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Laser diagnostics of C60 and C70 films by broadband surface acoustic wave spectroscopy
applied surface science ELSEVIER
Applied Surface Science 86 (1995) 591-596
Laser diagnostics of C60 and C70 films by broadband surface acoustic wave spectroscopy A.A. Kolomenskii 1, M. Szabadi, P. Hess * bzstitute of Physical Chemis#y, University of Heidelberg, D-69120 Heidelberg, Germany Received 27 May i994; accepted for publication 20 September 1994
Abstract A novel method is used for the determination of mechanical and elastic properties of thin films such as film thickness, density, Young's modulus, and Poisson's ratio. In this technique short laser pulses (nanosecond to picosecond) are used to excite a surface acoustic wave (SAW) pulse and laser probe beam deflection or a piezoelectric foil detector are employed for time-resolved detection of the resulting surface displacements. Fourier transformation of the oscillatory signals detected at distances of several millimeters to centimeters yields the dispersion of the phase velocity, which can be used for the accurate determination of film properties. Fullerite films (C6o and C7o) with thicknesses of 0.7-2.1 /~m on silicon and quartz-glass substrates were investigated. The nonlinear dispersion curves were obtained experimentally with a maximum value of the product of film thickness and SAW wave number of Ymax= 0.32 for the C60 films and %nax= 0.18 for the C7O films. The frequency bandwidth was limited by the attenuation of the surface acoustic waves in the fullerite films. The film parameters were evaluated by fitting the measured dispersion curve to a theoretical model. For the C60 films a density of 1.67 + 0.02 g/cm 3, Young's modulus of 10_+ 2 GPa, and Poisson's ratio of 0.25 _+0.08 were found. For the C70 films the corresponding values were 1.64 + 0.02 g/cm 3, 4 + 1 GPa, and 0.35 + 0.1.
1. Introduction Mechanical and elastic properties of films are important characteristics of materials which may be used for the investigation of their microscopic structure and the evaluation of their quality. They reflect the purity, bonding configuration and homogeneity of the film. Properties of very thin films may be different from those of bulk materials. Surface acoustic waves (SAWs) are an efficient
* Corresponding author. Fax: +49 6221 564255. IOn leave from General Physics Institute, Moscow 117942, Russian Federation.
tool for evaluating elastic and mechanical properties of thin films. SAW pulses propagate along the surface to be investigated and experience a measurable influence exerted by a film as thin as one-hundredth to one-thousandth of their wavelength. Several film parameters influence the propagation of SAWs. For their determination, measurements in a large frequency range are necessary. In broadband SAW spectroscopy of heterogeneous systems [1-4] a SAW pulse ('broadband wave packet') is excited by a short laser pulse. The technique is noncontact when optical means for excitation and detection of the SAW pulses are employed and is applicable for a wide range of materials. The broadband registration of SAW pulses has also been
0169-4332/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 01 69-4332(94)00383-1
592
A~A. Kolomenskii et aL /Applied Surface Science 86 (1995) 591-596
demonstrated with a PVDF transducer contacting the surface along a narrow edge [5]. We demonstrate the possibilities of this technique by applying it to fullerite films. The fullerites are a new class of solid carbon material consisting of fullerene molecules such as C6o or C70. After the synthesis of C60 single crystals had been demonst-rated [6] first studies of the physical properties [7] of these van der Waals solids revealed unusual transitions in their microstructure. The mechanical and elastic properties of fullerite films are still not known very well.
