Thermal Stress Development in Low Dimensional Silicon Film: An Analytical Approach

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.