Methods for latent image simulations in photolithography with a polychromatic light attenuation equation for fabricating VIAs in 2.5D and 3D advanced packaging architectures

As demand accelerates for multifunctional devices with a small footprint and minimal power consumption, 2.5D and 3D advanced packaging architectures have emerged as an essential solution that use through-substrate vias (TSVs) as vertical interconnects. Vertical stacking enables chip packages with increased functionality, enhanced design versatility, minimal power loss, reduced footprint and high bandwidth. Unlocking the potential of photolithography for vertical interconnect access (VIA) fabrication requires fast and accurate predictive modeling of diffraction effects and resist film photochemistry. This procedure is especially challenging for broad-spectrum exposure systems that use, for example, Hg bulbs with g-, h-, and i-line UV radiation. In this paper, we present new methods and equations for VIA latent image determination in photolithography that are suitable for broad-spectrum exposure and negate the need for complex and time-consuming in situ metrology. Our technique is accurate, converges quickly on the average modern PC and could be readily integrated into photolithography simulation software. We derive a polychromatic light attenuation equation from the Beer-Lambert law, which can be used in a critical exposure dose model to determine the photochemical reaction state. We integrate this equation with an exact scalar diffraction formula to produce a succinct equation comprising a complete coupling between light propagation phenomena and photochemical behavior. We then perform a comparative study between 2D/3D photoresist latent image simulation geometries and directly corresponding experimental data, which demonstrates a highly positive correlation. We anticipate that this technique will be a valuable asset to photolithography, micro- and nano-optical systems and advanced packaging/system integration with applications in technology domains ranging from space to automotive to the Internet of Things (IoT).