Thermal Characteristics of an Aluminum Thin Film due to Temperature Disturbance at Film Edges

Phonon transport in an aluminum thin film is simulated due to a temperature disturbance across the film. The Boltzmann equation is introduced to formulate the radiative transport in the electron and lattice sub-systems. The transient and frequency dependence of the phonon transport is considered, and dispersion relations are accommodated to account for the group velocities in the analysis. Electron-phonon coupling is employed to couple the energy transport across the electron and lattice sub-systems. An equivalent equilibrium temperature is presented to assess the characteristics of the phonon intensity in the film. Temperature predictions are validated with data presented in a previous study. It is found that the equivalent equilibrium temperature differs significantly from that obtained from the two-equation model. The film thickness influences the transport characteristics of the film, in which case the time to reach an almost quasi-steady temperature is shorter for the thin film ($$L_{x}= 0.25 \,\upmu \hbox {m}$$Lx=0.25μm, where $$L_{x}$$Lx is the film thickness) than that corresponding to the thick film ($$L_{x}= 2 \,\upmu \hbox {m}$$Lx=2μm). In the diffusion limit (when the Knudsen number $$Kn=\varLambda /{L_x }\rightarrow 0$$Kn=Λ/Lx→0, where $$\varLambda $$Λ is the mean free path), it is demonstrated that the radiative transport equation reduces to the formulation of the two-equation model.