Development of Noise Measurements. Part 6. Opposing Method in Stepless Shifting Regulation

Transcription

1 Sensors & Transucers, Vol. 55, Issue 8, August 03, pp Sensors & Transucers 03 by IFSA Development of Noise Measurements. Part 6. Opposing Metho in Stepless Shifting Regulation Bohan STADNYK, Svyatoslav YATSYSHYN, Iryna HRYTSYN, Khrystyna LEVYTSKA National University Lviv Polytechnic, Institute of Computer Technologies, Automation an Metrology, Banera str., Lviv, 7903, Ukraine Tel.: Receive: 8 July 03 /Accepte: August 03 /Publishe: 0 August 03 Abstract: It is consiere the hyraulic technique an stuie nanoobject stepless shifting means along the Z-axis with the working liqui monomolecular layer thickness orer error. Systematic multiplicative error elimination is obtaine by means of the opposing metho usage when calibrating. Copyright 03 IFSA. Keywors: Nanoshift, Shift stepless control along the Z-axis, Relative error, Opposing metho of error minimization, Calibration.. Introuction Accuracy an stability problems of 3-D positioning are consiere to be principal in the nanotechnology. Authors [] employ a combination of simulation techniques to moel three ifferent physical properties of the opant atom, accessible in an experiment, an then use this information to triangulate the opant position to ±.5 nm in two irections an ± 5 nm in the thir irection. Toay there are 3-D positioning precise means of nanomachines, shift mechanism in atomic-force microscopes (later AFM) an familiar to them means. To reuce the scanner positioning error along the axes X an Y the AFM is preliminarily calibrate by the lateral stanar. The calibration consists in stanar surface measurement with the help of AFM an further usage of obtaine length unit as a stanar []. It is more complicate to calibrate along the axis Z. Paper [3] focuses on the on the esign an calibration of an elastically guie vertical axis that will be applie in a small high precision 3D Coorinate Measuring Machine aiming a volumetric uncertainty of 5 nm. In the metrology part of this paper the calibration methos to etermine the linearity as well as motion straightness an axis rotation errors were iscusse. Finally first calibration results of Z-axis show nanometer repeatability of the probing point over the 4 mm stroke of this axis. The causes of the short-term variations with a banwith of about ± 0 nm are uner investigation. Error compensation may reuce the resiual error of the probing point to the nanometer level. So a step stanar [4] is use for calibration with next calculation by the calibration results calibration coefficient C z. To etect scanner nonlinearities the calibration measurements are carrie out by the means of ifferent height step stanars set, in other wors by the multivalue measure proucing of which is very complicate. At the same time own calibration coefficient C z (h) is calculate for every stanar, an calibration 300 Article number P_SI_38

2 Sensors & Transucers, Vol. 55, Issue 8, August 03, pp coefficients for interim height stanars will be calculate by the linear interpolation. For instance, the key features of stanars TGZ set of NT-MDT firm are given in the Table [5]. Table. Stanar TGZ features as multivalue height measure. Material Silicium Stanar size mm 3 Certificate area size Central part 33 mm Structure type Perio Height One-imensional right-angle structure 3.0 μm TGZ 9± nm TGZ 04±.5 nm TGZ3 540± nm A number of aitional requirements appear uring the preparation to the calibration on the multivalue step stanar: Stanar lateral positioning in horizontal plane the structure must be locate in the centre of controlle range; The structure must be locate at angle of 90 0 to the measurement irection; Measurement spee is chosen so to provie the minimal istortion of structure fronts; Gauge range must excee in 4 times the step with (to provie the measurement ata sufficient quantity). After calibration measurements proviing the next stage is the step height estimation, for instance, in accorance with the metho of ISO 5436 [4]. Here, the step height calibration artefact is a machine block of steel. It automatically etects the steps an calculates the step height or groove epth accoring to the mentione stanar. In this case the average step height is evaluate to 57 nm. All samples values of which