Thermal Stresses in Micro- and Nanostructures

Thermal management of micro/nanostructures is important from the device efficiency and performance point of view. Due to space limitations, heat generation results in large temperature gradients across the device, which in turn develops large thermal strain and high stress levels in the heated region. In some cases, the device size becomes comparable to the characteristic length of the workpiece material, such as mean free path, equilibrium base analysis, such as Fourier heating law, fails to predict correct temperature rise across the device. In addition, in short time periods, energy transport across the device does not follow the continuum principles because of the nonequilibrium behavior. When formulating the energy transport at micro/nanoscale, care must be taken to include the nonequilibrium effect on the transport. In the present chapter, thermal analysis associated with stress formation at micro/nanolevels is presented in detail. In order to resemble the micro/nanoscale heat transfer and stress field, a laser irradiation of the surfaces is considered, incorporating the volumetric heat source to resemble the absorption process. The analytical treatment of temperature and stress fields is presented for various conditions, including elastic and plastic behavior of the irradiated surface. The solution of the hyperbolic form of heat equation incorporating the nonequilibrium transport is presented, and the closed form solution for the resulting stress field is demonstrated. Since the energy transport is involved with the mechanical work done against the thermal expansion, thermomechanical coupling is incorporated in the analysis to demonstrate the effect of thermomechanical coupling on the stress field. Surface evaporation takes place at high intensity heating situations, resulting in the formation of high recoil pressure at the vapor–solid interface, which in turn causes the development of the plastic wave propagating into the substrate material. This issue is also addressed at the micro/nanolevels.