Vanadium Dioxide | MSE 510 Term Paper | Shamus E. O'Keefe Dec. 5, 2012 |

Vanadium oxides are interesting materials owing to their unique physical and chemical properties. Vanadium dioxide (VO2) may be the most interesting, and as a result possibly the most studied of the class. VO2 is a strongly correlated electron system that exhibits a dramatic metal-insulator transition (MIT) near room temperature. In addition to the MIT, VO2 has also been shown to possess high temperature superconductivity and colossal magnetoresistance[2]. Thin films made of VO2 have been made into novel electronic devices including waveguides, thermochromic windows, ultra-fast optical switches, photonic crystals, and bolometers. The large diversity of physical and chemical properties that they can thus possess make them technologically important and a rich ground for basic research. We will review this and other properties of VO2 and discuss how the bonding and crystallographic symmetry give rise to these properties. Let us begin with the basics…
In bulk form, vanadium oxides display different oxidation states and V–O coordination spheres. In VO2, we have V+4 and O-2 with coordination numbers of 6 and 3, respectively. Using Pauling electronegativities (V=1.6, O=3.5) we see that ΔE > 1.7, indicating ionic bonding. Indeed, this is the case in the monoclinic phase. However, since there is a difference in electronegativity, we know that the bond has polar character. As VO2 undergoes the MIT near the critical temperature Tc=68oC, it is accompanied by a structural transformation and a transition from ionic bonding to metallic bonding[1]. Below Tc, the semiconducting phase takes the monoclinic structure; above Tc the metallic phase takes the tetragonal structure (seen in Figure 1.).

Figure 1. Metallic tetragonal phase VO2. (*original artwork)
The mechanism behind the transition is not well understood and continues to be debated. Some experts contend that the doubling of the c parameter in the monoclinic phase resembles that of a Peierls transition[7]. The Fermi sphere must expand to accommodate additional kf vectors and it reaches the very limit of the Brillouin zone creating an opening in the energy band (depicted in Figure 2a). The other school of thought is that the transition resembles a Mott-Hubbard transition where the high density of free carriers forms a field that screens the nuclei, resulting in a decreased Coulombic attraction (depicted in Figure 2b)[7].

Figure 2. a) An increase in the size of the unit cell opens a gap, b) Mott-Hubbard transition where the free carriers screen the nuclei. (*original artwork using source data from [5])

The stable phase is actually the higher temperature metallic phase, often called rutile. Stable from 68 oC up to 1540 oC, it has space group P42/mmm (#136). Tetragonal cell parameters are a=b=4.55 Å, c=2.88 Å, and Z=2. This group has high symmetry with V+4 surrounded by an O-2 octahedra that share edges resulting in a chain along the c axis as depicted in Figure 3. The low temperature monoclinic phase is a metastable phase. Here, we see a pattern of octahedra aligned perpendicular as depicted in Figure 4; however, the octahedra are now distorted. Instead of a single V-V distance as in rutile, there are now two different V-V distances, leading to a doubling of the c axis. The distortion results in a decrease of symmetry and takes the space group P21/c (#14). Monoclinic cell parameters are a=5.75 , b=5.42, and c=5.38, and Z=4.

Figure 3. a) Projection along the [001] with white for vanadium @ z=0 and light green for vanadium @ z=1/2, b) projection along [010] depicting the chains built by the black vanadium atoms. (*original artwork using source data from [8])

Figure 4. a) Projection along the [100], b) projection along [010] with heavy black lines depicting the V-O doublet. (*original artwork using source data from [8])
Both phases are based on a scaffold of O-2 atoms in a bcc host lattice. The V+4 atoms are added to one of the six possible octahedral sites that exist for the bcc oxygen unit cell; of the possible 6 locations, only 1/6 of the possible site are occupied. Atomic positions of each phase can be seen in Table 1.

| | | | | | | | | | | | | | Monoclinic phase | | Tetragonal phase | | | | | | | | | | | | | | | | | x | y | z | | | x | y | z | | | V1 | 4i | 0.803 | 0 | 0.725 | | V | 16j | 0.1894 | 0.0176 | 0.0118 | | | V2 | 4i | 0.902 | 0 | 0.3 | | O1 | 16j | 0.1674 | 0.0012 | 0.3743 | | | O1 | 4i | 0.863 | 0 | 0.991 | | O2 | 8i | 0.1634 | | 0.3416 | | | O2 | 4i | 0.738 | 0 | 0.373 | | O3 | 8i | 0.1352 | | 0.893 | | | O3 | 4i | 0.934 | 0 | 0.595 | | | | | | | | | O4 | 4i | 0.642 | 0 | 0.729 | | | | | | | | | | | | | | | | | | | | |
Table 1. Atomic positions for monoclinic and tetragonal VO2 phases.

