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Electrical probing for dimensional micro metrology
CIRP Journal of Manufacturing Science and Technology 1 (2008) 59–62
Contents lists available at ScienceDirect
CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj
Electrical probing for dimensional micro metrology J. Hoffmann *, A. Weckenmann, Z. Sun Chair Quality Management and Manufacturing Metrology, University Erlangen-Nuremberg, Germany
A R T I C L E I N F O
A B S T R A C T
Article history:
Each dimensional measurement is based on probed points on the surface of the measured object. However, the well-established tactile and optical probing techniques face limitations when small and delicate objects with complex shape have to be measured. With tactile measurements there is always the danger of damaging the workpiece by the probing force and the measurable point rate is quite low. With optical probing there is a principal resolution limit and accessibility to complex surfaces is hindered by the limited acceptable surface slope. Also undercuts are not measurable. To overcome these limitations a probing system based on an electrical probing interaction with a direct current of a few nanoamperes has been developed, tested and compared with traditional technologies. With this probing system coordinate measurements of micro parts as well as nanometer resolved surface topography measurements are feasible. By applying a wide range of probes accessibility problems can be drastically reduced compared to tactile or optical micro probing systems. ß 2008 CIRP.
Available online 11 July 2008 Keywords: Scanning tunnelling microscope (STM) Coordinate Measuring Machine (CMM) Sensor
1. Introduction By far the most devices for dimensional metrology are composed out of an axes system and an either tactile or optical probing system. With the axes system the relative position between the probing system and a workpiece is manipulated and the absolute position of the probing system is measured, while the probing system determines the relative position of points on the workpiece surface with respect to a reference point in the probing system. While appropriate axes systems for micro and even nanometrology are commercially available [1–4], there are still many obstacles to overcome for the construction of a universal probing system capable for most topography and coordinate measurements on complex shaped micro-sized parts. 2. Limitations of optical and tactile probing For 2.5 D topography measurements (only one height value can be measured at each point of the lateral plane) very often optical probing systems are used due to the achievable high point rate, the typically good resolution in beam direction and the nondestructive functional principle. Drawbacks on the other hand are difficulties in measuring high surface slopes and the diffraction limit of lateral resolution (Abbe limit) [5]. This can be illustrated at
* Corresponding author. E-mail address: [email protected] (J. Hoffmann). 1755-5817/$ – see front matter ß 2008 CIRP. doi:10.1016/j.cirpj.2008.06.002
measurements of a white light interferometer, although it generally applies to far field optical measurements. Fig. 1 shows a measurement of a part of a MEMS device performed with a Taylor-Hobson TalySurf CCI white light interferometer with 50 Mirau objective. The two aluminium contacts are connected with a 200 nm wide carbon bridge that could be evidenced by conductivity measurements but not by optical measurements due to the width being smaller than the mean wavelength of the interferometer light source. The carbon bridge also causes heavy artefacts in the optical measurement of the contacts, Fig. 1 inside by ellipse. Additionally all points on the steep flanks are result of interpolation, but not of measurement and hence do not give any real information. Interpretation of those areas can thus be misleading. The maximum measurable slope angle for optical methods is always considerably below 908 (strict geometrical limit), a typical value is around 30–458 depending on the surface roughness, the numerical aperture of the objective and the method of measurement [6] so that, in general, only small portions of true threedimensional objects (e.g., spheres) can be measured. The necessity for a direct linear connection between the point to be probed and the optical sensor causes further limitations of optical systems for true 3D measurements (several surface points may have the same lateral position, e.g., at undercuts) of complex parts. This is one of the reasons why virtually all probing systems for 3D coordinate measuring machines detect the workpiece surface by touching it with a probing element and measuring the probing force or the displacement of the probing element due to the probing force [7].
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Fig. 1. Abbe limit of lateral resolution shown at the measurement of an MEMS device.
