Theoretical study of the limits of the 3ω method using a new complete quadrupole model

A new quadrupole model is presented to solve the heat transfer equations in a conventional geometry used in the measurement of thermal conductivity of thin films by the 3ω method. It takes into account the following aspects often neglected in the previous works: thermal resistance in the heater, anisotropy of the thin film, thermal contact resistances and the limited thickness of the sample. The quadrupole model allows us also to compare the Cahill and Duquesne formulas and to find their applicability limits. The average temperature rise is calculated to validate the quadrupole model, it presents a deviation lower than 3.5% compared to the numerical simulation in the range of frequency from 1 Hz to 10 KHz.