We must discuss the density of electronic states near the Fermi level to further our understanding of the two distinct phases and the details of the MIT transition. Remember, V+4 has only 1 d electron. The band structure [of each phase] depicted in Figure 5 is predicted as a result of V 3d and O 2p hybrids. A key element, as we learned in class, is the fact that the band structure possesses the same symmetry as the lattice. In the monoclinic phase, the V-V dimers and thereby lattice distortion, causes the dll band to split into bonding and antibonding and the shift of π* band up and away from the Fermi level. As seen in Figure 5. a gap develops between the bottom of the π* and the top of the dll. Sources have measured the dll splitting to be 2.5 eV and the optical band gap to be 0.7 eV. On the other hand, both the dll and π* phases of the tetragonal phase have regions above and below the Fermi level, which is what one would expect from a metallic phase[2].

Figure 5. Band structure of VO2 monoclinic and tetragonal phases. (*original artwork using source data from [2])
The physical transformation at the MIT has shown to be percolative[5]; metallic puddles first nucleate, then quickly grow until the metallic phase percolates throughout the lattice. During this transformation, if one measures reflectance using scattering techniques, an interesting feature can be observed. When the wavelength of the incident radiation is the same as the characteristic size of the metallic puddle, the reflectance actually decreases. As the puddles grow and merge, the reflectance then abruptly begins to increase.
Again, by themselves, the phases do not possess remarkable properties; it is the MIT that distinguishes VO2. We will now examine the electrical and optical properties of each phase and the associated striking contrast and try to draw a correlation to what we know about the bonding and structure. Beginning with electrical properties, we see the electrical resistivity ρ with temperature for a bulk VO2 crystal in Figure 6. We can see that the resistivity jumps by nearly 104, with some reports of 106 in highly pure single crystal specimens[10]. The ratio of the two different resistivities can be taken as a measure of the switching performance. In the monoclinic phase, the exponential behavior of the resistivity can be explained by the thermal generation of free carriers. In the case of electrons, conductivity σ is: σ = n q μn where n is the electron concentration in the conduction band, q is the electron charge, and μn is the carrier mobility. The temperature dependence is: n(T) = Nc exp(Ef-EckT) where Nc is the DOS, Ef is the energy of the Fermi level, Ec is the lowest energy available in the conduction band, and k is Boltzman’s constant.

Figure 6. Electrical resistivity of the the monoclinic insulating phase and the tetragonal metallic phase of VO2. (*original artwork using source data from [5])
An abrupt change in optical properties happens in concomitance with the sharp electronic transition. In the optical, infared, and terahertz spectra the reflectance increases with the transition to the metallic tetragonal phase. Sources have shown as high as a 90% increase in reflectivity at the MIT. The optical switching that occurs can be as fast as 10-13 s when triggered via excitonic means. An important parameter for switching applications is the dynamic range of transmittance, defined as DT = Tmax / Tmin, where T is transmittance[12]. Figure 7. shows transmittance vs. wavelength.

Figure 7. Optical transmittance of the monoclinic insulating phase and the tetragonal metallic phase of VO2. (*original artwork using source data from [10])
Beyond the aforementioned applications, the potential exists to replace some thin film photoconductors in certain research realms. For instance, Optical Electrophoretic Tweezers (OET) use an amorphous silicon thin film as a photoconductor to generate an electric field gradient. The impedance switching in amorphous silicon is on the order of 1.5 mS (mili-seimens), and therefore strictly limits the working conductivity of the liquid medium. With a higher impedance switching, VO2 could, in theory, allow for higher conductivity mediums to be utilized, opening the door for a host of interesting OET experiements in the biological and liquid storage device realms.We have shown many of the basic properties of VO2 can be elucidated from the bonding and crystal structure, specifically the symmetry. Save for the high temperature super conductivity and collosal magnetoresistance, what makes VO2 a promising material is the Metal-to-Insulator transition. One can envision myriad applications beyond its mainstay as a catalyst. One day the smart windows in our homes may “magically” become reflective as the temperature increases, or maybe thin films that conduct from the simple touch of a finger will find their way into our portable devices. And yet while it continues to be a hotbed of research, there are areas that are not yet well understood.

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