1 ω , 2 ω , and 3ω methods for measurements of thermal properties
Abstract
3 ω methods are commonly used to measure the thermal conductivity of a substrate adjacent to a strip heater or the thermal conductivity and specific heat of a suspended wire. Here we consider the general case of a line heater that is also used to sense temperature. Analysis of all harmonics is presented in terms of generic thermal and electrical transfer functions and is readily adapted to other experimental configurations. We identify voltage signals at 2ω and 1ω that contain the same information about the thermal properties as the 3ω signal. The 2ω voltage requires a dc offset at the current source. The 1ω voltage requires a very stable current source, but eliminates the need for higher-harmonic detection, and is advantageous for studying the dynamics of systems with very fast thermal response times. The 1ω,2ω, and 3ω methods compare favorably with experiments using a suspended platinum wire and a line heater on a Pyrex substrate. With a modern lock-in amplifier, no common-mode voltage subtraction is necessary, which simplifies the experiment compared to the common practice of balancing a bridge or using a multiplying digital-to-analog converter. We also show that the widespread practice of using a voltage source to approximate a current source is only valid when the sample resistance is small compared to the total electrical resistance of the circuit, and derive and experimentally verify a correction factor to be used otherwise.
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Electrical resistance thermometry has been applied to measure the thermal conductivity of low-dimensional solids in both direct and modulated current configurations.
“Electrical resistance thermometry has been applied to measure the thermal conductivity of low dimensional solids (films, membranes, wires, and bridges) [13-15] in both direct [16-20] and modulated (1-omega, 2-omega, 3-omega) [21,22] current configurations.”
From Mean Free Path Effects on the Experimentally Measured Thermal Conductivity of Single-Crystal Silicon Microbridges (2013) · cites this paper as [22]
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A semianalytical solution for the 3ω method including the effect of heater thermal conduction
Gurrum, S. P., King, W. P., & Joshi, Y. K. (2008) · Journal of Applied Physics · doi:10.1063/1.2937254 · Cited by 19 · see citing works
Qiu, L., Zheng, X., Zhu, J., & Tang, D. (2011) · Review of Scientific Instruments · doi:10.1063/1.3626937 · Cited by 18 · see citing works
A Micro-Thermal Sensor for Focal Therapy Applications
Natesan, H., Hodges, W., Choi, J., Lubner, S., Dames, C., & Bischof, J. C. (2016) · Scientific Reports · doi:10.1038/srep21395 · Cited by 18 · see citing works
Self-citationFeng, B., Ma, W., Li, Z., & Zhang, X. (2009) · Review of Scientific Instruments · doi:10.1063/1.3153464 · Cited by 18 · see citing works
Bodzenta, J., Chirtoc, M., & Juszczyk, J. (2014) · Journal of Applied Physics · doi:10.1063/1.4891872 · Cited by 17 · see citing works
Lotfi, A., Navaei, M., & Hesketh, P. J. (2019) · ECS Journal of Solid State Science and Technology · doi:10.1149/2.0231906jss · Cited by 17 · see citing works
Alsanğur, R., Doganay, S., Ateş, İ., Turgut, A., Cetin, L., & Rebay, M. (2023) · Diamond and Related Materials · doi:10.1016/j.diamond.2023.110716 · Cited by 16 · see citing works
3ω correction method for eliminating resistance measurement error due to Joule heating
Guralnik, B., Hansen, O., Henrichsen, H. H., Beltrán-Pitarch, B., Østerberg, F. W., Shiv, L., Marangoni, T. A., Stilling-Andersen, A. R., Cagliani, A., Hansen, M. F., et al. (2021) · Review of Scientific Instruments · doi:10.1063/5.0063998 · Cited by 16 · see citing works
- Authors
- Dames, C., & Chen, G.
- Affiliations
- Massachusetts Institute of Technology (US)
- Venue
- Review of Scientific Instruments
- Publisher
- AIP Publishing
- Published
- 2005-12-01
- Volume
- 76
- Issue
- 12
- ISSN
- 0034-6748 (ISSN-L)
- 1089-7623
- OpenAlex
- W2094240247
- Cited by
- 275
- References
- 13
- Citations by year
- 2026: 8 · 2025: 16 · 2024: 13 · 2023: 12 · 2022: 15 · 2021: 18 · 2020: 9 · 2019: 15 · 2018: 17 · 2017: 14 · 2016: 18 · 2015: 20 · 2014: 18 · 2013: 15 · 2012: 19
- FWCI
- 2.65
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Review of Scientific Instruments (publishedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Engineering › Mechanics of Materials › Thermography and Photoacoustic Techniques
- Physical Sciences › Engineering › Mechanical Engineering › Mechanical and Thermal Properties Analysis
- Keywords
- 3ω method, thermal conductivity measurement, specific heat measurement, harmonic analysis, common-mode voltage, lock-in amplifier, Pyrex substrate, platinum wire
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