1. Introduction

It has been observed that LER/LWR has a significant impact on semiconductor devices [1]. Namely, the more substantial the LER the worse the circuit’s performance. Moreover, LER is unlikely to scale down at the same rate as the smallest feature width does (or even, according to ITRS: LER is at best staying constant) [2]. From these observations it follows that having a shrinking smallest feature width (CD, Critical Dimension) and constant LER the latter becomes a more and more significant fraction of the overall CD error budget. Therefore, the CD control throughout the lithography–process becomes essentially a LER control. Seen in this light it is clear that there is a growing need for developing a solution which is able to determine the LER with sufficient precision.

2. The investigated object

This paper’s primary focus is on LER control using scatterometry, an optical method that is gaining in importance in semiconductor industry [3, 4]. It relies on comparing an optical response (scatter signature) to certain incident radiation of an unknown diffracting structure with a set of signatures of known structures; the best–fit between the two is assumed to reconstruct the unknown one. In the present investigation the “unknown object” is a 100nm–pitch grating with 50nm–wide (CD50), 60/75/90nm–high (h) resist lines on 40nm BARC (bottom anti–reflection coating) layer deposited on silicon.

To the edges of grating’s lines a realistic roughness is applied, meaning that its power spectral density (PSD) is resembling the spectral characteristics of a low–pass filter, see Fig. 1a [5]. This is contrary to sinusoidal or square “roughness” investigated by Institut für Technische Optik (ITO) and National Institute of Standards and Technology (NIST) in the past [6, 7]. As per findings of the authors such a simplification delivers erroneous scatter signatures. This has also been reported by NIST [8].

 

Fig. 1 Power spectral density (PSD) of a typical (per data available, [5]) rough edge (a) and a realistic rough line it yields as an example (b). The two important parameters of the PSD are cut-off frequency ξ₀ (here 0.011/nm) and the log–log slope m (here −3).

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Two set–ups: Θ₀₀ and Θ₉₀ are employed to investigate the LER gratings. In all cases the illumination wavelength is greater than 320nm. From the grating’s pitch of 100nm it follows that only zeroth diffraction order is propagating, therefore in reflection “diffracted” equals “reflected” (see Fig. 2). Two variants of each set–up are considered:

 

Fig. 2 Investigated set–ups. One needs to note that s–polarized incidence (E⃗_s) in Θ₀₀ is y–polarized while in Θ₉₀ — x–polarized.

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In each case “scatter signature” means reflected intensity as a function of either incidence angle α or wavelength λ.

All the results presented below are produced by ITO’s versatile RCWA solver — Microsim [9]. Simulated are 300nm–long segments of a single period of the line (the other dimension is then 100nm) with the sidewall angle of 90°. An example stochastic realization of such a segment is pictured in Fig. 1b. In the context of the presented results, for a fixed PSD multiple stochastic realizations of a rough line deliver scatter signatures which are similar enough, so it is sufficient to use only one realization during the simulations. All the simulations are run using 55 (−27...27) harmonics in both directions (x and y).

3. The impact of LER on scatter signatures

To illustrate the impact of LER on scatter signatures the following are observed:

When plotted on top of each other, see Fig. 3, in the big picture (Fig. 3a) there is hardly any difference between the two. Only a closer investigation (Fig. 3b–2) reveals the underlaying pattern — it instantly appears that the signature of CD50+LER grating does not follow the signature of CD50 no–LER grating.

 

Fig. 3 Although in the big picture (3a) the signatures of CD50+LER gratings () are indistinguishable from CD50’s signature (), taking a closer look (3b–2) one can observe an offset between the two. For instance the σ = 3 LER+CD50’s signature follows the signature of CD49.3. The family of gradient bands is scatter signatures of CD49.0, . . . , CD51.0 no–LER gratings. As one can observe, the two windows (1, 2) in 3a have the same size, yet they yield different local sensitivities (3b).

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The aforesaid underlaying pattern is that “does not follow” means certain specific offset, so that i.e. the scatter signature of CD50 grating carrying σ = 3nm of LER can be best–fit to the signature of LER–free grating of CD49.3, see Fig. 3b–2. This observation gives rise to two questions. Is this effect of a general nature? Does one observe the same offset in CD for both set–ups? Curiously, the answer to the former question is “yes”, whereas to the latter one is “no”. It is pictured in Fig. 4, where the best–fitting CD as a function of incidence angle α for three resist heights h in variable–angle variant of the set–ups presented in section 2 is shown. The results are interesting in a number of respects.