2. Experimental
2.1. Experimental setup The bandwidth of the excited SAW pulse depends on the degree of space-time localization of the interaction of laser light with the solid. The amplitude of the excited SAW pulse is determined by the density and the rate of energy deposition by laser radiation. For efficient excitation of broadband SAW pulses it is therefore necessary to use short and well focused laser pulses with a wavelength corresponding to a high optical absorption coefficient in the investigated material. The SAW pulses were excited by a pulsed nanosecond or picosecond Nd:YAG laser operating in the third harmonic at 355 rim. The pulse durations and maximum pulse energies were 8 ns, 35 mJ and 180 ps, 25 mJ, respectively. After expansion and appropriate reduction of the pulse energy the laser radiation was focused onto the sample in a strip with dimensions 7/zm × 10 mm using a system of three cylindrical lenses. The focus line could be scanned along the sample surface with an accuracy of better than 1 /zm to probe at different distances from the
foil detector with an edge curvature of 5 /xm possessed a higher sensitivity than the optical detection scheme (the minimal measurable surface displacement was about 0.5 ~,) and allowed ringing-free measurements to be carried out up to 300 MHz [5]. The detected signal was preamplified, stored and averaged by a digital storage oscilloscope (Tektronix TDS 540) with an analog bandwidth of 500 MHz and a sampling rate of 1 Gigasamples/s triggered by a fast UV-photodiode. To obtain a dispersion curve of good quality several hundred to several thousand acoustic pulses were averaged in the time domain. To avoid distortions by bulk acoustic modes and to increase the signal/noise ratio the SAW pulse was recorded in a time gate. The phase and the amplitude of a spectral component of the SAW pulse were determined as functions of frequency by performing a fast Fourier transformation. By using these functions for a pair'of SAW pulses measured at two different distances separated by 4-11 mm the dispersion curve and the attenuation were evaluated.
2.2. bwestigated samples The fullerite films were deposited on the (111) plane of a silicon crystal or quartz-glass substrate using high purity C6o (99.9%) or C70 (99.4%) materials in a thermal evaporator at deposition rates of 3-10 nm/min. On the quartz substrates the films had a thickness of 995 _ 10 nm (C~0) and 665 4- 5 nm (Cv0). On the silicon substrates the thicknesses were 2110 + 20 nm (C60) and 950 + 10 nm (C70) as measured with a profilometer and evaluated more precisely with the SAW technique. All the measurements were performed at room temperature and atmospheric pressure.
2.3. Laser excitation of SA W pulses
source.
The excited SAW pulses propagated along a distance between 14 and 25 mm from the source and were recorded by one of the detection methods. The probe beam deflection scheme enabled measurements of a surface inclination of 5 × 10-6 tad, corresponding to a minimal measurable surface displacement of about 2 A for a single pulse in the frequency range of maximum sensitivity around 250 M I - . The
At moderate laser radiation intensities a linear thermoelastic excitation mechanism takes place. With increasing intensity and average heating the generation mechanism may become nonlinear due to the temperature dependence of the thermoelastic parameters. For the films on quartz substrates with SAW pulse excitation in the thermoelastic regime and recording of the acoustic signal by the foil detector a
A.A. Kolomenskii et al. /Applied Surface Science 86 (1995) 591-596
nonlinear increase of the amplitude and the frequency bandwidth of the SAW pulse was observed at a surface energy densities of about 0.015 J / c m 2. When the laser intensity is larger than some definite value, which depends on the material and laser pulse duration, ablation of the surface occurs and new mechanisms connected with the recoil momentum of ablated species or optical breakdown become predominant in SAW generation. For C60 and C70 films the surface ablation started at a surface energy density of 0.01-0.02 J / c m 2. At surface energy density of about 2 J / c m 2 the ablation mechanism was used for the investigation of the samples on silicon substrates, since in this case efficient generation of SAW in this substrate was possible. SAW pulses excited by the ablation mechanism were detected by probe beam deflection. The ablation mechanism provides a higher efficiency of photoacoustic transformation, however, when it is necessary to avoid damage of the sample (non-destructive testing) this mechanism is not applicable and the thermoelastic regime of SAW excitation must be used.
