model were obtained by fitting the experimental data in succession from
cathodic to anodic applied potentials using a simplex algorithm.
S9
II.
ADDITIONAL FIGURES AND DISCUSSION:
II.1 Surface Photovoltage (SPV) Setup and the SPV Tauc plot.
a
b
Figure S1. (a) Instrumental setup illustrating the surface photovoltage signal pathway. (b)
Transient photocurrent for an electrochemically cleaned {100}-faceted iron pyrite single crystal.
The SPV signal for iron pyrite single crystals was experimentally determined to be
proportional to the absorption coefficient (α) by fitting the photoinjected current (Qph) using the
band-to-band optical absorption equation: (hv Qph) = B(hv - Eg)1/n where B is assumed to be
constant, as shown in Figure 3c, d insets in the main text. Based on the fitting results for n, SPV
Tauc plots were constructed (Figure 3c, d in the main text).
II.2 Additional Details of the Pump-Probe Spectroscopy of Pyrite Crystals
S10
Figure S2. Reflective pump probe power study on a {100}-faceted iron pyrite single crystal: (a)
Pump power is changed while probe power is kept constant. Energies given are per pulse. (b)
The maximium values from panel a are plotted against pump energy with the best proportional
fit. (c) Reflective pump probe spectroscopy measurement on a natural pyrite crystal and the
corresponding exponential decay fit.
II.3 Impact of Mechanical Polishing and Surface Treatments on the Photoelectrochemical
Performance of Pyrite Crystals
Figure S3. The J-V curves under dark (green curve) and simulated 1 Sun (100 mW/cm2) (blue
curve) for a {100}-faceted iron pyrite after mechanical polishing (using alumina slurries of 1 µm,
100 nm, and 50 nm) followed by HNA etching. Note that the blue curve is almost completely
overlapped with the green curve. The pyrite electrode showed metallic-like behavior with no
photoresponse during illumination. After electrochemical cleaning (see procedures in SI Section
I.4), the photoactivity of the electrode was restored (red and black curve).
II.4 Comparison of XPS Sulfur 2p Peaks between Iron Pyrite and Cobalt Pyrite Films
S11
Figure S4. XPS sulfur 2p peak analysis for (a) iron pyrite (FeS2) and (b) metallic cobalt pyrite
(CoS2) polycrystalline thin films after electrochemical cleaning, when measured using a XP
spectrometer with source-to-analyzer angle (α) geometries of 45° (~60° angular acceptance) and
90° (~4° angular acceptance), using an Al Kα source. The pyrite films were synthesized by
thermal sulfidation of the corresponding metal films.S3 For α = 45° geometry the observed sulfur
species are almost identical for both pyrite structures with the exception of the shoulder peak
observed at low binding energy, which has a core level shift (CLS) with respect to bulk disulfide
of 0.8 eV for iron pyrite and 1.2 eV for cobalt pyrite. On the other hand, at α = 90°, dramatic
differences in photoemission anisotropy among chemical species revealed the presence of the 1.2
eV CLS sulfur species in iron pyrite. Considering that iron pyrite is a semiconductor and cobalt
pyrite is a metal, the presence of the 0.8 eV CLS sulfur species only in iron pyrite suggests that
the CLS of these species is caused by the space charge region (band bending), in other words due
to the difference between the bulk and surface Fermi level (i.e. the barrier height). Therefore, the
0.8 eV CLS sulfur specie observed in iron pyrite for α = 45° geometry can be identified as the
S12
outermost surface disulfides (S22-), while the 1.2 eV CLS sulfur species observed for both pyrite
films can be identified as monomeric sulfurs (S2-).
II.5 Complete Analogous Circuit Model for EIS Analysis
Figure S5. (a) Complete analogous circuit model for the wide frequency range of 250 kHz−1 Hz
for the EIS analysis of the {100}-faceted iron pyrite single crystals. Nyquist impedance plots for
the observed high frequency (b) and medium frequency (c) response at a representative applied
potential (DC) of 0.39 V vs Fc0/+. The high frequency arc can be attributed to the free carrier
chemical potential (Cµ) which was observed to change weakly with applied voltage. On the other
hand, the medium frequency (2.2 kHz−1 Hz) response in panel c can be attributed to the defect
state response, from which the ionization of the deep donor states results in the formation of the
abrupt space charge region. Therefore, to study the space charge region we focus on the medium
frequency response, which allows the simplification of the analogous circuit model by ignoring
the contribution of the chemical capacitance (Cµ) to the circuit model shown in Figure 8b of the
main text.
