## Snapshot phase sensitive scatterometry based on double-channel spectral carrier frequency concept |

Optics Express, Vol. 19, Issue 24, pp. 23790-23799 (2011)

http://dx.doi.org/10.1364/OE.19.023790

Acrobat PDF (1183 KB)

### Abstract

Spectroscopic ellipsometry is one of the most important measurement schemes used in the optical nano-metrology for not only thin film measurement but also nano pattern 3D structure measurement. In this paper, we propose a novel snap shot phase sensitive normal incidence spectroscopic ellipsometic scheme based on a double-channel spectral carrier frequency concept. The proposed method can provide both Ψ(λ) and Δ(λ) only by using two spectra acquired simultaneously through the double spectroscopic channels. We show that the proposed scheme works well experimentally by measuring a binary grating with nano size 3D structure. We claim that the proposed scheme can provide a snapshot spectroscopic ellipsometric parameter measurement capability with moderate accuracy.

© 2011 OSA

## 1. Introduction

1. H. Huang and F. L. Terry Jr., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films **455-456**, 828–836 (2004). [CrossRef]

7. M. G. Moharam, E. Grann, D. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating,” J. Opt. Soc. Am. A **12**(5), 1068–1076 (1995). [CrossRef]

8. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. **12**(5), 1077–1086 (1995). [CrossRef]

1. H. Huang and F. L. Terry Jr., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films **455-456**, 828–836 (2004). [CrossRef]

2. X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. **14**(2), 97–111 (2001). [CrossRef]

*R*|

_{p}^{2}and |

*R*|

_{s}^{2}, respectively, over a broad spectral range in real time by using oblique incidence spectroscopic ellipsometry that employs a Wollaston prism and two spectroscopic channels. However, it could not measure the phase difference Δ which can provide higher sensitivity than the amplitude ratio Ψ in various spectroscopic ellipsometry applications [3

3. B. S. Stutzman, H. Huang, and F. L. Terry Jr., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B **18**(6), 2785–2793 (2000). [CrossRef]

4. H. Huang, W. Kong, and F. L. Terry Jr., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. **78**(25), 3983–3985 (2001). [CrossRef]

*R*,

_{TE}*R*, and

_{TM}*R*, where

_{φ}*φ*is any system polarizer angle taken between 0° and 90°. The first two spectra

*R*and

_{TE}*R*, which are acquired by orienting a polarizer transmission axis to be either parallel or perpendicular to the grating lines, are used to calculate the ellipsometric parameter tan(Ψ) from the square root of

_{TM}*R*/

_{TM}*R*, and the second ellipsometric parameter cos(Δ) is determined by including the third spectrum in the calculation. As mentioned, this approach requires three spectra to obtain both Ψ and Δ in the normal incidence scheme [5

_{TE}5. W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. Mui, “Line-profile and critical dimension measurements using a normal incidence optical metrology system ,” in *Advanced Semiconductor Manufacturing 2002 IEEE/SEMI Conference and Workshop* (IEEE, 2002), pp. 119–124.

9. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. **72**(1), 156–160 (1982). [CrossRef]

12. D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. **50**(19), 3360–3368 (2011). [CrossRef] [PubMed]

13. L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. **24**(18), 1314–1316 (1999). [CrossRef] [PubMed]

14. D. Kim, S. Kim, H. J. Kong, and Y. Lee, “Measurement of the thickness profile of a transparent thin film deposited upon a pattern structure with an acousto-optic tunablefilter,” Opt. Lett. **27**(21), 1893–1895 (2002). [CrossRef] [PubMed]

15. K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. **24**(21), 1475–1477 (1999). [CrossRef] [PubMed]

15. K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. **24**(21), 1475–1477 (1999). [CrossRef] [PubMed]

## 2. RCWA based scatterometry theory

^{th}order diffracted beam is collected by a spectroscopic system [2

2. X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. **14**(2), 97–111 (2001). [CrossRef]

7. M. G. Moharam, E. Grann, D. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating,” J. Opt. Soc. Am. A **12**(5), 1068–1076 (1995). [CrossRef]

8. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. **12**(5), 1077–1086 (1995). [CrossRef]

^{th}order diffracted beam is reflected from the grating following the Snell’s law. In order to describe the 3D shape of the binary grating fully, we need to define the grating period

*L*, the binary grating depth

*d*and the fill-factor

*f*which means the fraction of the grating period occupied by the ridge area of the grating. In general case, however, it is needed to slice the grating to the z-direction in order to model an arbitrary 3D shape using the RCWA algorithm. Figure 1(b) shows one simple case for the trapezoidal shape modeling. The total depth

*d*of the trapezoidal shape grating is sliced to generate

*l*rectangular shaped binary gratings which have the depth data

*t*

_{1},

*t*

_{2}, ...

*t*, respectively as illustrated in Fig. 1(b). And also, for each sliced binary grating, the fill-factor become

_{l}*f*

_{1},

*f*

_{2}, ...

