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Light-induced chemical vapour deposition painting with titanium dioxide
Applied Surface Science 208–209 (2003) 663–668
Light-induced chemical vapour deposition painting with titanium dioxide E. Halary-Wagner, T. Bret, P. Hoffmann* Institute of Imaging and Applied Optics, School of Engineering, Swiss Federal Institute of Technology Lausanne EPFL, CH-1015 Lausanne EPFL, Switzerland
Abstract Light-induced chemical vapour deposits of titanium dioxide are obtained from titanium tetra-isopropoxide (TTIP) in an oxygen and nitrogen atmosphere with a long pulse (250 ns) 308 nm XeCl excimer laser using a mask projection set-up. The demonstrated advantages of this technique are: (i) selective area deposition, (ii) precise control of the deposited thickness and (iii) low temperature deposition, enabling to use a wide range of substrates. A revolving mask system enables, in a single reactor load, to deposit shapes of controlled heights, which overlap to build up a complex pattern. Interferential multi-coloured deposits are achieved, and the process limitations (available colours and resolution) are discussed. # 2003 Elsevier Science B.V. All rights reserved. PACS: 81.15 (Fg,Gh); 81.05.Je; 42.62.-b; 82.80.Ch Keywords: Chemical vapor deposition; Excimer laser; Titanium dioxide; Decorative coatings
1. Introduction Decorative coloured coatings based on oxide materials have been produced, either by interferential selfcolouring [1] or by adding a dye [2]. Titanium dioxide is highly adapted for this application thanks to its specific properties, including chemical inertness, heat stability, hardness, low toxicity, self-cleaning under UV, high index of refraction and optical transparency in the visible range of the spectrum. Pulsed excimer laser-induced deposition of TiO2 from titanium tetraisopropoxide (TTIP) and oxygen exhibits several advantages: (i) the substrate temperature for deposition can be as low as room temperature [3–7], suggesting that a broad variety of thermo-fragile substrates can be *
Corresponding author. Tel.: þ41-216936018; fax: þ41-216933701. E-mail address: [email protected] (P. Hoffmann).
used; (ii) selective area deposition is achieved strictly in the irradiated area [8] and (iii) the deposited thickness is found to vary linearly with the number of laser pulses, allowing a very precise control [9]. In this work, we give evidence of these advantages and combine them to realize decorative coatings, consisting of complex multi-shape deposits with controlled interference colours on very different substrates.
2. Experiment The experimental set-up of our home made lightinduced chemical vapour deposition (LICVD) reactor was previously reported elsewhere [8]. Briefly, a long pulse (250 ns) XeCl excimer laser (Lambda Physik LPX 61oi, 308 nm) irradiates perpendicularly a substrate placed in a horizontal tubular CVD chamber on a temperature-controlled plate. TTIP (reservoir
0169-4332/03/$ – see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0169-4332(02)01421-6
664
E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
Table 1 Experimental conditions for deposition on different substrates Substrate
Si
Glass
PMMA
Polycarbonate
Substrate temperature (8C) Fluence (mJ cm2) Repetition rate (Hz) Number of pulses
60–210 50–400 1–20 200–5000
60–210 50–400 1–20 500–5000
60 10 5–10 2–5 104
60 10 5–10 2–5 104
temperature 30 8C) is brought in the chamber by an oxygen carrier gas flow (43 sccm) while nitrogen (150 sccm) is flushed onto the reactor window to prevent deposition on it. The total pressure in the chamber is kept at 10 mbar. The laser energy is measured by a pyro-electric detector (Newport) and regulated by an attenuator. A fused silica lens (focal length 18.9 cm) is used to project the image of a mask on the substrate with variable magnification (0.25– 1.2). In order to deposit multi-level patterns, a revolving mask system was developed. The mask was laser cut with a Nd:YAG in 300 mm thick stainless steel plates with 70 mm lateral resolution. It consists of several designed openings regularly distributed on an opaque disk. By rotating the mask around a fixed axis, the openings are sequentially placed, with precise angular control, in the beam path, so that their images superimpose. Shining Ni excimer laser pulses through each opening i results in a deposit with differently exposed areas. The substrates were glass microscope slides, silicon wafers, polycarbonate and
poly(methyl-methacrylate) (PMMA) plates. The process conditions (substrate temperature, laser fluence, number of pulses) were adapted to each case, and the successfully tested ranges are reported in Table 1. The deposited thicknesses were measured by profilometry (Tencor Alphastep 200 or Dektak). Diffuse reflectance spectra were acquired by UV-Vis reflectometry under 88 incident irradiation using an integration sphere (Perkin-Elmer Lambda 19). Indexes of refraction were measured by spectral ellipsometry. The images were obtained by optical microscopy (Zeiss, Axiotech Vario 25 HD) combined with a CCD camera.
