Manipulating Surface Potentials of Metal Oxides Using Semiconductor

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Manipulating Surface Potentials of Metal Oxides Using Semiconductor Heterojunctions Navaneetha Krishnan Nandakumar, and Edmund G. Seebauer J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11657 • Publication Date (Web): 22 Feb 2016 Downloaded from http://pubs.acs.org on March 1, 2016

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The Journal of Physical Chemistry

Manipulating Surface Potentials of Metal Oxides Using Semiconductor Heterojunctions Navaneetha K. Nandakumar† and Edmund G. Seebauer* Department of Chemical and Biomolecular Engineering University of Illinois, Urbana, IL 61801, USA

Abstract: Controlling the free-surface electrostatic potential of semiconducting metal oxides offers possibilities for improving the performance of sensors, and catalysts and photocatalysts. However, methods to exert such control have typically proven to be inexact and unreliable. The present work demonstrates an approach based on semiconductor heterojunctions, wherein an oxide substrate with controlled carrier concentration supports a much thinner layer. The layer is too thin to absorb all the charge that would normally transfer, so some of the excess charge propagates to the free surface and changes the surface potential. A combination of standard heterojunction analysis via Poisson’s equation and surface potential measurements verifies the workability of this concept for thin polycrystalline V2O5 grown on polycrystalline anatase TiO2.

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1. Introduction Heterojunctions composed entirely of metal oxide semiconductors have been investigated for use in numerous applications including solar cells1, electronic devices2-3, gas sensors4-5, photocatalysts6-8 and other catalysts9-11. In some of these applications, one of the oxide layers composing the junction presents a free surface to the ambient fluid medium. If the junction interface and the free surface are in close enough spatial proximity, the charge exchange that normally occurs between the two semiconductors extends all the way to the free surface through the space charge region. Figure 1 shows such a case schematically in the case of a thin layer of vanadia (V2O5) in contact with TiO2. The layer is too thin to absorb all the charge that would normally transfer, so it is natural to ask where the unaccommodated charge goes, or whether it transfers at all. In cases where the ambient fluid medium is a gas or a liquid of low ionic strength, and the surface Fermi energy is not otherwise pinned, the answer determines the nature of the band bending within the thin layer and the value of the free-surface potential Vs. These two attributes of the layer in turn influence the magnitude and spatial extent of the electric fields present near the surface (for photocatalysts), as well as the Lewis acid-base character of the surface12 (for catalysts and sensors). The available literature does not appear to have addressed this question directly. The present work employs a standard Anderson model for semiconductor heterojunctions to predict the likely value of Vs for thin polycrystalline V2O5 deposited on polycrystalline anatase TiO2. Ultraviolet photoelectron spectroscopy and kelvin probe measurements verify the accuracy of these predictions. The results provide evidence that oxide heterojunctions may be designed with a priori choice Vs.

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Figure 1. Band-diagram schematics for n-TiO2, n-V2O5 isotype heterojunctions for thick and thin layers of V2O5

2. Physical picture: Heterojunctions with a very thin layer When the material on one side of a heterojunction becomes sufficiently thin, its bulk can no longer absorb all the charge that would otherwise exchange. The layer becomes thinner than its space charge layer would otherwise be. The heterojunction structure can respond in several ways − usefully examined in sequence as the layer becomes progressively thinner down to the asymptotic limit of one monolayer. In a semi-infinite heterojunction, charge exchange occurs across the interface to equalize the chemical potential throughout the structure. The charge exchange normally involves electrons and holes that populate the conduction and valence bands of the respective sides.

