The Impact of Bulk Trapping Phenomena on the Maximum Attainable

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C: Energy Conversion and Storage; Energy and Charge Transport

The Impact of Bulk Trapping Phenomena on the Maximum Attainable Photovoltage of Semiconductor-Liquid Interfaces Asif Iqbal, Shuaishuai Yuan, Zi Wang, and Kirk H. Bevan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06854 • Publication Date (Web): 02 Oct 2018 Downloaded from http://pubs.acs.org on October 6, 2018

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The Journal of Physical Chemistry

The Impact of Bulk Trapping Phenomena on the Maximum Attainable Photovoltage of Semiconductor-Liquid Interfaces Asif Iqbal,∗ Shuaishuai Yuan, Zi Wang, and Kirk H. Bevan∗ Division of Materials Engineering, Faculty of Engineering, McGill University, Montréal, Québec, Canada E-mail: [email protected]; [email protected]

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract In this work, we present a generic semiclassical approach for theoretically evaluating the impact of bulk trap states on the maximum attainable photovoltage in solar-assisted water splitting reactions. Our method explicitly considers the charge contribution due to the capture and emission of conduction band electrons and valence band holes by trap states situated in the bandgap, integrated within a self-consistent solution procedure for calculating electrostatic and charge transport properties. Utilizing the hematite photoanode as our model system, our approach reveals that bulk trap states may significantly degrade both the maximum attainable photovoltage and the concentration of mobile electrons (majority carriers) in the conduction band. These results, suggest that bulk trap states can have two primary consequences in photoanodes. First, they may limit the degree to which a favourable cathodic shift in the photocurrent can be achieved (by lowering the maximum attainable photovoltage). Second, they may impede the extraction of majority carriers at the bulk-electrode contact (by lowering the conduction band carrier concentration). Both of these phenomena are commonly observed in the state-of-the-art hematite photoanodes. Our semiclassical analysis is further supported by first-principles calculations of hematite, which suggest that electron polarons impact adversely upon the maximum attainable photovoltage of oxide photoanodes. In general, this work underscores the importance of engineering the bulk electronic properties of photoelectrodes, and is intended to further assist the design of photoanodes en route to low cost unassisted solar water splitting.

1

Introduction

In recent years, there has been a resurgence of water splitting research seeking to convert intermittent solar energy into storable eco-friendly chemical fuels such as H2 . 1–3 By utilizing inexhaustible solar energy and earth-abundant materials, photocatalytic based water splitting aims to provide large-scale and economical green fuel production. 4,5 Consequently, photocatalytic semiconductor-liquid (SL) junctions comprised of earth-abundant metal-oxides 2


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capable of solar-assisted water splitting (e.g., TiO2 , α-Fe2 O3 , BiVO4 , WO3 ), are currently considered an important component en route to low-cost H2 production. 6–8 In the same spirit, a large body of research has been directed towards understanding the key bottlenecks that impede the realization of efficient low-cost water splitting in such photoelectrodes. 1,6 It is now widely accepted that economical water splitting photoelectrodes can only be realized by combining experimental and theoretical efforts, with the aim of unraveling the fundamental processes governing artificial photosynthesis. 2 Research work in this area has generally attributed several physical mechanisms to the limited photocatalytic performance of oxide photoanodes, including: (1) extraordinarily short minority carrier collection lengths (often on the order of few nm); (2) comparatively low light absorption coefficients; (3) high rates of electron-hole recombination at the surface and in the bulk; and (4) the sluggish rate of interfacial carrier transport/reactions. 7–11 Efforts to improve photoelectrochemical (PEC) performance have primarily focused on engineering the SL interfacial region of photoanodes – i.e., where the photogenerated “minority” carriers are collected and subsequently transferred to the liquid environment. 12–14 This makes sense, since improved interfacial hole transfer in photoanodes translates into superior solar-to-chemical fuel production yields. 14,15 Conversely, the impact of bulk processes on the efficiency of photoanodes has not been as widely explored in the literature. However, as emphasized by Wang and co-workers, 9–11 the goal of economical unassisted solar water splitting can only be accomplished through the simultaneous enhancement of the photocurrent (through improved minority carrier collection and transfer) and the photovoltage (through efficient generation of the photogenerated majority and minority carriers in the semiconductor bulk). Interestingly, this key experimental observation is in agreement with results obtained from recent semiclassical modeling advances in the description of photocatalytic SL junctions. 16–19 Moreover, both of these conditions can only be achieved through minimal trapping, reduced recombination, and superior carrier extraction in the bulk. The photovoltage (Vph ), a thermodynamic quantity arising due to electron-hole pair gen-

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eration, is coupled with the photocurrent (Jph ) extracted from an anodic SL junction. 9–11,20–22 In practice, the maximum attainable photovoltage (Vph|max ) at an anodic SL junction is a highly important metric, since Vph provides an essential cathodic shift in the onset of the anodic photocurrent. 9–11,20 This is important because a sufficiently large cathodic shift towards the H2 evolution potential can enable unassisted water splitting. 9–11,20 Crucially, poor carrier transport properties in metal-oxide semiconductors (such as low bulk conductivity, trapping, and inefficient carrier extraction at the back contact) are often linked to a degradation in Vph . 23–26 For example, experimental studies on hematite photoanodes have demonstrated that bulk trap states impact upon on the measured photocurrent density of photoanodes. 23,27 In extreme cases, the complete absence of a photocurrent coupled with a negligible or vanishing photovoltage has also been reported in the literature. 27 Others have associated the formation of a “dead-layer” near the back contact of photoanodes to defect states generated due to lattice mismatch between the photocatalytic material and the underlying substrate. 26 Likewise, small-polaron conduction properties, as well as the dynamics of the intermediate defect states inside the band gap, have been correlated with the poor electron transport properties often exhibited by metal-oxide semiconductors. 25,28–35 Additionally, the doping behavior of extrinsic impurities (i.e., activation of the dopants) 26,36 in metal oxides and the optimal structuring of nano-electrodes for the transport of carriers, remain pressing questions that impact upon bulk processes. 23,37 All of these observations underscore the need for a deeper experimental and theoretical understanding of how bulk processes impact upon the performance of water splitting photoelectrodes. In this work, we present a theoretical study aimed at understanding how bulk trap states may impact upon the maximum attainable photovoltage (Vph|max ) and the majority carrier transport properties of photoanodes. Our analysis extends the trapping/detrapping theoretical methodology developed for solid-state semiconductor devices 38–43 into the domain of water-splitting photoanodes. From this we are able to theoretically explore how trap densities and distributions impact upon: band bending electrostatics, the populations of free

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and trapped carriers, the maximum achievable Vph|max , etcetera. The role of both acceptor and donor type trap states state are evaluated in this manner. Using this methodology, it is shown that bulk trap states can significantly lower the maximum attainable photovoltage (Vph|max ) and therefore significantly impede a desirable cathodic shift in the photocurrent (for unassisted solar water splitting). It is also demonstrated that trap states can substantially lower the number of band carriers and thereby detrimentally impact upon bulk conductivity (a significant factor in limiting the overall photocurrent). These findings are further supported by first-principles calculations, which suggest that electron polarons may adversely impact upon the maximum attainable photovoltage of oxide photoanodes, as well as experimental observations reported in the literature. In a nutshell, this work underscores the importance of bulk engineering of photoanodes, through the minimization of carrier trapping, when designing PEC devices.

