Microscale Thermal Characterization for Two Adjacent Dielectric Thin Films

Abstract

Heat conduction in two adjacent layers of dielectric thin e lms are analyzed by solving an equation of phonon radiative transfer. In the present work, the physical model is derived with an equilibrium temperature at the imaginary black interface, so that the two layers can be linked. Moreover, the effective mean free path can be corrected by the phonon scattering rate on grain boundaries of imperfect interface. Chemical-vapor-deposited diamond layer on silicon is chosen as the structure of the test case. The studies found that the interface is a critical issue in microscale thermal characteristics; for example, a temperature jump at the interface characterizes the effective thermal conductivity on diamond e lm and ine uences the temperature level on the silicon substrates. Energy transmission to the other layer increases the temperature jump at the interface and lowers the temperature level on the silicon substrate without changing the phonon mean free path. The disorder interface with various grain structures increases the phonon scattering rate and shortens the effective mean free path signie cantly; therefore, the temperature gradient across the diamond e lm increases and the normalized temperature jump at the interface is decreased substantially. Nomenclature C = heat capacity d = grain size I = phonon intensity k = thermal conductivity N = number of atoms q = heat e ux T = temperature t = time U = internal energy V = phonon group velocity a = energy transmission coefe cient h = grain boundary scattering strength u = Debye temperature L = phonon mean free path m = cosine of the angle between the phonon propagation velocity and the x direction t = relaxation time V = solid angle Subscripts D = defects or at Debye temperature eff = effective quantity G = grain GB = grain boundary i = medium i j = medium j S = at imaginary interface U = Umklapp process v = spectral quantity