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A controlled-force stylus displacement probe
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A controlled-force stylus displacement probe D. G. Chetwynd,* X. Liu,* and S. T. Smitht Centre for Nanotechnology and Microengineering, University of Warwick, Coventry, UK, tPrecision Engineering Laboratory, University of North Carolina at Charlotte, Charlotte, NC, USA A novel design of displacement profiler with a controllable stylus force is presented. It provides highly controlled conditions for contact measurement of, for example, small step heights or surface roughness. Incorporating an electromagnetic force actuator and force feedback control, the profiler provides electronically selectable contact force in the range of 0.01-10 m N and gives a constant static and dynamic loading. In a typical configuration, it has a range of a few micrometers with a discrimination to better than 1 nm at a bandwidth higher than that of a conventional stylus instrument. © Elsevier Science Inc., 1996
Keywords: stylus instruments; surface profiling; force controb capacitive sensing Introduction There continues to be ever increasing demand for measurements of microdisplacement and the metrology of smooth surfaces, especially at the nanometer level in the applications of precision or superprecision engineering and nanotechnology. Applications are found in many fields and range from highly specialized components to massproduced ones: consider, for example, optical components for laser interferometers, lenses for compact disk players, telescopes and mirrors to reflect X-rays. The commercial atomic force microscope and scanning tunneling microscope (AFM/STM) offers a high resolution in both vertical and horizontal directions but with a limited range, normally only a few tens of micrometers. It is adequate for study of physical surfaces where atomic structures are the main interest. However, from an engineering point of view, the surface function is not only related to small-scale, local features of a surface but often more seriously related to its general features in a larger scale, with lateral ranges of millimeters or more. Stylus techniques remain in demand for measuring surface topography at both micrometer and nanometer levels vertically with large lateral ranges. They are capable of measuring height variation to 0.1 nm with lateral a resolution down to 0.1 pm by using low thermal expansion materials Address reprint requests to Dr. D. G. Chetwynd, Centre for Nanotechnology and Microengineering, University of Warwick, Coventry, UK. Precision Engineering 19:105-111, 1996 © Elsevier Science Inc., 1996 655 Avenue of the Americas, New York, NY 10010
and a very sharp stylus tip. 1'2 The fidelity of surface measurement by stylus methods is affected, physically and geometrically, by the interactions between the stylus tip and the surface being measured. The physical or mechanical interactions are mainly from tracking force, 3 frictional force, 4 and dynamic force, s and the geometrical interaction is from the shape and dimension of the stylus tip. 6-8 There is generally a compromise between limiting the contact stress at the tip and keeping the tracking force high enough for the stylus to follow the surface faithfully at reasonable measurement speeds: conventional instruments tend to use forces in the 0.1-100 mN range, the smaller values being used with smoother surfaces. With a very sharp stylus tip, a small stylus force and a slow traverse speed has to be used to avoid any risk of surface damage. However, at a light load, the spring rate of a stylus system and its dynamic force cause significant variations in the contact force, which may degrade the measured result through the variation of elastic deflection in the surface and stylus system. Therefore, a constant and low stylus force is important for nanometer scale metrology and desirable at the micrometer scale.
Instrumentation A schematic diagram of the profiler is shown in Figure 1. The probe has three active parts; the electromagnetic force actuator, a leaf spring suspension support, and a differential capacitive sensor. This combination is used to obtain high sensitivity while avoiding risks of cross talk between sub0141-6395/96/$15.00 PII S0141-6359(96)00008-6
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Mechanical design Overall, the sensor head is approximately 30-mm high and roughly a 25-mm square in cross section. It is intended primarily for use with the probe acting in a vertical axis, although operation in other orientations is possible. The mechanical loop structure is designed for low overall mass, while preserving a mounting system that can be used in many situations. With the exception of the stylus, which may be changed and so is outside immediate control, a low-expansion metrology loop strategy has been used to obtain thermal stability. The outer frame, mounting bracket, and much of the electrode systems are made of the ultralow expansion glass-ceramic "Zerodur", and elsewhere other low expansion materials or matched paths are used. The main section of the frame carries a pattern of slots for use as a kinematic clamp to hold the probe to the instrument within which it is being used. A central hole allows a screw fixing by which a spring can supply a force closure for this clamp. The top electrode of the differential capacitive sensor is an integral part of the main section, so ensuring high-quality registration of the gauge to the major loop of the instrument. The lower electrode is part of the base section of the probe head, also of Zerodur, and is clamped to the main section. The surfaces of these two parts that carry the electrodes are first optically polished to provide precision and rigidity at the clamped interface and then etched back in suitable places to give the required spacing for the electrodes, which are aluminium films evaporated onto the recessed surfaces. Because the recesses are single steps, shallow compared as to other dimensions of the electrodes, simple thermal evaporation is adequate for this. An upper section is clamped to the main section (all three parts are held by one pair of through bolts) and carries the coil of the force actuator held in a V-groove by a 106
simple clamp. This section is of aluminiunn because the force actuator is almost insensitive to small axial displacements; therefore, expansion there is not a significant issue. 9 The aluminium block acts as a heatsink for the small amount of heat dissipated in the coil, and by placing this at the top of the assembly, it can be convected to the atmosphere with minimal effect on the rest of the probe. A pair of beryllium-copper ligaments (leaf springs) is used to support a silica tube, forming a simple linear leaf-spring mechanism which defines the line of action of the probe. Each is cut from a 50-pm foil to give wide end pieces joined by two leaf springs 8-mm long, 4-mm wide, and spaced 18-ram apart at their center lines. At its upper end, a neodymium-boron-iron magnet forms the second element of the force actuator. At the lower ligament, the tube abuts a supporting bush and an extension rod of Zerodur, which forms the stylus location pin. The two ligaments are trapped between the three sections of the outer structure when they are clamped. The mismatch of expansion coefficients between the silica tube and the Zerodur frame may cause a slight fluctuation in the parallelism of the ligaments, but this has negligible effect on performance. Part of the lower ligament is used as the central, moving electrode of the capacitive gauge, so all the stylus arm that is directly part of the metrology loop is of Zerodur. The steps on the frame that carry the outer electrodes are etched asymmetrically, with the lower one larger than the upper. Ligament deflection attributable to the selfweight of the stylus assembly, partly supported by the force actuator, then causes the electrode to sit in the center of the gap. This ensures that, in normal operation, the ligaments are always bending in the same direction, because it is as they pass through the undeflected position that imperfections in the clamping are most likely to impose nonlinearities on the dynamics. The stylus mounting pin is similar to those used on the Rank-Taylor-Hobson Talystep and Nanostep instruments. This both allows for ease of comparison between instruments and provides a ready source of well-defined tips. Finally, a simple outer case of sheet aluminium provides both mechanical protection and additional electrical screening for the capacitive gauge.
