Article Cite This: Chem. Mater. 2017, 29, 10095−10103
pubs.acs.org/cm
Computational Screening of Useful Hole−Electron Dopants in SnO2 Miglė Graužinyte,̇ * Stefan Goedecker, and José A. Flores-Livas* Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland S Supporting Information *
ABSTRACT: Doped tin dioxide (SnO2) is an important semiconductor that is already used in diverse applications. However, to determine the entire potential of this material in more advanced applications of optoelectronics, further improvements in electrical properties are necessary. In this work, we perform an extensive search for useful substitutional dopants of SnO2. We use a well-converged protocol to scan the entire periodic table for dopants, finding excellent agreement between our predictions and those substitutional dopants that have been experimentally examined to date. The results of this large-scale dopant study allow us to better understand the doping trends in this important transparent conductive oxide material.
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INTRODUCTION The combination of optical transparency and high electrical conductivity enables transparent conductive oxide (TCO) materials to be used for a wide range of applications, from simple smart window coatings to organic light-emitting diodes and futuristic see-through displays.1−4 The niche of these futuristic materials is heavily dominated by electron (n−)doped SnO2, In2O3, and ZnO. Currently, many optoelectronic applications are primarily based on indium oxide;5,6 this material is taking the lead with its superior conductivity, while tin and zinc oxides are close runners-up, having promising yet not quite sufficient properties for widespread use as electronic materials.7,8 In spite of that, the advantage of earth abundance (and hence a production cost lower than that of indium) has spurred a sizable experimental and computational effort aimed at understanding and enhancing the properties of Zn and Sn oxides.9−20 To bring SnO2 on a level playing field with indium-based TCOs, a thorough understanding of useful dopants is needed. Unfortunately, the use of different codes (i.e., basis sets), exchange-correlation functionals, and approaches used to overcome deficiencies inherent to the level of theory has resulted in a large scatter of results that are hardly, if at all, comparable with each other. Even the cause of unintentional n-type doping is still an open debate in the scientific community,13,21−23 with contradicting predictions reported for oxygen vacancies and cation interstitials, which have been blamed for decades for the unintentional n-type TCO conductivity. This has even led to the proposal of hydrogen interstitials and hydrogen trapped in oxygen vacancy sites as an alternative explanation for the unintentional n-type doping in conductive oxides.22 Needless to say, examination of external dopants suffers from similar issues. It is well-known that Kohn−Sham density-functional theory (KS-DFT) band structures systematically underestimate the band gap for semiconductor materials. The band gap problem © 2017 American Chemical Society
of standard density functionals is particularly troublesome in the case of TCOs.13,24 For instance, the calculated generalized gradient approximation (GGA-PBE) band gap of SnO2 is 0.6 eV, while experimental results indicate a direct gap of 3.6 eV.25 Different approaches have been used to alleviate this problem. A posteriori corrections, such as the use of scissor operators or alignment schemes, simple extrapolation,21 or different variants of DFT+U,26 are a major cause for the conflicting results in the literature, and the validity of many such approaches has been called into question, when it comes to accurate defect level predictions.27 Hybrid-functional HSE calculations, which include a fraction of the exact Hartree−Fock exchange, are often seen to improve the band gaps of semiconducting materials. However, for SnO2, a further increase in the standard α = 0.25 fraction of the exact exchange is required to recover the experimental band gap,16,28 a necessity for accurate defect formation energy calculations. While fitting the band gap via α might be justified for the SnO2 host, the resultant parameter could easily be inappropriate when other substitutional elements are consider. In fact, in the case of zinc oxide, recent G0W0 “single-shot” calculations have shown that the increased fraction of exact exchange, while capturing the experimental band gap, leads to predictions of thermodynamic transition levels that are worse than those of the “standard” HSE functional.20 Further works by Lany and Zunger29,30 conclude that the generalized Koopman’s theorem and not the experimental band gap should be used to find an appropriate choice of α in metal oxide materials. While all the methods mentioned above for band gap correction require adjustable parameters, in stark contrast, the PBE0 hybrid functional predicts the correct band gap of SnO2 Received: September 12, 2017 Revised: November 13, 2017 Published: November 13, 2017 10095
DOI: 10.1021/acs.chemmater.7b03862 Chem. Mater. 2017, 29, 10095−10103
Article
Chemistry of Materials without any adjustments. This allows, in principle, ab initio defect calculations in SnO2 that are completely free of parameters yet has been utilized in only a single p-type dopant study.19 Incongruous to the various studies of n-type dopants, even if often limited to a handful of defects each, that have been considered by different groups using variants of the HSE hybrid functional.16−18,28 In this work, we use PBE0 to perform a parameter-free large-scale defect study of SnO2. This allows us to bring the preexisting dopant studies on a comparable level of theory and, more significantly, to deepen our understanding of this important TCO material as we shed light not only on the behavior of isolated defects but also on overall doping trends.
