*3.6. E*ff*ects of Annealing Temperature on Crystal Size*

The full width at half maximum (FWHM) values of the peaks in the XRD patterns can be derived from the following Scherrer formula [35]:

$$D = 0.9 \times \lambda / \\$\csc\theta\tag{2}$$

where *D* is the grain size, β is the XRD peak FWHM, λ is the wavelength of the incident light, and θ is the diffraction angle of the incident light. In the XRD process, λ and θ have constant values. Consequently, the grain size, *D*, and FWHM, β, are inversely related. (Cullity and Stock 2001). Figure 7 shows the FWHM and crystal grain size values of the present Ti:SnO2 films. Note that the as-deposited film has a small crystal structure, and hence the FWHM and crystal size values are also calculated carefully. However, for an annealing temperature of 300 ◦C, the Ti:SnO2 film has a crystalline structure with a grain size of around 14.89 nm. As the annealing temperature is increased, the crystalline structure becomes more pronounced. Consequently, the grain size decreases, while the FWHM increases. For the maximum annealing temperature of 500 ◦C, the grain size is equal to approximately 11.56 nm, while the FWHM increases to 0.8.

**Figure 7.** The full width at half maximum (FWHM) and grain size of as-deposited and annealed Ti:SnO2 films.
