Sensor and actuator considerations for precision, small machines: a review

Transcription

1 UCRL-JRNL Sensor and atuator onsiderations for preision, small mahines: a review S. T. Smith, R. M. Seugling April 1, 005 Preision Engineering

2 Dislaimer This doument was prepared as an aount of work sponsored by an ageny of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, epress or implied, or assumes any legal liability or responsibility for the auray, ompleteness, or usefulness of any information, apparatus, produt, or proess dislosed, or represents that its use would not infringe privately owned rights. Referene herein to any speifi ommerial produt, proess, or servie by trade name, trademark, manufaturer, or otherwise, does not neessarily onstitute or imply its endorsement, reommendation, or favoring by the United States Government or the University of California. The views and opinions of authors epressed herein do not neessarily state or reflet those of the United States Government or the University of California, and shall not be used for advertising or produt endorsement purposes.

3 Sensor and atuator onsiderations for preision, small mahines: a review Stuart T. Smith, Rihard M. Seugling Center for Preision Metrology, UNC Charlotte, Charlotte, NC 83 Lawrene Livermore National Laboratory, Livermore, CA Abstrat This artile reviews some design onsiderations for the saling down in size of instruments and mahines with a primary aim to identify tehnologies that may provide more optimal performane solutions than those, often established, tehnologies used at marosopi, or onventional, sales. Dimensional metrology within emerging appliations will be onsidered for meso- through miro- down to nanometer level systems with partiular emphasis on systems for whih preision is diretly related to funtion. In this paper, attention is limited to some of the more fundamental issues assoiated with saling. For eample, atuator work or power densities or the effet of noise on the sensor signals an be readily evaluated and provide some guidane in the seletion for any given size of devie. However, with redutions in sale these parameters and/or phenomena that limit performane may hange. Within this review, the authors have tried to assess these omple inter-relationships between performane and sale, again from a fundamental perspetive. In pratie, it is likely that the nuanes of implementation and integration of sensor, atuator and/or mehanism designs will determine funtionality and ommerial viability of any partiular system development. Corresponding author stusmith@un.edu This work was performed in part under the auspies of the U.S. Department of Energy by University of California, Lawrene Livermore National Laboratory under ontrat No. W-7405-Eng-48. 1

4 1.0 Introdution Although, small-sale mahine tools and instruments, suh as lathes, have been built for many years in the wath-making and other industries, a limited number of these systems have been inorporated into modern manufaturing. Most of the small sale mahine tools and instruments are merely a saled down version of a onventional mahine. Typially the auray or preision of these small mahines is no better, more often worse, than that of high-quality maro mahines/instruments. In an effort to identify areas of future researh, fundamental onsiderations are used to assess the fidelity of possible approahes to ommon design problems. At etremes of saling, it is obvious that some requirements of mahines and instruments suh as primary atuation methods or position sensing, for eample, may be best ahieved using different tehnologies. It is important that designers beome aware of both the available tehnologies as well as the relevant performane measures as a funtion of dimensional sale. With this in mind, it will then be possible to identify transitions in sale at whih different tehnologies will provide a more optimal solution to a design need. Key features ommon to the mehanial systems being onsidered in this review are the ability to provide work in a ontrolled manner and the use of sensors for feedbak of proess ondition, partiularly relative motions. Based on the fous of saling down, two major mahine requirements are disussed, these being; atuators to provide position and/or generate work and sensors for deteting surfaes and measuring relative motions. The dimensional sales of the systems lassifiations referred to in this tet are 1. Meso-systems, being intermediate between human sale devies and mirometer mehanisms, implies that major dimensions of suh a system will typially be measured in millimeters.. Miro-engineering is the intermediate region in whih mirometers are more sensibly used to speify funtional toleranes. This length sale is often onsidered to inorporate MEMS proessing.

5 3. Nano-engineering is onsidered to be any proess resulting in devies of defined struture or assembly in whih the nanometer is the most sensible unit for speifying dimensions or toleranes. Preision at marosopi sales is usually onsidered to start with range to auray, or range to resolution performane at around 1 part in 10 5 or better. A similar riterion applied to meso-systems immediately implies that, if preision is to be maintained, total errors should be below 10-8 m or so. In pratie, eonomis ditates that suh high preision only be maintained when absolutely neessary for the funtion of the devie. Currently, it is our eperiene that, when assembling small mahines using available small parts, tolerane stak-up often leads to unaeptable degradation of performane. In many proesses, to ontrol to the relevant preision will require development of metrology and atuation systems of onsiderably better performane than urrently available from marosopi devies. Consequently, these simple onsiderations indiate that dimensional metrology and mehanism design for small-sale mahines must ahieve reliable measurement and positional auray at, or approahing, nanometer levels. It is possible that, as the size of systems redue; major differenes are likely to inlude the following. 1. It may be viable to inorporate metrology systems within manufature and/or assembly.. There are likely to be more metrology systems, possibly one for every devie. 3. It must be possible to manufature these heaply and utilize automated assembly. 4. Power onsumption will be low while, for systems with inherent losses, effiieny will be diffiult to maintain or improve. 5. New, or onsiderably more ompat, methods of ommuniation and data handling will be required. Connetors and interfaes often aount for a major fration of the volume of a iruit. 3