3. Results and discussion 3.1. Control of colour with the thickness In our set up with fixed gas flow conditions, the deposited thickness e (in nm) was previously shown
Fig. 1. Example of precise control of the deposited thickness and corresponding deposit colours: 13 single deposits (optical microscope images above) of 2:5 2:5 mm2 were realized by varying the number of pulses (silicon substrate, T ¼ 110 8C, F ¼ 200 mJ cm2).
E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
665
Fig. 2. UV-Vis reflectivity spectra of the 13 samples from Fig. 1 as a function of the number of pulses. Local maxima li are highlighted (corresponding to the constructive interference for order i).
[9] to be described by Eq. (1): Ea e ¼ Nr0 F exp ¼ NrF;T RT
3.2. Revolving mask system: multi-level deposits, varying shapes and substrates (1)
where N is the number of pulses, F is the fluence (mJ cm2), Ea is the Arrhenius activation energy (Ea ¼ 21:3 kJ mol1), R is the gas constant, T is the substrate temperature and r0 is a constant (r0 0:1 (nm per pulse)/(mJ cm2)). By fixing the fluence and the substrate temperature (which both affect the physico-chemical properties of the deposits [7,9]), single deposits were realized by varying the number of pulses. The measured deposited thicknesses are shown in Fig. 1, as well as the resulting interference colours (which principle can be found in [10]). Reflectivity measurements are shown in Fig. 2: all spectra exhibit a peak l1 in the visible that red-shifts with increasing thickness. The high refractive index of the films (2.6 at 600 nm according to ellipsometry [9]) allows for high reflectivity, good colour contrast for small thickness differences and the coverage of all the colours of the visible spectrum with film thicknesses lower than 150 nm. Moreover, it can be calculated (in good agreement with the observation) that the colour change with incident light angle is weak. Based on the reflectivity measurements, colours were quantitatively assigned positions on the 2D chart from the CIE 1931 recommended as international standard of colourimetry [11] (see Fig. 3). Colours and saturations obtained appeared close to those of other decorative processes [12].
As an example of the complex shapes and lateral resolution of the multi-level patterns that can be achieved, a mask was designed to realize Sierpinski-like patterns [13] with seven generations of successively inscribed triangles, so that each generation reaches a given thickness, corresponding to a given colour. Individual deposits carried out through each opening of the mask as well as an example of the pattern obtained with successive superimposed irradiations through all the openings are presented in Fig. 4. Fig. 5 evidences the correspondence between the deposited thickness and the colour of such a pattern
Fig. 3. Correlation of the obtained colours of the 13 samples from Fig. 1 with the international standards of colourimetry (CIE 1931), obtained from the reflectivity spectra and tabulated reference values for 108 incident light [15].
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E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
Fig. 4. Left side: individual deposits through the different openings of the Sierpinski-like triangle mask (glass substrate, T ¼ 140 8C, F ¼ 250 mJ cm2, N ¼ 2000 pulses). These deposits are transparent; therefore, the optical microscope images are taken in reflection. The slight colour variation within each deposit is due to a non-optimised spatial homogeneity of the laser pulse intensity. Right side: Overlap pattern obtained (silicon substrate, T ¼ 140 8C, F ¼ 200 mJ cm2, N ¼ 1000 pulses for each opening). A good colour contrast is achieved for thicknesses below 80 nm.
Fig. 5. Comparison between an optical microscope image of a Sierpinski-like pattern and its 3D profile (limited to 60 mm lateral resolution) (glass substrate, T ¼ 140 8C, F ¼ 250 mJ cm2, N ¼ 2000 þ 500 pulses for each opening).
