## 3 Results and Discussions
### Optical Properties  
Figure 2 represents the UV-visible spectra of TiO\({}_{2}\) and Ba/TiO\({}_{2}\) photoanode materials. Ba/TiO\({}_{2}\) exhibited a significant visible absorption above 400 nm, which was an indication of changes occurring in the optical absorption of TiO\({}_{2}\) photoanode material due to metal doping. Peak edges of Ba/TiO\({}_{2}\) photoanode showed some regular and trivial blue shifts  
Figure 1: XRD patterns of Ba/TiO\({}_{2}\), TiO\({}_{2}\) photoanodes along with the reference JCPDS data 21-1272.  
comparative to TiO\({}_{2}\) photoanode. The blue shift was attributable to the Burstein-Moss effect, leading to the movement of Fermi level towards the conduction band due to an increase in electron concentration because of Ba doping [44; 45]. It is very useful to increase the photocurrent density and also the charge transfer resistance of synthesized photoanodes. The absorption of TiO\({}_{2}\) and Ba/TiO\({}_{2}\) were at 415 nm and 400 nm, respectively. Optical band gap values were determined by using Tauc plots as presented in Figure 3a. Ba/TiO\({}_{2}\) photoanode (3.26 eV) ha a higher band gap value compared to TiO\({}_{2}\) photoanode (3.21 eV) because of quantum confinement effects observed due to the smaller size of as-synthesized samples. According to the theory of quantum efficiency, the holes of valence band and conduction band electrons are confined by the potential barrier of the surface. As a result, the band gap energy is increased with decreasing size of synthesized particles [46; 47]. The increase in band gap of doped TiO\({}_{2}\) can be interpreted in terms of [PERSON]'s transition effect and Burstein-Moss (BM) effects. According to [PERSON]' criteria, the band gap of the donor combines with the conduction band of the host material [48], while BM effects present a relationship between the band gap and concentration of carriers [49; 50], as given below:  
\[E_{g}^{BM}=\left(\frac{h^{2}}{2\lambda m_{e}}\right)\left(3\pi^{2}N_{e}\ \right) \tag{5}\]  
where \(\lambda\), \(h\), and \(m_{e}\) are the effective reduced mass of TiO\({}_{2}\), [PERSON]'s constant and the electron free mass, respectively. According to the \(BM\) effect, the carrier density of semiconductors increases with Ba doping, which causes the Fermi level to shift into the conduction band [51]. Due to this doping, the low energy transition is clogged, and broadening in the band gap takes place [52]. This novel effect of Ba doping on optical properties can pave the way to its extended use in optoelectronic and photovoltaic applications. The value of \(n\) coefficient is determined by the Tauc relationship (Equation (6)). The n coefficient is related to the possible transition of electrons. For indirect allowed electronic transition, its value is 2 and 3 for indirect forbidden transitions. \[\alpha h\theta=A\ (h\theta-E_{g})^{n} \tag{6}\]  
\[n=\frac{ln\ (\alpha h\theta)}{\ln\left(h\theta-E_{g}\right)} \tag{7}\]  
Figure 2: UV-visible spectra of synthesized TiO\({}_{2}\) and Ba/TiO\({}_{2}\) photoanodes. where \(\alpha\) is the absorption coefficient, \(h\) is [PERSON]'s constant, and \(A\) is absorption constant [53]. From the slope of ln \(\mathrm{F}^{\otimes}\) vs. ln \((-\
u-E_{g})\), the value of n is determined. The result listed in Table 2 represents the approximated value of \(n=2\) for TiO\({}_{2}\) and Ba/TiO\({}_{2}\), which is in agreement with values in the literature for TiO\({}_{2}\), which is an indirect semiconductor [54]  
Figure 4 presents the UV-visible absorption spectrum of dye molecule-adsorbed TiO\({}_{2}\) and Ba/TiO\({}_{2}\) photoanodes. The Ba/TiO\({}_{2}\) photoanode had high absorption compared to the TiO\({}_{2}\) photoanode. The increased absorption was due to the increasing surface area of the Ba/TiO\({}_{2}\) photoanode, which was also confirmed by XRD results. This behavior enhances photocurrent density in DSSCs.