2 2.1

Method Idealized Semiconductor-Aqueous Junctions

To begin with, let us briefly revisit the ideal band diagram alignment of a photocatalytic SL junction as shown in Fig. 1 – consisting of a perfectly crystalline semiconductor (without any bandgap states) and an aqueous solution with pH > 7. 16–18 Here, the semiconductor is assumed to serve as a photoanode (n-type) performing solar-assisted water oxidation. 1,6 All photoelectrochemical reactions are assumed to occur at the semiconductor-aqueous interface, namely, the oxygen evolution reaction (OER) and oxygen reduction reaction (ORR). 44–46 To simplify our analysis, we have assumed that the photoanode is robust against corrosion and only electrochemically active to OH− /O2 species. 16,44 Therefore, in our model, the liquid Fermi-level (EL ) is solely determined by OH− /O2 species and is aligned with the electron (EF n ) and hole (EF p ) quasi-Fermi levels when the junction is resting in the dark, which is illustrated in Fig. 1a. 16,17 This is known as the open circuit condition or “OCC 5


(a)

Photoanode: n-type (dark) Vbi EC

-

- - - - - - - -

+

(Bulk)

+

+ k t,p

(SCR)

EFn

Vph≈Vbi

EL (OH-/O2)

OH-

EV

O2

(TCO)

(Liquid)

-

EFp

+ + + + +

(Bulk)

+

Eref (H+/H2)

OHkt,n

Photocatalytic Interface

EV +

+

EC - - - - - - - - Bulk Photoandoe / Substrate Interface

Bulk Photoandoe / Substrate Interface

EG

Eref (H+/H2)

OHPhotocatalytic Interface

EFn = EFp

(TCO)

kt,n O2

(b)

Photoanode: n-type (illuminated)

O2 EL (OH-/O2)

OH-

kt,p

O2 (Liquid)

Figure 1: Idealized band-diagram alignments of a crystalline semiconducting photoanodeaqueous junction under (a) dark and (b) illuminated conditions, with no externally applied potential and in the absence of carrier trapping. 9,16,22 Schematic (a) represents the opencircuited SL junction at equilibrium (OCC dark) and therefore, EF n = EF p = EL . 16,44 Due to the electric-field in the SCR, photoexcited carriers are separated and driven in opposite directions. Schematic (b) displays the open-circuit SL junction under solar illumination (OCC under illumination). Here, the photoanode maximizes Vph , which is achieved by suppressing Vbi and is characterized by a near complete flattening of the semiconductor bands. QuasiFermi level splitting also occurs under illumination. at dark” and characterized by zero interfacial current (J = 0). Throughout our discussion, we utilize the reversible hydrogen electrode (RHE) as the reference electrode (marked as Eref in Fig. 1), which sets EL at +1.23 V vs. RHE. 1,47 In addition, the SL junction is characterized by the formation of a built-in potential (Vbi ) that is distributed throughout the span (Lscr ) of the space charge region (SCR). Here, Lscr provides a rough estimate of the the hole collection distance in this PEC configuration. Conversely, the bulk of the electrode is characterized by a quasi-neutral region, and an interface between the photoanode and substrate [e.g., transparent conductive oxide (TCO)]. 14,27 Finally, kt,p and kt,n represent the rate of interfacial hole and electron transfer leading to the OER (desired water oxidation reaction) and ORR (undesired, backward reaction), respectively. 16,44 Under solar illumination, as shown in Fig. 1b, the SL junction exhibits the photogeneration of electron-hole pairs (depicted by the splitting of EF n and EF p ) and a photovoltage (a thermodynamic quantity, directly related with the Gibbs free energy of the photogenerated 6

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electron-hole pairs). 21 The photovoltage (Vph ) is usually detected experimentally via various “flatband” measurements related to semiconductor band flattening. 9,20–22 One of the essential design goals of unassisted solar-water splitting, as experimentally demonstrated by Wang and co-workers, 9–11 is to maximize Vph under the open circuit condition (also known as the open circuit voltage or Voc ) – since a larger Vph increases the cathodic shift in the onset of the photocurrent. However, the maximum value of Vph is intrinsically limited by the magnitude of Vbi , which represents the offset between the flatband condition under illumination and band bending in the dark (compare Figs. 1a and 1b). 9,20–22,46,48–50 The schematic band alignment in Fig. 1b illustrates this particular situation (open circuit condition or ‘OCC under illumination’), where the illuminated photoanode is operated at the flatband potential without any external bias source and the generated photovoltage approaches its maximum limit of Vph|max ≈ Vbi . Nevertheless, the generation of Vph|max (Fig. 1a → Fig. 1b) entails the efficient separation of the photogenerated electrons and holes by directing them oppositely inside the semiconductor. 16,48 Holes are collected at the anodic semiconductor-aqueous interface, whereas the electrons are collected at the substrate/electrode back contact in the bulk (see also Fig. 1). 24 Lastly, the photocurrent (Jph ) will depend on how quickly interfacial holes are transferred to reactants – a kinetic constraint where rapid hole transfer produces a high yield and sluggish hole transfer produces a low yield for solar-to-chemical conversion. 15–18 Importantly, the concept of Vph|max = Vbi is frequently mentioned in earlier work by considering photoelectrodes comprised of a crystalline semiconductor. 21,49–51 Crucially, carrier trapping by defect states inside the semiconductor bandgap can dramatically lower Vbi and consequently Vph|max , thereby reducing the much needed cathodic shift in Jph towards unassisted solar water splitting. Trap states can also dramatically lower the number of free carriers available to carry current from the SL interface into the bulk/electrode region (and thereby also limit Jph ). We shall explore both of these aspects in the next section.