S13
II.6 Bulk and Surface Defect State DOS from EIS Analysis
Figure S6. Density of states (DOS) for the (a) bulk deep donor and (b) surface states calculated
form the EIS results of CDS vs V using Eq. 9 from the main text. Note that for the auxiliary x-axis
on the top the conduction band (EC) and valence band (EV) edges were defined as EC = 0 and EV
= Eg. Peak fitting was performed using a Gaussian function of the form: + (0.5(( )/) ). The area density of surface states was calculated to be NA = 1.4 × 1015 cm-2 from the
peak area using the equation: ⋅ 2 ⋅ /2. The energy position of the surface states (EA)
was estimated to be EA = 1.12 eV using the peak center.
II.7 Poisson Equation and Graphical Method.
In order to theoretically evaluate the properties of the intrinsic space charge region for the
{100}-faceted iron pyrite single crystals, we utilized the Poisson equation:S4
()
ψ (S1)
! !
where ψ is the internal potential, x is the distance from the surface, E is the electric field, ρ(x) is
the net charge density distribution, ε0 is the permittivity of free space, ε is the dielectric constant
of iron pyrite.
Based on the experimental results discussed in the main text, donors and
acceptors are spatially separated between bulk and surface, respectively. The bulk is dominated
S14
by a high density of deep donor states (~ 1020 cm-3) and bulk acceptor states can be neglected
since no evidence for them was found, either due to their absence or net auto-compensation with
donor states. The outermost surface can be considered as an acceptor-like state, given the
characterized acceptor state density of 1015 cm-2 (in comparison to the iron atom density of 7 ×
1014 cm-2 on the {100} surface of pyrite). Thus, the charge equilibration with the bulk is
analogous to a junction between two distinct electronic structures. Consequently, when
evaluating the space charge we can simply consider only their contribution to surface Fermi level
pinning at the valence band edge. Therefore, the corresponding Poisson equation for the iron
pyrite single crystals can be simplified to:
()
$ ψ %p() n() + ND+()((S2)
! !
! !
where V is the applied potential, x is the distance from the surface, e is the elemental charge, p(x)
is the distribution of holes, n(x) is the distribution of electrons, and ND+ is the distribution of
ionized deep donor states. The distribution of electrons (n) and holes (p) for Fermi level energies
within band gap can be described using the Maxwell-Boltzmann approximation:
) * exp +
,- .,/
01
2 , 4 exp +
,5 .,/
01
2(S3)
(Note we here define EC = 0 and EV = Eg since the activation energy for donor states was
experimentally measured with respect to the conduction band). While the ionization of deep
donor states can be described using a Fermi-Dirac distribution:
789: (; ) <= (; ) <
1 + >< +
,/ .,9 (S4)
2
01
Figure S7a shows a representation of the charge distribution using the graphical method. The
parameters utilized are summarized in Table S1. From the charge neutrality condition n = p +
S15
ND+, a free carrier concentration of 2 × 1015 cm-3 was obtained, which is in agreement with the
free carrier concentration obtained from the room temperature Hall measurement (Figure 2c,
main text). Furthermore, the charge neutrality condition demonstrates the agreement between the
electrical transport measurements (Figure 2, main text) and the results obtained from the EIS
circuit model fitting analysis (Figure 9, main text). Most importantly, Figure S7a shows two
significant deviations from classical behavior. Firstly, the net charge density in the space charge
region cannot be considered as constant until the deep donor states are ionized. Therefore, an
abrupt junction cannot be defined until the Fermi level is at the half occupancy of the deep donor
states (F1/2) which can be defined based on a Fermi-Dirac distribution (Eq. S4) as:
7@/ (< ln(1/>< ) BC)
(S5)
Secondly, for Fermi level energies within the band gap (EC ≤ EF ≤ EV), the concentration of holes
(p) is always smaller than ND+. The implication of this dependence is that the space charge
region will not reach an exponential dependence following the population of holes given by Eq.