6 6. It will be neessary to ahieve higher bandwidths and resolution than normally required of maro-sale metrology instruments. 7. Alignments of moving aes and subsequent errors will be partiularly diffiult to adjust and measure. 8. Measurement frames enompassing the whole instrument may not add signifiant ost and, being small, may be relatively insensitive to environmental variations. 9. Volumetri dimensions for measurement systems and fores imposed by the sensing devies should be low relative to the fores of the proess. A question that has not, in our view, reeived suffiient attention is the distintion between these different realms of tehnologial endeavor. In pratie, it is both logial and, probably, fair to say that we are onsidering a ontinuum of omponent sales inorporated into any modern mahine. Currently, it is ommon to distinguish different sales by the proesses used in manufature. As manufaturing and assembly proesses develop and adapt, it is likely that these distintions will be less lear and designers will be required to inorporate tehnologies overing all dimensional sales as a matter of ourse. However, there are important features to be onsidered as dimensional sales redue. Primary among these are 1. There is a ertain ut-off after whih the use of manual assembly, that has been spetaularly useful and essential in the development of tehnologies so far, is no longer viable.. Phenomena within mehanisms that produe signifiant mehanial fores may hange (i.e. ontat fores, adhesion fores, menisus effets, eletri dipoles, van der Waals and Casimir fores) thereby requiring additional onsideration in the alulation of two-body surfae interations. 3. Saling an hange the relative dynamis of phenomena. For eample heat transfer is often onsiderably slower than mehanial motion at maro-sales 4

7 while thermal agitation might be the fastest means of providing motile fores at moleular levels. From another perspetive, thermal epansion, whih is a major limiting influene on possible preision in a large mahine, may be insignifiant at smaller dimensions. 4. As the net removal or deposition volumes redue, other manufaturing proesses, redutive or additive, previously onsidered too slow, may provide eonomi prodution rates. Suh onsiderations may provide a guide to favorable saling in the seletion of proesses and omponents. Consider a mahine or instrument arriving in a bo weighing approimately 50 kg or less, able to fit sparingly on a desktop and apable of produing or measuring parts with a preision of 1 part in 10 6 given a work volume of several m 3. As already mentioned, given the preision stated, the resolution of the mahine or instrument would have to be on the order of tens of nanometers over entimeter ranges. The onept seems very straight forward given the advaned tehnology of today. However, why don t these types of mahines show-up in manufaturing plants around the world? Simply saling down urrent tehnologies used in modern omputer ontrolled mahine tools or instruments would initially give the impression of providing for urrent manufaturing needs. However, this may not be viable beause the omple nature of the interrelated physial and hemial interations at different sales often urtails the designer s ability to shrink a omple mahine/instrument without areful onsideration of how the redution-to-pratie of suh a system would perform under real operating onditions. Suh issues are beyond the sope of this review. However, to ahieve preision, small atuator and sensor systems are neessary enabling tehnologies of meso- and smaller sale systems. Fortunately, there are limited numbers of possibilities for these and an assessment of the relative merits of available options in terms of the effets of saling is presented in this review. Atuator methods urrently onsidered inlude; piezoeletri, eletrostati, eletromagneti, magneto-stritive, hydrauli/pneumati, thermal and shape memory. 5

8 One partiular measure of the fidelity of these atuators is the theoretial maimum amount of work and/or power that an be produe per unit volume oupied by the atuator (alled the work density or, when saled by the dynami bandwidth, power density). Considering speifi implementations it is found that some of these methods maintain performane (piezo-eletri, hydrauli, eletrostati) as sales redue while eletromagneti atuators tend to ehibit redued work density and thermal-based atuators appear to improve. Identifiation of the sales at whih different tehniques dominate will help the designer to selet the appropriate tehnology for a given appliation. Suh analysis also provides information about other parametri saling fators suh as drive voltage amplitudes, fores et. A number of implementation issues will also be onsidered. A similar approah has been applied to sensors for small-sale systems suh as optial (line sale, interferometri, diffrative, position sensitive detetors) and eletromagneti. In this later ategory it is neessary to split the ategories into transduers and displaement sensor systems. In our study we have attempted to identify the relevant saling parameters and assess their relative influene as sale redues..0 Displaement sensors.1 General onsiderations Displaement sensors may be onsidered any transdution method that results in a deterministi variation in output for a hange in relative position between two objets. Outside of ost, in terms of performane measures signal to noise, repeatability and stability tend to be the most important parameters for the assessment of potential preision. In many ases a smooth and ontinuous variation of output with displaement will provide adequate means for the determination of relative displaements. Periodi rulings an be used with most of the onsidered sensing methods to enable an inrease in preision by effetively repeating the short-range performane while inreasing total range in proportion to the number of periods. However, in this ase, auray also depends upon the auray of the periodi ruling. For eample, in optis it is possible to 6

