FEM-Assisted Study Of 3omega Thermal Conductivity Measurement

As an electrical thermal conductivity measuring method,the 3ωmethod is fast,sensitive and simple in structure making,which shows promise in development and research value.Measurement with flexible,low-cost,and fast probe-based devices,i.e.the contact 3ωmethod,is an emerging research hotspot in this field.The current ideal mount-type devices are shackled in terms of production costs and flexibility,while devices with simple substrates,masking,and other low-cost processes are facing the dilemma of non-ideal conditions,such as mathematical approximation failure and difficulty in solving the analytical models of multilayer structures.For this kind of analytical difficulties results from complex solution domain,the finite element method has significant superiority and reliability to accurately extract data to analyze the influence of each parameter.This work takes the contact 3ωmeasurement devices with low processing requirement,mass production advantage,and flexible application to various scenarios as the research object,the finite element analysis as the research method to investigate the following content:First,the finite element modeling method for contact 3ωmeasurement was explored,including the test scenarios based on low-cost processing such as Kapton substrate and Al₂O₃ contact layer,the equivalent approximation and boundary conditions of the model,and the dynamic optimization of the model size and mesh dissection.An efficient and reliable contact 3ωfinite element model was established,which was within 5%error of the test results with classic 3ωstructure and literature structures,thus a new solution was found for the problem of difficult mathematical analysis of contact 3ωmeasurement.Second,the influence of non-ideal factors under low-cost processing such as wide electrode,thermal contact resistance and thin film layer thickness was investigated.The failure under non-ideal conditions of the current mainstream slope-method was analyzed based on the finite element method.For the slope-method,an electrode with the half-width higher than 100μm on a simple Kapton substrate would bring a shift that above100%on the result,this shift would be more than 50%under a high thermal contact resistance of 10^-4 K·m²/W,while the thickness of the contact layer and electrode within 50～500 nm had less than 3%effects on the result.Wide electrode and high thermal contact resistance are the non-ideal factors that have the most significant effects on the measurement.Third,the extraction method of thermal contact resistance in contact 3ωmeasurement was established.Based on the frequency dependence of the thermal penetration depth,the sensitive variables that have critical influence on the test signal were studied by the finite element model,and a measuring method that distinguishes the contact resistance and the thermal conductivity by divided frequency range fitting was proposed.The method could be used for non-ideal scenarios with electrodes half-width above 50μm,10^-5～10^-4 K·m²/W thermal contact resistance,and could measure samples in the thermal conductivity range of 1～10 W/m·K,enabling contact 3ωmeasurement by low-cost process devices.