Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers

This paper presents a mathematical model to design and fabricate micro-ball lens array using thermal reflow in two polymer layers. The experimental results showed that micro-ball lens arrays were fabricated and integrated onto a planar substrate. Two polymer layers were coated onto a silicon substrate. The upper layer was a photoresist. The lower layer was a polyimide material. The polyimide was expected to form a pedestal to sustain the ball lens after the heat reflow process. Once the patterned polymer is heated above its glass transition temperature, the melting polymer surface will change into a spherical profile for minimizing its surface energy. A successful micro-ball array was formed in the photoresist through the different glass transition temperatures between two polymer materials. The interactive force between two material interfaces caused by surface tension causes the upper profile to form a spherical profile. This also forms the polyimide pedestal into a trapezoid with arc sides. The error in the fabricated micro-ball lens characteristics was 8% between the theoretical models used to predict the photoresist pattern thickness. This model is feasible for fabricating various sized micro-ball lens arrays