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Appl. Phys. A 66, S857–S860 (1998)
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S858

    Given that the novel STM is intended for use in metrology
and atomic manipulation, the resolution and accuracy s...
S859

                                                                                        transfer function of this co...
S860
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1998 Appl. Phys. A 66 (1998), p857 design and construction of a high resolution 3 d translation stage for metrological applications

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1998 Appl. Phys. A 66 (1998), p857 design and construction of a high resolution 3 d translation stage for metrological applications

  1. 1. Appl. Phys. A 66, S857–S860 (1998) Applied Physics A Materials Science & Processing © Springer-Verlag 1998 Design and construction of a high-resolution 3D translation stage for metrological applications K.R. Koops1 , R. Banning1 , P.M.L.O. Scholte1 , W. Chr. Heerens1 , J.M.T.A. Adriaens2 , W.L. de Koning2 1 DelftInstitute of Microelectronics and Submicrontechnology, Faculty of Applied Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands (Fax: +31-15/2783251, E-mail: koops@duttfks.tn.tudelft.nl) 2 Mathematical System Theory Group, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, The Netherlands Received: 25 July 1997/Accepted: 1 October 1997 Abstract. The nonlinear and hysteretic behavior of piezo ac- in the perpendicular direction. The accurate position informa- tuators used in scanning probe techniques limits the accu- tion provided by this sensor enables the implementation of racy of the quantitative interpretation of the measurements. a position feedback controller for the lateral as well as the per- In this paper we present the design of a novel ultra-high pendicular direction of the probe. Using physical knowledge vacuum (UHV) compatible scanning tunneling microscope of the behavior of the translation stage and the piezo actua- (STM) that is equipped with a newly developed capacitive tors, a model-based position tracking and control system is translation sensor. The sensor has been configured to meas- currently implemented on a digital signal processing (DSP) ure translations in the lateral as well as in the perpendicu- system. lar direction with sub-Ångstrom resolution. In combination with a model-based digital feedback system, accurate probe positioning and control will be possible, making this instru- 1 Novel design ment suitable for metrological purposes, nanolithography and atomic manipulation. The usual approach in STM design is to maximize the me- chanical resonance frequencies of the microscope with re- spect to the measurement and control bandwidth. In this way the influence of out-of-band resonance modes is, in general, Since the introduction of scanning probe technology the tech- minimized. However, when these modes are inadvertently ex- nique has been troubled by the nonlinear and hysteretic be- cited owing to unforeseen circumstances, their amplitudes havior of the piezoelectric actuators (PEAs). The resulting can rise to unacceptable levels and render useful measure- image deformations are, in general, difficult to detect; on the ments impossible. Following an altogether different design lateral scale of atomic excursions the piezos behave fairly lin- strategy, the fundamental mechanical resonances of the STM early, but on a larger scale, where the nonlinear and hysteretic are now designed to lie within the measurement bandwidth in behavior of the actuators becomes significant, the atomic lat- order to be able to control the dynamic behavior. The transfer tice is no longer visible as a reference. Only on a regular function for frequencies beyond the measurement bandwidth grid of mesoscopic structures can the image deformations is designed to sufficiently suppress excitations. In addition, be clearly observed [1]. Although such measurements can be the natural frequency of the stage including the sensor and the used for a qualitative examination of the sample, accurate piezos is chosen well below the sampling rate of the DSP sys- quantitative interpretation is difficult. The best approach for tem in order to satisfy the Nyquist criterion [2]. For a natural correcting the nonideal piezo characteristics is independent frequency of the system of 1 kHz in combination with a sam- measurement of the actual position of the probe relative to pling rate of 10 kHz for the DSP system, the system’s overall the sample. Because of the high resolution, simplicity and stiffness k, its total mass m, and its overall damping c should UHV compatibility of capacitive translation sensors we have be such that decided to employ this technique in a new scanning probe microscope. Previous studies [1] have already shown the pos- k √ sibility of linearizing both lateral displacements in a proto- = 4π 2 × 106 Hz2 , c= 2km (1) m type set-up by means of capacitive sensors and an analog proportional integral derivative (PID) controller [2]. In this The rigid connection between stage and sensor system only paper a newly developed monolithic capacitive 3D translation introduces resonance frequencies several orders of magnitude sensor is presented and its integration in a scanning tunnel- higher than the 1 kHz of the stage. Since the stage acts as ing microscope (STM) is described. This sensor is capable a lowpass filter, the effects of these high-frequency resonance of detecting sub-Ångstrom displacements in the lateral and modes are negligible.