Opposite to light propagation, mechanical force can be transmitted along defined curved and articulated paths, i.e., the stylus carrying the probing element. Also it is possible with a spherical probing element to exert a force in any direction, whereas optical systems usually only establish their probing interaction in one direction (mostly z). Measurement of high slopes, undercuts and interior features in different orientations demands for such directionally independent probing and guided propagation of the probing interaction Fig. 2. Also the resolution limit does not apply to tactile probing systems, what is used, e.g., in atomic force microscopy [1], where a fine tip with a curvature radius considerably below the wavelength of visible light is used to scan surfaces. So the topography of the sample is transformed into a movement of the cantilever the tip is attached to. The much larger backside of the cantilever then enables optical measurement of its movement. Unfortunately tactile probing also shows principal disadvantages. The serial measurement and the necessity of moving mass for probing leads to a much lower measurable point rate by unit time and the force needed for probing might cause damages of the workpiece and/or the probe [8,9]. Up to now there is no tactile micro probing system that gives the possibility of using articulated or arborescent stylii [10], so many advantages of macroscopic tactile 3D probing systems do not apply to miniaturized systems. When the size of the probing element is reduced for the benefit of better accessibility to small interior features, higher spatial resolution and lower moment of inertia, several challenges directly arise from the tactile working principle. Hertzian stress in the contact area grows quickly with smaller tip balls [7], raising the
Fig. 2. Improved 3D ability by guided propagation of the probing interaction.
danger of plastic deformation of the workpiece and large measurement errors [8]. For a ruby probing sphere of 0.125 mm plastic deformation of 5 nm has been reported when an aluminium surface is probed with a force of less than 1 mN [9], which is challenging to be controlled appropriately especially because also dynamic forces are to be considered. As the stem diameter has to be smaller, than the tip ball diameter, also stylus bending may get critical and lead to deteriorated signal to noise ratio when small tip balls are used. In comparison to static contact force, the dynamic probing force F = ma (m: moving probe mass, a: deceleration upon contact) can be much higher depending on the moving probe mass and the approach speed, what is limiting the usable approach speed in practice [8,9]. With fiber probes [7] it is possible to probe with very low static probing force (e.g., 1 mN) reducing the risk of damaging the workpiece to a minimum. On the other hand they have strictly limited capability for 3D measurements due to the non-isotropic flexibility of the glass fiber stylii and the typically optical measurement of the probe position. In summary real 3D measurement of complex shaped parts is in general only feasible using directionally independent probing and guided propagation of the probing interaction. Both can be achieved to a large extent with mechanical probing using spherical probing elements and articulated stylii. Mechanical force is a very useful probing interaction for large and medium sized mechanically stable parts, but meets its limits when very small probing elements have to be employed or delicate structures are to be probed. A forceless probing interaction that gives the possibility of directionally independent probing and guided propagation of the interaction is thus highly desirable. 3. Electrical probing For 2.5 D topography measurement of conductive and semiconductive workpieces the possibility of electrical probing is used in field emission microscopy [11] and scanning tunnelling microscopy [12] already and proved the excellent achievable resolution and non-destructiveness there for one dimensional probing. Electrical probing interactions or the measurable information about it (i.e., current) can be easily guided along a defined path by using an appropriately shaped conductor. Also it is feasible to use a spherical electrode as probing element, so the prerequisites for real three-dimensional probing are given for the electrical interaction. To investigate the practical usability of electrical probing for the measurement of complex shaped parts an experimental probing system [13] was designed, set-up and integrated into a long-range nanopositioning unit with Laser-interferometric position measurement [14]. The function of the probing system is based on the measurement of a small direct current (0–100 nA) which results from a bias voltage between 2 and 2 V between probe and workpiece when the distance between both is sufficiently small. The relationship between probe travel during approach to the surface and the resulting current can be evaluated by simultaneously recording the probe signal and the HeNe-Laser interferometer signal of the nanopositioning unit in the axis parallel to probe movement, Fig. 3. For the depicted curves, a bias voltage of 1 V was used between a high alloy steel sample and a tungsten carbide probing sphere (d = 0.3 mm). The probe was approached and subsequently withdrawn four times with a speed of 20 nm/s. The current decreases with increasing relative distance; however, at small relative distances, a drastic non-linear changing is observed for a current higher than 14 nA. Especially the lower
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Fig. 3. Characteristic curves of the electrical probing system when approaching to a surface and withdrawing from the surface (four cycles). Fig. 5. Realization of vastly differing measuring ranges on a ground steel plate.
