Article pubs.acs.org/JPCC
Hole Transport in Nonstoichiometric and Doped Wüstite Maytal Caspary Toroker† and Emily A. Carter*,†,‡ †
Department of Mechanical and Aerospace Engineering, ‡Program in Applied and Computational Mathematics, and Gerhard R. Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544-5263, United States ABSTRACT: We propose ways to enhance the conductivity of wüstite (i.e., naturally p-type FeO), a visible-light-absorbing, inexpensive, abundant, and nontoxic potential alternative material for solar energy conversion devices. Unfortunately, the conversion efficiency of FeO is inhibited by its low hole conductivity. Increasing the iron vacancy concentration or adding p-type dopants improves FeO conductivity by increasing the number of holes; however, it is not known which strategy introduces larger energy traps that would hinder hole conductivity. Here we employ the small polaron model along with ab initio calculations on electrostatically embedded clusters to analyze the local trapping effects of iron vacancies and several substitutional p-type dopants that are soluble in FeO, including copper, nitrogen, lithium, and sodium, and also hydrogen as an interstitial dopant for comparison. We find that vacancies create stronger traps than dopants and that copper and nitrogen dopants form deeper traps than lithium, sodium, or hydrogen. Furthermore, hydrogen repels the hole and substantially decreases the trap formed by an iron vacancy. Because of the shallower traps formed compared to vacancies, lithium-, sodium-, or hydrogen-doped, nanostructured or alloyed FeO may be worth evaluating as a p-type semiconductor for solar energy conversion applications. energy conversion in photovoltaics,13 enabling absorption of light in the visible (highest intensity) region of the solar spectrum. Finally, the calculated conduction band minimum of FeO is positioned above the free energy required for producing several fuels, and therefore FeO could possibly be used as a photocatalyst for reducing water or carbon dioxide.14 FeO has two major problems. The first is that at room temperature the bulk phase of FeO is thermodynamically unstable.15 The existence of FeO at the nanoscale is controversial. Some argue that FeO does not exist at any temperature on the nanoscale.16 However, FeO in its bulk rocksalt structure has been observed at room temperature as a nanofilm17 and as nanometer-sized islands.18 These findings suggest that FeO might be stable in a nanowire array configuration that would be optimum for light absorption and charge separation.19 Moreover, alloying may stabilize FeO (as well as improve its key solar energy conversion properties).20 Hence, fabricating FeO as a nanostructure or alloy may resolve this first problem. A second problem that limits the functionality of FeO and many other metal oxides is low conductivity,21 due to ionic lattice distortions that electrostatically interact with charge carriers. A large number of hole carriers are present in FeO from an unusually large number of iron vacancies (as high as 16%). FeO is therefore naturally p-type, i.e., the majority of
I. INTRODUCTION Alternative energy resources are essential in light of the accumulation of carbon dioxide in the Earth’s atmosphere, one of several fossil fuel usage shortcomings.1 A promising clean and renewable source of energy for generating electricity and fuel is solar energy. However, current photovoltaics composed of (poly)crystalline silicon are too expensive to compete against fossil fuels, partially because they are produced through an expensive and energy-intensive purification process.2 Fuel production is even more challenging: no photoelectrode or photocatalyst reported to date has sufficiently high incidentphoton-to-fuel conversion efficiency for practical deployment.3,4 Hence, global energy demands require research and development of less expensive and more efficient photonconverting materials. Low-cost synthesis and processing is a major incentive for considering semiconducting metal oxides.5 A particularly inexpensive metal oxide, a corrosion product of iron (one of the ten most abundant elements),6 is wüstite (i.e., iron(II) oxide, FeO). Given that iron sulfides serve as efficient electron transfer agents in biological systems, 7 analogous iron compounds might be exploitable in solar cells.8,9 Here we consider oxides rather than sulfides due to cost and service lifetime considerations (oxides are less likely than sulfides to corrode). Another advantage of FeO is that it has an optical band gap in the visible range of the solar spectrum (Egap = 2.4 eV),10,11 which is not too far from the estimated ideal band gap for, e.g., water splitting photocatalysis (∼2.0 eV).12 A small absorption peak has also been detected near 1.3 eV,10,11 which is not far from the ideal band gap of ∼1.5 eV for efficient solar © 2012 American Chemical Society
Received: May 16, 2012 Revised: July 1, 2012 Published: July 23, 2012 17403
dx.doi.org/10.1021/jp3047664 | J. Phys. Chem. C 2012, 116, 17403−17413
The Journal of Physical Chemistry C
Article