ε(q1/q2) =
RESULTS AND DISCUSSION Substitutional Dopants. We considered a total of 63 substitutional dopants for the Sn site, DSn. For optoelectronic applications, both good conductivity and optical transparency are required. Two features of a substitutional defect were, therefore, chosen to represent these requirements: defect formation energy, EFD, as a function of charge, q, and the electronic density of states (DOS). All DSn sites resulting in deep localized defect states are likely to act not only as chargetrapping centers but also as color centers. Thus, an electronic structure with a defect-state-free band gap is a good indicator of a suitable dopant element. The DOS also allows for evaluation of the fundamental band gap, direct at Γ in rutile SnO2. An optical band gap with a minimum of 2.8 eV is required to maintain transparency. Defect formation energies allow the determination of the stable charge state of DSn at a given Fermi energy, εF. For ntype conductors, εF should lie close to the conduction band and the substitutional dopant should be positively ionized (donated one or more electrons to the conduction band), while for ptype conductors, εF should lie close to the valence band and the substitutional dopant should be negatively ionized (donated one or more holes to the valence band). Defect formation energies of a given charge state were calculated using eq 1.
(2)
Figure 1. Schematic illustration of the calculation recipe used for substitutional defect evaluation.
used. All the dopants were first calculated with the GGA-PBE level of theory within DFT, and if both the conditions described above, desired stable charge state and defect-free band gap, were fulfilled, a subsequent hybrid-functional calculation cycle was performed to verify the result. The choice of PBE for prescreening is justified by the following considerations. In the SnO2 host, hybrid-functional calculations shift the valence band and conduction band edge states predicted by PBE, resulting in a simple opening of the band gap. In this context, the PBE calculations are qualitatively similar to hybrid PBE0 for any emergent defect states that are rigidly shifted together with the relevant band edge. This should indeed always be the case for a perturbative host state, the ideal doping scenario. In contrast, for a localized defect state, this is not a guaranteed condition. Nevertheless, the reduced band gap of PBE will tend to stabilize a donating charge state, when compared to PBE0, while the opposite behavior, a charge neutral PBE state becoming a donor on the PBE0 level of theory, is extremely unlikely, as this would require the defect-state energy to be shifted by an amount larger than the relevant band edge shift itself. Bulk Properties. First, we assessed the dependence of the volume on the functional employed. The Birch−Murnaghan35 equation of state was used to fit energy−volume curves for SnO2 as predicted with PBE, PBE0, and HSE06 exchange-
∑ ni(μi + Δμi ) + q(εVBM + ΔεF) i
+ Ecor
q2 − q1
Thermodynamic transition levels indicate the value of ΔεF at which the substitutional defect changes its stable charge state. Strong structural relaxations between different charge states can, nevertheless, create kinetic barriers that stabilize an excited charge state above its thermodynamic transition level.34 It is clear that accessing all this information for all the elements in the periodic table using hybrid-functional calculations is computationally prohibitive. To circumvent this issue, the computational workflow illustrated in Figure 1 was
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E DF = E Dq − ESnO2 −
E DF(q1 , ΔεF = 0) − E DF(q2 , ΔεF = 0)
(1)
where EqD is the energy of a supercell containing a defect atom D in charge state q, ESnO2 is the energy of the same size supercell of pure SnO2, ni is the number of atoms of species i that was added (ni > 0) or subtracted (ni < 0) to create the defect, μi is the chemical potential of species i in its pure phase, Δμi defines the boundaries imposed on the total chemical potentials of species i due to secondary phase formation (further information about the reference phases can be found in the Supporting Information), εVBM is the position of the valence band maximum of pure SnO2, and ΔεF is the position of the Fermi level with respect to εVBM. In this work, we regard ΔεF as a free parameter, though it is, in principle, constrained by all the defects and/or defect complexes contained in the system. Finally, Ecor contains all additional correction terms. This includes a charge interaction correction and a potential alignment term. For the final PBE0 calculations, we further include a band-filling correction term.33 Thermodynamic transition levels ε(q1/q2) between two charged states q1 and q2 of a substitutional defect were calculated using eq 2. 10096