2. Thus, the space charge region will only reach a weak inversion condition when the surface
Fermi level is pinned at the valence band edge.
Figure S7. (a) Representation of the charge concentration as a function of Fermi level energy
using the graphical method. Equation S3−5 and parameters in Table S1 were used for the
S16
construction of this plot. The bulk Fermi level is represented as EF and the intrinsic level as ni.
(b) Absolute value of the area charge (DEF |DF* |) in the space charge region as a function of
Fermi level energy, obtained by numerical integration of equation S6 and using equation S7.
Table S1: Parameters utilized in the Poisson equation. NC, NV, and ε were obtained from
previous report.S1 EC and EV were defined for convenience. ED was obtained from the electrical
transport properties, while ND was obtained from the electrochemical impedance spectroscopy
fitting results. For gD we utilized a previously proposed ligand field model for sulfur vacancies as
an estimate.S5
Parameters
NC (cm-3)
EC (eV)
NV (cm-3)
EV (eV)
Eg (eV)
ND (cm-3)
ED (eV)
gD
ε (pyrite)
Values
3.0 × 1018
0
8.5 × 1019
0.83
0.83
2.1 × 1020
0.452
4
10.9
The space charge dependence can be illustrated by plotting the area charge (QSC) as a function
of Fermi level energy. Through the integration of the Poisson equation (Eq. S2), the electric field
(E) can be related with the net charge density as a function of potential (ρ(ψ)):
KL
KM
L
I
I
1
I
H
J( ) H (I)I ; where ! !
N
L
1
H (I)I (S6)
2
! !
S17
The electric field (E) was obtained by numerical integration using Eq. S3−5 and the parameters
in Table S1, which was then used to calculate the area charge (QSC) utilizing the Gauss’s Law:
DF* ! !
(S7)
Figure S7b shows the absolute value of the area charge (DEF |DF* |) as a function of Fermi
level energy, from which a classical depletion dependence of Q ~ (EC + EF)1/2 (based on an
abrupt junction) is observed only after EF = F1/2. Therefore, the space charge can be divided into
two regions: a non-constant space charge region where the charge distribution is dependent on
the ionization of deep donor states (Eq. S4); and an abrupt space charge region where the charge
distribution can be consider as being a constant, specifically as ND. Due to a high density of
ionized donor states, the abrupt space charge region has a very narrow width. Consequently,
when the surface Fermi level is pinned at the valence band edge, the formation of an abrupt
surface space charge region introduces a tunneling region that limits the barrier height. A general
expression for the barrier height (ΨN) or idealized open circuit voltage (VOC) in the presence of
deep donor states with concentration of ND ≥ NC, NV; can be defined as (with EC = 0 and EV =
Eg):
Ψ8 (< ln(
1
)BC) ; (TUVB)(S8)
><
Additionally, Figure S7b shows no strong inversion region within band gap energies, since the
area charge does not reach a dependence of Q ~ exp (EC + EF). Therefore, Figure S7b confirms
that only a weak inversion dependence is achieved when the surface Fermi level is pinned at the
valence band edge.
II.8 Mott-Schottky Equation for Deep Donor States.
S18
The classical Mott-Schottky equation allows the determination of carrier concentration and
flat band potential, under the assumption of shallow states as dopants.S6 In contradiction to this
classical assumption, a high density of deep donor states (ND ≥ NC, NV) was observed for the
{100}-faceted iron pyrite single crystals. Thus, a new expression must be obtained for a
semiconductor with deep donor states as dopants. The Mott-Schottky equation for a high density
of deep donor states can be obtained by solving the Poisson equation (Eq. S2) utilizing equation
S6. As discussed above, a space charge region based on an abrupt junction can only be assumed
to form for Fermi level energies beyond the half occupancy of the deep donor states (F1/2) (Eq.
S5). Within this region the deep donor states can be assumed to be fully ionized, thus ND+ = ND.
