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Roughness-Induced Acoustic Second-Harmonic Generation during Electrochemical Metal Deposition on the Quartz-Crystal Microbalance Susanne Wehner,† Katrin Wondraczek,‡ Diethelm Johannsmann,‡ and Andreas Bund*,† Institute of Physical Chemistry and Electrochemistry, Dresden University of Technology, Mommsenstrasse 13, D-01062 Dresden, Germany, and Institute of Physical Chemistry, Clausthal University of Technology, Arnold-Sommerfeld-Strasse 4, D-38678 Clausthal-Zellerfeld, Germany Received August 25, 2003. In Final Form: January 7, 2004 This paper reports on the relation between the surface roughness and emission of compressional waves from the surface of an electrochemical quartz-crystal microbalance. The detection of the compressional waves took place with an ultrasonic microphone and the quartz crystal itself. As a model process, the electrochemical deposition of copper from an acidic copper sulfate solution has been chosen. For this system, the roughness of the layer can be tuned via the current density. Roughness may be a source of the longitudinal waves at twice the frequency of the exciting shear wave (acoustic second-harmonic generation, ASHG) if the flow profile above the quartz-crystal surface is not entirely laminar. Slight deviations from the laminar flow can be reached at high amplitudes of oscillation. Comparing the ASHG efficiency of a rough and smooth surface, we find that the rough surface is more efficient in generating second-harmonic waves. This suggests that ASHG can be used to obtain a roughness parameter independent from the resonance frequency or bandwidth (damping) of a quartz-crystal resonator. Such an independent determination of roughness should be very interesting in practical applications.
Introduction A well-established application of the thickness-shearmode resonators is the electrochemical quartz-crystal microbalance (EQCM), which is based on the fact that the resonance frequency depends on the surface mass loading of a quartz crystal (for reviews, see refs 1 and 2). If the deposited layer is rigid and smooth, the frequency shift is directly proportional to the areal mass density on the quartz.3 If, on the other hand, the layer is rough on the length scale of the penetration depth of the shear wave δ (δ ∼ 180 nm for a quartz oscillating in water at 10 MHz), the interpretation of the frequency shift becomes complicated.4 The situation becomes even more difficult if the layer is viscoelastic.5 Given the practical importance of roughness, it would be highly desirable to have an independent parameter quantifying the roughness. Such a roughness parameter would help to disentangle the effects of trapped liquid and hydrodynamics on rough surfaces from the effects of a deposited mass. One approach to assessing the roughness is to combine the EQCM with techniques such as atomic force microscopy6 or surface plasmon resonance spectros* Author to whom correspondence should be addressed. Phone: +49 (0)351 463 34351. Fax: +49 (0)351 463 37164. E-mail:
[email protected]. † Dresden University of Technology. ‡ Clausthal University of Technology. (1) Buttry, D. A. In Electroanalytical ChemistrysA Series of Advances; Bard, A. J., Ed.; Marcel Dekker: New York, 1991; Vol. 17, p 1. (2) Hillmann, R. In Encyclopedia of Electrochemistry, Instrumentation and Electroanalytical Chemistry; Bard, A. J., Stratmann, M., Unwin, P. R., Eds.; Wiley-VCH: Weinheim, Germany, 2003; Vol. 3, p 230. (3) Sauerbrey, G. Z. Phys. 1959, 155, 206-222. (4) Daikhin, L.; Gileadi, E.; Katz, G.; Tsionsky, V.; Urbakh, M.; Zagidulin, D. Anal. Chem. 2002, 74, 554-561. (5) Bund, A.; Schneider, M. J. Electrochem. Soc. 2002, 149, E331E339.
