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Optical end point sensing and digital control of a scanning tunneling microscope Chahal, Anthony M. 1993

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OPTICAL END POINT SENSING AND DIGITAL CONTROL OF A SCANNINGTUNNELING MICROSCOPEByAnthony M. ChahalB. Eng. McGill University, Montreal, 1990.A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF ELECTRICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAApril 1993© Anthony M. Chahal, 1993Date:Department of Electrical EngineeringThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1W5In presenting this thesis in partial fulfilment of the requirements for an advanced degree at theUniversity of British Columbia, I agree that the Library shall make it freely available for refer-ence and study. I further agree that permission for extensive copying of this thesis for scholarlypurposes may be granted by the head of my department or by his or her representatives. Itis understood that copying or publication of this thesis for financial gain shall not be allowedwithout my written permission.AbstractThe problem addressed in this thesis is that of digitally controlling a Scanning TunnelingMicroscope and implementing end point sensing to close the control loop for accurate X—Ypositioning of the microscope tip. This first part entails modifying a microscope with an analogcontroller so that it may be interfaced to a DSP system running on a personal computer. Thesecond part is designing and incorporating an optical end point sensor into the head of themicroscope to improve absolute position control of the tip in the scanning plane by overcominghysteresis and creep in the piezoelectric scanning tube actuator. The sensor would also improvethe repeatability of imaging and facilitate random access positioning of the tip to allow for moresophisticated scanning trajectories.The digital controller was successfully implemented. Images of sputtered gold obtainedwith the new controller were of comparable quality to those obtained using a microscope underanalog control. A single axis version of the sensor was developed which was used independentlyof the microscope to measure the hysteresis and creep that were present in the piezoelectricactuator. The sensor had a resolution of 8.5 urn, but was not completely integrated into thedigital control and imaging system.iiTable of ContentsAbstract^ iiList of Tables^ vList of Figures^ viAcknowledgments^ viii1 STM Basics 11.1 History ^ 11.2 Motivation 31.3 Proposed Changes ^ 42 The PZT Actuator 72.1 Piezoelectric Crystals ^ 72.1.1^Fundamental Properties and Equations of Motion ^ 72.1.2^Material Properties ^ 102.1.3^Actuator shapes 122.2 STM Actuator ^ 152.3 Deflection Equations 163 The Sensor 213.1 The Lateral Effect Diode ^ 213.2 Preliminary Sensor Work 253.3 Theoretical Sensitivity ^ 263.4 Split Detector ^ 29iii4 STM Setup and Sensor Construction^ 304.1 Physical Setup ^  304.1.1 Mechanical Setup ^  304.1.2 Optical Setup  314.2 Circuit Design ^  324.3 Other System Hardware ^  345 Building and Testing^ 355.1 General Approach  355.2 Circuit Testing ^  365.3 Problems  435.3.1 Optical Problems ^  435.3.2 Circuit Problems  455.3.3 Spectrum Analysis of Sensor ^  485.4 Construction of the STM Head  495.5 Summary of Results ^  496 DSP System and Control Strategy^ 526.1 Overview of Hardware ^  526.2 DSP Hardware Details  526.3 Control System ^  546.3.1 Hardware Aspects ^  546.3.2 Software Aspects  556.4 Z-axis Control ^  577 Conclusions^ 597.1 Further Work ^  60Bibliography^ 61ivList of Tables5.1 SC-4D Sensor resolution for the first differential scheme^ 395.2 SC-4D Sensor resolution for the second differential scheme with biasing. ^ 395.3 SC-10D Sensor resolution for first differential scheme. ^ 405.4 SC-10D Sensor resolution for second differential scheme with biasing^ 405.5 SC-4D Sensor resolution for the transimpedance circuit with voltage offset. 415.6 SC-10D Sensor resolution for transimpedance circuit with voltage offset^ 415.7 Sensor resolution for transimpedance circuit with the new SC-4D.^ 425.8 Sensor resolution for transimpedance circuit with the laser diode optics and thenew SC-4D^ 42List of Figures1.1 Feedback control loop for the Z motion of the STM. ^  11.2 Scanning tube actuator. ^  21.3 Basic setup of an STM head.  22.4 Basic deformations of PZT Ceramics. ^  82.5 (A) PZT block with electrodes at zero potential. (B) Electric field of oppositepolarity as the poling voltage. (C) Electric field of the same polarity as the polingvoltage. ^  92.6 Hysteresis curves for PZT. ^  102.7 PZT linearity. ^  112.8 PZT creep.  122.9 (A) Stack assembly. (B) Strip. (C) Laminate. ^  132.10 (A) PZT tube and (B) PZT segment. ^  142.11 (A) Unimorph and (B) Bimorph.  142.12 Tripod actuator for STM using three coupled strips in extension/contractionmode. ^  152.13 Exaggerated static deflection of tube. ^  172.14 Uniform beam under bending moment forms a circular arc. ^  172.15 Infinitesimal segment of a bent beam. ^  182.16 Tube deflects forming a circular arc.  193.17 One dimensional position sensitive detector ^  223.18 Two dimensional PSD's: (A) duolateral (B) tetralateral^  233.19 Basic one dimensional PSD ^  27v i3.20 Plot of sensor resolution versus incident power ^  284.21 End point sensor mounted on STM head  304.22 Amplification of deflection of LED spot on sensor by increasing distance betweensensor and LED. ^  314.23 Basic two stage amplifier circuit to decode the sensor output. ^ 335.24 Setup for testing the resolution of the sensor. ^  355.25 First differential scheme^  365.26 Second differential scheme with biasing. ^  365.27 Transimpedance circuit with voltage offsetting to prevent saturation^ 375.28 Optical setup with laser diode collimating lens and longpass filter. ^ 445.29 Two stage amplifier circuit with high gain transimpedance stage and a low passfilter on the differential stage^  465.30 Coherence plot of the spectral analysis data from the sensor circuit. ^ 485.31 Sensor output revealing creep that exists in the scanning tube.  505.32 Hysteresis plot for the scanning tube. ^  516.33 Three components of the STM  536.34 Flowchart of control and imaging software. ^  566.35 Image of sputtered gold obtained with the tunneling current under digital control. 58viiAcknowledgmentsI would like to thank my supervisor, Dr. S.E. Salcudean for his guidance, generosity andpatience. Many thanks are due to the people at Quantum Vision Inc., in particular Dr. T.Tiedje, Andrew Brown and John Smith for their insight and technical support. I would alsolike to thank my fellow students and friends for their encouragement. A final note of thanksgoes to my father for giving me the freedom to make my own mistakes and for understandingwhat it's all about.ViiiChapter 1STM Basics1.1 HistoryThe Scanning Tunneling Microscope (STM) pioneered by Binnig and Rohrer in the early 80's,relies on the electrical properties of conductive samples to obtain "topographic images". Thisnew type of microscope has yielded images of sub-atomic resolution. Image acquisition is basedon a tunneling current which flows between the tip of the microscope and the sample. TheSTM tip is mounted on an actuator that scans the sample just above the surface. A voltageis applied to the tip which causes a current to flow across the gap to the electron cloud of asample's atoms. The end of the tip is typically one or two atoms wide. The magnitude ofthe current varies inversely with the sample/tip gap. As an actuator scans the tip across thesample, the tunneling current fluctuates as the gap changes according to surface features suchas atoms. A feedback control loop, as shown in Figure 1.1, is used to maintain a constant gapbetween the tip and the sample. The tunneling current is the input to the controller, whichdetermines a voltage to apply to the actuator thereby controlling the gap (and the current).The actuator is a Piezoelectric transducer which deforms under an applied voltage. Leadz(V)Amp^PZT 1(z)Feedback <ControllerFigure 1.1: Feedback control loop for the Z motion of the STM.1ControlCodePCImageAcquisitionMotion Stage^ TipSample holderHV DriversCurrentMeasurementChapter 1. STM Basics^ 2yz-y ElectrodeFigure 1.2: Scanning tube actuator.Figure 1.3: Basic setup of an STM head.Zirconate Titanate is one such piezoelectric ceramic, more commonly referred to as PZT. Severaldifferent shapes have been used, with the most common one being a hollow tube depicted inFigure 1.2. The tube is divided into four "ribs" or sections which can be controlled by placingthem at different potentials. Depending on the sign and magnitude of the potential across agiven rib, it will either expand or contract lengthwise. One end of the tube is fixed in place,while the tip is mounted on the free end. By varying the potential of opposite ribs, the tubecan be made to bend in an arc, thus allowing the tip to scan in an X—Y sweep. The tube canalso be lengthened or contracted, hence giving the tip three degrees of freedom. The motionrange of the actuator depends on the dimensions of the tube, the type of piezoelectric crystaland the potential applied across the tube. The motion range is usually on the order of micronsfor the X—Y sweep and for the Z axis.The sample is usually mounted on a stage directly below the tip on the scanning tube.Chapter 1. STM Basics^ 3The stage is used to move the sample towards the tip until a tunneling current is detected.Once the current is present, a feedback control loop is used to maintain constant current (andhence constant tunneling gap) by driving the tube with an applied voltage in the Z—direction.As the tip sweeps across the sample the tip follows the contours of the surface. By recordingthe applied voltage necessary to maintain constant tunneling current and the correspondingvoltages to deflect the tube in the X—Y direction, a "topographic" map of the surface can beconstructed. The depth map is not a true topographic map of the sample, but a surface ofconstant tunneling probability. If the sample is pure, i.e. composed of a single type of moleculeor atom, there is a high correlation between the two surfaces. This fact also makes ScanningTunneling Microscopy an ideal method for detecting impurities in samples [1].The introduction of the STM generated a new family of microscopes [2, 3]. The spin-offs thatwere created were based on similar technology as the STM, but had different capabilities. TheAtomic Force Microscope (AFM), for example, is capable of imaging non-conducting specimens,unlike the STM which is limited to conducting or semiconducting specimens. Other variants,such as the Laser Force Microscope (LFM) and the Magnetic Force Microscope (MFM), havebeen developed to scan samples with a greater gap between the tip and the sample to reducethe risk of damaging or contaminating the sample. These devices have allowed scientists to mapatomic and molecular shapes, electrical, magnetic and mechanical properties and temperaturevariations at resolutions never before achieved without modifying or damaging the specimenwith high energy radiation [4].1.2 MotivationPZT actuators suffer from natural phenomena such as aging, creep, and hysteresis due to theinherent physical properties of the ceramic. They display mechanical resonance based on theirgeometrical shape and phase lag in the frequency response of the electromechanical system.All these properties limit the performance of the STM, making it difficult to acquire accurateimages.Chapter 1. STM Basics^ 4In order to consistently produce images over time, it is required that the STM setup remainconstant or that the necessary adjustments be made to compensate for any possible changes.It is difficult