Drift compensation for automatic nanomanipulation with scanning probe microscopes

IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 3, NO. 3, JULY 2006 199

Drift Compensation for Automatic NanomanipulationWith Scanning Probe Microscopes

Babak Mokaberi, Student Member, IEEE, and Aristides A. G. Requicha, Fellow, IEEE

Abstract—Manipulation of nanoparticles with atomic force mi-croscopes (AFMs) has been under development for a decade andis now well established as a technique for prototyping nanodevicesand for other applications. Until now, the manipulation process forparticles with sizes of a few nanometers has been very labor inten-sive. This severely limits the complexity of the structures that canbe built. Particle sizes on the order of 10 nm are comparable to thespatial uncertainties associated with AFM operation, and a userin the loop has been needed to compensate for these uncertainties.This paper addresses thermal drift, which is the major cause of er-rors for AFMs operating in ambient conditions. It is shown thatdrift can be estimated efficiently by using Kalman filtering tech-niques. This approach has firm theoretical foundations and is vali-dated by the experimental results presented in this paper. Manipu-lation of groups of 15-nm particles is demonstrated under programcontrol, without human intervention over a long period of time,in ambient air and at room temperature. Coupled with existingmethods for high-level motion planning, the manipulation capabil-ities introduced here will permit assembling, from the bottom up,nanostructures that are more complex than those being built todaywith AFMs.

Note to Practitioners—Nanomanipulation with scanning probemicroscopes (SPMs) has potential applications in nanodevice andsystem prototyping, or in small-batch production if multitip arraysare used instead of single tips. However, SPM nanomanipulation isstill being used primarily in research labs. A major obstacle to itswider use is the labor and time involved in the process. These arelargely due to spatial uncertainty in the position of the tip (whichis analogous to a robot’s end effector) relative to the sample beingmanipulated. Today, a skilled user is needed to determine wherethe tip is and to correct manipulation errors due to inaccurate po-sitional estimates. The major cause of this spatial uncertainty isthermal drift between the tip and the sample. At the time scalesrelevant to manipulation, the drift can reach values comparable tothe size of the objects, especially if these are below 10 nm. Thetechniques discussed in this paper compensate for the drift and en-able automated manipulation, with associated savings in time andlabor, and increased complexity of the resulting structures.

Index Terms—Atomic force microscopes (AFMs), Kalman fil-tering, nanoassembly, nanomanipulation, nanorobotics, scanningprobe microscopes, spatial uncertainty.

Manuscript received October 29, 2004; revised June 23, 2005. This work wassupported in part by the National Science Foundation under Grants EIA-98-71775 and DMI-02-09678. An earlier version of this paper was presented at theIEEE International Conference on Robotics and Automation, New Orleans, LA,April 25–30, 2004. This paper was recommended for publication by AssociateEditor N. Xi and Editor M. Wang upon evaluation of the reviewers’ comments.

The authors are with the Laboratory for Molecular Robotics, Univer-sity of Southern California, Los Angeles, CA 90089-0781 USA (e-mail:[email protected]; [email protected]).

Digital Object Identifier 10.1109/TASE.2006.875534

I. INTRODUCTION

ATOM manipulation with scanning probe microscopes(SPMs) was first demonstrated in the early 1990s, and

manipulation of particles with sizes on the order of a fewnanometers to the tens of nanometers soon followed (see [1],[2], and references therein). Today, particles with diametersof 10 nm are manipulated routinely with atomic force mi-croscopes (AFMs) at the University of California’s (USC’s)Laboratory for Molecular Robotics (LMR) and elsewhere.(The AFM is a specific type of SPM that exploits interatomicforces between a sharp tip and a sample.) Nanomanipulationoperations are used to prototype nanoscale devices, and torepair or modify nanostructures built by other means.

Manipulation of small nanoparticles (with diameters below30 nm, for example) in ambient conditions (i.e., at room

temperature, in air or in a liquid, and without stringent en-vironmental controls, requires extensive user intervention tocompensate for the many spatial uncertainties associated withAFMs and their piezoelectric drive mechanisms). Uncertaintiesare introduced by phenomena that range from nonlinearities inthe voltage-displacement curves that characterize the piezos,to creep, hysteresis, and thermal drift. The latter is the majorcause of spatial uncertainty in our lab and is due primarily tothermal expansion and contraction of the AFM components.For example, a 1 change in temperature will cause a 50-nmchange in the length of a mechanical part that is 5 mm long(assuming a typical expansion coefficient of 10 C).

