When processing wafers, one of the most significant factors is die size. While the opening size of the die is not important relative to the final product’s dimensions, it is very important for achieving the best yield possible. Die size is calculated by using a formula known as the circle square formula. It also is necessary to consider the effect of the Die swell, a buildup of low-molecular-weight polymers inside the opening of the die.

Die size is calculated using the circle square formula

The die per wafer calculation is a geometric process, and it correlates to the circle square formula. If you imagine a circle with a certain number of squares, the total number of dice would fill the square. To calculate the die size per wafer, you’ll need the size of the circle itself, plus the mathematical number Pi. Usually, a 300mm wafer is approximately 11.8 inches in diameter, so a square of that size would be a square.

A circle’s area is equal to its diameter times its radius. You can use the formula to determine die size by dividing a circle into small sections. When the circle is divided into smaller sections, it forms a parallelogram or a rectangle, depending on the diameter. The radius is r, and the area is C. The circumference formula will return a number that is either a rectangle or a parallelogram.

Die opening size is not critical relative to the final product dimensions

A study of the relationship between the size of the die opening and the dimensions of the final product has shown a positive correlation between the lower die opening and the bending shape. However, there are some limitations to this relationship, and there are many factors that must be taken into account when interpreting experimental results. The bending shape and the size of the lower die opening are both directly related, but the relative importance of these factors varies depending on the material and the type of dies.

A rule of thumb is to choose an opening size that is eight times the thickness of the material. This rule does not account for tonnage limits and springback. If the size of the opening is too small, excess tonnage may be a problem. Nevertheless, this rule applies to all materials. If the material you’re forming is 6 in. thick, select a die opening size that equals eight times that thickness.

Die swell is caused by low-molecular-weight polymer build-up

This property is attributed to low-molecular-weight polymer content, which increases the elasticity of the melted extrudate during the die-swell process. This phenomenon is often related to the length-to-diameter ratio of the extrudate, as well as the entry rate and shape of the die. More recent studies have focused on particle-filled polymers due to their wider engineering applications. In particular, this type of polymer is capable of swelling, albeit under conditions of high-temperature and high-shear rates.

Die swell behavior of polymeric materials should also be relevant in short capillary flow. However, it is difficult to predict the exact deterministic behavior of die swell under these conditions because of the complexity of entrance effects in polymer melts flowing in a short capillary. To further improve our understanding of die swell, we should consider other factors, such as the presence of capillary walls.

Die yield is a single most important factor in wafer processing costs

In semiconductor manufacturing, die yield is the single most important factor in the cost of the process. Without it, there would be no semiconductors. However, if you improve yield, you can reduce costs and sustain higher profitability. This process is complex, but it can be made easier by leveraging industry 4.0 technologies. Below are three key steps to improve die yield. Read on to find out more.

First, we need to consider the type of dies to be manufactured. FinFET logic devices, for example, have fine geometries and a vertical structure. They are also more prone to process variability. Besides, 3D NAND flash memory is more susceptible to contamination. Consequently, this process requires more sophisticated equipment and advanced techniques. The single most significant factor in wafer processing costs is die yield.

Die swell is compensated for by die adjustments

Thermoplastic melts undergo shear and extension stresses when passing through the die. The melt recovers elastically once exiting the die, manifesting as contraction in length and expansion in cross-section. Die swell can range from ten to one hundred percent, depending on the material, extrusion speed, and die geometry. Die swell can also occur due to variations in the design of the die, such as its size, complexity, and design.

During the extrusion process, a deposit can accumulate on the outer surface of the die. The deposit affects the quality of the extruded tubing. Cleaning the die deposit requires shutting down the extrusion line, which is costly and time-consuming. In addition, further work must be carried out to minimize the frequency of die drool. Therefore, proper die adjustments should be made in a timely manner.