current part (lower than 14 nA) can be used for dimensional measurement due to the good repeatability. It is assumed that these phenomena are consistent with the occurrence of current flowing between narrowly separated electrodes (probe and sample), which is widely known as tunnel effect [12,15]. Both show an exponential behaviour and very similar electron transmission coefficients at similar bias voltages; however, the slope of the curve of the investigated probing system is much smaller, than for conventional scanning tunnelling microscopes, which are using probes with a much smaller radius of curvature (e.g., 10 nm) and typically work in vacuum. Exact theoretical calculation of the curve is hindered by the fact that there is no common analytical solution for the three-dimensional barrier model and that the one-dimensional approximation of the barrier is not valid for probes with a much larger radius of curvature compared to the probe-sample distance [16]. Additionally in ambient atmosphere Schottky-emission may lead to a much lower effective barrier height what can explain the large observed range, low slope of the characteristic curve [17] and the differences to theoretically predicted characteristic curves for operation in ultra high vacuum [18]. The decreasing slope of the curve for probes with larger radii of curvature has also been observed by other groups in conventional scanning tunnelling microscopy, Fig. 4 [16], where it is always aimed at small radii of curvature for the benefit of better lateral resolution. It is worthy to point out that the usefulness of the investigated measurement system for real 3D measurements stems from the fact that it is sensitive to the full three-dimensional structure of the surface due to the employment of spherical probes with very large radii (e.g., 0.15 mm) compared to conventional STM tips. 4. Experimental results For evaluating system performance for dimensional metrology and comparability of the results with tactile and optical measure-
Fig. 4. Characteristic curves of a commercial STM with a sharp tip (a) and a blunt tip (b) [16].
ments, 2.5 D topography measurements with ranges between 1 mm 1 mm and 10 mm 10 mm as well as 3D coordinate measurements of a micro ball bar have been performed and compared with commercial optical and tactile high-end metrology devices. 4.1. 2.5 D topography measurements For 2.5 D surface topography measurements the distance dependent current can be used for controlling the z-position of the probe during scanning along x or y axis, so that the probe follows the surface topography with constant distance. When using a sharp probe, lateral resolution well below the Abbe limit for optical measurements can be achieved, Fig. 5. The effective achievable resolution is considerably better than expected from the radius of curvature of the used probe (r = 15 mm), so it has to be assumed that only a small portion of the spherical tip end is effectively in interaction with the surface to be probed. The scanning speed has been reduced from 100 mm/s for the largest measurement range in Fig. 5 to 1 mm/s for the smallest one. At each measuring range 1000 1000 measurement points have been collected. Due to the robustness and virtual absence of wear and drift of the electrical probing system also very large measuring ranges up to 25 mm 25 mm are feasible with the experimental set-up. 4.2. 3 D coordinate measurements The ability for probing true three-dimensional objects can be investigated at the measurement of spheres, which show normal vectors in all directions. This is also reflected in the procedure for determining 3D probing uncertainty of probing systems for coordinate measuring machines according to ISO 10360. There a hemisphere of negligible form deviation is probed with 25 evenly distributed points and the maximum deviation from the Gaussian fit is evaluated. Fig. 6 shows a measurement of a polished steel sphere electrically probed with a monolithic tungsten carbide probe with a 0.3 mm tip ball. Before the measurements no form calibration of the tip ball was done, so the data represents a combination of probing uncertainty (not reproducible) and (reproducible) form deviations of the probing sphere and the measured sphere. The maximum deviation of the measured data from a Gaussian fit sphere is 1.085 mm, while the mean difference per point between two subsequent measurements is only 37 nm (maximum difference: 151 nm), so the shown deviation from the Gaussian sphere represents the form deviation of the probing sphere (form
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probe, resulting in a current of about 1 mA. After that the probed sphere was measured with an Alicona Infinite Focus Microscope and a Taylor-Hobson TalySurf CCI white light interferometer, Fig. 7. When measured with real electric contact (1 mA) scratches of up to 300 nm depth are left on the measured surface after only one measurement, while even after 300 measurements no trace at all could be found when the current was limited to 5 nA by appropriate distance control, Fig. 7. 6. Summary
Fig. 6. Measurement results at a steel sphere d = 4 mm with 25 evenly distributed probing points.
