Extending the 3ω method for thin-film analysis to high frequencies

Abstract

Although the 3ω method was originally introduced to measure the thermal conductivity of bulk material and was later developed further to include thin-film materials, many thermal and geometrical parameters influence the 3ω signal. We show that several of these parameters can be determined simultaneously from a single 3ω measurement. With the commonly used frequency range, however, some parameter combinations cannot be determined uniquely. To overcome this problem we have developed an electronic setup for measurements from 5 Hz up to 200 kHz. We show numerically and experimentally that we can determine four physical parameters from a single measurement in this frequency range. This makes the 3ω method very suitable for microelectronics and microsensor testing, where physical parameters should ideally be determined by purely electrical measurements.

Thin-film aerogel thermal conductivity measurements via 3ω

“…It has been shown [21] that a significant portion of 3ω data is insensitive to variations in thermal diffusivity depending on sample properties and geometry. More specifically, at low enough frequencies.…”

“…Subsequently the technique was expanded to measure superlattices [16], fluids [17] and carbon nanotube arrays [18].While the 3ω technique has also been utilized to measure properties of porous materials such as bulk xerogels [19] and 55% porous aerogel films with thermal conductivities as low as 0.14 W/mK [20] this study reports the first use of 3ω for determining the thermal conductivity of high porosity silica aerogel films. The 3ω technique was advantageous for this study due to its sensitivity to individual layers in multilayer structures [21,22], high accuracy and repeatability [13], and its ability to eliminate convective as well as radiative error [23].…”

Analysis of the 3-omega method for thermal conductivity measurement

“…Previous authors [5][6][7][8][9][10][12][13][14][15][16][17][18][19][20][21][22][23][24][30][31][32]35,37] have simplified the problem by neglecting the heater thickness, as in Fig. 1(b); thus only the rectangular region ABCG has to be considered.…”

“…This needs to be taken into account when using direct extensions of the integral solution, Eq. (23), for measurements at high frequencies [13,18].…”

“…Moon et al [13] showed that a much simpler formula exists at the high-frequency limit which can be used for specific heat measurement. The integral solutions have also been extended to measure the thermal properties of thin films [14][15][16][17][18][19][20][21] and liquid materials [13,[22][23][24]. Other than heater-on-substrate configurations, several authors have also developed the 3x method for suspended wires, such as nanowires [25] and nanotubes [26][27][28][29].…”