E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
667
Fig. 6. Example of edge definition achieved between different levels (silicon substrate, T ¼ 210 8C, F ¼ 200 mJ cm2, N ¼ 1000 þ 1000 pulses for each generation).
Fig. 8. Examples of deposits obtained on polymer substrate: (a) on polycarbonate; (b) on PMMA. The good transparency of the deposits in transmission is evidenced by the structure of the background placed beside the polymer sample.
comparing a 3D profile with the optical microscope image. Figs. 6 and 7 show details of other Sierpinski-like patterns, exhibiting edge resolution quality between different levels of the pattern with 10 mm radius of curvature (Fig. 6) and a zoom on the smallest triangle generation of 30 mm in diameter (Fig. 7). As already shown elsewhere [8], the resolution in our system is
limited by the optical set-up and could be improved by reducing the optical aberrations. Examples of deposits obtained on polymer substrates are shown in Fig. 8. For polymer substrates, low substrate temperature as well as low fluences (see Table 1) are needed in order to prevent polymer damage. Detailed characteristics of polymer deposition will be discussed elsewhere [14].
Fig. 7. Example of smallest triangle details achieved (glass substrate, T ¼ 210 8C, F ¼ 150 mJ cm2, N ¼ 1000 þ 500 pulses for each generation).
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E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
4. Conclusion and future developments The proposed process to realize coloured coatings is very flexible, and the possibility to realize, in a parallel exposure, high-resolution (around 1000 dpi) personalized patterns, stable in time and non-toxic is demonstrated over multi-square-millimeter area. Titanium dioxide is as an excellent material for this application, yielding bright interferential colours weakly depending on the observation angle. To improve the process, the mask could be replaced by a computer-controlled array of switchable holes, thus varying the pattern faster and more easily. Optimizing the wavelength and power of the light source may permit to overcome the high cost of UV-excimer laser photons, to increase the growth rates on polymers, and to illuminate wider areas. Such a process may eventually provide longterm paintings without the need for restorations. Acknowledgements The authors are very thankful to Dr. T. Sidler and C. Amendola (IOA, EPFL) for the mask laser cutting, to Dr. O. Banakh (LMSO, Ecole d’Inge´ nieurs de Neuchaˆ tel) for the spectral ellipsometric measurements, and to T. Lippert (PSI, Villigen) for access to a 3D
profilometer. This work was partially supported by the Swiss National Research Science Foundation.
References [1] R.L. van Renesse, Optical Document Security, second ed., Artech House, Boston, 1998. [2] S. Ja¨ ger, Thin Solid Films 286 (1996) 154. [3] K. Tokita, F. Okada, J. Appl. Phys. 80 (1996) 7073. [4] E. Halary, G. Benvenuti, F. Wagner, P. Hoffmann, Appl. Surf. Sci. 154/155 (2000) 146. [5] A. Watanabe, Y. Imai, Thin Solid Films 348 (1999) 63. [6] A. Watanabe, T. Tsuchiya, Y. Imai, Jpn. J. Appl. Phys. 39 (2000) 120. [7] A. Watanabe, T. Tsuchiya, Y. Imai, Thin Solid Films 406 (2002) 132. [8] E. Halary-Wagner, P. Lambelet, G. Benvenuti, P. Hoffmann, J. Phys. IV 11 (2001) Pr3–825. [9] E. Halary-Wagner, PhD thesis no. 2650, Swiss Federal Institute of Technology Lausanne, Switzerland, 2002. [10] E. Hecht, Physique, De Boek Universite´ , Paris, 2000. [11] J.R. Coaton, A.M. Marsden, Lamps and lighting, fourth ed., Arnold, London, 1997. [12] R.A. Bolomey, L.M. Greenstein, J. Paint Tech. 44 (1972) 39. [13] M.W. Sierpinski, C.R. Acad. Sci. (Fr.) 160 (1915) 302. [14] E. Halary-Wagner, F. Wagner, P. Hoffmann, EuroCVD 14 (2002), submitted for publication. [15] DIN 5033-1-DIN 55929, (Beuth, 2000), 9.
