Resist roughness plays a key role in pattern transfer

Einstein is reported to have once said, “Everything should be made as simple as possible, but not simpler.” Maybe one ought to keep this quote in mind when coping with the increasing complexity of the physicochemical processes at work in the manufacture of modern integrated circuits, which is being driven by demand for smaller, faster, and cheaper electronic devices. Consider, for example, the nanoscale pattern transfer from a resist layer to its substrate (see Figure 1). Due to its abundance and its effects on the quality of the final circuit feature, it has attracted increased attention recently in double-patterning 193nm and extreme UV lithography, which are the two strong candidates for the fabrication of sub-20nm patterns in near-future electronic circuits.

Figure 1. Schematic of a two-layer stack with sidewall roughness (a) before and (b) after pattern transfer.

Pattern transfer is performed by an ionized gas called plasma: ions and neutral species are produced by an electrical discharge and etch the substrate where it is unprotected by a ‘resist.’ Pattern transfer from a resist to the substrate is a complex process involving a large number of interrelated factors. These include, for example, the local flux of plasma gas species (ions and neutral species) on the feature (e.g., line), their interactions with the resist and substrate material, the product redeposition, the shape of the resist profile, and its sidewall roughness (the so-called line edge roughness, LER). Understanding and controlling pattern transfer ideally requires taking all of these factors into account. But is this really necessary? Do all these factors contribute equally to the final outcome of the shape and the sidewall morphology of the printed features? Or, in the spirit of Einstein's quote, can appropriate simplifications be made and implemented in a modeling approach that can explain and predict experimental results?

The majority of published work focuses on the interactions of plasma species with resist material, assuming initially smooth resist sidewalls or unrealistic deterministic morphologies.¹ In our work, we emphasize a realistic representation of the resist line's morphology (i.e., the slope of the line and its sidewall roughness) before plasma etching. However, we use a simple ion-driven model for etching.^2–4

The sidewall roughness, according to recent advances in its metrology and characterization, exhibits fractal characteristics, and a three-parameter model can be successfully used for its characterization involving: the root-mean-square roughness, σ, quantifying the amplitude of sidewall fluctuations; the correlation length, ξ, characterizing the spatial extent of correlations; and the roughness exponent, α, measuring the relative contribution of high-frequency fluctuations to the total roughness.⁵

More specifically, our model assumes a simplified two-layer stack (resist and substrate)—see Figure 1—and implements two basic procedures. In the first procedure, a rough plane surface—see Figure 2(a)—is generated with predefined roughness parameters (σ, ξ, and α) and is superimposed onto a smooth 3D line: see Figure 2(b). The outcome is a synthesized 3D line with realistic roughness resembling a true resist line after lithography and before pattern transfer: see Figure 2(c). In the second procedure, pattern transfer is approximated with an anisotropic etching process, where the sidewalls of the underlying substrate are determined only by the shadowing of the (unidirectional) incident ions from the eroding protrusions of the initial resist sidewall and the resist etch selectivity: see Figure 2(d).⁴

Figure 2. (a) A plane with specific roughness parameters (root-mean-square roughness σ = 2, spatial extent of roughness ξ = 20, and roughness exponent α = 0.4). (b) A 3D smooth line. (c) A 3D rough line coming from the superimposition of the plane rough surface—Figure 1(a)—onto the smooth 3D line: see Figure 1(b). (d) The 3D line of the substrate after plasma etching and removal of resist. Notice the formation of striations at the sidewall of the substrate.

As with all models, their validation depends upon their predictive power when compared with experiments. Here, our simple model has shown remarkable success. First, it is evident from Figure 2(d) that the model reproduces the common experimental observation of curtain-like structures on the sidewalls after pattern transfer. Second, both experimental results⁶—Figure 3(a)—and modeling predictions—Figure 3(b)—exhibit a linear trend of the substrate 3σ_S versus resist 3σ_R with a slope tan ω ∼0.5 (R stands for resist and S for substrate). The linear relation occurs above a low LER limit 3σ_R^*, revealing the beneficial role of pattern transfer for LER reduction at sufficiently large resist LER.

Figure 3. (a) Experimental⁶ and (b) modeling results for the substrate LER after pattern transfer (3σ_S)versus the resist LER before pattern transfer (3σ_R). The modeling results are taken for resist thickness 150nm, correlation length 30nm, roughness exponent 0.6, etching depth 150nm, and resist profile slope (θ_R) 84.7°. Notice the almost quantitative agreement of the model predictions and experimental measurements. tan ω: Slope of the linear trend.

Simple argument, inspired by our modeling, shows that σ_R^*∼ξ_R/(ctan θ_R), with c∼2.0–2.5. Therefore, the proposed rule of thumb for reducing LER during pattern transfer is that the following inequality holds: (σ_R/ξ_R) tan θ_R>1/c. The model also predicts that the reduction is favored for small ξ_R, α_R, and large resist thickness.

Third, we consider the frequency spectrum of LER quantified by power spectral density (PSD, the square of Fourier transform amplitudes), which provides a more detailed characterization of sidewall morphology. Experimental results show that pattern transfer affects mainly the middle and high frequencies and less the low frequencies: see Figure 4(a) and (b).^7,8 Figure 4(c) and (d) demonstrates that this is also captured by our simple model: at small σ_R, pattern transfer reduces the middle- and high-frequency part of the spectrum, while at higher σ_R, the low-frequency components are also affected.

Figure 4. Power spectral densities (PSD) of the resist LER before pattern transfer and the substrate LER after pattern transfer calculated from experimental measurements for two resists (a and b)⁷ and from the modeling results for two different resist LER σ_R(c and d). In the modeling results, the correlation length, the roughness exponent, the thickness, and the sidewall angle of the initial resist line were 30nm, 0.6, 150nm, and 86.2°, respectively. The etching selectivity was 3 and the etching depth was 150nm. Notice the qualitative capturing of the experimental behavior from modeling.

In conclusion, despite its simplicity, the model seems to predict the main experimental trends revealing the critical role of resist LER in the quality of pattern transfer, while it provides simple rules of thumb for making technological decisions. However, further simplifications by overlooking either the shadowing or the smoothing caused by the etching of the resist protrusions limit the predictive power of the modeling, bringing to mind the final words of Einstein's advice. Our next step is to make more detailed representations of the morphology of resist lines, including anisotropy, roundness, and footing. We are also investigating the limits of the model and considering the impact of more complicated plasma-resist interactions.