The feasibility of electrical probing for 2.5 D topography measurements and also true 3D coordinate measurements has been demonstrated. Special advantages of electrical probing are the enormous flexibility towards the measuring task, the very good repeatability, non-invasiveness and good robustness compared to optical or tactile probing. A principal disadvantage is the limitation to conductive samples. Due to the fact that the probe stem only has to conduct a very small current, but practically no mechanical force, further miniaturization and application of multiple articulated and or arborescent stylii for the access to complex interior workpiece features is expected to be possible.
References
Fig. 7. Investigation of invasiveness with optical microscopy (left) and white light interferometry (right).
deviation specified by manufacturer: 2 mm) and the measured sphere (form deviation specified by manufacturer 135 nm) rather than the probing uncertainty of the electrical probing system. The distance between two spheres of an Invar ball bar could be measured with a standard deviation of 36 nm (90 measurements) and in reasonable agreement (difference 109 nm) with the commercial micro CMM Werth VideoCheck UA 400 (MPE = 0.6 mm). Main difficulty for evaluation of measurement uncertainty is the lack of electrically conductive standards which are calibrated with appropriate uncertainty. Further investigations for evaluating measurement uncertainty are in progress. 5. Investigation of invasiveness When probing micro parts it is often critical to ensure noninvasiveness, so that the measured object is not altered by the measurement. Invasiveness of electrical probing has been investigated by repeated 2.5 D measurements of the same surface area and changing fast and slow scan axis. As this could not reveal any traces caused by the measurement, a cross shaped scan path on a steel sphere has been measured 300 times with adequate settings (control set point 5 nA). After that three of the four arms of the cross have been measured once with real electric contact to the
[1] Danzebrink, H.-U., Koenders, L., Wilkening, G., Yacoot, A., Kunzmann, H., 2006, Advances in Scanning Force Microscopy for Dimensional Metrology, Annals of the CIRP, 55/2: 841–879. [2] Hansen, H.N., Carneiro, K., Haitjema, H., De Chiffre, L., 2006, Dimensional Micro and Nano Metrology, Annals of the CIRP, 55/2: 721–744. [3] Jaeger, G., Gruenwald, R., Manske, E., Hausotte, T., Fuessl, R., 2004, A Nanopositioning and Nanomeasuring Machine: Operation-Measured Results, Nanotechnology and Precision Engineering, 2/2004 (2): 81–84. [4] Hoffmann, J., Weckenmann, A., 2006, Coordinate Measurements with Nanometer Resolution, in: Proceedings of VIIth International Scientific Conference, Coordinate Measuring Technique (03.-05.04.2006, Bielsko-Biala, Poland), pp.113–122. [5] Schwenke, H., Neuschaefer-Rube, U., Pfeifer, J., Kunzmann, H., 2002, Optical Methods for Dimensional Metrology in Production Engineering, Annals of the CIRP, 51/2: 685–700. [6] Neugebauer, M., Ehrig, W., Jusko, O., Neuschaefer-Rube, U., 2008, The Influence of Surface Roughness on the Maximum Slope Angle Measurable with Area Based Optical Sensors, in: Proceedings of XII International Colloquium on Surfaces (28.