Optical properties of a thin layer of the Vanadium dioxide at the metal state

Abderrahim Ben Chaib1., Abdesselam Mdaa2 Izeddine Zorkani1., Anouar Jorio1. 1 Physics laboratory of solid FSDM Fès, university Sidi Mohamed Ben Abdellah, Morocco. 2 Laboratory of the thin layers and surface treatment by plasma ENS-Fès, Morocco. Abderrahim Ben Chaib abderrahim-196@hotmail.com Abdesselam Mdaaabdou261175@gmail.fr Izeddine Zorkani izorkani@hotmail.com Anouar Jorio a_jorio@hotmail.com


INTRODUCTION
The vanadium dioxide is a relevant thermochrome material because of these enormous technological nano applications in photonic, with an energy gap of 0.

Methods
We use the Drude model [11] for the dielectric function : ε ∞ → 1, for the state metal ԑ ∞ : the high frequency permittivity of the electronic transition.Г  : the frequency of collision.
: the frequency plasma.
: the frequency of the incidental photon in (ev).
ԑ : the permittivity complexes material ԑ 1 : the real part of the complex permittivity.
ԑ 2 : the imaginary part of the complex permittivity.
By using this model, we can make a simulation of the VO₂ constant optics according to the energy ω (ev) of the incidental photon, while being based on the film parameters of VO₂ according to the table [10,12], and by taking an oscillator for the temperature θ = 85°C.
0 : Frequency of resonance for the oscillator of energy corresponding to the peak of absorption in electronvolt.
: The oscillator strength j of Lorentz.

𝛾 𝑗
: The widening of each oscillator j knowing damping.

Let us note:
T: transmittivity of a thin layer of VO₂.R : reflectivity of a thin layer of VO₂ for the normal incidence.α : the absorption coefficient of a thin layer of VO₂.n: the index of refraction of material.k: the coefficient of extinction of material.

T=30°C T=85°C
0,67 -0,46 1,11 Model of Drude, based simulation and modeling 7 ev [1,2], detecting ultra-violet [3,4], optical memory whose principle is based on the hysteresis loop at the time of this transition from the reversible phase [5,13,14,15,16] and the intelligent panes [6,18].A dramatic change of these thin layers' optical properties is clearly observed.Several theoretical studies were made to explain the answer of the dielectric function for these two phases: metal and semiconductor.Abbate and Mossanek [ 7] extracted the dielectric response from VO₂. Verlor et al. [8] studied the dielectric function of massive VO₂ by using the method of the reflectivity and transmittivity.Currently, Kakiuchida et al. [9] used the ellipsometric spectroscopy (SE) for the determination of the constant optics of the vanadium dioxide's thin layers.

Figure 1 .
Figure 1.Variation of the real permittivity part ε 1 according to energy of the incidental photon.

Figure 2 .
Figure 2. Variation of the imaginary permittivity part ε 2 according to the energy of the incidental photon.

Figure 3 .
Figure 3. Variation of the index of refraction n according to energy of the incidental photon.

Figure 4 .
Figure 4. Variation of the coefficient of extinction k according to energy of the incidental photon.

Figure 5 .
Figure 5. Variation of the reflectivity R according to energy of the incidental photon.

Figure 6 .
Figure 6.Variation of the transmittivity T according to energy of the incidental photon.

Figure 7 .
Figure 7. Variation of the index of refraction n and the coefficient of extinction k according to the energy of the incidental photon.

Figure 8 .
Figure 8. Variation of the transmittivity T and the reflectivity R according to the energy of the incidental photon.

Figure 9 .Figure 10 .
Figure 9. Variation of the absorption's coefficient α according to the energy of the incidental