J. Eur. Opt. Society-Rapid Publ. 22, 2( 2026) 17
Figure 6.( a) Dependency of ln( a) with photon energy for Bi 2-x Mn x O 3 thin films,( b) urbach energy vs Mn concentration.
Figure 7. The direct energy gap for the Bi 2-x Mn x O 3 thin films.
that occurs when the material absorbs a photon. For the most common types of transitions, the direct allowed transitions which A ¼ 1 and the indirect allowed transitions
2
which A = 2. Thehm dependence of( ahm) 2 is plotted in Figure 7. The data presented in the Figure indicates that the linear part of( ahm) 2 plot versus( hm) exhibits a clearer linearity. This finding implies that a direct electronic transition predominates in the thin films under investigation. This was observed in a previous study for Co-dopped ZnO thin films [ 32 ]. The calculated values of the direct band gap energy( E opt g
) are listed in Table 2. The reduction in the direct energy band gap of Bi 2-x Mn x O 3 thin films with increasing Mn content is primarily due to the introducing of Mn-3d states, which modify the electronic structure through hybridization with O-2p orbitals and / or the creation of defect-related energy levels. Structural changes and charge compensation mechanisms may also contribute [ 33, 34 ]. This band gap narrowing suggests that Mn doping can be used to tailor the optical and electronic properties of Bi 2 O 3 for specific applications, such as photocatalysis or photovoltaic devices, where a reduced band gap enhances performance under visible light.
The observed increase in the extinction coefficient( K) of Bi 2-x Mn x O 3 thin films with increasing Mn content( x = 0 to 0.1) and the corresponding enhancement of the peak at approximately 280 nm suggest a stronger absorption of light, likely due to the embedding of Mn into the Bi 2 O 3 lattice, as shown in Figure 8. This increase in K indicates a higher probability of photon absorption, which can be attributed to the introduction of Mn-3d electronic states that enhance the material’ s interaction with incident light, particularly in the ultraviolet region [ 33 ]. The peak at 280 nm, which intensifies with higher Mn content, likely corresponds to an electronic transition involving these Mn-related states or defect levels, such as charge transfer between Mn and O orbitals, aligning with the previously noted band gap reduction from 3.6 eV to 3.29 eV. This enhanced absorption and peak intensity with increasing Mn doping suggests improved optical activity, potentially making the material more effective for applications like photocatalysis, as the additional Mn-induced states facilitate greater light harvesting in the UV spectrum.
Analysis of a material’ s refractive index( n) iscrucial for determining the local electric field and electronic polarization of its constituent atoms or ions. The refractive index is typically determined by measuring the transmittance( T) andreflectance( R) spectra, as established in previous studies [ 18 ].
n ¼ ð1 þ RÞ! 2 0: 5
ð1 þ RÞ þ
� k 2 þ 1: ð9Þ ð1 � RÞ ð1 � RÞ
Figure 9a illustrates the wavelength-dependent refractive index of Bi 2-x Mn x O 3 thin films. The increased Mn content elevates the refractive index, attributed to modifications in the electronic and structural properties of the material, enhancing its optical performance. This improvement is promising for applications in light manipulation and advanced optical devices. The refractive index values, measured across a wavelength range of 200 – 1000 nm, align closely with the Cauchy formula [ 35 ]. Additional optical properties were derived from these refractive index values, with dispersion parameters proving essential for optimizing optical communication systems and spectral dispersion control devices. A comprehensive understanding of the films’ optical behavior requires detailed knowledge of the single oscillator energy( E 0) and dispersion energy( E d), which are related to photon energy( hv) through the Wemple-DiDomenico model [ 36 ].