## Characterization of high density through silicon vias with spectral reflectometry |

Optics Express, Vol. 19, Issue 7, pp. 5993-6006 (2011)

http://dx.doi.org/10.1364/OE.19.005993

Acrobat PDF (1816 KB)

### Abstract

Measurement and control is an important step for production-worthy through silicon vias etch. We demonstrate the use and enhancement of an existing wafer metrology tool, spectral reflectometer by implementing novel theoretical model and measurement algorithm for high density through-silicon via (HDTSV) inspection. It is capable of measuring depth and depth variations of array vias by Discrete Fourier Transform (DFT) analysis in one shot measurement. Surface roughness of via bottom can also be extracted by scattering model fitting. Our non-destructive solution can measure TSV profile diameters as small as 5 μm and aspect ratios greater than 13:1. The measurement precision is in the range of 0.02 μm. Metrology results from actual 3D interconnect processing wafers are presented.

© 2011 OSA

## 1. Introduction

4. W. H. Teh, R. Caramto, J. Qureshi, S. Arkalgud, M. O’Brien, T. Gilday, K. Maekawa, T. Saito, K. Maruyama, T. Chidambaram, W. Wang, D. Marx, D. Grant, and R. Dudley, “A route towards production-worthy 5 μm x 25 μm and 1 μm x 20 μm non-Bosch through-silicon-via (TSV) etch, TSV metrology, and TSV integration,” IEEE 3DIC Conference, 2009.

5. F. Liu, R. R. Yu, A. M. Young, J. P. Doyle, X. Wang, L. Shi, K.-N. Chen, X. Li, D. A. Dipaola, D. Brown, C. T. Ryan, J. A. Hagan, K. H. Wong, M. Lu, X. Gu, N. R. Klymko, E. D. Perfecto, A. G. Merryman, K. A. Kelly, S. Purushothaman, S. J. Koester, R. Wisnieff, and W. Haensch, “A 300-mm wafer-level three-dimensional integration scheme using tungsten through-silicon via and hybrid Cu-adhesive bonding,” Proc. International Electron Devices Meeting (IEDM) (2008) p. 599.

9. P. K. Schenck, D. L. Kaiser, and A. V. Davydov, “High throughput characterization of the optical properties of compositionally graded combinatorial films,” Appl. Surf. Sci. **223**(1-3), 200–205 (2004). [CrossRef]

11. H. T. 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. TSV samples and Instrumentation

### 2.1 TSV Samples Detail

### 2.2 Reflectometer Configuration

## 3. Theoretical model

### 3.1 Modified theoretical model of the reflectance spectrum

12. Y. S. Ku and F. S. Yang, “Reflectometer-based metrology for high-aspect ratio via measurement,” Opt. Express **18**(7), 7269–7280 (2010). [CrossRef] [PubMed]

*α*and

*(1-α)*are the portion of the illuminated silicon top surface and the via opening respectively.

*E*is the electrical field incident onto the silicon surface and the via area. The via depth is

_{o}*d*, and the wavelength isλ. The reflectance intensity

*I*, which is the sum of the two reflected beams from the silicon surface and the via bottom surface is:The third term of Eq. (1) indicates that the electrical field reflectances must be combined using their proper phase angle difference.

*r*. The simulated reflectance intensity can be calculated by multiplying the reflecting factor

_{si}^{+}*r*:Consider the case of a silicon via array with 5 μm CD and 10 μm pitch, the illuminated surface areas of the top silicon surface and the via bottom surface is roughly 81% ( =

_{si}^{+}*α*) and 19% ( = 1-

*α*) of the total surface area respectively if the illumination is normal incidence into TSV sample surface as shown in Fig. 1(a) . However, the low-magnification objective (4X) has a maximum measurable slope of 2.0° (≅ sin

^{−1}0.035) as shown in Fig. 1 (b) thus light propagation is severely attenuated in the via region. The maximum measurable depth is estimated as 71.5 μm ( = TopCD/2/tan 2.0°), the corresponding aspect ratio (AR) is about 14.3( = 71.5 μm /5 μm). The effective illumination area radius R of via bottom with varying via depth can be calculated by Eq. (3) and it is listed in Table 1 . The ratio of the effective illumination area in via bottom area to the top via opening area is expressed as

*f*.We modified the reflectance intensity of Eq. (2) by adding the coefficient

*f*: Figure 1(c) shows the attenuation of the reflectance spectrum for via depth 50.0 um with measurable slope of 2.0° compared to the one with normal incidence. The effective illumination area radius in the via bottom is about 0.75 um as listed in Table 1, which is only about 30% compared to the top via radius.