 

Fig. 4 The effective–CD interpolated from CD+LERs’ signatures recorded by variable–angle scatterometry. Figure shares the legend with Fig. 5. Discontinuities roughly correspond to the areas of low local sensitivity in scatter signatures, see Fig. 2. As such, those areas are of little interest from the point of view of metrology and erroneous (discontinuous) effective–CD they deliver may easily be disregarded.

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For one thing the observed effect is anisotropic — depending on the incident polarization (either E⃗_y or E⃗_x) the same LER+CD50 is interpolated to a CD either higher or lower than that of a CD50. For another thing, the more LER is applied to the grating the more offset from CD50 the best–fitting CD is. What is more, the observed effect seems to be of general nature — for a fixed polarization for any resist height, for any incidence angle the best–fitting CDs are the same (as long as one avoids discontinuities, see Fig. 4 with the corresponding comment in its caption). As a result, for a given polarization and LER amount a single effective–CD can be assigned. Then, the effective–CD also does not depend on the wavelength — it can be seen for “continuous” spectrum in Fig. 5, which shows the effective–CD obtained from scatter signatures that are recorded in fixed–angle variant of set–ups presented in section 2. Finally, the observed effect means that it is not possible to detect LER using just one scatterometric measurement. For instance, the σ = 3 LER+CD50 under E⃗_y illumination always exhibits the effective–CD of 49.3nm, rendering it indistinguishable from the perfect grating with 100nm–pitch and Critical Dimension of 49.3nm. Only through adding the second polarization (E⃗_x in this case) is one able to observe that the grating is no longer CD49.3, since now it acts as CD50.4. For this reason the conclusion follows that polarization discrimination is essential in scatterometric LER metrology. Only by considering a second polarization in a scatterometric measurement is one able to detect a change in the offset from the original CD (CD50 in our case), that is the effective–CD, which in turn can be related to the magnitude of LER.

 

Fig. 5 The effective–CD interpolated from CD+LERs’ signatures recorded by fixed–angle scatterometry.

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4. The effective–CD

As already stated, the more LER is applied to the grating the lower (under E⃗_y illumination) or the higher (under E⃗_x illumination) effective–CD is observed. For three discrete magnitudes of roughness this is shown in Figs. 4 and 5. The continuous relationship between the effective–CD and LER (or, more specifically, its σ) is pictured in Fig. 6. The curves are determined using just one set of parameters (see description of Fig. 6), however from the observation that the effective–CD is constant one can expect that they would look similar for any other parameters as well: CD =−0.041σ² − 0.097σ + CD₀ and CD = 0.039σ² + 0.014σ + CD₀. This is why it is assumed, that the polynomials are a general description of LER’s impact on the effective–CD. To verify this assumption for the selected parameters, two gratings have been tested, CD50 and CD51. Various amounts of LER have been applied to the both and respective effective–CDs have been determined. As one can easily notice, there is virtually no difference between the two sets of polynomials. For this reason it seems reasonable to assume that polynomials are general not only for all sets of parameters, but also (at least) for all CDs close to 50nm.

 

Fig. 6 The relationship between the effective–CD and LER. It seems to be uniform for (at least) all CDs of approximately 50nm.

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In all the above considerations only one power spectral density is used, that is: cut–off frequency and the slope are fixed at ξ₀ = 0.011/nm and m = −3, respectively, see Fig. 1. When one allows those parameters to vary, too, effective–CD polynomials become polynomial surfaces, see Fig. 7. One can easily observe that the cut-off frequency has a significant impact on effective–CDs while the impact of the log–log slope is almost negligible. However, the above results are consistent — the less harmonics in the spectrum the effective–CD parabolas are less “spread” (Fig. 7a). The steeper the slope the less high harmonics in the spectrum, ergo — the effective–CD parabolas are less “spread”, too (Fig. 7b).

 

Fig. 7 Effective–CD surfaces. While two parameters of the roughness are varying, the third one is fixed at its most typical value (indicated above the surfaces). As can be expected, the upper surfaces correspond to results from E⃗_x, the bottom ones – from E⃗_y.

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While the above effective–CD surfaces mean that the difference in effective–CDs cannot be uniquely assigned to specific LER, they still clearly show that in the presence of LER two different effective–CDs are to be expected under two perpendicular polarizations of illumination (E⃗_x and E⃗_y).

5. Conclusion

It has been shown that: