Inversion for Thermal Properties with Frequency Domain Thermoreflectance

Abstract

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.

Measurements of Thermal Resistance Across Buried Interfaces with Frequency-Domain Thermoreflectance and Microscale Confinement

“…Many recent studies have focused on the development of techniques to characterize the thermal resistance across interfaces that are 10s to 100s of μm below the surface of a material. − Such interfaces are abundant in modern devices, including multilayer microelectronics packaging, , wide bandgap materials and devices, , power electronics architectures, ,, and memory storage systems, and are fast becoming the largest bottleneck to sufficient heat dissipation in the next generation of these applications. Critically, interfaces at these depths are extremely challenging to characterize using existing steady-state techniques, − which are limited to spatial resolutions above several hundred μm’s, or with advanced optical pump–probe thermoreflectance techniques, which probe at depths that range between nm’s to single-digit μm below a sample surface. , Most recent techniques have relied on augmentations to existing thermoreflectance systems; for instance, several studies achieve larger thermal penetration depths by extending the range of modulation frequencies applied to the pump beam. − In general, improvements in thermal penetration depth ( δ = 2 α / f ; α is thermal diffusivity, f is modulation frequency) have been limited to <10 μm due to spreading in the upper transducer layer …”