12. Y. S. Ku and F. S. Yang, “Reflectometer-based metrology for high-aspect ratio via measurement,” Opt. Express **18**(7), 7269–7280 (2010). [CrossRef] [PubMed]

### 3.2 Theoretical model of the via bottom roughness

13. H. E. Bennett and J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. **51**(2), 123–129 (1961). [CrossRef]

*σ*, defined as the root mean square deviation of the surface from the mean surface level. where

*R*, is the specular reflectance of the rough surface and

_{s}*R*that of a perfectly smooth surface of the same material. Existence of undesirable surface roughness is quite possible because it naturally formed by plasma etching process. Thus we further modified the reflectance intensity of Eq. (4) by combining the Eq. (5):

_{o}### 3.3 Theoretical model of the via depth variation

#### 3.3.1 High aspect ratio silicon vias array

#### 3.3.2 High aspect ratio silicon vias array with oxide hard mask

*d*as the via depth from the topmost surface to the bottom of via and

*d*is the optical thickness of oxide film which is equal to

_{oxide}*n(λ)**0.6 μm. The refractive index of oxide

*n(λ)*is a constant 1.46 over our measured wavelength range (375-780 nm). The refractive index of silicon varies with the wavelength range (6.706 at 375 nm to 3.696 at 780 nm) [15]. The light incident on the oxide film surface divides into reflected and refracted portions. The refracted beam reflects again at the oxide film-silicon interface. Part of the light may reflect internally again and continue to experience multiple reflections within the oxide film layer until it has lost its intensity. The electrical field reflecting from oxide film can be expressed according to multiple reflection of thin film interference:Where

*r*is reflecting coefficient from top oxide film,

_{12}*t*is transmitting coefficient from air into oxide film,

_{12}*r*is reflecting coefficient from oxide-silicon interface,

_{23}*t*is transmitting coefficient from oxide into air,

_{21}*r*is reflecting coefficient from oxide-air interface within the oxide film. The light signal drops to about 1% in an internal reflection within the oxide film layer in our case [16]. The electrical field reflecting from via bottom can be expressed as:The combined total reflectance spectrum

_{21}## 4. Data evaluation algorithm

### 4.1 Discrete Fourier Transform algorithm for depths extraction

*k*). Thus recalibration of spectral data by spline interpolation and zero-padding combined with tapered window prior to DFT is introduced. Usually there is more than one via of the HDTSV array irradiated by the illumination spot; we implement the DFT analysis approach to obtain via depths and identify the depth variations within one shot measurement. Figure 5 shows the DFT frequency spectrum which is calculated from the simulation data in Fig. 3. The DFT result shows that the frequency for the two via depths are well separated from each other. Figure 6 shows the DFT frequency spectrum which is calculated from the high frequency term of the simulation data in Fig. 4. The DFT result shows three frequencies which are corresponding to the optical path depth:

*d-2d*( = 48.2 μm),

_{oxide}*d-d*( = 49.1 μm) and

_{oxide}*d*( = 50.0 μm) respectively. The optical thickness of oxide film:

*d*=

_{oxide}*n(λ)*d*which is 0.9 μm ( = 1.46*0.6 μm). Because the oxide-silicon surface acts like a mirror, a stronger signal (

_{physical thickness}*d-d*) can be acquired compared to the detection of the light reflected by the top of oxide film (

_{oxide}*d*). An attenuated signal at corresponding optical path depth

*d-2d*is coming from the light bounding twice in oxide film then transmitted out top surface interfere with the light reflected from via bottom. In addition to the film thickness and the optical constants, other properties such as the roughness of the via bottom also influence the amplitude of the reflectance. The DFT can handle the difficulty of separating the dense peaks and valleys, as well as combined modulation effect of the high frequency oscillations.

_{oxide}### 4.2 Measurement Uncertainty Evaluation

*D*is determined by the total number of the discrete sampling data

*N*and the sampling interval

18. R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express **12**(10), 2156–2165 (2004). [CrossRef] [PubMed]

*ΔD*is around 0.36 μm.