copy.7 The drawback of these combined techniques is their relatively complicated experimental setup. In this paper, we explore whether nonlinear effects can provide additional information on surface roughness. In general, nonlinear effects in the operation of the EQCM in liquids are small. Klenerman and co-workers have recently used third-harmonic generation to probe rupture events.8,9 We report on the search of a roughness parameter based on the hypothesis that roughness might lead to the emission of compressional waves at the second harmonic, 2f. Second-harmonic generation and its use for interfacial sensing is well-established for optical waves.10 Here, we apply a similar concept for acoustics. Experimental Section AT-cut quartz crystals (10 MHz, optically polished) with gold electrodes (thickness, 100 nm; area, 22 mm2) were used as obtained from the supplier (KVG Neckarbischofsheim, Germany). All of the electrochemical measurements were performed with an EG&G potentiostat/galvanostat (model 263A, PAR Oakridge, TN) in a polytetrafluoroethylene cell. In a three-electrode arrangement, one gold electrode of the quartz crystal was used as the working electrode, a copper rod, as the counter electrode, and a saturated calomel electrode, as the reference electrode. Copper was galvanostatically deposited at varying current densities (-0.125, -0.25, -0.5, and -1 mA cm-2) up to a total charge of -0.3 C cm-2 at room temperature from an unpurged and unstirred commercial copper sulfate electrolyte containing 55 g L-1 of Cu2+ (Cupracid Ultra, Atotech, Berlin, Germany). (6) Bund, A.; Schneider, O.; Dehnke, V. Phys. Chem. Chem. Phys. 2002, 4, 3552-3554. (7) Bund, A.; Baba, A.; Berg, S.; Johannsmann, D.; Lu¨bben, J.; Wang, Z.; Knoll, W. J. Phys. Chem. B 2003, 107, 6743-6447. (8) Dultsev, F. N.; Ostanin, V. P.; Klenerman, D. Langmuir 2000, 16, 5036-5040. (9) Dultsev, F. N.; Speight, R. E.; Fiorini, M. T.; Blackburn, J. M.; Abell, C.; Ostanin, V. P.; Klenerman, D. Anal. Chem. 2001, 73, 39353939. (10) Bain, C. D. Curr. Opin. Colloid Interface Sci. 1998, 3, 287-292.
10.1021/la0355646 CCC: $27.50 © 2004 American Chemical Society Published on Web 02/11/2004
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Figure 1. Schematic representation of the experimental setup. The surface morphology of the Cu films was investigated by scanning electron microscopy (50 kV) with a Zeiss DSM 982 Gemini microscope (Carl Zeiss, Oberkochen, Germany). The electrical admittance Y ) G + iB of the resonator near the resonance frequency was measured with a network analyzer (model E5100A, Agilent Technologies, USA). Notice that for a damped resonator the resonance frequency is a complex quantity, f * ) f + iΓ, whose imaginary part is the half-band-half-width (bandwidth, for short) Γ of the resonance curve.11,12 Resonance frequency f and bandwidth Γ were determined from a fit of resonance curves to the admittance spectra (for details, see ref 12). An ultrasonic microphone (type Z4K, Agfa, Huerth, Germany) was placed at a distance of about 5 mm above the resonator to detect the compressional waves (Figure 1). The signal from the microphone was fed into the second channel of the network analyzer. It turned out that acoustic second-harmonic generation (ASHG) was more efficiently detected with the quartz plate itself than with the microphone. In a way, the quartz plate is a microphone placed directly at the source. The ASHG signal was acquired via a high-speed lock-in amplifier (model SR 844 RF, Stanford Research Systems, Sunnyvale, CA), where the lock-in amplifier was referenced to the output of the network analyzer. The network analyzer continuously performed frequency sweeps around the resonance frequency. If not otherwise specified, a drive level of 5 dBm was used. The ASHG signal displayed resonance curves, the amplitude of which was used for further analysis. Fitting resonance curves to the raw data from the lock-in amplifier is essential, because it allows the subtraction of an offset of electronic origin.