-29.01.2008, Chemnitz, Germany), pp.258–267. [7] Weckenmann, A., Estler, T., Peggs, G., McMurtry, D., 2004, Probing Systems in Dimensional Metrology, Annals of the CIRP, 53/2: 657–668. [8] van Vliet, W.P., Schellekens, P., 1996, Accuracy Limitations of Fast Mechanical Probing, Annals of the CIRP, 45/1: 483–488. [9] Meli, F., Kueng, A., 2007, AFM Investigation on Surface Damage Caused by Mechanical Probing with Small Ruby Spheres, Meas Sci Technol, 18:496– 502. [10] Neugebauer, M., Hilpert, U., Bartscher, M., Gerwien, M., Krystek, M., Schwehn, C., Trenk, M., Goebbels, J., 2008, Untersuchungen zur Messung von Mikrogeometrien mit großen taktilen KMGs und Anwendung bei einem Pru¨fko¨rper fu¨r Mikro-CT-Messungen, Tm – Technisches Messen, 75:187–198. [11] Young, R., 1972, The Topografiner—An Instrument For Measuring Surface Microtopography, Rev Sci Instrum, 43:999–1011. [12] Binnig, G., Rohrer, H., Gerber, C., Weibel, E., 1982, Surface Studies by Scanning Tunneling Microscopy, Phys Rev Lett, 49/1: 57–61. [13] Weckenmann, A.; Hoffmann, J., A Novel Pseudo-Tactile Zero Indicating Probe for Nanometrology, 9th International Symposium on Measurement and Quality Control, ISMQC (21.-24.11.2007, Chennai, India), Proceedings, 173–177. [14] Hausotte, T., 2002, Nanopositionier- und Messmaschine, Ph.D. thesis, Technische Universita¨t Ilmenau; Ilmenau Verlag ISLE. [15] Simmons, J.G., 1963, Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film, J Appl Phys, 34/6: 1793–1803. [16] NT-MDT Co. (Ed.), 2008, Observed Physical Quantities in STM, http:// www.ntmdt.com/Documents/169_1.3%20Obser_Phys_Quantities_in_STM.pdf as of 31/03/2008. [17] Jahanmir, J., West, E.P., Rhodin, T.N., 1988, Evidence of Schottky Emission in Scanning Tunneling Microscopes Operated in Ambient Air, Appl Phys Lett, 52/ 24: 2086–2088. [18] Houze´, F., Boyer, L., 1991, A Quantitative Approach to the Effects of Surface Topography on Tunneling Current between Two Large Rough Metal Bodies, J Phys Cond Matter, 3:4655–4675.
Contents lists available at ScienceDirect
CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj
Electrical probing for dimensional micro metrology J. Hoffmann *, A. Weckenmann, Z. Sun Chair Quality Management and Manufacturing Metrology, University Erlangen-Nuremberg, Germany
A R T I C L E I N F O
A B S T R A C T
Article history:
Each dimensional measurement is based on probed points on the surface of the measured object. However, the well-established tactile and optical probing techniques face limitations when small and delicate objects with complex shape have to be measured. With tactile measurements there is always the danger of damaging the workpiece by the probing force and the measurable point rate is quite low. With optical probing there is a principal resolution limit and accessibility to complex surfaces is hindered by the limited acceptable surface slope. Also undercuts are not measurable. To overcome these limitations a probing system based on an electrical probing interaction with a direct current of a few nanoamperes has been developed, tested and compared with traditional technologies. With this probing system coordinate measurements of micro parts as well as nanometer resolved surface topography measurements are feasible. By applying a wide range of probes accessibility problems can be drastically reduced compared to tactile or optical micro probing systems. ß 2008 CIRP.