excee the threshol level are accepte as high level, an others as low one. In this case the noise problem is neglecte uner this metho usage that is not always acceptable, for instance, at step height small values. The step height h is calculate as the ifference between high level an basic plane level. To create Z-shift realization means the mentione metho is not enough as well as the thickness special measure usage: monomolecular layer coating, multilayer film etc. The main shortcomings of the mentione means are graation positioning, some measure quantity necessity, calibration process complication an its significant uration an cost. means along the axis Z-elaboration (within nm) of the nanomachine or other evice, for instance AFM contact assembly. 3. Theoretical an Practical Basis of Hyraulic Unit Creation for Nanosize Objects Shift Along the Z-axis During the creation of hyraulic positioning unit along the axis Z of the nanomachine with proviing stepless shift an position control possibility along this axis it is propose to use hyraulic potential. To this purpose U-shape hyraulic construction is propose with ens of larger (D = 00 mm) an smaller ( = 0.3 mm) iameter. Diameters ratio is D equal: 0.0 mm / 0.3 mm In the case of liqui level shift control in the narrow en with error ±.5 μm it is appeare the possibility to provie stepless an quite accurate level isplacement in the wie en. This is the object of this stuy. Hyraulic positioning is base on the laws of liqui motion an balance. The main part of hyraulic unit consists of two hermetic cyliners of ifferent iameters connecte by the interim iameter tube. The space in cyliners is partly fille of liqui (generally with istille water, alcohol etc.). The height set levels of liqui column in every cyliner are fixe as zero levels. Spontaneous or enforce liqui level shift, for instance, in the small iameter tube or en, is etecte by means of micrometer hea (Fig. ). Fig.. The unit of nanosize objects hyraulic positioning: - shift micrometer hea; cantilever; 3 float with mounte research nanoobject.. Work Goal The work goal is stepless highly precise nanoshift hyraulic technique evelopment an positioning 3.. Measurement Operation In the motionless fixe tube its pivot sinks by the shift micrometer hea pressing hyraulic liqui to the 30

3 Sensors & Transucers, Vol. 55, Issue 8, August 03, pp wie cyliner. Consequently the liqui level is increase in this en on h. It results to weak but appreciable liqui level increase in the wie en. In accorance with joine vessels law the level increases on H in the wie en. Floating plate mounte in this wie en lifts the same as the stuie nanoobject mounte on it. In this case the conition of liqui quantity invariability uner pouring from one en to another one can be escribe by the next formula: D D H h. If we use A as constant 4 4 for this unit construction then with mentione above D 400 ens iameters A So we have 0.09 got the formula specifying the level rops changes in wie ( H ) an narrow ( h ) evice ens. h H () Accoringly with error approach principles [6] the relative errors of liqui level change in both evice ens are linke between each other by the formula getting from (): A ( H ) ( h ) A, () where ( h ) is the evice relative error specifie by the inaccuracy of the rop level measurement by the micrometer hea; A is the evice relative error specifie by the inaccuracy of constant value A which can reach significant values an, even, change uring the experiment. Let s consier consequently these two error components an abilities to ecrease or/an eliminate them. The first error component is etermine by the following way. So far as liqui level measurement rop in the narrow en is 5 μm then the evice measurement step is H etermine by the formula () in the wie en is 5.0 μm / =. nm. Micrometer hea absolute error in accorance with passport is ±.5 μm. Its value inclue to the result of the level shift in the wie en is ± 0.55 nm. Hereby the absolute measurement error of the liqui shift level in the wie en is specifie by the micrometer hea inaccuracy. The step measurement refinement result with value error is equal to nm. Otherwise the relative measurement error of hyraulic shift on. nm specifie by the micrometer hea capabilities is estimate as + 50 %. In the case of liqui level shift control in the narrow en with error ±.0 μm it seems possible to reach the relative measurement error of hyraulic shift 0 %. Hereinafter the unknown secon component of the evice error the relative error of constant A value etermination. 