Thermal excitation of the low dimensional silicon film is introduced and an analytical approach is adopted for the solution of the transport equation. In the analysis, the phonon radiative transport equation is converted into an integral form of the Fredholm equation of the second kind. The analytical approach is extended to include the formulation of thermal stresses for the following cases: (i) stress-free at the edges and (ii) one edge is constrained to have maximum stress while the other edge is set to be stress-free. The analytical and numerical results are evaluated for comparisons. The findings demonstrate that both results are in good agreement. The dimensionless temperature rise at the film mid-thickness becomes sharp for small thickness film. The peak value of thermal stress at the film mid-thickness becomes larger as the film thickness is reduced further. Stress waves generated initially are compressive at the film mid-thickness and they become tensile at both ends of the stress-free film, which becomes more apparent as time increases. Two consecutive compressive and tensile stresses are generated at the mid-thickness of the film as the stress boundary condition is changed to the maximum stress at one edge of the film.

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低维硅膜的热应力发展：一种分析方法

介绍了低维硅膜的热激发，并采用解析方法求解了输运方程。在分析中，将声子辐射输运方程转换为第二种Fredholm方程的积分形式。分析方法已扩展为包括以下情况的热应力公式：（i）边缘无应力，并且（ii）一个边缘被约束为具有最大应力，而另一边缘设置为无应力。评估分析和数值结果以进行比较。研究结果表明，这两个结果吻合良好。对于小厚度的膜，在膜的中间厚度处无因次的温度升高变得尖锐。随着膜厚度的进一步减小，膜中厚度处的热应力的峰值变大。最初产生的应力波在薄膜的中间厚度处是压缩性的，并且在无应力薄膜的两端处变为拉伸性，随着时间的增加，应力波会变得更加明显。当应力边界条件改变为膜的一个边缘处的最大应力时，在膜的中间厚度处会产生两个连续的压应力和拉应力。