Displacement gauging Capacitive sensing allows very precise practical measurement, because a capacitor does not suffer the Johnson noise or shot noise associated with the use of resistors and semiconductors. Modern electronics provide high resolution on measurement of capacitance, of the order of 10-18-10 -19 F for the low-bandwidth regime with good DC stability of interest here. 1°'11 One major source of noise is the variation of stray capacitance of the sensor OCTOBER/NOVEMBER 1996 VOL 19 NO 2/3
Chetwynd et al.: Controlled-force stylus displacement probe plates, circuit, and wiring cable layout, and often a large variation of stray capacitance between the sensor plate and the sample might be seen when lowering the probe onto the sample. With nonconductive samples, an electrostatic charge could be generated that causes charge redistribution on the sensor plates and thus changes the sensor signal. Guarding and screening reduces such effects but only to a certain level. Hence, a differential capacitive sensor is used here in which two capacitors having nearly identical characteristics work in a push-pull mode. The method is well known for its high sensitivity and high rejection to such common mode disturbances as variations of stray capacitances, thermal drift, and electromagnetic interference. The better the two capacitors match in perf o r m a n c e , the h i g h e r the r e j e c t i o n of such variations. The displacement of the probe tip is monitored, through the moving electrode, by the differential capacitive sensor. The central moving electrode is an integral part of the lower ligament of the probe. It is larger than the two static electrodes, thus helping to protect against fringe effects. They are each rectangular (with the longer edge perpendicular to the paper in the view of Figure 1) 10 mm x 3 mm. Atthe neutral position, the nominal gap for each capacitor is about 25 pm. A large gap is chosen here to facilitate alignment of the moving electrode, while the reduced sensitivity is compensated by the differential operation mode. In operation, an upward displacement of the probe tip deflects the ligament cantilever, and, thus, increases the upper capacitance and decreases the lower one, providing a differential signal that is detected by an AC bridge. The bridge signal is amplified and filtered to give an output proportional to the stylus displacement and at the same time is partially fedback through a current drive unit to the force actuator to maintain a constant tracking force.
Force actuator The force actuator consists of a n e o d y m i u m boron-iron magnet, 3-ram diameter, and 2-mm long and a coil assembly with internal and external diameters of 4 and 10 mm, respectively, and length of 12 ram. The magnet is attached to one end of the cantilever assembly and positioned axially and near the end of the coil through which an electric current is passed. The interaction of the magnetic field gradient of the coil and the permanent magnet produces a force on the latter that is directly proportional to the current, nonhysteretic, independent of small axial displacements of the magnet, and highly reproducible. 9 The optimum position of the magnet relative to the coil is that which maximizes the force for any given current. A specially designed current drive has been built that can provide a stable, electrically set, static contact force at the neutral position with a noise PRECISION ENGINEERING
level of less than 1 tJN. Force variation caused by the deflection of the ligaments as the probe is traversed over a surface is controlled by a proportional feedback loop. This proportional signal is generated from the output of the differential capacitive sensor and then fed to the input of the current drive, where it modulates the current/force about its set point to compensate for force variation attributable to the deflection of the ligaments as the probe is traversed. The drive current can be varied up to -130 mA with a relative precision of 2 x 10 -5 . It is noted that the mechanical design is such that the force actuator should always act "upw a r d " to balance the self-weight of the stylus assembly, so the drive current is normally negative: specifying it thus avoids potential confusion with the various control strategies that can be applied.
Force control loop As shown in Figure 2, the profile of a surface imposes a displacement on the stylus assembly, which is registered by the differential capacitive sensor. The changes in capacitance are detected by an AC bridge system specifically designed for gauge applications, with extremely good stability under static signals: a slightly modified version of the commercial NS2000 (Queensgate Instruments, Ltd). The bridge output is a voltage closely linear with the displacement of the gauge. This is preamplified and then passed to both an output unit and a feedback control unit. At the output unit, the signal is filtered at two optional bandwidths and further amplified to give a voltage output proportional to the surface profile, while at the other unit, the signal is fed through a proportional controller to the current drive and the magnet/coil actuator to adjust the force at the stylus. Owing to its position input, the force feedback loop can, potentially, be configured into t w o modes; positive mode and negative mode. Note here that "positive" implies that upward movement of the stylus causes a lifting force; that is, the change in the force is in the same direction as the change in the displacement. The positive feedback, which is the present configuration, is used to main-
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Figure 2 Block diagram of the controlled force stylus displacement profiler 107
Chetwynd et al.: Controlled-force stylus displacement probe tain the contact force between the stylus tip and a specimen at a fairly constant level (the set force), while the negative feedback mode can be used, in effect, to stiffen the leaf spring support. The former has higher sensitivity and modest bandwidth. The latter provides a higher bandwidth at the cost of lower sensitivity and an increased variation of contact force with stylus displacement, but may have applications where the measuring speed is of major importance. A third possibility is to feed back a displacement derivative term that can set the damping to give a near-ideal dynamic behavior for surface following. This mode has been demonstrated on other systems, 5 where it was shown to be more effective to use a separate velocity sensor. Because a compact probe head was desired here, this approach has not been implemented in the present device.
