Patent Publication Number: US-2022231171-A1

Title: Method of controlling oxygen vacancy concentration in a semiconducting metal oxide

Description:
RELATED APPLICATION 
     The present patent document claims the benefit of priority under 35 U.S.C. 119(e) to U.S. Provisional Patent Application No. 63/137,971, which was filed on Jan. 15, 2021, and is hereby incorporated by reference in its entirety. 
    
    
     FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with government support under DMR 13-06822 and DMR 17-09327 awarded by the National Science Foundation (NSF). The government has certain rights in the invention. 
    
    
     TECHNICAL FIELD 
     The present disclosure is related generally to defect engineering and more specifically to controlling defects in semiconducting metal oxides. 
     BACKGROUND 
     Concentration and spatial distribution of oxygen vacancies (V o ) may influence a variety of technologically relevant aspects of commercially important binary oxide semiconductors (e.g., ZnO and TiO 2 ) and perovskites having the general formula ABO 3 . For ZnO, those aspects may include parasitic green emission in ultraviolet emitters, photocarrier recombination rates in photocatalysts, ferromagnetism in spintronics, piezoelectricity in nanogenerators, and free electron density in p-n junctions. For TiO 2 , those aspects may include electroforming in resistive memory devices, electrocatalysts of nanoparticles in ammonia production, photocatalysis in water splitting, anapole excitation in light harvesting, electrochemistry in energy storage, and wavelength selectivity in ultraviolet (UV) photodetectors. Perovskites currently find primary application in photovoltaic solar cells, but also have potential applications in sensors, catalyst electrodes, certain types of fuel cells, lasers, memory devices and spintronics. Synthesis methods for oxide semiconductors normally leave behind variable and often unpredictable concentrations of V o , and at typical fabrication temperatures the vacancies exhibit minimal mobility. Oxygen interstitial atoms (O i ) move far more rapidly, however, and under oxygen-rich conditions may have more thermodynamic stability. Consequently, post-synthesis introduction of O i  to eliminate V o  or to adjust vacancy concentration more precisely would be advantageous for a broad array of applications in microelectronics, optoelectronics, photovoltaics, electrochemistry and photocatalysis. 
     BRIEF SUMMARY 
     A method of controlling oxygen vacancy concentration in a semiconducting metal oxide includes exposing a treated surface of a crystalline metal oxide to water at a temperature and pressure sufficient to maintain the water in a liquid phase. During the exposure, a portion of the water is adsorbed onto the treated surface and dissociates into atomic oxygen and hydrogen. The atomic oxygen is injected into and diffuses through the crystalline metal oxide, forming isolated oxygen interstitials and oxygen defect complexes. The isolated oxygen interstitials replace oxygen vacancies in the crystalline metal oxide. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A-1D  show diffusion profiles of  18 O for the non-polar (10 1 0) treated surface of ZnO and the non-polar (110) treated surface of TiO 2  upon exposure to  18 O-labeled water, where  FIGS. 1B and 1D  present the data on a normalized semi-logarithmic scale. 
         FIG. 1E  shows a diffusion profile of  18 O for the (−201) treated surface of Sn-doped Ga 2 O 3  upon exposure to  18 O-labeled water. 
         FIGS. 2A-2C  show Arrhenius plots of net injection flux (F), mean diffusion length (λ), and effective diffusivity (D eff ) based on the  18 O diffusion profiles measured for ZnO (10 1 0) and TiO 2  (110). 
         FIGS. 2D-2F  show Arrhenius plots of F, λ, and D eff  based on  18 O diffusion profiles measured for Ga 2 O 3  (100). 
         FIG. 3A  plots log D eff  versus 1/k B T for Zn-terminated, O-terminated, and nonpolar ZnO treated surfaces exposed to liquid water to obtain oxygen injection in comparison with prior published gas-based experiments. 
         FIG. 3B  plots log D eff  versus 1/k B T for TiO 2  treated surfaces exposed to liquid water to obtain oxygen injection in comparison with prior published gas-based experiments. 
         FIG. 4A  plots net injection flux (F) as a function of 1/k B T for the Zn-terminated, O-terminated, and nonpolar ZnO treated surfaces exposed to liquid water for oxygen injection. 
         FIG. 4B  plots mean diffusion length (λ) as a function of 1/k B T for the Zn-terminated, O-terminated, and nonpolar ZnO treated surfaces exposed to liquid water for oxygen injection. 
         FIG. 5A  plots net injection flux (F) as a function of 1/k B T for a treated TiO 2  (110) surface illuminated by UV light during water exposure at a temperature of 40° C., in comparison to analogous data obtained with red laser light and light-shielding (dark) conditions. 
         FIG. 5B  plots mean diffusion length (λ) as a function of 1/k B T for a treated TiO 2  (110) surface illuminated by UV light during water exposure at a temperature of 40° C., in comparison to analogous data obtained with red laser light and light-shielding (dark) conditions. 
         FIG. 6A  plots mean net injection flux (F) for a (110) rutile TiO 2  surface exposed to liquid water for oxygen injection while under a bias voltage. 
         FIG. 6B  plots mean diffusion length (λ) for a (110) rutile TiO 2  surface exposed to liquid water for oxygen injection while under a bias voltage. 
         FIG. 7  shows a metal cation (Mn) diffusion profile obtained from exposing a (110) rutile TiO 2  surface to an aqueous solution comprising MnCl 2  at two different levels of pH while under a bias voltage. 
     