AFM vendor software usually compensates for piezo nonlin-earities. Hysteresis effects can be greatly reduced by scanningalways in the same direction, and creep effects can be nearlyeliminated by waiting a few minutes after each large motionof the scanner (although this is very inefficient). In addition,modern, top-of-the-line instruments are equipped with feedbackloops that claim positioning errors below 1 nm in the , planeof the sample [3]. Feedback can compensate for nonlinearities,hysteresis, and creep, but not tip drift (see Section II-B). Drifttends to increase with time, which implies that complicated as-semblies cannot be completed without frequent user interaction.Moreover, most of the AFMs in use today either have no ,feedback, or their feedback loops have noise levels of severalnanometers, which are too large for the manipulation of parti-cles with sizes 10 nm. These machines are normally operatedopen loop for the small scan sizes used in the manip-ulation of small nanoparticles to avoid introducing additionalnoise through the feedback circuitry. With or without , feed-back, drift compensation remains a crucial issue for successfulnanomanipulation.

1545-5955/$20.00 © 2006 IEEE

200 IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 3, NO. 3, JULY 2006

Fig. 1. (a) Four images from a 180-nm region of a sample, taken at 8-minintervals. The objects shown are Au nanoparticles with 15-nm diameters.(b) Schematic diagram of an AFM machine. (c) A spatial asperity below the tip.

Typical assemblies of small nanoparticles built by nanoma-nipulation today consist of some ten particles, and may takean experienced user a whole day to construct [13]. To movetoward more complex assemblies requires that the manipulationprocess become more automated, and this, in turn, requirescompensation of the spatial uncertainties associated withAFMs—especially drift, which is the most pernicious one, aswe have argued above.

The remainder of this paper discusses the characteristics ofdrift, how to estimate it, and compensate for it, our implemen-tation of drift compensation, and experimental results.

II. DRIFT CHARACTERIZATION

A. Problem

Successive AFM scans of a sample without changing anyscanning parameters will appear as translated versions of thesample surface, as shown in Fig. 1(a). This is the physical man-ifestation of drift in the , plane of the sample. There is alsodrift in the direction but it will be ignored in this paper, be-cause it usually is reasonably well compensated by the feed-back system and has little impact on nanomanipulation. Notethat, unlike atoms, particles of the sizes we are discussing in

this paper do not diffuse over the surface at room temperature;they are fixed with respect to the surface. Many experimental ob-servations indicate that the drift is essentially a translation (norotation is involved) and the drift velocity is approximately con-stant over periods of several minutes, but changes on a longertime scale. A drift-compensated instrument would produce thesame image in each panel of Fig. 1(a). The problem addressedin this paper is how to achieve drift compensation in such a waythat not only images of the same region are constant in time, butother processes, in particular, programmed sequences of manip-ulation operations, can also be carried out as if drift did not exist.

Several authors have reported simple approaches to drift com-pensation [4]–[8]. These approaches assume that the drift ve-locity is constant and compute it by comparing successive im-ages. The major drawback of these procedures is their failureto adapt when the drift velocity changes. They can be used forcorrecting images taken over a period of time of approximatelyconstant drift, but cannot support a sequence of nanomanipu-lation operations, which requires real-time compensation overrelatively long durations.

B. Spatial Analysis

Consider a typical AFM, schematically shown in Fig. 1(b).For concreteness, we assume that the sample is placed on top ofthe scanner and that the unloaded (i.e., undeflected) cantileverand tip (or their average positions when the AFM is operatedin dynamic mode) are fixed in space, except for drift. This isthe most common AFM configuration; other configurations inwhich the sample is fixed and the cantilever moves can be ana-lyzed by trivial changes to the arguments below. Consider alsoa sample which consists of a flat surface with a very sharp as-perity on it (a spatial impulse), as shown in Fig. 1(c). For sim-plicity, we ignore the coordinate in the following discussionand the figure. In an ideal situation with a contact mode scan,the tip remains at a fixed height touching the flat surface until itencounters the asperity. Then, the scanner moves very quicklydownward (it contracts) for the tip to remain in contact with thefeature, maintaining the same applied force. If we record theheight of the tip in a coordinate system attached rigidly to thesample (or, equivalently, to the top of the scanner) as a functionof the coordinate of the tip in the same system, this gives usthe true topography of the sample, which is the desired output.(A similar argument holds also for vibratory, or dynamic modeoperation.)