Light-induced chemical vapour deposition painting with titanium dioxide E. Halary-Wagner, T. Bret, P. Hoffmann* Institute of Imaging and Applied Optics, School of Engineering, Swiss Federal Institute of Technology Lausanne EPFL, CH-1015 Lausanne EPFL, Switzerland
Abstract Light-induced chemical vapour deposits of titanium dioxide are obtained from titanium tetra-isopropoxide (TTIP) in an oxygen and nitrogen atmosphere with a long pulse (250 ns) 308 nm XeCl excimer laser using a mask projection set-up. The demonstrated advantages of this technique are: (i) selective area deposition, (ii) precise control of the deposited thickness and (iii) low temperature deposition, enabling to use a wide range of substrates. A revolving mask system enables, in a single reactor load, to deposit shapes of controlled heights, which overlap to build up a complex pattern. Interferential multi-coloured deposits are achieved, and the process limitations (available colours and resolution) are discussed. # 2003 Elsevier Science B.V. All rights reserved. PACS: 81.15 (Fg,Gh); 81.05.Je; 42.62.-b; 82.80.Ch Keywords: Chemical vapor deposition; Excimer laser; Titanium dioxide; Decorative coatings
1. Introduction Decorative coloured coatings based on oxide materials have been produced, either by interferential selfcolouring [1] or by adding a dye [2]. Titanium dioxide is highly adapted for this application thanks to its specific properties, including chemical inertness, heat stability, hardness, low toxicity, self-cleaning under UV, high index of refraction and optical transparency in the visible range of the spectrum. Pulsed excimer laser-induced deposition of TiO2 from titanium tetraisopropoxide (TTIP) and oxygen exhibits several advantages: (i) the substrate temperature for deposition can be as low as room temperature [3–7], suggesting that a broad variety of thermo-fragile substrates can be *
Corresponding author. Tel.: þ41-216936018; fax: þ41-216933701. E-mail address: [email protected] (P. Hoffmann).
used; (ii) selective area deposition is achieved strictly in the irradiated area [8] and (iii) the deposited thickness is found to vary linearly with the number of laser pulses, allowing a very precise control [9]. In this work, we give evidence of these advantages and combine them to realize decorative coatings, consisting of complex multi-shape deposits with controlled interference colours on very different substrates.
2. Experiment The experimental set-up of our home made lightinduced chemical vapour deposition (LICVD) reactor was previously reported elsewhere [8]. Briefly, a long pulse (250 ns) XeCl excimer laser (Lambda Physik LPX 61oi, 308 nm) irradiates perpendicularly a substrate placed in a horizontal tubular CVD chamber on a temperature-controlled plate. TTIP (reservoir
0169-4332/03/$ – see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0169-4332(02)01421-6
664
E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
Table 1 Experimental conditions for deposition on different substrates Substrate
Si
Glass
PMMA
Polycarbonate
Substrate temperature (8C) Fluence (mJ cm2) Repetition rate (Hz) Number of pulses
60–210 50–400 1–20 200–5000
60–210 50–400 1–20 500–5000
60 10 5–10 2–5 104
60 10 5–10 2–5 104
temperature 30 8C) is brought in the chamber by an oxygen carrier gas flow (43 sccm) while nitrogen (150 sccm) is flushed onto the reactor window to prevent deposition on it. The total pressure in the chamber is kept at 10 mbar. The laser energy is measured by a pyro-electric detector (Newport) and regulated by an attenuator. A fused silica lens (focal length 18.9 cm) is used to project the image of a mask on the substrate with variable magnification (0.25– 1.2). In order to deposit multi-level patterns, a revolving mask system was developed. The mask was laser cut with a Nd:YAG in 300 mm thick stainless steel plates with 70 mm lateral resolution. It consists of several designed openings regularly distributed on an opaque disk. By rotating the mask around a fixed axis, the openings are sequentially placed, with precise angular control, in the beam path, so that their images superimpose. Shining Ni excimer laser pulses through each opening i results in a deposit with differently exposed areas. The substrates were glass microscope slides, silicon wafers, polycarbonate and
poly(methyl-methacrylate) (PMMA) plates. The process conditions (substrate temperature, laser fluence, number of pulses) were adapted to each case, and the successfully tested ranges are reported in Table 1. The deposited thicknesses were measured by profilometry (Tencor Alphastep 200 or Dektak). Diffuse reflectance spectra were acquired by UV-Vis reflectometry under 88 incident irradiation using an integration sphere (Perkin-Elmer Lambda 19). Indexes of refraction were measured by spectral ellipsometry. The images were obtained by optical microscopy (Zeiss, Axiotech Vario 25 HD) combined with a CCD camera.