to compensate for these changes using the present open loop analog control of theX—Y position because hysteresis, creep and aging cannot be predicted accurately.Hysteresis in the actuator causes a shift in the tip position on alternating scan directions. Iftopographic data were collected on both directions of the sweep, the image would appear "de-focused" as if alternate lines of the image were shifted according to the hysteresis. Accordingly,data is only collected on a single direction of the sweep, slowing down the image acquisitionrate.The mechanical resonances and the phase lag limit the frequency at which the tip can bedriven hence limiting the image acquisition rate. Driving the scanning tube too fast in the X—Yplane in open loop makes it difficult if not impossible to obtain coherent image data since thetip position and driving voltages do not correspond at high frequencies.Originally, STM's were controlled with analog controllers, but now some manufacturers haveswitched to digital based systems. The choice of analog was based on their low cost and highspeed. Analog controllers limit the system performance by making it difficult and impracticalto tune the controller gains.1.3 Proposed ChangesBy implementing end point sensing in conjunction with a DSP based digital control system, wehope to overcome some of the problems that plague current STM systems and offer the followingadvantages: more accurate tip positioning, programmable tip positioning, compensation foraging and creep, increased scan rate by overcoming hysteresis, multiple image acquisition, moresophisticated scanning trajectories. Overall system performance and flexibility will be increased.End point sensing in the X—Y direction will allow us to close the control loop for the X—Yscan yielding a more accurate tip position. X—Y position information will no longer be obtainedby the voltages that drive the PZT actuator, but directly from the sensor output. The endChapter 1. STM Basics^ 5point sensor could also be used in conjunction with a calibration signal to adjust the feedbackcontroller gains to compensate for aging in the PZT actuator. This would allow consistentlyreproducible images to be acquired over time. The absolute position information from thesensor can be used to overcome creep in the actuator and make it easier to servo to a point.Repeatability of images is crucial for any experiment requiring minutes or hours for completion.There are two ways in which images could be acquired. The first way would be to servo to anX—Y location, maintain the raster scanning pattern, and collect Z measurements on a uniformgrid. Image processing with this type of data would be quite simple. The second method wouldbe to continue driving the tube in the X—Y plane in open loop while collecting X—Y data fromthe end point sensor and Z data with the current scheme. This would probably yield fasterimage acquisition, but the images would be on an irregular grid. This method would requiremore sophisticated image processing techniques.An optical scan correction system has already been applied to an AFM to overcome creep,hysteresis and non-linear motion of the piezoelectric actuator [5]. The implementation consistsof two separate sensors, one for each scanning axis. The results show a marked reduction inimage distortion by either feedback control or image correction techniques. Feedback controlusing the optical sensor provided the best results. The image correction technique introducedsome blurring into the image due to interpolation errors. The optical end point sensor presentedin this thesis uses a single sensor for two-dimensional position information while scanning. Theimplementation also takes advantage of the optical geometry of the sensor to amplify the motionof the end point, thereby increasing the resolution of the sensor.The end point sensor should be free of hysteresis and should observe and quantify thehysteresis in the actuator. More importantly, using the end point sensor to determine position,image data can be accurately obtained in any scanning direction, thus immediately doublingthe scan rate.By changing the bias voltage between the tip and the sample, different images can beobtained of the same sample which provide more information about the surface composition. AChapter 1. STM Basics^ 6DSP based system would make it easy to repeat a single scan line while changing the tip/samplebias. This would allow multiple images to be obtained rather easily. Sub-images of differentscales could easily be acquired to focus on specific surface features.Currently, the scan pattern is generated by driving the actuator electrodes with a saw-tooth wave. With increased control capabilities, the scanning trajectory could be optimized toincrease scanning speed and reduce unnecessary actuator vibrations. Arbitrary scan patternscould also be generated with ease, such as a spiral searches. Another way to optimize thescanning procedure would be to automatically adjust the scan line spacing according to detectedfeatures in a single scan line. The scan would be automatically adjusted to compensate for thesmoothness or regularity of the sample. This would reduce the gathering of redundant surfaceinformation and hence increase the scanning speed.With increased control and programmability of the tip position comes the possibility ofmanipulating or modifying surface features by pulsing the tip voltage [6]. This could eventuallylead to nano-manipulation and nano-fabrication [7].The STM featured in our design is based on an existing product developed by QuantumVision Inc. . Many of the existing analog circuits and the imaging software were integrated intothe final design. The head, containing the actuator, the tip and the sample was completelyredesigned to incorporate the optical sensor. The analog control loop for the tunneling junctionwas replaced by a digital implementation for all axes and merged with the imaging code.Chapter 2The PZT Actuator2.1 Piezoelectric Crystals2.1.1 Fundamental Properties and Equations of MotionThe PZT actuator is the heart of the STM. The ability to position objects with such precisionstems from the physical properties of piezoelectric crystals. The direct piezoelectric effectrefers to the electric potential generated in certain naturally occurring crystals when pressureis applied to them. The converse is also true that when a potential is applied to such a crystalit undergoes deformation. Quartz, Rochelle salt and barium titanate are examples of naturalpiezoelectric crystals.Piezoelectric ceramics, such as PZT, do not naturally exhibit this phenomenon. Theseceramics must first be polarized in an electric field. This polarization is not permanent, but de-teriorates with time. The ceramic may be depolarized by heating it to its "Curie Temperature"at which the electric dipoles become randomly oriented.The deformation that the ceramics experience when a potential is applied depends on theceramic's shape, the poling axis and the direction of the applied electric field. The poling axisrefers to the direction along which electric dipoles in a ceramic have become aligned by theapplication of a strong electric field during a poling procedure. Deformation of the ceramic inone axis is accompanied by deformations in the other axes. For example, given that an expansionoccurs in one direction, there is a corresponding contraction in another. These complementarydeformations may or may not compensate for each other and hence can result in a net volumechange of the ceramic. A ceramic usually exhibit two of the following three types of deformationsimultaneously when subjected to a potential across its surfaces: thickness shear, face shear or(A) THICKNESS SHEAR(B) THICKNESS EXPANSIONChapter 2. The PZT Actuator^ 8(C) FACE SHEARFigure 2.4: Basic deformations of PZT Ceramicsthickness expansion. These deformations are individually shown in Figure 2.4 1 .Let us use a block of PZT, as shown in Figure 2.5(A), as an example to demonstrate thepiezoelectric effect. The X—Y--Z axes are denoted by 1-2-3 respectively. The PZT is polarizedin the positive Z direction and has electrodes on both X—Y planes of the block. By convention,the 3-direction is always the direction of polarization. Since this is a uniaxial system ( i.e. poledalong one axis ) the 1 and 2-directions are equivalent and hence for simplicity, the X and Ydimensions of the block are both 1. The Z dimension has a thickness t.When an electric field E is applied to the block of the same polarity as the polarization P,the block expands in the 3-direction, while simultaneously contracting in the 1 and 2-directionsequally ( see Figure 2.5(B) ). If E is applied opposite to P, the PZT contracts in the 3-direction,while expanding parallel to the electrodes ( see Figure 2.5(C) ). These strains s are related tothe applied electric fields by way of a piezoelectric strain tensor d:8 dE^ (2.1)The coefficients did of the tensor are the ratio of the strain in one axis and the strengthof the electric field in the same or a different axis with all external stresses constant. The'This figure is based on one found in a Vernit.ron report.(C)marChapter 2. The PZT Actuator^ 932(B)<— I(A)Figure 2.5: (A) PZT block with electrodes at zero potential. (B) Electric field of oppositepolarity as the poling voltage. (C) Electric field of the same polarity as the poling voltage.first subscript refers to the direction of the applied electric field while the second refers to thedirection of the induced strain. For example d31 is the ratio of the strain in the 1-direction dueto an applied field in the 3-direction.If we examine strain in the 3-direction due to the applied field across the electrodes, we cansubstitute s = At/t and E = V/t into equation (2.1) to obtain:At = d33 V^(2.2)Similarly, we can obtain an expression for the dimensional change in the 1 or 2-directiondue to the same applied field by substituting s = A//1 into equation (2.1) yielding:d31 V^(132VI^t t (2.3)OUCOa-) 0.24Soft PZT,—, 0.48 15% HysteresisHard PZT200^800Voltage (Volts)Chapter 2. The PZT Actuator^ 10Figure 2.6: Hysteresis curves for PZT.2.1.2 Material PropertiesNatural phenomena of aging, creep, hysteresis, nonlinearity, compliance (inverse of stiffness)seriously affect the performance of piezoelectric ceramics as actuators. These phenomena varydepending on whether or not the ceramic is 'hard' or 'soft'. Hard PZT materials have a Curietemperature above 300° C and are not easily poled or depoled except at high temperatures.This stability increases linearity and lowers hysteresis. Typical d constants for hard PZT areon the order of:d33 = 225 x 10 -12 m/V^ (2.4)d31 = —100 x 10 -12 rn/V (2.5)A potential of 100 V across a block with such typical constants and of thickness 1 mm andlength 2 cm, would cause the block to lengthen or contract by 0.2 pm.Soft PZT materials have Curie temperatures below 200° C and are easily poled or depoledby strong electric fields at room temperature. The d constants are larger hence producinglarger displacements, but the linearity and hysteresis are worse. Large dielectric constants andhigher dissipation factors also limit the frequency at which they can be driven.Hysteresis, which occurs in all piezoelectric ceramics, is the difference in strain that occursMaximumDeviation2412Chapter 2. The PZT Actuator^ 1160^120Voltage (Volts)Figure 2.7: PZT linearity.when a particular applied voltage is approached from a higher voltage or from a lower voltage. Ahysteresis curve can be obtained by plotting extension versus voltage while the applied voltageis increased from zero to some value and then decreased back to zero. Hysteresis is measuredas the percentage of the maximum