For

quantitative analysis to describe the charge exchange, Poisson’s equation for the electric potential ψ must be solved with suitable boundary conditions at the interface and deep within the bulk of the two semiconductors. The (suitably referenced) deep-bulk potential is assumed to decay to zero. An early and simple interfacial boundary condition proposed by Anderson 3



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idealizes the semiconductors as though they were still far-separated.13 Chemical bonding effects at the interface are neglected, which in some cases create defects and other perturbations that alter the idealized charge exchange. Neglecting these complications, the Anderson rule is usually stated as follows: the discontinuity in the conduction band edges EC equals the difference in electron affinities χ between the two materials: ∆EC = χ1 – χ2

(1)

The problem then becomes mathematically well-defined so that a solution for ψ throughout the structure is possible. However, when one side of the heterojunction becomes so thin that ψ can no longer decay to zero outside the space charge region near the interface, that side becomes incapable of absorbing all the electrons or holes that seek to exchange. Several non-exclusive possibilities exist. Consider first the case wherein the layer is only slightly thinner than the space charge region would otherwise be. Bulk traps absorb additional charge, and the space charge layer thins down correspondingly. This scenario is most likely in highly defected single crystals or polycrystalline material, wherein a large number of energy states exists within the band gap that are close in energy to the conduction or valence band as appropriate. The free surface absorbs additional charge, either within defect sites such as kinks or surface vacancies, or directly within surface bonds (such as V-O on vanadia). Such absorption of charge should induce measureable changes in EF (and Vs) at the surface. Those changes would affect E at the surface (with implications for carrier drift in photocatalysis), as well as the Lewis acidbase character of surface bonds12, with implications for adsorption and catalysis.

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Consider next the case wherein the layer becomes extremely thin (approaching the asymptotic limit of one monolayer). The layer’s electronic bands, defects and surface become saturated with charge and incapable of absorbing the all the electrons or holes that would transfer in a standard heterojunction.

As a result, less net charge transfers, and the space charge layer in the

semiconductor support thins down. The present work examines the intermediate case of a thin layer wherein ψ can no longer decay to zero, but is not so thin that the total amount of charge transfer decreases dramatically.

3. Quantitative Model: the TiO2-V2O5 heterojunction 3.1. Classical semi-infinite media Classical electrostatic analysis of heterojunctions via Poisson’s equation has been detailed in numerous well-known textbooks and other treatises.14 The V2O5/TiO2 heterojunction is a Type II “staggered gap” structure, wherein the band-gaps of the two semiconductors partially overlap each other, and is depicted in the second panel of Fig. 1. Undoped polycrystalline TiO215 and V2O516 are both intrinsically n-type materials due to excess of donor native defects. Anatase TiO2 typically has a bulk Fermi energy near 4 eV, while the value for V2O5 is closer to 6.7 eV. Upon the formation of the junction, electrons flow from TiO2 into V2O5, creating a depletion region in TiO2 and an accumulation region in V2O5. For semiconductor layers that are semi-infinite on each side of the junction, the spatial distribution of the electric potential ψ is obtained by solving Poisson’s equation:

= − + −

(2),

where ND and NA respectively denote the donor and acceptor concentrations, and n and p represent the electron and hole concentrations as a function of position x. We designate V2O5 as 5



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region 1 and TiO2 as region 2. Poisson’s equation can be solved separately within each semiconductor with the boundary conditions: ψ = 0 as x → ±∞

(3)

ψ = ψb1 (region 1) at x = x0

(4)

ψ = ψb2 (region 2) at x = x0

(5),

where x0 denotes the position of the interface. Solution of Eqs. (2)-(5) yields the values of E = –dψ/dx at the interface as: |E1(x0) | =

|E2(x0) | =

− 1 − !"# $

(6)

(7)

Here, q represents the electronic charge (1.6×10-19 C); k is the Boltzmann constant; T is temperature, and ε is the dielectric constant. However, in this treatment, ψb1 and ψb2 remain unknowns. Determination of these quantities requires application of the Anderson rule together with the condition requiring continuity of electric displacement at the interface. The Anderson Rule necessitates that the total bandbending on both sides equal the built in potential: (8),

ψb1 + ψb2 = |EF1 – EF2|

where EF1 and EF2 represent the bulk Fermi energies of the isolated semiconductors. The continuity of electric displacement requires that: (9).

