The analysis of the optical properties of a material is largely based on the knowledge of its complex dielectric constant, denoted ε = ε₁ − iε₂, where ε₁ represents the real part (related to dispersion) and ε₂ the imaginary part (related to absorption). In the framework of our study, particular attention is paid to the real part ε₁, as it plays a decisive role in the description of the Coulomb interaction within an exciton, especially for ground states such as the 1S exciton. Our work focuses specifically on solid vanadium dioxide (VO₂), a material known for its remarkable electronic and optical properties, particularly around its metal–insulator transition. We focus on the behavior of the 1S exciton, seeking to determine its energy and its influence on the optical properties of the material. To do this, we solve the Schrödinger equation of exciton using a variational approach, based on the effective mass approximation. This method makes it possible to estimate the binding energy of the exciton and to extract a functional expression of ε₁ as a function of the energy E of the exciton. Then, using the Maple software, we proceed to numerical simulations to plot the evolution of the real dielectric constant ε₁ as well as the refractive index n as a function of the energy E of the 1S exciton. These simulations are performed both in the immediate vicinity of the VO₂ bandgap, and well beyond, in order to cover a wide range of photonic energies. From these results, we deduce two fundamental optical quantities: the reflectivity R and the transmittivity T of the massive VO₂, for a normal incidence of photons on the surface of the material. In this context, we consider a weakly absorbent semiconductor state, which simplifies the analytical expressions of R and T while maintaining an acceptable precision for physical interpretation. This study aims to better understand the optoelectronic behavior of VO₂ in its semiconductor phase, and to demonstrate the importance of excitons in modifying its optical properties, especially in the low-energy domain where these quasiparticles dominate light-matter interactions.

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Study of the Optical Response of Vanadium Dioxide (VO₂) from the Complex Dielectric Constant

  • Abderrahim Ben Chaib,
  • Mohammed Zouini,
  • El Mehdi El Khattabi,
  • Mourad Boutahir,
  • Kalpana Sahoo

摘要

The analysis of the optical properties of a material is largely based on the knowledge of its complex dielectric constant, denoted ε = ε₁ − iε₂, where ε₁ represents the real part (related to dispersion) and ε₂ the imaginary part (related to absorption). In the framework of our study, particular attention is paid to the real part ε₁, as it plays a decisive role in the description of the Coulomb interaction within an exciton, especially for ground states such as the 1S exciton. Our work focuses specifically on solid vanadium dioxide (VO₂), a material known for its remarkable electronic and optical properties, particularly around its metal–insulator transition. We focus on the behavior of the 1S exciton, seeking to determine its energy and its influence on the optical properties of the material. To do this, we solve the Schrödinger equation of exciton using a variational approach, based on the effective mass approximation. This method makes it possible to estimate the binding energy of the exciton and to extract a functional expression of ε₁ as a function of the energy E of the exciton. Then, using the Maple software, we proceed to numerical simulations to plot the evolution of the real dielectric constant ε₁ as well as the refractive index n as a function of the energy E of the 1S exciton. These simulations are performed both in the immediate vicinity of the VO₂ bandgap, and well beyond, in order to cover a wide range of photonic energies. From these results, we deduce two fundamental optical quantities: the reflectivity R and the transmittivity T of the massive VO₂, for a normal incidence of photons on the surface of the material. In this context, we consider a weakly absorbent semiconductor state, which simplifies the analytical expressions of R and T while maintaining an acceptable precision for physical interpretation. This study aims to better understand the optoelectronic behavior of VO₂ in its semiconductor phase, and to demonstrate the importance of excitons in modifying its optical properties, especially in the low-energy domain where these quasiparticles dominate light-matter interactions.