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J. Eur. Opt. Society-Rapid Publ. 22, 2( 2026)
Figure 11. The variation of( a) SELF,( b) VELF, and( c)( SELF / VELF) with vs hv for Bi 2-x Mn x O 3.
resulting from Mn incorporation. The quality factor( Q-factor), which quantifies a material’ s ability to store and release energy, is depicted in Figure 10d as a function of photon energy( hm) forBi 2-x Mn x O 3 thin films. As photon energy increases, the Q-factor rises, indicating improved energy storage or reduced energy dissipation. This suggests enhanced energy efficiency and lower dielectric losses at higher photon energies. At the high frequencies, materials with low-loss dielectric responses typically exhibit less pronounced energy dissipation, a trend corroborated by the measured behavior of the real and imaginary components of the dielectric constant.
The characterization of electron transitions in thin films relies on two crucial parameters: the Surface Energy Loss Function( SELF) and the Volume Energy Loss Function( VELF) [ 36, 49, 50 ]. The ratio of SELF to VELF describes these electron transitions across both low and high energy ranges within the examined thin film [ 36 ]. For the current films, SELF and VELF can be calculated using a specific equation [ 50 ], with the results illustrated in Figures 10a and 10b. e 2
SELF ¼; ð17Þ ðe 1 þ 1Þ 2 þ e 2
VELF ¼ e 2: ð18Þ e 2 1 þ e 2
2
From Figures 11a, 11b, it is observed that both SELF and VELF values rise with an increasing Mn content. This is associated with changes in electron transition energy due to the incorporation of Mn into the thin films. Figure 11c illustrates the ratio of SELF / VELF against photon energy, indicating that the addition of Mn affects the electron transitions within the films.
An essential measure for understanding the electronic characteristics of thin films is the optical( r Opt) and electrical conductivity( r elec), which is closely connected to the dielectric properties that describe how the materials interact with radiation. Using the values of the parameters a, n, andk, the following relations can be used to generate r Opt and r elec [ 51, 52 ]:
2 r Opt ¼ anc 4p and r elec ¼ knc 2p: ð19Þ
The wavelength, the absorption coefficient, the refractive index, and the speed of light are denoted by k, a, n, and c. The variation of r Opt and r Elec of the Bi 2-x Mn x O 3 thinfilm with the wavelength is intr in Figures 12a and 12b. As the Mn content rises, it is noticed that both r Opt and r Elec increase as well; the maximum optical and electrical conductivity was achieved for the highest Mn content. This could be ascribed to the modifications made to the thin films’ electrical structure as a result of adding Mn. Also, this is related to the enhanced absorption coefficient due to the doping with Mn [ 53 ]. The degree of polarization is closely correlated with the electric susceptibility for any polarizable material. The material’ s electric susceptibility quantifies how easily it polarizes when subjected to an electric field. A material with a high electric susceptibility will polarise more significantly in an electric field, which in turn reduces the net electric field within the material. The Electric susceptibility( v c) can be found using the following expression [ 51 ]: v c ¼ 1 4p n2 � K 2 � n 2
0: ð20Þ
The equation includes n, K, andn 0 parameters which represent the thin film’ s refractive index, extinction coefficient, and the index of refraction for the surroundings, respectively. As illustrated in Figure 12c, the electric susceptibility v c increases proportionally with the Mn-to-Bi content in the film. This trend arises because Mn incorporation modifies the electronic band structure, altering the material’ s interaction with applied electric fields. Additionally, the disparity in polarizability between Mn and Zn ions enhances v c as Mn content increases, as polarizability directly influences charge distribution under external fields.
The nonlinear refractive index( n 2) and the linear( v 1) and nonlinear( v 3) susceptibilities of a material are expressed as follows [ 54 ]:
v ð1Þ ¼ E d = E 0 4p; ð21Þ