ε1E1 (x0) = ε2E2 (x0)

Solution of Eq. (9) (making use of Eqs. (6), (7) and (8)) yields ψb1 and ψb2. In moving away from the interface within the depletion region of TiO2, ψ decays quadratically to zero. Similar movement away from the interface within the accumulation region of V2O5 also 6


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leads to a decay of ψ to zero, but with a more complicated functional form that must be calculated numerically and can be obtained in normalized form from the literature.17 The band edges EC and EV typically represent electron potentials rather than electric potentials, and therefore their variations behave in the same way as ψ but with opposite sign. Table 1 shows the physical properties used as inputs for these equations. The TiO2 employed in the present experiments underwent extensive electrical characterization15, 18, and was n-type with a known concentration of donors (mainly at grain boundaries) that was used to calculate EF (using a known value of conduction band density of states NC). No similar characterization was performed for the V2O5, so despite well-known difficulties18 with literature reports of carrier concentrations in metal oxides, a literature value was employed16. Similar problems plague measurements of work function on metal oxides19, wherein small differences in surface preparation or measurement conditions can lead to large shifts in Ф. A literature value for work function was used as a proxy for the bulk Fermi level position (EF) for V2O5. Since a reliable value of the conduction band density of states (NC) of V2O5 could not be obtained from literature, both EF and Nd were taken from literature.

Table 1. Parameters used to calculate band-bending and band energy profiles.

Parameter

TiO2

V2O5

Dielectric constant (εr)

31

5.3

Electron affinity (eV)*

3.9

6

7



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Conduction band effective 7.9×1020 density of states Nc (cm-3) Valence band effective density of states Nv (cm-3) Donor concentration Nd (cm-3) Band gap Eg (eV)*

1.8×1019 8.3×1016 1×1016 3.2

Work function Φ1 (eV)**

2.3 6.7

* Room temperature value. ** Referenced to the vacuum level.

Figure 2. Calculated band diagram for the V2O5-TiO2 heterojunction, with two example values of Nd in TiO2. Energies are referenced to EF, with x0 set to 0. Figure 2 shows the calculated band diagram for the V2O5-TiO2 system, with energies referenced to EF, and x0 set to zero. The behavior of the bands corresponds to well-known patterns in such structures. The TiO2 is more electron-rich than the V2O5, and therefore electrons flow from the TiO2 into the V2O5 until the electrostatic potential rises sufficiently in the vicinity 8


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of the interface to inhibit further electron flow. Near the interface, the bands of TiO2 bend upward while those of V2O5 bend downward. The TiO2 near the interface suffers a net depletion of electrons, while the corresponding space charge region within V2O5 experiences an accumulation. Generally speaking, the depletion region within TiO2 is considerably wider than the accumulation region in V2O5. The depletion region in TiO2 narrows down as Nd increases. However, increasing the carrier concentration in TiO2 promotes more electron exchange and therefore increased band-bending in V2O5 as well as a wider accumulation region. Notably, most of the total potential change across the junction occurs on the TiO2 side of the junction. Put another way, the degree of band bending is much higher within the TiO2. This behavior results partly from the much higher dielectric constant of TiO2 compared to V2O5. Also, the bands in an accumulation region approach an interface with considerably higher slope than in an equivalent depletion region, leading to a higher electric field. Eq. (9) and Eq. (6) then lead to small values of ψb1.

(a)

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(b)

Figure 3. Calculated EC in (a) TiO2 and (b) V2O5 vs. distance from the heterojunction interface, for various levels of Nd in the TiO2 layer. Energies referenced to EF, with x0 = 0.

Fig. 3a shows a close-up view of the variation of the conduction band edge EC (referenced to the Fermi level) in the TiO2 layer as a function of distance from the heterojunction interface. The family of curves represents different donor concentrations in the TiO2. The change in Nd translates into different values of EC-EF in the bulk. The magnitude of bending decreases with Nd in the TiO2, changing about 0.3 eV. Fig. 3b shows an equivalent diagram for the V2O5 side of the junction. The net accumulation of electrons increases as Nd within the TiO2 increases. Most of the band-bending occurs within the first 5 nm, regardless of Nd in the TiO2. (Nd within the V2O5 does not change in these simulations.) The magnitude of bending increases with Nd in the TiO2, up to about 0.3 eV (equal and opposite to the corresponding effect in TiO2. Beyond 20nm, the bands in V2O5 are little affected by the TiO2.