Available online 11 July 2008 Keywords: Scanning tunnelling microscope (STM) Coordinate Measuring Machine (CMM) Sensor
1. Introduction By far the most devices for dimensional metrology are composed out of an axes system and an either tactile or optical probing system. With the axes system the relative position between the probing system and a workpiece is manipulated and the absolute position of the probing system is measured, while the probing system determines the relative position of points on the workpiece surface with respect to a reference point in the probing system. While appropriate axes systems for micro and even nanometrology are commercially available [1–4], there are still many obstacles to overcome for the construction of a universal probing system capable for most topography and coordinate measurements on complex shaped micro-sized parts. 2. Limitations of optical and tactile probing For 2.5 D topography measurements (only one height value can be measured at each point of the lateral plane) very often optical probing systems are used due to the achievable high point rate, the typically good resolution in beam direction and the nondestructive functional principle. Drawbacks on the other hand are difficulties in measuring high surface slopes and the diffraction limit of lateral resolution (Abbe limit) [5]. This can be illustrated at
* Corresponding author. E-mail address: [email protected] (J. Hoffmann). 1755-5817/$ – see front matter ß 2008 CIRP. doi:10.1016/j.cirpj.2008.06.002
measurements of a white light interferometer, although it generally applies to far field optical measurements. Fig. 1 shows a measurement of a part of a MEMS device performed with a Taylor-Hobson TalySurf CCI white light interferometer with 50 Mirau objective. The two aluminium contacts are connected with a 200 nm wide carbon bridge that could be evidenced by conductivity measurements but not by optical measurements due to the width being smaller than the mean wavelength of the interferometer light source. The carbon bridge also causes heavy artefacts in the optical measurement of the contacts, Fig. 1 inside by ellipse. Additionally all points on the steep flanks are result of interpolation, but not of measurement and hence do not give any real information. Interpretation of those areas can thus be misleading. The maximum measurable slope angle for optical methods is always considerably below 908 (strict geometrical limit), a typical value is around 30–458 depending on the surface roughness, the numerical aperture of the objective and the method of measurement [6] so that, in general, only small portions of true threedimensional objects (e.g., spheres) can be measured. The necessity for a direct linear connection between the point to be probed and the optical sensor causes further limitations of optical systems for true 3D measurements (several surface points may have the same lateral position, e.g., at undercuts) of complex parts. This is one of the reasons why virtually all probing systems for 3D coordinate measuring machines detect the workpiece surface by touching it with a probing element and measuring the probing force or the displacement of the probing element due to the probing force [7].
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Fig. 1. Abbe limit of lateral resolution shown at the measurement of an MEMS device.
Opposite to light propagation, mechanical force can be transmitted along defined curved and articulated paths, i.e., the stylus carrying the probing element. Also it is possible with a spherical probing element to exert a force in any direction, whereas optical systems usually only establish their probing interaction in one direction (mostly z). Measurement of high slopes, undercuts and interior features in different orientations demands for such directionally independent probing and guided propagation of the probing interaction Fig. 2. Also the resolution limit does not apply to tactile probing systems, what is used, e.g., in atomic force microscopy [1], where a fine tip with a curvature radius considerably below the wavelength of visible light is used to scan surfaces. So the topography of the sample is transformed into a movement of the cantilever the tip is attached to. The much larger backside of the cantilever then enables optical measurement of its movement. Unfortunately tactile probing also shows principal disadvantages. The serial measurement and the necessity of moving mass for probing leads to a much lower measurable point rate by unit time and the force needed for probing might cause damages of the workpiece and/or the probe [8,9]. Up to now there is no tactile micro probing system that gives the possibility of using articulated or arborescent stylii [10], so many advantages of macroscopic tactile 3D probing systems do not apply to miniaturized systems. When the size of the probing element is reduced for the benefit of better accessibility to small interior features, higher spatial resolution and lower moment of inertia, several challenges directly arise from the tactile working principle. Hertzian stress in the contact area grows quickly with smaller tip balls [7], raising the
Fig. 2. Improved 3D ability by guided propagation of the probing interaction.