3.. Metrological Experience of the Error Measurement Systematic Component Minimization The error correction possibilities analysis enables to ivie the absolute aggregate measurement error into three components: a) an aitive error α which is inepenent from the value of measure quantity Х an is also calle zero error; b) the error non from the characteristic. nonlinearity; c) the multiplicative error m = δ m X which is proportional to Х an is calle the sensitivity error. The aitive component can be easily etecte if Х=0. To etect nonlinear error component it shoul be use multivalue measures or scale converters. The multiplicative component can be etecte uner presence of the measure or the scaleconverter. Relative multiplicative error δ m can be eliminate by the means of the single-channel unregulate measure by the way of the measurement evice verification if the Х 0 value is known (in our case - h 0 ) an next ivision an multiplication. For measurement accuracy improvement an multiplicative component minimization can be use the opposing metho [7]. The metho point consists in that the measure quantity HX is compare twice with regulate measure - H N; H N ; besies that before the secon measurement it is rearrange with the measure. Consequently this quantity value with the eliminate measurement error multiplicative component can be gaine: H H H X N N 3.3. Hyraulic Device Calibration There is a real operation realizing before or after the measurement operation an is assigne to eliminate mentione above multiplicative error component. In the current case it is assigne to ecrease or/an eliminate the secon component (in the formula ) of the shifte liqui level relative error etermination in the wie evice en, in other wors to set accurately Z-coorinate in the nanomachine. The calibration operation (Fig. ) is on principle inverse to the measurement operation. The liqui level in the wie en is change with the help of plunger connecte at this time to micrometer hea. After the liqui balance setting in two ens the liqui level shift in the narrow en is measure by the means of the Vernier-caliper gauge. Simultaneously the micrometer hea is move to the wie evice en. It provies the plunger shift an liqui level on value that meets the level shift in the narrow en uring the measurement. So h H 5 μm. In this case the mentione shift when the constant A value is equal to specifies the 30

4 Sensors & Transucers, Vol. 55, Issue 8, August 03, pp liqui level shift in the narrow evice en on h AH =. mm. Uner this, evice constant A is etermine from: A h (4) H Fig.. Unit calibration for hyraulic positioning: - micrometer hea; control linear scale of the liqui level shift. Having place (4) into () liqui column height esire change in the wier en can be foun: h H H H X h h h (5) Column height change ΔH x numerical value assessment gives 5 m /. mm = 0.00 m =. nm. The error component is absent here that is specifie by the evice constant A unknown value. But completely known components of relative measurement error of the liqui level isplacement appear. The next formula escribes it. Aggregate relative error of the liqui level change measurement in the wie evice en can be obtaine by the ifferentiating (5): h ( H X ) h h h (6) Uner the conition of the micrometer hea ouble usage when level measurement is conucte with relative error 50 %, the aggregate relative error of before specifie new liqui level in the wie en excees slightly 00 % ( 40 % in the case of liqui level shift control in the narrow en with error ±.0 μm). By the way the secon component in (6) insignificant (substantial level shift can be measure quite precisely with relative error not more than %). In the conitions of the stuie nanoobject height single fixing so far as the unknown ieal fixing result it is more correctly to work not within the error approach but on the basis of the uncertainty approach. Accoringly with last one [9], [6] the height fixing result is more correctly to write in the form of reaout result with establishe expene stanar uncertainty of type A that is in our case ± 0 / 3 (4 / 