difference in extension, at a given voltage, of the maximumextension. Soft PZT materials may exhibit hysteresis as large as 20%, while hysteresis for hardPZT materials is usually about 2%. Figure 2.6 shows typical hysteresis curves for hard and softPZT. Actuator construction, operating voltage and load variations also affect hysteresis.The relationship between strain and applied voltage in Figure 2.7 is not perfectly linear assuggested by equation (2.1). Linearity is also measured as a percentage by plotting extensionversus applied voltage as for hysteresis, except that only the increasing voltage curve is used.A least squares approximation to the data is made to obtain the best straight line fit to thedata. Linearity is then given as the maximum percent deviation of the data to the line of bestfit. Values for hard PZT materials are roughly 1% while values range from 2% to 10% for softPZT materials.All piezoelectric ceramics exhibit creep. A ceramic responds to a step change in voltage withan initial change in dimension within fractions of a millisecond, followed by a smaller changeover a longer time period. The smaller change in dimension is in the same direction as the initialChapter 2. The PZT Actuator^ 12A Axo^ILx100^200Time (Seconds)Figure 2.8: PZT creep.change caused by the voltage step. This dimensional change can be either a contraction or anexpansion along a given direction. Creep, as the name implies, refers to the slower secondaryresponse to the voltage step. From Figure 2.8 we see that creep is usually larger for decreasingvoltage. This creep in extension is measured as a fraction of the initial change and is usuallybetween 1% and 20%.Aging of a ceramic refers to the deterioration of its piezoelectric properties such as dielectricconstant, coupling, and elastic modulus. The changes in constants occur logarithmically withtime after poling. For example, if a given constant is 1000, 1 hour after poling and drops to990 after 10 hours, 980 after 1000 hours, then the change would be rated at 1% per decade oftime. Aging rates depend on ceramic composition and manufacturing methods. Exact agingrates are difficult to determine and hence so are exact property values. Rates are usually givenas less than some nominal value, while values for different properties are given for a specifictime after poling. With aging comes stability in property values.2.1.3 Actuator shapesDifferent geometries and physical arrangements with piezoelectric ceramics have been used tocreate electromechanical transducers, such as inch worm motors, speakers, bimorphs and stripedChapter 2. The PZT Actuator^ 13(B)MotionMotionP(A)^ (C)Figure 2.9: (A) Stack assembly. (B) Strip. (C) Laminate.tubes, which are currently used in most STM's today.Actuators are designed to take advantage of d31 and/or d33 to generate motion. Two simpleexamples are (1) stack assemblies and (2) strips and laminates. From equation (2.2), we knowthat the absolute extension At depends only on the applied voltage. Thus, by stacking discswe can obtain more motion per volt along the polarization direction. The expression for stackextension thus depends on Nd, the number of discs.Stack extension = Ndd33V^ (2.6)Conversely, if motion is desired perpendicular to the poling direction, the ratio of lengthto width of the ceramic strip becomes the critical factor to determine the extension per volt.Recalling thatStrip extension = 1(131 v t (2.7)we can maximize the extension per volt by making the strips long and thin. To compensatefor the loss of strength and rigidity, the strips can be bonded together with alternating polingdirections to form laminates.e \^..^kee o^,'‘‘.^...^■, v, .........../.^.0,.. ' '^....^/,...•e XMetal(A)^(B)Chapter 2. The PZT Actuator^ 14(A)^(B)Figure 2.10: (A) PZT tube and (B) PZT segment.Figure 2.11: (A) Unimorph and (B) Bimorph.Tubes and segments have a similar geometry to strips, but their curvature gives themimproved structural rigidity. They are radially poled with electrodes on the interior and exteriorwalls. The tubes are difficult to manufacture and the wall thickness is crucial to uniform motion.The tube extension is given by:Tube extension = id31vw (2.8)Segments are sections of tubes and have the same equation for extension.Another group of simple actuators is based on the unimorph and bimorph. The underlyingconcept is similar to the motion of a bimetallic strip in a thermostat. Differences in strain inthe bonded strips, cause the assembly to bend, moving one end while the other remains fixed inZ Piero ElementY Pies. Hemet.1E••••■•XChapter 2. The PZT Actuator^ 15TipFigure 2.12: Tripod actuator for STM using three coupled strips in extension/contraction mode.place. One strip is under tensile stress, while the other is under compressive stress. Bimorphsand unimorphs can also be made to move like strips. They can provide a large motion range,on the order of 100 microns, but are not mechanically powerful and typically have low resonantfrequencies. Mechanical strength can be improved by clamping both ends and allowing themiddle to move and also by using discs supported along the perimeter rather than strips. Theunimorph is not suitable for sensitive positioning applications due to drift caused by thermalexpansion of the metal strip.Striped geometries have the advantage of allowing motion in more than one direction byusing a single actuator with multiple electrodes. The striped tube shown in Figure 2.13 usesthe same idea of opposing contraction and expansion in the bimorph, to create a bendingmotion. With four equal stripes, three dimensional motion can be achieved. Simple extensionor contraction is achieved by treating the four stripes as a single surface with a common potentialas in a regular tube.2.2 STM ActuatorThe first piezoelectric actuators used in STM's were constructed from three separate transducersjoined at a single point along mutually orthogonal axes as shown in Figure 2.12. These actuatorswere soon replaced by striped tube actuators such as the one shown in Figure 1.2 [8]. These newtube scanners, apart from being easier to fabricate, have greater motion range in all directionsand higher resonance frequencies in the z direction along the axis of the cylinder. This allows forChapter 2. The PZT Actuator^ 16greater scan rates and better disturbance rejection from ambient vibrations. Another advantageover the tripod design is the elimination of image distortion in the x-y plane due to thermalexpansion of the transducer elements. This is the case only if the tip is mounted in the centerof the tube to take advantage of its cylindrical symmetry.The resonance frequencies of the scanning tube in the x and z directions are a function of thematerial properties and the geometry of the actuator [9]. The higher the resonance frequenciesthe faster the STM tip can scan a sample. This advantage in scanning speed cannot be achievedwithout a trade-off in scanning range. The resonance frequencies for the longitudinal (z) modeand lateral displacement (x) mode are given the following expressions:f - 4/0.56vo-=ix(2.9)(2.10)where vs = (pSg) 1 / 2 is the speed of sound in the ceramic actuator with the electrodes held ata constant potential 2 .The actuator chosen in our implementation is a striped tube of length L = 2.1 x 10 -2 m,radius r = 5.6 x 10 -3 m and thickness t = 1 x 10 -3 m. The strain tensor component isd31 = -215 x 10 -12 7/2/volt, the speed of sound is vs = 3.0 x 103 m/s. Based on equations 2.9and 2.10 and the above parameters, the scanner tube has resonance frequencies of h 36 kHzand fx = 21.5 kHz.2.3 Deflection EquationsUsing geometry and the deformation equations from Section 2.1.1, we can derive the equationsfor static deflections of the striped tube. The derivation is based on beam theory and uniformbending. The striped tube is viewed as a beam undergoing uniform bending when two opposingstripes are driven with the necessary potentials causing one stripe to expand and the other tocontract, as in Figure 2.13.2This is an approximation ignoring the effects of the tube being clamped at one end.Horizontal deflectionChapter 2. The PZT Actuator^ 17• ,•.; •1;• s,Figure 2.13: Exaggerated static deflection of tube.Tensile stress, s > 0Neutral line,Figure 2.14: Uniform beam under bending moment forms a circular arc.When a bending moment is applied to a beam, it experiences stresses and strains. Assumingthe composition of the beam is uniform, it will have a constant curvature with part of the beamunder compressive stress and the other under tensile stress (refer to Figure 2.14 ). Furthermore,if the cross section of the beam is uniform and symmetric, the neutral line will be along themiddle of the cross section [10]. By knowing the bending moment and the flexural rigidityof the beam, the curvature and hence the stress and strain at any point in the beam can bedetermined. Conversely, if we use the deformation equations we can determine the strain fromthe applied voltage to the stripes of the tube and work backward to obtain the curvature andhence the static deflection.We approximate the tube used in the STM with a beam of length L and square cross sectionw. A bending moment is applied yielding a radius of curvature p, which is measured from theneutral line in the bent beam. The radial distance of any point in the beam above or belowChapter 2. The PZT Actuator^ 18Figure 2.15: Infinitesimal segment of a bent beam.the neutral line is is given by y. The curvature is simply lip. The bending moment issufficiently small to ensure that 0, the angle subtended by the curved beam is also quite small.By definition, the length of the arc along the neutral line remains a constant length L. Thesegment has strain s > 0 for y > 0 and s < 0 for y < 0.If we examine an infinitesimal segment of the bent beam, we obtain the following expressionfor strain as a function of y:S(p y)d0 — pd0pd0yOver the complete length of the tube, we then have:p0 = L^ (2.14)9 =^ (2.15)OrGeometrically, the bent beam is represented by arc AC and the horizontal deflection by theline segment AD in Figure 2.16. The bending is exaggerated for the purpose of visualization.Chapter 2. The PZT Actuator^ 19Figure 2.16: Tube deflects forming a circular arc.The deflection is given by:AD = AE cos 0▪ (BE — BA) cos 0^ p) cos 0c:s• p(1 — cos 0)(2.16)(2.17)(2.18)(2.19)By determining the strain at a point a distance y from the neutral line, we can use equa-tion (2.12) to determine p. We can then obtain 0 from equation (2.14) and hence solve for thehorizontal deflection in equation (2.19). Assuming that we know the strain at y = w/2 thenandP = —2s2sLzu0 = ^(2.20)(2.21)Making use of the small angle approximation for cos 0, and substituting equations (2.20)and (2.21) into equation (2.19) we get:p02AD =2sL 2w(2.22)(2.23)Chapter 2. The PZT Actuator^ 20The original striped tube can be approximated by a beam of width 2r, where r is the radius.If only two opposing stripes are considered to be driven, then the strain at y = w/2 r is simplythe strain of one stripe. From equation (2.3) we have:s= d31 V (2.24)tThis leads to the final result:d3i VHorizontal deflection = L22rt^ (2.25)This formula overestimates the true deflection anywhere from 10% to 20% depending onthe relative dimensions of the tube [11] 3 . A more practical number is the deflection per volt,which will be used later to help determine the resolution of the sensor. Based on the dimensionsof our tube, L = 2.1 x 10 -2 m, r = 5.6 x 10 -3 m and t =1 x 10 -3 m, and the strain tensorcomponent d31 = —215 x 10 -12 m/V, we obtain the following result for the deflection per volt:de flectionIV = 8.5 nm/V^ (2.26)3 According to the results of the finite element analysis computed in reference [11] a tube with these dimensionswould overestimate the deflection by^15% .Chapter 3The Sensor3.1 The Lateral Effect DiodeThe Lateral Effect Diode is a semiconductor device that can be used as a position sensitivedetector (PSD). It is an optical transducer that converts "photon current" to electric current.It differs from other detectors ( split cells and quadrant detectors ) in that it contains a singleactive element. Position information is obtained by taking advantage of the geometry of thedevice, rather than profiling the intensity pattern of the incident light on the surface. The lateralcell divides the photocurrent generated within the substrate, which is achieved by applyingmultiple ohmic contacts on the back of the device. A single axis detector can be made byplacing two electrodes at opposite ends of the sensor. Similarly, a dual axis detector can beconstructed by placing two pairs of opposing electrodes perpendicular to each other.Suppose we have a one dimensional PSD as shown in Figure 3.17, with a light beam hittingits surface. A charge proportional to the energy of the incident photon is generated at the pointof incidence. The intrinsic electric field in the p-n junction prevents the electron-hole pairs inthe depletion region from recombining, sweeping the holes to the p-layer and the electrons to then-layer. The p-layer acts as a current divider, splitting the current between the two electrodes.The proportion of the current in each electrode will depending on the location of the centroid ofthe incident light beam. The current in each electrode is inversely proportional to its distancefrom the centroid. From Kirchoff's Current Law, we have:Io = 1-1 + 12^ (3.27)21Il= 2L12 —IO 2LL — xL xChapter 3. The Sensor^ 22Incident Light•c--- p layern layerphotocurrent•L L[12]fIOFigure 3.17: One dimensional position sensitive detectorIf p is the resistivity of the p-layer then we have:12 (L — x)p =^+ x)p, (3.28)providing that both electrodes are at the same potential.Solving equations (3.27) and (3.28) simultaneously, we obtain the following expressions forthe electrode currents as a function of the light spot position.(3.29)(3.30)Conversely, by combining equations (3.29) and (3.30) we can solve for x and determine theposition of the light spot as a function of the currents.—x= L IZIl +(3.31)Equation (3.31) would precisely determine the location of the incident light beam if it were tocontact the surface of the PSD at a point. The incident light is more likely diffuse in which casethe location of the centroid is determined by equation (3.31). These devices are not perfectly+ Il- 1-1y = L (3.33)Chapter 3. The Sensor^ 23(A)^ (B)Figure 3.18: Two dimensional PSD's: (A) duolateral (B) tetralateral.linear with values ranging from ±0.5% linearity near the center, to ±5% linearity near the edgeof the active area [13]. This is mainly due to the non-uniformity of the sheet resistance. Ifmotion of the light spot is restricted to the center of the device, where the relative distance ofthe spot to each electrode is almost the same, then these non-uniformities tend to average outmore than at the periphery of the detector. Another cause of non-linearity in the output of atwo-dimensional device is that a shift in the linear position of the light spot with respect to thecenter of the device is not linear with respect to the cartesian axes that are defined by the fourelectrodes [13].This device can be easily expanded to two dimensions by using two orthogonal sets ofelectrodes. These two sets of electrodes can either be on the same side of the device (tetralateral)or on opposite sides (duolateral) of the p-n junction. The position information for the devicesshown in Figure 3.18 are much the same as for the one dimensional case.(3.32)x = Lh13 + 14Two important factors that affect the operation of PSD's in their associated circuits arejunction capacitance Cj and dark current Id. Junction Capacitance affects PSD operation onlyChapter 3. The Sensor^ 24when the light source is pulsed. The Junction Capacitance is analogous to the capacitance ofa parallel plate capacitor and decreases with reverse bias and increases with active area [14].This can be seen by examining the capacitance formula below:Ks AE0Cj = W^ (3.34)where Ks is the relative dielectric constant of the semiconductor, eo is the permittivity of freespace, A is the area and W is the depletion region width (analogous to the plate separation).Increasing the reverse bias across the p-n junction in the PSD increases the depletion regionW, hence lowering Cj. This effectively reduces the frequency response of the PSD if we treatit as an equivalent shunt resistance R, in parallel with Cj.Dark current is the leakage current through the p-n junction that occurs when the device isoperated in the dark under a reverse bias. It is a combination of diffusion current, generation-recombination current, surface current and avalanche current. Diffusion current is the flow ofmajority carriers across the p-n junction due to carrier concentration differences on either sideof the junction. The driving force is thermal motion not particle repulsion or attraction as inthe case of drift current. Generation-recombination current is caused by the cycle of creationand annihilation of electron-hole pairs. This process occurs at special generation-recombinationcenters which are either special impurity atoms (not doping impurities) or at lattice defects.Surface current refers to the tendency of carriers to travel along the surface due to repulsiveforces among the carriers themselves. Avalanche current occurs once the reverse bias voltageapproaches the breakdown voltage of the semiconductor. Once a critical level of the electricfield in the semiconductor is reached, carriers are accelerated to the point that collisions withatoms have sufficient energy to create an electron-hole pair. These three carriers can then allbe accelerated again to continue the process and hence cause an "avalanche" of carriers to flow.Dark current is white noise that gets superimposed onto the photocurrent signal when the PSDis operated under a light source. It arises from leakage current in the photodiode. UnlikeJunction Capacitance, Dark current increases with both reverse bias and active area [14].The sensitivity of these devices can be judged by a figure of merit known as Noise EquivalentChapter 3. The Sensor^ 25Power (NEP). It is the incident signal power that produces an rms Signal-to-Noise ratio ofone. NEP determines the minimum detectable signal power. Also important is the minimumresolvable displacement of a PSD, which shall be dealt with in Section 3.3.Photodiodes can be used in two modes of operation: Photoconductive (PC) and Photovoltaic(PV). In the Photoconductive mode, the device is operated under a reverse bias, resulting in alower Junction Capacitance, greater depletion region, lower series resistance, shorter rise timeand a linear response in photocurrent over a wider range of intensities. However, increasing thereverse bias increases shot noise due to a greater Dark Current.There is no reverse bias applied in the Photovoltaic mode, hence no Dark Current. Thusthe only source of noise in the device is thermal noise. Sensitivity to low light levels is greaterthan in the Photoconductive mode, but frequency response is lower due to a higher JunctionCapacitance.3.2 Preliminary Sensor WorkPreliminary work on an end point sensor was done by Allan J. Kelley [15]. The setup consistedof a first surface mirror mounted on the free end of a bimorph, which deflected a Helium-Neonlaser beam onto a one dimensional PSD. The motion of the bimorph would cause a lateraldisplacement of the laser beam on the PSD resulting in a change in the output currents fromthe electrodes. The PSD was used in the Photovoltaic mode with the two electrodes connectedto separate transimpedance amplifiers. The two outputs of the first stage were then fed intoa high gain differential amplifier, whose output represented the difference in current / 2 — /1 .Division by the sum of the currents was not done because the level of light incident on the PSDremained relatively constant'.The resolution of the sensor was tested by moving the bimorph in 100 A steps using aBurleigh Inchworm. The sensor circuit output was sampled by an A/D converter in an IronicsVME cage and a D/A output was used to drive the Inchworm. This calibration was done'Division by the sum compensates for changes in the incident light level.Chapter 3. The Sensor^ 26for several gains on the differential stage. Results were plotted for values of the feedbackresistor, Rf ranging from 100 KS2 to 1 M1-2 and then extrapolated to determine the sensitivityat Rf = 10 Mft. However, the implicit linearity in this relationship does not hold for highvalues of Rf.Increasing Rf has a twofold effect, increasing both the signal and the noise. The increasein signal is directly proportional to the feedback resistance, while the increase in noise 2 isproportional to \/Rf . This yields an overall increase in the signal-to-noise ratio proportionaltofnif. This would imply that we could achieve an infinite signal-to-noise ratio which isobviously impossible. The reason this doesn't happen is because of amplifier noise sources,which are usually defined in terms of input noise current in and noise voltage e„. The signalcurrent from the PSD and the noise voltage of the amplifier have different frequency responses,hence different noise sources will be dominant depending on the value of Rf [16].Although the setup for the STM is different, the work done by Allan Kelley was a valuablestep in developing the present sensor circuit. The laser was replaced by an infrared LED andvarious biasing and amplification schemes were tried which eventually led to the final designfound in Section Theoretical SensitivityThe concept of Noise Equivalent Power can be extended from the minimum signal power de-tectable, to the minimum displacement resolvable by the detector, Ax [17]. This incrementalchange in position causes an incremental change in the signal current. If we equate this Alto the noise in the system( PSD and associated amplifier circuits ) to obtain a signal-to-noiseratio of one, then we can obtain a value for Ax in terms of the incident light energy, the PSDcharacteristics and the amplifier characteristics.Recalling the construction of a one dimensional PSD, let us suppose that we have an activearea of width 2L and a detector responsivity of RA A/W for light of wavelength A. If the2 Thermal noise due to the resistor.LChapter 3. The Sensor^ 27Figure 3.19: Basic one dimensional PSDincident light beam is assumed to be monochromatic of energy Pd then the photocurrent is:= PdRA^ (3.35)From equations (3.29) and (3.30) for the electrode currents we can obtain Aui. and A/2 due toan incremental change in the light spot position, Ax, and hence Al, the overall change in thesignal current./oAxA/1 =2L/0AxA/2 = 2LFrom equations (3.36) and (3.37) we obtain the overall current change of:Al = I0Ax PdRAAs(3.36)(3.37)(3.38)There are three sources of noise to consider in the system. The first is thermal noise in thedetector leading to a detector noise current equivalent to:zikT^ AR /Hz,RsId = (3.39)0 1.6^18010-0.2^0.4^0.6^0.8^1^12^1.4Incident Power (w)4.543. 5C 3. 0O 2Cr 1.510.5S. 2.5Chapter 3. The Sensor^ 28Figure 3.20: Plot of sensor resolution versus incident powerwhere R3 is the resistance between the electrodes on the PSD 3 . The second source is the shotnoise of the Dark and signal currents, namely:/sh = V2/0 A/ ./Hz,^ (3.40)where q is electronic charge. The final source is the effective input noise current of the ampli-fiers:e 2=^A/\/Hz^ (3.41)Since these noise sources are uncorrelated, they can be added in quadrature to obtain a totalnoise value:In^4kT R2= 2Ioq A/VHz (RMS)^ (3.42)R,Equating the expressions for LI and In, yield a signal-to-noise ratio of one, allowing us tosolve for Ax, the minimum resolvable displacement 4 .'