*3.4. Transmittance*

Figure 3 shows the optical transmittance properties of the various Ti:SnO2 thin films. For the as-deposited film, the mean transmittance has a low value of approximately 58% due to the poor effect of the replaced Sn for the Ti atom. However, the transmittance improves significantly in the annealed samples, particularly in those annealed at temperatures of 300 ◦C or more. In conventional ITO films, the optical energy gap theoretically increases as the carrier concentration increases, since the Fermi level moves into the conduction band and the electrons on the valence band are forced to jump to the conduction band, thereby requiring more energy and resulting in the so-called Burstein–Moss effect [31,32]. However, the optical energy gap rises with a decreasing carrier concentration. Such a phenomenon may be due to an interaction effect between ion compounds. For example, Zn2<sup>+</sup> and Sn4<sup>+</sup> ions coexist in IZTO films and trigger the generation of a donor-accepter pair, which reduces the energy gap and mitigates the Burstein–Moss effect. For the present Ti:SnO2 films, the carrier concentration decreases following annealing at temperatures higher than 200 ◦C (see Figure 2). However, the energy gap and mean transmittance both increase (see Table 2 and Figure 3, respectively). For an annealing temperature of 200 ◦C, the improvement in the transmittance is very modest (i.e., from around 58% for the as-deposited sample to approximately 60% for the annealed sample). However, for an annealing temperature of 300 ◦C, the film undergoes a transformation from a homogenous crystalline structure and the mean transmittance improves to almost 75%. Furthermore, as the annealing temperature increases, the transformation toward a crystalline structure becomes more complete (see Figure 1) and hence the mean transmittance increases. Thus, the film annealed at a temperature of 500 ◦C shows the maximum mean transmittance of approximately 74.2%.

**Table 2.** Effects of annealing temperature on energy gap (*Eg*) of Ti:SnO2 films.


**Figure 3.** Optical transmittance of as-deposited and annealed Ti:SnO2 films.

Figure 4 shows the relationship between the optical absorption coefficient (α) and photon energy(*h*ν) for the Ti:SnO2 film. The optical band gap (*Eg*) is calculated as follows with the equation [33,34]:

$$\alpha \text{lrb} = A(\text{lrb} - E\_{\%})^{1/2} \tag{1}$$

where α is the absorption coefficient, ν is the frequency of incident light, h is the Planck's constant, and *A* is constant. The optical band gap is extrapolating the straight-line portion of the plot to the energy axis. Table 2 shows the calculated values of the optical band gap for the present Ti:SnO2 thin films. Furthermore, an Eg value greater than 3 eV is regarded as excellent. Referring to Table 2, the Eg value of the present Ti:SnO2 films increases with an increase in annealing temperature and is equal to 3.28 eV at an annealing temperature of 500 ◦C. Moreover, an Eg value greater than 3 eV is obtained for all of the films annealed at a temperature of 300 ◦C or more.

**Figure 4.** The (α*h*ν) <sup>2</sup> against photon energy (*h*ν) of Ti:SnO2 films under different annealing temperatures.