9 eploit near field probes to read a grating of sub-wavelength pith, while using apaitane it is possible to use an almost arbitrarily small tip [1, ] and again read from a periodi struture. Magneti sensing from a periodi magneti struture is ommonplae in the magneti data storage industry and it is possible to disriminate sub-mirometer magneti features in some ases. It is not always neessary that the rule have eat periodiity and in some ases it is possible to read displaements from a random pattern of known harateristi leading to a pseudo-absolute sale. However, ommon to most of these methods is the requirement for the sensing element to be in near proimity to the sale and usually with a separation omparable to the finest features on the sale (diffrative sensors that effetively average over many lines of a grating represent an eeption). Often times these are referred to as near-field probes and represent a generalized approah to small-sale (often highly loalized), long-range position sensors. In this ase, there will be onstraints on the neessary preision of aligning the sale with that of the moving platform to provide suffiient signal ontrast during traverse. It is also ommon to utilize multiple measurements of the periodi grating with a lateral phase separation to enable amplitude independent, diretionally sensitive measurement of displaement. Again, the preision of suh tehniques are predominantly limited by signal ontrast. Other near-field phenomena are adequately represented by the sensing elements ommonly used in sanned probe mirosopy utilizing ontat based or near-surfae interations suh as eletrostati, tunneling, van der Waal, menisus, Casimir, magneti resonane, optial, ion ondutane, thermal, squeeze-film and piezoeletri. Of eah of these phenomenologial interations there are a large variety of methods for onditioning the signals to derive different surfae interation information. In many ases, ombinations of these interations are either eploited or impinge upon the interpretation of the measured signals.. Optial A omprehensive study of the methods and tehniques for optial measurement of displaement ould fill libraries. In this setion we will restrit our attention to only those fators affeted by saling to small size. In partiular, as the mehanisms redue from 7

10 meso- to miro- sale, the size of omponents will typially be omparable to the wavelength of visible light. Whether or not this imposes pratial limitations on optial position measurement methods will be seen in the future...1 Laser interferometry Ignoring tehnial error soures, the fundamental limits to interferometer resolution are determined by noise in the laser soure and the detetors [3, 4]. Mathing both noise soures to produe an equal ontribution, the bandwidth, B, limited resolution in displaement d an be shown to be h B d, (1) πηnep where h is Plank s onstant, is the veloity of light in a vauum, η is the quantum effiieny of the detetor and NEP is the noise equivalent power of the detetor. Using ommerially available detetors a noise level of pm over bandwidths of many khz are theoretially possible. In pratie, there are a large number of other fators that limit auray and resolution in the implementation of a partiular interferometer method. For eample, most ommerial interferometers utilize frequeny splitting with eah frequeny traversing the two paths within the interferometer. These are reombined and the Doppler shifted beat frequeny used as a measure of displaement. The use of polarizing optis and imperfetions in the assembly or optial omponents often lead to errors that are onsiderably larger than those due to detetion and laser noise [5]. At meso- and miro-sales, interferometer pakages will require small optis to ompatly integrate within a system. As well as the usual environmental effets suh as orretions in air for pressure, humidity and temperature, there is also aperture orretion given by [6] R s s f Δ =, () where R is the radius of the soure (aperture stop or ore of fiber-opti light guide), s is the measured length hange of the optial path based on laser frequeny and f the 8

11 ollimator foal length. Typially, for a meso- system with laser soure oming from a fiber feed, R 10 5 m, ollimated at f 10 3 m, it is possible that this partiular error term may introdue a limit on preision of the order one part in 10 5 or worse. Other orretion fators depend on the path length in air. Fortunately, while the effets are often more signifiant for interferometers with large ranges, produing path length variations of the order of parts in 10 7, this represents typial unertainties of nanometers for ranges of less than 10 mm. Another problem is the size of the laser soure. Conventional HeNe an provide stabilities of better than 1 part in 10 7 at reasonable ost and with small line width (long oherene length) but the laser tubes are of the order of tens of entimeters in length. Laser diodes with grating stabilization might realize stabilities of the order of parts in 10 7 but are limited in their oherent lengths [7]. Eletrial urrent (or parameter) stabilized diode interferometers with stabilities of the order parts in 10 5 to 10 6 are likely to beome available in the near future [8]. Currently, ranges of greater than 100 μm with measurement unertainties of better than 10 nm are being laimed. In priniple, it is possible to enhane oherene (redue line-width) by filtering through a Fabry-Perot avity. However, it is not lear whether this an be ahieved without resulting in a bulky soure. Interferometers using small optis have been developed by Renishaw, PTB with the frequeny stabilized laser diode, the Tropel small bore interferometer [9], Dunn et al., 00, Swiss-based small optis manufaturers Fisba [10]. Like some of the larger optial interferometers, to keep the bulky laser head out of the mahine and away from harsh environmental effets, the laser beams are fed to the optial system through an optial fiber. In some systems the fiber itself forms an intrinsi omponent of the interferometer, thereby further reduing the size and number of optial omponents. Suh systems are often alled fiber interferometers [11]. White light probes have been developed to measure loal heights on surfaes. In many ways suh systems ontain similar elements to a Mihelson interferometer. In this ase the white light is split between a stationary referene and the seond is foused onto an area of the surfae to be measured. When the two beams are reombined, there 9

12 will be interferene with the intensity depending on the path lengths of the two beams and wavelength that will generally average out to a mean intensity. In the ase where both beams have the same optial path length, all frequenies will onstrutively interfere with similar phase shifts resulting in an inrease in intensity signal. Hene, it is possible, by hanging the path lengths to reord the orresponding hange in intensity at any point and use this information to reonstrut the three dimensional topography of the surfae refletions. However, in suh a system, loal surfae height is transferred to a displaement of the stationary mirror, or referene surfae, relative to the speimen surfae. The point at whih this measurement is triggered is ompliated by the surfae refletive properties of the speimen being measured and the spetral ontent of the illumination. Given these limitations, it is possible to monitor surfae height variations at nanometer levels while sanning surfae heights measured in millimeters. Other advanes in data proessing and system design have enabled dynami sanning of relatively large areas with movie apabilities providing visualization of motions and distortions in mirometer sized mehanisms (MEMS). An alternative white light tehnique is to fous the light to a point on the surfae and monitor wavelength maima upon reombination with a referene. Variants on this inlude onfoal imaging in whih the white light is foused through a lens to reate a wavelength-dependent foal spot. Again monitoring the wavelength on refletion or hasing the foal point refleted bak through a lens enables a measure of the surfae height from a referene. This enables fast measurement of surfae displaements with nanometer resolution over measurement ranges of hundreds of mirometers (range-toresolution of better than 10 5 ) and requiring spot sizes typially less than a millimeter [1]... Linesale interferometry There are a number of suppliers of linesales for the measurement of both linear and angular motion [13]. Generally, sales are supplied in the form of a bolt-on linear sale or in tape form with self adhesive for ease of installation with a separate read head. In general, high-preision linesale interferometers utilize hange in intensities of the various orders of refletion from a finely sribed diffration grating. With any grating, one of the limitations is the size of the illumination spot relative to the spaing of the 10

13 grating,, whih are, in turn limited by the diffration angle, φ n, of orders n governed by the relation nλ sin φ =, (3) where λ is the wavelength of illumination on the grating by the inident beam. Clearly this funtion must be less than 1, thereby setting a limit on the spaing of the grating for a given wavelength and thereby imposing a limit on saling. For eample a grating of 1 μm illuminated with a wavelength of 0.78 μm will have first order diffration peaks at angles of ± 51. Similar limitations apply to transmission gratings. Reent designs have enabled the use of integrated optis for ompat optial sensor systems of major linear dimensions of less than 10 mm. An eample of this is the ommerially available sales of Sony that use 100 nm grating pith with quadrature detetion yielding a signal pith of 400 nm [14]. With suitable phase measurements, resolutions of better than 10 nm are possible. For a suitable geometry of linesale and analyzer gratings at the sensor [15], the phase, Ω, of any individual order of diffration as a funtion the relative position of the grating,, is given by nπ Ω =. (4) The output intensity at the sensor, I o, is proportional to ( 1+ os(ω) ) I. (5) o This orresponds to a periodi variation in intensity at twie that of the grating period,. Other designs may inrease this further to 4 or more variations per period. By monitoring the symmetri orders it is possible to derive a diretionally sensitive measurement of motion of the grating relative to the optial probe. At redued sales, the effet of the relative spot size is to influene the disrimination of different orders. For a spot size oupying N grating periods, the 11

14 intensity of refletion at an angle θ from the point of inidene an be approimated from [16] Nkθ kθ sin sin 4 I f, (6) kθ kθ sin 4 where N is the number of lines in the field of the inident beam and k is the wave number (= π / λ ). It an be seen by plotting the above equation that the disrimination of eah diffration order will diminish with the relative spot size. In general, mainly beause of problems with alignment errors, alibration of sales and fringe interpolation, linesales typially provide 5 nm 10 nm resolution with some etending down to sub-nanometer. At the etremes of performane, it has been shown that linesales an provide displaement repeatability at better than 0.5 nm [17] and alibration failities at PTB in Germany and Mitutoyo in Japan have demonstrated unertainties of better than 30 nm in the alibration of sales longer than 500 mm [18]. Currently, there is a lot of ativity in the field of small-sale optial form and displaement measuring devies. Reent developments inlude pattern reognition of 3-D interferograms, diode laser interferometry [19] and many variants of near-field sanning optial mirosopy and related probing tehniques [0, 1]. It is lear that efforts are being made to derease the size of these measurement systems, while maintaining or inreasing their resolution apabilities...3 X-ray interferometry X-ray interferometry is often referred to, with some voifierous opponents to this, as the -ray equivalent of the Mah-Zehnder interferometer. Being based on the lattie spaing of a rystal, it is intrinsially aurate to better than parts in 10 7, is portable and an be alibrated to two orders of magnitude better than this. Additionally it an operate in air with little influene of refrative inde beause of the low unit derement (i.e. near unity refrative inde) of materials at -ray wavelengths. 1

15 In priniple, it is possible to shrink -ray interferometers to produe a linesale in whih the splitter and mirror need be only large enough to diffrat the -ray beam whih, in turn an be miro-foused to sub-millimeter ross setion. The analyzer would then be limited only by the length of the available rystal. Currently, rystals of near thermodynami perfetion an be obtained in lengths of up to 1.0 m. In pratie, there are onsiderable tehnologial barriers in implementing this interferometer. Most demanding is alignment with angular deviations of better than a few tens of nano-radians and mirometer separation toleranes between the three rystals being neessary. Another onstraint is the speed of the interferometer that is limited by the intensity of available soures and detetor quantum effiieny. The epense, size and safety onsiderations assoiated with high intensity -rays has limited this measurement tehnique to a few researh labs sattered around the world..3 Capaitane Capaitane is ommonly utilized for preision measurement of relative displaement. Like any single degree of freedom system the voltage noise will be fundamentally limited by Brownian motion [] of harge suh that 1 CV 1 q 1 = = kt, (7) C where C is the apaitane, V is the applied voltage, q is the stored harge, k is Boltzmann s onstant ( J K -1 ) and T is the absolute temperature. In pratie, suh a noise flaw ould only be realized if a perfet signal onditioning iruit was to eist. In pratie, apaitane is measured by providing an osillating voltage (or urrent) aross (through) the apaitor and measuring the reatane of the apaitive element. Noise soures in suh a measurement inlude 1. Osillator noise. This is a funtion of the osillators hosen and will manifest as ombinations of amplitude and phase omponents. Typially it is the amplitude that is most diffiult to ontrol. However, this situation is hanging with digital 13