\/LAx = ^4kT^z _2747 "rClqPdRA(3.43)For our setup, we used an SC-4D detector manufactured by UDT with an active area of6.45 mm 2 , RA = 0.35 A/W and R, = 4.61 kSt. The LT1007 op-amps in the circuit were low3 The units indicate that the noise is bandwidth dependent.4 The factor of Ali is because I n is an RMS value.Chapter 3. The Sensor^ 29noise, with en = 3.8 nVI-/Hz. The incident power was measured to be P.-, 0.5 mW. Fromequation (3.43) we calculate Ax to be ti 1 Á/3.4 Split DetectorSplit detectors are another type of position sensors. They differ from lateral cells in that theiractive area is segmented into two halves for a one-dimensional sensor or into four quadrantsfor a two-dimensional sensor. For a two-dimensional sensor, each segment has an electrode.Photocurrents arising from the fraction of the light spot in each quadrant are used to calculateposition information according to the same sum and difference equations as for the lateral cells.The minimum detectable position change for a split detector based on one manufacturer'sspecifications is at least one order of magnitude greater than what can be achieved with a PSD. The following equation gives a value for this minimum in Angstroms:Minimum Detectable Position Change = 1.5 (3.44)where Af is the system bandwidth in Hz and H is the light spot power density in W/cm 2 .Given a power density of 8 x 10 -3 1/11/cm2 and a bandwidth of 3 kHz, we get a resolutionfigure of roughly 92 nm. The minimum detectable position change in Angstroms for a PSD bythe same manufacturer is given by the following equation:Minimum Detectable Position Change = 4 x 10 -4 (3.45)where P is the total light power on the device in W. Given the same bandwidth of 3 kHz andthat the maximum power that the device can absorb is 0.18 x 10 -3 W, we obtain a resolutionof approximately 1.6 A which agrees with the theoretical calculations in Section 3.3.'These figures are based on a quadrant detector and a PSD manufactured by SDC.Chapter 4STM Setup and Sensor Construction4.1 Physical Setup4.1.1 Mechanical SetupTo detect motion of the scanning tube with a PSD, it is necessary that any horizontal deflectionin the x-y plane cause a corresponding lateral shift of a light spot shining on the active area ofthe PSD. To accomplish this, an infrared LED is mounted on the tip end of the scanning tubein a nylon cap. The LED shines into the tube parallel to the z-axis. A PSD is centered on thez-axis a distance away from the fixed end of the tube as shown in Figure 4.21.In the default position, the LED shines on the center of the PSD, resulting in equal photocur-rent in all four electrodes. In practice this is difficult to achieve due to mechanical alignmentof the components and the alignment of the LED optical axis. However, the amplifier circuitcan be adjusted to compensate for a nominal value in the output. From Section 2.3 we recallhow the tube bends under an applied voltage, causing a static deflection. Since the nylon capInfrared LEDFigure 4.21: End point sensor mounted on STM head30displacement of light spotd2LED beam^d=f(z,V)dldOz2position of sensordeflected tubeFigure 4.22: Amplification of deflection of LED spot on sensor by increasing distance betweensensor and LED.Chapter 4. STM Setup and Sensor Construction^ 31is secured to the lip of the tube, it remains perpendicular to the tangent of the bent tube atthe free end. Hence, the LED shines in the direction of that tangent, thereby intersecting theplane of the sensor off center. This displacement of the light spot causes the photocurrents tobecome unequal resulting in an output voltage from the amplifier circuit.4.1.2 Optical SetupThe first sensor design used a Siemens IRL-500 LED which came in plastic molded case. Theemission beam had a half angle of 2.5° with the optical axis within 2.5° of the center. TheSC-4D detector had an active area of 6.45 mm 2 with sides of length 2.55 mm. The size ofthe active area and the angle of the beam are the limiting factors that determine the distancethat the sensor can be placed from the LED. The further the sensor is placed, the greater thedisplacement of the light spot from the z-axis as can be seen in Figure 4.22. Thus it is possibleto amplify the "signal" by simple geometry. However, as the sensor gets further from the LED,the greater the diameter of the light spot becomes, eventually extending beyond the active areaof the sensor. The overall displacement is given by:d = — ztan131171'^L2d rt 2rt (4.46)Chapter 4. STM Setup and Sensor Construction^ 32This expression reduces to equation 2.25 for the case of z = 0. The amplification can bequite significant. Given the same parameters for the tube as in Section 2.3 which yieldedd = 8.5 nm/V, we have a displacement of (1 — z)d where z, the position of the sensor, isgiven in centimeters from the base of the tube.In order to reduce the size of the light spot, a lens was placed between the LED and thesensor. Lenses of various focal length from 6 — 25 mm were used to maximize the distancebetween the LED and the sensor. A further refinement was making a nylon cap with a tinypinhole (1mm) to reduce the spot size before focusing. These tests were done on an opticalrail using grid paper to simulate the sensor. The light spot was measured on the grid paper bysight with an infrared viewer. The best arrangement was found using lens with a 9 mm focallength, with the LED and the sensor equidistant from the lens.4.2 Circuit DesignThe first circuit that was used with the sensor was a two stage amplifier network. The first stagewas a transimpedence amplifier, one per electrode, connected to the sensor in the photovoltaicmode. The second stage was a high gain differential amplifier, one per axis, taking the differenceof the currents to obtain position information. Since the incident light energy is assumed tobe relatively constant there is no need to divide by the sum of the photocurrents. Dividing bythe sum of the currents normalizes the output of the PSD. This results in consistent positioninformation even with fluctuations in intensity and hence current. This assumption is validif the spatial distribution of the light spot is the same at all intensities. External infraredemissions are minimized by keeping the sensor and LED enclosed within the scanning tube andthe aluminum block on which it is mounted.To minimize noise, the leads from the PSD were kept as short as possible. The first stage opamps were equipped with first order low pass filters with a cutoff frequency of 15 kHz. Trimpotswere added to the op amps to compensate for thermal drift and any slight misalignment in theoptics. By adjusting the trimpots the output voltage could be zeroed when no potential wasC2Chapter 4. STM Setup and Sensor Construction^ 33C 1R1R2 T C2 V = f(R4, R3, R2, R1, C2, C1) Figure 4.23: Basic two stage amplifier circuit to decode the sensor output.Chapter 4. STM Setup and Sensor Construction^ 34applied to the scanning tube. The circuit was tested with various gains R 4 /R3 . Several problemssuch as low and high frequency noise, ground loops, improper shielding and optical problems ledto many refinements and trying different circuits, which are chronicled in the following chapter.4.3 Other System HardwareThe scanning tube was excited by two high voltage drivers from the original design by QuantumVision Inc. Each high voltage board had an inverted and non-inverted output used to drive apair of axes, X—Z or Y—Z. Originally, these boards were populated with BB 3485 JM op ampswhich provided a range of +145 V. These boards were later replaced by boards containingApex PA 85 op amps which had a swing of ±200 V. These drivers were mounted in a cagecontaining the remainder of the STM electronics: the tunneling current input amplifier, the tipbiasing circuit and the DSP interface electronics. This cage is described in greater detail inSection 6.1. For the purpose of testing the end point sensor, only the high voltage boards wereneeded. An independent verification of the resolution would require the entire STM setup (allthe tunneling circuitry, DSP and the PC) to facilitate image acquisition. By comparing surfacefeatures of known magnitude with the X—Y sensor outputs, we could obtain a second resolutionmeasurement.ScanningTube --".Aluminum BlockPSDSensorCircuitChapter 5Building and Testing5.1 General ApproachIn Section 2.3 we obtained an expression for the static deflection of the scanning tube for agiven applied potential. This information can be used to determine the minimum resolvabledisplacement of the sensor by a practical approach. By driving the scanning tube in a singleaxis with a square wave of known amplitude, the tube will oscillate about the neutral positiona known distance based on equation (2.25), causing the light spot to move across the PSD. Thesensor circuit will respond to this excitation and output a square wave signal. The amplitudeof the driving square wave is reduced until the signal-to-noise ratio of the sensor output is onein a bandwidth of 3 kHz. This amounts to reducing the amplitude until the square wave is nolonger discernible from the background noise. The resolution of the sensor is then given by thedisplacement due to that minimum amplitude.OscillationsFigure 5.24: Setup for testing the resolution of the sensor.35Chapter 5. Building and Testing^ 36Figure 5.25: First differential scheme.CfvinRfCDCD0^ VoT fFigure 5.26: Second differential scheme with biasing.Resolution = (deflection per volt) x (Minimum Amplitude)^(5.47)The resolution was tested in a single axis by connecting a signal generator to one highvoltage driver and comparing the driving signal with the sensor output on a scope.5.2 Circuit TestingThree basic sensor circuit designs were used in the resolution tests. All the circuits wereassembled on the same type of ground plane vector prototype boards with soldered connectionsfor all components except the op amps and feedback resistors, which were inserted into ICsockets for ease of testing. The results documented in this section were all achieved using theChapter 5. Building and Testing^ 37Figure 5.27: Transimpedance circuit with voltage offsetting to prevent saturation.Chapter 5. Building and Testing^ 38same op amps and optical components, unless otherwise indicated. The op amps were LinearTechnology LT 1037 CN8 precision low noise op amps and the optical source was a HamamatsuL2791-02 infrared LED with no optical enhancements other then the lens with which the LEDis packaged. Each circuit was also tested with two PSD's from the same manufacturer but withdifferent size active areas: (1) SC-4D, (2) SC-10D.The three basis circuits are:• Simple differential circuit.• Differential circuit with biasing.