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Langmuir 2006, 22, 9062-9066
Measurements of Interface Stress of Silicon Dioxide in Contact with Water-Phenol Mixtures by Bending of Microcantilevers Xijing Zhang* and David G. Cahill Center of AdVanced Materials for the Purification of Water with Systems, Department of Materials Science and Engineering, UniVersity of Illinois, Urbana, Illinois 61801 ReceiVed April 15, 2006. In Final Form: July 28, 2006 We use the bending of silicon microcantilevers to measure changes in mechanical stress at interfaces between phenol-water mixtures and SiO2. The curvature of the microcantilever is measured by an optical system that combines a rapidly scanning laser beam, a position-sensitive detector, and lock-in detection to achieve a long-time stability on the order of 6 mN m-1 over 4 h and a short-time sensitivity of better than 1 mN m-1. Thermally oxidized Si shows the smallest changes in interface stress as a function of phenol concentration in water. For hydrophilic SiO2 prepared by chemical treatment, the change in interface stress at 5 wt % phenol in water is larger than that of thermally oxidized Si by -60 mN m-1; for SiO2 formed by exposure of the silicon microcantilever to ozone, the change in surface stress is larger than that of thermally oxidized Si by -330 mN m-1.
I. Introduction Interface stress is the derivative of the free energy of an interface with respect to elastic strain. The Shuttleworth equation1 relates the interface stress g to the free energy of the interface per unit area γ. For isotropic materials, g is a scalar.
g ) γ + ∂γ/∂
(1)
If the free energy increases when an elastic deformation increases the area of the interface, g > 0 and the interface stress is said to be “tensile”. When g < 0, the interface stress is said to be “compressive”. At the surface of a liquid, or at the interface between two liquids, the interface stress and interface free energy per unit area are equivalent, g ) γ. But at the interface between a solid and a liquid or at the interface between two solids, g * γ. Only in rare situations is the absolute value of γ of solid interfaces directly accessible to experiment; changes in g, on the other hand, can be measured quantitatively using, for example, the bending of thin cantilever beams. Changes of surface or interface stress created by adsorption have been widely studied for clean crystal surfaces in ultrahigh vacuum and in electrochemical environments.2 Some of the earliest experiments on electrochemical systems were performed by Gokhshtein3 more than 30 years ago. Fredlein and Bockris4,5 used a sensitive laser beam deflection method to measure changes in the bending of a cantilever electrode produced by the dependence of interface stress on electrochemical potential. More recently, changes in interface stress during UHV or electrochemical processes have been measured by Martinez,6 Brunt,7,8 and Stafford.9,10 * Corresponding author. E-mail:
[email protected]. (1) Shuttleworth, R. Proc. Phys. Soc. A 1950, 63, 444-457. (2) Haiss, W. Rep. Prog. Phys. 2001, 64, 591-648. (3) Gokhshtein, A. Y. Dokl. Akad. Nauk SSSR 1969, 187, 601-604. (4) Fredlein, R. A.; Damjanovic, A.; Bockris, J. O. M. Surf. Sci. 1971, 25, 261-264. (5) Fredlein, R. A.; Bockris, J. O. M. Surf. Sci. 1974, 46, 641-652. (6) Martinez, R. E.; Augustyniak, W. M.; Golovchenko, J. A. Phys. ReV. Lett. 1990, 64, 1035-1038. (7) Brunt, T. A.; Chabala, E. D.; Rayment, T.; Oshea, S. J.; Welland, M. E. J. Chem. Soc., Faraday Trans. 1996, 92, 3807-3812. (8) Oshea, S. J.; Welland, M. E.; Brunt, T. A.; Ramadan, A. R.; Rayment, T. J. Vac. Sci. Technol. B 1996, 14, 1383-1385.