16 osillators. This will be onsidered an inetriable noise present in the arrier signal and having both 1/f and white omponents.. Amplifier noise. It is assumed that the output from a Wheatstone bridge is monitored by an instrumentation amplifier, the input being a single harmoni arrier frequeny. In suh a iruit the amplitude depends on the imbalane of the bridge. Stray apaitane effets will not be inluded in this analysis. The output noise per root frequeny, e s, from the amplifier of voltage gain zero impedane from the soure is given by e = e G, (8) s n V G V with where e n is the input noise typially of the order 1 nv Hz -1/ for a preision instrumentation amplifier at frequenies above 1 khz. Beause we will be using arrier frequenies of 1 khz or greater the 1/f noise omponent is onsidered negligible. Adding a soure impedane s [ e + ktz + ( i Z ) e ] BG n Z s the amplifier output noise is given by e = +, (9) 4 s n s o V where i n is the input noise figure (often less than 1 pa Hz -1/ at frequenies higher than 1 khz), B is the bandwidth, and e o is the osillator noise per root Hertz (assumed to be zero for the present purposes). The above values have been used to derive Figures 1 and and represent the theoretial noise limits as a funtion of geometry. As an eample, onsider a soure of the form of a transformer ratio on one arm and mathed apaitanes making up the other [3]. This an reasonably be modeled a half bridge input to one terminal and a zero soure impedane on the other. The soure impedane is Z Z Z 1/ ω C C 1 o s = =. (10) Z1 + Z 1/ jω C + 1/ jω Co Coω 1 14

17 Noise (pm/hz 1/ ) pf 0 pf 30 pf 40 pf 50 pf Nominal displaement (μm) Figure 1: Noise as a funtion of gap for a number of apaitane values. Eletrode Radius (mm) Range Nominal displaement (μm) 50 pf 40 pf 30 pf 0 pf 10 pf Sensor Range ( m) Figure : Combined plot of the eletrode radius and sensor range as a funtion of nominal displaement. Illustrates some important performane parameters of typial parallel plate apaitane gages. For high preision measurements it is most ommon to utilize the more sensitive variable gap onfiguration onsidered below over the variable area. Typially, for a apaitane gage we seek to utilize a range inorporating apaitane in the ratio 1::3. 15

18 This gives rise to the important relationship that the range of the apaitane gage is 4/3 times the nominal value defined at the enter value of apaitane. In general, the apaitane ratio from a nominal value an be epressed by k1 Co Co : k : C. (11) o The apaitane range is given by the differene between the maimum and minimum displaement given by k o 1 k o = o 1 k1 1 k. (1) It an be readily verified that the 1::3 (k values of 1/ and 3/ respetively) rule provides a apaitane range of 4/3 of the nominal eletrode separation. Consequently, at the maimum eletrode separation the apaitane will be redued to a value of 1/ of the referene. This will inrease the soure resistane by 17% (1/6). Substituting (10) into (9) for the maimum soure resistane yields s [ e + kt / 3C + (i / 3C ) e ] BG e = ω ω +. (13) n 4 o n o o V In pratie, this appears to be dominated by the amplifier urrent noise followed by thermal noise. It an readily be shown that the output voltage from the transformer ratio bridge for small hanges in one apaitane is given by VbsGV Vout = = S 4 o d. (14) Additionally the nominal separation is related to this nominal apaitane by o εa =, (15) C o 16

19 where is the displaement of the apaitane eletrode, V bs is the bridge supply voltage and S d is the sensitivity of the bridge iruit in units of volts per meter. This an be epressed in alternative forms given by S d VbsG = 4o V VbsGV C = 4εA o. (16) From equations (13), (14) and (15), the displaement noise is given by e B = [ e + 4kT / 3C ω + (i / 3C ω ) + e ] n 16 = V bs o 1 S d [ e + 4kT / 3C ω + (i / 3C ω ) + e ], n o o n o n o o G V o, (17) in units of [m Hz -1 ]. In general, the amplitude (with sign hange aross bridge balane) of arrier frequeny is provided by the synhronous demodulator. Taking the square root of equation (17) gives the displaement noise of the iruit e B 4o = en + 4kT / 3C ω V bs oω + (in / 3C o ) + eo. (18) In the design of a apaitane gage, there are three onsiderations; range, eletrode geometry and noise floor. Basially it is required that the noise floor of the apaitane gage is less than a design goal. Typially this would be the desired resolution of the measurement system at an aeptable bandwidth. In pratie, this ould always be ahieved with a suffiiently large eletrode area. However, this is impratial for reason of eletrode alignment requirements (aeptable parallelism) and volume oupied. A omparison of these trade-offs an be seen from the design harts of Figures 1 and. From this it is lear that there are limits on size being fundamental and dependent upon the preision of the measurement eletronis. 17