However, in a real AFM, when the tip contacts the top ofa feature, such as the spatial impulse of Fig. 1(c), what wemeasure is the voltage applied to the vertical piezo motorversus the voltage applied to the horizontal motor. If we ig-nore (or compensate for) hysteresis and creep, and assume thatthe AFM is properly calibrated and compensates for nonlineari-ties in the voltage-displacement curve, the voltages can be con-verted into piezo extensions and . But the position ofthe scanner (or sample) with respect to the base of the instru-ment does not equal the piezo extension because there is driftbetween the sample and the base. Rather, the scanner positionis , where is the scanner drift. (We assumethe drift is a translation, based on experimental observations,as noted earlier.) In other words, even without applied voltages,

MOKABERI AND REQUICHA: DRIFT COMPENSATION FOR AUTOMATIC NANOMANIPULATION 201

the scanner is moving (drifting) with respect to the base. In ad-dition, the tip is itself drifting with respect to the base. Thus, theposition of the tip with respect to the base is . The po-sition of the tip with respect to the sample, which is the desiredtopography signal, is the difference between the position of thetip and the position of the sample, both measured with respectto the base

(1)

The combined effect of these two drifts is what we callsimply AFM drift. To image the impulse of Fig. 1(c), the tipmust be on top of the feature and, therefore, the tip position withrespect to the sample must be constant. Since the drift varieswith time, it follows from (1) that the piezo extension and cor-responding applied voltage vary with time and so do the images.To stabilize the image and compensate for the drift, it sufficesto change the origin of the axis by . This can be done bychanging the offset values associated with a scan, which is pre-cisely what our system does, as we will show later. It is alsoclear from (1) that the drift between two instants of time and

can be measured by subtracting the corresponding piezo ex-tensions for an impulse feature. These can be read directly fromthe images of the feature taken at times and . (In practice,the situation is more complicated because the features imagedare not pure impulses, as we will see below.)

Feedback in the horizontal directions , is normally used inAFMs to ensure that the scanner is in the correct position withrespect to the base. Therefore, , feedback can compensate(within the noise level constraints of the system) for nonlinear-ities and scanner-base drift. However, it cannot compensate fortip-base drift.

C. Statistical Properties

The behavior of the drift depends on such factors as temper-ature, humidity, the construction of the instrument, and thermalexpansion coefficients. In our lab, drift velocities tend to varyfrom 0.01 to 0.1 nm/s. Therefore, for 256 256 pixel imagestaken at a 1-Hz rate (these are typical values), the drift betweentwo successive images can be as much as 25.6 nm, which islarger than the diameter of the particles we normally manipulate.

Fig. 2(a) shows a time series of drift displacement values inthe and directions, which was measured by comparing im-ages of the same feature taken at sampling times 30 s apart.These measurements were performed after an initial period of2–3 h of AFM operation, to let the instrument stabilize. Im-mediately after the AFM is turned on, the drift is considerablylarger. The corresponding velocities inferred from the figuresare approximately constant for several minutes, and then changein a seemingly random manner. The power spectra of the drifttime series are shown in Fig. 2(b) and exhibit most of the signalpower in the frequency band below 5 10 Hz, which corre-sponds to a time constant of about 30 min. The slow-varyingcharacter of the drift compared to the typical time required fora manipulation operation, which is, at most, a few seconds,makes it possible to estimate drift while performing a series ofmanipulations.

Fig. 2. (a) Measurement of drift in x and y directions over 215 min, with asampling time of 30 s. (b) Corresponding power spectral density using the Welchmethod. Most of the signals’ power is concentrated in the frequency band below5�10 Hz.

III. ESTIMATION AND COMPENSATION OF DRIFT

A. Drift Measurement

The basic method for the measurement of drift involvestracking a number of fixed features in the sample. We employtwo methods depending on the sample type.