Adsorption processes in liquids also produce changes in interface stress, but the interactions of material surfaces with liquid mixtures have been much less studied than surfaces under UHV or electrochemical conditions. The adsorption and selfassembly11 of alkanethiol molecules on Au induce a compressive interface stress12 on the order of 250 mN m-1. The recognition of conformational changes of proteins can be realized via surface stress changes on functionalized microcantilever surfaces,13,14 although the stress response in these experiments was relatively small, approximately 5 mN m-1. Butt studied changes in interface stress for silicon nitride in contact with water as a function of pH and salt concentration.15 A change in pH from 2 to 12 produced an increase in interface stress of 40 mN m-1, and an increase of salt concentration from 0 to 1 M increased the stress by 75 mN m-1. Cherian et al.16 studied the effects of Ca2+ ions on silicon nitride surfaces and found a large change in interface stress that saturated at 400 mN m-1 at a Ca2+ concentration of 30 mM. Interface stress can be connected to the microscopic physics and chemistry of the interface using the definition of interface force dipole;17 the force dipole is a tensor quantity given by
mRβ )
∑R RRFβR
(R, β ) x, y, z)
(2)
which is the mechanical moment of a set of forces FβR acting at points RR. The interface stress is the average (per unit area) of the shear component of the force dipoles at the interface. Thus, if an adsorbate is bonded to a surface through forces that act normal to the surface, we do not expect a large change in the (9) Kongstein, O. E.; Bertocci, U.; Stafford, G. R. J. Electrochem. Soc. 2005, 152, 116-123. (10) Stafford, G. R.; Kongstein, O. E.; Haarberg, G. M. J. Electrochem. Soc. 2006, 153, 207-212. (11) Dubois, L. H.; Nuzzo, R. G. Annu. ReV. Phys. Chem. 1992, 43, 437-463. (12) Berger, R.; Delamarche, E.; Lang, H. P.; Gerber, C.; Gimzewski, J. K.; Meyer, E.; Guntherodt, H. J. Science 1997, 276, 2021-2024. (13) Fritz, J.; Baller, M. K.; Lang, H. P.; Rothuizen, H.; Vettiger, P.; Meyer, E.; Guntherodt, H. J.; Gerber, C.; Gimzewski, J. K. Science 2000, 288, 316-318. (14) Moulin, A. M.; Oshea, S. J.; Badley, R. A.; Doyle, P.; Welland, M. E. Langmuir 1999, 15, 8776-8779. (15) Butt, H. J. J. Colloid Interface Sci. 1996, 180, 251-260. (16) Cherian, S.; Mehta, A.; Thundat, T. Langmuir 2002, 18, 6935-6939. (17) Pimpinelli, A.; Villain, J. Physics of Crystal Growth; Cambridge University Press: New York, 1998; p 232, p 270.
10.1021/la061032o CCC: $33.50 © 2006 American Chemical Society Published on Web 09/12/2006
Interface Stress of SiO2 in Water-Phenol Mixtures
Langmuir, Vol. 22, No. 21, 2006 9063
Figure 1. Schematic diagram of the optical system used to measure the curvature of the microcantilever.
interface stress unless either the adsorbate bonds also modify the lateral bonding between atoms near the interface or the adsorbates have strong lateral interactions with their neighbors. We expect the largest changes in interface stress when an adsorbate participates in strong lateral, or bridging, interactions with multiple sites on the surface.18,19 II. Experiment Details A. Cantilever Bending. Silicon microcantilevers are extremely sensitive detectors of mechanical stress.2,16,20,21 A cantilever, however, can only measure an imbalance in stress; that is, the bending of a cantilever is only sensitive to the differences in interface stress on the two sides of the cantilever. For a cantilever immersed in a liquid, this requires that the two sides of the cantilever have different compositions or chemistries; ideally, the interface stress on one side of the cantilever should be only weakly dependent on changes in experimental conditions so that changes in stress at the interface under study will dominate the measurement. Stoney’s equation connects the bending curvature C of a cantilever to the difference of interface stresses on the two sides of a cantilever, g0 and gt. ∆g ) gt - g0 )
Yt2C 6(1 - ν)
(3)
where Y and ν are the Young’s modulus and Poisson ratio of the cantilever material, respectively, and Y/(1 - ν) is the biaxial modulus. For (001)-oriented Si, Y/(1 - ν) ) 1/(s11 + s12) ) 180.5 GPa,22 where sij are the cubic elastic stiffness constants. Stoney’s equation is accurate when the bending of the cantilever is small, the length L of the cantilever is large compared with its width w, and the width is much larger than the thickness t; these conditions are well-satisfied here: l ) 450 µm, w ) 50 µm, t ) 2 µm. B. Optical System for Measuring the Cantilever Curvature. A schematic diagram of the optical system we use to measure the curvature of the silicon microcantilever is shown as Figure 1. A He-Ne laser beam strikes the center of a mirror that undergoes angular oscillations with an amplitude of 1.32° and a frequency of 133 Hz. A lens of focal length 40 mm collimates the beam into a scanning line of length L ) 3.7 mm. The next two lenses (F ) 200 mm and f ) 20 mm) demagnify the scanning line by a factor of 10 to 0.37 mm to fit onto the 0.45-mm-long cantilever. After the beam is reflected from the microcantilever and exits the liquid cell, the angle between the reflected beams at either end of the scanning line is θ ) 2lCn ) 2(f/F)LCn, where n is the refractive index of the liquid, and C is the curvature of the microcantilever. The angles in the reflected beam are demagnified by a factor of f/F after traveling back through the objective lens f and the lens F. (18) Pimpinelli, A.; Villain, J. Physics of Crystal Growth; Cambridge University Press: New York, 1998; Appendix M. (19) Ibach, H. Surf. Sci. Rep. 1997, 29, 195-263. (20) Stevenson, K. A.; Mehta, A.; Sachenko, P.; Hansen, K. M.; Thundat, T. Langmuir 2002, 18, 8732-8736. (21) Boiadjiev, V. I.; Brown, G. M.; Pinnaduwage, L. A.; Goretzki, G.; Bonnesen, P. V.; Thundat, T. Langmuir 2005, 21, 1139-1142. (22) Brantley, W. A. J. Appl. Phys. 1973, 44, 534-535.
