Elastic properties of VO2 from first-principles calculation

doi:10.1016/j.ssc.2013.05.011

Solid State Communications

Volume 167, August 2013, Pages 1-4

https://doi.org/10.1016/j.ssc.2013.05.011 Get rights and content

Highlights

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The R, M₁ and M₂ phases are mechanically unstable with increasing pressure.
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The R and M₂ phases of VO₂ are predicted to be harder than the M₁ phase.
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The anisotropy of the M₂ phase is found to be larger than the M₁ and R phases.

Abstract

We used first-principles methods to calculate the elastic properties of rutile (R) structure and monoclinic (M₁: space group $P 2_{1} / c$ , M₂: space group C2/m) structure VO₂, including single-crystal elastic constants c_ij's, polycrystalline bulk modulus, shear modulus, Young's modulus and elastic anisotropy ratio. We found that the energy difference among the R, M₁ and M₂ phases is small, indicating that it is easy to transit among them under a perturbation. Furthermore, from the pressure dependence of c_ij's, we also found that the structural instability (or phase transition) will occur when the volumes of the three phases are slightly smaller than their equilibrium volumes. Additionally, the R and M₂ phases are predicted to be harder than the M₁ phase, indicated by their larger bulk moduli and shear moduli. The elastic anisotropy of the M₂ phase is larger than the M₁ and R phases. The presently predicted elastic properties of VO₂ provide helpful guidance for the strain energy estimation and stress analysis in nano-electronic devices.

Introduction

At room temperature vanadium dioxide (VO₂) is a semiconductor with a monoclinic (M₁) structure (space group $P 2_{1} / c$ ), while at a high temperature it is a metal with a tetragonal rutile (R) structure (space group $P 4_{2} / mnm$ ) [1]. The phase transition temperature is $\sim 68 ° C$ [2]. The crystal will change from the M₁ structure to the R structure with the temperature increase, associated with electrical conductivity jumps by several orders of magnitude [3], [4]. Moreover, it is found that VO₂ will change from a monoclinic phase (space group $P 2_{1} / c$ , M₁) to a monoclinic phase (space group C2/m, M₂) under strain or doping, accompanied with a significant increase of resistance and a strong piezoresistive effect [5]. The transition between these phases is reversible [6]. The phase transition properties and electrical properties of VO₂ make it have a wide range of potential applications in optoelectronic devices, such as micro switches, field effect transistors, gas detectors, varistors, and phase change memory [6], [7], [8].

It is well known that the knowledge of the elastic properties of VO₂ is highly desired for VO₂ integration in nano and thin-film electronic devices, for example, the strain energy estimation and stress analysis in thin-film devices [9]. Furthermore, the elastic properties, such as elastic constants c_ij, bulk modulus, shear modulus, Young's modulus and elastic anisotropy characteristic, are the basis for selecting mechanical materials and the commonly used parameters in engineering design [10], [11], [12]. However, only the Young's modulus of VO₂ has been measured based on the stress–strain data [10], and the first-principles bulk modulus of the R phase has been predicted in terms of the generalized-gradient approximation (GGA) [12]. Until now no systematic studies have been done on the elastic properties of the R phase, M₁ phase and M₂ phase VO₂, which inhibit the fundamental understanding and fabrication of VO₂. The lack of knowledge of the elastic properties in VO₂ therefore inspires the present research.

In this work, we systematically study the elastic properties of the R phase, M₁ phase and M₂ phase VO₂, including single-crystal elastic constants c_ij's, polycrystalline bulk modulus, shear modulus, Young's modulus and elastic anisotropy characteristic, and discuss the pressure dependence of c_ij's.

Section snippets

Computational method

First-principles calculations were carried out using a generalized gradient approximation (with its version optimized for solids [PBEsol]) [13] to density functional theory (DFT) as implemented in the VASP package [14]. In the first-principles calculation, we used a 400 eV energy cutoff and a 9×9×9 Monkhorst-Pack k-point mesh for the R phase (7×7×7 for the M₁ and M₂ phases) when relaxing the structures. When calculating the elastic constants of VO₂, we used a 500 eV energy cutoff and an 11×11×11

Results and discussion

The energy–volume curves and the pressure–volume curves of the R phase, M₁ phase and M₂ phase VO₂ are shown in Fig. 1. The total energies of these phases are very close. For instance, the total energy of the M₂ phase is just $\sim 0.5 meV / atom$ higher than those of the R phase and M₁ phase, suggesting that a small perturbation from outside may make the phase transition to occur among them. This is consistent with the well-known experimental report of metal insulator transition (MIT) [17] and

Conclusions

We have systematically studied the elastic properties of VO₂ with a rutile (R) structure and monoclinic (M₁, M₂) structure within the GGA approach. Additionally, the elastic properties of polycrystalline aggregates (bulk modulus, shear modulus, Young's modulus and elastic anisotropy) are also determined and compared with experiments and theoretical predictions. It is found that the total energies of the R, M₁ and M₂ phases are very close, indicating that it is easy to transit among them under a

Acknowledgment

The authors would like to thank Professor Jingbo Li, Institute of Semiconductors, Chinese Academy of Sciences, for his helpful discussion, and thank Mr. Kamlesh Patel and Mr. Jonathan Banfill for their help in language.

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Elastic properties of VO2 from first-principles calculation

Highlights

Abstract

Introduction

Section snippets

Computational method

Results and discussion

Conclusions

Acknowledgment

Solid State Commun.

Solid State Commun.

Mater. Sci. Eng. R

J. Cryst. Growth.

Solid State Commun.

Phys. Rev. Lett.

Phys. Rev.

MRS Commun.

Nano Lett.

Appl. Phys. Lett.

Nano Lett.

Appl. Phys. Lett.

J. Phys.: Condens. Matter.

Phys. Rev. Lett.

Elastic properties of VO₂ from first-principles calculation