    
    
     DETAILED DESCRIPTION 
     A liquid-based method of replacing oxygen vacancies with interstitial oxygen in a semiconducting metal oxide has been developed. As indicated above, control over the concentration and spatial distribution of oxygen vacancies in oxide semiconductors may enable advances in fields ranging from photocatalysis to optoelectronics. In contrast to a previous gas-based method of manipulating vacancy concentration that utilizes elevated temperatures (e.g., &gt;500° C.) and very low pressures (e.g., &lt;10 −4  Torr), the new method can inject atomic oxygen into oxide semiconductors at relatively low temperatures and atmospheric pressure, thereby reducing hurdles toward manufacturability. Fast injection may require removal of monolayer-level surface contaminants and the elimination of bonds between adsorbed oxygen atoms and any species other than the oxide semiconductor surface. 
     The method entails exposing a treated surface of a crystalline metal oxide comprising oxygen vacancies to liquid water at a temperature and pressure sufficient to maintain the water in a liquid phase. In one example, the temperature is less than 100° C. and the pressure is atmospheric pressure. The water may include H 2 O, H 2   18 O (where  16 O is replaced with  18 O), and/or  2 H 2 O (where  1 H is replaced with  2 H). The treated surface may be understood to be an atomically-clean or substantially poison-free surface of the metal oxide semiconductor, as will be discussed later. During the exposure, some amount of the water is adsorbed onto the treated surface and dissociates into atomic oxygen (e.g.,  16 O and/or  18 O) and hydrogen. The atomic oxygen is injected into and diffuses through the crystalline metal oxide, forming isolated oxygen interstitials as well as defect complexes. Injection may be promoted with a bias voltage or with ultraviolet radiation, as discussed below. The isolated oxygen interstitials may replace or “annihilate” the oxygen vacancies in the crystalline metal oxide. Beneficially, dissociation of the liquid water on the treated surface does not lead to incorporation of hydrogen, which is typically an unwanted species, into the crystalline metal oxide. Typically, the crystalline metal oxide may include a vacancy concentration on the order of 1×10 16  cm −3  prior to the method, and all or substantially all (e.g, greater than 99%) of the oxygen vacancies over a predetermined depth may be annihilated by the oxygen interstitials, such that O i  becomes the majority oxygen-related native point defect. 
     The exposure to the liquid water may take place for a time duration sufficient for diffusion of the atomic oxygen into the crystalline metal oxide to occur (e.g., to the predetermined depth), after which the exposure of the treated surface to the liquid water may be halted. Typically, the diffusion profile may be approximated by x 2 =6Dt, where x represents distance (e.g., the predetermined depth referred to above), D represents diffusion coefficient, and t represents time duration of the exposure to liquid water. Typically, the time duration is in a range from about 10 min to about 120 min, or from about 30 min to about 90 min. Generally speaking, however, the time duration may be at least about 10 min and as high as several days, e.g., up to about 100 hours, which can significantly impact the distance traveled by the oxygen interstitials, as discussed further below. 
     The crystalline metal oxide may be described as being single-crystalline (monocrystalline) or polycrystalline. In examples in which the crystalline metal oxide is single-crystalline, the crystalline metal oxide may exhibit a crystal lattice structure that is devoid of grain boundaries. Typically, the crystalline metal oxide comprises a semiconducting metal oxide such as TiO 2 , ZnO, Ga 2 O 3 , SrTiO 3 , SnO 2 , In 2 O 3 , ITO, WO 3 , Cr 2 O 3 , CuO, Co 2 O 3  and/or a perovskite having the general formula ABO 3 , where A and B are metal cations such as Ti, Zn, Ga, Sr, Sn, In, W, Cr, Cu and/or Co. In some examples, the crystalline metal oxide may include a dopant such as Al, As, Ce, Er, Fe, Ga, Mg, N, P, Sb and/or Y. Also or alternatively, the crystalline metal oxide may have at least one linear dimension of about 1 micron or less, or about 100 nm or less, e.g., the crystalline metal oxide may take the form of a thin film having a thickness of about 1 micron or less, or about 100 nm or less. Alternatively, the crystalline metal oxide may comprise a nanorod or nanoparticle having two or more linear dimensions of about 1 micron or less, or about 100 nm or less. 
     Notably, the atomic oxygen injected from the surface is believed to be a mobile species comprising oxygen interstitials (O i ) rather than oxygen vacancies (V o ) or another oxygen-containing complex. (The terms “oxygen interstitials,” “interstitial oxygen,” and “O i ” are used interchangeably throughout this disclosure.) Evidence for this includes diffusion mechanism changes for exemplary metal oxide crystals (TiO 2 , ZnO and Ga 2 O 3  in these examples) that signify a mobile intermediate that is not V o . For example, exponential profile shapes on a normalized scale and measured values for effective diffusity (D eff ) exceed those for V o  mediation by 2-8 orders of magnitude and are consistent with values predicted by O i . Literature quantum calculations predict O i  to have a lower formation enthalpy than V o  under the experimental conditions. The impact of the surface on diffusion is illustrated by diffusion data for ZnO, where diffusion parameters discussed below (D eff , λ and F) may vary depending on the surface (e.g., c-axis Zn-terminated and O-terminated, and a-axis nonpolar). 
     The oxygen interstitials are mobile enough even at room temperature to find a defect or species, in addition to oxygen vacancies, to react or complex (i.e., sequester) with. The defect complexes may include native cation vacancies or interstitials, adventitious hydrogen, extended defects, or other species. In other words, the defect complexes formed by the injection of atomic oxygen into the crystalline metal oxide may include interstitial oxygen (O i ) and a metal cation vacancy (V M ), a metal cation interstitial (M i ), hydrogen (H), and/or an extended defect, such as an edge disclocation. Examples of oxygen defect complexes include O i —H, O i —V M , and/or O i -M i , where M represents a metal cation such as, but not limited to, Ti, Zn, Ga, Sr, Sn, In, W, Cr, Cu and/or Co. The concentration of O i  may be quite low (with the concentration of V o  being even lower), and may depend upon how tightly the O i  are bound to the various kinds of sequestration sites that are available. Given the relatively low process temperatures of the liquid-based method compared to prior gas-based methods, different defect complexes may be formed by the dissociation of liquid water on the treated surface. In particular, O i  may form complexes with hydrogen (the O i —H complexes mentioned above) that were not previously known to exist as stable complexes in ZnO and TiO 2 . 