Experiments and results Displacement calibration The characteristics of displacement and the contact force of the probe were tested in a metrology laboratory with temperature and humidity controlled at 20 _+ 1°C and 40 _+ 5% RH. An IBM PS/2 model 70 computer and a Metrabyte DAS-16 data-acquisition board were used for all data acquisition and processing. Displacement tests were carried out by loading the probe tip against a digital piezoelectric translator (DPT from Queensgate Instruments, Ltd.), which provides direct reading and repeatability to 1 nm, referenced to its internal capacitive gauge. The DPT was ramped to give specific ranges, and the response of the probe was recorded. Factoryprovided calibration against laser interferometry indicates that over any part range used in our tests its linearity is considerably better than 0.1%, so the results given below are dominated by the errors of the probe, with little chance of significant "accidental" error compensation occurring. Using different parts of the DPT range to test the same part of the probe's range gave further confidence to this opinion. For reasons of flatness of the moving electrode (beryllium-copper foil with a thickness of 50 IJm) and its parallelism to the fixed electrodes, the two capacitors are not exactly the same in capacitance at the nominal gap. The best balance point, is, then, not necessarily in the center of the gap between the fixed electrodes. In consequence, the effective output of the sensor is from - 6 - 0 V as the stylus is lifted. Further lifting will short the two electrodes and, thus, cause the output to jump to the +14 V. For a required range, say a few micrometers, the sensor could be operated anywhere within this effective output range, although the calibration will be slightly different at different points because of the nonlinearity of the gauge and cantilever parasitic distortions. Figure 3 shows a typical plot of the probe output against the displacement of the DPT, 108
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Force calibration The characteristic of the force actuator was tested by loading the probe onto a force-measuring device, made from a linear (notch hinge) elastic mechanism and an inductive transducer (based on the Talystep gauge head), which was calibrated by dead weight l o a d i n g ) T h e monitored readings of current, force, and the probe output as a ramp voltage was input through a D/A converter to the current drive are plotted in Figure 4. Linearity of this force actuator is excellent. It is noted that a current Calibr~io~ of Variabk focm probe
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Chetwynd et al.: Controlled-force stylus displacement probe of -58.83 mA is needed to lift the stylus assembly, which weighs about 0.95 g. Thus, the loading force can be varied between near zero up to 10 mN; whereas, a positive current will deliver even higher force.
Force compensation The stability of the contact force between the stylus tip and a surface was tested by attaching the whole probe to a DPT, and loading its stylus against the force measuring device. The DPT was ramped to give a displacement of about 1 pro, which should cause the probe to deflect by the same amount. The output of the probe, the force at the stylus tip, and the current were monitored. Results of measurements on contact force and displacement with and without feedback force compensation are plotted in Figure 5in which the solid line represents the result with the feedback and the dashed line is without feedback. In both cases, the nominal contact force was 1.0 raN. With the feedback compensation, the contact force between the tip and the surface is kept nearly constant, with slightly over 10 pN total variation on the up-slope ramp but well below 10 IJN on the down-slope ramp. The relatively large variations of force at the start-up and the turning points are attributable to the combined characteristic of the DPT response time, the proportional feedback, and the voltage to current drive when responding to this artificial signal: operation on continuous signals would be much smoother once the servo had settled. Without the feedback on, the contact force varied nearly 0.7 mN, and this caused the output of the probe to change by about 0.1 IJm less than it should because of deflection of
the force-measuring device and indentation of the tip into the relatively compliant aluminium surface. Tests were also made at a more general condition. A signal produced previously from a Talysurf 5 as it traversed on a copper specimen that had been polished and then lightly abraded was applied to the DPT to simulate the situation of the probe being traversed over a surface. The bandwidth of this signal, limited by the Talysurf response, was well within that of the DPT, so the simulation should have good fidelity. As the probe was forced to deflect, the displacement output, contact force, and the current were monitored and are plotted in Figure 6. It can be seen that, with the feedback, the force varied over a range of about 19 pN. This is slightly higher than expected and is thought to be attributable to the step changes of the input signal that was sent through a D/A converter being too fast for the feedback loop to cope with. (It is possible that transients at the DPT as it is stepped from point to point could have contributed to the effect seen, but our experience with such systems suggests that a significant contribution is unlikely.) Smaller variation would occur with real surfaces that are normally continuous and smooth. As seen from the graph, the force, without feedback on, varied nearly 0.5 mN. Small but noticeable deviations in profile occur, especially at the peaks when the compensation is switched off, and these are not all artifacts of the measurement method. The largest differences are a few tens of nanometers, about 10% of the total height for this profile. Provided the distortion is not indicative of surface damage, profile errors of this type and size are probably negligible for situations where an averaging parameter such as Rq is adequate, of some con0.6
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Chetwynd et al.: Controlled-force stylus displacement probe cern if peak amplitudes are required, but could be of considerable importance if, say, peak curvatures were being used for tribological studies. At both sets of tests, with ramps and with simulated inputs, the feedback force produced by the drive current is a mirror image of the additional force attributable to the deflection of the cantilever.