danger of plastic deformation of the workpiece and large measurement errors [8]. For a ruby probing sphere of 0.125 mm plastic deformation of 5 nm has been reported when an aluminium surface is probed with a force of less than 1 mN [9], which is challenging to be controlled appropriately especially because also dynamic forces are to be considered. As the stem diameter has to be smaller, than the tip ball diameter, also stylus bending may get critical and lead to deteriorated signal to noise ratio when small tip balls are used. In comparison to static contact force, the dynamic probing force F = ma (m: moving probe mass, a: deceleration upon contact) can be much higher depending on the moving probe mass and the approach speed, what is limiting the usable approach speed in practice [8,9]. With fiber probes [7] it is possible to probe with very low static probing force (e.g., 1 mN) reducing the risk of damaging the workpiece to a minimum. On the other hand they have strictly limited capability for 3D measurements due to the non-isotropic flexibility of the glass fiber stylii and the typically optical measurement of the probe position. In summary real 3D measurement of complex shaped parts is in general only feasible using directionally independent probing and guided propagation of the probing interaction. Both can be achieved to a large extent with mechanical probing using spherical probing elements and articulated stylii. Mechanical force is a very useful probing interaction for large and medium sized mechanically stable parts, but meets its limits when very small probing elements have to be employed or delicate structures are to be probed. A forceless probing interaction that gives the possibility of directionally independent probing and guided propagation of the interaction is thus highly desirable. 3. Electrical probing For 2.5 D topography measurement of conductive and semiconductive workpieces the possibility of electrical probing is used in field emission microscopy [11] and scanning tunnelling microscopy [12] already and proved the excellent achievable resolution and non-destructiveness there for one dimensional probing. Electrical probing interactions or the measurable information about it (i.e., current) can be easily guided along a defined path by using an appropriately shaped conductor. Also it is feasible to use a spherical electrode as probing element, so the prerequisites for real three-dimensional probing are given for the electrical interaction. To investigate the practical usability of electrical probing for the measurement of complex shaped parts an experimental probing system [13] was designed, set-up and integrated into a long-range nanopositioning unit with Laser-interferometric position measurement [14]. The function of the probing system is based on the measurement of a small direct current (0–100 nA) which results from a bias voltage between 2 and 2 V between probe and workpiece when the distance between both is sufficiently small. The relationship between probe travel during approach to the surface and the resulting current can be evaluated by simultaneously recording the probe signal and the HeNe-Laser interferometer signal of the nanopositioning unit in the axis parallel to probe movement, Fig. 3. For the depicted curves, a bias voltage of 1 V was used between a high alloy steel sample and a tungsten carbide probing sphere (d = 0.3 mm). The probe was approached and subsequently withdrawn four times with a speed of 20 nm/s. The current decreases with increasing relative distance; however, at small relative distances, a drastic non-linear changing is observed for a current higher than 14 nA. Especially the lower
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61
Fig. 3. Characteristic curves of the electrical probing system when approaching to a surface and withdrawing from the surface (four cycles). Fig. 5. Realization of vastly differing measuring ranges on a ground steel plate.
current part (lower than 14 nA) can be used for dimensional measurement due to the good repeatability. It is assumed that these phenomena are consistent with the occurrence of current flowing between narrowly separated electrodes (probe and sample), which is widely known as tunnel effect [12,15]. Both show an exponential behaviour and very similar electron transmission coefficients at similar bias voltages; however, the slope of the curve of the investigated probing system is much smaller, than for conventional scanning tunnelling microscopes, which are using probes with a much smaller radius of curvature (e.g., 10 nm) and typically work in vacuum. Exact theoretical calculation of the curve is hindered by the fact that there is no common analytical solution for the three-dimensional barrier model and that the one-dimensional approximation of the barrier is not valid for probes with a much larger radius of curvature compared to the probe-sample distance [16]. Additionally in ambient atmosphere Schottky-emission may lead to a much lower effective barrier height what can explain the large observed range, low slope of the characteristic curve [17] and the differences to theoretically predicted characteristic curves for operation in ultra high vacuum [18]. The decreasing slope of the curve for probes with larger radii of curvature has also been observed by other groups in conventional scanning tunnelling microscopy, Fig. 4 [16], where it is always aimed at small radii of curvature for the benefit of better lateral resolution. It is worthy to point out that the usefulness of the investigated measurement system for real 3D measurements stems from the fact that it is sensitive to the full three-dimensional structure of the surface due to the employment of spherical probes with very large radii (e.g., 0.15 mm) compared to conventional STM tips. 4. Experimental results For evaluating system performance for dimensional metrology and comparability of the results with tactile and optical measure-
Fig. 4. Characteristic curves of a commercial STM with a sharp tip (a) and a blunt tip (b) [16].