2.4. Determination of film properties from the dispersion of SAWs Each spectral component in the broadband surface acoustic wave pulse has a different penetration depth into the solid, which is determined approximately by the corresponding acoustic wavelength. Therefore, for a layered system consisting of a film on a substrate, the high frequency components, having shorter wavelengths and concentrating more in the film, propagate slower or faster than the low frequency components, which penetrate deeper into the substrate. The resulting dispersion effect depends on the relationships between the mechanical and elastic properties of the film and the substrate. For a given frequency value f and a given combination of the film and substrate properties the phase velocity of the corresponding spectral component depends on the dimensionless product y = kh of the wave number k = 2~rf/v(f) (v(f) being the SAW phase velocity) and the film thickness h. The case in which the phase velocity decreases with increasing frequency (v(y ~ O) > v(y ~ ~)) corresponds to a 'softer film material' or 'loading' of the substrate
593
(normal dispersion). The opposite situation, i.e. when the phase velocity increases with increasing frequency (v(y ~ 0) < v(y ~ ~)), is referred to as the case of a 'harder film material' or 'stiffening' of the substrate (anomalous dispersion). The dispersion curves were described theoretically by the exact solution of the wave equations taking into account the boundary conditions at the free film surface and the substrate-film interface [8]. This model was developed for anisotropic substrates (silicon) and for an isotropic substrate (quartz-glass). For the films on the quartz-glass substrate a comparison with the approximate model [9] valid only for small values of the parameter Y was performed. The parameters for the best fit represent the solution of the inverse problem for determination of the film properties. Let fm~x be the maximum frequency in the signal spectrum with a signal/noise ratio sufficient for the measurement and kma x be the corresponding wave number. Then the capability for the determination of film properties depends on the value achieved for the parameter Ymax-- kmax h. If in the experiment a value of Ymax< 0.1 is obtained, usually the determination of only one film parameter is possible. For larger values of Ymax tWO or even three film parameters may be determined.
3. Results and discussion
In Fig. 1 the measured dispersion curves and the calculated best fits for two fullerite films are shown which were determined in the [112] direction of the (111)-plane of a Si single crystal substrate. Note that in these measurements the frequency range of the dispersion curves was limited not by the frequency bandwidth of the experimental setup but by the beginning of strong SAW attenuation. The attenuation was caused by the film and therefore increased with film thickness. For a C70 film (950 nm) a value Ymax= 0.18 was achieved and the attenuation was found to be approximately the same as for a much thicker C60 film (2110 nm, Yma×= 0.28). This means that in the C70 material the attenuation is stronger than in the C60 material. Measurements were also performed for the [110] direction of Si(111). Since the characteristics of SAW
594
A.A. Kotomenskii et aL/Applied Surface Science 86 (1995) 591-596 4800
f
t
fullerite/ Si(111 ) E
4700
'5 O
4600 C GO ~ x ......... 4500
4400
0
50 100 Frequency (MHz)
150
Fig. 1. Measured SAW dispersion curves (fat lines formed by superimposed squares) and calculated best fits (thin solid lines) for fullerite films on the (111)-plane of Si substrates corresponding to the [112]-direction: C6o film (2110 nm), C70 film (950 nm).
pulses propagating in this direction are different from those of the [112] direction, the dispersion curves had a somewhat different shape. Therefore these measurements provided additional information for the evaluation of film parameters. In Fig. 2 the dispersion curves for two fullerite films on quartz-glass substrates are presented. The calculated best fits for the dispersion curves are also plotted. The values of the parameter 7m~x were 0.32
3 4 0 0 ~ - - - - ~ fullerite/qua r t z - ,
!
~
!
'
i
._-, 3 3 0 0 - -
:
3zoo
3100
0
, ', ! 50 100 150 Frequency (MHz)
200
Fig. 2. Measured SAW dispersion curves (squares) and calculated best fits (thin solid lines) for fullerite films on quartz-glass substrates: C6o film (995 rim), C7o film (665 rim).