3. Results and discussion 3.1. Control of colour with the thickness In our set up with fixed gas flow conditions, the deposited thickness e (in nm) was previously shown
Fig. 1. Example of precise control of the deposited thickness and corresponding deposit colours: 13 single deposits (optical microscope images above) of 2:5 2:5 mm2 were realized by varying the number of pulses (silicon substrate, T ¼ 110 8C, F ¼ 200 mJ cm2).
E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
665
Fig. 2. UV-Vis reflectivity spectra of the 13 samples from Fig. 1 as a function of the number of pulses. Local maxima li are highlighted (corresponding to the constructive interference for order i).
[9] to be described by Eq. (1): Ea e ¼ Nr0 F exp ¼ NrF;T RT
3.2. Revolving mask system: multi-level deposits, varying shapes and substrates (1)
where N is the number of pulses, F is the fluence (mJ cm2), Ea is the Arrhenius activation energy (Ea ¼ 21:3 kJ mol1), R is the gas constant, T is the substrate temperature and r0 is a constant (r0 0:1 (nm per pulse)/(mJ cm2)). By fixing the fluence and the substrate temperature (which both affect the physico-chemical properties of the deposits [7,9]), single deposits were realized by varying the number of pulses. The measured deposited thicknesses are shown in Fig. 1, as well as the resulting interference colours (which principle can be found in [10]). Reflectivity measurements are shown in Fig. 2: all spectra exhibit a peak l1 in the visible that red-shifts with increasing thickness. The high refractive index of the films (2.6 at 600 nm according to ellipsometry [9]) allows for high reflectivity, good colour contrast for small thickness differences and the coverage of all the colours of the visible spectrum with film thicknesses lower than 150 nm. Moreover, it can be calculated (in good agreement with the observation) that the colour change with incident light angle is weak. Based on the reflectivity measurements, colours were quantitatively assigned positions on the 2D chart from the CIE 1931 recommended as international standard of colourimetry [11] (see Fig. 3). Colours and saturations obtained appeared close to those of other decorative processes [12].
As an example of the complex shapes and lateral resolution of the multi-level patterns that can be achieved, a mask was designed to realize Sierpinski-like patterns [13] with seven generations of successively inscribed triangles, so that each generation reaches a given thickness, corresponding to a given colour. Individual deposits carried out through each opening of the mask as well as an example of the pattern obtained with successive superimposed irradiations through all the openings are presented in Fig. 4. Fig. 5 evidences the correspondence between the deposited thickness and the colour of such a pattern
Fig. 3. Correlation of the obtained colours of the 13 samples from Fig. 1 with the international standards of colourimetry (CIE 1931), obtained from the reflectivity spectra and tabulated reference values for 108 incident light [15].
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E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
Fig. 4. Left side: individual deposits through the different openings of the Sierpinski-like triangle mask (glass substrate, T ¼ 140 8C, F ¼ 250 mJ cm2, N ¼ 2000 pulses). These deposits are transparent; therefore, the optical microscope images are taken in reflection. The slight colour variation within each deposit is due to a non-optimised spatial homogeneity of the laser pulse intensity. Right side: Overlap pattern obtained (silicon substrate, T ¼ 140 8C, F ¼ 200 mJ cm2, N ¼ 1000 pulses for each opening). A good colour contrast is achieved for thicknesses below 80 nm.
Fig. 5. Comparison between an optical microscope image of a Sierpinski-like pattern and its 3D profile (limited to 60 mm lateral resolution) (glass substrate, T ¼ 140 8C, F ¼ 250 mJ cm2, N ¼ 2000 þ 500 pulses for each opening).