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2.2 2.2.1

Semiconductor-Aqueous Junctions with Bulk Trapping Modeling Charge Trapping inside Semiconductors

Up to now, in our discussion of semiconductor-liquid junctions in Sec. 2.1, we have assumed an idealized semiconducting photoanode that is perfectly crystalline and therefore free from any intermediate trap states lying in the bandgap. However, in practice, semiconductors may contain trap states inside the bandgap that capture electrons from the conduction band and/or holes from the valence band. In the case of metal-oxide semiconductors, as discussed in the introduction, these intermediate states originate from: lattice mismatch between the substrate and photoanode, 23,26,27 morphological defects, 25,28,29 polaronic bound states, 30–35 oxygen vacancies, 54,55 extrinsic impurities, 36,56 etcetera. To understand the impact of such trap states on photoanodes, we shall utilize a semiclassical model describing the trapping/detrapping dynamics of intermediate bandgap states. The approach we employ was originally developed to understand the operation of solid-state semiconductor devices prone to trapping. 38,39,57 A particular example would be the simulation of silicon heterojunction solar cells. 58–60 Now, Fig. 2 presents a generic picture of carrier trapping/detrapping events by intermediate states. Here, we show trap states with both acceptor and donor characteristics inside a bandgap. Acceptor states are considered to be negatively charged when filled by electrons and charge neutral when empty. 53 This is shown in the upper inset of Fig. 2, where the acceptor states located below the Fermi level are occupied by electrons and therefore, contribute negative charge (ρT |A < 0). Conversely, the empty acceptor states located above the Fermi level remain charge neutral (ρT |A = 0). On the other hand, donor-type states (see the lower inset of Fig. 2) are positively charged if they contain holes (ρT |D > 0) and are considered charge neutral when filled by electrons (ρT |D = 0). 53 The exchange of carriers between bulk trap states and the semiconductor bands are represented by capture (trapping) and emission (detrapping) constants. These are respectively modeled by cn and en for electrons, and cp and ep for holes. 38–40 In terms of water-splitting

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(TCO)

EF = EFn = EFp

(Photoanode: n-type) EC

ρT|A = 0

ET|A

Filled

Energy

Empty

Acceptor-Type

ρT|A< 0

- - - - - - -

cn,A -

-

EFn = EFp

-

cp,D

Donor-Type

+ +

Empty

+

(Bulk)

ρT|D> 0 EF = EFn = EFp ET|D

Filled

EV

Energy

Bulk Photanode/ Substrate Interface

+

ρT|D= 0

Figure 2: Electron and hole capture/emission by trap states distributed in a semiconductor. With the inclusion of trap states, electron and hole transport deviates from that of an idealized crystalline semiconductor. 38–40 This is illustrated by the capture of mobile electrons and holes, which should be separated and collected at the substrate/electrode and photocatalytic SL interfaces, respectively. Depending on the nature of the trap states and the types of carriers captured, the electrons/holes trapped by these states may or may not contribute to the overall charge balance. 52,53 This is shown in the insets drawn for acceptor-type (upper) and donor-type (lower) states.

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photoanodes, the trapping and detrapping of photogenerated carriers represents a significant deviation from the ideal picture of the crystalline photoanodes discussed in the previous section. 6,24,25 To understand the degree to which trapping removes us from the idealized photoanode picture, we need to formally describe the distribution of carriers in the semiconductor bands and trap states. From this we shall be able to calculate their impact on the electrostatic potential (φ) and Vbi , by utilizing standard self-consistent numerical techniques, while conserving charge neutrality along the entire photocatalytic SL junction. 16,61 In this regard, the concentration of the mobile electrons in the conduction band (ncb ), by assuming non-degenerate carrier statistics, may be described by 41–43 EC (x, φ) − EF n (x) . ncb (x, φ) = NC exp − kB T

(1)

Similarly, pvb represents the mobile holes in the valence band and is given by 41–43 pvb (x, φ) = NV exp

EV (x, φ) − EF p (x) kB T

.

(2)

Here, both ncb and pvb explicitly vary with φ and the space vector x. Moreover, EC and EV are the conduction and valence band edges, kB is Boltzmann’s constant, and T is the temperature. Finally, NC and NV represent the effective density of states in the conduction and valence bands, respectively. Here, we considered non-degenerate carrier statistics, which is a common assumption in the state-of-the-art semiclassical modeling of photocatalytic SL junctions. 18,62,63 Furthermore, we have also considered the presence of both acceptor (gT |A ) and donor (gT |D ) states that are distributed in energy (E) between the valance band maximum (EV+ ) and conduction band minimum (EC− ). 39,40 Accordingly, by considering trap-assisted capture and emission processes leading to Shockley-Read-Hall (SRH) generation and recombination, the concentration of electrons captured by an acceptor state characterized by E, x

10


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and φ can be expressed as 38,40 cn ncb (x, φ) + cp p1 (x, E) , nT |A (E, x, φ) = gT |A (E) cn [ncb (x, φ) + n1 (x, E)] + cp [pvb (x, φ) + p1 (x, E)]

(3)

where,

E − EF i (x) n1 (x, E) = ni (x) exp kB T

(4)

and

EF i (x) − E p1 (x, E) = ni (x) exp kB T

(5)

respectively represent the concentrations of electrons and holes if the semiconductor Fermilevel falls at E. Where, EF i is the intrinsic Fermi level. Thus, the total charge contribution from a distribution of acceptor states is 40,52,53 − EC

Z ρT |A (x, φ) =

EV+

nT |A (E, x, φ) dE.

(6)

Similarly, the concentration of holes captured by a donor state located at energy E, position x and electrostatic potential φ is given by 38,40

cn n1 (x, E) + cp pvb (x, φ) pT |D (E, x, φ) = gT |D (E) , cn [ncb (x, φ) + n1 (x, E)] + cp [pvb (x, φ) + p1 (x, E)]

(7)

and the total charge provided by the distribution of donor states is expressed as Z ρT |D (x, φ) =

− EC

EV+

pT |D (E, x, φ) dE.

(8)

Finally, the net charge contribution from the distribution of bulk trap states of both acceptorand donor-type is computed as

ρT (x, φ) = ρT |D (x, φ) − ρT |A (x, φ) .