The first method is applicable only when the objects to bemanipulated have a known and simple shape. This is usuallythe case in our experiments, in which we manipulate sphericalparticles. For these particles, drift can be measured by trackingthe center of a particle.

We search for the center of a spherical particle as follows.First, we look for the highest point of a single line scan in the

direction (Fig. 3). Then, we scan along a single line in thedirection and passing through the previously found high point.We find the highest point of this scan, pass an line throughit, and find a new maximum, continuing the process until wereach a desired accuracy. (This process fails if the first line scanmisses the particle altogether.)

The second method uses a general approach, applicable toobjects of arbitrary shapes, and involves correlating images, byusing the three following steps.

1) Selection of Tracking Window: We typically use a 6464 window, which can be scanned in a few seconds and normallycontains enough features for successful tracking. The area isselected by maximizing an interest operator, defined in termsof the following characteristics [9], [14]:

• distinctness of features from immediate neighbors;• global uniqueness of the features (in the whole image);• invariance of features under expected distortions.


Fig. 3. Successive single line scans for finding the center of particle.

Fig. 4. Optimal tracking window. Horizontal stripes in the image are due toline-by-line flattening.

In order to evaluate the optimality of the selected window interms of these criteria, we first construct the matrix

(2)

where and are the gradients of the image in the anddirections, and the sum is over all of the pixels in the window.Assuming a constant noise level in the image, the optimumwindow is selected in regions in which the eigenvalues of areapproximately equal to each other. This ensures that the selectedwindow does not contain a straight edge or a strongly orientedtexture. We also require that the confidence ellipse (defined by

) be smaller than those obtained from neighboringwindows. This ensures maximum local separability or distinct-ness of points in the selected window (for more details, see [14]).Fig. 4 shows a standard scan of nanoparticles and the optimumselected tracking window.

2) Coarse Computation of Translation: The normalizedcross-correlation between two images is a good measure oftheir similarity. It is defined mathematically as

(3)

where and are the two images, assumed to have zero mean,and the summations are over the discretized values of and .If is a perfect translation of by , then the cross-cor-relation exhibits a peak at , and the peak valueis 1. In this case, the rest of the points in take valuesbetween 0 and 1, depending on how well the two images matchat each translation. In general, the match is not perfect,and we use the , values that correspond to the maximumvalue of the correlation function as the measured translation,and the peak value as an indication of how well the two imagesmatch. The cross-correlation is computed efficiently in the fre-quency domain, by using the fast Fourier transform (FFT).

3) Fine Computation of Translation: The cross-correlationcomputation is done with pixel accuracy, which may not besufficient for successful nanomanipulation. Subpixel accuraciescan be obtained by the following procedure [9]. First, the cross-correlation method is used to find a coarse value for the transla-tion ( , ), say. Then, is expressed as a first-orderexpansion of

(4)

where is a noise term that includes higher-order effects, andand are subpixel translations. Next, a best estimate for

the deltas is computed by least square estimation over the entirepicture. Finally, the refined estimate for the translation is givenby and . In our experience, byusing this method, accuracies in the order of 1/10th of a pixeldimension can be easily achieved (for example, if we scan a1- m area in 256 256 pixel size, the drift can be measuredwith an error of less than 0.4 nm).

Observe that both techniques for measuring drift require acoarse estimate of the drift value. Without an approximate po-sition for the spherical particle whose position we want to mea-sure, the search procedure may fail, or produce grossly wrongvalues, because the first single line scan may well miss the par-ticle altogether or, even worse, hit a different particle. The cor-relation-based technique also may fail if the images in the se-lected windows are too different. This may produce low corre-lation values or even spurious peaks that do not correspond tothe translation we want to find.

The particle-center search procedure is very fast. Travelingat m/s, which is a relatively slow speed, good estimatesrequire less than a second for particles 10 nm. The correlationmethod takes longer, on the order of 10 s for a 64 64 pixelwindow, but is more generally applicable.

B. Dynamic Model of Drift

We need a dynamical model of the drift to be able to esti-mate and predict it by using Kalman filtering techniques. Weassume decoupled dynamics for the drift in and directions.Although in reality (especially in tube-shape scanners) there issome correlation between the two directions, our assumptiongreatly simplifies the compensation system design and imple-mentation and produces satisfactory results, as we will showlater in Section IV-E.