E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
667
Fig. 6. Example of edge definition achieved between different levels (silicon substrate, T ¼ 210 8C, F ¼ 200 mJ cm2, N ¼ 1000 þ 1000 pulses for each generation).
Fig. 8. Examples of deposits obtained on polymer substrate: (a) on polycarbonate; (b) on PMMA. The good transparency of the deposits in transmission is evidenced by the structure of the background placed beside the polymer sample.
comparing a 3D profile with the optical microscope image. Figs. 6 and 7 show details of other Sierpinski-like patterns, exhibiting edge resolution quality between different levels of the pattern with 10 mm radius of curvature (Fig. 6) and a zoom on the smallest triangle generation of 30 mm in diameter (Fig. 7). As already shown elsewhere [8], the resolution in our system is
limited by the optical set-up and could be improved by reducing the optical aberrations. Examples of deposits obtained on polymer substrates are shown in Fig. 8. For polymer substrates, low substrate temperature as well as low fluences (see Table 1) are needed in order to prevent polymer damage. Detailed characteristics of polymer deposition will be discussed elsewhere [14].
Fig. 7. Example of smallest triangle details achieved (glass substrate, T ¼ 210 8C, F ¼ 150 mJ cm2, N ¼ 1000 þ 500 pulses for each generation).
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E. Halary-Wagner et al. / Applied Surface Science 208–209 (2003) 663–668
4. Conclusion and future developments The proposed process to realize coloured coatings is very flexible, and the possibility to realize, in a parallel exposure, high-resolution (around 1000 dpi) personalized patterns, stable in time and non-toxic is demonstrated over multi-square-millimeter area. Titanium dioxide is as an excellent material for this application, yielding bright interferential colours weakly depending on the observation angle. To improve the process, the mask could be replaced by a computer-controlled array of switchable holes, thus varying the pattern faster and more easily. Optimizing the wavelength and power of the light source may permit to overcome the high cost of UV-excimer laser photons, to increase the growth rates on polymers, and to illuminate wider areas. Such a process may eventually provide longterm paintings without the need for restorations. Acknowledgements The authors are very thankful to Dr. T. Sidler and C. Amendola (IOA, EPFL) for the mask laser cutting, to Dr. O. Banakh (LMSO, Ecole d’Inge´ nieurs de Neuchaˆ tel) for the spectral ellipsometric measurements, and to T. Lippert (PSI, Villigen) for access to a 3D
profilometer. This work was partially supported by the Swiss National Research Science Foundation.
References [1] R.L. van Renesse, Optical Document Security, second ed., Artech House, Boston, 1998. [2] S. Ja¨ ger, Thin Solid Films 286 (1996) 154. [3] K. Tokita, F. Okada, J. Appl. Phys. 80 (1996) 7073. [4] E. Halary, G. Benvenuti, F. Wagner, P. Hoffmann, Appl. Surf. Sci. 154/155 (2000) 146. [5] A. Watanabe, Y. Imai, Thin Solid Films 348 (1999) 63. [6] A. Watanabe, T. Tsuchiya, Y. Imai, Jpn. J. Appl. Phys. 39 (2000) 120. [7] A. Watanabe, T. Tsuchiya, Y. Imai, Thin Solid Films 406 (2002) 132. [8] E. Halary-Wagner, P. Lambelet, G. Benvenuti, P. Hoffmann, J. Phys. IV 11 (2001) Pr3–825. [9] E. Halary-Wagner, PhD thesis no. 2650, Swiss Federal Institute of Technology Lausanne, Switzerland, 2002. [10] E. Hecht, Physique, De Boek Universite´ , Paris, 2000. [11] J.R. Coaton, A.M. Marsden, Lamps and lighting, fourth ed., Arnold, London, 1997. [12] R.A. Bolomey, L.M. Greenstein, J. Paint Tech. 44 (1972) 39. [13] M.W. Sierpinski, C.R. Acad. Sci. (Fr.) 160 (1915) 302. [14] E. Halary-Wagner, F. Wagner, P. Hoffmann, EuroCVD 14 (2002), submitted for publication. [15] DIN 5033-1-DIN 55929, (Beuth, 2000), 9.