## 5. Results and discussions

*α*) and 19%( =

*1-α*) of the total surface area respectively. The oscillation from the via depth is particularly obvious in the long wavelength region as shown in the upper right side of Fig. 8(a). A preliminary fit to the experimental spectrum which only considers the frequency of the oscillation based on the phase angle difference was obtained using the Eq. (2) with a depth

*d*of 65.08 um. According to Eq. (3), the ratio of the effective illumination area in via bottom to the top via opening area (5 um CD in this case) can be calculated from the maximum measurable depth (71.5 um as listed in Table 1) and the via depth (65.08um from the above theoretical modeling fitting), which is about 0.8% ( =

*f*). Thus the portion of the illuminated via bottom areas is further attenuated from 19% of the via opening ratio by multiplying 0.8% for the reflectance calculation as expressed in Eq. (4). Then a nice fit to the experimental spectrum was obtained using the modified theoretical model expressed in Eq. (6) with the root mean square bottom roughness of 110 nm. A cross-section SEM result in Fig. 8(b) shows the bottom surface roughness is in a range of tens to hundred nm which is agreeable to our theoretical estimations.

*d*of 36.27, 36.70, 38.00, 38.55, 39.86 and 41.28 μm respectively, and each depth accompanies two more optical path depths

*d-2d*and

_{oxide}*d-d*. The optical thickness of oxide film:

_{oxide}*d*=

_{oxide}*n(λ)*d*which is around 0.87 μm ( = 1.46*0.596 μm). For example, the first set of via depth data marked with red color value is 34.53( =

_{physical thickness}*d-2*0.87*), 35.40( =

*d-0.87*) and 36.27 μm ( =

*d*). Some of the attenuated signal at corresponding via depth

*d-2d*was too weak which merge into neighboring peak and cause slightly peak broadening. Some residual spikes in few microns range were observed in cross section SEM result as shown in Fig. 11 which agrees with our DFT results of over a 5 μm depth variations.

_{oxide}## 6. Summary

## Acknowledgment

## References and links

1. | ITRS Assembly & Packaging2009. |

2. | H. Singh, C. Rusu, and V. Vahedi, “Etch challenges for 3-D integration,” 3rd Workshop on Plasma Etch and Strip in Microelectronics 2010, Grenoble, France. |

3. | M. Puech, J. M. Thevenoud, J. M. Gruffat, N. Launay, N. Arnal, and P. Godinat, “Fabrication of 3D packaging TSV using DRIE,” Symposium on Design, Test, Integrate ion and Packaging of MEMS/MOEMS, 2008. |

4. | W. H. Teh, R. Caramto, J. Qureshi, S. Arkalgud, M. O’Brien, T. Gilday, K. Maekawa, T. Saito, K. Maruyama, T. Chidambaram, W. Wang, D. Marx, D. Grant, and R. Dudley, “A route towards production-worthy 5 μm x 25 μm and 1 μm x 20 μm non-Bosch through-silicon-via (TSV) etch, TSV metrology, and TSV integration,” IEEE 3DIC Conference, 2009. |

5. | F. Liu, R. R. Yu, A. M. Young, J. P. Doyle, X. Wang, L. Shi, K.-N. Chen, X. Li, D. A. Dipaola, D. Brown, C. T. Ryan, J. A. Hagan, K. H. Wong, M. Lu, X. Gu, N. R. Klymko, E. D. Perfecto, A. G. Merryman, K. A. Kelly, S. Purushothaman, S. J. Koester, R. Wisnieff, and W. Haensch, “A 300-mm wafer-level three-dimensional integration scheme using tungsten through-silicon via and hybrid Cu-adhesive bonding,” Proc. International Electron Devices Meeting (IEDM) (2008) p. 599. |

6. | M. Puech, J. M. Thevenoud, and J. M. Gruffat, “DRIE for MEMS devices,” Advanced Packaging, 2008. |

7. | D. Marx, D. Grant, R. Dudley, A. Rudack, and W. H. Teh, “Wafer thickness sensor (WTS) for etch depth measurement of TSV,” IEEE International Conference on 3D System Integration, 2009. |

8. | M. Knowles, “Optical metrology for TSV process control,” 3D Interconnect Metrology at SEMATECH Workshop during SEMICON West 2009. |

9. | P. K. Schenck, D. L. Kaiser, and A. V. Davydov, “High throughput characterization of the optical properties of compositionally graded combinatorial films,” Appl. Surf. Sci. |

10. | Y. Feng, X. Zhang, B. Cheung, Z. Liu, M. Isao, and M. Hayashi, “OCD study of critical dimension and line-shape control of shallow-trench-isolation structures,” Proc. SPIE |

11. | H. T. 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 |

12. | Y. S. Ku and F. S. Yang, “Reflectometer-based metrology for high-aspect ratio via measurement,” Opt. Express |