The drift behavior is very similar to that of a maneuveringtarget, in which the velocity is approximately constant for a rel-atively large amount of time, and then changes randomly. A suit-able model for such targets was introduced by Singer for radartracking of manned air vehicles [12]. Singer’s model uses an ac-celeration that is correlated in time. Intuitively, this implies thatif a target is accelerating at a time , it is likely to be still accel-erating at a time , for sufficiently small . We model thedrift acceleration by a first-order Markov process governedby the first-order differential equation

(5)

with a corresponding exponential autocorrelation

(6)

Here, and are the variance and time constant of ac-celeration, respectively, and is white noise with a variance

.Thus, the state-space formulation for the drift in the direc-

tion is

(7)

where and are the drift displacement and velocity, re-spectively. (Similar equations apply to the direction in thisuncoupled system.)

The corresponding discrete-time equations for a sampling pe-riod are

(8)

where , is a 3 1 process noise,and the transition matrix is given by

(9)

In this model, the dynamics of drift can be expressed in termsof three parameters: the variance or magnitude of drift acceler-ation, the time constant, and the sampling interval.

C. Kalman Filter Estimation of Drift

The state of the drift defined in (8) can be estimated recur-sively by Kalman filtering. (We consider only the direction,because the system is decoupled; a similar treatment applies tothe direction.) Given the current state estimateand the state error covariance , the filter predictsthe state and covariance at the next time step by the standardequations

(10)

(11)

Fig. 5. Block diagram of the AFM and the drift compensator.

Here, is the covariance of the process noise, which can becomputed in terms of , , and (see [11] and [12] for theactual expressions).

The measurement is modeled as a linear combination of thedrift state corrupted by uncorrelated noise, i.e.,

(12)

in which and is a sequence of white noise,independent of the process noise , and with covariance

.The drift displacement is measured by the techniques dis-

cussed earlier, in Section III-A. We use the premeasurement es-timate of the drift to change the origin of the coordinates whenwe position the first scan line (for the sphere center search) or thewindow used for the cross-correlation computation. This changeof origin ensures that we do not miss the particle in the first linescan, or that the windows used in the correlation method are nottoo different. Thus, the measured value is given by

(13)

where is the distance between the origins of coordinates usedto make the two measurements, and is given by

(14)

and is the amount of measured drift as explained in Sec-tion III-A. The Kalman filter computes the Kalman gain anduses the measurement to update the state estimateand the error covariance by the standard formulas [11].

IV. IMPLEMENTATION AND RESULTS

A. System Architecture

The overall system architecture is shown in Fig. 5. The filtermaintains current estimates of drift displacement and error co-variance. The drift displacement is written onto the offset regis-ters of the controller. This is equivalent to a change of origin. Forexample, if the offset is 20 nm and a tip motion to nmis requested, the controller applies to the piezo the voltage re-quired to move the tip by 30 nm. If the drift estimate was perfect,this procedure would ensure that successive requests for scansfrom to nm, say, would produce always the sameimage. The filter also maintains the last acquired image or par-ticle location (depending on which drift measurement technique


Fig. 6. Synchronization of the drift compensator with the AFM.

is used), together with the corresponding offsets and samplingtimes.

The image or scan line data that result from a measurementjob are first preprocessed. The raw data from the trackingwindow are flattened line by line to remove the existing slope.Then, a threshold is applied to the image for discarding the ar-tifacts due to the image flattening. Finally, the whole data fromthe window are offset to a zero mean. In the case of tracking aparticle using its center, each single line scan is smoothed witha fourth-order infinite impulse response (IIR) filter.

After the raw data are processed, they are passed to the trans-lation analyzer, which compares them with the previous imageor particle position and computes the displacement, taking intoconsideration the changes of origin associated with the offsets.The Kalman filter uses the measured drift and the current esti-mates to update the state and the covariance.