11


(9)


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In our analysis of ρT , we have approximated gT |A and gT |D to take a normal distribution with respect to energy (see Fig. 2), following state-of-the-art modeling efforts regarding trap states inside disordered semiconductors by the device physics community (e.g., amorphous silicon). 58–60 For instance, in our computation, gT |A is given by 60 " # ˜T |A E − ET |A 2 N exp − . gT |A (E) = √ WT |A π WT |A

(10)

√ Here, ET |A and WT |A / 2 respectively are the location of the peak and the standard devia˜T |A is the total number of acceptor-type trap states in tion of the distribution in eV, and N the bandgap in cm−3 . 60 Importantly, a normal distribution conserves the total number of ˜T |A ) even when the peak location and spread are altered. Consequently, this propstates (N erty allows us to investigate the impact of the same number of states as a function of their energetic location (shallow → deep) and/or spread (degree of localization). Similarly, gT |D , denoting the distribution of the donor-states, is expressed as 60 " # ˜T |D E − ET |D 2 N gT |D (E) = √ exp − , WT |D π WT |D

(11)

√ where, ET |D and WT |D / 2 respectively are the location of the peak and the variance of ˜T |D is the concentration of the donor-type trap states along the the distribution in eV, and N energy-axis. However, to systematically assess the influence of both acceptor-type and donortype trap states on the photoelectrochemical performance of photoanodes, we have defined three parameters. Firstly, ζ =

˜T N + ND

denoting the ratio of the total number of trap states with

˜T = N ˜T |A or N ˜T = N ˜T |D when acceptor respect to the ionized doping concentration, where N or donor trap states are examined, respectively. Secondly, fpeak =

ET −EV EG

representing the

location of the peak of the distribution as a fraction of bandgap energy referred from the valence band edge, where ET = ET |A or ET = ET |D when acceptor or donor trap states are examined, respectively. Thirdly, σs to characterize the energetic distribution of trap states,

12


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where WT |A = WT |D = σs × kB T and kB T ≈ 25 meV at room temperature. 2.2.2

Electrostatics of Photocatalytic SL Junctions with Bulk Trap States

By taking into account the net charge contribution from bulk trap states given by Eq. (9), the overall charge balance along the entire semiconductor-liquid junction can be expressed as ρsc + ρT + ρL = 0.

(12)

Here, ρsc = ND+ − NA− + pvb − ncb represents the charge contribution from the crystallinity of the semiconductor, where ND+ and NA− are respectively the concentrations of ionized impurities of donor and acceptor species (which always remain ionized due to their close proximity to the band edges). 41 Additionally, ρL is the charge in the liquid, balancing the charge in the semiconductor electrode and can be further broken down into 61

ρL = zn+ − zn− + cH + − cOH − .

(13)

[ − z (φ − φb )/kB T ] Eq. (13) is commonly known as the Gouy-Chapman model. 64–66 Here, n+ = c+ sup e [z (φ − φb )/kB T ] are, respectively, the concentrations of the electrochemically inacand n− = c− sup e − tive cations and anions forming the supporting electrolyte – where c+ sup and csup are their bulk

concentrations and z denotes the charge number. 61,64 Furthemore, cH + = c0H + e[ − (φ − φb )/kB T ] and cOH − = c0OH − e[ (φ − φb )/kB T ] , respectively, represent the concentrations of H+ and OH− ions in the liquid – again, c0H + and c0OH − are their bulk concentrations. Finally, φb is the electrostatic potential in the bulk of the liquid that is arbitrarily chosen as our electrostatic reference potential. With the aid of Eq. (12), Poisson’s equation for the SL junction can be written as 61 ε

d2 φ dε dφ + = − [ρsc + ρT + ρL ] . 2 dx dx dx

(14)

Where, ε is the dielectric constant that varies along the space vector x, since the semiconductor and liquid generally possess different values of ε. 1,47 Finally, the electrostatics of the 13



SL junction under dark can be obtained by numerically solving Eq. (14) using standard selfconsistent numerical techniques. 42,43,61 In particular, solving Poisson’s equation (Eq. (14)) in this manner treats the SL junction as “adaptive Schottky contact”, which allows the potential drop inside the liquid to change as a function of surface state charging, semiconductor doping and the applied bias. . Moreover, it enables one to capture both pinning and unpinning of the semiconductor band-edges at the solid-liquid interface. 16,61

3

Results

3.1

Crystalline Hematite Photoanode-Aqueous Junction

As a model system, we have considered an n-type hematite photoanode performing the water oxidation reaction. 24,25,67–70 Hematite (α-Fe2 O3 ) has been widely investigated for solarassisted water splitting applications due to its inexpensive synthesis, suitable bandgap (1.9 eV 2.2 eV) and superior chemical stability in aqueous solutions of pH ≥ 7. 1,6–8,71 In this part of our simulation, we have assumed a hematite photoanode with a bandgap (EG ) of ∼ 2.1 eV, immersed in an aqueous solution of pH = 13.6. 67 The extrinsic donor concentration is ND ∼ 3.96×1020 cm−3 , which is computed by assuming 1% of substitutional impurities and utilizing the hematite lattice parameters. 72 Importantly, hematite photoanodes doped at this level (1020 cm−3 ) remain “non-degenerate” due to its high effective density of states (NC and NV ). This characteristic is commonly observed in metal oxide semiconductors (see the supporting information). 18,73,74 To maintain consistency with the photocatalysis literature, all the calculated energy band diagrams are drawn with respect to RHE, which is located 4.44 eV below the standard vacuum level reference commonly found in the device physics literature. 1,17,47 Fig. 3 presents the computed electrostatics of an idealized crystalline hematite photoanode equilibrated with an aqueous solution (equivalently, OCC at dark). As can be seen in Fig. 3a, the calculated energy band diagram demonstrates a constant Fermi level (EF n = 14


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EFn = EFp

2

(OH-/O2)

EG ≈ 2.1 eV EV

3 0

10

EL

20

Position (nm)

Carrier Density (cm-3)

1

Interface

Energy (V vs. RHE)

Vbi ≈ 0. 68 V

EC

(b)

1020

(Crystalline α-Fe2O3)

10

30

60

Ionized Donor = ND+

1010 10

(c) SCR Charge Density (Coul.cm-3)

(a)

0

40

Electron = ncb

0

Hole = pvb

20

-10

0

5

10

(SCR)

Lscr ≈ 5 nm

15

Position (nm)

20

25

0

(Bulk) 0

5

10

15

Position (nm)