and 0.18 for the C6o (995 nm) and C7o (665 nm) films, respectively. For the excitation of SAW pulses in the sample with the C~ film the picosecond-laser was used, which allowed a somewhat higher frequency range to be reached. All other experiments were performed with nanosecond laser pulses. The low-frequency limit of the measured dispersion curves of about 10-20 MItz was determined by the influence of the bulk shear acoustic signal and diffraction as well as by the lower sensitivity of the detection equipment in the low-frequency domain. All dispersion curves obtained for fullerite films correspond to the case of normal dispersion as expected for soft materials held together by van der Waals forces. To evaluate the film properties the following procedure was used. The measured dispersion curve was shifted to fit the low-frequency limit of SAW propagation equal to the well known value for the SAW velocity in the substrate. Usually this offset correction was less than +3 m/s. Then, using the film thickness measured with the profilometer, other film parameters were varied in sufficiently wide intervals, and for every set of parameters a mean square deviation of the theoretical and experimental dispersion curves was calculated. The set of parameters with minimum deviation provided the best estimate of the film properties. Using this set of parameters the thickness of the film was evaluated more precisely and then other parameters were also corrected with a modified Levenberg-Marquardt algorithm. This procedure was repeated several times and the parameters obtained were checked by starting at different values. The described procedure was proved by test measurements with metal films and demonstrated convergence in the vicinity of the actual set of the film properties. A comparison of the results obtained for films on quartz-glass substrates with the exact model [8] and with the approximate model [9] has shown that even for a relatively small value of %,× = 0.18 (C~0 fiim) the approximate model provides values of Poisson's ratio which are about 30% lower, while the other properties are approximately the same. For the film with %~x -- 0.32 (C60 film) the value of the density obtained with the approximate model was about 2% lower and that of Young's modulus about 20% lower. Thus, for precise evaluation of the film parameters
AA. Kolomenskii et al. /Applied Surface Science 86 (1995) 591-596
595
Table 1 Parameters of fullerite films Film material
Density (g/cm 3)
Young's modulus
Poisson's ratio
(GPa) C60
C70
1.67 _+ 0.02 1.64 4- 0.02
10 4- 2 4 4- 1
0.25 + 0.08 0.35 4- 0.1
even for small values of ')'max~ 0.1 to 0.3 the exact model should be used. The evaluated properties of the investigated fullerite films are presented in Table 1. In the present experiments sufficiently large values of the parameter 3'max could be achieved, and therefore the determination of the density, and the less accurate evaluation of Young's modulus and Poisson's ratio was possible. In addition the longitudinal and transverse sound velocities were calculated from the experimental data as presented in Table 1. The uncertainty in the determination of the film thickness (which also includes the variation of the thickness due to film inhomogeneity) introduces the main error in the evaluation of the film density. The resulting scatter of the best fit values of the film properties obtained for different films and measurements determines the main error in the evaluation of Young's modulus and Poisson's ratio. It should be noted however, that the measurements performed with a sufficiently homogeneous film provide much smaller errors for Young's modulus and Poisson's ratio than those indicated in Table 1. Thus, for the determination of these parameters the described method potentially processes a higher accuracy of about a few percent. The obtained values of the C60 film properties are somewhat different but consistent with the results of previous measurements [10]. The data show that Young's modulus for the C60 films is lower than that for a C60 single crystal (15.9 GPa) [7]. This may be connected with the amorphous microstructure of the film. For C70 films Young's modulus and the density were found to be lower than the values obtained for C6o films. This is in agreement with the results of calculations [11] showing that the most stable pack-
Longitudinal sound velocity
Transverse sound velocity
(kin/s)
(kin/s)
2.7 _+0.3 2.0 4- 0.4
1.5 _+0.2 1.0 4- 0.2
ing of the fullerene molecules in a C70 crystal has a lower density than that for a C60 crystal.
4. Conclusion In this work broadband surface acoustic wave spectroscopy for the determination of mechanical and elastic properties of thin films is described. With this technique fullerite films (C60, C70) were investigated. The density, Young',s modulus and Poisson's ratio of these carbon films have been evaluated for the first time with this method.
Acknowledgements One of the authors (A.A.K.) would like to thank the Humboldt Foundation for a fellowship. Financial support of this work by the Bundesministerium fiir Forschung und Technologie under contract No. 13N6005 5 and the Fonds der Chemischen Industrie is gratefully acknowledged.
References [1] L. Konstantinov, A. Neubrand and P. Hess, in: Topics in Current Physics, VoI. 47, Ed. P. Hess (Springer, Berlin, 1989) p. 273. [2] M. Lorenz, J.A. Vogel, A.J.A. Bruinsma and A.J. Berkhout, Nondestr. Test. Eval. 5 (1990) 187. [3] A. Neubrand, L. Konstantinov and P. Hess, in: Physical Acoustics, Eds. O. Leroy and M.A. Breazeale (Plenum, New York, 1991) p. 55I. [4] A. Neubrand and P. Hess, J. Appl. Phys. 71 (1992) 227. [5] H. Coufal, R. Grygier, P. Hess and A. Neubrand, J. Acoust. Soc. Am. 92 (1992) 2980.