Therefore, before the scanning beams pass through the focusing lens F′ ) 500 mm, the difference in the angles of the beams at either end of the scanning line are θ′ ) 2(f2/F2)LCn. The quarter-wave plate and polarizing beam splitter direct the majority of the laser power to the microcantilever and back toward the position-sensitive detector placed at the focal point of lens F′. Beams separated by an angle θ′ are transformed into displacements d ) F′θ′ by the lens F′. The output of the position-sensitive detector is normalized by the electronics so that 1 mV corresponds to a displacement of 1 µm, independent of the laser power. This normalized signal from the position-sensitive detector is measured by a lock-in amplifier. The rms output of the lock-in amplifier V is then proportional to the curvature of the cantilever C)
x2F2V f2nLFβ
(4)
where β is the calibration constant of the position-sensitive detector, 1000 V m-1. The other beam splitter, lens, and the CCD camera comprise an optical microscope that we use to position the scanning laser beam on the cantilever. A fiber ring-light (not shown) provides dark-field illumination of the cantilever so that the cantilever can be accurately placed at the focal point of the microscope objective f by focusing the image of the cantilever on the CCD camera. C. Sample Preparation. We used three varieties of SiO2 in our experiments: (i) SiO2 formed by thermal oxidation of silicon microcantilevers for 10 min in air at 950 °C; (ii) hydrophilic SiO2 formed by chemical treatment of thermally oxidized Si; and (iii) SiO2 formed by exposing the silicon microcantilever to ozone. In all cases, the other side of the microcantilever is coated by sputter deposition with a 2-nm-thick film of Ti followed by a 20-nm-thick film of Au. Thus, all of our measurements are for the differences between the changes in the interface stress on the SiO2 side of the microcantilever and the Au-coated side of the microcantilever. Hydrophilic SiO2 surfaces can be produced using the so-called “Standard Cleaning 1” (SC-1)23 process; in our case, the microcantilever, after thermal oxidation and deposition of the Au film, is immersed in a mixture of H2O, H2O2, and NH4OH with a volume ratio of 10:1:1 at a temperature near 70 °C for 10 min. The contact angle of these surfaces with water is approximately 10°. To form the ozone-treated surfaces, we first coat one side of the as-received cantilever with Au and then expose the cantilever for 30 min to ozone generated in a 15 × 15 × 15 cm3 box by an Hg lamp. We estimated the ozone concentration in the box by measuring the attenuation UV light intensity I in the wavelength band 246 nm < λ < 263 nm measured with a photodiode and band-pass optical filter. I(x) ) I0 exp(-σcx)
(5)
where x ) 10 cm is the distance of the UV detector to the UV light source, σ ) 1.1 × 10-17 cm2 /molecule is the optical absorption cross-section near λ ) 254 nm,24 and c is the ozone concentration. After the Hg lamp has been turned on for 30 min, the typical ozone concentration measured in this way is c ) 5 × 1014 molecule/cm3, or 20 ppm. We used X-ray photoelectron spectroscopy (XPS) to confirm that the oxidation state of the Si was consistent with SiO2 and used Auger electron spectroscopy to verify that the surface was not contaminated by carbon- or nitrogen-containing species. The water contact angle of SiO2 surfaces formed in this way is approximately 3°. Because the thickness of the microcantilever is critical for accurately deriving the interface stress from the measured curvature, see eq 3, we use picosecond laser acoustics to measure the thickness of each microcantilever. Picosecond acoustics25 is a pump-probe (23) Kern, W.; Puotinen, D. A. RCA ReV. 1970, 31, 187-206. (24) Hearn, A. G. Proc. Phys. Soc. 1961, 78, 932-940. (25) Thomsen, C.; Grahn, H. T.; Maris, H. J.; Tauc, J. Phys. ReV. B 1986, 34, 4129-4138.