20 Comparison of these figures with urrently state of the art sensors is only possible if the harateristis of the first amplifiation stage and ratio k are known. Ignoring this and noting that the following two graphs are based on rather onservative estimates for amplifier noise figures, it is found the noise data from ommerial suppliers, although lose, often surpasses that shown in these plots. Typially, the differene from these plots and available sensors is within fator of and therefore gives a reasonable estimate of ahievable preision in term of seleting and appropriate ADC (i.e. hose an ADC of preision better than 1 bit that predited for the sensor). However, ahieved noise levels will depend upon implementation and we onsider that these graphs are representative of what might urrently be realisti for many appliations..4 Indutane The so-alled linear variable differential indutor (LVDI) has been used as the sensing element in the Talystep stylus profilometer for upwards of fifty years and still represents one of the best methods for measurement of nanometer sized step heights for alibration of film thikness monitors in thin film deposition units. Again, it is ommon to measure variations in reatane using an AC driven Wheatstone bridge. Assuming equal indutors on eah arm of the bridge of nominal value, L o, the output voltage, v o, for a hange in indutane, one arm is ± ΔL, of the indutors on v o ΔL = vs. (19) L To assess the performane of a simple indutive probe, onsider a magnetially permeable ore of length l and permeability μ having a oil of N turns surrounding it. If this ore terminates from forming a loop so that there is an air gap of length nearby permeable target that forms a further part of the ore, see Figure 3. Upon a with a eitation of the oil with a urrent I there will be an indued magneti flu Φ given by 18

21 19 a a a A l A NI NI μ μ + = Φ =. (0) where A μ and A A represent the permeability and effetive area of the gap respetively. Figure 3: Shemati diagram of an indutive sensor utilizing a permeable target. The indutane L of the sensor an be approimated from = + = Φ = a a a a a a o a a a o a a a l A A l A A L l A A L l A A N l A I N L μ μ μ μ μ μ μ μ μ (1) For very small air gaps, so that only the seond term in parentheses is signifiant, a small hange in displaement will produe a orresponding hange in indutane suh that Δ + + Δ a a a o l A A L L L μ μ 1, () Effetive ore length and area, A l, Coil of N turns i,ω a Core, Target Air gap

22 N μ A ΔL a A μ a l Δ. (3) As with apaitane, the noise limit of suh a sensor an be determined from the amplifier performane and the output impedane of the bridge. With an ideal referene arm of the bridge, the output impedane is Z 0 jωl =. (4) Using the same proedures as stated previously, the noise power of this sensor is s [ e + L kt + ( i L / ) e ] BG e = ω ω +. (5) n n o V In this ase it an be seen that the noise will inrease with the arrier frequeny. A variant on the differential indutor is the linear variable differential transformer (LVDT). LVDT s an onsume low power and operate in high vauum, as a non-ontat position sensor that has nanometer resolution and entimeter range [4]. In terms of saling, for either a transformer or differential indutor it is neessary to inorporate at least two separate loops of ondutor with eah having as many turns as possible to inrease indued voltage. A permeable material must also be introdued into these loops and will eperiene an indued magneti flu, the density of whih is inversely proportional to area of ross setion through whih the flu passes. Currently, as far as the authors are aware, suh transduers are manufatured and assembled using onventional wires as ondutors and ferrite materials to reate the permeable paths. Typially, these are of marosopi sale with most manufaturers providing miniature sensors of the order 6 mm - 8 mm diameter and 10 mm 0 mm long. Some LVDI s have been manufatured with total dimensions of around 5 mm 5 mm 5 mm and able to sense displaements of up to 00 μm and with signal to noise ratio of approimately 1 part in 10,000. By inreasing amplifier gains, resolutions of better than 50 pm have been observed with a range of around nm [5]. At smaller sales, it is diffiult to manufature multi-turn oils having sub-millimeter dimensions and inorporate 0

23 permeable materials. While it might be possible to manufature these omponents using MEMS or similar proesses, it is not lear that oils of adequate performane an be readily produed..5 Resistane To the author s knowledge, diret methods for using resistane as a measure of displaement have not found widespread appliation for preision measurement. For limited rotations potentiometers have been used as a method of feedbak for spindle rotation. For eample, in the auto industry these are sometimes used for throttle position, steering angles et. However, these have been almost universally supereded by optial or magneti enoders for more preise sensor appliations. For limited range motions, piezo-resistive strain gages have been used for many deades to detet strain of piezoeletri atuators either by attahing the gage diretly to the atuator element or indiretly by monitoring strain of the fleure in whih the atuator is onstrained. Having upwards of 50 times the sensitivity of onventional metal strain gages, relatively high preision measurements are possible. For eample, typial ommerial atuators having a range of 0 μm will laim resolutions of better than 5 nm with bandwidths of around 1 khz. Typially, metalli resistors have gage fators of around and maimum elasti strains of the order 0.4 % while voltage noise is often measured in mirovolts over bandwidths of around 1 khz [6]. A simplisti alulation indiates signal to noise ratios of the order , a figure omparable to those quoted for ommerial devies Proimity probes are also produed using this sensing method and, suitably designed; demonstrate sub-atomi resolution, although at the epense of limited range..6 Magneti There are a number of different sensors that an be used to measure magneti fields. Partiular sensors, suh as SQUID s (super-onduting quantum interferene detetors) or flugate sensors an ehibit very high sensitivities but are urrently limited in terms of a relatively large power onsumption and size. Promising sensors for the detetion of magneti fields are those based on spin-dependent ondution suh as giant magneto- 1