     The presence of O i —H complexes can have a drastic effect on the properties of a semiconducting metal oxide by converting hydrogen to an acceptor of electrons. Atomic hydrogen, which is often unavoidably incorporated within metal oxide semiconductors during synthesis, typically acts as a positively-charged donor of electrons, thereby adding unintentional n-type character to the semiconducting metal oxide and inhibiting fabrication of p-type semiconducting devices. However, the O i —H defect complexes formed upon O i  injection may act as negatively-charged acceptors of electrons, promoting p-type behavior. Advantageously, O i —H complexes may exist as electron acceptors over ranges of electronic conditions at which H would otherwise exist as an electron donor. Thus, controllable O i  injection, which can annihilate oxygen vacancies in parallel with forming defect complexes, may be technologically more important in crystalline metal oxides where the concentration of hydrogen exceeds that of oxygen vacancies. 
     The activation energy or injection barrier for the incorporation of oxygen interstitials into the subsurface of TiO 2  and ZnO if found to lie only 0.1-0.2 eV above the lattice site-hopping barrier, which itself is 1 eV or less. These values allow for technologically useful injection rates near room temperature. For example, the lattice site-hopping barriers for O i  in a-axis ZnO and TiO 2  are about 0.6 eV and 0.9 eV, respectively. It is believed that small injection barriers may be found for a wide variety of metal oxides, not just for TiO 2  and ZnO. Hopping barriers of 1 eV or less together with injection barriers exceeding the hopping barriers only slightly may enable diffusion lengths of tens to thousands of nanometers at only a few tens of degrees above room temperature (e.g, 30° C. to &lt;100° C.). It is believed that significant incorporation of interstitial oxygen can occur in this temperature range if the water exposure yields adsorbed oxygen and if co-adsorbates do not poison incorporation sites or raise the injection barrier. Generally speaking, the activation energy or injection barrier appears to be influenced by the type of metal oxide, presence of neighboring adsorbates, charge state of the O defect, and surface reconstruction. The depth of O i  penetration may depend on the type of metal oxide, charge state of the oxygen defect, and/or the concentration of sequestration sites, as well as how strongly the O i  bonds to these sites. 
     Isotopic oxygen self-diffusion experiments confirm the injection and diffusion of a mobile oxygen defect into TiO 2 , ZnO, and Ga 2 O 3  single crystals when the treated surface is exposed to liquid water as described above.  FIGS. 1A-1D  show diffusion profiles of  18 O for the non-polar (10 1 0) treated surface of ZnO and the non-polar (110) treated surface of TiO 2  upon exposure to  18 O-labeled water at temperatures from 30° C. to 80° C. under 1 atm of pressure for 60 minutes.  FIGS. 1B and 1D  present the diffusion data of  FIGS. 1A and 1C , respectively, on a normalized semi-logarithmic scale.  FIG. 1E  shows comparable diffusion profiles for the (−201) treated surface of Sn-doped Ga 2 O 3  upon exposure to  18 O-labeled water at temperatures from 60° C. to 80° C. under 1 atm of pressure for 60 minutes. 
     The isotopic concentration profiles yield composite parameters including several physical effects. Referring again to  FIGS. 1B and 1D , net injection flux (F) of the mobile defect can be determined from the y-axis intercept and mean diffusion length (λ) can be determined from the slope of the concentration profiles. The effective diffusivity (D eff ) for use in a standard diffusion equation can be computed from F and λ. Net injection flux provides insight into the rate at which the treated surface creates mobile O i , and the mean diffusion length provides insight into the immobilization of mobile O i  by bonding to sequestration sites in the crystalline metal oxide.  FIGS. 2A-2C  show Arrhenius plots of net injection F, λ, and D eff  based on the  18 O diffusion profiles measured for ZnO (10 1 0) and TiO 2  (110), and  FIGS. 2D-2F  show Arrhenius plots of F, λ, and D eff  based on  18 O diffusion profiles measured for Ga 2 O 3  (100). 
     Diffusion upon exposure to liquid water is found to be vastly faster than would be extrapolated from prior published gas-based work of the inventor on clean surfaces (“ref. 1”) and even more so in comparison with others that include monolayer levels of surface contamination (“refs. 2-9”), as illustrated in  FIG. 3 , which plots log D eff  versus 1/k B T for Zn-terminated (Zn—ZnO (0001)), O-terminated (O—ZnO (000 1 )), and nonpolar (NP—ZnO (10 1 0)) ZnO surfaces. Analogous data are shown in  FIG. 3B  for TiO 2  (110). The blue, yellow and red curves represent prior published gas-based diffusion data from the inventor for clean, sulfur-poisoned (0.1 monolayer of adsorbed sulfur), and Ti-enriched defective TiO 2  (110) surfaces, respectively. 
     Different crystallographic orientations of the crystalline metal oxide yield different atomic structures at the treated surface. The explanation for the faster diffusion rate may stem from surface cleanliness and the nature of the solid sequestration sites. As shown in  FIG. 4A  for ZnO, F varies slightly with crystallographic orientation, which demonstrates the key role of the treated surface in determining behavior. However, the variations are modest and are not expected to complicate possible manufacturing processes. Notably λ is a bulk property of the crystalline metal oxide and remains substantially unaffected by orientation, as shown by the data of  FIG. 4B . 
