Microscale Extraction of Effective Permittivity and Permeability for Microwave Selectively Heated Solder Paste Applied in Flexible Electronics

Flexible hybrid electronics (FHEs) have experienced many excellent developments in recent years. However, massively assembling surface-mounted components (SMDs) on flexible and thermally fragile substrates is a challenge that needs to be urgently addressed. In this work, first, we propose a method to obtain the effective permittivity ( ${\varepsilon }_{\text {eff}}$ ) and permeability ( ${\mu }_{\text {eff}}$ ) of solder paste by numerical simulation at the microscopic scale based on the Nicolson-Ross–Weir (NRW) method through the effective medium model. Interestingly, the solder paste, the mixture of flux and metallic particles, has a positive value of imaginary part of effective permeability ( $\boldsymbol {\mu }_{\mathbf {eff}}^{\prime \prime }$ ), despite there being no magnetic material in the composite. Moreover, the loss tangent of the effective permeability (tan $\boldsymbol {\delta }_{{\mu }\text {eff}}$ ) was much greater than that of the permittivity. $\boldsymbol {\varepsilon }_{\text {eff}}$ and $\boldsymbol {\mu }_{\text {eff}}$ of the solder paste were subsequently measured. The experimental results show a nonzero $\boldsymbol {\mu }_{\text {eff}}^{\prime \prime }$ and high tan $\boldsymbol {\delta }_{\boldsymbol {\mu }\text {eff}}$ , verifying the theoretical prediction. Then, a microwave separated magnetic field system with a frequency auto-tracking algorithm was developed to selectively heat solder paste on a substrate. The experimental results revealed that the solder paste could be melted in 10 s in a microwave magnetic field, whereas the substrate without solder paste could not be heated under the same conditions. In the microwave electric field, the substrate was burned due to plasma formation. The joints welded by microwave had a high pull-off strength and low resistance. In general, the research results provide guidance for the preparation of solder paste for microwave heating and the development of microwave welding equipment for FHEs.