• Transimpedance circuit with voltage offsets.and are shown in Figures 5.25, 5.26 and 5.27, respectively.The goal of these tests is to maximize the signal-to-noise ratio of these circuits and determinewhich will yield the best resolution. Two ways by which to increase the signal strength are (1)by increasing the feedback resistor and (2) by increasing the LED intensity and therefore thephotocurrent. Both of these methods were tried on each circuit. The tests were done with theLED at a maximum intensity with 60 mA flowing through it. The values of Cf, Cl and C2in the circuits were chosen to maintain the filter cutoffs as close as possible to 3 kHz. Thefollowing results are based on a deflection per volt of 8.5 nm/V as derived in Section 2.3, andwere obtained by driving the actuator with a square wave input at 100 Hz and keeping theLED held at a constant intensity.The differential circuits were tested in the hope that they would have lower noise thanthe transimpedance circuit since there is only a single amplification stage. Tables 5.1 and 5.2contain the results for the two differential schemes using the SC-4D PSD, a tetralateral devicewith an active area of 6.45 mm 2 . In both cases, the resolution increased with R1, eventuallyreaching a limit due to noise.These results in Table 5.2 were achieved with a bias voltage V& = —12 V. The biasingvoltage was adjusted from 0 to —12 V with the best results occuring at —12 V. Reverse biasingChapter 5. Building and Testing^ 39Table 5.1: SC-4D Sensor resolution for the first differential scheme.Rf (MC2) Square WaveAmplitude (volts p-p)Resolution (nm)0.33 60 2551.5 30 1274.7 17 727.7 18 779.8 18 77Table 5.2: SC-4D Sensor resolution for the second differential scheme with biasing.R f (Mil) Square WaveAmplitude (volts p-p)Resolution (nm)0.33 32 1361.5 20 854.7 17 727.7 18 779.8 18 77of the PSD is supposed to reduce the signal-to-noise ratio while increasing the bandwidth to theMHz range. Surprisingly, the resolution was increased at lower gain with biasing as opposed towithout biasing. At higher gain no change in the resolution was detected. Since the circuit wasoperating with the LED in a non-pulsed mode, bandwidth improvements were inconsequential.It was discovered that if the biasing was increased beyond —13 V, the output of the op-ampsaturated at the negative rail. This was due to the PSD breaking down and hence acting asa short circuit. This would put the op-amp inputs at R.-, Vb driving the output down to thenegative rail.The same differential circuits were tested with the larger SC-10D with slightly better resultsas shown in Tables 5.3 and 5.4. The SC-10D was chosen for comparison because is has a largeractive area (100 mm 2 ). It was difficult to ensure that the light spot was completely within theactive area of the SC-4D, but such was not the case with the larger SC-10D. This comparisonalso served to ensure that the SC-4D was operating as a true PSD. However, with the largerChapter 5. Building and Testing^ 40active area of the SC-10D, there is greater dark current, which had an impact on the noise levelonce biasing of the PSD was implemented. The dark current in SC-10D is three times that ofthe SC-4D 1 .Table 5.3: SC-10D Sensor resolution for first differential scheme.R f (MQ) Square WaveAmplitude (volts p-p)Resolution (nm)0.33 43 1831.5 11.4 484.7 10.4 446.4 12 519.8 13.2 56Table 5.4: SC-10D Sensor resolution for second differential scheme with biasing.R f (MS2) Square WaveAmplitude (volts p-p)Resolution (nm)0.33 60 2551.5 13 554.7 10.4 446.4 12 519.8 13.4 57The voltage offset circuitry in the transimpedance circuit is an enhancement from the basicsensor circuit presented in Section 4.2. The voltage offsets are necessary to prevent the tran-simpedance op amps of the first stage from saturating due to the increased LED intensity. Thisis not a problem in the differential schemes due to their inherent common mode rejection 2 .The voltage offsets compensate for the DC voltage drop due to increased photocurrent, therebydecreasing the output voltage of the transimpedance op amps. Not only does this allow anincrease in the signal, but it also doubles the output range, making it —15 to +15 V.Figure 5.27 shows the setup for increasing the signal current while preventing the output'Refer to UDT data sheets2 This is not a problem unless the op amp is severally imbalanced.Chapter 5. Building and Testing^ 41from saturating. The offset voltage is increased by adjusting the trimpots Rb. The LEDintensity was increased to its maximum by increasing the current flow through it to 60 mA viaan independent voltage source. The offset circuit includes a low pass filter with a 1 Hz cutoffto reduce any high frequency noise. By adjusting Vbl and Vb2 for each axis, the outputs canbe kept from saturating and can also be kept balanced so that the differential output is still afunction of h - /2. The results for the resolution are shown in Table 5.5.Table 5.5: SC-4D Sensor resolution for the transimpedance circuit with voltage offset.Rf (MS2) Square Wave Resolution (nm)Amplitude (volts p-p)1.5 21.5 914.7 20.5 876.8 20 85The results in Table 5.5 were achieved using an old batch of SC-4D detectors. No significantimprovement was detected by increasing the gain. The same circuit tested with the SC-10Dachieved a much better resolution as shown by the results in Table 5.6.Table 5.6: SC-10D Sensor resolution for transimpedance circuit with voltage offset.R f (MQ) Square WaveAmplitude (volts p-p)Resolution (nm)1.5 4.3 18.34.7 2.4 10.26.4 2.3 9.89.8 2.5 10.6Another test was conducted with the SC-4D in the transimpedance configuration using thesame ground plane vector board as was used to generate the results in Table 5.6 with theSC-10D. A new batch of SC-4D's was used, having a lower shunt resistance and inter-electroderesistance (by a factor of two) than the one used for the previous tests. The results are highlycomparable to those achieved with the SC-10D on the same board.Chapter 5. Building and Testing^ 42Table 5.7: Sensor resolution for transimpedance circuit with the new SC-4D.R1 (MQ) Square WaveAmplitude (volts p-p)Resolution (nm)0.33 6.0 25.51.5 2.5 10.64.7 2.2 9.46.4 2.2 9.4After examining the size of the incident light spot relative to the smaller SC-4D, a third PSDof intermediate size was tried in the transimpedance circuit based on the fact that it providedsuperior resolution as demonstrated by the preceding results. Unfortunately, UDT Sensors Inc.does not manufacture such a PSD, so the Hamamatsu S1743 with an active area of 16.8 mm 2 ,was chosen to be tested. The polarity of the junction is opposite to that of the UDT sensorswhich required that the polarity of the offset voltages be changed and a second offset voltagecontrol be added to the ground pin. The results were not quite as good as with the UDT sensorswith respect to noise levels of the outputs of the transimpedance stages. Noise signals exceeded1 V p — p, while the resolution was worse by a factor of two over the best results achieved.Table 5.8: Sensor resolution for transimpedance circuit with the laser diode optics and the newSC-4D.Rf (MQ) Square WaveAmplitude (volts p-p)Resolution (nm)1.5 2.4 10.64.7 2.0 8.56.4 2.2 9.49.8 2.2 9.4Following these tests on the PSD's and the three circuits, laser diode optics instead of theLED were tested with the ground plane vector board containing the SC-4D PSD with thetransimpedance circuit. The resolution results are detailed in Table 5.8. The results reveal aslight improvement in the resolution over the same circuit with the LED.Chapter 5. Building and Testing^ 435.3 Problems5.3.1 Optical ProblemsSeveral optical arrangements were tried to insure proper operation of the PSD. The goal was tominimize the diameter of the light spot and maximize the distance between the sensor and theLED. The first arrangement made use of a white nylon cap to hold the Siemens LED and a lensto focus the beam and reduce the spot size to within the active area of the smallest PSD, theSC-4D (6.45 mm2 ). Along with reducing the light spot diameter, the lens also reduces someof the geometric amplification gained by increasing the PSD/LED separation. A new cap witha pinhole had a significant effect on the spot diameter. Further testing of the optics togetherwith the sensor electronics revealed a drop in the total photocurrent when the tube deflectionexceeded a certain deflection. This was due to the light spot moving off the active area.A new LED by Hamamatsu, the L2791-02, with a 2° emission beam was tried in place ofthe Siemens diode. The Hamamatsu proved superior overall. It has a smaller package whichis steel, with a glass lens, as opposed to the plastic molded case of the Siemens diode. Theleads were also stronger and easier to bend to make room for the STM tip. Unfortunately, bothdiodes suffered from problems with mechanical alignment of the optical axis, being off by asmuch as 3°. To compensate for this, the several nylon caps were drilled off center by 1°, 2°,and 3°. The diodes were tested for mechanical alignment before being glued into the cap andeventually into the scanning tube. If the diode was off center, then it was rotated within thenylon cap until the beam approached the center axis. If the beam was still off center, then a capwith a hole drilled with a greater compensation angle was used and the alignment re-checked.The sensor testing resumed with the new diode in place only to reveal the same problem.Closer examination of the light spot revealed a faint halo about the bright center of the lightspot. This was mostly due to diffraction of the light spot through the pinhole and partly due toaberration from the lens. A double pinhole was constructed with two metal discs and a nyloncasing to hold the LED. This arrangement had no significant effect when used with or withoutChapter 5. Building and Testing^ 44Infrared Laser DiodeFigure 5.28: Optical setup with laser diode collimating lens and longpass filter.a lens. The next step was removing both the pinhole and the lens which led to improvedperformance of the sensor. The light energy reaching the PSD is much greater without any lensor pinhole, hence the signal level in the amplifier circuit is also greater. Also, removing the lenseliminates the loss of geometric amplification that it caused.Another problem related to the optics was noise due to ambient light. At first it was assumedthat the LED and PSD were both isolated from ambient light within the STM head. Noisein the circuit in the form a 60 Hz signal was finally attributed to the fluorescent lab lights.Apparently, the white nylon LED cap was translucent and not opaque. The white nylon wasreplaced with black nylon which considerably reduced the noise signal.A third device was tested for the optics to hopefully achieve a smaller spot size. A PhilipsAlGaAs CQL60A infrared laser diode was tested with a collimating lens cap. The peak emissionof 820 nm is within 10% of the maximum responsivity of the PSD's. The spot size was easilyreduced to a 1 mm diameter over a range of 2 — 20 cm from the laser diode. Though thelaser diode was superior to the LED's, it did have a larger package and higher output power.The laser diode case was filed down on one side to accommodate the tip holder in the nyloncap. The Philips laser diode has a maximum optical output power of 10 mW, which causedthe sensor circuit outputs to saturate even at low gain. The offset voltages were incapable ofreducing the outputs because it was the PSD that was actually saturated. The first attempt atChapter 5. Building and Testing^ 45reducing the incident power on the PSD by inserting a plastic polarizing filter was unsuccessful.The second filter tested, an 850 nm longpass color glass filter, successfully reduced the incidentpower. The glass filter was inserted directly in front of the PSD with no apparent degradationin the quality of the light spot. The final setup is shown in Figure 5.28.The most notable difference between using the LED and the laser diode was the ease withwhich the light spot was centered on the PSD. One disadvantage was an oscillatory drift ofthe sensor outputs that was not present with the LED. This drift was attributed to the laserdiode electronics and not the sensor circuit. Unfortunately, the differential amplifier stage ofthe transimpedance circuit did not remove the drift at the final output of the sensor. Testingrevealed that the drift was caused by