Furthermore, the concentration of holes at the valence band can be ignored since it magnitude
does not overcome the concentration of ionized donor states ND+. Therefore, Eq. S6 can be
solved by integrating from F1/2 (Eq. S5), assuming ρ(ψ) = ND+, and substituting ND+ by ND:
K4
KM
H
K4
X Y;Z/[ KM
$
$
J X Y ! !
4
H < J$
4(;Z/[ )
(7@/ )
%$ (< ln(1/>< ) BC)((S9)
2
2
! ! <
Since the electric field (E) is orders of magnitude larger for Fermi level energies beyond F1/2, the
term E2(F1/2)/2 can be ignored. Then using Eq. S7 the capacitance (CSC) can be obtained by
taking the derivative of the area charge (QSC) with respect to voltage:
]F* DF*
(S10)
$
From this the Mott-Schottky relationship for a high density of deep donor states can be obtained:
S19
1
2
(< ln(1/>< ) BC)((S11)
(! ! )%$ ]F*
<
From Eq. S11 a linear relationship is obtained for 1/CSC2 vs V with a slope corresponding to the
concentration of deep donor states and an x-intercept that corresponds to the half occupancy of
the deep donor states (F1/2, Eq. S5).
Simulated 1/Csc2 vs V for the abrupt space charge region. The validity of the Mott-Schottky
relationship derived for deep donor states (Eq. S11) can be verified by simulating a plot of 1/CSC2
vs V using Eq. S6, 7, 10. These equations were solved by numerical substitution using
parameters in Table S1. Figure S8 shows the simulated 1/CSC2 vs V plots when assuming the
charge density as ρ(ψ) = e (ND+) and ρ(ψ) = e (p + ND+ − n). In both cases a linear regime is
observed, with a slope corresponding to the deep donor state concentration and an x-intercept
that corresponds to the half occupancy of the deep donor states (F1/2, Eq. S5). Therefore, Figure
S8 validates the derived Mott-Schottky relationship for deep donor states. Furthermore, Figure
S8b shows a change in slope (plot maximum) corresponding to the transition into a weak
inversion region. Thus, the simulated 1/CSC2 vs V plots also support the analysis of the EIS circuit
model fitting results for iron pyrite single crystals (Figure 9, main text).
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Figure S8. Simulated 1/CSC2 vs V plots using (a) ρ(ψ) = e ND+, and (b) ρ(ψ) = e (p + ND+ − n) as
charge density. The plots were generated by solving Eq. S6, 7, 10 through numerical substitution
using parameters in Table S1. Note that the accuracy of the derived Mott-Schottky relationship
improves with wider band gap energies.
Simulated 1/Csc2 vs V for the abrupt space charge region in the inversion regime. To
validate our analysis of the EIS fitting results in the inversion region, we simulated a plot of
1/CSC2 vs V for Fermi level energies beyond the valence band edge (EV). Within this regime the
population of holes can be described using the zero Kelvin approximation for the Fermi-Dirac
distribution, commonly used for degenerated semiconductors:S4
∗b/
2√2 _`
3 ℏ
(4 ; )b/ (S12)
where _`∗ is the effective hole mass, reported to be _` 2.2 ∙ _e . Figure S9a shows the
simulated 1/CSC2 vs V plot when assuming the charge density as ρ(ψ) = e (p + ND+ − n), from
which a change in dependence can be observed at the valence band edge energy (EV). Thus,
Figure S9a provides theoretical evidence to support the assignment of the valence band edge
potential for the EIS fitting results of the iron pyrite single crystals (Figure 9b, main text).
Furthermore, when contribution of surface acceptor states is considered, i.e. ρ(ψ) = e (p + ND+ −
n − NA−), no significant difference was observed for the simulated 1/CSC2 vs V plot (Figure S9b).
S21
Figure S9. Simulated 1/CSC2 vs V plots using (a) ρ(ψ) = e (p + ND+ − n), and (b) ρ(ψ) = e (p +
ND+ − n − NA−) as charge density. The plots were generated by solving Eq. S6, 7, 10 through
numerical substitution using parameters in Table S1. For Fermi level energies beyond the
valence band edge (EV), Eq. S12 was used for the population of holes. To describe the ionization
of the surface acceptor states (NA) a Fermi-Dirac distribution was utilized (analogous to Eq. S4).
