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

Nan Chen,1,#

Tao Li,1,#

Yin Wang,2

Li Pan,1

Wenzhong Bao,2 

Zhen Chen1,*,Email

1Jiangsu Key Laboratory for Design & Manufacture or Micro/Nano Biomedical Instruments, School of Mechanical Engineering, Southeast University, Nanjing 210096, China

2State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 200433, China

#These authors contibuted equally.

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, V, 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 (=sqrt(KC), where is the heat capacity). Moreover, we propose a current-sweep scheme, in which the slope of the V  vs. I1ω3 relation is used to extract both 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.

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