thermal sensitivity of the transistors in the laser diodedriver circuit. Temperature variations would cause the intensity of the light spot to fluctuate,hence affecting the photocurrent in PSD. A more temperature insensitive driver circuit wasused to eliminate this problem.5.3.2 Circuit ProblemsThe first sensor circuit was assembled on a breadboard for convenience. After initial testing iswas deemed necessary to reduce wire lengths and increase the compactness of the entire circuit.The following generations of sensor circuits were assembled on vector prototype boards exceptfor radically different designs, which were also tested on breadboards first. The vector boardsprovided several options for a ground plane, better connections (soldered as opposed to frictionclips), and had no inherent capacitance effects as did the breadboard. Different schemes weretried with a ground plane in an effort to eliminate ground loop noise and improve shielding.The circuit also went through two printed circuit board (PCB) designs before reaching itspresent state. The first PCB was designed for the basic sensor circuit shown in Figure 4.23based on preliminary sensor testing with the bimorph. The first PCB suffered from drift, 60 Hznoise and ground loop noise. The grounding connections were not made to a common locationand the components were spaced too far. Following the tests on this PCB came the testing ofChapter 5. Building and Testing^ 46ClR1CDR2 T C2Figure 5.29: Two stage amplifier circuit with high gain transimpedance stage and a low passfilter on the differential stage.the three circuits in Section 5.2 on vector boards before making the final PCB.The first major change in the circuit design was to make the gain of the transimpedancehigh rather than the gain of the differential stage. The idea behind this is simple. Maximize thesignal as much as possible before introducing any more noise. This was successful in reducingsome of the noise. With this change came the need for a low pass filter on the differential stageas well.By far the biggest problem has been 60 Hz noise. This has been confirmed by runninga spectrum analyzer on the sensor circuit which is described in detail in Section 5.3.3. Onesource was eliminated by making a new LED cap from black nylon isolating the LED and PSDfrom ambient light ( see Section 5.3.1 ). The 60 Hz noise was diminished but not completelyeliminated. Another source was believed to be the power supply for the LED and the circuit.RiRPSDR2 = R1 RPSD '(5.48)Chapter 5. Building and Testing^ 47Batteries were tried as a power supply, but the electronics drew too much current, draining thebatteries quickly and causing a drift in the output signals. We returned to using an encapsulatedpower supply but added a voltage regulator and low pass filter with a cutoff below 1 Hz to drivethe LED. This reduced the noise across the LED from 30 mV p— p down to 2 mV p— p.One version of the circuit was plagued by drift as large as 500 mV/hr. It was discoveredthat the drift was thermal, when the outputs were observed to vary as the circuit was enclosedor exposed. We finally realized that the non-inverting inputs of the transimpedance amplifierswere simply grounded rather than being connected to temperature compensating resistors. Anew value for R2 was chosen to match the input impedances of the seen by each input of theop amps.where RPSD is the equivalent resistance of the PSD from any electrode to ground. ReplacingR2 in the sensor circuit eliminated the large thermal drifts.In terms of hardware, several components were tested in a effort to reduce noise and im-prove the sensor resolution. One significant change was using lower noise op amps. Originally,the circuits were assembled with BB OPA111 low noise op amps, with input noise voltage of= 8 nV/firz and CMRR of 90 dB 3 . These were later switch to HA-5127A op amps witha typical input noise voltage e n = 3.0 nV/V'Hz and a minimum CMMR of 114 dB. Unfortu-nately, these new op amps had a different pullout than the Burr Brown op amps, forcing thecircuit boards to be redesigned. The final version of the circuit contains LT 1037 CN8 whichhave the same pullout as the Harris op amps and a slightly better typical input noise voltage,er, = 2.5 nV/V-HZ and a minimum CMMR. of 110 dB.3 All values is taken from manufacturer's data booksChapter 5. Building and Testing^ 48Coherence Function0. 1Frequency (Hertz)Figure 5.30: Coherence plot of the spectral analysis data from the sensor circuit.5.3.3 Spectrum Analysis of SensorA software based spectrum analyzer was used to study the frequency response and noise char-acteristics of the sensor circuit. The analyzer was written in MATLAB and C and was imple-mented in a UNIX environment. The software performs calculations based on the input andoutput signals of a given plant. The software generates a random input signal with a desiredfrequency content and maximum amplitude. The input signal is ported through a D/A board toexcite the plant and the output read back into memory via an A/D board. Fourier transformsare applied to the I/O signals to calculate the spectral functions of the signals, the frequencyresponse of the plant and the coherence function. The coherence function is a measure of thevalidity of the results. The closer the coherence is to one, the more meaningful the results are.To analyze the sensor, a random signal was used to drive the actuator causing the lightspot to move accordingly. The output of one transimpedance stage was measured and fedback into the spectrum analyzer. The coherence function in Figure 5.30 reveals a significantnotch, dropping below 0.4 at 60 Hz. This is indicates that power spectrum of the output has asignificant component at 60 Hz which is not present in the input signal. This implies that theChapter 5. Building and Testing^ 4960 Hz is external noise.5.4 Construction of the STM HeadThe STM head was redesigned several times to accommodate lens, PSD's of various sizes andthe circuit itself. The reasons are twofold in the case of the PSD's. Since PSD's of with differentactive areas come in different size packages, the heads had to be machined to insure that eachwas centered properly. Secondly, the orifices for the PSD's had to match their sizes as closelyas possible to prevent ambient light from affecting their operation. The final design consisted ofan aluminum disk five inches in diameter and one inch thick with the scanning tube and sensoron opposite faces. Several disks were machined to fit on the sensor side of the head to holdvarious size PSD's, making it easier for testing. Two larger disks were bored out to fit over thetube and the sensor completely enclosing the head. Both caps provided optical shielding fromambient light. The sensor cap was lined with mu-metal, providing electromagnetic shielding aswell. The only openings in the casing were for power supply wires to the sensor electronics andthe LED, output wires from the sensor circuit and high voltage driving signals to the scanningtube.5.5 Summary of ResultsThe laser diode optics and ground plane vector board circuit with the SC-4D in the tran-simpedance configuration achieved the best results. The intensity of the light spot incident onthe PSD was the most significant factor in improving the resolution. The intensity was alwaysmaximized for each circuit that was tested.Hysteresis and creep for the particular PZT scanning tube used in our setup were measuredusing the sensor operating in a single axis. A 10 Hz square wave input was applied to twoopposing electrodes and the sensor was used to record the position of the tip in terms of volts.The results shown in Figure 5.31 indicate that the tube has a creep of 6.5%. This value isobtained by measuring the slow change in deflection as a percentage of the larger intial deflectionChapter 5. Building and Testing^ 502 0.080UTRIG 2^11 .19 .!.^= 3.6mssnu:...........paIMINIMP&PLE1WI11111111tamsFigure 5.31: Sensor output revealing creep that exists in the scanning tube.Chapter 5. Building and Testing^ 51.AU '1 -.AU 20 . 00^1U6 U,%.T= I- 6 . 6S A Um 5L iT 1I.^•.....•-7,-,....,.•,.....".,.,X ,_ .•.,.,• .•.^.,,5 U..,:::••-•-•0 . 2 y SAMPLE 1 0 lin sFigure 5.32: Hysteresis plot for the scanning tube.in response to a square wave input to the actuator. Figure 5.32 is a hysteresis loop obtained byplotting the sensor output versus the driving voltage on an opposing pair of electrodes. Frommeasurements taken off the plot, the hysteresis is calculated to be 11.5%. These results arewithin the norm for soft PZT.Chapter 6DSP System and Control Strategy6.1 Overview of HardwareThe STM hardware can be separated into three components for the practicality of discussion.• STM head: The head is an aluminum block upon which is mounted a translation stagewith a sample holder, the PZT tube actuator with the laser diode and tip, the laser diodedriver circuit, the tunneling current pre-amplifier circuit and the position sensor circuit.• PCB cage: The cage is a standard rack mount cage divided into two parts. The front halfcontains slots for prototype and custom PCB's. The back half contains the ±15 V and±210 V power supplies and connectors for cables to the STM head. The divider betweenthe two is a back plane used for interconnections between the PCB's, the I/O connectorsand the power supplies. The cage contains the tunneling current input amplifier circuit,the tip/sample bias control circuit, the D/A and A/D interface circuits and the highvoltage driver circuits for the actuator.• PC: The PC is a 486-33 MHz based system running DOS and Windows. The system isequipped with a Spectrum TMS320C30 DSP board with two additional I/O boards.6.2 DSP Hardware DetailsThe main DSP board has 2 16 bit A/D and D/A channels on board. Both channels are clockedon the same trigger signal, whether it be an internal timer or an external signal. The input andoutput of each channel make use of the same shift register so that at each sampling intervalthe sampled signal value must be read before a new value is written to the output. If a write52VDSP Side:^- I/O timing- Control codePC Side: - Overall STM control code- Image acquisition- Control parameter adjustmentChapter 6. DSP System and Control Strategy^ 53Tunnelling Pre-AmpSensor CircuitLED Voltage RegulatorAluminum STM Head25Tunnelling CurrentInput AmplifierBias VoltageControlD/A & A/D Interface High Voltage DriversA/D for TunnelingCurrent and X-YPositionD/A DrivingSignals for X, Yand ZX& Z Y& ZThe CageThe PCFigure 6.33: Three components of the STM.Chapter 6. DSP System and Control Strategy^ 54command occurred before a read command was issued, the shift register would be overwrittenand the same value that was outputted would be read. Both the inputs and outputs are filteredthrough lowpass filters. The cutoff frequency of these filters can be modified by changing SILresistor packs on the board. The D/A channels are available as filtered or non-filtered outputs.The filters on the A/D channels can not be bypassed without custom modification of the board.The channels have a range of +3 V.Two add-on boards also used are 16 channel D/A board and a 32 channel A/D board. Theseboards communicate with the main board via a bus called the DSP Link. Both of these boardsare 12 bits and also implement some filtering of the signals. All the outputs on the 16 channelboard are synchronized and filtered with an adjustable cutoff frequency. The outputs have anon board reference voltage that produce an output range of +8.2 V. This reference voltagecan be bypassed by an external reference source to yield a lower voltage range with the same12 bits. This makes it possible to have all the DSP outputs ( the dual channels from the