13. | H. E. Bennett and J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. |

14. | V. C. Venugopal and A. J. Perry, “Method for in-situ monitoring of patterned substrate processing using reflectometry,” US patent 7019844. |

15. | M. Bass, |

16. | K. C. Huang, “The study of high aspect ratio TSV metrology,” master thesis, National Tsing Hua University, 2010. |

17. | ITRS Metrology 2007 ed.2007. |

18. | R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express |

**OCIS Codes**

(120.3940) Instrumentation, measurement, and metrology : Metrology

(300.6550) Spectroscopy : Spectroscopy, visible

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: October 14, 2010

Revised Manuscript: February 9, 2011

Manuscript Accepted: March 7, 2011

Published: March 17, 2011

**Citation**

Yi-Sha Ku, Kuo Cheng Huang, and Weite Hsu, "Characterization of high density through silicon vias with spectral reflectometry," Opt. Express **19**, 5993-6006 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-5993

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### References

- ITRS Assembly & Packaging2009.
- H. Singh, C. Rusu, and V. Vahedi, “Etch challenges for 3-D integration,” 3rd Workshop on Plasma Etch and Strip in Microelectronics 2010, Grenoble, France.
- M. Puech, J. M. Thevenoud, J. M. Gruffat, N. Launay, N. Arnal, and P. Godinat, “Fabrication of 3D packaging TSV using DRIE,” Symposium on Design, Test, Integrate ion and Packaging of MEMS/MOEMS, 2008.
- W. H. Teh, R. Caramto, J. Qureshi, S. Arkalgud, M. O’Brien, T. Gilday, K. Maekawa, T. Saito, K. Maruyama, T. Chidambaram, W. Wang, D. Marx, D. Grant, and R. Dudley, “A route towards production-worthy 5 μm x 25 μm and 1 μm x 20 μm non-Bosch through-silicon-via (TSV) etch, TSV metrology, and TSV integration,” IEEE 3DIC Conference, 2009.
- F. Liu, R. R. Yu, A. M. Young, J. P. Doyle, X. Wang, L. Shi, K.-N. Chen, X. Li, D. A. Dipaola, D. Brown, C. T. Ryan, J. A. Hagan, K. H. Wong, M. Lu, X. Gu, N. R. Klymko, E. D. Perfecto, A. G. Merryman, K. A. Kelly, S. Purushothaman, S. J. Koester, R. Wisnieff, and W. Haensch, “A 300-mm wafer-level three-dimensional integration scheme using tungsten through-silicon via and hybrid Cu-adhesive bonding,” Proc. International Electron Devices Meeting (IEDM) (2008) p. 599.
- M. Puech, J. M. Thevenoud, and J. M. Gruffat, “DRIE for MEMS devices,” Advanced Packaging, 2008.
- D. Marx, D. Grant, R. Dudley, A. Rudack, and W. H. Teh, “Wafer thickness sensor (WTS) for etch depth measurement of TSV,” IEEE International Conference on 3D System Integration, 2009.
- M. Knowles, “Optical metrology for TSV process control,” 3D Interconnect Metrology at SEMATECH Workshop during SEMICON West 2009.
- P. K. Schenck, D. L. Kaiser, and A. V. Davydov, “High throughput characterization of the optical properties of compositionally graded combinatorial films,” Appl. Surf. Sci. 223(1-3), 200–205 (2004). [CrossRef]
- Y. Feng, X. Zhang, B. Cheung, Z. Liu, M. Isao, and M. Hayashi, “OCD study of critical dimension and line-shape control of shallow-trench-isolation structures,” Proc. SPIE 5375, 1173–1182 (2004). [CrossRef]
- H. T. 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 Films 455–456, 828–836 (2004). [CrossRef]
- Y. S. Ku and F. S. Yang, “Reflectometer-based metrology for high-aspect ratio via measurement,” Opt. Express 18(7), 7269–7280 (2010). [CrossRef] [PubMed]
- H. E. Bennett and J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51(2), 123–129 (1961). [CrossRef]
- V. C. Venugopal and A. J. Perry, “Method for in-situ monitoring of patterned substrate processing using reflectometry,” US patent 7019844.
- M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009) Vol. 4.
- K. C. Huang, “The study of high aspect ratio TSV metrology,” master thesis, National Tsing Hua University, 2010.
- ITRS Metrology 2007 ed.2007.
- R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express 12(10), 2156–2165 (2004). [CrossRef] [PubMed]

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