3. E95 and the K1 Factor

k1 and E95

Figure 3: k1 and E95

Now, let’s discuss about the relationship between E95 and the k1 factor. The k1 factor indicates the difficulty of the lithography process; it is determined by the target design rule, numerical aperture (NA), and laser exposure wavelength according to the following formula:

k1 = Design Rule * NA of Lithography Tool/Laser Exposure Wavelength

In general, to achieve a higher yield in the mass-production process of semiconductors, k1 is set to near 0.4 while the NA and laser exposure wavelength of the lithography tool are determined based on the set k1 value. However, as the target design rule continues to become finer, the k1 value needs to be reduced to near 0.3 due to the NA limit of the lithography tool and the difficulty in shortening of the exposure wavelength. For example, achieving 90 nm in a KrF process or 65 nm in an ArF process requires reduction of the k1 value. From the viewpoint of cost, reducing k1 allows use of the laser with a fairly low NA and longer wavelength, thus reducing the equipment cost to subsequently lowering the manufacturing cost of semiconductor devices. Use of a KrF laser instead of an ArF laser for the 90-nm technology node is a typical example of this trend.

On the other hand, reducing the k1 value may cause the yield to be lowered because it limits the process margin. To enhance the yield, the resolution needs to be increased by improving the reticle while immersion lithography technology needs to be introduced to increase the NA of lithography tool in pseudo manner.

E95 makes a great contribution to reduction of the k1 factor. Figure 3 shows the upper limit required for each k1 factor. As this figure indicates, a narrower E95 is required as the k1 factor becomes smaller. The reason is that a smaller distribution of spectrums is required to reduce the impact of the chromatic aberration generated in a lithography tool as the target design rule becomes smaller. For example, the maximum E95 was approx. 1.8 pm for the target design rule of 150 nm in a KrF process with a k1 factor of 0.4. On the other hand, the E95 must be reduced to 0.8 pm for the target design rule of 90 nm in a KrF process with a k1 factor of 0.3 to reduce the impact of chromatic aberration for better resolution. The E95 corresponding to each k1 factor shown in figure 3 becomes the requirement for achieving the resolution required for imaging the target design pattern.

E95 Stability

Impact of E95 Stability on CD Uniformit

Figure 4: Impact of E95 Stability on CD Uniformit

For the generation with a k1 factor of 0.4 or more, it was considered that there was no problem if the E95 varies within its set upper limit. As the k1 factor becomes smaller than 0.4, however, fluctuation of the E95 directly impacts on the CD.

Figure 4 shows the estimated variance of the CD (variance per 1 pm) caused by fluctuation of the E95 for each k1 factor. While it varies slightly depending on the illumination condition and the characteristics of the photoresist used, it plots an almost average result. The data shown in this figure indicates that the CD varies by 7 to 8 nm as the E95 varies only 1 pm even if the k1 factor becomes 0.3 for the KrF process. This variation is four times greater than that for the KrF process with the k1 factor of 0.4. For the ArF process, meanwhile, it has been confirmed that the variation produces an impact twice as large as that for the KrF process. That is, if the k1 factor is reduced to 0.3 for the ArF process, the CD will vary 14 to 16 nm. Such a CD error at this level cannot be ignored, and represents a big difficulty. Therefore, it is apparent that improvement of the stabilization of the E95 is a big challenge for the next-generation lithography process.

As proved in this survey, the E95 produces an especially large impact on isolated lines but a small impact on dense lines. That is, bias generated in a pattern with a mixture of isolated and dense lines is closely related to the E95. This will be studied in detail in the following lectures.

We have discussed the factor that causes fluctuation of the E95, and have quantitatively indicated the impact of the E95 upon the CD. The next lecture will introduce a technology for stabilizing the E95, which is developed by Gigaphoton to stabilize the CD.