24 resistane, (GMR) [7] and spin dependent tunneling (SDT) sensors as well as anisotropi magneto-restritive (AMR), or Hall and 3-D Hall sensors [8] all of whih an be ompat, are sensitive to small fields or an be onfigured as gradiometer sensors. These types of onfigurations, in general, require low power, operate over a very broad range of frequenies and an be readily manufatured and miniaturized using miroeletroni proesses. In fat, it is possible to use GMR sensors of similar type to those used in magneti dis data storage read heads to obtain positional information with resolution in the region of a few tens of nanometers [9, 30]. In priniple, there is no reason why this annot be used for position measurement if inorporated for the detetion of urrents in a wire patterned for a speifi measurement (i.e. radial lines or a periodi meander for rotational or linear measurements). Alternatively, it might be possible to use the read head diretly to detet patterned magneti domains on a referene. The simplest referene would be a periodi grid that ould, for eample, be written onto a magneti tape and then adhered to a surfae. However, the ease of manufaturing arrays of suh sensors readily enables absolute or inremental enoder onfigurations [31] for graysale or quadrature type displaement measurements..7 Eddy urrent A simple eddy urrent probe for monitoring displaement between a surfae and a irular oil at a distane z above the surfae is given by [3] π μn r L = l t 0 I 1 l + e α ( r, r ) α 5 αl 1 + α α + 1 ( ) ( ) α α αl l+ z αz α l+ z 1 [ e + e e ] dα, (6) where I ( r r ) = J ( ) 1, αr α r1 1 d, (7)

25 1 1 ( α + jωμσ ) α =, (8) t is the differene between the inner and outer radius, r, r 1, of the eitation oil, l is the length of the oil, μ is the permeability of the speimen surfae material, σ is the eletrial ondutivity of the speimen surfae material, ω is the frequeny of eitation and α and are dummy variables of integration. Correspondingly, there will be a repulsive fore between the surfae and oil of value F z i = i = L z π μn r l t I ( r1, r ) 5 α αz αl αl α α 1 ( e ( e e + 1) ) dα. α + α 0 1 (9) These equations an be solved numerially to show the dependene of indutane and fore with separation. For a flat oil of 40 turns, an inside diameter of 8.0 mm, an outside diameter of 1.0 mm and a wire diameter of 0. mm being driven at a frequeny of 0 KHz, 0.35 V at a urrent of 0.70 A, is shown in Figure 4. In most instanes, as with apaitane sensors, the fores might be onsidered insignifiant when ompared to the size of the sensor. In pratie, the referene surfae should be relatively flat, larger than the oil and etend to a depth onsiderably greater than the skin depth, δ, given by 1/ ( ) δ = ωμσ. (30) A disadvantage is that the sensitivity is dependent upon the materials type and it is possible that the eddy urrents an ause loal heating of the target surfae, whih must also be an eletrial ondutor. Suh eddy urrent based indutive probes an have high resolution and bandwidth and have the additional advantage that eletrial onnetion to the target surfae is not neessary. Typial ommerial probes will resolve to within tens of nanometers over millimeter ranges. The limit on range is set by the size of the oil or diameter at whih the magneti field is being generated. For eample, if a irular oil is used to generate the osillating fields, it is found that, as a rule of thumb, the field generated by the oil is 3

26 substantially attenuated at a distane approimately equal to its mean radius. Consequently, this type of sensor might be onsidered as a probe with a measurement zone etending a maimum of the oil radius while also requiring a speimen surfae of irular dimension twie that of the oil outer diameter. Fore (mn) Voltage = 0.35 V Current = 0.7 A Frequeny = 0K Wire dia. = 0. mm Inner dia. = 8 mm Outer dia. = 1 mm indutane measured theory Indutane theory Indutane meas Liftoff (mm) Indutane (mh) Figure 4: Dependene of indutane and fore on separation. Theoretial and measured values are shown. Alternatives, to indutive oils an be found in the use of sensing elements to detet the magneti fields produed by the eddy urrents. In priniple suh probes an be made with the sensors suitably plaed and biased to measure only the field of the eddy urrents independent of the eitation field [33]. Suh probes an also be miniaturized to produe loalized measurement of surfaes for pattern reognition and, possibly, lateral position measurement [34]..8 Proimity probes A proimity probe is onsidered to be any sensing method that provides a measurable signal as it is brought into lose proimity to a surfae. Often proimity probes are used as a means of ommuniating a translation from a relatively small area on a surfae; in a oordinate measuring mahine (CMM), stylus profilometer or sanned probe mirosope 4

27 (SPM) this is the probe. This is then ommuniated to an atuator that an move the probe and reord subsequent displaements. In suh systems, it is also apparent that there is still the requirement for a displaement measuring system. One area in whih the saling of proimity sensors has seen etensive development is the in the field of SPM sensors. Sensing methods inlude tunneling, strain gage, near field optial, thermal, ion ondutane or apaitane. The relative merits and limitations of these proimity sensors are 1. Small probes an measure surfae heights in a small and loalized area (sometimes with resolution of better than one atom for the smallest of probe tips).. When ontrolling the probes to maintain a null signal level, as long as the sensing harateristi as a funtion of tip/sample interation is stable and repeatable, the auray is little influened by non-linearity. 3. Etremely high resolution and bandwidth measurement of variations in the probe to surfae interation are possible. 4. Most probes provide only proimity information and do not have the intrinsi apability for the measurement of displaement. This is usually transferred to another displaement measurement transduer of the types outlined above. 5. In priniple, any of these probes ould be used to detet variations of, and therefore represent a sensing method for, a periodi sale. In the initial sanned probe mirosope designs of Young, et al. [35, 36], the proimity sensing method was Fowler-Nordheim field emission from a sharp eletrode tip and later efforts were attempted to utilized eletron tunneling at tip-speimen spaing of less than nm and lower applied voltage levels. Problems with relative vibrations between probe tip and surfae prevented sanning until a deade later, Binnig, et al. [37, 38], were able to redue the mehanial noise and ahieve atomi sale images on silion, for a brief review see [39]. 5