     As evidenced by the logarithmic concentration profiles (e.g.,  FIGS. 1B and 1D ), some amount of the atomic oxygen may diffuse within the crystalline metal oxide to a depth of tens of nanometers, e.g., about 20 nm or more in the example of ZnO, and about 60 nm or more in the example of TiO 2 , where greater diffusion depths may be correlated to higher temperatures of liquid water exposure. Preferably, the atomic oxygen may diffuse to depths up to about 50 nm or higher, up to about 65 nm or higher, or up to about 80 nm or higher, depending on the metal oxide, temperature of exposure, and/or time duration of exposure. For long time durations of liquid water exposure (e.g., at least 10 h, and up to or greater than 100 h), the diffusion depth may reach 300-1,000 nm in crystalline metal oxides such as ZnO and TiO 2 . In Ga 2 O 3 , which is of interest for high-power electronics, O i  may diffuse nearly 3,000 nm at 60-80° C. with at least 1 h of liquid water exposure, which suggests that diffusion of about 30,000 nm (30 microns) may be achieved within 100 h of exposure time. It is believed there are few or no sequestration sites for the O i  in Ga 2 O 3 , and also that the O i  diffuse with a small activation barrier of 0.2 eV, such that diffusion over nearly macroscopic distances may be achieved. This suggests that the depth to which the oxygen interstitials can diffuse may depend on the type and concentration of sequestration sites available in the crystalline metal oxide. Generally speaking, diffusion depths of at least about 20 nm and up to 30 microns may be achievable depending on the time duration and temperature of liquid water exposure, the type of metal oxide, the type and concentration of sequestration sites, and possibly other factors. For some crystalline metal oxides, such as ZnO and TiO 2 , the diffusion depths may typically range from about 20 nm to about 1,000 nm (1 micron). For other crystalline metal oxides, such as Ga 2 O 3 , the diffusion depths may typically range from about 1 micron to about 30 microns. 
     It is postulated that greater diffusion depths may be achieved by exposing the treated surface of the crystalline metal oxide to liquid water at a temperature above 100° C. and at a pressure greater than 1 bar (100 kPa), where the pressure is sufficient to keep the water in the liquid phase at the selected temperature and the temperature is high enough to enhance diffusion. For example, the temperature of the liquid water may be in a range from about 150° C. to about 250° C. when the pressure is in a range from about 10 bar (1 MPa) to about 20 kbar (2 GPa). At such elevated temperatures, oxygen interstitials injected into the crystalline metal oxide may penetrate to greater diffusion depths, such as a diffusion depth of 100 nm or greater, 1 micron or greater, 10 microns or greater, or even 100 microns or greater. The enhanced diffusion may be due at least in part to the lower stability of defect complexes at the elevated temperatures, as such complexes can sequester oxygen interstitials and consequently inhibit their mobility. After the exposure of the treated surface to the elevated temperature (&gt;100° C.) and pressure conditions (&gt;1 bar), the temperature may be gradually quenched below 100° C. and the pressure reduced to atmospheric conditions, at which point defect complexes rendered unstable at elevated temperatures may form in the crystalline metal oxide. Both the oxygen interstitials and defect complexes may be distributed at greater depths following the above-described high pressure process. 
     As indicated above, the method is carried out using a treated surface. Low bond coordination of surface atoms relative to bulk atoms facilitates creation or destruction of point defects on atomically-clean crystalline metal oxides. Suitably treated surfaces offer a means for manipulating the populations of bulk defects, most notably for materials such as semiconductors where defects may significantly influence technologically relevant material properties. The removal of strongly bonded adsorbates, such as carbon and/or sulfur on TiO 2  or ZnO, is deemed critical for manipulating defect populations. Even in at coverages well below one monolayer, such adsorbates may prove capable of poisoning the kinetic pathways responsible for defect exchange between the surface and bulk. Other adsorbates, such as water, atomic hydrogen, and sodium and/or chlorine from dissolved NaCl, may adsorb onto the surface but may not act as poisons (e.g., by interfering with the isotopic profiles). 
     Accordingly, the treated surface is preferably an atomically-clean or substantially poison-free (contaminant-free) surface of the metal oxide semiconductor. Ideally, the treated surface includes a concentration of impurity species of 0.01 ML (about 1% of a monolayer) or less. In some cases, the concentration of impurity species may be about 0.005 ML or less, or as low as about 0.001 ML. The treated surface may comprise a polar or non-polar surface, where, in the former case, the polar surface may be cation- or anion-terminated, as in the examples described above. 
     A method to prepare a suitably treated surface has been developed. The method includes degreasing a surface of the crystalline metal oxide, followed by wet etching of the surface and/or vacuum annealing of the crystalline metal oxide. The degreasing may comprise exposing the surface to acetone, isopropyl alcohol, ethanol and/or methanol by, for example, immersion in an ultrasonic bath. Vacuum annealing may entail heating the surface at a temperature in a range from about 400° C. to about 550° C. at an oxygen pressure P O2  in a range from about 1×10 −6  Torr to about 1×10 −4  Torr. Typically, the heating is carried out from 30 minutes to 24 hours. A vacuum annealing treatment in O 2  at 500° C. for 6 h is employed to prepare the treated surface of the Ga 2 O 3  described above in reference to  FIG. 1E . The wet etching, when employed to prepare the treated surface, may comprise exposing the surface to hydrogen peroxide (H 2 O 2 ) and/or ammonium hydroxide (NH 4 OH) under suitable conditions, as described below for ZnO and TiO 2 . 
     Aqueous H 2 O 2  may serve as an oxidant through formation of the hydroperoxide ion HO 2   −  and is also acidic. Single-crystalline ZnO may be readily etched by H 2 O 2  as well as by either acidic or basic solutions. Foreign adsorbates may become soluble either by dissolution of the zinc oxide or by direct oxidation. Relatively high etching temperatures (e.g., 70-80° C.) may be required to obtain optimal behavior, although such temperatures may lead to increased surface roughening. 
     Exemplary aqueous wet etching solutions for single-crystalline ZnO (e.g., ZnO (0001)) are described in Table 1 below. For example, exposing a ZnO surface to an aqueous solution comprising 5-20% H 2 O 2  for 5-20 min at a temperature in the range of 25-80° C. may be effective. Preferably, the aqueous solution comprises 10-20% H 2 O 2  for 10-20 min at a temperature of about 70-80° C. 
     Table 1. Exemplary ZnO Wet Etching Solutions and Conditions 
       
