## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Sample** & \(\mathbf{C_{110}}\) & \(\mathbf{C_{200}}\) & \(\mathbf{C_{211}}\) & \(\mathbf{\sigma}\) & \
\begin{tabular}{c} **(110) FWHM** \\ (°) \\ \end{tabular} &
\begin{tabular}{c} **Crystallite Size from (110)** \\ **(nm)** \\ \end{tabular} \\ \hline As-Mo & 2.24 & 0.04 & 1.02 & 0.59 & 0.459\({}^{\circ}\) & 18.5 \\ Mo-700 & 2.41 & 0.05 & 0.97 & 0.64 & 0.436\({}^{\circ}\) & 19.4 \\ Mo-800 & 2.69 & 0.06 & 0.87 & 0.73 & 0.385\({}^{\circ}\) & 22.0 \\ Mo-900 & 2.46 & 0.00 & 1.04 & 0.67 & 0.358\({}^{\circ}\) & 23.6 \\ Mo-1000 & 0.56 & 0.00 & 1.47 & 0.45 & 0.339\({}^{\circ}\) & 25.0 \\ Mo-1100 & 0.58 & 0.00 & 1.46 & 0.45 & 0.3464 & 25.0 \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of texture coefficient, preferred orientation, (110) full width at half maximum (FWHM), and crystallite size, calculated from the (110) peak of Mo thin films, as a function of annealing temperature. they start to grow in size, almost linearly, with an annealing temperature from 700 \({}^{\circ}\)C to 1000 \({}^{\circ}\)C, see Figure 5. The value finally reaches 24-25 nm and stays relatively unchanged, between samples Mo-1000 and Mo-1100. The electrical property of Mo thin film was analyzed by examining the sheet resistance of the samples obtained through 4 PP measurements. The resistivity of the film was then obtained by dividing the sheet resistance by the thickness of the film (i.e., 1 \(\upmu\)m from cross-sectional FESEM). Results of this study are listed in Table 2. The evolution of resistivity as a function of annealing temperature is also plotted in Figure 5 (line + solid square), where the resistivity of Mo thin films reduces with increasing annealing temperature, before it saturates when annealed above 1000 \({}^{\circ}\)C. This trend is obviously opposite to the change in Mo crystallite size on the same plot. Electrical properties of Mo thin films fabricated in this work were mainly affected by sub-grain boundary electron scatterings and background electron scatterings. At room temperature measurement, the electron mean free path (EMFP) in Mo was 39.5 nm [17; 18], which was two orders of magnitude smaller than the thicknesses of Mo thin films in this paper. This made the contribution of external size effect, if at all, to the thin film resistivity due to surface electron scatterings that were insignificant in comparison with background electron scatterings. Therefore, it is safe to assume a unity specular reflection coefficient of \(p=1\)[19]. On the contrary, the estimated Mo crystallite sizes from XRD were in the range of 18-25 nm. These values were comparable to the EMFP, and thus the internal size effect of thin film resistivity results from the sub-grain electron scatterings could not be ignored. As a result, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Sheet Resistance (m\(\Omega\)/\(\square\))** & **Resistivity (\(\upmu\Omega\) cm)** \\ \hline As-Mo & 310.1 & 31 \\ Mo-700 & 267.4 & 27 \\ Mo-800 & 227.5 & 23 \\ Mo-900 & 204.3 & 20 \\ Mo-1000 & 116.6 & 12 \\ Mo-1100 & 113.5 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of sheet resistance and resistivity of Mo thin films, as a function of annealing temperature. Figure 5: Evolution of Mo crystallite size and resistivity of Mo thin films, as a function of annealing temperature. the resistivity of Mo thin films can be described using the model established by [PERSON] (MS model) in Equation (4) [19], under the Matthiessen's rule [20; 21]. \[\frac{\rho_{f}}{\rho_{0}}=\left[1-\frac{3}{2}\alpha+3\alpha^{2}-3\alpha^{3} \text{ln}\left(1+\frac{1}{\alpha}\right)\right]^{-1} \tag{4}\]  
where \(\rho_{f}\) and \(\rho_{0}\) are the resistivity of the thin film and the corresponding single crystal bulk material (5.3 \(\upmu\Omega\) cm for Mo [17]), respectively. \(\alpha\) is a factor related to the EMFP \(\lambda_{RT}\) at room temperature, the Mo crystallite size \(D\) in the thin film, and the grain boundary reflection coefficient \(R\), following the expression in Equation (5).