Results When copper was deposited from the commercial electrolyte at small current densities, very rough layers were obtained (Figure 2a). Because of the high surface roughness, the damping increased strongly (Figure 3b). At the same time, the frequency shift (Figure 3a) was larger than expected from Faraday’s law, assuming 100% current efficiency.6,21 Increasing the absolute value of the current density produced fine-grained and much smoother deposits (Figure 2b) with a frequency shift δf (Figure 4a) corresponding to the calculated values from the Sauerbrey equation.3 There was virtually no increase in bandwidth (Figure 4b). Around the fundamental frequency (10 MHz), compressional waves could be easily detected with the microphone. The frequency dependence of the microphone’s response is also given by a resonance curve, where (11) Tabidze, A. A.; Kazakov, R. Kh. Izmer. Tekh. 1983, 14, 24-27. (12) Johannsmann, D.; Mathauer, K.; Wegner, G.; Knoll, W. Phys. Rev. B 1992, 46, 7808-7815.
Figure 2. Scanning electron micrographs of the Cu layers deposited at -0.125 mA cm-2 (a) and at -1.0 mA cm-2 (b).
the amplitude varies with distance and overtone order.13 It was verified by experiments in air that the response of the microphone was not caused by electronic cross talk. Searching for ASHG from rough surfaces, we monitored the ASHG signal during electrodeposition, i.e., the amplitude of the signal emitted from the quartz around 20 MHz. The roughness strongly increases during deposition if the currents are small. Figure 5 shows the raw data from the lock-in amplifier and derived amplitudes. These data were collected in solution on the bare gold surface of the quartz. With increasing driving power, the ASHG amplitude increased (Figure 5b). As will be outlined in the Discussion section, the ASHG intensity should show (13) Wondraczek, K.; Johannsmann, D. In preparation.
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Figure 3. Resonance frequency shift δf (a) and damping shift δΓ (b) as obtained from the conductance spectra (O) and transmittance of sound to the microphone (b) during the Cu deposition from the Cupracid electrolyte at a current of -0.125 mA cm-2. The straight line in panel (a) is the prediction from Faraday’s law and the Sauerbrey equation.
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Figure 5. Raw data from the lock-in amplifier. (a) Frequency dependence for a drive power of 5, 3, 1, -1, -3, and -5 dBm (top to bottom). An offset of the electronic origin has been subtracted. (b) Amplitude of the fitted resonance curves versus drive voltage. The straight line indicates the expected quadratic dependence.
Figure 6. ASHG signal normalized to the square of the fundamental amplitude Inorm(2ω) for different deposition currents: -0.125 mA cm-2 (4), -0.25 mA cm-2 (3), -0.5 mA cm-2 (O), and -1.0 mA cm-2 (0).
Figure 4. Resonance frequency shift δf (a) and damping shift δΓ (b) from the conductance spectra (O) and transmittance of sound to the microphone (b) during the Cu deposition from the Cupracid electrolyte at a current of -1.0 mA cm-2. The straight line in panel (a) is the prediction from Faraday’s law and the Sauerbrey equation.
a quadratic dependence on the lateral speed of the quartz plate. At the moment, it is unclear why the drive level dependence of the ASHG signal is more than quadratic (Figure 5b, solid line). We introduce a parameter Inorm(2ω), which is the ratio of the ASHG signal and square of the fundamental. Inorm(2ω) is normalized with respect to the square of the fundamental, because the ASHG signal should be quadratic in the amplitude of the fundamental. The coefficient Inorm(2ω) is related to the properties of the interface and should quantify the surface roughness (where other mechanisms for second-harmonic generation are conceivable, as well). Figure 6 shows the development of Inorm(2ω) for four different deposition rates. Inorm(2ω) has been normalized to its value at t ) 0 for the ease of comparison. As can be seen, the efficiency of the generation of acoustic second-harmonic waves increases upon the growth of a rough layer. Because small absolute current densities produce very rough Cu layers (Figure 2a), the data support the hypothesis that ASHG can be used to monitor the development of surface roughness at least qualitatively. Performing the experiments under conditions where the layer is smooth (squares in Figure 6) resulted in almost constant values of Inorm(2ω).
