Abstract

The structures of ultrathin sputtered Cr/C multilayers were determined by high-resolution transmission electron microscopy. The evolution of layer thickness errors, interdiffusion and interfacial roughness were simulated using time series models. The results show that with increasing of interdiffusion and roughness the multilayer thickness ratio changes, thereby influencing the optical performance. All structural parameters show good correlation with and influence adjacent layers. The system errors of the deposition equipment can also be evaluated by the models.

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  1. H. Jiang, A. Michette, S. Pfauntsch, D. Hart and M. Shand, “Design of narrowband multilayer for Cr Kα X-rays,” in Proceedings of PIER (Xi’an, China, 2010), pp. 61–65.
  2. W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, and I. K. Schuller, “Cumulative disorder and x-ray line broadening in multilayers,” Phys. Rev. B Condens. Matter 34(8), 5955–5958 (1986).
    [CrossRef] [PubMed]
  3. H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
    [CrossRef]
  4. A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
    [CrossRef]
  5. I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
    [CrossRef]
  6. E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
    [CrossRef] [PubMed]
  7. S. Deng, H. Qi, K. Yi, Z. Fan, and J. Shao, “Effect of defects on the reflectivity of Cr/C multilayer soft X-ray mirror at 4.48nm,” Appl. Surf. Sci. 255(16), 7434–7438 (2009).
    [CrossRef]

2010

H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
[CrossRef]

2009

S. Deng, H. Qi, K. Yi, Z. Fan, and J. Shao, “Effect of defects on the reflectivity of Cr/C multilayer soft X-ray mirror at 4.48nm,” Appl. Surf. Sci. 255(16), 7434–7438 (2009).
[CrossRef]

2006

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

2003

A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
[CrossRef]

1993

E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
[CrossRef] [PubMed]

1986

W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, and I. K. Schuller, “Cumulative disorder and x-ray line broadening in multilayers,” Phys. Rev. B Condens. Matter 34(8), 5955–5958 (1986).
[CrossRef] [PubMed]

Aschentrup, A.

A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
[CrossRef]

Bader, S. D.

E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
[CrossRef] [PubMed]

Bijkerk, F.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Bruynseraede, Y.

W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, and I. K. Schuller, “Cumulative disorder and x-ray line broadening in multilayers,” Phys. Rev. B Condens. Matter 34(8), 5955–5958 (1986).
[CrossRef] [PubMed]

Deng, S.

S. Deng, H. Qi, K. Yi, Z. Fan, and J. Shao, “Effect of defects on the reflectivity of Cr/C multilayer soft X-ray mirror at 4.48nm,” Appl. Surf. Sci. 255(16), 7434–7438 (2009).
[CrossRef]

Enkisch, H.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Fan, Z.

S. Deng, H. Qi, K. Yi, Z. Fan, and J. Shao, “Effect of defects on the reflectivity of Cr/C multilayer soft X-ray mirror at 4.48nm,” Appl. Surf. Sci. 255(16), 7434–7438 (2009).
[CrossRef]

Fullerton, E. E.

E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
[CrossRef] [PubMed]

Gijs, M.

W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, and I. K. Schuller, “Cumulative disorder and x-ray line broadening in multilayers,” Phys. Rev. B Condens. Matter 34(8), 5955–5958 (1986).
[CrossRef] [PubMed]

Hachmann, W.

A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
[CrossRef]

Heinzmann, U.

A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
[CrossRef]

Homma, H.

W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, and I. K. Schuller, “Cumulative disorder and x-ray line broadening in multilayers,” Phys. Rev. B Condens. Matter 34(8), 5955–5958 (1986).
[CrossRef] [PubMed]

Jiang, H.

H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
[CrossRef]

Kleineberg, U.

A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
[CrossRef]

Lim, Y.

A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
[CrossRef]

Louis, E.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Muellender, S.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Nedelcu, I.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Pearson, J.

E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
[CrossRef] [PubMed]

Qi, H.

S. Deng, H. Qi, K. Yi, Z. Fan, and J. Shao, “Effect of defects on the reflectivity of Cr/C multilayer soft X-ray mirror at 4.48nm,” Appl. Surf. Sci. 255(16), 7434–7438 (2009).
[CrossRef]

Schuller, I. K.

W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, and I. K. Schuller, “Cumulative disorder and x-ray line broadening in multilayers,” Phys. Rev. B Condens. Matter 34(8), 5955–5958 (1986).
[CrossRef] [PubMed]

Sevenhans, W.

W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, and I. K. Schuller, “Cumulative disorder and x-ray line broadening in multilayers,” Phys. Rev. B Condens. Matter 34(8), 5955–5958 (1986).
[CrossRef] [PubMed]

Shao, J.

S. Deng, H. Qi, K. Yi, Z. Fan, and J. Shao, “Effect of defects on the reflectivity of Cr/C multilayer soft X-ray mirror at 4.48nm,” Appl. Surf. Sci. 255(16), 7434–7438 (2009).
[CrossRef]

Sinha, S. K.

E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
[CrossRef] [PubMed]

Sowers, C. H.

E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
[CrossRef] [PubMed]

Tichelaar, F.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

van de Kruijs, R. W. E.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Wang, X.

H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
[CrossRef]

Wang, Z.