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For completeness, the probe was tested on a grating specimen for surface profiling to the nanometer level. A nominally 40-nm peak-to-valley amplitude sinusoidal grating was used, measured with a tip radius, about 10 IJm, large compared to its pitch of 0.86 pm to provide a periodic signal of about 20-nm amplitude. Although a convenient way of obtaining a smaller signal, the large size of the stylus tip used causes the profile of the grating to be somewhat distorted in shape. For such a surface, the tip radius of the stylus has to be less than about 0.9 pm if it is to follow accurately. 12 A piezoelectric driven x-y stage from Queensgate Instruments was used to translate the specimen. Figure 8shows an SEM micrograph of the grating surface and the profile of the surface measured by the probe. The profile shows general consistency, small features, and a noise level that add further confidence that the probe behaves properly on nanometer sized featu res.
The ability to provide a spring-rate compensation through the force feedback allows a much stiffer set of ligaments to be used to support the probe arm than is otherwise the case. This, in turn, leads to greater stiffness in other (parasitic) motions and so reduces sensitivity to any twisting or lateral displacement generated from friction between the tip and the surface during traversing. The uncompensated spring rate was evaluated by inputting a step current into the coil while the probe was freely suspended, following the calibration of the coil, above. The mean value was found to be 612.7 N m -1. From the dynamic tests described above, the compensated effective spring rate is around 10 N m - ' f o r typical signals, but there is relatively low confidence on this value, because it is near the limits of measurement capability that involves the resolution of the force-measuring device, loading, and contact conditions. By a simple "hammer test" of the probe, hanging free, the primary response was found to be about 235 Hz. Figure 7 shows the response of the probe to a gentle tap as recorded by a digital spectrum analyzer, Advantest TR9403: the direct output of the instrument is shown with the upper trace indicating the time record of output voltage and the lower one a Bode plot in dB (arbitrary zero reference) against log frequency. The observed resonance is caused by the lowest mode vibration of the moving gauge electrode. The resonance of the whole probe and the ligament assembly is about 60
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Chetwynd et al.: Controlled-force stylus displacement probe r~sl~oiis'e. Making the electrode simply part of the lower ligament achieves this but introduces potential errors, because it is so thin. Experience from the evaluation of the probe not only shows good characteristics but indicates that, within reason, the mass is not critical. It appears, therefore, that even better performance may be obtainable with a more rigid electrode. This w o u l d have the added advantage of making the assembly of the probe somewhat easier. Thus, we propose to build and evaluate a modified version of the system that has glass reinforcement over the whole area of the electrode, rather than just a small support at the stylus pin.
Conclusion A new stylus-type profilometer with force control has been demonstrated that is capable of measuring surface features up to a few micrometers with a resolution of better than 1 nm. The contact force between the stylus tip and the surface being measured can be varied for different requirements and then kept constant during measurement. Force variation about the 1 mN nominal can be reduced to b e l o w 50 pN and profile f i d e l i t y i m p r o v e d through the reduction of " l o s t m o t i o n " from elastic deformations.
Acknowledgments The authors express their gratitude to L. Davis, H. Hingle, and t e c h n i c i a n s in the Centre for Nanotechnology and Microengineering, University of War-
PRECISION ENGINEERING
wick. S p o n s o r s h i p from DTI National Measurements Programme, Project MPU 8/01.8 in enabling the initial prototype testing is acknowledged.
References 1 Garratt, J. D. and Bottomley, S. C. "Technology transfer in the development of a nanotopographic instrument," Nanotechnology 1990, 1, 38-43 2 Lindsey, K., Smith, S. T. and Robbie, C. J. "Subnanometre surface texture and profile measurement with Nanosurf 2," Ann ClRP 1988, 37, 519-522 3 Chetwynd D. G., X. Liu and Smith, S. T. "Signal fidelity and tracking force in stylus profilometry," Int J Mach Tools Manuf 1992, 32, 239-245 4 Liu, X., Smith, S. T. and Chetwynd, D. G. Frictional forces between a diamond stylus and specimens at low load. "Wear", 1992, 157, 279-294 5 Liu, X., Chetwynd, D. G. and Smith, S. T. "Improvement of fidelity of surface measurement by active damping controls," Meas Sci Technol 1993, 4, 1330-1340 6 Whitehouse, D.J. Handbook of Surface Metrology. Philadelphia & London: Institute of Physics, 1994, 378-600 7 Whitehouse D. J. "'A revised philosophy of surface measuring systems," Proc Inst Mech Engs 1988, 202, 169-185 8 Thomas, T. R., ed. Rough Surfaces, London: Longman, 1982, 21-24 9 Smith, S.T. and Chetwynd, D. G. "An optimised magnetcoil force actuator and its application to precision elastic mechanisms," Proc Inst Mech Engs 1990, 204C, 243-253 10 Jones, R. V. and Richards, J. C. S. "The design and some applications of sensitive capacitance micrometers," J Phys E Sci Instrum 1973, 6, 589-600 11 Neubauer, G., Cohen, S. R., McClelland, G. M., Horne, D. and Mate, C. M. "Force microscopy with a bidirectional capacitance sensor," Rev Sci Instrm 1990, 61, 2296-2308 12 Bennett, J. M. and Dancy, J. H. "Stylus profiling instrument for measuring statistical properties of smooth optical surfaces," Appl Optics 1981, 20, 1785-1802
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A controlled-force stylus displacement probe D. G. Chetwynd,* X. Liu,* and S. T. Smitht Centre for Nanotechnology and Microengineering, University of Warwick, Coventry, UK, tPrecision Engineering Laboratory, University of North Carolina at Charlotte, Charlotte, NC, USA A novel design of displacement profiler with a controllable stylus force is presented. It provides highly controlled conditions for contact measurement of, for example, small step heights or surface roughness. Incorporating an electromagnetic force actuator and force feedback control, the profiler provides electronically selectable contact force in the range of 0.01-10 m N and gives a constant static and dynamic loading. In a typical configuration, it has a range of a few micrometers with a discrimination to better than 1 nm at a bandwidth higher than that of a conventional stylus instrument. © Elsevier Science Inc., 1996