Figure 7. Dependence of the ASHG signal Inorm(2ω) on the current density at a fixed total charge of -0.25 C cm-2 for a total of 14 experiments.
Figure 7 summarizes the normalized values Inorm(2ω) for a range of current densities and a fixed total charge of -0.25 C cm-2. The variability of Inorm(2ω) for each current density can be explained with the fact that the development of roughness depends on factors that were poorly controlled (such as the density of nucleation sites). However, the correlation between the growth rate and ASHG efficiency is evident. Discussion It is well-known that the thickness-shear-mode (ATcut) quartz-crystal resonators in liquids emit the compressional waves at the same frequency as the shear waves.14 This effect is assumed to be related to the finite (14) Lin, Z.; Ward, M. D. Anal. Chem. 1995, 67, 685-693.
Roughness-Induced Acoustic Second-Harmonic Generation
lateral extension of the quartz plate and energy trapping.15 Compressional waves are a nuisance in conventional quartz-crystal microbalance (QCM) measurements because they decrease the quality factor (Q factor) of the resonator. Moreover, they may be reflected at the walls opposing the quartz resonator and give rise to secondary resonances16 and concomitant artifacts in the data. Notice, however, that the interest here is not on compressional waves emitted at the fundamental frequency. For reasons of symmetry, these waves cannot be related to the surface roughness. A mechanism that converts shear flow above a rough surface into compressional waves can be intuitively suspected, because the asperities are in the way of the shear flow and deviate the flow of the liquid in the vertical direction. For conditions of laminar flow, however, the roughness-induced vertical components of the flow average out over the area of the quartz-crystal resonator. Because of volume conservation, the total amount of liquid moving upward must be equal to the amount of liquid moving downward. The effects of roughness should be limited to an increased dissipation and, possibly, an increased apparent mass loading. The issue of an increased (or decreased) apparent mass is connected to the question of slip and air bubbles trapped in the cavities, which caused some debate in the literature.17,18 Urbakh and Daikhin as well as Etchenique and Brudny have published a series of papers where they calculate the reactive and dissipative roughness-induced forces as well as the concomitant shifts in frequency and bandwidth.4,19-23 These authors assume a nonslip boundary condition and a clean, gas-free contact between the resonator surface and the liquid. Because the vertical components of flow average out under the conditions of laminar flow (that is, linear hydrodynamics), the mechanism producing vertical pressure above an oscillating rough surface must scale as the square of the lateral speed. It must be a nonlinear effect. There is a second argument in favor of a quadratic dependence on the speed, which is based on symmetry. When the direction of the shear movement is reversed, it should have no effect on the sign of the vertical stress. If the vertical pressure were proportional to the shear movement, the vertical pressure would change sign with the direction of the movement, which does not make sense physically. A source of hydrodynamic pressure, which is quadratic in velocity, is provided by the nonlinear term F(v∇)v (where F is the density and v is the speed) in the Navier-Stokes equation. Because of this quadratic dependence, the roughness-induced pressure waves are expected to occur at even harmonics of the resonance frequency. A more detailed treatment will be given in a later paper. Following this argument, compressional waves at the secondharmonic frequency can only be generated when the conditions of laminar flow are not satisfied. For laminar flow, all of the stress-strain relations are linear, and second-harmonic generation is forbidden. (15) Schneider, T. W.; Martin, S. J. Anal. Chem. 1995, 67, 33243335. (16) Bund, A.; Schwitzgebel, G. Anal. Chim. Acta 1998, 364, 189194. (17) McHale, G.; Lucklum, R.; Newton, M. I.; Cowen, J. A. J. Appl. Phys. 2000, 88, 7304-7312. (18) Thompson, M.; Nisman, R.; Hayward, G. L.; Sindi, H.; Stevenson, A. C.; Lowe, C. R. Analyst 2000, 125, 1525-1528. (19) Urbakh, M.; Daikhin, L. Langmuir 1994, 10, 2836-2841. (20) Urbakh, M.; Daikhin, L. Phys. Rev. B 1994, 49, 4866-4870. (21) Urbakh, M.; Daikhin, L. Langmuir 1996, 12, 6354-6360. (22) Etchenique, R.; Brudny, V. L. Electrochem. Commun. 1999, 1, 441-444. (23) Etchenique, R.; Brudny, V. L. Langmuir 2000, 16, 5064-5071.