20

25

Figure 3: Calculated electrostatics of an idealized PEC junction between a perfectly crystalline hematite photoanode and an aqueous solution (pH = 13.6). 67 The computed band diagram in (a) exhibits the equilibration of Fermi levels on both sides of the SL interface. As can be seen from (b), the electron concentration in the bulk approaches the dopant concentration – expected for efficient n-type doping. Furthermore, with a span of ∼5 nm, the SCR region approximates the short minority carrier collection length commonly observed in hematite photoanodes. 7 EF p = EL ) at +1.23 V vs. RHE. In addition, the photoanode exhibits Vbi ∼ 0.68 V, setting the maximum limit of the photovoltage (Vph|max ) extractable from this hematite-based PEC system (in the event of perfect flattening of the semiconductor bands upon illumination). 48 As expected, the hematite portion of the interface is depleted of electrons, within a SCR span of Lscr ∼5 nm, roughly correlating with the hole collection length reported in the literature (see Figs. 3b-c). 7,15 Interestingly, this idealized picture of a hematite photoanode demonstrates “satisfactory” electron conductivity due to efficient n-type doping. Meaning, all the excess electrons contributed by donor-impurities (e.g., ND+ : Ti4+ , Si4+ ) are elevated to the conduction band and become mobile electrons (ncb ). This is evident from Fig. 3b, where the bulk is characterized by ND+ ≈ ncb – delineating the complete ionization of extrinsic dopants. Importantly, efficient electron conduction in the bulk of a photoanode is needed to suppress electron-hole recombination in the photo-active SCR region, and therefore indirectly influences the interfacial electrochemical reaction. 1,25 Nevertheless, electron mobility and conductivity 30,34,35 (along with its extraction 14,25 at the substrate/electrode interface) is extraordinarily low in practical hematite-based photoanodes. This is often linked with the presence of intermediate defect trap states 25–27,75 and the ‘small polaronic’ nature of carrier 15

conduction in hematite 30,33–35 – a topic we will explore next.

3.2

Impact of Bulk Trap States on the Photoelectrochemical Performance of Hematite Photoanodes Impact of Acceptor-Type Trap States (b)

5

ζ = 1.48

σs = 1

10 5

EV

EC

0

0.5

fpeak

15

Position (nm)

20


(Bulk) 0

5

10

Position (nm)

25

5

1 0

EC

10

15

Position (nm)

20

0

25

(Bulk) 0

5

10

15

Position (nm)

60

20

25

(SCR)

40

2

Lscr ≈ 2 nm

20

EV 5

10

15

Position (nm)

20

25

0

(Bulk) 0

5

10

15

Position (nm)

pvb 0

5

20

25

10

15

Position (nm)

25

(g) ncb

pvb 0

5

10

15

Position (nm)

25

ρT|A

1010

ncb

0

10-10

20

(j)

1020

10

20

ρT|A

100

10-10

(i)

(h) Vbi ≈ 0.06V

EFn = EFp

0

10-10

1010

20

ncb

100

1020

Lscr ≈ 3 nm

40

EV

1

20

(SCR)

60

2

0

15

(f)

EFn = EFp

3

0

25

(e) Vbi ≈ 0.23V

EC

1

3

EG ≈ 2.1 eV

Energy (V vs. RHE)

0

(a)

10

ρT|A

1010


0

(d)

1020


x 1027

SCR Charge Density (Coul. cm-3)

20

EV

0

Energy (V vs. RHE)

DOS (m-3 eV-1)

15

Lscr ≈ 4 nm

40

EFn = EFp

fpeak = 0.7 ( e -- g ) fpeak= 0.6 ( h -- j )

(SCR)

60

2 3

fpeak = 0.8 ( b -- d )

Vbi ≈ 0.42V

EC

1

(c)


Energy (V vs. RHE)

0


3.2.1

pvb 0

5

10

15

Position (nm)

20

25

Figure 4: Calculated electrostatics of a hematite photoanode with a distribution of acceptor traps as expressed by Eq. (10), characterized by ζ = 1.48 and σs = 1. The impact of shallowto deep-level states are computed by varying fpeak from 0.8 (b-d, marked in green), through to 0.7 (e-g, marked in purple) and 0.6 (h-j, marked in red). As can be seen from the energy band diagrams in (b), (e) and (h), the built-in potential is gradually reduced, simultaneously decreasing the extent of Vph|max . A reduction in Lscr (corresponding to the hole collection length) is also correlated with decreasing fpeak in (c), (f) and (i). The capture of conduction band electrons (ncb ) by acceptor traps (nT |A ) is also visible in (d), (g) and (j). We begin by analyzing the impact of acceptor-type trap states on hematite photoanodes, as summarized by the computed results in Figs. 4 and 5. The practical source of these 16

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trap states can be linked to the capture and localization of conduction band electrons (ncb ) by: (1) defect states at the TCO/hematite interface (forming the ‘dead layer’); 23,26,27 (2) intermediate trap states in the bulk of hematite; 25,28,29 and (3) Fe2+ -like polaronic states. 30–35 Electrons captured by these acceptor traps give rise to the net trapped charge ρT |A as described by Eq. (6). Let us consider a distribution of acceptor traps that are gradually lowered deeper into the band gap, while fixing ζ = 1.48 and σs = 1 (as shown in Fig. 4a). Specfically, we consider fpeak at the values of 0.8 (green, Fig. 4b-d), 0.7 (purple, Fig. 4e-g) and 0.6 (red, Fig. 4h-j). This provides an excellent metric for studying the relative influence of shallow and deep level acceptor traps. In our estimate of ζ, we have assumed that 1.5% of ˜T |A ≈ 5.88 × 1020 cm−3 (see the Fe3+ sites are replaced by lattice defects or equivalently, N the supporting information). From our calculated results in Fig. 4, the impact of the acceptor traps is found to be two-fold as their distribution is lowered deeper into the band gap: (1) the progressive reduction of available conduction band electrons (ncb ); (2) the gradual reduction of both Vbi (a measure of Vph|max ) and the span of the SCR (a rough measure of the hole collection length). The progressive impact of deepening acceptor traps on ncb can be seen in Figs. 4d, 4g and 4j. As acceptor states are placed further into the bandgap (fpeak : 0.8 → 0.6), the capture of the conduction band electrons becomes more prominent with ncb in the bulk dropping from 7.87×1015 cm−3 to 6.92×108 cm−3 . This can be compared with the idealized trap free value of 3.96×1020 cm−3 electrons in the conduction band (see Figs. 3b and 4d, 4g and 4j). Such low concentrations of electrons in the conduction band, due to trapping, can further contribute to the poor electron conductivity and inefficient doping observed in hematite samples. 30,34,35 It may even be that exceptionally high trap densities at the substrate/electrode interface significantly impede electron extraction (by lowering ncb ), thereby further enhancing electron-hole recombination in the bulk/SCR region and reducing the transfer of holes to the water oxidation reaction. 25 Likewise, the progressive impact of deepening acceptor traps on Vph|max can be seen by

