A thermal conductivity varying 3D numerical model for parametric study of a silicon-based nano thermoelectric generator

This paper employs a novel approach, integrating a two-step Fuch-Sondheimer reduction method with the phonon relaxation approximation method, to comprehensively study the structural design of silicon-based thermocouples for enhanced thermoelectric generator performance. The analysis provides the detailed information regarding the size and temperature-dependent thermal conductivity for various silicon nanostructures, facilitating the construction of a 3D numerical simulation model. Doping concentration and temperature dependent electrical conductivity, Seebeck coefficient and contact resistance were incorporated into the model as well. This enables the 3D model to incorporate adjustments made to the thermocouple structure and initialization conditions, allowing for automatic numerical computation of the generator's specific power density and providing a more thorough understanding of its behavior. To validate the model, experimental data from the literature is employed. The results highlight the significance of thermocouple packing fraction as a determining factor for maximizing device performance. Also, a strategic structural design approach is recommended to achieve a balance between thermocouple thermal conductivity, thermal resistance, and electrical resistance, thus improving the overall performance. Based on the model predictions, with a thermocouple thickness of 2 μm, a width of 60 nm, a specific power density of approximately 16.2 μW/cm2.K2 is projected. These findings demonstrate the potential applicability of silicon-based thermoelectric generators for effective heat recycling from electronic devices.