DOI: 10.1021/acs.chemmater.7b03862 Chem. Mater. 2017, 29, 10095−10103
Article
Chemistry of Materials
charge states for ΔεF at the CBM. Pure PBE calculations predict 19 elements as potential n-type donors [colored orange (q = 1) and purple (q = 2)]. On the basis of their densities of states, the 19 elements were separated into three categories: (a) elements that do not strongly affect the electronic structure of SnO2 and should act as good n-type donors, highlighted by a solid black outline in Figure 2, (b) elements that do not form defect states inside the band gap but induce strong distortions close to the CBM that warrant further investigation, marked by a dashed outline in Figure 2, and (c) transition d metals resulting in defect states lying inside the band gap due to metal−d and O−2p orbital interactions (plots of DOS can be found in the Supporting Information). Clear trends across the periodic table can be identified, with electron donor regions seen within the transition metals and the elements of groups V and VII. Two intriguing outliers to the general trend can also be spotted: (i) Te, the only element of those in group VI acting as a double donor in a +2 charge state, and (ii) Au, offering up an electron, despite its typical +3 oxidation state. This (as will be shown in more detail below) is in fact an artifact of PBE preferentially stabilizing electrondonating states. Because of the small band gap, the induced defect states for the two elements are predicted to be energetically close to the CBM, artificially increasing the total energy of the charge neutral state, when compared to hybridfunctional results. With the use of hybrid-functional calculations, the outliers are seen to disappear, acquiring the same charge state as the rest of the elements in the group. Te is found to be charge neutral, while Au is stable in the negative charge state. PBE formation energies under Sn-poor conditions, when DSn formation is favorable, are shown in Figure 3 as a function of ΔεF for all 19 n-type dopants. Panels a−c correspond to the three categories outlined above. The points at which a change in slope is seen for Os and Tc indicate the thermodynamic transition levels. Both elements undergo a q = 2 to q = 1 transition as the Fermi level passes the midgap region. However, as mentioned previously, the localized defect states seen inside the band gap for elements of panel c are likely to negatively impact the optical and electronic properties of SnO2. These elements were, thus, excluded from more detailed investigations.
correlation functionals. Table 1 summarizes the results. Clearly, both hybrid functionals greatly improve over the PBE results Table 1. Lattice Parameters, Bulk Moduli, and Electronic Gaps of Rutile SnO2 Calculated with Different Functionals a (Å) c (Å) x EF (eV) B0 (GPa) B0 ′ EG (eV) a
Exp.
PBE
HSE06
PBE0
4.73a 3.18a 0.307a −6.0b 205a 7.4a 3.6c
4.82 3.24 0.306 −4.9 165 5 0.63
4.75 3.19 0.306 −5.2 203 5 2.8
4.75 3.19 0.306 −5.2 204 5 3.6
From ref 31. bFrom ref 32. cFrom ref 25.
upon comparison of experimental and calculated structural parameters, as well as the bulk moduli. However, only PBE0 reproduces accurately the experimental band gap without the need for further adjustments to the fraction of exact exchange. It is worth mentioning that for all functionals used, a marked dependence between the volume and the band gap was found. This is particularly evident for hybrid functionals; the use of a PBE instead of a PBE0 optimized lattice results in a drastic 0.6 eV change in the band gap calculated by PBE0. This leads to the following. (i) The large lattice constant variation of approximately 2% between PBE and PBE0 results corresponds to a pressure on the order of 10 GPa. The magnitude of this pressure is the same as that of the lattice strain induced by the substitutional elements studied in this work. (ii) To have a correct and accurate result, electronic PBE0 band calculations are necessary and PBE0 volumes are mandatory (i.e., it is not consistent to use PBE volumes with hybrid-functional calculations for these materials, as has been previously attempted18). For the sake of completeness, we further compare the PBE0 heat of formation and find it is in nice agreement with the previous (−5.29 eV) value reported by Scanlon et al.19 HSE06 values reported by Varley et al.28 are also within 0.2 eV of our result. All functionals are seen to significantly underestimate the experimentally measured value. n-Type Dopants. Figure 2 summarizes the prescreening formation energies for n-type dopants by showing the stable
Figure 2. Stable PBE charge state of a substitutional atom on a Sn site, when ΔεF is at the CBM: blue,