*f*, respectively.

_{l}*d*), the periodic dielectric function is expandable with a Fourier series having a period

*L*aswhere

8. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. **12**(5), 1077–1086 (1995). [CrossRef]

*E*is the incident normalized electric field and

_{inc,y}## 3. Proposed snapshot phase sensitive scatterometry: theory and simulation

*h*is defined as the distance between the imaginary reference plane and the object plane, as illustrated in Fig. 2. In this section, the detail signal processing steps for obtaining the two spectroscopic ellipsometric parameter Ψ(λ) and Δ(λ) only by using the two spectra acquired by the dual spectrometer channels are described sequentially through simulation.

*I*and

_{TE}*I*are generated by using Eqs. (6) and (7). Here, we assume the reference wave is perfectly collimated plane wave which has constant intensity distribution throughout the entire wavenumber range for calculation simplicity. And also, the object wave can be generated accurately enough to replicate the real spectra diffracted from the periodic nano pattern object by using the RCWA algorithm described in section 2. Finally, each spectrum data is a function of the nano pattern 3D geometry, i.e., the grating period, fill-factor, height and side-angle which are depicted in Fig. 1. In this way, we can generate both the total phase functions

_{TM}*Φ*and

_{TE}*Φ*, and the visibility amplitude functions γ

_{TM}*and γ*

_{TE}*, which are dependent on the nano pattern geometry as follows:*

_{TM}*E*and

_{r,TE}*E*represent the reference wave traveling to the reference mirror and the object wave that goes to the nano pattern object for the TE mode, respectively.

_{t,TE}*k*is the wave number defined by 2π/

*λ*. Also, Φ

*(*

_{TE}*k*) represents the total phase function that consists of the carrier frequency term 2

*kh*and the phase term

*ϕ*that is dependent on the pattern geometry, while

_{TE}*i*represents the DC terms for the transverse electric mode

_{0,TE}_{.}Eq. (7) represents the spectrum data we expect to acquire for the transverse magnetic mode. We can see that all expressions in Eq. (7) are exactly same as those in Eq. (6) except for the subscript TM.

*i*and

_{0,TE}*i*for each mode has been subtracted in the beginning stage of the simulation for calculation simplicity. In order to check the feasibility over wide range of wavenumbers, the simulation has been performed for wavenumbers ranging from 10 to 30 (cm

_{0,TM}^{−1}).

*h,*as shown in Fig. 3(c) and 3(d).(Notice that the Fig. 3(c) and 3(d) represent only the amplitude data in the spectral frequency domain. The signal processing such as DC term removal and the object term windowing should be performed for the entire complex data obtained by the FFT step).

*(*

_{TE}*k*), γ

*(*

_{TM}*k*) and two unwrapped total phase functions

*ϕ*(

_{TE}*k*),

*ϕ*(

_{TM}*k*)). After obtaining those four functions, it’s straightforward to calculate the two SE parameters Ψ and Δ by using Eq. (5). It should be noted here that we can remove the spectral carrier frequency

*h*perfectly, which means that in contrast to the conventional single-channel carrier frequency technique in spatial domain [9

9. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. **72**(1), 156–160 (1982). [CrossRef]

11. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. **24**(5), 291–293 (1999). [CrossRef] [PubMed]

*h*since the 2

*kh*term is always canceled out in calculating the phase difference Δ. This is the key point of the double-channel spectral carrier frequency concept proposed in this paper.

## 4. Experimental results

*L*,

*d*,

*f*. According to the repeatedly measured data by AFM, the averaged period of the grating is 320.3nm( ±4.1nm) and the fill-factor is 0.63. And also, the averaged pattern depth

*d*is measured at several points by AFM and it turns out to be 92.1nm ( ±2.6nm).

*I*and

_{TE}*I*are measured simultaneously as shown in Fig. 7(a) . For generating such high frequency spectral interferograms in the spectral domain, we need to induce the spectral carrier frequency

_{TM}*h*defined as the distance between the imaginary reference plane and the object plane as described in Fig. 2. In this experiment, we used a 100W Tungsten-Halogen lamp as the broadband light source, a Nikon Michelson interferometer( ×2.5), a Wollaston prism with the aperture size of 10mm by 10mm, and two palm-size spectrometers having the spectral measurement range around from 450nm to 550nm.

*(*

_{TE}*k*), γ

*(*

_{TM}*k*) and two wrapped total phase functions

*ϕ*(

_{TE}*k*),

*ϕ*(

_{TM}*k*)). In the experiment, the phase unwrapping has not been used. Without the unwrapping step, however, we could get accurate reliable phase difference Δ. After obtaining those four functions, it’s straightforward to calculate the two SE parameters Ψ and Δ by using Eq. (5). As mentioned, it should be noted that we can remove the spectral carrier frequency

*h*perfectly since the 2

*kh*term can be subtracted fully in calculating the phase difference Δ for all the wavenumber

*k*.