28 A tunneling probe onsists of an eletrially ondutive sharp tip that is brought into lose proimity to an eletrially ondutive surfae. With applied voltage differenes of a few tenths of a volt, there will be an eponential inrease in urrent as the separation redues. Typially this will range from pioamps to miroamps with separation hanges of around one nanometer. Using a logarithmi amplifier it is possible to obtain a sensitivity of many gigavolts per meter over, of ourse, a very limited range. In pratie, suh a probe is sensitive to the separation of the outermost asperity of its tip and is therefore etremely loalized and, for measuring surfaes that are smoother than the tip geometry, may be onsidered to measure the proimity at a point on the surfae. However, a drawbak with tunneling is that it requires eletrially ondutive surfaes, must maintain nanometer level separations and is suseptible to surfae ontamination. For these reasons, tunneling probes are not widely used in meso and miro sale appliations. While tunneling probes may not be partiularly popular today, beause of their spetaular ability to disriminate individual atoms, whih in turn, fueled the imaginations of nanotehnology visionaries aross a broad range of sientifi and ommerial disiplines, they were predominantly responsible for the eplosive emergene of the sanned probe mirosope industry. Among the many proimitysensing methods that have been developed, by far the most ommon is the so-alled atomi fore probe [40]. This also omprises a sharp tip that is brought into lose proimity or ontat with a point on the surfae. However, it is the interation fore that is transformed to a displaement (or, equivalently, strain) and it is this displaement that is then measured to determine proimity. In pratie, given suffiient sensitivity it is possible to monitor both non-ontat (eletri dipole, van der Waals/Casimir, gas squeeze film) and ontat (menisus, elasti) fores with this form of sensor [41]. While, tunneling probes, optial levers, apaitane and (piezo-resistive) strain gaging have been used to determine the fore of interation, in general it is neessary to use a larger surfae or volumetri sensing area to determine a measure of the fore thereby inreasing the footprint of this probe. However, all of these an be readily produed using maro to MEMS and, reently, nano manufaturing proesses and therefore suh probes an be readily saled. 6

29 3.0 Atuators There are an almost limitless number of atuator designs that an be employed in a given system using any number of mehanisms. In general, the major figures of merit quantifying the performane of different atuator methods as they apply to a speifi mahine appliation inlude 1. Mahine volume/atuator volume.. Range/resolution, or preision, requirements. 3. Effiieny, measured as a ratio of power delivered to a proess to that supplied to the atuator. 4. Type of oupling between atuator and objet to whih fore is to be applied. Generally this an be lassified as either ontat or non-ontat. 5. Bandwidth, generally measured by available power-density. Also at issue is the onnetion to the motion ontrol system. In partiular, there is a onern in design with the removal or redution of parasiti motion of the driver. There are relatively few atuators that an be applied to mahines at smaller sales. This is rather surprising in view of the sale of biologial proesses. However, in engineering systems, we are restrited in the seletion of power soures and it is onsiderably more effiient to generate power using marosopi systems and hannel this into the meso-sale mahine. Novel power soures inlude 1. Solar.. Eletro-rheologial fluids [4]. 3. RF absorption. 4. Miniature ombustion [43, 44]. 5. Fuel ells. 6. Biologial systems, ellular or life-based. 7

30 While interesting, a disussion of these is outside of the sope of this paper and epertise of the authors. However, these are, for the most part, alternative ways of produing eletriity that will then be onverted bak to work through some atuation mehanism. It is these primary atuator mehanisms that form the basis of the disussions in this setion. Assuming that energy soures are available, the main lasses of atuator likely to find appliation in meso- and miro-systems in preision mahine design inlude 1. Piezoeletri. Eletromagneti 3. Eletrostati 4. Pneumati 5. Hydrauli 6. Thermal 7. Shape memory Thermodynamially, it an be demonstrated that all atuators, in the proess of doing work on a system will generate heat. In pratie this an severely limit performane of instrument and mahine mehanisms. Therefore, atuators suh as voie oils and purely eletromagneti or eletrostati atuators an provide highly effiient eletromehanial oupling and, therefore, dissipate minimal amounts of heat at the drive. In other ases it may be desirable to loate the atuator remote from the mehanism. In this ase it is then neessary to transfer the work mehanially to the mahine. This an be very effiiently ahieved using push-rods or, possibly, pulleys. In this ase, the desirable saling of the atuator mehanism might also help determine the nature of the work transfer mehanism. For eample, beause eletromagneti atuators favorably sale to large devies, it might be desirable to use one large motor and use this to drive multiple smallsale mahines, just like the power soures in fatories in the late nineteenth and early twentieth entury! 8