17



comparing Fig. 3a with Figs. 4b, 4e and 4h. In the absence of trapping, the idealized hematite photoanode is predicted to have a maximum photovoltage of Vph|max ≈ Vbi ≈ 0.68 V (see Fig. 3a). When acceptor traps are localized near the conduction band at fpeak = 0.8, this lowers to Vph|max ≈ Vbi ≈ 0.42 V (see Fig. 4b). Moreover, as the trap states are lowered to fpeak = 0.7 and fpeak = 0.6, Vph|max falls further to ∼ 0.23 V and ∼ 0.06 V, respectively. This reduction in Vph|max and Vbi occurs because the hematite bulk Fermi level is forced to drop closer to the valance band maximum as the filled trap states drop lower. As the hematite Fermi level drops, it draws closer to the electrochemical potential of the aqueous solution (at +1.23 vs. RHE) and thereby lowers built-in voltage (Vbi ) which is achieved through the equilibration between the hematite and liquid electrochemical potentials (see the discussion pertaining to Fig. 1). Importantly, this trapping driven collapse in Vbi severely limits the degree to which the photocurrent onset may be shifted cathodically by the photovoltage – a crucial and necessary component of unassisted solar water splitting. 9–11,20 Similar trends have been observed in Mott-Schottky measurements of photoanodes, 10 where the flatband potential also moves towards the anodic direction and hinders the desired cathodic shift of the photocurrent onset. Overall, acceptor traps limit Vph|max far shy of its theoretical maximum (estimated from Vbi for an electrode without trapping), by capturing the conduction band electrons. Therefore, a photoanode prone to acceptor trapping is bound to operate at more anodic potential with respect to the H2 -evolution potential at 0 V vs. RHE. It is also important to note that acceptor traps may also lower the width of the SCR as shown in Figs. 4c, 4f and 4i. These results suggest SCR lengths in the range of 2-4 nm, in agreement with the extrodinarily short minority carrier collection lengths reported for hematite photoanodes in the literature. 1,7,15,36 This picture of the SCR/interfacial region suggests that acceptor trap states often mandate the application of large reverse potential to facilitate the interfacial hole collection/reaction – as is commonly supplied to practical hematite photoanodes (e.g. photocurrent saturation at 1.3 V vs. RHE and beyond). 67 The shift of the electrode flatband potential vs. RHE is summarized in Fig. 5a, where it is shown

18


Page 18 of 36

that significant acceptor trapping results in a marked anodic shift upon illumination. Thus acceptor trapping can considerably impede the desirable cathodic shift in the onset of the photocurrent (by degrading Vph|max ). (a)

0.42V

1

0.23V 0.65

0.7

fpeak

0.75

ζ= 0

0.6

ζ= 0.99

0.8

0 0.5

ζ= 1

σs = 1

0.6

0.4

ζ= 1.01 ζ= 1.5 ζ= 10

0.2

0.06V 0.6

0.4

(c)

Vph|max (V)

0.6

Vph|max (V)

Potential (V vs. RHE)

0.8

1.2

(b)

(Vph|max)

0.7

0.8

fpeak

ζ= 0.99

fpeak = 0.7 ζ= 1 ζ= 1.01

0.2

EC

0.9

ζ= 0

1

0 10-1

ζ= 1.5 ζ= 10

100

σs

101

Figure 5: (a) Potential of the hematite photoanode vs. RHE, operating at the dark OCC (green diamond) and flatband condition (yellow square) drawn for the acceptor states as presented in Fig. 4. The flatband potential becomes increasingly anodic as the acceptor states are placed deep in the bandgap, leaving limited room for the desired cathodic shift of the photocurrent onset. 9 (b) Evolution of Vph|max as a function of the location of the peak of the distributed acceptor states. Here, we have assumed σs = 1 and ζ is allowed to change as 0 (grey), 0.99 (green), 1 (yellow), 1.01 (pink), 1.5 (purple) and 10 (red). (c) Evolution of Vph|max as a function of the spread of the distribution. In this case, fpeak is assumed to be fixed at 0.7 and ζ is allowed to take the same values as in the case of (b). Our analysis thus far is based upon acceptor traps with a fixed breadth (σs = 1) and fixed relative concentration (ζ = 1.48). We will now further explore how varying these two parameters can alter the impact of acceptor traps. Fig. 5b presents the evolution of Vph|max as the peak position of acceptor traps is gradually lowered deeper into the bandgap (fpeak : 1 → 0.5) for increasing values of ζ and a constant value of σs = 1. It can be seen that Vbi ≈ Vph|max is dramatically lowered by acceptor traps located deep in the bandgap. The collapse in Vph|max proceeds quite rapidly when the concentration of acceptor traps exceeds the ionized dopant density (ζ ≥ 1). Consequently, when acceptor traps approach midgap (fpeak → 0.5) and ζ ≥ 1, acceptor states can completely annihilate the built-in potential (Vbi → 0, Vph|max → 0) resulting in a hematite photoanode that fails to produce a photovoltage and photocurrent of any significance. This theoretical insight provides a plausible explanation for the extremely low photocurrents observed in hematite photoanodes that 19


are not annealed at high temperatures, supporting the hypothesis that high temperature annealing facilitates the removal of deep level traps. 27,71,76,77 It is also worthwhile to examine the evolution of Vph|max as a function of the trap-distribution breadth (σs ) as presented in Fig. 5c. Here the peak location of the distribution is fixed at fpeak = 0.7 and ζ is allowed to vary from 0 to 10. Fig. 5c reveals that Vph|max is reduced substantially as the spread of the acceptor states gets narrower (becomes more localized in energy). This occurs because electrons in acceptor traps with narrower distributions are less easily promoted thermally to the conduction band, which in turn results in a lowering of the semiconductor Fermi level and a subsequent reduction in Vbi (as discussed earlier). Again, in Fig. 5c we see that Vph|max is substantially degraded when the acceptor trap concentration exceeds the ionized donor concentration (ζ ≥ 1) – though broadening in the trap distribution does help to some degree.

