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.