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Figure 2. Changes in optical reflectivity ∆R measured by a probe optical pulse following the generation of an acoustic wave by a pump optical pulse at t ) 0; the x-axis of this plot shows the time delay between the pump and probe. The pump and probe pulses are incident on the Au-coated side of the microcantilever. The small feature in the optical reflectivity at t ) 215 ps is created by the arrival of the longitudinal acoustic wave at the back surface of the cantilever, and the feature at t ) 430 ps is created by the echo of this acoustic pulse after it has returned to the front surface.
Figure 3. Schematic drawings of the liquid cell: (a) side view, (b) top view. The other side of the thermoelectric device shown in (a) is attached to a heat sink and cooling fan (not shown). optical technique that uses a Ti:sapphire laser or other ultrafast laser oscillator to generate longitudinal acoustic waves and detect the arrival time of these acoustic waves at surfaces or interfaces. A typical trace for the change in optical reflectivity as a function of delay time between the pump and probe is shown as Figure 2. The longitudinal sound speed in (100) Si is 8.43 nm/ps.26 For this cantilever, the transit time of the acoustic wave is 215 ps and the cantilever thickness is 1.82 µm. D. Liquid Cell and Measurement Procedure. The liquid cell we use in our experiment is assembled from poly(dimethylsiloxane) (PDMS), a piece of a Si wafer, and a silica glass window, see Figure 3. The piece of PDMS is cut into a ring shape with the central volume of 0.4 mL. We use two pieces of aluminum and four screws to press the window and the PDMS onto the wafer. The microcantilever sample is placed on the wafer, and another small piece of PDMS is squeezed between the sample and the window to fix the microcantilever in place. Prior to assembly, each piece of the cell is cleaned in ethyl alcohol to minimize the possibility of transferring contaminants from the surfaces of the liquid cell to the surfaces of the microcantilever. (26) McSkimin, H. J.; Andreatch, P. J. Appl. Phys. 1964, 35, 2161-2165.
Zhang and Cahill
Figure 4. Long-term stability of the interface stress change of a sample in the water-filled cell. The interface stress is converted from the output signal of the lock-in amplifier using eqs 3 and 4. The drift of the stress is approximately 6 mN m-1 over 4 h. A Pt resistance thermometer is attached to the bottom Al plate, and a temperature controller and thermoelectric device stabilize the temperature of the cell at 23 °C. We use silicone grease to improve thermal contact between the bottom side of the Si wafer and the Al plate. A high degree of temperature stability is important in these experiments because the differential thermal expansion of the Au film and the silicon microcantilever produce a significant change in the curvature of the microcantilever; if this thermal expansion stress is mistakenly interpreted as an interface stress, a temperature change of only 1 K produces a change in interface stress of approximately 50 mN m-1. This stress is given by the product of the biaxial modulus of the (111)-oriented Au layer 6/(4s11 + 8s12 + s44) ) 6/{4/[(c11 + 2c12)] + 1/c44)} ) 190 GPa,22,27 the Au layer thickness, 22 nm, and the difference between the thermal expansion coefficients of Au, 1.4 × 10-5 K-1, and Si, 0.26 × 10-5 K-1. Two syringe pumps, one containing pure water and a second containing a 5 wt % phenol-water mixture, are connected to the liquid cell through a mixing T-connector, a computer-controlled valve, and a syringe needle that serves as the input orifice to the liquid cell. The concentration of the liquid mixture in the cell is controlled by setting different dispensing speeds for the two syringe pumps. In each measurement cycle, we (i) open the valve, and dispense a total of 5 mL of liquid through the cell in 2.5 min; (ii) halt the liquid dispensing, close the valve, and allow the temperature to stabilize for 10 min; and finally (iii) record the curvature of the microcantilever. This cycle of events is then repeated for the next concentration of the phenol-water mixture. E. Sensitivity and Stability. We evaluated the sensitivity of the measurement by collecting data for three test configurations: a microcantilever in air, a microcantilever in water, and a solid mirror. In all cases, the output signal of the lock-in amplifier is converted to an interface stress using eqs 3 and 4. The rms noise of the signal from a microcantilever measured in air, 0.3 mN m-1, is similar to the rms noise measured when the microcantilever is replaced by a solid mirror; as expected, vibrations of the cantilever are not a limiting factor in the measurements. With the cantilever mounted in the liquid cell filled with water, the noise-level of interface stress is larger by a factor of approximately 2, 0.65 mN m-1. The long-term stability of the measurement is also good, see Figure 4. In this example, the stress shifts by approximately 6 mN m-1 after 4 h. Since the measurement interval in our experiments is typically 10 min, this slow drift in the measurement is not a limiting factor in our experiments. The precision and stability of our measurement system are both approximately an order of magnitude better than the approach described by Butt.15
III. Results Phenol-water mixtures were chosen for this initial study as a model system for amphophilic contaminants in water.28,29 The (27) Lide, D. R. CRC Handbook of Chemistry and Physics, 80th ed.; CRC Press LLC: Boca Raton, FL, 1999; pp 12-37. (28) Roostaei, N.; Tezel, F. H. J. EnViron. Manage. 2004, 70, 157-164. (29) Benalla, H.; Zajac, J.; Partyka, S.; Roziere, J. Colloids Surf. A 2002, 203, 259-271.