Impact of Donor-Type Trap States

8

ζ= 10 ζ= 1 ζ= 0.1

0.69

x

10

26

(b)

0.7

fpeak = 0.92 fpeak = 0.90 fpeak = 0.88

6

Vph|max (V)

(a)

0.7

ncb (m-3)

3.2.2

Vph|max (V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 36

0.69

σs = 1

0.68

σs = 1

0

0.5

fpeak

1

4 -1 10

10

0

ζ

10

1

0.68 10-1

(c) fpeak = 0.9 ζ= 10 ζ= 1 ζ= 0.1

100

σs

101

Figure 6: Calculated electrostatics of a hematite photoanode only with donor traps, as expressed by Eq. (11). Part (a) depicts the evolution of Vph|max with respect to the peak position of donor traps inside the bandgap (fpeak ), assuming a fixed energetic breadth σs = 1 and varying the relative concentration (ζ) from 0.1 (red) to 1 (green) and 10 (purple). Whereas (b) depicts the electron doping activity of donor traps located close to the conduction band for various values of ζ and fpeak . This is also shown in (c), where enhanced broadening of σs results in an increase in Vph|max by raising the Fermi level slightly through the donation of electrons to the conduction band. Next, we shall theoretically analyze the impact of the donor traps on the photoelectrochemical performance of hematite photoanodes – assuming the absence of any acceptor 20


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traps. That being said, in this case, we have utilized Eq. (11) to model the distribution of donor traps. As discussed in the literature, donor traps in hematite can arise from oxygen vacancy defects (Vo ). 54,55 Similar to our analysis of acceptor traps, we have evaluated the impact of donor traps on Vph|max as a function of both fpeak and σs (see Fig. 6). As can be seen in Fig. 6a, the influence of the donor states is negligible as fpeak is swept across the bandgap of an n-type hematite photoanode. This is because filled donor traps do not contribute to the overall charge balance of an n-type semiconductor. 53 Only if the donor traps are placed close to EC , can they participate by beneficially donating further electrons to the conduction band (in the same manner as extrinsic dopants, as shown in Fig. 6b). This leads to a small increase in Vph|max (or, equivalently, Vbi ) by raising the Fermi level as shown in Fig. 6a. Similarly, donor traps with large spread can donate electrons to EC and offer a small increase in Vph|max (as presented in Fig. 6c). Thus, bulk donor traps are generally benign or beneficial with respect to the carrier concentration and maximum achievable photovoltage of n-type photoanodes (as shown in Fig. 6a, c). This beneficial impact of “donor traps” on the electron concentration is in agreement with measurements in the literature, where conductivity improvements have been linked to donor-type oxygen vacancies and extrinsic dopants. 36,54,55,78–80 In approximate agreement with the findings of Fig. 6, MottSchottky measurements have also exhibited roughly the same flatband potential (meaning negligible change in Vph|max or Vbi ) and a lowered Mott-Schottky slope (implying increased conductivity) in the presence of such donor-type states. 78,80

3.2.3

Estimating the Impact of Polaronic States on the Maximum Attainable Photovoltage

In many oxide based anodes, electron polaron states are an intrinsic form of acceptor trapping. 7,32,81–83 They form due to strong electron-phonon coupling and therefore can be present even in a “perfect crystal”. 32,82 Thus, electron polarons can determine the true theoretical photovoltage maximum for even “perfectly synthesized” anodes and are the last topic of

21



consideration in this study. They differ from other forms of acceptor trapping, in that their concentration can never exceed the total number of free electrons in a material – since they are a product of self-trapping. Such polarons are usually formed by electrons donated by intentionally introduced donor species. In the case of hematite, self-trapped electrons (polarons) are identifiable by temperature dependent electrical conduction measurements indicating thermally activated hopping between neighbouring Fe2+ and Fe3+ atoms. 30–33 To further refine our semiclassical parameters we have conducted first-principles electronic structure calculations of polaron trapping in hematite. More precisely, we have utilized the density functional theory (DFT+U) with additional on-site Hubbard corrections at Fe3+ (UF e3+ ) and Fe2+ (UF e2+ ) atoms to estimate the energetic location of polaronic states (ET |A ) inside the band gap of hematite. 32 To this end we have explored a range of U values on the polaron sites (UF e2+ ) while keeping the U value on Fe3+ ions (UF e3+ ) fixed at 4.3 eV as shown in Table 1. The details of our first-principles calculations may be found in the supporting information to this paper. Figs. 7a-b present the calculated electronic structure of α-Fe2 O3 with UF e3+ = UF e2+ = 4.3 eV. The presence of an electron polaron state can be seen within the band gap at ET |A = 0.782 eV below the conduction band (for a comparison to experimental values see the supporting information). 33 This corresponds to fpeak = 0.64 when considering a band gap of EG = 2.2 eV as computed from our first-principles calculations. 32,33 In general, we have found that the polaronic peak cannot be raised to much more than 0.573 eV from the conduction band minimum (corresponding to UF e2+ = 3.5 eV). Calculations with smaller values of UF e2+ were attempted but convergence difficulties were encountered – indicating that the polaronic state might not be stable at much lower UF e2+ values. Let us continue with our semiclassical approach, as presented in Sec. 2, by considering the electrons localized at Fe2+ -like polaronic states in hematite as a distribution of acceptortype states. Since the number of self-trapping electron polarons cannot exceed the number of ˜T |A = N + → ζ = 1. Now with ET |A and donors (providing such electrons) we shall assume N D

22


Page 22 of 36

Page 23 of 36

Table 1: Energetic Location of Electron Polarons (ET |A ) from DFT+U Calculations and Corresponding Upper Bound Estimates of Vph|max UF e2+ (eV)a ET |A (eV) fpeak (eV) Vph|max (V)b 3.5 0.573 0.74 0.63 V 4.0 0.702 0.68 0.61 V 4.3 0.782 0.64 0.59 V a b holding UF e3+ = 4.3 eV; assuming σs = 12.7.

(a)

(b)

40

PDOS

PDOS

20 EV

EC

EG

0

-20

~0.782eV fpeak ≈ 0.64

-40

-5.5

Energy(eV) (c)

(d)

Vph|max (V)

EFn = EFp

2

EG =2.2 eV EV

4

0

0.7

Vbi ≈ 0.71V

EC

fpeak = 0.74 0.6 fpeak = 0.68 fpeak = 0.64

0.63 V 0.61 V 0.59 V

10

15

Position (nm)

20

25

0.95

0.5

σs = 12.8

0.4 5

1

Without polaron(ζ= 0)

10

ζ=1 -1

10

0

σs

ρT|A/ND+ (Arb.)