ments, 2.5 D topography measurements with ranges between 1 mm 1 mm and 10 mm 10 mm as well as 3D coordinate measurements of a micro ball bar have been performed and compared with commercial optical and tactile high-end metrology devices. 4.1. 2.5 D topography measurements For 2.5 D surface topography measurements the distance dependent current can be used for controlling the z-position of the probe during scanning along x or y axis, so that the probe follows the surface topography with constant distance. When using a sharp probe, lateral resolution well below the Abbe limit for optical measurements can be achieved, Fig. 5. The effective achievable resolution is considerably better than expected from the radius of curvature of the used probe (r = 15 mm), so it has to be assumed that only a small portion of the spherical tip end is effectively in interaction with the surface to be probed. The scanning speed has been reduced from 100 mm/s for the largest measurement range in Fig. 5 to 1 mm/s for the smallest one. At each measuring range 1000 1000 measurement points have been collected. Due to the robustness and virtual absence of wear and drift of the electrical probing system also very large measuring ranges up to 25 mm 25 mm are feasible with the experimental set-up. 4.2. 3 D coordinate measurements The ability for probing true three-dimensional objects can be investigated at the measurement of spheres, which show normal vectors in all directions. This is also reflected in the procedure for determining 3D probing uncertainty of probing systems for coordinate measuring machines according to ISO 10360. There a hemisphere of negligible form deviation is probed with 25 evenly distributed points and the maximum deviation from the Gaussian fit is evaluated. Fig. 6 shows a measurement of a polished steel sphere electrically probed with a monolithic tungsten carbide probe with a 0.3 mm tip ball. Before the measurements no form calibration of the tip ball was done, so the data represents a combination of probing uncertainty (not reproducible) and (reproducible) form deviations of the probing sphere and the measured sphere. The maximum deviation of the measured data from a Gaussian fit sphere is 1.085 mm, while the mean difference per point between two subsequent measurements is only 37 nm (maximum difference: 151 nm), so the shown deviation from the Gaussian sphere represents the form deviation of the probing sphere (form
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probe, resulting in a current of about 1 mA. After that the probed sphere was measured with an Alicona Infinite Focus Microscope and a Taylor-Hobson TalySurf CCI white light interferometer, Fig. 7. When measured with real electric contact (1 mA) scratches of up to 300 nm depth are left on the measured surface after only one measurement, while even after 300 measurements no trace at all could be found when the current was limited to 5 nA by appropriate distance control, Fig. 7. 6. Summary
Fig. 6. Measurement results at a steel sphere d = 4 mm with 25 evenly distributed probing points.
The feasibility of electrical probing for 2.5 D topography measurements and also true 3D coordinate measurements has been demonstrated. Special advantages of electrical probing are the enormous flexibility towards the measuring task, the very good repeatability, non-invasiveness and good robustness compared to optical or tactile probing. A principal disadvantage is the limitation to conductive samples. Due to the fact that the probe stem only has to conduct a very small current, but practically no mechanical force, further miniaturization and application of multiple articulated and or arborescent stylii for the access to complex interior workpiece features is expected to be possible.
References
Fig. 7. Investigation of invasiveness with optical microscopy (left) and white light interferometry (right).
deviation specified by manufacturer: 2 mm) and the measured sphere (form deviation specified by manufacturer 135 nm) rather than the probing uncertainty of the electrical probing system. The distance between two spheres of an Invar ball bar could be measured with a standard deviation of 36 nm (90 measurements) and in reasonable agreement (difference 109 nm) with the commercial micro CMM Werth VideoCheck UA 400 (MPE = 0.6 mm). Main difficulty for evaluation of measurement uncertainty is the lack of electrically conductive standards which are calibrated with appropriate uncertainty. Further investigations for evaluating measurement uncertainty are in progress. 5. Investigation of invasiveness When probing micro parts it is often critical to ensure noninvasiveness, so that the measured object is not altered by the measurement. Invasiveness of electrical probing has been investigated by repeated 2.5 D measurements of the same surface area and changing fast and slow scan axis. As this could not reveal any traces caused by the measurement, a cross shaped scan path on a steel sphere has been measured 300 times with adequate settings (control set point 5 nA). After that three of the four arms of the cross have been measured once with real electric contact to the
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