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Exemplary ZnO Wet Etching Solutions and Conditions 
               
            
           
           
               
               
               
               
            
               
                 Solution 
                 Solution composition 
                 Time (min) 
                 Temperature (° C.) 
               
               
                   
               
               
                 Hydrogen 
                 10% H 2 O 2   
                 5, 10, 20 
                 25, 80 
               
               
                 peroxide 
                 20% H 2 O 2   
                 5, 10, 20 
                 25, 80 
               
               
                   
                 30% H 2 O 2   
                 5, 10, 20 
                 25, 80 
               
               
                 Ammonia 
                 1:2 of 30% NH 4 OH:H 2 O 
                 40 
                 25 
               
               
                   
               
            
           
         
       
     
     In contrast, H 2 O 2  is not found to prove effective as a wet etchant for enhancing injection into single-crystalline TiO 2 . Mineral acids such as phosphoric acid (H 3 PO 4 ), sulfuric acid (H 2 SO 4 ), and hydrofluoric acid (HF) can readily etch TiO 2 ; however, these also may not be beneficial for preparing the treated surface of TiO 2  since they may lead to deposition of unwanted foreign elements or adsorbates. NH 4 OH and related bases such as NaOH and Na 3 PO 4  all exhibit a small but nonzero ability to dissolve TiO 2 , with Na 3 PO 4  being an order of magnitude more active than NaOH, which in turn is an order of magnitude more active than NH 4 OH. However, NH 4 OH is preferred because of the potential of desorbing the cation as NH 3 , thereby lessening the possibility of leaving behind foreign elements. Indeed, NH 4 OH does prove effective as a wet etchant for TiO 2 , presumably by the mechanism of simple dissolution of the titanium dioxide since the wet etchant exhibits no special capability for oxidation. Notably, the efficacy is found to be diminished by the addition of H 2 O 2  either together with the NH 4 OH or in sequence after it. 
     Exemplary aqueous wet etching solutions for single-crystalline TiO 2  (e.g., TiO 2  (110)) are described in Table 2 below. For example, exposing a TiO 2  surface to an aqueous solution comprising NH 4 OH for 30-50 min at a temperature of 25-30° C. or, more preferably, to an aqueous solution comprising 1:2 of 30% NH 4 OH:H 2 O for 40 min at a temperature of 25° C. may be effective. Etchants based on phosphoric acid (H 3 PO 4 ) are also examined, but these are found by subsequent chemical characterization to deposit significant quantities of phosphorous. Since adsorbed sulfur is known to impede oxygen exchange in TiO 2  and ZnO, a similar inhibition is expected for phosphorous. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Exemplary TiO 2  Wet Etching Solutions and Conditions 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Temper- 
               
               
                   
                   
                 Time 
                 ature 
               
               
                 Solution 
                 Solution composition 
                 (min) 
                 (° C.) 
               
