## 3 Simulation Study  
FEM-based COMSOL software was employed to simulate the temporal temperature, displacement, and photoacoustic signal. A three-dimensional geometry model was built to simulate the photoacoustic signal, by Heat Transfer in Solids Module and Solid Mechanics Module. Geometry was reduced to one-fourth of the whole sample structure to save simulation time. The results for the two modules with different incident light densities are shown below. For simplicity, to show the results of photothermal and photoacoustic phenomena and their feasibility, a homogeneous, isotropic cylindrical silicon model with a height of 1 mm and a radius of 4 mm was constructed (model 1), as shown in Figure 1. A 266 nm pulsed light source was perpendicularly incident on the center of the top surface of the cylinder. A pulsed laser was used to generate ultrasound, which was modeled as a Gaussian beam in the form of f(t) = t/t0 e\({}^{-\text{t}/t}\)0 vs. time domain, where t0 represents the rise time of the pulse, and g(t) = e\({}^{-\left(x^{2}+y^{2}\right)/t_{0}^{2}}\)) at space with temporal incident intensity of 160 \(\upmu\)J with an absorption coefficient of 0.8, where r0 represents half-width at 1/e\({}^{2}\)-intensity point. The time and space profiles of the laser pulse are shown in Figures 2 and 3, respectively. \begin{table}
\begin{tabular}{c c c} \hline
**Properties/Parameters** & **Value** & **Unit** \\ \hline Thermal conductivity of Al & 238 & W/(m \(\cdot\)K) \\ Thermal conductivity of Cu & 400 & W/(m \(\cdot\)K) \\ Thermal conductivity of silicon & 1.38 & W/(m \(\cdot\)K) \\ Heat capacity of silicon & 703 & J/(kg \(\cdot\)K) \\ Coefficient of thermal expansion of Al & 23 \(\times\) 10\({}^{-6}\) & 1/K \\ Coefficient of thermal expansion of Cu & 17 \(\times\) 10\({}^{-6}\) & 1/K \\ Coefficient of thermal expansion of silicon & 2.55 \(\times\) 10\({}^{-6}\) & 1/K \\ Density of Al & 2700 & kg/m3 \\ Density of Cu & 8960 & kg/m3 \\ Density of silicon & 2330 & kg/m3 \\ Young’s modulus of silicon & 73 & GPa \\ Poisson’s ratio of silicon & 0.278 & 1 \\ Speed of sound in silicon & 5700 & m/s \\ Initial temperature & 293.15 & K \\ Initial pressure & 0 & Pa \\ \hline \end{tabular}
\end{table} 
Table 1: Properties at T \(\approx\) 293 K and parameters used in numerical modeling. As it takes time for heat and sound to propagate, different detection points were chosen to measure the temperature and displacement of the material. The temperature curve can illustrate whether the heat propagates to this point, and the displacement curve can verify whether the fluctuation at this point is caused by thermal effects or sound waves. The distribution of temporal temperature is plotted in Figure 4, showing a very fast period of increase (around 0.04 us) from room temperature to the highest temperature and a very slow descending process from the peak temperature to room temperature. The displacement diagrams of different positions on the aluminum are shown in Figure 5.  
Figure 1: The model of cylindrical silicon in model 1. Figure 3: Gaussian laser pulse space profile with \(r_{0}=100\) μm. Figure 2: Temporal profile of Gaussian laser pulse with \(t_{0}=8\) ns. As evident from the results in Figure 5a, the displacement of the center point (0, 0, 1 mm) showed a rapid trend at the very beginning and then slowly declined after reaching a peak value, but none of the curves is similar to the jitter of the sound wave. This is because the displacement change caused by temperature was far greater than that caused by pressure at the center point, which was the strongest incident energy point. Additionally, because of the small energy and the accuracy of the grid, there are steep changes in the curve, which may lead to unsmooth curves.