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Note that this treatment implicitly treats both sides of the heterojunction as uniform media. The effects of polycrystallinity, porosity, grain boundaries, and deviations in charged defect concentrations near surfaces, interfaces and grain boundaries are all neglected.

3.2. Thin layer and truncation approximation As discussed in Section 2, several possibilities exist when the V2O5 layer is too thin to accommodate all the charge transfer predicted by the analysis of Sec. 3.1. Perhaps the simplest approximation is to retain the mathematical solutions for band behavior shown in Fig. 3, but to truncate the band edge profiles at the position of the free surface. In other words, EF is taken to lie (with respect to the band edges) at the energy position given by the semi-infinite solution. This approximation is likely to work best for free surfaces having densities of intra-gap surface states that are either small or uniformly distributed in energy. That way, EF is unlikely to pin at the free surface. This approximation has the effect of simply neglecting the transferred charge given by the semi-infinite medium solution that lies beyond the surface. However, in accumulation layers the vast majority of transferred charge resides near the interface. Thus, such an approximation may be acceptable for most purposes. We note that the numerical values of certain material properties in the model could deviate from bulk values as the film becomes very thin. For example, strain effects sometimes induce changes in dielectric constants at optical frequencies even for semiconductor films as thick as 1000nm.20 However, we surmise the largest sources for possible error in the model stem from the uniform medium assumption (with polycrystalline, sometimes-discontinuous films), the truncation approximation, and use of the standard Anderson rule for band offsets. 11



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4. Experiment 4.1. Heterojunction synthesis Heterojunction test structures were synthesized on Si(100) substrates of approximate dimensions 1 cm × 1 cm.

Anatase TiO2 was grown in amorphous form by atomic layer

deposition according to protocols described previously18.

Subsequent annealing at 550°C

yielded polycrystalline anatase whose detailed characterization has also been described elsewhere.15 The crystalline films were 100 nm thick, and capacitance-voltage measurements15 yielded a carrier concentration of ~1017 cm-3. Polycrystalline V2O5 films of various thicknesses were grown atop the anatase by chemical vapor deposition at 200°C according to methods detailed elsewhere.21 Film thicknesses were determined by single-wavelength ellipsometry, using a measured refractive index of 2.3 for V2O5. The TiO2 refractive index was taken to be 2.05 for determination of the V2O5 film thickness in the multilayer structure.22

4.2. Characterization Crystallinity of the anatase and vanadia was determined by X-ray diffraction using a Philips X’Pert diffractometer with Cu Kα radiation (0.154 nm wavelength) in glancing angle mode (1°). Surface morphology was examined by scanning electron microscopy with a Hitachi S-4800 scanning electron microscope operating at an acceleration voltage of 15 kV and an emission current of 10 µA. Cross-sectional images were also obtained to confirm the film thicknesses determined by ellipsometry.

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To determine the conformality of the thin V2O5 films on TiO2, the surface morphology of several specimens was examined with an Asylum Research MFP-3D atomic force microscope in tapping mode using silicon probes (Budget Sensors) having aluminum reflex coating and a resonant frequency of 300 kHz. Selected specimens were also studied by Kelvin probe force microscopy (KPFM) using the same instrument with Si probes having a Cr/Pt conductive coating and a resonant frequency of 75 kHz. The value of EF at the surface was measured with ultra-violet photoelectron spectroscopy (UPS) using a Physical Electronics PHI 5400 spectrometer. Helium I radiation (21.2 eV) was employed.

5. Results 5.1. Crystallinity X-ray diffraction confirmed that the TiO2 was crystalline anatase with a [101] orientation (peak at ~25.5⁰)15. The V2O5 grown atop the anatase was crystalline with a preferred [001] orientation (peak at ~20.4⁰), similar to material synthesized previously on silicon as reported elsewhere.21 Figure 4 shows example spectra. The average crystallite size for the V2O5 film was calculated to be 18nm.

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Figure 4. XRD spectra of V2O5 films of various thicknesses on ~100 nm thick TiO2 films

5.2. Film morphology Electron microscopy as shown in Fig. 5 indicated that the deposited vanadia had a typical grain size of about 50 nm that did not vary appreciably with film thickness. Above thickness of about 20 nm, the vanadia covered the titania substrate entirely. However, vanadia films below this thickness were not entirely continuous, thereby exposing some of the underlying anatase.

