## 3 Analysis and Discussion
\begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Coefficient of diffusion of holes \(D_{p}\) & 1.2 \(\times\cdot\)10\({}^{-3}\) m\({}^{2}\)s\({}^{-1}\) \\ Coefficient of diffusion of electrons \(D_{e}\) & 3.6 \(\times\) 10\({}^{-3}\) m\({}^{2}\)s\({}^{-1}\) \\ Lifetime of excess charge carriers \(\tau\) & 5 \(\times\) 10\({}^{-6}\) s \\ Energy gap \(E_{G}\) & 1.12 eV \\ Velocity of surface recombination \(S_{g/b}\) & 2–24 ms\({}^{-1}\) \\ Coefficient of thermal diffusivity \(D_{T}\) & 9 \(\times\) 10\({}^{-5}\) m\({}^{2}\)s\({}^{-1}\) \\ Thermal conductivity \(k\) & 150 Wm\({}^{-1}\)K\({}^{-1}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Electronic, thermal, and geometrical properties of silicon samples used in the analysis of the model [18; 61]. lines depict the total signal resulting from both sources. (Legend: \(s_{g}\) = 6 ms\({}^{-1}\) (solid line), \(s_{g}\) = 10 ms\({}^{-1}\) (dashed line), \(s_{g}\) = 14 ms\({}^{-1}\) (dash-dot line)). As shown in Figure 5, in plasma-opaque and thermally thin samples, carrier recombination does not alter the shape of the signal but does affect its maximum value (blue and green lines). When the parameter \(s_{g}\) is low (below 6 ms\({}^{-1}\)), the contribution of recombination sources is negligible, and the signal is primarily determined by lattice thermalization (solid red and green lines). However, as \(s_{g}\) increases, recombination effects become more significant. For \(s_{g}\) = 14 ms\({}^{-1}\), recombination sources play a dominant role in temperature change (dash-dot green and blue lines in Figure 5). From Figure 5, it can also be observed that the time-domain temperature signal for a thermally thin semiconductor sample reaches a steady value of zero after a time equal to 2\(T\). This indicates that the settling time is equal to twice the duration of the optical pulse. In cases where the signal does not reach a peak during the pulse duration, it is not appropriate to work with parameters such as rising time or falling time; instead, it is much more suitable to consider the slope of the rising or falling curve. Figure 5 shows that the slopes of the rise after the leading edge of the excitation and the slope of the fall after the trailing edge of the pulse are equal and depend on the surface recombination velocities. To investigate the impact of the charge carrier diffusivity (the semiconductor electronic property) on the shape of the time-domain temperature signal, Figure 6 presents the signal for a thermally thin and plasma-opaque p-doped Si sample (\(l_{s}\) = 140 \(\upmu\)m, \(D_{e}\) = 3.6 \(\times\) 10\({}^{-3}\) m\({}^{2}\)s\({}^{-1}\)). The red line represents the signal resulting from lattice thermalization (fast heat source), while the blue lines indicate the signal from surface recombinations at different \(s_{g}\) values. The green lines show the total signal caused by both sources: \(s_{g}\) = 6 ms\({}^{-1}\) (solid lines), \(s_{g}\) = 10 ms\({}^{-1}\) (dashed lines), and \(s_{g}\) = 14 ms\({}^{-1}\) (dash-dotted lines). As seen in Figure 6, for the plasma-opaque and thermally thin p-doped sample, the recombination of charge carriers similarly affects the time domain temperature signal as in the n-doped sample (Figure 5). Specifically, it does not influence the shape or settling time, but it does impact the maximum value of the signal in the time domain (indicated by the blue and green lines in Figures 5 and 6) and the slopes of both the rising and falling curves. However, in the case of the p-doped sample, minority carriers are electrons, which have a diffusion coefficient three times larger (as shown in Table 1). Therefore, at the same  
Figure 5: The normalized time-domain temperature signal for a thermally thin and plasma opaque n-doped silicon sample. The red line represents the signal resulting from lattice thermalization (fast heat source), while the blue lines indicate the signal from surface recombinations at different \(s_{g}\) values.