Reexamining the 3-omega technique for thin film thermal characterization

The 3-omega method is widely used to measure thermal properties of thin films and interfaces. Generally, one-dimensional heat conduction across the film is assumed and the film capacitance is neglected. The change in the in-phase (real part) temperature response for the film-on-substrate case relative to the substrate-only case is, therefore, attributed to the sum of the bulk thermal resistance of the film and the thermal boundary resistance between the film and the substrate. Based on a rigorous and intuitive mathematical derivation, it is shown that this approach represents a limiting case, and that its use can cause significant errors in rather realistic situations when the underlying assumptions are not met. This article quantifies the error by introducing a new parameter called the ratio function R, which modifies the film thermal resistance and mathematically shows that it depends only on three dimensionless parameters that combine thermal properties and geometries of the film and the heated linewidth. A new data reduction scheme is suggested accordingly to determine the film thermal conductivity (cross-plane), anisotropic thermal conductivity ratio between the in-plane direction and the cross-plane direction, and the interface thermal conductance.