A semianalytical solution for the 3ω method including the effect of heater thermal conduction

Abstract

A semianalytical solution for the 3ω method is derived to account for thermal conduction within the metallic heater. The existing uniform heat flux approximation between the metal heater and substrate is replaced by a more realistic uniform heat generation condition within the metal heater. Although this correction does not affect thermal conductivity measurements in the original 3ω method, it is shown that significant errors can result when it is applied for thermal conductivity anisotropy measurements. For low thermal conductivity films, the error in the anisotropy ratio can be as high as 50%.

3-Omega Method for Thin Films with the Non-Fourier Boundary Condition

“…The 3 x method is geared inherently toward dielectric substances, but it has also been used for conductive samples such as polyaniline [6], Carbon nanotube (CNT) arrays [7], and thermoelectric materials [8]. However, when the method is applied to anisotropic samples, especially low-thermal-conductivity films, significant errors may occur [9].…”

Analytical solutions of the heat diffusion equation for 3ω method geometry

“…Approximate expressions have been derived in the low frequency [2] and high frequency regimes [6]. Series expansions and semianalytical solutions of the temperature have been put forward recently in the case of a finite thickness strip on a finite solid [7] [8]. In the present paper, we consider a semi-infinite solid and we derive analytical expressions for the temperature distribution at the surface and for the mean temperature of the metallic strip (neglecting the strip thickness and thermal boundary resistance).…”