Keywords: stylus instruments; surface profiling; force controb capacitive sensing Introduction There continues to be ever increasing demand for measurements of microdisplacement and the metrology of smooth surfaces, especially at the nanometer level in the applications of precision or superprecision engineering and nanotechnology. Applications are found in many fields and range from highly specialized components to massproduced ones: consider, for example, optical components for laser interferometers, lenses for compact disk players, telescopes and mirrors to reflect X-rays. The commercial atomic force microscope and scanning tunneling microscope (AFM/STM) offers a high resolution in both vertical and horizontal directions but with a limited range, normally only a few tens of micrometers. It is adequate for study of physical surfaces where atomic structures are the main interest. However, from an engineering point of view, the surface function is not only related to small-scale, local features of a surface but often more seriously related to its general features in a larger scale, with lateral ranges of millimeters or more. Stylus techniques remain in demand for measuring surface topography at both micrometer and nanometer levels vertically with large lateral ranges. They are capable of measuring height variation to 0.1 nm with lateral a resolution down to 0.1 pm by using low thermal expansion materials Address reprint requests to Dr. D. G. Chetwynd, Centre for Nanotechnology and Microengineering, University of Warwick, Coventry, UK. Precision Engineering 19:105-111, 1996 © Elsevier Science Inc., 1996 655 Avenue of the Americas, New York, NY 10010
and a very sharp stylus tip. 1'2 The fidelity of surface measurement by stylus methods is affected, physically and geometrically, by the interactions between the stylus tip and the surface being measured. The physical or mechanical interactions are mainly from tracking force, 3 frictional force, 4 and dynamic force, s and the geometrical interaction is from the shape and dimension of the stylus tip. 6-8 There is generally a compromise between limiting the contact stress at the tip and keeping the tracking force high enough for the stylus to follow the surface faithfully at reasonable measurement speeds: conventional instruments tend to use forces in the 0.1-100 mN range, the smaller values being used with smoother surfaces. With a very sharp stylus tip, a small stylus force and a slow traverse speed has to be used to avoid any risk of surface damage. However, at a light load, the spring rate of a stylus system and its dynamic force cause significant variations in the contact force, which may degrade the measured result through the variation of elastic deflection in the surface and stylus system. Therefore, a constant and low stylus force is important for nanometer scale metrology and desirable at the micrometer scale.
Instrumentation A schematic diagram of the profiler is shown in Figure 1. The probe has three active parts; the electromagnetic force actuator, a leaf spring suspension support, and a differential capacitive sensor. This combination is used to obtain high sensitivity while avoiding risks of cross talk between sub0141-6395/96/$15.00 PII S0141-6359(96)00008-6
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Figure 1 Schematic diagram of the constant force displacement probe systems. The design process must consider together the strengths and weaknesses of all the subsystems if optimum performance is to be obtained, but it is convenient to consider them separately below.
Mechanical design Overall, the sensor head is approximately 30-mm high and roughly a 25-mm square in cross section. It is intended primarily for use with the probe acting in a vertical axis, although operation in other orientations is possible. The mechanical loop structure is designed for low overall mass, while preserving a mounting system that can be used in many situations. With the exception of the stylus, which may be changed and so is outside immediate control, a low-expansion metrology loop strategy has been used to obtain thermal stability. The outer frame, mounting bracket, and much of the electrode systems are made of the ultralow expansion glass-ceramic "Zerodur", and elsewhere other low expansion materials or matched paths are used. The main section of the frame carries a pattern of slots for use as a kinematic clamp to hold the probe to the instrument within which it is being used. A central hole allows a screw fixing by which a spring can supply a force closure for this clamp. The top electrode of the differential capacitive sensor is an integral part of the main section, so ensuring high-quality registration of the gauge to the major loop of the instrument. The lower electrode is part of the base section of the probe head, also of Zerodur, and is clamped to the main section. The surfaces of these two parts that carry the electrodes are first optically polished to provide precision and rigidity at the clamped interface and then etched back in suitable places to give the required spacing for the electrodes, which are aluminium films evaporated onto the recessed surfaces. Because the recesses are single steps, shallow compared as to other dimensions of the electrodes, simple thermal evaporation is adequate for this. An upper section is clamped to the main section (all three parts are held by one pair of through bolts) and carries the coil of the force actuator held in a V-groove by a 106
simple clamp. This section is of aluminiunn because the force actuator is almost insensitive to small axial displacements; therefore, expansion there is not a significant issue. 9 The aluminium block acts as a heatsink for the small amount of heat dissipated in the coil, and by placing this at the top of the assembly, it can be convected to the atmosphere with minimal effect on the rest of the probe. A pair of beryllium-copper ligaments (leaf springs) is used to support a silica tube, forming a simple linear leaf-spring mechanism which defines the line of action of the probe. Each is cut from a 50-pm foil to give wide end pieces joined by two leaf springs 8-mm long, 4-mm wide, and spaced 18-ram apart at their center lines. At its upper end, a neodymium-boron-iron magnet forms the second element of the force actuator. At the lower ligament, the tube abuts a supporting bush and an extension rod of Zerodur, which forms the stylus location pin. The two ligaments are trapped between the three sections of the outer structure when they are clamped. The mismatch of expansion coefficients between the silica tube and the Zerodur frame may cause a slight fluctuation in the parallelism of the ligaments, but this has negligible effect on performance. Part of the lower ligament is used as the central, moving electrode of the capacitive gauge, so all the stylus arm that is directly part of the metrology loop is of Zerodur. The steps on the frame that carry the outer electrodes are etched asymmetrically, with the lower one larger than the upper. Ligament deflection attributable to the selfweight of the stylus assembly, partly supported by the force actuator, then causes the electrode to sit in the center of the gap. This ensures that, in normal operation, the ligaments are always bending in the same direction, because it is as they pass through the undeflected position that imperfections in the clamping are most likely to impose nonlinearities on the dynamics. The stylus mounting pin is similar to those used on the Rank-Taylor-Hobson Talystep and Nanostep instruments. This both allows for ease of comparison between instruments and provides a ready source of well-defined tips. Finally, a simple outer case of sheet aluminium provides both mechanical protection and additional electrical screening for the capacitive gauge.
