Generalized “Slope Method” of the 3to Analysis to Measure the Thermal Conductivity and Heat Capacity of Solids: Frequency-vs. Current-sweep

Abstract

Due to its simplicity and accuracy, the “slope method” is commonly used to measure the thermal conductivity, k, of solids in the traditional 3ω analysis, in which the slope of the linear relation between the 3ω voltage, V3ω, and the logarithm of the angular frequency, ln (ω), is inversely proportional to k in the low-frequency limit. Here, we generalize this “slope method” to the high-frequency limit to extract the effusivity, e (= √KC, where C is the heat capacity). Moreover, we propose a current-sweep scheme, in which the slope of the V3ω vs. I31ω relation is used to extract both k and C. This current-sweep scheme is more reliable when k and/or C are frequency-dependent or the qualified frequency range is so narrow that discretization artifacts may be introduced to the frequency-sweep scheme. This generalized “slope method” is validated using control experiments on a glass substrate in the temperature range of 78 – 300 K. A two-heater scheme is proposed to measure the frequency-dependent k and C.