mainDSP board and the 16 channels from this board ) on the same voltage range. The 32 channelinput board has a range of +2.5 V for the full 12 bit scale. The inputs are multiplexed so thatonly four signals may be sampled at once.The main DSP is equipped with dual port and regular memory. The DSP processor com-municates with the PC via interrupts and by writing data to dual port memory which the PCcan access. The PC can also access the regular DSP memory but not without halting the DSPprocessor.6.3 Control System6.3.1 Hardware AspectsCurrently, STM tips are scanned in open loop by ramps to the X and Y driving signals. Closingthe loop for X—Y position control requires reading the position information from the sensor,calculating the error from the desired position and determining a suitable control signal tocorrect the error. The signals to be read in through the A/D channels are the X and Y positionChapter 6. DSP System and Control Strategy^ 55which are voltages which are scaled to the range of ±2.5 V for compatability with the DSP.Once sampled, the values are compared with a setpoint and a control signal is determinedaccording to a PID control law. The control signals, one for each axis, are then outputtedthrough the D/A channels and sent to the cage where they are amplified by the high voltagedrivers before reaching the actuator. Thus instead of applying ramping voltages, we simplychange the setpoints to obtain a desired position or scanning trajectory. Each axis has itsown PID control loop. The X and Y axes rely on the optical sensor while the Z axis relies onmeasuring the tunneling current.6.3.2 Software AspectsThe flowchart shown in Figure 6.34 contains the basic skeleton of the control algorithm and theway it fits in with the imaging aspect of the code. The code is split into two halves, one runningunder the PC and the other running under the DSP. The PC launches the DSP code and thetwo communicate via interrupts and flags and parameters through the dual ported memory ofthe DSP. The control loop for the tip position in the DSP code is continually running, whileimaging and parameter values are controlled from the PC side.The sampling rate of the control loop is limited by the time necessary to perform A/Dconversions and the amount of calculations performed within the loop. The simplest case ishaving only the Z-axis under digital control, with the X-Y position being controlled by rampsignals in open loop. Including only the X-axis to the control loop (via the sensor output)increases the control loop period by adding arithmetic calculations. No extra time is requiredfor the A/D conversion of the single axis sensor output since conversions for the two onboardA/D channels are done simultaneously. Adding a third input to the control loop for the Y-axisrequires using one of the channels from the 32 channel A/D board which has slower conversionsthan the onboard channels even once the input multiplexers of 32 channel board are set forusing a single channel.The control loop period for the simple case of only Z-axis control is 15 its. If nothing butNO-Setup Windows &Parameters-Load & Launch DSPCodeDSPUpdateParameters ? Imaging ?-Send New Parameters -Receive and DisplayImage DataStop &ImageComplete ?Abort ?Start-Set Parameters-Begin Timer InterruptRead XYZ-Calculate Errors &Outputs Using PIDControl LawOutput XYZ-Send Image DataChapter 6. DSP System and Control Strategy^ 56Figure 6.34: Flowchart of control and imaging software.Chapter 6. DSP System and Control Strategy^ 57this interrupt driven control loop were running, the sampling rate would be roughly 66.6 kHz.A certain amount of overhead must be added to this for gathering image data and sending it tothe PC. Adding the X-axis control code increases the period of the control loop by 3.5 its andadding the Y-axis control code increases the loop by a further 6.9 its. For three axis controlthe sampling rate would be 39.4 kHz.6.4 Z-axis ControlThe digital control loop implemented is based on the analog controller that is currently beingused by Quantum Vision Inc. to control their microscopes. The proportional and derivativeterms were coded but the gains were set to zero, reducing the PID controller to a pure integratoras in the analog case. Once the coding was complete, the digital controller was tested in parallelwith an analog controller that was in use. The tunneling current was fed to both controllers andthe output voltages to drive the actuator were monitored to determine if the digital controllerbehaved correctly.The next step was to actually control the tip of a microscope while it was stationary inthe X—Y plane. The controller was able to servo to the setpoint tunneling current within1 nA and track changes in the setpoint. The final test of the Z-axis controller was to get themicroscope to image a sample. Before this could be achieved, a few modifications were madeto the setup. A more rigid sample holder assembly was made to reduce the effect of ambientvibrations. The original ribbon cables from the DSP to the cage were replaced by shieldedcables, significantly reducing noise. Many days were spent learning how to tune the tunnelingand scanning parameters and cutting new tips after crashing them into the sample. The controlparameters, namely the integrator gain and the integration limits were adjusted according tothe value of the tunneling current setpoint and the scan rate. With the help of the peoplefrom Quantum Vision Inc., the STM finally yielded images such as the one in Figure 6.35of sputtered gold. This image was obtained with the DSP sampling the tunneling current at33.3 kHz and an image point being taken every four control loop periods. The size of the imageChapter 6. DSP System and Control Strategy^ 58Figure 6.35: Image of sputtered gold obtained with the tunneling current under digital control.is approximately 150 nm by 150 nm.Chapter 7ConclusionsThe objective of this project was to achieve digital control of an STM with optical end point sens-ing in order to realize the following advantages: more accurate tip positioning, programmabletip positioning, compensation for creep and hysteresis and more sophisticated scanning tra-jectories. The STM was successfully operated under closed loop digital control of the Z-axis(tunneling current junction) while the X-Y position of the tip was controlled in open loop. Theimages achieved were of equal quality to similar images obtained with an analog controller. Anintegrator was used with limiting to prevent integrator wind up. The digital controller offersgreater flexibility and ease of use for tuning the control parameters.An optical end point sensor was implemented and its resolution was determined to be 8.5 nmbased on an approximation for the deflection per volt of the PZT actuator. This resolution ofthis sensor would have to be improved by at least one order of magnitude to be useful forimaging features as small as 10 nm. The sensor was good enough to provide measurements ofhysteresis and creep of the actuator. The hysteresis and creep were measured to be 11.5% and6.5% respectively by using the end point sensor in single axis operation.The majority of the time spent on this project was devoted to the optical end point sensor. Adetailed comparison of different circuits for the sensor was conducted. A variety of experimentswere performed with circuit layouts, grounding schemes, PSD biasing schemes and shielding.Several different electronic components and semiconductor devices were tried in the hope ofreducing noise and increasing the sensor resolution.Trying to achieve sub-atomic resolution for the sensor proved to be a tougher challenge thanwas initially anticipated. Refining such sensitive electronics requires not only great skill and59Chapter 7. Conclusions^ 60knowledge but also a fair amount of intuition. The hardware and software was pushed closed tothe limits of existing technology. The op amps were chosen for their low noise and high commonmode rejection, the diodes had the narrowest beam that we could find, and the control codewas optimized to overcome delays in the A/D converters of the DSP to achieve the greatestsampling rate possible.7.1 Further WorkSingle axis testing of the end point sensor while imaging will be necessary to determine itsusefulness in overcoming hysteresis and creep in the actuator. This can be done by comparingtwo images of the same sample that have been obtained with and without single axis end pointsensing. Images obtained by driving the X-Y scan in open loop while gathering data on boththe forward and reverse scans would appear "unshifted", while those obtained by driving theX-axis in closed loop would appear relatively undistorted depending on how well the sensorcorrected for hysteresis.Independent verification of the sensor resolution should be done to confirm the approxima-tion. This requires imaging a sample with regular or grid-like features of known dimension.The minimum resolvable displacement that the sensor could distinguish could be obtained byexamining the pixel size of the features in the resultant image.The final step to completing the project would be dual axis end point sensing and thecomplete integration of the control and imaging code. This would provide the user with a morereliable STM with better repeatability and scanning flexibility.Bibliography[1] Robert J. Hamers. Stm comes of age. Physics Today, January 1989.[2] H.Kumar. Wickramasinghe. Scanning probe microscopy: Current status and future trends.Journal of Vacuum Science and Technology. A, Vacuum, Surfaces, and Film, 8(1), Jan/Feb1990.[3] H.Kumar. Wickramasinghe. Scanned-probe microscopes. Scientific American, October1989.[4] P.K. Hansma et al. Scanning tunneling microscopy and atomic force microscopy: Appli-cation to biology and technology. Science, 242, October 1988. pp. 209 - 216.[5] R.C. Barrett and C.F. Quate. Optical scan-correction system applied to atomic forcemicroscopy. Review of Scientific Instruments, 62(6), June 1991.[6] D.M. Eigler and E.K. Schweizer. Positioning single atoms with a scanning tunnellingmicroscope. Nature, 344(6266), April 1990.[7] Conrad Schneiker et al. Scanning tunnelling engineering. Journal of Microscopy, 152,November 1988. pp. 585-596.[8] G. Binnig and D.P.E. Smith. Single-tube three-dimensional scanner for scanning tunnelingmicroscopy. Review of Scientific Instruments, 57(8), August 1986.[9] T. Tiedje and A. Brown. Performance limits for the scanning tunneling microscope. Jour-nal of Applied Physics, 68(2), July 1990.[10] James M. Gere and Stephen P. Timoshenko. Mechanics of Materials, chapter Stresses inBeams, page 254. PWS-Kent Publishing Company, 1990.[11] R.G. Carr. Finite element analysis of scanning tubes. Journal of Microscopy, 152, Novem-ber 1988.[12] Richard Lloyd Smith. Development and tracking of an infrared target tracking system.Master's thesis, University of British Columbia, 1990.[13] William Light. Non-contact optical position sensing using silicon photodetectors. UnitedDetector Technology, April 1982.[14] Application of silicon photodiodes. United Detector Technology.[15] Allan J. Kelley. Elec 475 systems laboratory: Optical position sensor for scanning tun-nelling microscopy. Technical report, Dept. of Electrical Engineering, University of BritishColumbia, April 1991.61Bibliography^ 62[16] The Handbook of Linear IC Applications, chapter Photodiode monitoring with op amps,pages p. 192 — 201. Burr-Brown Corporation, 1987.[17] Brian 0. Kelly and Robert I. Nemhauser. Techniques for using the position sensitivity ofsilicon photodetectors to provide remote machine control. In 21st Annual IEEE MachineTool Conference, 1973.


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