Displacement gauging Capacitive sensing allows very precise practical measurement, because a capacitor does not suffer the Johnson noise or shot noise associated with the use of resistors and semiconductors. Modern electronics provide high resolution on measurement of capacitance, of the order of 10-18-10 -19 F for the low-bandwidth regime with good DC stability of interest here. 1°'11 One major source of noise is the variation of stray capacitance of the sensor OCTOBER/NOVEMBER 1996 VOL 19 NO 2/3
Chetwynd et al.: Controlled-force stylus displacement probe plates, circuit, and wiring cable layout, and often a large variation of stray capacitance between the sensor plate and the sample might be seen when lowering the probe onto the sample. With nonconductive samples, an electrostatic charge could be generated that causes charge redistribution on the sensor plates and thus changes the sensor signal. Guarding and screening reduces such effects but only to a certain level. Hence, a differential capacitive sensor is used here in which two capacitors having nearly identical characteristics work in a push-pull mode. The method is well known for its high sensitivity and high rejection to such common mode disturbances as variations of stray capacitances, thermal drift, and electromagnetic interference. The better the two capacitors match in perf o r m a n c e , the h i g h e r the r e j e c t i o n of such variations. The displacement of the probe tip is monitored, through the moving electrode, by the differential capacitive sensor. The central moving electrode is an integral part of the lower ligament of the probe. It is larger than the two static electrodes, thus helping to protect against fringe effects. They are each rectangular (with the longer edge perpendicular to the paper in the view of Figure 1) 10 mm x 3 mm. Atthe neutral position, the nominal gap for each capacitor is about 25 pm. A large gap is chosen here to facilitate alignment of the moving electrode, while the reduced sensitivity is compensated by the differential operation mode. In operation, an upward displacement of the probe tip deflects the ligament cantilever, and, thus, increases the upper capacitance and decreases the lower one, providing a differential signal that is detected by an AC bridge. The bridge signal is amplified and filtered to give an output proportional to the stylus displacement and at the same time is partially fedback through a current drive unit to the force actuator to maintain a constant tracking force.
Force actuator The force actuator consists of a n e o d y m i u m boron-iron magnet, 3-ram diameter, and 2-mm long and a coil assembly with internal and external diameters of 4 and 10 mm, respectively, and length of 12 ram. The magnet is attached to one end of the cantilever assembly and positioned axially and near the end of the coil through which an electric current is passed. The interaction of the magnetic field gradient of the coil and the permanent magnet produces a force on the latter that is directly proportional to the current, nonhysteretic, independent of small axial displacements of the magnet, and highly reproducible. 9 The optimum position of the magnet relative to the coil is that which maximizes the force for any given current. A specially designed current drive has been built that can provide a stable, electrically set, static contact force at the neutral position with a noise PRECISION ENGINEERING
level of less than 1 tJN. Force variation caused by the deflection of the ligaments as the probe is traversed over a surface is controlled by a proportional feedback loop. This proportional signal is generated from the output of the differential capacitive sensor and then fed to the input of the current drive, where it modulates the current/force about its set point to compensate for force variation attributable to the deflection of the ligaments as the probe is traversed. The drive current can be varied up to -130 mA with a relative precision of 2 x 10 -5 . It is noted that the mechanical design is such that the force actuator should always act "upw a r d " to balance the self-weight of the stylus assembly, so the drive current is normally negative: specifying it thus avoids potential confusion with the various control strategies that can be applied.
Force control loop As shown in Figure 2, the profile of a surface imposes a displacement on the stylus assembly, which is registered by the differential capacitive sensor. The changes in capacitance are detected by an AC bridge system specifically designed for gauge applications, with extremely good stability under static signals: a slightly modified version of the commercial NS2000 (Queensgate Instruments, Ltd). The bridge output is a voltage closely linear with the displacement of the gauge. This is preamplified and then passed to both an output unit and a feedback control unit. At the output unit, the signal is filtered at two optional bandwidths and further amplified to give a voltage output proportional to the surface profile, while at the other unit, the signal is fed through a proportional controller to the current drive and the magnet/coil actuator to adjust the force at the stylus. Owing to its position input, the force feedback loop can, potentially, be configured into t w o modes; positive mode and negative mode. Note here that "positive" implies that upward movement of the stylus causes a lifting force; that is, the change in the force is in the same direction as the change in the displacement. The positive feedback, which is the present configuration, is used to main-
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Figure 2 Block diagram of the controlled force stylus displacement profiler 107
Chetwynd et al.: Controlled-force stylus displacement probe tain the contact force between the stylus tip and a specimen at a fairly constant level (the set force), while the negative feedback mode can be used, in effect, to stiffen the leaf spring support. The former has higher sensitivity and modest bandwidth. The latter provides a higher bandwidth at the cost of lower sensitivity and an increased variation of contact force with stylus displacement, but may have applications where the measuring speed is of major importance. A third possibility is to feed back a displacement derivative term that can set the damping to give a near-ideal dynamic behavior for surface following. This mode has been demonstrated on other systems, 5 where it was shown to be more effective to use a separate velocity sensor. Because a compact probe head was desired here, this approach has not been implemented in the present device.