H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
[CrossRef]

Watanabe, M.

H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
[CrossRef]

Westerwalbesloh, T.

A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
[CrossRef]

Wu, X. Z.

E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
[CrossRef] [PubMed]

Xu, J.

H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
[CrossRef]

Yakshin, A. E.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Yi, K.

S. Deng, H. Qi, K. Yi, Z. Fan, and J. Shao, “Effect of defects on the reflectivity of Cr/C multilayer soft X-ray mirror at 4.48nm,” Appl. Surf. Sci. 255(16), 7434–7438 (2009).
[CrossRef]

Zhu, J.

H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
[CrossRef]

Zoethout, E.

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Appl. Phys., A Mater. Sci. Process.

A. Aschentrup, W. Hachmann, T. Westerwalbesloh, Y. Lim, U. Kleineberg, and U. Heinzmann, “Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction,” Appl. Phys., A Mater. Sci. Process. 77(5), 607–611 (2003).
[CrossRef]

Appl. Surf. Sci.

S. Deng, H. Qi, K. Yi, Z. Fan, and J. Shao, “Effect of defects on the reflectivity of Cr/C multilayer soft X-ray mirror at 4.48nm,” Appl. Surf. Sci. 255(16), 7434–7438 (2009).
[CrossRef]

J. Appl. Phys.

H. Jiang, J. Zhu, J. Xu, X. Wang, Z. Wang, and M. Watanabe, “Determination of layer-thickness variation in periodic multilayer by X-ray reflectivity,” J. Appl. Phys. 107(10), 103523 (2010).
[CrossRef]

Phys. Rev. B Condens. Matter

E. E. Fullerton, J. Pearson, C. H. Sowers, S. D. Bader, X. Z. Wu, and S. K. Sinha, “Interfacial roughness of sputtered multilayers: Nb/Si,” Phys. Rev. B Condens. Matter 48(23), 17432–17444 (1993).
[CrossRef] [PubMed]

W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, and I. K. Schuller, “Cumulative disorder and x-ray line broadening in multilayers,” Phys. Rev. B Condens. Matter 34(8), 5955–5958 (1986).
[CrossRef] [PubMed]

Thin Solid Films

I. Nedelcu, R. W. E. van de Kruijs, A. E. Yakshin, F. Tichelaar, E. Zoethout, E. Louis, H. Enkisch, S. Muellender, and F. Bijkerk, “Interface roughness in Mo/Si multilayers,” Thin Solid Films 515(2), 434–438 (2006).
[CrossRef]

Other

H. Jiang, A. Michette, S. Pfauntsch, D. Hart and M. Shand, “Design of narrowband multilayer for Cr Kα X-rays,” in Proceedings of PIER (Xi’an, China, 2010), pp. 61–65.

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Figures (12)

Fig. 1
Fig. 1

Period thicknesses of the two samples and the fitted curves.

Fig. 2
Fig. 2

Evolution of layer thickness, time series fitting and forecast for sample 1.

Fig. 3
Fig. 3

Evolution of layer thickness, time series fitting and forecast for sample 2.

Fig. 4
Fig. 4

Cross sections of Cr/C multilayer near to the substrate (left) and the surface (right) for sample 1.

Fig. 5
Fig. 5

Average density profile and its 1st derivative curve (sample 1, layers 32-37); the four types of interdiffusion are expressed respectively in dense slash (V1), sparse slash (V2), dense grid (V3) and sparse grid (V4).

Fig. 6
Fig. 6

The interdiffusion evolution, time series fitting and forecast for sample 1.

Fig. 7
Fig. 7

Interdiffusion evolution, time series fitting and forecast for sample 2.

Fig. 8
Fig. 8

Comparison of interdiffusion and layer thicknesses for the two materials in the two samples.

Fig. 9
Fig. 9

Evolution of roughness for sample 1.

Fig. 10
Fig. 10

Evolution of roughness for sample 2.

Fig. 11
Fig. 11

AFM measurements of the surfaces of the two samples.

Fig. 12
Fig. 12

Hard X-ray reflectivity of sample 1 and fitted curve.

Tables (3)

Tables Icon

Table 1 Time Series Analysis for Evolution of Layer Thicknesses

Tables Icon

Table 2 Time Series Analysis for Interdiffusion Evolution

Tables Icon

Table 3 Comparison Between XRR Fitted, TEM Analysis and Design Target

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

d t d t 1 = φ 0 + i = 1 p φ i ( d t i d t i 1 ) + α t i = 1 q θ i α t i ,
σ α 2 = V a r [ ( d t + 1 d t ) φ 0 i = 1 p φ i ( d t + 1 i d t i ) ] 1 + i = 1 q θ i 2 .
α t = σ t ε t  and   σ t 2 = a 0 + i = 1 m a i α t i 2    .
ρ ( z ) = ρ bulk ( 1 1 π z e s 2 / 2 V 2 ds ) ,
Sample 1:  r Cr-on-C, t = 0.89 r C-on-Cr, t + 0.01 ,                   r C-on-Cr, t = 0.53 r Cr-on-C, t + 0.11. Sample 2:  r Cr-on-C, t = 0.87 r C-on-Cr, t + 0.02 ,                   r C-on-Cr, t = 0.69 r Cr-on-C, t + 0.08.

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