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The strength of the nonlinear terms in hydrodynamics is estimated by the Reynolds number, which compares nonlinear inertial effects (scaling as the square of the speed) to the viscous drag. The nonlinear term in the Navier-Stokes equation is significant for large Reynolds numbers. The Reynolds number, Re, is given by
Re )
FvL η
(1)
where F ≈ 103 kg m-3 and η ≈ 10-3 Pa s are the density and viscosity of the liquid, respectively, v is the velocity, and L is a characteristic length. For the characteristic length, we use the lateral scale of roughness, which is measured in micrometers for the systems investigated in this paper (Figure 2a). For a 10 MHz quartz in water driven at a power of 5 dBm, a Reynolds number on the order of 0.02 results (see the Appendix). This order of magnitude is consistent with observations. If, under ordinary conditions, Re was more than unity, the wellproven equations describing the QCM operating in liquids could not be applied. These equations assume linear acoustics. On the other hand, a value of Re ∼ 0.02 certainly encourages one to search for nonlinear effects. Future papers will deal with a quantitative derivation of ASHG amplitudes for the limit of small roughness using a perturbation approach and with experiments on surfaces with a well-defined topography. Conclusions Compressional waves were detected in parallel to measurements of deposited mass and dissipation with a quartz-crystal microbalance. Interestingly, there is a second-harmonic component that could be monitored with the quartz crystal itself. Second-harmonic generation is related to nonlinear phenomena and should be proportional to the Reynolds number. Furthermore, the experiments showed that the ASHG efficiency is related to the surface roughness. This can provide information on the surface roughness that is independent of shifts in frequency and bandwidth. Given the importance of roughness in QCM applications in liquids, such a roughness parameter will have a considerable practical value (e.g., for process monitoring in electroplating applications). Acknowledgment. Financial support from Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie is gratefully acknowledged. Appendix: Calculation of the Reynolds Number We start from the definition of the Reynolds number in eq 1. For the characteristic length L, we use the lateral scale of roughness of about 1 µm as determined from the scanning electron micrographs (Figure 2). The velocity v is given by24
v ) ωu0
(A1)
and further
u0 )
2 1 Q d U nπ 2 26
(
)
(A2)
where ω is the radial frequency, n is the overtone order (here, n ) 1), Q [)f/(2Γ)] is the quality factor, u0 is the amplitude of lateral displacement, (1/2)d26U is the offresonant displacement induced by a quasi-static voltage (24) Martin, B.; Hager, H. J. Appl. Phys. 1989, 65, 2630-2635.
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U, and d26 ()3.21 pm/V) is the piezoelectric coefficient. The factor 2/π is caused by the fact that on resonance the pattern of shear displacement is given by a cosine with antinodes at the quartz surface, whereas the quasi-static displacement pattern is a straight line with a constant shear angle. A typical value for the Q factor in liquids is 104. The voltage is related to the driving power in dBm (decibels relative to 1 mW of power) by the relation
U ) 224 mV × 10P[dBm]/20
(A3)
The displacement can then be expressed as
u0 )
1 f d 224 mV × 105/20 ) 0.34 nm nπ 2Γ 26
(A4)
where the experimental values of f ()10 MHz) and Γ ()6000 Hz) were used. It results in a speed of
v0 ) 2πfu0 ) 0.02 m s-1
(A5)
With eq 1, this yields a Reynolds number of Re ∼ 0.02. When higher driving voltages are applied or quartzes with a higher Q factor are used, a Reynolds number of Re ∼ 0.1 is easily obtained. Even with the Reynolds number realized in our experiments, it suffices to produce the acoustic second harmonics. LA0355646