Experiments and results Displacement calibration The characteristics of displacement and the contact force of the probe were tested in a metrology laboratory with temperature and humidity controlled at 20 _+ 1°C and 40 _+ 5% RH. An IBM PS/2 model 70 computer and a Metrabyte DAS-16 data-acquisition board were used for all data acquisition and processing. Displacement tests were carried out by loading the probe tip against a digital piezoelectric translator (DPT from Queensgate Instruments, Ltd.), which provides direct reading and repeatability to 1 nm, referenced to its internal capacitive gauge. The DPT was ramped to give specific ranges, and the response of the probe was recorded. Factoryprovided calibration against laser interferometry indicates that over any part range used in our tests its linearity is considerably better than 0.1%, so the results given below are dominated by the errors of the probe, with little chance of significant "accidental" error compensation occurring. Using different parts of the DPT range to test the same part of the probe's range gave further confidence to this opinion. For reasons of flatness of the moving electrode (beryllium-copper foil with a thickness of 50 IJm) and its parallelism to the fixed electrodes, the two capacitors are not exactly the same in capacitance at the nominal gap. The best balance point, is, then, not necessarily in the center of the gap between the fixed electrodes. In consequence, the effective output of the sensor is from - 6 - 0 V as the stylus is lifted. Further lifting will short the two electrodes and, thus, cause the output to jump to the +14 V. For a required range, say a few micrometers, the sensor could be operated anywhere within this effective output range, although the calibration will be slightly different at different points because of the nonlinearity of the gauge and cantilever parasitic distortions. Figure 3 shows a typical plot of the probe output against the displacement of the DPT, 108
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and the displacement taken in the central region of the permitted range. The linearity of the probe (here quoted as rms deviation from the linear least-squares straight line fit, because measurement noise overly influences peak deviations) is 0.2% over a range of _+1 pm. There is no noticeable hysteresis within this range. The slope ofthe least-squares line then gives a calibrated sensitivity for the probe of 0.27 V pm -1. Doubling the range reduced the linearity to approximately 0.5%.
Force calibration The characteristic of the force actuator was tested by loading the probe onto a force-measuring device, made from a linear (notch hinge) elastic mechanism and an inductive transducer (based on the Talystep gauge head), which was calibrated by dead weight l o a d i n g ) T h e monitored readings of current, force, and the probe output as a ramp voltage was input through a D/A converter to the current drive are plotted in Figure 4. Linearity of this force actuator is excellent. It is noted that a current Calibr~io~ of Variabk focm probe
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actuator OCTOBER/NOVEMBER 1996 VOL 19 NO 2/3
Chetwynd et al.: Controlled-force stylus displacement probe of -58.83 mA is needed to lift the stylus assembly, which weighs about 0.95 g. Thus, the loading force can be varied between near zero up to 10 mN; whereas, a positive current will deliver even higher force.
Force compensation The stability of the contact force between the stylus tip and a surface was tested by attaching the whole probe to a DPT, and loading its stylus against the force measuring device. The DPT was ramped to give a displacement of about 1 pro, which should cause the probe to deflect by the same amount. The output of the probe, the force at the stylus tip, and the current were monitored. Results of measurements on contact force and displacement with and without feedback force compensation are plotted in Figure 5in which the solid line represents the result with the feedback and the dashed line is without feedback. In both cases, the nominal contact force was 1.0 raN. With the feedback compensation, the contact force between the tip and the surface is kept nearly constant, with slightly over 10 pN total variation on the up-slope ramp but well below 10 IJN on the down-slope ramp. The relatively large variations of force at the start-up and the turning points are attributable to the combined characteristic of the DPT response time, the proportional feedback, and the voltage to current drive when responding to this artificial signal: operation on continuous signals would be much smoother once the servo had settled. Without the feedback on, the contact force varied nearly 0.7 mN, and this caused the output of the probe to change by about 0.1 IJm less than it should because of deflection of
the force-measuring device and indentation of the tip into the relatively compliant aluminium surface. Tests were also made at a more general condition. A signal produced previously from a Talysurf 5 as it traversed on a copper specimen that had been polished and then lightly abraded was applied to the DPT to simulate the situation of the probe being traversed over a surface. The bandwidth of this signal, limited by the Talysurf response, was well within that of the DPT, so the simulation should have good fidelity. As the probe was forced to deflect, the displacement output, contact force, and the current were monitored and are plotted in Figure 6. It can be seen that, with the feedback, the force varied over a range of about 19 pN. This is slightly higher than expected and is thought to be attributable to the step changes of the input signal that was sent through a D/A converter being too fast for the feedback loop to cope with. (It is possible that transients at the DPT as it is stepped from point to point could have contributed to the effect seen, but our experience with such systems suggests that a significant contribution is unlikely.) Smaller variation would occur with real surfaces that are normally continuous and smooth. As seen from the graph, the force, without feedback on, varied nearly 0.5 mN. Small but noticeable deviations in profile occur, especially at the peaks when the compensation is switched off, and these are not all artifacts of the measurement method. The largest differences are a few tens of nanometers, about 10% of the total height for this profile. Provided the distortion is not indicative of surface damage, profile errors of this type and size are probably negligible for situations where an averaging parameter such as Rq is adequate, of some con0.6
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Chetwynd et al.: Controlled-force stylus displacement probe cern if peak amplitudes are required, but could be of considerable importance if, say, peak curvatures were being used for tribological studies. At both sets of tests, with ramps and with simulated inputs, the feedback force produced by the drive current is a mirror image of the additional force attributable to the deflection of the cantilever.