0

Potential (V vs. RHE)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

1

0.9

0.85 10-1

-5

-4.5

Energy(eV)

-4

(e) fpeak = 0.74 fpeak = 0.68 fpeak = 0.64 ζ=1

10

0

σs

101

Figure 7: (a)-(b) α-Fe2 O3 orbital projected density of states (PDOS) of the polaronic ground states as calculated from first-principles (with UF e3+ = UF e2+ = 4.3 eV). The electron polaron PDOS peak is more visible in (b) and is localized at ET |A = 0.782 eV below the conduction band (fpeak = 0.64). (c) Calculated energy band diagram of the idealized α-Fe2 O3 -aqueous junction (using first-principles derived parameters). The photoelectrochemical junction is characterized by Vbi = 0.71 V. (d) Evolution of Vph|max as a function of σs for fpeak = 0 (dotted line), fpeak = 0.64 (red), 0.68 (purple) and fpeak = 0.74 (green). (e) Evolution of the concentration of the self-trapped electrons in polaronic states as a fraction of the total donated electron concentration and as a function of σs . We assume ζ = 1 for all calculations in (d) and (e).

23



˜T |A in hand, Eq. 10 can be utilized to explore the energetic distribution of polaron acceptor N states by varying its spread (σs ). A first-order estimation of σs for polaronic states can be performed by utilizing a first-principles derived two-site electron transfer model (discussed in the supporting information), resulting in a upper bound of approximately σs ≈ 12.7 in hematite. 84 Fig. 7c shows the refined band diagram of the idealized hematite-aqueous junctions considering ND+ = 3.85×1020 cm−3 and EG = 2.2 eV (corresponding to the first-principles derived band gap). As depicted, the idealized hematite-aqueous junction exhibits Vbi = 0.71 V, elucidating the maximum attainable photovoltage or Vph|max . This idealized electrostatic picture of the SL junction changes dramatically as electrons are self-trapped by polaronic states. Fig. 7d depicts the evolution of Vph|max as a function of the spread of the polaronic states (σs ) for the first-principles derived fpeak values presented in Table 1. Clearly, the presence of the polaronic states degrades Vph|max from its idealized value, where the extent of the degradation becomes more severe with: (1) the degree of localization (low σs ); and (2) the distance of these states from the conduction band edge (low fpeak ). Both of these observations are in agreement with our earlier analysis in Sec. 3.2.1. Importantly, our upper bound estimate of σs = 12.7 in hematite, places a corresponding upper estimate on Vph|max between 0.59 V (at fpeak = 0.63) and 0.63 V (at fpeak = 0.74) for perfectly crystalline hematite anodes – as summarized in Table 1 and shown in Fig. 7d. These values correspond well with the photovoltage values reported in the literature. 9–11,27 This is, in turn, directly limits the extent of the crucial cathodic shift of the photocurrent onset in hematite photoanodes in the absence of any further morphological defects. Finally, let us explore the fraction of electrons self-trapped in polaronic states (ρT |A ) as a function of σs with respect to the donor concentration ND+ as shown in Fig. 7e. In this case, ρT |A → 1 corresponds to the drastic reduction of ncb , in agreement with the practical observation of extraordinary low electron conductivity in hematite photoanodes. 24,25,30,33 However, as the broadening of the polaronic state (σs ) is increased, more electrons are

24


Page 24 of 36

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able to gain enough energy to hop up to the conduction band reducing ρT |A < 1. Thus, it is plausible that enhanced polaron broadening can somewhat improve the conductivity of hematite photoanodes at exceptionally high doping concentrations. Nevertheless, it is important to note that our semi-classical model assumes a fixed polaron DOS distribution (at ζ = 1) and does not account for the dynamical nature of electron self-trapping. Therefore it does not fully reflect the corresponding decrease in the polaron DOS when electrons are promoted to the conduction band in the regime ρT |A < 1. This dynamical impact is likely to be small for the system properties considered herein, a full consideration of dynamical trapping within this semi-classical model is left for future work.

4

Conclusion

We have presented a self-consistent numerical method for theoretically estimating the impact of bulk trapping phenomena on the maximum attainable photovoltage at semiconductorliquid interfaces. This was accomplished by extending state-of-the-art descriptions of electron and hole trapping in semiconductors common to the solid-state device physics literature. By considering the concentration and energetic distribution of bulk trap states, our study revealed that: (1) acceptor-type bulk trap states can significantly lower the maximum attainable photovoltage and (2) may dramatically lower the number of free carriers. These effects were specifically investigated in hematite, where trapping induced lowering of the maximum photovoltage can be correlated with a reduced cathodic shift in the photocurrent onset. Likewise, lower concentrations of mobile electrons due to trapping can be linked to the extraordinarly low electron conductivity and mobility in hematite; particularly, non-polaronic trapping by high concentrations of crystalline defects that may arise at the interface between a photoanode and a conducting back electrode (e.g., TCO). The negative impact of acceptor trap states were determined to intensify as they became more localized in energy and/or were lowered deeper below the conduction band minimum. Conversely, donor-type trap

25



states were determined to have a negligible impact on heavily doped n-type photoanodes – and may even be a little beneficial, if raised close enough to the conduction band to donate electrons. Finally, we assessed the impact of electron polaron states, which can be viewed phenomenologically as an intrinsic form of acceptor trapping, with the aid of first-principles calculations. It was determined that electron polaron trap states likely further reduce the maximum achievable photovoltage of hematite photoanodes in a range that lies near experimentally reported photovoltages. In this study we have not evaluated the impact of surface trapping states on the photovoltage (as independent from the bulk distribution), nor have we examined the impact of specific surface modifications/heterostructures, this is left for future work.

Acknowledgement The authors would like to acknowledge the financial support from NSERC of Canada and FQRNT of Québec, and the computational resources provided by the Canadian Foundation for Innovation, CalculQuebec and Compute-Canada.

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35



Energy

Graphical TOC Entry

EG

Delocalized electrons

EC

A Measure of the Maximum Attainable Photovoltage

S

DO

EC

Localized

Vbi

EV

(TCO)

n-type α Fe2O3 +

+

(Bulk)

36

Photocatalytic Interface

EFn = EFp

-

holes

kt,n

-

-

DO S Delocalized

-

- - - - - - -

EV electrons

Bulk Photanode/ Substrate Interface

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

+

(SCR)

kt,p

O2

0 V vs. RHE

OH- 1.23 – Vbi vs. RHE (Flatband Potential) 1.23 V vs. RHE

OHO2 (Liquid)


Page 36 of 36

The Impact of Bulk Trapping Phenomena on the Maximum Attainable

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