The Stochastic Variation of EUV Source Illumination

Wafer lithography systems essentially transfer an image pattern recorded on a mask to a wafer substrate, through a process of projection imaging. The projection of an entire image is the key to very high throughput, which drives the productivity of the process. At the same time, however, the sufficient input power of the light source is generally taken for granted. For the deep ultraviolet (DUV) systems, KrF and ArF (248 nm and 193 nm respective wavelength) excimer lasers have been sufficiently powerful for the purpose. However, for EUV (13.5 nm wavelength) sources, sufficient power is difficult to come by.

Although recent coverage of the stochastic issues of EUV have focused on defects which occur at very low rates which still cannot be ignored [1,2], or on the process variation (P-V) ranges [3], at a fundamental level, there is another key aspect which should not be ignored. The stochastic aspects of EUV imaging originate in the low photon density of the image at the wafer, which is directly related to availability of source power.

As will be shown below, the image formed at the wafer is conventionally a multitude of diffraction patterns added together. Each pattern originates from the illumination of the mask by a point source of light, from a given direction corresponding to that source. This setup is also formally known as Kohler illumination [4]. When considering the exposure dose at the wafer, it is important to recognize that this is actually the sum of doses allocated to each diffraction pattern. Fundamentally different diffraction patterns should have their respective photon numbers separately counted. With lower photon numbers per diffraction pattern, the Poisson shot noise of each pattern is relatively greater, to a more significant degree than by just considering the total photon dose.

The basics of lithographic imaging

Light from the source is collected by the condenser and focused to what is referred to as the "entrance pupil" of the projection optics. Along the way, the light is incident upon the mask or reticle. Each point of the light source forms a fairly collimated beam onto the mask, with the direction corresponding to its location in the source. This light from each source point is then diffracted by the image pattern on the mask. Typically the pattern is somewhat repetitive, and the diffraction pattern consists of a spectrum of "diffraction orders." This diffraction can be analyzed rigorously today. For now, what needs to be realized is that each source point produces a different interference pattern, and the photons making up the interference pattern are not to be mixed up with the photons making up another diffraction pattern from another source point. In the following analyses, it is convenient to represent the collection of source points as spread out evenly in the tangential or azimuthal as well as radial directions as shown below (Figure 1):

Figure 1. Source points sampled azimuthally and radially. The entire space is also known as the pupil.

The center is the direction of the optical axis, while the off-center points correspond to directions at angles with the optical axis, with the radii representing the sines of those angles. For the EUV systems, the optical axis itself changes direction, due to the reflections that necessarily must occur along the optical path. The parameter s is defined as the radius divided by the numerical aperture (NA).

7nm Metal Clip

The first example we'll look at is a rectangular array with 36 nm pitch in x, 108 nm pitch in y. It is a simplified representation of 7nm metal layer. The wavelength is taken to be 13.5 nm and the NA is 0.33. The interference patterns are classified according to which diffraction orders are included. There is always a zeroth order. Then there are other orders, which are obtained by increments in wavelength/x-pitch as well as wavelength/y-pitch. The orders with equal increment distances can be grouped together. For example, (1,0) and (-1,0) can be grouped together, as well as (0,1) and (0,-1). (1,1), (1,-1), (-1,1) and (-1,-1) are grouped together. The number of orders in each group can be up to 2 in some cases, 4 in others. By identifying each interference pattern with a specific number of orders in each group, all the possible interference patterns can be listed with the corresponding source points. Considering all points out to s=0.9, the following trend is observed (Figure 2).

Figure 2. Trend of number of interference patterns vs. radius

The source points at larger radii result in more interference patterns, as different azimuthal angles can affect which orders are projected; those which fall outside the NA are rejected. This trend also leads to another observation, regarding pupil fill (Figure 3).

Figure 3. Trend of number of interference patterns vs. pupil fill

The larger pupil fill also has more interference patterns. This inevitably means the same exposure dose will have photons divided among more interference patterns, so that each interference pattern gets noisier. The noise is represented as a variation in photon number, but this also can be effectively seen as a variation in the number of source points contributing the photons to the particular interference pattern. The metal clip is expected to retain the large pupil radii, as sufficiently small pupil radii cannot resolve 36 nm pitch. Thus, the retained larger pupil radii form an "annular" illumination shape (Figure 4).