Interface Stress of SiO2 in Water-Phenol Mixtures
Figure 5. Measured changes in interface stress for a microcantilever sample with SiO2 formed by exposure of Si to ozone. In this series of measurements, the composition of the liquid in the cell is alternated between pure water and some concentration of phenol in water, and the cycle is repeated three times before changing to a different composition of phenol in water. The phenol concentration was varied from 5 to 1 wt % and back to 5 wt %. The total measurement time is approximately 11 h.
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Figure 7. Changes in the interface stress of thermally oxidized Si and hydrophilic SiO2 in phenol-water mixtures. In these series of measurements, the composition of the liquid in the cell is alternated between pure water and a 5 wt % concentration of phenol. In both cases, the total measurement time is approximately 3 h.
Figure 8. Average of the four sets of data from Figure 6 with comparisons to averages of the changes in the interface stress of two thermally oxidized Si samples and three hydrophilic SiO2 samples. Error bars denote the standard deviation of the measurements. Figure 6. Changes in interface stress versus concentration of phenol in water for SiO2 formed by exposure of Si to ozone. The four sets of data are for two experimental runs, labeled “run 1” and “run 2” of the type shown in Figure 5 using two different samples, labeled #1 and #2.
solubility of phenol in water is 8.66 wt %;30 we limited the highest concentration of phenol in our experiments to 5 wt % to avoid any complications that might arise by working near a phase boundary. When analyzing the raw data, we must take into account the small increase ∆n in the optical index of refraction of the phenolwater mixture relative to pure water. At 5 wt % phenol in water,31 ∆n ) 0.011. (The index of refraction of pure water is 1.331.) This is not a trivial correction to the measurement of the changes in the curvature of the microcantilever, see eq 4, because the microcantilever has a substantial background curvature created by stress in the Au and SiO2 layers and residual stress inhomogeneities introduced by the fabrication of the microcantilever. In other words, changes in curvature that result from changes in the interface stress are typically only a small fraction of the total curvature of the microcantilever, and even a small value of ∆n must be taken into account. We first consider data for SiO2 formed by exposure of the as-received cantilever to ozone, see Figures 5 and 6. Figure 5 shows the interface stress measured during cycling between pure water and some concentration of phenol in water. By alternating the concentration back and forth in this way we verify that the changes are reversible and reproducible. Figure 6 shows the averages of these measurements as a function of the phenol concentration. The reproducibility of the data from one run to the next is good; the reproducibility from one sample to the next is not as satisfying, but some general features are still clear: the (30) Lide, D. R. CRC Handbook of Chemistry and Physics, 80th ed.; CRC Press LLC: Boca Raton, FL, 1999; pp 8-96. (31) Campbell, A. N.; Campbell, A. J. R. J. Am. Chem. Soc. 1937, 59, 24812488.
change in interface stress is not linear in the phenol concentration and has a greater dependence on phenol concentration near the middle of the concentration range than at the ends. The change in interface stress consistently approaches ∆g ) -330 ( 30 mN m-1 at a phenol concentration of 5 wt %. The average of these four measurements is included in the summary shown as Figure 8. The changes in interface stress for the other two varieties of SiO2 (thermally oxidized Si and hydrophilic SiO2 formed by SC-1 treatment) are relatively small, and therefore we only studied changes in the liquid from pure water to a 5 wt % phenol solution, see Figure 7. This procedure was repeated on two samples of thermally oxidized Si and three samples of hydrophilic SiO2; the averages of those measurements are also included in the summary shown as Figure 8.
IV. Discussion and Conclusions We emphasize that the data summarized above are for the imbalance in the interface stress at the two sides of the microcantilever: (i) the Au-coated side of the microcantilever, and (ii) the side of the microcantilever that has SiO2 exposed to the liquid mixture. Thus, we cannot, for example, conclude that the interface stress of thermal oxide in contact with pure water is
