intensity of a monochromatic light equation

#Intensity of a monochromatic light equation Pc#

This elastic material reduces or eliminates material stress induced by a mismatch in the coefficient of thermal expansion (CTE) between adjacently packaged devices. This VIA array can be used in a build-up interposer in 2.5D, wherein the interposer substrate comprises an elastic material with a low Young’s modulus, such as an acrylic polymer. The corresponding electroplated Cu VIA array is shown in Fig. In 3D architectures, successive chips are bonded to one another in a vertical stack with orientations such as front-to-front, front-to-back and back-to-back, where each chip comprises VIAs that connect the top and bottom surfaces 12, 14.įigure 1a shows a photoresist relief mold array for the bottom-up electroplating of Cu VIAs. An interposer is an insulating substrate for I/O redistribution comprising vertical interconnect access (VIA) conductive materials, such as Cu, that interconnect the top and bottom surfaces to form through-substrate vias (TSVs) 13. In 2.5D architectures, an array of chips is bonded to an interposer 12. These qualities are essential for next-generation technologies in domains such as high-end computing, mobile devices, radio frequency (RF), automotive, space, artificial intelligence (AI), biotechnology and the Internet of Things (IoT) 4, 8, 9, 10, 11. Light propagation prediction and modeling enable ambitious photomask designs for film patterning that drive the cutting edge of 2.5D and 3D advanced packaging architectures with increased functionality, enhanced design versatility, reduced power consumption, small form factor and high bandwidth 1, 2, 3, 4, 5, 6, 7. Photolithography is a process whereby a photosensitive film, or photoresist, is exposed to light. 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). 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 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 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.

#Intensity of a monochromatic light equation Pc#

Our technique is accurate, converges quickly on the average modern PC and could be readily integrated into photolithography simulation software. 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. This procedure is especially challenging for broad-spectrum exposure systems that use, for example, Hg bulbs with g-, h-, and i-line UV radiation. Unlocking the potential of photolithography for vertical interconnect access (VIA) fabrication requires fast and accurate predictive modeling of diffraction effects and resist film photochemistry. Vertical stacking enables chip packages with increased functionality, enhanced design versatility, minimal power loss, reduced footprint and high bandwidth. 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.