Figure 4. Stochastic variation per interference pattern, for 36 nm x 108 nm rectangular array

The standard deviation is easily 10% or more, per interference pattern, for a dose of 30 mJ/cm2, when just considering the 18 nm x 2 nm line end region. One or two source points might "flicker" from location to location. Also note, we have not considered here the effects of defocus. If defocus were included, then even different locations contributing the same interference pattern may have to be differentiated, and their photon numbers separated, resulting in further increase of photon noise. For the perspective, if ArF photons were used at the same dose, with the same interference patterns, the noise is roughly a quarter of that seen with EUV. In that case, no source point flickering would be practically observed.

For this example, interference patterns which do not support the 36 nm line pitch (those beginning with '0' in the graph above) are always included, making it a sub-optimal patterning choice. Such interference patterns contribute rounding and/or rippling. Consequently, it is preferable to first create a series of lines and then cut them. This is considered in our next example.

30 nm pitch line cut (DRAM or 5nm)

The second example we'll consider involves cut patterns for 30 nm pitch lines. This may be used for 15 nm half-pitch DRAM, as well as 5nm foundry node metal layers. The cut pattern is actually a staggered array, with an x-pitch of 60 nm and a y-pitch of 90 nm. The staggered structure simplifes the diffraction order spectrum somewhat - odd orders, those who x-indices and y-indices add up to an odd number, conveniently vanish. Consequently, there are fewer interference patterns to account for, although the relative stochastic variation is still significant for most orders (Figure 5).

Figure 5. Stochastic variation per interference pattern, for 60 nm x 90 nm staggered array 

The easy way to remind oneself why this happens is to realize that each interference pattern only gets an allocated dose on the order of 1 mJ/cm2, which is less than one photon per square nanometer. This is clearly deep in the noise territory.

The individual interference patterns by themselves generate images which can be as different as night and day. Below I show the images for the "21000000" and "20100000" patterns (Figure 6):

Figure 6. Different images produced by different interference patterns

Hence, the changing of relative weights will affect the pattern appearance.

The sparse line cut pattern can use a wide annular or conventional circular illumination. Furthermore, the pitch between cuts can also be widened. However, this also increases the number of possible interference patterns, each being a different combination of diffraction orders. Hence, the photon density per interference pattern can only decline.

Conclusion

The reliance on conventional or annular illumination for sparse patterns such as line cuts or dense two-dimensional patterns like clips from the metal layer lead to the consideration of the presence of a multitude of interference patterns, which results in the splitting of photons into many groups each with a much smaller photon number density. This is illustrated below (Figure 7) for the two cases described above, with each differently colored point representing the interference pattern for a different combination of diffraction orders.

Figure 7. Interference pattern distribution within pupil for 60 nm x 90 nm staggered array (left) and 36 nm x 108 nm rectangular array (right). Each color represents a specific diffraction order combination.

This is not so much a problem for DUV lithography, but a readily recognized problem for EUV lithography, where shot noise is already widely observed. The effect is quantitatively equivalent to a stochastically "flickering" EUV pupil source. If defocus is also to be included for consideration, further differentiation among source points will be required, resulting in further division of photons into even smaller groups, resulting in even more significant noise.

Restricting the illumination source points can put all the photons into one target interference pattern, which would resolve the stochastic concern for a given feature pattern. However, these points would generate multiple interference patterns for another feature pattern. For example, selecting source points which only produce the “20100000” interference pattern for the 60 nm x 90 nm staggered array produces six different patterns for the 36 nm x 108 nm rectangular array (Figure 8). Consequently, if both feature patterns are in the same layout, at least one will suffer stochastic issues from EUV photons being divided into smaller groups.

Figure 8. (Left) Source points which produce the 20100000 interference pattern for the 60 nm x 90 nm staggered array. (Right) The same source points produce multiple interference patterns for the 36 nm x 108 nm rectangular array.

As the move to higher k1 has always been the motivation for the move to EUV, as well as high-NA EUV in the future, the scenarios where circular or annular illumination is used are an obvious application, which must address the stochastic variation issue with much higher doses.

References

[1] A. Frommhold et al., Proc. SPIE 11147, 1114708 (2019).

[2] P. De Bisschop and E. Hendrickx, Proc. SPIE 10957, 109570E (2019).

[3] A. V. Pret et al., Proc. SPIE 10583, 105830K (2018).

[4] https://www.iue.tuwien.ac.at/phd/kirchauer/node53.html