Inversion for Thermal Properties with Frequency Domain Thermoreflectance

3D integration of multiple microelectronic devices improves size, weight, and power while increasing the number of interconnections between components. One integration method involves the use of metal bump bonds to connect devices and components on a common interposer platform. Significant variations in the coefficient of thermal expansion in such systems lead to stresses that can cause thermomechanical and electrical failures. More advanced characterization and failure analysis techniques are necessary to assess the bond quality between components. Frequency domain thermoreflectance (FDTR) is a nondestructive, noncontact testing method used to determine thermal properties in a sample by fitting the phase lag between an applied heat flux and the surface temperature response. The typical use of FDTR data involves fitting for thermal properties in geometries with a high degree of symmetry. In this work, finite element method simulations are performed using high performance computing codes to facilitate the modeling of samples with arbitrary geometric complexity. A gradient-based optimization technique is also presented to determine unknown thermal properties in a discretized domain. Using experimental FDTR data from a GaN-diamond sample, thermal conductivity is then determined in an unknown layer to provide a spatial map of bond quality at various points in the sample.