The parameters utilized were obtained from Figure S6b: acceptor state density of NA ~ 1 × 1015
cm-2/0.5 unit cell ~ 1 × 1022 cm-3 with energy position EA ~ 1.1 eV. A triply degenerated valence
band (Fe 3dt2g) was used as the degeneracy (gA).S7
Simulated Band Bending Scheme. Using the calculated space charge capacitance for iron
pyrite single crystals a band bending scheme can be simulated by defining the barrier height (Ψ)
as the difference between bulk and surface Fermi level (Ψ = EF (Bulk) − EF (Surface)) and calculating
the distance from the surface (x) using the ideal capacitor equation:
! ! ⁄]F* (S13)
Figure S10a shows the profile for the space charge region, which shows that most of the
change in the barrier height (band bending) occurs within 5−10 nm away from the surface. Such
sharp surface band bending is a result of the charge density induced by the complete ionization
S22
of the deep donor states. Figure S10b is a schematic illustration of the charge density distribution
in the space charge as a function of the distance from the surface. The space charge can be
divided into two regimes: a non-constant region where the charge distribution follows the
ionization of deep donor states (Eq. S2), and an abrupt region where the charge distribution is
constant (~ ND). The abrupt space charge region introduces a sharp band bending at the surface
that results in a tunneling region and limits the usable barrier height. Figure S10b also illustrates
the charge distribution for surface states. The space charge region and acceptor states have
different signs for ionized charges which are spatially separated. The spatial separation can be
approximated as the distance between two Fe atomic planes, in other words half a unit cell
(a/2).S7 Thus, the charge neutrality condition under equilibrium conditions is defined as QSC = –
QSS. This charge separation results in an interfacial dipole. Changes in the surface charge density
(– QSS) are responsible for the observed energy band unpinning (changes in work function) in the
photoelectrochemical experiments (Figure 5b in the main text).
The resulting simulated band bending scheme (Figure S10) also provides further evidence to
support the XPS analysis in Figure 7 of the main text, since it demonstrate that most of the band
bending occurs within a scale comparable to the escape depth of photoemitted S2p electrons for
the experimental parameter used in the XPS measurements. Therefore, a core level shift (CLS)
for the binding energy between surface and bulk species is expected to be caused by the field in
the space charge region.
S23
Figure S10. (a) Theoretical band bending diagram for the {100}-faceted iron pyrite single
crystals showing the non-constant and abrupt space charge regions. The plots were generated by
solving Eq. S6, 7, 10 through numerical substitution using parameters in Table S1. The total
space charge width or distance from the surface was calculated using Eq. S13. The edge of the
space charge region (vertical green dash line) was further refined using the experimental value
for the non-constant space charge width (WN), to account for the region where the free electrons
contribute to the charge distribution and electric field (space charge fall-off) as defined in the
depletion approximation. (b) Schematic illustration of the charge distribution in the space charge
region as a function of the distance from the surface (x). Note that for illustrative purposes the
axes are not to scale. The space charge region and acceptor states are spatially separated by ~
half a unit cell (a/2).S7
III. Supporting References:
(S1) Altermatt, P. P.; Kiesewetter, T.; Ellmer, K.; Tributsch, H. Sol. Energy Mater. Sol. Cells
2002, 71, 181-195.
(S2) Ennaoui, A.; Fiechter, S.; Pettenkofer, C.; Alonso-Vante, N.; Büker, K.; Bronold, M.;
Höpfner, C.; Tributsch, H. Sol. Energy Mater. Sol. Cells 1993, 29, 289-370.
(S3) Faber, M. S.; Lukowski, M. A.; Ding, Q.; Kaiser, N. S.; Jin, S. J. Phys. Chem. C 2014, 118,
21347.
(S4) Sze, S. M. Physics of Semiconductor Devices; John Wiley & Sons, 1981.
S24
(S5) Bronold, M.; Pettenkofer, C.; Jaegermann, W. J. Appl. Phys. 1994, 76, 5800.
(S6) Memming, R. Semiconductor Electrochemistry; Wiley-VCH, 2001.
(S7) Bronold, M.; Tomm, Y.; Jaegermann, W. Surf. Sci. 1994, 314, L931-L936.
S25