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A~A. Kolomenskii et al. /Applied Surface Science 86 (1995) 591-596
[6] W. K.r~tschmer, L.D. Lamb, Y,L Fostiropoulos and D. Huffman, Nature 347 (t990) 354. [7] X.D. Shi, A.R. Kortan, J.M. Williams, A.M. Kini, B.M. Savall and P.M. Chaikin, Phys. Rev. Lett. 68 (1992) 827. [8] G.W. Parnell and E.L. Adler, in: Physical Acoustics, Vol. 9, Eds. W.P. Mason and R.N. Thurston (Academic Press, New York, 1972) p. 35.
[9] H.F. Tiersten, J. Appl. Phys. 40 (1969) 770. [10] H. Coufal, K. Meyer, R.K. Orygier, M. de Vfies, D. Jertrich and P. Hess, Appl. Phys. A 59 (1994) 83. [11] Y. Cuo, N. Karasawa and W.A. Goddard III, Nature 351 (1991) 464.
Applied Surface Science 86 (1995) 591-596
Laser diagnostics of C60 and C70 films by broadband surface acoustic wave spectroscopy A.A. Kolomenskii 1, M. Szabadi, P. Hess * bzstitute of Physical Chemis#y, University of Heidelberg, D-69120 Heidelberg, Germany Received 27 May i994; accepted for publication 20 September 1994
Abstract A novel method is used for the determination of mechanical and elastic properties of thin films such as film thickness, density, Young's modulus, and Poisson's ratio. In this technique short laser pulses (nanosecond to picosecond) are used to excite a surface acoustic wave (SAW) pulse and laser probe beam deflection or a piezoelectric foil detector are employed for time-resolved detection of the resulting surface displacements. Fourier transformation of the oscillatory signals detected at distances of several millimeters to centimeters yields the dispersion of the phase velocity, which can be used for the accurate determination of film properties. Fullerite films (C6o and C7o) with thicknesses of 0.7-2.1 /~m on silicon and quartz-glass substrates were investigated. The nonlinear dispersion curves were obtained experimentally with a maximum value of the product of film thickness and SAW wave number of Ymax= 0.32 for the C60 films and %nax= 0.18 for the C7O films. The frequency bandwidth was limited by the attenuation of the surface acoustic waves in the fullerite films. The film parameters were evaluated by fitting the measured dispersion curve to a theoretical model. For the C60 films a density of 1.67 + 0.02 g/cm 3, Young's modulus of 10_+ 2 GPa, and Poisson's ratio of 0.25 _+0.08 were found. For the C70 films the corresponding values were 1.64 + 0.02 g/cm 3, 4 + 1 GPa, and 0.35 + 0.1.
1. Introduction Mechanical and elastic properties of films are important characteristics of materials which may be used for the investigation of their microscopic structure and the evaluation of their quality. They reflect the purity, bonding configuration and homogeneity of the film. Properties of very thin films may be different from those of bulk materials. Surface acoustic waves (SAWs) are an efficient
* Corresponding author. Fax: +49 6221 564255. IOn leave from General Physics Institute, Moscow 117942, Russian Federation.
tool for evaluating elastic and mechanical properties of thin films. SAW pulses propagate along the surface to be investigated and experience a measurable influence exerted by a film as thin as one-hundredth to one-thousandth of their wavelength. Several film parameters influence the propagation of SAWs. For their determination, measurements in a large frequency range are necessary. In broadband SAW spectroscopy of heterogeneous systems [1-4] a SAW pulse ('broadband wave packet') is excited by a short laser pulse. The technique is noncontact when optical means for excitation and detection of the SAW pulses are employed and is applicable for a wide range of materials. The broadband registration of SAW pulses has also been
0169-4332/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 01 69-4332(94)00383-1
592
A~A. Kolomenskii et aL /Applied Surface Science 86 (1995) 591-596
demonstrated with a PVDF transducer contacting the surface along a narrow edge [5]. We demonstrate the possibilities of this technique by applying it to fullerite films. The fullerites are a new class of solid carbon material consisting of fullerene molecules such as C6o or C70. After the synthesis of C60 single crystals had been demonst-rated [6] first studies of the physical properties [7] of these van der Waals solids revealed unusual transitions in their microstructure. The mechanical and elastic properties of fullerite films are still not known very well.