  2. 2. S858 Given that the novel STM is intended for use in metrology and atomic manipulation, the resolution and accuracy should be well below the dimensions of a typical atomic radius. We have therefore set the required resolution in the lateral direc- tions (x, y) to 30 pm and the resolution in the perpendicular direction (z) to 10 pm. The total scanning volume was taken 10 cm as 50 µm × 50 µm × 10 µm (x × y × z) resulting in a dynamic range of about 6 orders of magnitude, or 21 bits, in each direction. 2 The capacitive translation sensor Fig. 2. The electrode patterns of the 3D translation sensor In Fig. 1 a basic capacitive lateral translation sensor is schematically displayed. The upper electrodes 1 and 2 are in (2), the equation for the z configuration (the plane parallel driven with equal AC voltages of opposite phase. When the capacitor) is obtained. From this equation the desired reso- upper plate is positioned symmetrically over the lower elec- lution of 10 pm in the z direction yields a minimum total area trode 3, the capacitively induced currents will cancel out. for the z electrode of 3.5 cm2 . Given the minimum total areas When one of the plates is translated in the x direction the can- for the lateral and the z detection the overall lateral dimen- cellation will no longer be complete and a net current will sions of the sensor become 10 cm × 10 cm. Because accurate flow through the capacitor. Analysis reveals that fringing ef- alignment of the sensor plates with respect to each other and fects at the edges of the electrodes can be neglected if the with respect to the translation stage is crucial for optimum design rules [3] are adhered to. Consequently the relation be- performance, the electrode structures have been split into sev- tween the change in capacitance ∆C and the translation ∆x is eral sub-structures. Depending on the combination of elec- expressed by [3] trodes and the phase of the electrode signals, measurements in all six degrees of freedom can be performed [4]. 2εoεr ∆xL ∆C = (2) d 2.1 Modulo measurement technique In other words, the change in capacitance ∆C is linear in the translation ∆x and inversely proportional to the plate separa- Although the capacitive sensor itself is designed to provide tion d. The resolution is determined by the smallest detectable the required resolution over the full dynamic range, the sig- change in capacitance and is therefore linked to the total elec- nal conditioning electronics (i.e. phase-sensitive detectors) trode area and the plate separation. Out of this basic concept have a more limited dynamic range. The full scanning vol- a capacitive 3D translation sensor has been developed [4]. ume of the translation stage of 50 µm × 50 µm × 10 µm is Given the fact that a change ∆C in capacitance down to therefore mapped onto several regions of measurement. An 10−18 F can be measured, the required change in electrode auxiliary capacitor bank is used for each direction to provide area ∆A for a translation ∆x of 30 pm is given by so-called compensating capacitors that are switched parallel ∆A ∆Cd and in anti-phase with the sensor capacitors. The individual =L≥ (3) capacitance values of the compensator range from a unit value ∆x 2εo εr ∆x C to 210 × C. The binary code that is used to select the ap- The required length L of the electrode for a sensor plate sep- propriate value for the compensating capacitance is a direct aration d = 200 µm is therefore at least 38 cm. In order to representation of the 10 least significant bits (lsb) of the probe keep the dimensions of the sensor within acceptable limits position. With this strategy a modulo type measurement is re- the electrodes for the detection of the lateral translations have alized to exploit the full potential of the capacitive sensors been shaped in the folded configuration shown in Fig. 2. The and to obtain the required resolution and range at the expense electrodes for the detection of the z translation are situated of using an extra capacitor array. between the electrodes for the detection of the lateral transla- tion. In contrast to the lateral detection, the z capacitors detect the change in the plate separation. By ignoring the factor 2 3 The translation stage The translation stage is configured as a flexure because of the excellent mechanical properties for small range translations. The outer dimensions of the STM stage are mainly deter- 1 2 L mined by the size of the capacitive sensor and the size of the piezo stacks. In Fig. 3 the lower section of the stage is shown in detail. Spring-loaded piezo stacks are used to drive the cen- d 3 tre section of the stage in both lateral directions (x, y) via a lever mechanism. The lever mechanism is primarily used to decouple the x and y piezos and to minimize shear forces. D x Due to the placement of the flexures at the corners of the cen- Fig. 1. A basic capacitive translation sensor tre section the strain is confined to small areas in these regions
  3. 3. S859 transfer function of this controller is equal to z+1 K(z) = k I (4) z−1 When a square wave voltage is applied to the x-piezo, the cor- responding position changes are not instantaneous, as shown in Fig. 4. In other words, the open loop system requires a cer- Z Y tain amount of time to reach, in an oscillatory pattern, the Z stage Long range change in position corresponding to the altered applied volt- piezo stack age. Similar tests show that the response of the stage to a si- X Sensor plates nusoidal voltage signal is periodic but not perfectly sinusoidal Primary signal (Fig. 5). Consequently, when the position signal is displayed conditioning against the voltage signal, a cigar-shaped hysteresis loop re- Fig. 3. A schematic view of the lower section of the STM translation stage. sults (Fig. 6). With feedback controller (4) we can not only The second electrode plate (not shown) is positioned just above the one reduce the settling time of the position signal but also re- mounted in the lower section duce its oscillatory behavior (Fig. 7). The traces represent different settings of the controller K(z); k I = 500, 2000 re- spectively. Furthermore, for k I = 2000, an accurate response so distortion of the capacitive sensor plate (which forms one of the stage can be created as shown by the second trace part of the position sensor) is minimized. Although the capac- in Fig. 6, where the desired position signal is depicted against itive sensor described previously is capable of measuring x, y the actual position measurements. The fact that the width of and z translations, the construction of the stage allows for lat- the loop is small indicates that the desired and actual re- eral displacements of the central area only. Therefore, in this sponses are nearly identical. application, a separate z stage with a small capacitive sensor Additional testing of PID-type feedback controllers re- is used and is located at the mechanical and thermal centre of vealed a limited application area for each parameter setting. the stage. Almost every change in scanning parameters and/or change in sample required a retuning of the controller. A model-based position feedback controller is much more flexible and of- fers improved overall performance. However, for the design 4 Modelling and control of such a controller, a dynamic model of the translation stage is required. Availability of the position measurements offers the opportu- Theoretical considerations as well as experimental re- nity to use position feedback control as a means of improving sults suggest that PEAs exhibit dynamic behavior [5]. Con- the quantitative abilities of the microscope. In order to as- sequently, it is not permissible to partition the overall dy- sess the effects of position feedback control, we implemented namic model into a purely dynamic component and a purely a digital PI(D) type controller [2] on a prototype translation stage with an integrated 2D sensing system [1]. The z-domain 1.5 2.5 1 2 1.5 0.5 Position voltage [V] response Position voltage [V] 1 0 0.5 stimulus -0.5 0 -0.5 -1 -1 -1.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1.5 0.1 0.105 0.11 0.115 0.12 0.125 0.13 Time [s] Time [s] Fig. 5. Response of the stage to a sinusoidal stimulus without feedback Fig. 4. Transient response of the stage without feedback control control
  4. 4. S860 1.5 arable, as well as the fact that the overall system must be amenable to control technology, a model for the system dy- namics is needed in the form of a cascade combination of 1 a linear dynamic model and a dynamic hysteresis operator. Although the STM controller will be designed for overall control of the microscope, it should also be able to oper- Acquired position [V] 0.5 ate alongside existing STM hardware and software. Given the operational specifications, the DSP system must have a resolution of 21 bits or more. However, conversion mod- 0 ules compliant with such stringent specifications have traded resolution for speed. Fortunately, we do not need a 21-bit A/D open-loop conversion system because of the 10-lsb position measure- -0.5 response ment provided by the modulo measurement technique. Fur- thermore, once 21-bit position measurements are available, an effective 21-bit actuation capability can be created through -1 the use of parallel D/A channels of lower resolution. Operational considerations favor the introduction of pri- mary and secondary positioning phases. In the primary posi- -1.5 -1.5 -1 -0.5 0 0.5 1 tioning phase, the tip is brought into the starting position for the scan. With respect to this phase, accuracy is paramount in Desired position [V] comparison to speed. Execution of a scan relative to the start- Fig. 6. Open- and closed-loop response of the stage ing position is the task of the secondary positioning phase. Accuracy and speed are now equally important, implying that modulo measurement (i.e. capacitor switching) is unaccept- 1.5 able. For the purpose of maximizing operating flexibility, the kI = 2000 DSP system will be such that both the primary and the sec- ondary positioning phases can rely on independent A/D and 1 D/A channels. Finally, the sampling frequency of the digital control sys- tem has been set at 10 kHz. This means that both A/D and Position voltage [V] 0.5 D/A conversions as well as the numerical action necessary kI = 500 for real-time control must take place within a time span of 100 µs. The conversion time per channel is typically 5 µs 0 for the D/A module, and 2 µs for the A/D module. In other words, the time available for control action is reduced to 93 µs. -0.5 Acknowledgements. This research is supported by the Technology Founda- tion (STW). -1 References -1.5 0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 1. A.E. Holman, C.D. Laman, P.M.L.O. Scholte, W. Chr. Heerens, F. Tu- instra: Rev. Sci. Instrum. 67(5), 2274 (1996) Time [s] 2. C.L. Phillips, H. Troy Nagle: Digital Control System Analysis and De- sign, 3rd edn. (Prentice-Hall, Englewood Cliffs, NJ 1995) Fig. 7. Transient response of the stage for different settings of the PID 3. W.Chr. Heerens: J. Phys. E: Sci. Instrum. 19, 897 (1986) controller 4. W.Chr. Heerens: Mikromechanische Sensor- und Aktorarrays, Novem- ber, 47 (1996) 5. M. Goldfarb, N. Celanovic: IEEE Control Systems 17(3), 69 (1997) hysteretic component. From the literature [6–8] a hystere- 6. B.D. Coleman, M.L. Hodgdon: Int. J. Eng. Sci. 24(6), 897 (1986) 7. M.A. Krasnol’skiï, A.V. Pokrovskiï: Systems with Hysteresis (Springer- sis model in the form of a nonlinear differential equation is Verlag, Berlin, 1989) known. In view of the assessment that the dynamic and the 8. A.Visintin: Differential Models of Hysteresis (Springer-Verlag, Berlin, hysteretic behavior of the stage should be regarded as insep- 1994)

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