(a)

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(b)

(c)

(d) Figure 5. Scanning electron micrographs of V2O5 on TiO2 at vanadia thicknesses of (a) 5 nm (scale bar represents 1 um), (b) 9 nm, (c) 21 nm, and (d) 58 nm.

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Figure 6 shows atomic force micrographs of various vanadia surfaces. Thin vanadia films (Fig. 6(a), 6(b)) on silicon were quite smooth with rms roughness in the 1-2 nm range. For thicker films, the roughness increased to about 7 nm. At a given thickness, switching the substrate to anatase (Fig. 6(c), 6(d)) increased the roughness slightly, with the anatase surface itself serving as a significant source of roughness. For discontinuous vanadia films below 20 nm, the roughness decreased, but the underlying anatase showed through (Fig. 6(e)).

(a)

(b)

(c) 16


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(d)

(e) Figure 6. Atomic force micrographs of various vanadia surfaces (a) 7 nm V2O5/Si, very smooth film, (b) 20 nm V2O5/Si, (c) 21 nm V2O5/109 nm TiO2 – increased roughness due to roughness of TiO2 underlayer, (d) 89 nm V2O5/108 nm TiO2, (e) 5 nm V2O5/TiO2 showing TiO2 grain structure.

5.3. Surface potential KPFM scans showed a very uniform surface potential distribution across the areas scanned, within +/- 3% of the mean. 1µm x 1µm areas were probed on the samples.

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The work function was calculated using the secondary emission onset in the UPS spectra. Fig. 7 shows example spectra for vanadia grown directly on Si(100), wherein the work function, Φ, was 5.05 eV regardless of thickness. Due to well-known and varied systematic artifacts in such measurements,19 this value should not be compared directly with the value of 6.7 eV given in Table 1.

Figure 7: UPS spectra for a thin and a thick film of V2O5 on silicon Fig. 8 shows UPS spectra for several thicknesses of vanadia on anatase, together with a spectrum for pure anatase. For V2O5/TiO2, Φ was lower than for V2O5/Si, and varied with thickness of V2O5. At 5nm V2O5/TiO2, two secondary emission peaks were observed, likely corresponding to V2O5 particles and the free TiO2 surface. In this case, Φ for TiO2 was estimated to be 4.1 eV, indicating slight upward band-bending as Φ for virgin TiO2 was 3.9 eV.

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Figure 8. UPS spectra for vanadia films of various thicknesses grown on ~100nm anatase films: (a) 5nm (b) 21nm (c) 37nm (d) 62nm. A spectrum for pure anatase (23nm thick on Si) is also included (e). Based on these measurements, Fig. 9 shows the energy of the free-surface conduction band minimum in the vanadia as a function of the film thickness. Results are shown for both UPS and Kelvin probe measurements. As with UPS, the absolute values of the Kelvin probe measurements may not be easily compared with literature results.19 However, the relative values of both UPS and Kelvin probe measurements are directly comparable within Fig. 9. Superimposed on the experimental data is the prediction of the heterojunction model in the truncation approximation. The graph was plotted assuming that 60nm of V2O5 on TiO2 replicates the properties of bulk V2O5. Surface potentials from KPFM and work-function values from UPS of other specimens (relative to the 60nm case) were used to calculate band-bending and thus the band energy level.

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Figure 9. Conduction band energy minimum of the vanadia surface as a function of V2O5 film thickness

6. Discussion 6.1. Interpretation of surface potentials The results of Fig. 9 show clearly that the surface potential at the free surface of V2O5 can indeed be manipulated by supporting a thin film on TiO2 and varying the thickness of the V2O5 layer. Following both intuition and the quantitative reasoning outlined earlier, the magnitude of this effect increases as the film becomes thinner so that the free surface “sees” the underlying support with less screening. Both the direction and magnitude of the surface potential follow approximately what the quantitative heterojunction model predicts. This result suggests that the little or no pinning of the Fermi level of the V2O5 occurs either at the free surface or at the interface with TiO2. Based on the aggregated UPS and Kelvin probe measurements in Fig. 9, the results point to a slightly faster decline in Vs as the film thins down than the model predicts. We cannot discern whether this difference results from measurement errors or the inaccuracies in the model, which should increase as the film becomes thinner. On the measurement side, it is 20