2. Experimental
2.1. Experimental setup The bandwidth of the excited SAW pulse depends on the degree of space-time localization of the interaction of laser light with the solid. The amplitude of the excited SAW pulse is determined by the density and the rate of energy deposition by laser radiation. For efficient excitation of broadband SAW pulses it is therefore necessary to use short and well focused laser pulses with a wavelength corresponding to a high optical absorption coefficient in the investigated material. The SAW pulses were excited by a pulsed nanosecond or picosecond Nd:YAG laser operating in the third harmonic at 355 rim. The pulse durations and maximum pulse energies were 8 ns, 35 mJ and 180 ps, 25 mJ, respectively. After expansion and appropriate reduction of the pulse energy the laser radiation was focused onto the sample in a strip with dimensions 7/zm × 10 mm using a system of three cylindrical lenses. The focus line could be scanned along the sample surface with an accuracy of better than 1 /zm to probe at different distances from the
foil detector with an edge curvature of 5 /xm possessed a higher sensitivity than the optical detection scheme (the minimal measurable surface displacement was about 0.5 ~,) and allowed ringing-free measurements to be carried out up to 300 MHz [5]. The detected signal was preamplified, stored and averaged by a digital storage oscilloscope (Tektronix TDS 540) with an analog bandwidth of 500 MHz and a sampling rate of 1 Gigasamples/s triggered by a fast UV-photodiode. To obtain a dispersion curve of good quality several hundred to several thousand acoustic pulses were averaged in the time domain. To avoid distortions by bulk acoustic modes and to increase the signal/noise ratio the SAW pulse was recorded in a time gate. The phase and the amplitude of a spectral component of the SAW pulse were determined as functions of frequency by performing a fast Fourier transformation. By using these functions for a pair'of SAW pulses measured at two different distances separated by 4-11 mm the dispersion curve and the attenuation were evaluated.
2.2. bwestigated samples The fullerite films were deposited on the (111) plane of a silicon crystal or quartz-glass substrate using high purity C6o (99.9%) or C70 (99.4%) materials in a thermal evaporator at deposition rates of 3-10 nm/min. On the quartz substrates the films had a thickness of 995 _ 10 nm (C~0) and 665 4- 5 nm (Cv0). On the silicon substrates the thicknesses were 2110 + 20 nm (C60) and 950 + 10 nm (C70) as measured with a profilometer and evaluated more precisely with the SAW technique. All the measurements were performed at room temperature and atmospheric pressure.
2.3. Laser excitation of SA W pulses
source.
The excited SAW pulses propagated along a distance between 14 and 25 mm from the source and were recorded by one of the detection methods. The probe beam deflection scheme enabled measurements of a surface inclination of 5 × 10-6 tad, corresponding to a minimal measurable surface displacement of about 2 A for a single pulse in the frequency range of maximum sensitivity around 250 M I - . The
At moderate laser radiation intensities a linear thermoelastic excitation mechanism takes place. With increasing intensity and average heating the generation mechanism may become nonlinear due to the temperature dependence of the thermoelastic parameters. For the films on quartz substrates with SAW pulse excitation in the thermoelastic regime and recording of the acoustic signal by the foil detector a
A.A. Kolomenskii et al. /Applied Surface Science 86 (1995) 591-596
nonlinear increase of the amplitude and the frequency bandwidth of the SAW pulse was observed at a surface energy densities of about 0.015 J / c m 2. When the laser intensity is larger than some definite value, which depends on the material and laser pulse duration, ablation of the surface occurs and new mechanisms connected with the recoil momentum of ablated species or optical breakdown become predominant in SAW generation. For C60 and C70 films the surface ablation started at a surface energy density of 0.01-0.02 J / c m 2. At surface energy density of about 2 J / c m 2 the ablation mechanism was used for the investigation of the samples on silicon substrates, since in this case efficient generation of SAW in this substrate was possible. SAW pulses excited by the ablation mechanism were detected by probe beam deflection. The ablation mechanism provides a higher efficiency of photoacoustic transformation, however, when it is necessary to avoid damage of the sample (non-destructive testing) this mechanism is not applicable and the thermoelastic regime of SAW excitation must be used.
