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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 19967–19972
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About the influence of Line Edge Roughness on measured effective–CD

Bartosz Bilski, Karsten Frenner, and Wolfgang Osten  »View Author Affiliations


Optics Express, Vol. 19, Issue 21, pp. 19967-19972 (2011)
http://dx.doi.org/10.1364/OE.19.019967


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Abstract

Various reports state that Line Edge/Width Roughness (LER/LWR) has a significant impact on the integrated circuits fabricated by means of lithography, hence there is a need to determine the LER in–line so that it never exceeds certain specified limits. In our work we deal with the challenge of measuring LER on 50nm resist gratings using scatterometry. We show by simulation that there is a difference between LER and no–LER scatter signatures which first: depends on the polarization and second: is proportional to the amount of LER. Moreover, we show that the mentioned difference is very specific, that is — a grating with LER acts like a grating without LER but showing another width (CD, Critical Dimension), which we refer–to as effective–CD.

© 2011 OSA

1. Introduction

It has been observed that LER/LWR has a significant impact on semiconductor devices [1

1. K. Shibata, N. Izumi, and K. Tsujita, “Influence of line–edge roughness on MOSFET devices with sub–50nm gates,” Proc. SPIE 5375, 865–873 (2004). [CrossRef]

]. 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

2. International Technology Roadmap for Semiconductors, www.itrs.net.

]. 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

3. A. C. Diebold, Handbook of Silicon Semiconductor Metrology (CRC Press, 2001). [CrossRef]

, 4

4. A. E. Braun, “How CD–SEMs Complement Scatterometry,” Semicond. Int. Mag. (June2009).

]. 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

5. G. Gallatin, “SPIE Short Course 886: Line Edge Roughness.”

]. 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

6. W. Osten, V. Ferreras Paz, K. Frenner, T. Schuster, and H. Bloess, “Simulations of scatterometry down to 22nm structure sizes and beyond with special emphasis on LER,” in Frontiers of Characterization and Metrology for Nanoelectronics: 2009, E. M. Secula, D. G. Seiler, R. P. Khosla, D. Herr, C. M. Garner, R. McDonald, and A. C. Diebold, eds. (AIP Conference Proceedings, 2009). Vol. 1173, pp. 371–378.

, 7

7. B. C. Bergner, T. A. Germer, and T. J. Suleski, “Effect of line–width roughness on optical scatterometry measurements,” Proc. SPIE 7272, 72720U (2009). [CrossRef]

]. As per findings of the authors such a simplification delivers erroneous scatter signatures. This has also been reported by NIST [8

8. B. C. Bergner, T. A. Germer, and T. J. Suleski, “Effective medium approximations for modeling optical reflectance from gratings with rough edges,” J. Opt. Soc. Am. A 5, 1083–1090 (2010). [CrossRef]

].

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).

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:
  • fixed wavelength λ with floating incidence angle α (variable–angle scatterometry [3

    3. A. C. Diebold, Handbook of Silicon Semiconductor Metrology (CRC Press, 2001). [CrossRef]

    ]),
  • fixed incidence angle α with floating wavelength λ (fixed–angle scatterometry [3

    3. A. C. Diebold, Handbook of Silicon Semiconductor Metrology (CRC Press, 2001). [CrossRef]

    ]).

Fig. 2 Investigated set–ups. One needs to note that s–polarized incidence (E⃗s) in Θ00 is y–polarized while in Θ90x–polarized.

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

9. M. Totzeck, “Numerical simulation of high–NA quantitative polarization microscopy and corresponding near–fields,” Optik 112, 399–406 (2001).

]. 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:
  • scatter signatures of the LER grating described in section 2, that is CD50 with increasing amounts of LER applied to its edges, namely LER of σ = 1,2,3nm,
  • a family of scatter signatures of CD49, CD49.1, . . . , CD50.9, CD51 no–LER gratings (only the CD of each grating is allowed to vary around 50nm, in other respects they match the description in section 2).

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 (oe-19-21-19967-i001.jpg) are indistinguishable from CD50’s signature (oe-19-21-19967-i002.jpg), taking a closer look (3b–2) one can observe an offset between the two. For instance the σ = 3 LER+CD50’s signature oe-19-21-19967-i003.jpg 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).

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.

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

4. The effective–CD

As already stated, the more LER is applied to the grating the lower (under E⃗y illumination) or the higher (under E⃗x 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.

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 E⃗x, the bottom ones – from E⃗y.

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 (E⃗x and E⃗y).