Figure 1. Structures of representative wüstite (FeO) embedded clusters. Light blue spheres represent iron cations, red spheres oxygen anions, red vertices a few point charges that mimic oxygen anions in the environment, and gray spheres vacancies. Appropriate point charges and ECPs (not shown for clarity) are situated at other lattice sites of the embedding environment. Clusters without a vacancy but with an added hole are (a) [Fe2O10]−15, (b) [Fe4O18]−27, and (c) [Fe6O24]−35. Clusters with a vacancy are (d) [Fe2O10]−15 with one added hole and a vacancy present in one of sites V1 through V8 (the first five sites, denoted V1 through V5, involve removal of an Mg(II) capping ECP at that site, while the last three sites, denoted V6 through V8, reflect the absence of a +2 point charge at these sites), (e) the same cluster as in part d but with a second hole present at one of sites h1−h4 and h6−h8 represented by dark blue spheres near a vacancy so as to form an hJ−VJ pair (J = 1−4, 6−8; the second hole is modeled by replacing a +2 point charge with a +3 point charge), and (f) [Fe3O18]−28 with a vacancy present instead of a cation at the Fe1 site and with two holes added to the iron cations Fe2 and Fe3.
carriers are holes.22 The hole conductivity σ of FeO is strongly affected by its low intrinsic mobility23 σ = neμ
Both iron vacancies and p-type dopants enhance hole conductivity by increasing the hole concentration, n, which at the low temperature limit (kBT ≪ EA) is given by23
(1)
n∝
where n is the hole concentration, e is the charge of a hole, and μ is the hole mobility. Indeed, the measured hole mobility of FeO at 1000 °C is about three orders of magnitude lower than the hole mobility of GaAs at room temperature.23,24 The hole mobility of FeO is inhibited by an exponential dependence given by24−27
μ ∝ e−Ea / kBT
NA e−EA /2kBT
(3)
where NA is the number of “acceptor” states (orbitals that have energies above the Fermi level and that may donate holes to the valence band) and EA is the energy of the acceptor state relative to the valence band edge. Although both p-type dopants and iron vacancies increase the concentration NA of orbitals that contain holes, the energy EA needed to extract a hole from an orbital is sensitive to whether iron vacancies or p-type dopants are present, and to the elemental identity of the dopant. A large EA is not desired, because then holes are trapped, the concentration of mobile holes decreases, and hole conductivity is low. No study has yet determined whether iron vacancies or ptype dopants introduce larger energy traps EA that would suppress the hole conductivity of FeO; we do so here. In addition, no experiment or calculation has compared the effect of the dopants studied here, namely nitrogen, copper, lithium, sodium, and hydrogen, on the hole conductivity of FeO. In this paper we use ab initio quantum chemistry and the small polaron model to compare the effect of iron vacancies and dopants on the hole conductivity of FeO. In particular, we use electrostatically embedded cluster models to compare the local trapping energies of iron vacancies and dopants. This work continues our previous study where titanium dopants were found to create larger energy traps than zirconium, silicon, and germanium dopants for electron transport in hematite (Fe2O3).32 We will demonstrate that vacancies create larger energy traps for holes than dopants do, and that nitrogen and
(2)
The exponential behavior with temperature usually observed in conductivity experiments on transition metal oxides is generally interpreted as indicative of charge transport of a polaron quasiparticle with activation energy Ea (kB is the Boltzmann constant, T denotes the temperature, and Ea = 0.16 eV26 at 900−1300 °C for hole conductivity in FeO). Charge transport of a polaron is especially slow since charge moves together with lattice distortions of interacting ionic nuclei.28−31 It has been shown experimentally that the hole conductivity of FeO can be improved by increasing the hole concentration via adding p-type dopants or iron vacancies.24−27 Increasing iron vacancies from 5% to 11% elevates hole conductivity at 1300 °C by ∼80%.25 Alternatively, doping FeO with p-type dopants (which donate holes), such as 0.1 atom % copper, increases hole conductivity at 1300 °C by ∼8% (compared to undoped FeO with 5% vacancies).25 Doping FeO with n-type dopants (which donate electrons), such as chromium or titanium, is not productive as it decreases the number of holes and therefore decreases hole conductivity.25,27 17404
dx.doi.org/10.1021/jp3047664 | J. Phys. Chem. C 2012, 116, 17403−17413
The Journal of Physical Chemistry C
Article
copper create larger energy traps than lithium, sodium, and hydrogen in FeO. The paper is organized as follows. Section II includes computational details regarding the electrostatically embedded clusters used for calculating Marcus theory parameters,33 including the free energy for hole transfer between sites, which is associated with the trapping energy. Results and discussion of hole transport in FeO with iron vacancies and dopants are given in Section III. Finally, section IV provides concluding remarks on recommended ways to improve the conductivity of FeO, as well as general suggestions for improving the conductivity of other transition metal oxides.
Figure 2. Unrestricted Hartree−Fock electron density difference isosurfaces for the electrostatically embedded [Fe2O10]−15 density (with a hole) minus the electrostatically embedded [Fe2O10]−16 density (no hole) at the equilibrium geometry of the acceptor state in FeO. Light blue spheres represent iron cations (Fe1 and Fe2) and light red spheres represent oxygen anions. The right isosurface shows the location of the hole at Fe2; net charge changes at Fe1 are insignificant despite the presence of the left isosurfaces and are simply due to the degeneracy of the iron t2g orbitals and a change in which dorbital in Fe(II) is preferentially doubly occupied in the two states). Dark red (blue) represent the loss (gain) of electron density upon introduction of the hole. The MacMolPlt program was used for visualization,64 using 240 grid points along each axis, 0.125 Å as the grid increment, and 0.07 electron/bohr3 for the isosurface value.
II. COMPUTATIONAL DETAILS This section lists the computational details and procedures used to calculate Marcus theory parameters33 associated with the conductivity of FeO. This includes a description of the embedded clusters, basis sets, atomic spin ordering, and theory used. Unrestricted Hartree−Fock (UHF) theory was used for structural optimization to obtain hole donor and hole acceptor equilibrium states. Hole transfer between equilibrium states was modeled by invoking a linear reaction coordinate approximation. From energy curves along the reaction coordinate we extracted Marcus theory parameters. This procedure was done for clusters containing vacancies and/or dopants. Cluster Models. The smallest cluster used for modeling hole transport in FeO was [Fe2O10]−15, containing two nearestneighbor iron cations and ten oxygen anions (see Figure 1a), with an overall charge of −15 due to 10 oxygen ions with charge −2, one iron ion with charge +2, and one iron ion with charge +3 that contains a hole. The iron cations are octahedrally coordinated with oxygen anions to provide the correct ligand field. Adding more ions (see Figure 1a−c) changed the hole transfer activation energy by less than 0.02 eV and therefore the smallest cluster was deemed sufficient. The two iron cations function as hole donors and acceptors, because the hole localizes in an iron d-orbital, as determined by electron density differences (between that of an embedded cluster with, Fe2O10−15, and without a hole, Fe2O10−16, as seen in Figure 2). This location is consistent with experiments indicating that the valence band edge of FeO is comprised of iron d-orbitals (a Mott−Hubbard insulator).34 The Fe2O10−15 cluster was embedded in a point charge array meant to mimic the extended ionic crystal, where +2 and −2 point charges represent Fe and O ions, respectively. The point charge array was built, as done in earlier work on electron transport through hematite (Fe2O3),32 according to the experimental crystal structure.35 The cluster and point charges created a three-dimensional array of 7 × 7 × 7 unit cells (each unit cell is cubic and includes four formula units),36 or equivalently 14 × 14 × 14 layers of atoms and point charges. One layer of point charges was then deleted to form a 14 × 14 × 13 nonisotropic array in order to build an even distribution of charges around the cluster that produced no overall dipole. A smaller, minimal number of point charges (410 point charges rather than 2510) could have been used without significant changes (