^{−1}and 13.9 cm

^{−1}for better fitting results due to some uncertainty in the data of the refractive index of Si and Cr in other range.) It turned out that the measured nano pattern 3D shape has the period of 320nm, lower Cr width of 200nm, upper Cr width of 180nm and Cr height of 90nm. As can be seen in the final measurement results, the manufactured grating target sample designed to have originally a binary shape has the trapezoidal shape, which can happen in general due to the inherent grating manufacturing process limitation. Here, we need to notice that the proposed scatterometric approach can provide reliable upper Cr width as well as the lower Cr width, while the conventional SEM cannot provide. This result shows that the proposed scheme can provide a highly reliable solution for various nano technology areas which require a fast and simple non-destructive nano pattern 3D shape measurement capability.

## 5. Conclusion

*k*) and Δ(

*k*) are needed to be measured in a single shot.

## Acknowledgments

## References and links

1. | H. Huang and F. L. Terry Jr., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films |

2. | X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf. |

3. | B. S. Stutzman, H. Huang, and F. L. Terry Jr., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B |

4. | H. Huang, W. Kong, and F. L. Terry Jr., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett. |

5. | W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. Mui, “Line-profile and critical dimension measurements using a normal incidence optical metrology system ,” in |

6. | A. Sezginer, “Scatterometry by phase sensitive reflectometer,” U.S. Patent no. 6,985,232 B2 (Jan. 10, 2006). |

7. | M. G. Moharam, E. Grann, D. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating,” J. Opt. Soc. Am. A |

8. | M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. |

9. | M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. |

10. | Y. Ohtsuka and K. Oka, “Contour mapping of the spatiotemporal state of polarization of light,” Appl. Opt. |

11. | E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. |

12. | D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. |

13. | L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. |

14. | D. Kim, S. Kim, H. J. Kong, and Y. Lee, “Measurement of the thickness profile of a transparent thin film deposited upon a pattern structure with an acousto-optic tunablefilter,” Opt. Lett. |

15. | K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. |

16. | The Levenberg-Marquardt algorithm is available as lsqnonlin function by a commercial S/W MATLAB. |

**OCIS Codes**

(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(120.5820) Instrumentation, measurement, and metrology : Scattering measurements

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: August 31, 2011

Manuscript Accepted: October 17, 2011

Published: November 8, 2011

**Citation**

Daesuk Kim, Hyunsuk Kim, Robert Magnusson, Yong Jai Cho, Won Chegal, and Hyun Mo Cho, "Snapshot phase sensitive scatterometry based on double-channel spectral carrier frequency concept," Opt. Express **19**, 23790-23799 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23790

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### References

- H. Huang and F. L. Terry., “Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films455-456, 828–836 (2004). [CrossRef]
- X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular Spectroscopic Scatterometry,” IEEE Trans. Semicond. Manuf.14(2), 97–111 (2001). [CrossRef]
- B. S. Stutzman, H. Huang, and F. L. Terry., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B18(6), 2785–2793 (2000). [CrossRef]
- H. Huang, W. Kong, and F. L. Terry., “Normal-incidence spectroscopic ellipsometry for critical dimension monitoring,” Appl. Phys. Lett.78(25), 3983–3985 (2001). [CrossRef]
- W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. Mui, “Line-profile and critical dimension measurements using a normal incidence optical metrology system ,” in Advanced Semiconductor Manufacturing 2002 IEEE/SEMI Conference and Workshop (IEEE, 2002), pp. 119–124.
- A. Sezginer, “Scatterometry by phase sensitive reflectometer,” U.S. Patent no. 6,985,232 B2 (Jan. 10, 2006).
- M. G. Moharam, E. Grann, D. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating,” J. Opt. Soc. Am. A12(5), 1068–1076 (1995). [CrossRef]
- M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave anlysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am.12(5), 1077–1086 (1995). [CrossRef]
- M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am.72(1), 156–160 (1982). [CrossRef]
- Y. Ohtsuka and K. Oka, “Contour mapping of the spatiotemporal state of polarization of light,” Appl. Opt.33(13), 2633–2636 (1994). [CrossRef] [PubMed]
- E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett.24(5), 291–293 (1999). [CrossRef] [PubMed]
- D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt.50(19), 3360–3368 (2011). [CrossRef] [PubMed]
- L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett.24(18), 1314–1316 (1999). [CrossRef] [PubMed]
- D. Kim, S. Kim, H. J. Kong, and Y. Lee, “Measurement of the thickness profile of a transparent thin film deposited upon a pattern structure with an acousto-optic tunablefilter,” Opt. Lett.27(21), 1893–1895 (2002). [CrossRef] [PubMed]
- K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett.24(21), 1475–1477 (1999). [CrossRef] [PubMed]
- The Levenberg-Marquardt algorithm is available as lsqnonlin function by a commercial S/W MATLAB.

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