2.4. Determination of film properties from the dispersion of SAWs Each spectral component in the broadband surface acoustic wave pulse has a different penetration depth into the solid, which is determined approximately by the corresponding acoustic wavelength. Therefore, for a layered system consisting of a film on a substrate, the high frequency components, having shorter wavelengths and concentrating more in the film, propagate slower or faster than the low frequency components, which penetrate deeper into the substrate. The resulting dispersion effect depends on the relationships between the mechanical and elastic properties of the film and the substrate. For a given frequency value f and a given combination of the film and substrate properties the phase velocity of the corresponding spectral component depends on the dimensionless product y = kh of the wave number k = 2~rf/v(f) (v(f) being the SAW phase velocity) and the film thickness h. The case in which the phase velocity decreases with increasing frequency (v(y ~ O) > v(y ~ ~)) corresponds to a 'softer film material' or 'loading' of the substrate
593
(normal dispersion). The opposite situation, i.e. when the phase velocity increases with increasing frequency (v(y ~ 0) < v(y ~ ~)), is referred to as the case of a 'harder film material' or 'stiffening' of the substrate (anomalous dispersion). The dispersion curves were described theoretically by the exact solution of the wave equations taking into account the boundary conditions at the free film surface and the substrate-film interface [8]. This model was developed for anisotropic substrates (silicon) and for an isotropic substrate (quartz-glass). For the films on the quartz-glass substrate a comparison with the approximate model [9] valid only for small values of the parameter Y was performed. The parameters for the best fit represent the solution of the inverse problem for determination of the film properties. Let fm~x be the maximum frequency in the signal spectrum with a signal/noise ratio sufficient for the measurement and kma x be the corresponding wave number. Then the capability for the determination of film properties depends on the value achieved for the parameter Ymax-- kmax h. If in the experiment a value of Ymax< 0.1 is obtained, usually the determination of only one film parameter is possible. For larger values of Ymax tWO or even three film parameters may be determined.
3. Results and discussion
In Fig. 1 the measured dispersion curves and the calculated best fits for two fullerite films are shown which were determined in the [112] direction of the (111)-plane of a Si single crystal substrate. Note that in these measurements the frequency range of the dispersion curves was limited not by the frequency bandwidth of the experimental setup but by the beginning of strong SAW attenuation. The attenuation was caused by the film and therefore increased with film thickness. For a C70 film (950 nm) a value Ymax= 0.18 was achieved and the attenuation was found to be approximately the same as for a much thicker C60 film (2110 nm, Yma×= 0.28). This means that in the C70 material the attenuation is stronger than in the C60 material. Measurements were also performed for the [110] direction of Si(111). Since the characteristics of SAW
594
A.A. Kotomenskii et aL/Applied Surface Science 86 (1995) 591-596 4800
f
t
fullerite/ Si(111 ) E
4700
'5 O
4600 C GO ~ x ......... 4500
4400
0
50 100 Frequency (MHz)
150
Fig. 1. Measured SAW dispersion curves (fat lines formed by superimposed squares) and calculated best fits (thin solid lines) for fullerite films on the (111)-plane of Si substrates corresponding to the [112]-direction: C6o film (2110 nm), C70 film (950 nm).
pulses propagating in this direction are different from those of the [112] direction, the dispersion curves had a somewhat different shape. Therefore these measurements provided additional information for the evaluation of film parameters. In Fig. 2 the dispersion curves for two fullerite films on quartz-glass substrates are presented. The calculated best fits for the dispersion curves are also plotted. The values of the parameter 7m~x were 0.32
3 4 0 0 ~ - - - - ~ fullerite/qua r t z - ,
!
~
!