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important to note that for a surface with lateral heterogeneities, UPS measures the lowest value of work function that the surface irregularities expose. Moreover, for very thin specimens of V2O5, the SEM results of Fig. 5 indicated that both V2O5 and TiO2 are exposed. Thus, two distinct secondary electron UPS peaks are observed that pose challenges in deconvolution. For the Kelvin probe measurements, the results give a value that is averaged over the area of the probe.19 This systematic difference could account for some of the deviations seen between the two techniques in Fig. 9. As suggested early in the paper, inaccuracies in the model can come in several varieties. First, the Anderson rule neglects chemical bond formation at the interface, and is well known to give inaccurate results in many instances. Various improvements have been proposed over the years. These include: (i)

The common anion rule.23 The key premise is that the valence band is composed mainly of energy states associated with anions. Thus, materials with the same anions (such as O in the V2O5/TiO2 case should have very small valence band offsets.

(ii)

The gap state model.24 A postulated dipole layer at the interface leads to a conduction band offset is given by the difference in Schottky barrier height between the two materials. This model works well when the semiconductors are closely lattice matched.

(iii)

Heuristic corrections.25 Such methods sometimes work well for specific systems, such as the 60:40 rule used for GaAs/AlGaAs.

As band offset data exist for few oxide heterojunctions, and V2O5/TiO2 have no appreciable lattice matching, the latter two possibilities seem unlikely to offer improvements.

The

V2O5/TiO2 does nominally share a common anion, but these oxides have appreciably more ionic

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character than most systems reported in the literature, and the oxygen in the two materials occupies very different lattice geometries. Other possible inaccuracies include the truncation approximation and the various ways the system actually accommodates the excess electrons that the bulk (and apparently surface states) nominally cannot absorb. For example, otherwise inactive deep-gap energy states within crystallites or at grain boundaries may become active for absorbing charge when the driving force is sufficiently large. Or enhanced gas adsorption may occur − such as the reductive adsorption of O2 from the ambient to create O2-, O-, or O2- on the surface. Yet another source of uncertainty is the uniform-medium assumption that underlies the modeling. It is remarkable how well this assumption works, although there exists a successful precedent for using this approximation for polycrystalline thin film anatase.26 We note that Fig. 3b indicates that Vs should change in response to variations in carrier concentration of the underlying TiO2, in addition to variations in V2O5 thickness as described here. This laboratory has developed methods for controlling Nd in thin-film anatase15 over a range of roughly two orders of magnitude, from roughly 3×1015 to 3×1017 cm-3. Experiments were attempted to observe the predicted variations in Vs. However, in accord with the predictions of Fig. 3b, the observed effects were small even for the thinnest (5nm) V2O5 films, and were difficult to reproduce reliably due to lateral discontinuities that appear in the film under such conditions. Thus, we have not reported those results in the present work.

6.2. Application to other oxide heterojunction systems A more pronounced heterojunction effect would be expected if V2O5 were deposited on pTiO2. The materials would form a p-n junction. If the TiO2 were sufficiently p-type (i.e., with the 22


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isolated-material Fermi level falling below that of the V2O5), would electrons flow from V2O5 to TiO2, leading to depletion layers on both sides. A small advantage for system analysis would be that Poisson’s equation is solvable analytically on both sides of the heterojunction. A larger, more practical advantage is that depletion regions tend to be considerably wider than accumulation regions for the same absolute value of carrier concentration, leading to larger freesurface effects on the V2O5 for a given film thickness. Moreover, the bands in V2O5 would bend upward at the interface, meaning the free surface would become more electron-deficient. For heterogeneous catalysis, this effect translates into an increase in Lewis acidity and would thereby enhance reactions that requiring acid sites.12 Unfortunately, TiO2 is notoriously difficult to fabricate in p-type form for rather fundamental reasons.4, 27 Yet successful examples do appear in the literature.28-29 TiO2 was employed as the substrate in the present work in large measure because its physical and electronic properties as a semiconductor are well documented, and reliable protocols exist for measuring its carrier concentration. This knowledge base is not present to nearly the same extent for other oxide semiconductors, including V2O5. Thus, the analytical approach outlined here will, for the time being, remain difficult to perform for most semiconducting oxide pairs. Yet certain generalizations may yet be made − particularly for applications involving thin films such as gas sensors. Such sensors often comprise oxide semiconductors such as TiO2, ZnO, SnO2, CuO, WO3 and many others. Various heterojunction configurations have been reported extensively.30-32 Although many factors influence the behavior of the sensors, Vs is often one of them. The existing work does not yet seem to exploit the controllability of Vs through choice of underlayer support, carrier concentration, and overlayer thickness that is intrinsic to heterostuctures as demonstrated here.

Metal decoration of the free surface has also been 23



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employed to enhance performance.33 The effect of the metal may be modified by the electron richness of the layer on which it rests (via the Schwab effect), as has already been demonstrated in the context of heterogeneous catalysis.34 Supported semiconducting oxides such as V2O5 also find widespread use in catalysis with supports such as TIO2, MoO3, Nb2O5 and ZrO2 for the oxidative dehydrogenation of alkanes11, selective catalytic reduction of NOx10 and selective oxidation of alcohols.35

Many factors

influence the rates and selectivities of such reactions, including the electronegativity of the support cation, the oxidation state of the surface V atoms35 and the density of surface V species36 and other chemical interactions between the overlayer and support. Such factors are especially pronounced at the near-monolayer levels of V2O5 that are often employed. Yet the conceptual framework of heterojunction may yet offer insights from a condensed matter physics perspective that other perspectives may not yield so readily. Extension of this conceptual framework to core-shell nanoparticles (such as core-shell TiO2/V2O5) is also possible. However, depending upon the diameter of the core and the thickness of the shell, the extent of charge exchange may be sufficient to perturb the carrier concentrations in both the core and the shell from their bulk values.

Overall charge neutrality and

centrosymmetry (yielding a boundary condition of dψ/dx = 0 at the core’s center) would become important considerations in solving Poisson’s equation. Questions related to the extreme thinfilm limit mentioned briefly early in this article would also arise − e.g., how much charge can actually be exchanged when both the core and shell are limited by finite sizes. The present work has considered a Type II staggered-gap heterojunction. The analysis can be extended without complication to Type I “straddling-gap” configurations, wherein one semiconductor’s band-gap is contained completely within the band-gap of the other. Extension 24


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would be more complicated for Type III “broken-gap” configurations, wherein there is no overlap between the band-gaps of the semiconductors. Such structures may be semi-metallic in nature (e.g., the GaSb:InAs p-n heterojunction37).

7. Conclusion A conceptual framework for controlling the surface potential of metal oxide semiconductors has been demonstrated based on classical thin-film heterojunctions. In the test case of V2O5, Vs of the free surface was controlled in a way that was accurately predicted using a solution to Poisson’s equation for uniform semiconductor media together with the Anderson rule for conduction band offsets and a simple truncation approximation to account for a narrowdimension thin film. Possible complicating effects of charge screening at the interface, surface Fermi level pinning, void and grain-boundary geometry and the like did not dramatically change the expected behavior.

To the extent such effects can be minimized in other oxide

semiconductor systems, the analytical framework presented here should be quite general. As certain chemical properties of the free oxide surface, such as Lewis acidity, depend upon the surface potential and the availability of free carriers implied therein, the present approach offers a way to either directly control those aspects of surface behavior, or to provide insights into that behavior from a distinctive perspective.

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AUTHOR INFORMATION Corresponding Author * e-mail: [email protected] Telephone: +1-217-244-9214; Fax: +1-217-333-5052 Present Addresses † Maxim Integrated, Dallas, TX 75240, USA Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT We gratefully acknowledge funding from the National Science Foundation (DMR 07-04354, DMR 10-05720 and DMR 13-06822). One of us (NKN) was partially supported by a Drickamer Research Fellowship awarded by the University of Illinois.

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Manipulating Surface Potentials of Metal Oxides Using Semiconductor

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