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I came across an excellent review of stochastic effects involved in EUV lithography, in a paper by Peter De Bisschop of IMEC, published in the Oct-Dec 2017 issue of Journal of Micro/Nanolithography, MEMS, and MOEMS. In this post, (with his permission of course) I only briefly summarize the points which the reader can find covered in more detail in the paper: Peter De Bisschop, Stochastic effects in EUV lithography: random, local CD variability, and printing failures,J. Micro/Nanolith. MEMS MOEMS16(4), 041013 (2017) © SPIE.

Background: Why is stochasticity important?

Stochastic or random effects in lithography have gained significant interest recently with the combination of three trends:

- Fewer particles (photons) involved in the exposure process, when EUV is considered
- Smaller features requiring tighter CD control, despite having fewer photons involved
- Larger numbers of such smaller features in a product, requiring larger numbers of standard deviations in spec.

At the heart of the issue is the fact that light used in lithography is quantized as photons which randomly arrive at the resist surface from the source. The photon number is proportional to the product of the dose and the exposed area. For a given dose, a smaller feature uses fewer photons for exposure. Although one can target an average dose of photons, the ACTUAL number has some variation which is characterized by the standard deviation, which is the square root of the average photon number. The smaller the photon number, i.e., the lower the dose or the smaller the exposed feature area, the larger the % variation of the photon number or dose. This variation is often referred to as shot noise. In large feature populations, with more than billions of features, more than twelve standard deviations (+/- 6 standard deviations from the mean) need to be considered. In this case, the natural deviation of photon number from the mean corresponds in the worst case (â‰¥6 standard deviations) to a substantial dose variation, which could lead to printing failure.

Metrics for Stochastic Printing Failure

The first key point in this paper is the introduction of a metric to quantify stochastic printing failures. Such failures are considered not-ok or NOK features. There are two pixel-based NOK (pixNOK) metrics for line-space patterns, one for space bridging and one for line breaking:

Figure 1.Pixel-based NOK for space bridging (left) and line breaking (right).

In addition, there are entire-feature NOK metrics for bridging or missing contact or dot patterns:

Figure 2.NOK for bridged or merged contacts/dots (left) and missing contacts/dots (right).

Note that the NOK metrics do NOT have direct correlations to line edge roughness or local CD uniformity, though they may trend similarly. The CD measurements can be applied to most of the feature population, whereas the NOK failures would apply to a small minority of features (0.1% or less) so badly damaged that standard CD measurements cannot be taken.

Stochastic Failure CD Windows

Stochastic effects will obviously depend on certain lithographic aspects. The most obvious are feature size and dose, as both directly impact the photon number. However, the resist and focus also play important roles as well. While they do not directly involve photon number, the resist and focus do affect the exposure latitude (d(CD)/d(dose)), which determines the sensitivity of CD to dose errors, such as may arise from stochastic sources such as shot noise.

At smaller pitches, the window between bridging spaces and breaking lines, or between missing and bridging contacts or dots, becomes narrower. This can be thought of as a tradeoff between the feature size being too small and the space between features being too small, at a given pitch. When the window is closed, there is essentially no tolerance to stochastic effects at the given process condition.

Figure 3.Example (not claiming to be best possible performance) of a 32 nm pitch pixNOK(space) as a function of space post-etch CD, for positive-tone chemically amplified resist (left) or metal-containing non-chemically amplified resist (right).

The 32 nm pitch line/space pattern in Figure 3 shows a pixNOK failure rate between 10 and 100 ppm, for either standard positive-tone-developed (PTD) chemically amplified resist (CAR) as well as non-chemically amplified resist. The dose-to-size was ~30 mJ/cm^{2}. Note that the non-CAR tended to flatten out at a higher pixNOK (space) than the CAR.

Figure 4. Examples of measured LCDU and NOK as a function of mean post-litho CD for square contact arrays at three different pitches: 36 nm, 40 nm, and 80 nm. PTD-CAR, Quasar illumination.

In the examples of Figure 4, the 36 nm contact pitch CD window hardly exists, compared to the 40 nm pitch. Again, this can be considered the tradeoff between the contact being too small or the space between contacts being too small. On the other hand, for the 80 nm pitch, the missing feature cliff occurs at higher CD. The extended pitch dependence is considered further next.

Pitch and focus dependence

The pitch dependence of the NOK metric is partly linked to the normalized image log slope (NILS), defined as (exposure latitude)/ (dose at feature edge)*(feature width), as well as to the CD itself. The illumination in this case (Quasar, 25-deg opening) is optimum for 40-50nm pitch, while not fit for ~55-65 nm pitch (Figure 5). The paper demonstrates that NILS (which is worse for smaller CD) is a much better indicator for local CD uniformity (LCDU) than for NOK rate.

Figure 5. Post-litho LCDU (left) and NOK_missing (right) as a function of contact pitch for four different CDs.

For line-space patterns (Figure 6), the line-edge roughness (LER) and NOK pitch dependence (at ~30 mJ/cm^{2}) also trend similarly with pitch, just as with contact LCDU and NOK. However, LER is correlated better with exposure latitude than with NILS.

Figure 6. Post-litho LER (left) and pixNOK for space bridging (right) as a function of pitch for three different CDs.

Finally, in Figure 7, the effect of defocus is also shown to be much more dramatic than observed for CD or linewidth roughness (LWR), as can be seen for the following 36 nm half-pitch line-space pattern (Quasar illumination, PTD-CAR). Doses were varied for different CDs.

Figure 7. Post-etch Bossung plots for CD, LWR pixNOK(space bridging) and pixNOK(line breaking) for a 36 nm pitch line-space pattern, with Quasar illumination and PTD-CAR process.

Main observations

In summary, the stochastic effects of EUV lithography are manifest in more dramatic ways than simple CD variation.

- For line-space patterns, line roughness correlates well with exposure latitude. The line roughness does not correlate with pixNOK, although they can trend similarly across pitch.
- For contact/dot arrays, LCDU correlates well with NILS. NOK_missing does not correlate with LCDU, but they can trend similarly across pitch.
- Pitch-related effects can be divided into two parts: (a) at smaller pitches, there can be a much narrower (resist-dependent) CD window between missing/bridging contacts/dots or bridging spaces/breaking lines, due to the wider space vs. wider line tradeoff, and (b) effects due to NILS or exposure latitude or defocus can be associated with the choice of illumination; e.g., Quasar illumination for this paper's examples is optimum for 40-50 nm pitch but not compatible with the forbidden 55-65 nm pitch. The exposure latitude can be further affected by the resist.

Additional information

The paper also gives more details on measuring the NOK, other CD trends, as well as possible directions for minimizing stochastic effects. For further details, I highly encourage the reader to look up the paper, cited at the beginning. It is worth your time.