'
i
._-, 3 3 0 0 - -
:
3zoo
3100
0
, ', ! 50 100 150 Frequency (MHz)
200
Fig. 2. Measured SAW dispersion curves (squares) and calculated best fits (thin solid lines) for fullerite films on quartz-glass substrates: C6o film (995 rim), C7o film (665 rim).
and 0.18 for the C6o (995 nm) and C7o (665 nm) films, respectively. For the excitation of SAW pulses in the sample with the C~ film the picosecond-laser was used, which allowed a somewhat higher frequency range to be reached. All other experiments were performed with nanosecond laser pulses. The low-frequency limit of the measured dispersion curves of about 10-20 MItz was determined by the influence of the bulk shear acoustic signal and diffraction as well as by the lower sensitivity of the detection equipment in the low-frequency domain. All dispersion curves obtained for fullerite films correspond to the case of normal dispersion as expected for soft materials held together by van der Waals forces. To evaluate the film properties the following procedure was used. The measured dispersion curve was shifted to fit the low-frequency limit of SAW propagation equal to the well known value for the SAW velocity in the substrate. Usually this offset correction was less than +3 m/s. Then, using the film thickness measured with the profilometer, other film parameters were varied in sufficiently wide intervals, and for every set of parameters a mean square deviation of the theoretical and experimental dispersion curves was calculated. The set of parameters with minimum deviation provided the best estimate of the film properties. Using this set of parameters the thickness of the film was evaluated more precisely and then other parameters were also corrected with a modified Levenberg-Marquardt algorithm. This procedure was repeated several times and the parameters obtained were checked by starting at different values. The described procedure was proved by test measurements with metal films and demonstrated convergence in the vicinity of the actual set of the film properties. A comparison of the results obtained for films on quartz-glass substrates with the exact model [8] and with the approximate model [9] has shown that even for a relatively small value of %,× = 0.18 (C~0 fiim) the approximate model provides values of Poisson's ratio which are about 30% lower, while the other properties are approximately the same. For the film with %~x -- 0.32 (C60 film) the value of the density obtained with the approximate model was about 2% lower and that of Young's modulus about 20% lower. Thus, for precise evaluation of the film parameters
AA. Kolomenskii et al. /Applied Surface Science 86 (1995) 591-596
595
Table 1 Parameters of fullerite films Film material
Density (g/cm 3)
Young's modulus
Poisson's ratio
(GPa) C60
C70
1.67 _+ 0.02 1.64 4- 0.02
10 4- 2 4 4- 1
0.25 + 0.08 0.35 4- 0.1
even for small values of ')'max~ 0.1 to 0.3 the exact model should be used. The evaluated properties of the investigated fullerite films are presented in Table 1. In the present experiments sufficiently large values of the parameter 3'max could be achieved, and therefore the determination of the density, and the less accurate evaluation of Young's modulus and Poisson's ratio was possible. In addition the longitudinal and transverse sound velocities were calculated from the experimental data as presented in Table 1. The uncertainty in the determination of the film thickness (which also includes the variation of the thickness due to film inhomogeneity) introduces the main error in the evaluation of the film density. The resulting scatter of the best fit values of the film properties obtained for different films and measurements determines the main error in the evaluation of Young's modulus and Poisson's ratio. It should be noted however, that the measurements performed with a sufficiently homogeneous film provide much smaller errors for Young's modulus and Poisson's ratio than those indicated in Table 1. Thus, for the determination of these parameters the described method potentially processes a higher accuracy of about a few percent. The obtained values of the C60 film properties are somewhat different but consistent with the results of previous measurements [10]. The data show that Young's modulus for the C60 films is lower than that for a C60 single crystal (15.9 GPa) [7]. This may be connected with the amorphous microstructure of the film. For C70 films Young's modulus and the density were found to be lower than the values obtained for C6o films. This is in agreement with the results of calculations [11] showing that the most stable pack-
Longitudinal sound velocity
Transverse sound velocity
(kin/s)
(kin/s)
2.7 _+0.3 2.0 4- 0.4
1.5 _+0.2 1.0 4- 0.2
ing of the fullerene molecules in a C70 crystal has a lower density than that for a C60 crystal.
4. Conclusion In this work broadband surface acoustic wave spectroscopy for the determination of mechanical and elastic properties of thin films is described. With this technique fullerite films (C60, C70) were investigated. The density, Young',s modulus and Poisson's ratio of these carbon films have been evaluated for the first time with this method.
Acknowledgements One of the authors (A.A.K.) would like to thank the Humboldt Foundation for a fellowship. Financial support of this work by the Bundesministerium fiir Forschung und Technologie under contract No. 13N6005 5 and the Fonds der Chemischen Industrie is gratefully acknowledged.
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