               
                   
               
               
                 Hydrogen 
                 5% H 2 O 2   
                 5, 10, 20 
                 25 
               
               
                 peroxide 
                 10% H 2 O 2   
                 5, 10, 20 
                 25 
               
               
                 Ammonia 
                 1:2 of 30% NH 4 OH:H 2 O 
                 40 
                 25 
               
               
                 Base 
                 3:1 of 30% NH 4 OH:30% 
                 40 
                 60 
               
               
                 piranha 
                 H 2 O 2   
               
               
                 Sequential 
                 30% NH 4 OH → 30% H 2 O 2  → 
                 20 min 
                 25 
               
               
                 ammonia- 
                 H 2 O rinse 
                 each step 
               
               
                 peroxide 
               
               
                 Phosphoric 
                 85% H 3 PO 4   
                 10, 20, 40  
                 80 
               
               
                 acid 
               
               
                   
               
            
           
         
       
     
     Broadly speaking, the wet etchants investigated as described in the above tables involve aqueous solutions of H 2 O 2 , NH 4 OH, or combinations of the two at various concentrations and temperatures. A final rinsing with deionized water is also possible, as shown in the table for a sequential etch employing NH 4 OH→H 2 O 2 →H 2 O. 
     Isotopic exchange experiments show that high-temperature annealing in vacuum and wet etching are capable of opening pathways for defect exchange. The efficacy may follow from the removal of adsorbates and/or from the alteration of surface site geometry (e.g., by inducing surface reconstructions or altering surface roughness). Investigations of TiO 2  (110) and ZnO (0001) surfaces show that geometric effects play a much larger role for TiO 2  than for ZnO (0001). 
     Returning to the method of controlling vacancy concentration, the liquid water to which the treated surface of the crystalline metal oxide is exposed during the method may be part of an aqueous solution that includes additional components, e.g., one or more solutes and/or co-solvents. For example, the aqueous solution may include an amine or other basic species to adjust the pH of the aqueous solution to greater than 7. Experiments show that increased basicity can accelerate oxygen injection. In other examples, the aqueous solution may include an acidic species to adjust the pH of the aqueous solution to less than 7. Accordingly, the aqueous solution may comprise a pH of greater than 7, less than 7, or equal to 7. 
     The aqueous solution may also or alternatively include one or more salts, such as a metal salt or another water-soluble compound. Examples may include zinc fluoride, zinc chloride, manganese chloride, potassium hexafluorotitanate (IV) (K 2 (TiF 6 )), and/or ammonium titanyl oxalate ((NH 4 ) 8 [TiO(C 2 O 4 ) 2 ] 4 ). It is believed that the physics of cation (e.g., Ti +4 , Zn +2 ) injection may be similar to that of oxygen interstitials in that cation injection and diffusion may occur even at room temperature, or within tens of degrees of room temperature, as described above. Recent experiments demonstrating injection of Mn +2  into a TiO 2  surface are described below and show the impact of pH level on cation injection. 
     It is further contemplated that a bias voltage may be applied to electrodes in contact with the aqueous solution (or water) to promote injection of the cations and/or the atomic oxygen into the crystalline metal oxide. In some examples, the aqueous solution may include an electrolyte. Experiments show a strong electrochemical enhancement of oxygen interstitial injection. Both the injection rate and penetration depth may increase by up to one or two orders of magnitude by utilizing a bias voltage, as shown in the data described below. 
     In another approach, the treated surface may be illuminated with ultraviolet radiation during the exposure to the water/aqueous solution in order to enhance injection. Referring to  FIGS. 5A and 5B , experiments with TiO 2  (110) show that, when the treated surface is illuminated with UV light during water exposure at a temperature from 30−&lt;100° C. (40° C. in this set of experiments), the UV light enhances the exchange rate of O i  in comparison with red laser light (e.g., 635 nm diode laser) and light-shielding (dark) conditions. The UV light may have a wavelength selected to encompass photon energies higher than the band gap of the semiconducting metal oxide. Thus, the approach may be effective with narrow band gap semiconductors, e.g., highly-doped crystalline metal oxides, such as Ce- or Er-doped ZrO 2 , or N-doped TiO 2 . 
     Examples 
     Experimental Methods 
     All rutile TiO 2  specimens are single crystal and polished on one side. Undoped rutile TiO 2 (110) (MTI Corp.) is cut to 5-10 mm×5 mm×0.5 mm and is undoped. Atomic force microscopy indicates that the oxide has a surface roughness of &lt;5 Å. To remove surface poisons that may inhibit O i  creation, specimens of TiO 2 (110) are treated with a liquid solution of 30% NH 4 OH and H 2 O mixed in a 1:2 ratio for 40 min at 25° C. 