3) = ± (4.5) %. The calibration obtaine results enable to reach efficiency in Z-axis shift control in the nanomachine. To this purpose the calibrate unit with concrete etermine ration of two ens areas is use by appointment as escribe in the Fig.. If the average atoms size of liqui is approximately equal to 3Å = 0,3 nm then current evice enables to set the liqui level an nanoobject mounte on the floating platform with absolute error which is slightly more than atoms size. At the same time the work [8] gives close values of water film estimate thicknesses pretermitting the accuracy issue of their regulation an setting. For instance, thickness of a liqui layer seems to be of orer 0 Å at the temperatures up to 3-4 K below the melting point of ice. To etermine the thickness at temperatures closer to the melting point, larger simulation cells an more accurate estimates of the melting point are neee. The thickness of a liqui layers etermine in this work seems to be of the same orer of magnitue as etermine by Bluhm et al. [0] from photoelectron microscopy. Thanks to the wie evice en an layer-by-layer filling of the liqui this hyraulic positioning metho provies the require contact of cantilever an stuie nanoobject mounte on floating platform. During the stuy of cantilever Z-axis regulating capabilities or shift of the floating platform relative to it by the height with the help of mentione above it is able to fin the next one. Uner accurate settings of very small Z-axis values the movable means elements (hyraulic liqui molecules) etermine the noise evice features. Perhaps, in future it shoul be taken into account the viscosity fluctuating eviations. They may be specifie, for instance, by the temperature eviations from optimal regime, the iversions from the horizontality, the non-iscrete character of the every layer filling an some other factors. They etermine the noise threshol an limit the evice sensitivity. 4. Conclusions. Nanotechnology further progress is impossible without methos an means evelopment of nanosamples an sensitive elements stepless reciprocal shift along the Z-axis, for instance, probes an cantilevers that guarantee of tunnel an other phenomena stuies that eman exceptional shift accuracy.. Hyraulic metho an reciprocal shift means of the nanoobject an cantilever enable with the error 303

5 Sensors & Transucers, Vol. 55, Issue 8, August 03, pp of working liqui monomolecular layer thickness orer to provie their stepless shift along the Z-axis. 3. Simultaneously the systematic multiplicative component of aggregate error is eliminate by the opposing metho of error minimization usage in the course of the calibration stanar metho of the current error component elimination in the metrology. Therefore noise threshol is isplace in the irection of nanosizes an, as result, Z-axis accuracy setting is improve. References []. Nanoelectronic moeling for noninvasive spatial metrology, Nanowerk Nanotechnology Spotlight, Poste: May 08, 03. []. E. Manske, G. Jäger, R. Füßl, F.Balzer, T. Machleit, Nanomess - un Nanopositioniergeräte für ie nanometergenaue Positionierung, Messung un Bearbeitung von Oberflächen un Strukturen: Schwerpunkt: B5 Nanomessmaschinen, in: Sensoren un Messsysteme 0 / GMA/ITG-Fachtagung; 6 (Nürnberg), AMA Service GmbH, Wunstorf, Germany, -3 May 0, pp [3]. J. K. V. Seggelen et al., An Elastically Guie Machine Axis with Nanometer Repeatability, ( /pfs/7390.pf). [4]. ISO 5436, Nanometrology, Compliant Step Height Calibration, ( [5]. Calibration gratings, NT-MDT AFM Tips, Company NT-MDT, TGZ set ( [6]. М. Dorozovets, Elaboration of measurement results, Lviv Polytechnic eition, Lviv, Ukraine, 007. (in Ukrainian). [7]. V. Yatsuk, P. Malachivski, Methos of improving the measurement accuracy, Lviv, Besky-Bit, 008. (in Ukrainian). [8]. M. Cone, C. Vega, A. Patrykiejew, The thickness of a liqui layer on the free surface of ice as obtaine from computer simulation, Journ. of Chem. Phys., Vol. 9,, 008, p [9]. ICGM 04: 00, Evaluation of measurement ata, An introuction to the Guie to the expression of uncertainty in measurement an relate ocuments. [0]. H. Bluhm, D. Olgetree, C. Faley et al., The Premelting of Ice, Journ. Phys.: Conens. Matter., Vol. 4, 00, pp. L7-L Copyright, International Frequency Sensor Association (IFSA). All rights reserve. ( 304