5. Conclusion

It has been shown that:
  • the effect of LER on scatter signatures depends on its amount (Fig. 2),
  • a difference in the effective–CDs can be observed only by using two orthogonal directions of polarization (Fig. 5),
  • the effective–CD has a weak dependence on resist height, wavelength and incidence angle (Figs. 3, 4),
  • the difference in effective–CDs, measured with two orthogonal directions of polarization can be (non–uniquely) translated into information about the amount of LER.

Acknowledgments

The research leading to these results has received funding from the European Community’s Seventh Framework Programme under grant agreement no. 215723.

References and links

1.

K. Shibata, N. Izumi, and K. Tsujita, “Influence of line–edge roughness on MOSFET devices with sub–50nm gates,” Proc. SPIE 5375, 865–873 (2004). [CrossRef]

2.

International Technology Roadmap for Semiconductors, www.itrs.net.

3.

A. C. Diebold, Handbook of Silicon Semiconductor Metrology (CRC Press, 2001). [CrossRef]

4.

A. E. Braun, “How CD–SEMs Complement Scatterometry,” Semicond. Int. Mag. (June2009).

5.

G. Gallatin, “SPIE Short Course 886: Line Edge Roughness.”

6.

W. Osten, V. Ferreras Paz, K. Frenner, T. Schuster, and H. Bloess, “Simulations of scatterometry down to 22nm structure sizes and beyond with special emphasis on LER,” in Frontiers of Characterization and Metrology for Nanoelectronics: 2009, E. M. Secula, D. G. Seiler, R. P. Khosla, D. Herr, C. M. Garner, R. McDonald, and A. C. Diebold, eds. (AIP Conference Proceedings, 2009). Vol. 1173, pp. 371–378.

7.

B. C. Bergner, T. A. Germer, and T. J. Suleski, “Effect of line–width roughness on optical scatterometry measurements,” Proc. SPIE 7272, 72720U (2009). [CrossRef]

8.

B. C. Bergner, T. A. Germer, and T. J. Suleski, “Effective medium approximations for modeling optical reflectance from gratings with rough edges,” J. Opt. Soc. Am. A 5, 1083–1090 (2010). [CrossRef]

9.

M. Totzeck, “Numerical simulation of high–NA quantitative polarization microscopy and corresponding near–fields,” Optik 112, 399–406 (2001).

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(120.3940) Instrumentation, measurement, and metrology : Metrology

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: July 7, 2011
Revised Manuscript: August 24, 2011
Manuscript Accepted: August 24, 2011
Published: September 28, 2011

Citation
Bartosz Bilski, Karsten Frenner, and Wolfgang Osten, "About the influence of Line Edge Roughness on measured effective–CD," Opt. Express 19, 19967-19972 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-19967


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References

  1. K. Shibata, N. Izumi, and K. Tsujita, “Influence of line–edge roughness on MOSFET devices with sub–50nm gates,” Proc. SPIE5375, 865–873 (2004). [CrossRef]
  2. International Technology Roadmap for Semiconductors, www.itrs.net .
  3. A. C. Diebold, Handbook of Silicon Semiconductor Metrology (CRC Press, 2001). [CrossRef]
  4. A. E. Braun, “How CD–SEMs Complement Scatterometry,” Semicond. Int. Mag. (June2009).
  5. G. Gallatin, “SPIE Short Course 886: Line Edge Roughness.”
  6. W. Osten, V. Ferreras Paz, K. Frenner, T. Schuster, and H. Bloess, “Simulations of scatterometry down to 22nm structure sizes and beyond with special emphasis on LER,” in Frontiers of Characterization and Metrology for Nanoelectronics: 2009, E. M. Secula, D. G. Seiler, R. P. Khosla, D. Herr, C. M. Garner, R. McDonald, and A. C. Diebold, eds. (AIP Conference Proceedings, 2009). Vol. 1173, pp. 371–378.
  7. B. C. Bergner, T. A. Germer, and T. J. Suleski, “Effect of line–width roughness on optical scatterometry measurements,” Proc. SPIE7272, 72720U (2009). [CrossRef]
  8. B. C. Bergner, T. A. Germer, and T. J. Suleski, “Effective medium approximations for modeling optical reflectance from gratings with rough edges,” J. Opt. Soc. Am. A5, 1083–1090 (2010). [CrossRef]
  9. M. Totzeck, “Numerical simulation of high–NA quantitative polarization microscopy and corresponding near–fields,” Optik112, 399–406 (2001).

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