     Isotopic self-diffusion using liquid water employs a custom-designed apparatus wherein single crystals are immersed in 5 ml of  18 O-labeled water H 2   18 O (10 atomic %  18 O, Sigma-Aldrich) at temperatures ranging between 30 and 80° C. for 1 h in a laboratory air environment. The incorporated  18 O concentration profiles are measured by ex-situ time-of-flight secondary ion mass spectrometry (TOF-SIMS, PHI-TRIFT III instrument) employing a Cs ion beam source operating at 3 keV, with baseline concentrations checked against known isotopic fractions. In many cases multiple profiles are measured at up to three different places on a specimen&#39;s surface. 
     In cases where a bias voltage is applied, a Ag/AgCl reference electrode is also immersed in the aqueous solution, and the single crystal is connected to the electrodes of the electrochemical circuit using carbon tape. No electrolyte is added to the water in this example. Biases are applied using a potentiostat as part of the circuit. 
     In separate electrochemical experiments carried out at a temperature of 25° C. for 1 h to evaluate cation injection, MnCl 2  (0.5 M) is dissolved in the  18 O-labeled water and the pH is adjusted with hydrochloric acid to values of 2 and 4.5. 
     Modeling to Obtain Profile Metrics 
     Profile metrics are obtained using an analytical mesoscale approach based upon profile-by-profile determination of the slopes and intercepts in semi-logarithmic plots. The approach makes few assumptions about the kinetic mechanisms at play, and yields parameters representing composites of elementary-step rate constants. This approach works well in a short-time asymptotic limit wherein the mobile intermediate transporting the label becomes immobile at sequestration sites and remains there for the duration of the experiment. The profile slope yields the mean diffusion length λ while the intercept yields the net injection flux F. These two composite parameters yield a third useful profile metric, the effective diffusivity D eff . 
     The model assumes that only one sequestration event occurs for each O i  during the experiment—a plausible assumption because O i  retains appreciable mobility even at room temperature. This mobility, together with the stability of diffused profiles toward long-term storage near 25° C., indicates that any O i  present after injection ends soon becomes trapped. 
     Because the water is only 10% isotopically pure in  18 O, computation of the net injection flux F includes a factor of 10 to represent the total injected flux of both isotopes. D eff  is a phenomenological parameter that does not equal the tracer diffusivity (as it does in prior gas exchange experiments) because at these low temperatures, the solids are far from equilibrium. 
     Electrochemical Results 
     O i  Injection— FIGS. 6A and 6B  show log λ, which is indicative of the mean diffusion length of the atomic oxygen and log F, which is indicative of the net injection rate of the atomic oxygen, versus bias voltage. The data reveal enhancements of about 10 times in both penetration depth and injection rate. Surprisingly, the enhancements are found for both positive and negative biases. The data indicate a turn-on threshold of about ±0.1-0.2 V. 
     Cation Injection— FIG. 7  shows concentration profiles for Mn +2  in rutile TiO 2  corresponding to a bias voltage of +0.4 V vs Ag/AgCl, as measured by SIMS. The profiles correspond to as-received rutile TiO 2  prior to electrochemical exposure to the Mn-containing aqueous solution, and after electrochemical exposure to the Mn-containing aqueous solution. Diffusion of Mn is very clear at pH=4.5. It can be seen that Mn penetrates up to nearly 200 nm into single crystalline TiO 2  at room temperature under suitably chosen conditions of voltage bias and pH. Manganese is believed to diffuse in rutile via a mechanism involving interstitials. The data reveal that facile injection and diffusion of interstitial atoms near room temperature is not limited to oxygen, but extends to metal cations as well. This discovery may open the door to post-synthesis oxide doping with metal atoms, with possible applications in photocatalysis, diluted magnetic semiconductors, oxide electronics and others. 
     The subject matter of the disclosure may also relate to the following aspects: 
     A first aspect relates to a method of controlling oxygen vacancy concentration in a semiconducting metal oxide, the method comprising: exposing a treated surface of a crystalline metal oxide to water at a temperature and pressure sufficient to maintain the water in a liquid phase, whereby, during the exposure: a portion of the water is adsorbed onto the treated surface and dissociates into atomic oxygen and hydrogen, and the atomic oxygen is injected into and diffuses through the crystalline metal oxide, thereby forming isolated oxygen interstitials and oxygen defect complexes, wherein the isolated oxygen interstitials replace oxygen vacancies in the crystalline metal oxide. 
     A second aspect relates to the method of the first aspect wherein the water comprises H 2 O, H 2   18 O, and/or 2H 2 O. 
     A third aspect relates to the method of the first or the second aspect, wherein the temperature is less than 100° C. and the pressure is atmospheric pressure. 
     A fourth aspect relates to the method of the third aspect, wherein the temperature is in a range from about 30° C. to &lt;100° C. 
     A fifth aspect relates to the method of any preceding aspect, wherein at least some of the atomic oxygen diffuses within the crystalline metal oxide to a depth of about 20 nm to about 1,000 nm. 
     A sixth aspect relates to the method of any preceding aspect, wherein the temperature is at least 100° C. and the pressure is in a range from greater than about 1 bar (about 100 kPa) to about 100 kbar (about 10 GPa). 
     A seventh aspect relates to the method of any preceding aspect, wherein the temperature is in a range from about 150° C. to about 250° C. and the pressure is in a range from about 10 bar (about 1 MPa) to about 20 kbar (about 2 GPa). 
     A eighth aspect relates to the method of any preceding aspect, wherein at least some of the atomic oxygen diffuses within the crystalline metal oxide to a depth greater than 1,000 nm. 
     A ninth aspect relates to the method of any preceding aspect, further comprising, after a time duration sufficient for diffusion of the atomic oxygen to a predetermined depth within the crystalline metal oxide, halting the exposure of the treated surface to the water. 
     A tenth aspect relates to the method of the ninth aspect, wherein the time duration is in a range from about 10 minutes to 100 hours, from 10 minutes to about 120 minutes, and/or from about 30 minutes to about 90 minutes. 
     An eleventh aspect relates to the method of any preceding aspect, wherein the crystalline metal oxide comprises a semiconducting metal oxide selected from the group consisting of: TiO 2 , ZnO, Ga 2 O 3 , SrTiO 3 , SnO 2 , In 2 O 3 , ITO, WO 3 , Cr 2 O 3 , CuO, Co 2 O 3  and/or a perovskite. 
     A twelfth aspect relates to the method of any preceding aspect, wherein the crystalline metal oxide has at least one linear dimension of about 1 micron or less, or about 100 nm or less. 
     A thirteenth aspect relates to the method of any preceding aspect, wherein the treated surface is a polar surface, the polar surface being cation- or anion-terminated. 
     A fourteenth aspect relates to the method of any preceding aspect, wherein the treated surface is a non-polar surface. 
     A fifteenth aspect relates to the method of any preceding aspect, wherein the oxygen defect complexes comprise: interstitial oxygen (O i ) and a metal cation vacancy (VM), interstitial oxygen (O i ) and a metal cation interstitial (Mi), and/or interstitial oxygen (O i ) and hydrogen (H). 
     A sixteenth aspect relates to the method of any preceding aspect, wherein the oxygen defect complexes comprise interstitial oxygen (O i ) and hydrogen (H), and wherein, after the exposure of the treated surface to the water, the crystalline metal oxide exhibits increased p-type character compared to before the exposure. 
     A seventeenth aspect relates to the method of any preceding aspect, wherein the atomic hydrogen dissociated from the water remains on the treated surface. 
     An eighteenth aspect relates to the method of any preceding aspect, wherein the water is part of an aqueous solution comprising one or more solutes and/or co-solvents. 
     A nineteenth aspect relates to the method of any preceding aspect, wherein the aqueous solution comprises an amine or another basic species so as to comprise a pH of greater than 7. 
     A twentieth aspect relates to the method of any preceding aspect, wherein the aqueous solution comprises one or more salts. 
     A twenty-first aspect relates to the method of the twentieth aspect, wherein the aqueous solution comprises an electrolyte, and further comprising applying a bias voltage to electrodes in contact with the aqueous solution during the exposure. 
     A twenty-second aspect relates to the method of any preceding aspect, further comprising, during the exposure, illuminating the treated surface with ultraviolet radiation. 
     A twenty-third aspect relates to the method of the twenty-second aspect, wherein the ultraviolet radiation has a wavelength encompassing photon energies higher than a band gap of the crystalline metal oxide. 
     A twenty-fourth aspect relates to any preceding method, further comprising preparing the treated surface of the crystalline metal oxide, the preparing comprising: degreasing a surface of the crystalline metal oxide, followed by wet etching of the surface and/or vacuum annealing of the crystalline metal oxide, thereby forming the treated surface. 
     A twenty-fifth aspect relates to the method of the twenty-fourth aspect, wherein the wet etching comprises exposing the surface to hydrogen peroxide (H 2 O 2 ) and/or ammonium hydroxide (NH 4 OH). 
     A twenty-sixth aspect relates to the method of the twenty-fourth or twenty-fifth aspect, wherein the degreasing comprises exposing the surface to acetone, isopropyl alcohol, ethanol and/or methanol. 
     A twenty-seventh aspect relates to the method of any of the twenty-fourth through the twenty-sixth aspects, wherein the vacuum annealing comprises heating the surface at a temperature in a range from about 400° C. to about 550° C. at an oxygen pressure PO 2  in a range from about 1×10 −6  Torr to about 4×10 −4  Torr. 
     A twenty-eighth aspect relates to a semiconducting metal oxide made by the method of any preceding aspect. 
     Although the present invention has been described in considerable detail with reference to certain embodiments thereof, other embodiments are possible without departing from the present invention. The spirit and scope of the appended claims should not be limited, therefore, to the description of the preferred embodiments contained herein. All embodiments that come within the meaning of the claims, either literally or by equivalence, are intended to be embraced therein. 
     Furthermore, the advantages described above are not necessarily the only advantages of the invention, and it is not necessarily expected that all of the described advantages will be achieved with every embodiment of the invention.