Hz, but this characteristic is highly damped and was observed in the probe output signal only with great difficulty. Neither of these resonances will have significant effect within the design bandwidth of the probe.
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For completeness, the probe was tested on a grating specimen for surface profiling to the nanometer level. A nominally 40-nm peak-to-valley amplitude sinusoidal grating was used, measured with a tip radius, about 10 IJm, large compared to its pitch of 0.86 pm to provide a periodic signal of about 20-nm amplitude. Although a convenient way of obtaining a smaller signal, the large size of the stylus tip used causes the profile of the grating to be somewhat distorted in shape. For such a surface, the tip radius of the stylus has to be less than about 0.9 pm if it is to follow accurately. 12 A piezoelectric driven x-y stage from Queensgate Instruments was used to translate the specimen. Figure 8shows an SEM micrograph of the grating surface and the profile of the surface measured by the probe. The profile shows general consistency, small features, and a noise level that add further confidence that the probe behaves properly on nanometer sized featu res.
The ability to provide a spring-rate compensation through the force feedback allows a much stiffer set of ligaments to be used to support the probe arm than is otherwise the case. This, in turn, leads to greater stiffness in other (parasitic) motions and so reduces sensitivity to any twisting or lateral displacement generated from friction between the tip and the surface during traversing. The uncompensated spring rate was evaluated by inputting a step current into the coil while the probe was freely suspended, following the calibration of the coil, above. The mean value was found to be 612.7 N m -1. From the dynamic tests described above, the compensated effective spring rate is around 10 N m - ' f o r typical signals, but there is relatively low confidence on this value, because it is near the limits of measurement capability that involves the resolution of the force-measuring device, loading, and contact conditions. By a simple "hammer test" of the probe, hanging free, the primary response was found to be about 235 Hz. Figure 7 shows the response of the probe to a gentle tap as recorded by a digital spectrum analyzer, Advantest TR9403: the direct output of the instrument is shown with the upper trace indicating the time record of output voltage and the lower one a Bode plot in dB (arbitrary zero reference) against log frequency. The observed resonance is caused by the lowest mode vibration of the moving gauge electrode. The resonance of the whole probe and the ligament assembly is about 60
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General observations On this first prototype, there was considerable motivation to minimize the mass supported directly by the spring ligaments to the benefit of its dynamic
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Chetwynd et al.: Controlled-force stylus displacement probe r~sl~oiis'e. Making the electrode simply part of the lower ligament achieves this but introduces potential errors, because it is so thin. Experience from the evaluation of the probe not only shows good characteristics but indicates that, within reason, the mass is not critical. It appears, therefore, that even better performance may be obtainable with a more rigid electrode. This w o u l d have the added advantage of making the assembly of the probe somewhat easier. Thus, we propose to build and evaluate a modified version of the system that has glass reinforcement over the whole area of the electrode, rather than just a small support at the stylus pin.
Conclusion A new stylus-type profilometer with force control has been demonstrated that is capable of measuring surface features up to a few micrometers with a resolution of better than 1 nm. The contact force between the stylus tip and the surface being measured can be varied for different requirements and then kept constant during measurement. Force variation about the 1 mN nominal can be reduced to b e l o w 50 pN and profile f i d e l i t y i m p r o v e d through the reduction of " l o s t m o t i o n " from elastic deformations.
Acknowledgments The authors express their gratitude to L. Davis, H. Hingle, and t e c h n i c i a n s in the Centre for Nanotechnology and Microengineering, University of War-
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wick. S p o n s o r s h i p from DTI National Measurements Programme, Project MPU 8/01.8 in enabling the initial prototype testing is acknowledged.
References 1 Garratt, J. D. and Bottomley, S. C. "Technology transfer in the development of a nanotopographic instrument," Nanotechnology 1990, 1, 38-43 2 Lindsey, K., Smith, S. T. and Robbie, C. J. "Subnanometre surface texture and profile measurement with Nanosurf 2," Ann ClRP 1988, 37, 519-522 3 Chetwynd D. G., X. Liu and Smith, S. T. "Signal fidelity and tracking force in stylus profilometry," Int J Mach Tools Manuf 1992, 32, 239-245 4 Liu, X., Smith, S. T. and Chetwynd, D. G. Frictional forces between a diamond stylus and specimens at low load. "Wear", 1992, 157, 279-294 5 Liu, X., Chetwynd, D. G. and Smith, S. T. "Improvement of fidelity of surface measurement by active damping controls," Meas Sci Technol 1993, 4, 1330-1340 6 Whitehouse, D.J. Handbook of Surface Metrology. Philadelphia & London: Institute of Physics, 1994, 378-600 7 Whitehouse D. J. "'A revised philosophy of surface measuring systems," Proc Inst Mech Engs 1988, 202, 169-185 8 Thomas, T. R., ed. Rough Surfaces, London: Longman, 1982, 21-24 9 Smith, S.T. and Chetwynd, D. G. "An optimised magnetcoil force actuator and its application to precision elastic mechanisms," Proc Inst Mech Engs 1990, 204C, 243-253 10 Jones, R. V. and Richards, J. C. S. "The design and some applications of sensitive capacitance micrometers," J Phys E Sci Instrum 1973, 6, 589-600 11 Neubauer, G., Cohen, S. R., McClelland, G. M., Horne, D. and Mate, C. M. "Force microscopy with a bidirectional capacitance sensor," Rev Sci Instrm 1990, 61, 2296-2308 12 Bennett, J. M. and Dancy, J. H. "Stylus profiling instrument for measuring statistical properties of smooth optical surfaces," Appl Optics 1981, 20, 1785-1802
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