The scheduling of filter operation is performed according tothe flowchart of Fig. 6. Requests for drift measurements aremade from the compensator to the AFM (see the bottom of theflowchart), and the AFM acknowledges the request. This indi-cates that a time slot has been assigned to the filter to performany operation necessary for the drift measurement (i.e., either animaging scan or a series of line scans). Observe that drift mea-surement requires tip motion and, therefore, has to be scheduled

by the AFM controller after the end of any executing processthat also moves the tip. The Kalman filter starts the drift mea-surement procedure once it receives the acknowledgment fromthe AFM. The current estimates of drift are updated by usingthe measurement and are provided as new and offsets to theAFM. From this point until the next measurement, the filter usesthe prediction (10) and (11) to compute the most up-to-date es-timates of and offsets at times , a given sampling intervalapart. Typically, this prediction update sampling period is onthe order of a few seconds and much smaller than the defaultmeasurement sampling interval , which can go from 30 s toseveral minutes. During the intermeasurement period, the errorcovariance is also monitored (as a measure of uncertainty in theestimates) and once it exceeds a user-specified threshold, a re-quest for a new measurement is sent to the AFM machine. Oth-erwise, the measurements are scheduled at the periodic defaultmeasurement times apart.

B. Hardware and Software

The system is implemented on an AutoProbe CP-R AFM(Park Scientific Instruments, now Veeco Instruments). The driftcompensation software runs on top of our own Probe ControlSoftware (PCS) for nanomanipulation which, in turn, is imple-mented through the vendor supplied application programminginterface (API). (A version of PCS is now commercially avail-able.) The API maintains its own job queue, with no preemptivescheduling. Before any job that involves tip motion is executed,we check for updated offset values to ensure that we compen-sate for drift in all imaging and manipulation operations.

C. Selection of Drift Model Parameters

For a fixed-order Kalman filter to be optimal (in the sense ofhaving minimum error covariance), the filter parameters haveto be selected as close as possible to the real signal’s param-eters. These parameters are the measurement noise covariance

, acceleration time constant , and acceleration noise vari-ance . Any mismatch between the filter parameters and thereal parameters results in suboptimality of the Kalman filter gain[10].

The estimation of measurement noise covariance is basedon the autocorrelation of the innovation sequence [15]. The in-novation sequence is defined as

(15)

The innovation process for an optimal Kalman filter is whiteGaussian noise. Using the algorithm of Mehra [15], [16], theautocorrelation of the innovation process is used to estimate

once the filter reaches a steady-state condition. This can bechecked by looking at the state covariance and, in our case, istypically achieved in 5 min–10 min. By using this method, thevalue of is estimated to be about 1.2 nm for the set of datain Fig. 2(a).

The estimation of and is more complicated. Sincethe number of samples in drift measurements is small (thetypical sampling time is in the range of 30–120 s before thefilter reaches the steady-state condition, and thereafter may behigher), we have run a simulation for different values ofand using the measurement data in Fig. 2(a). The criterion


Fig. 7. Contour plot of isolines of the cost function (16) versus � and�. Theminimum of J occurs at � = 0:048 nm =min and � = 0:11 min .

for choosing these two parameters is the minimization of themean square of the prediction errors, i.e.,

(16)

The procedure for the selection of and is as follows.

1) Take a series of drift measurements with some small sam-pling time (30 s in our case).

2) Divide these samples into a set of measurement-predic-tion intervals in such a way that each measurement in-terval is followed by a prediction interval (in our case, weused 5-min measurement and 10-min prediction). Run afilter simulation in which we use measurements 30 s apartfor 5 min, do not measure for 10 min (use prediction only),then measure again for 5 min at 30-s intervals, and so on.Do this for various values of the parameters.

3) With the computed from the Mehra’s method, searchfor the minimum value of (16). Fig. 7 shows the con-tour plot of isolines of and its minimum at

nm min and min .

D. Sensitivity of Parameters

The sensitivity of the Kalman filter with respect to a param-eter is defined as

(17)

where can be any of the parameters , , or while theother two parameters are kept constant at their nominal valueswhich correspond to the minimum of the cost function (seeSection IV-C). Theoretically, the sensitivity vanishes at the ex-tremum values of the cost function (16).

By studying the sensitivity curves in Fig. 8, it is clear thatchoosing the parameters below their nominal values has amore negative impact on the performance than selecting highervalues. However, it should be noted that higher parametervalues imply a larger prediction error (16).

Fig. 8. Sensitivity of J to parameters R , � and �. In each curve, theother two parameters have been kept constant at their nominal values of R =

1:2 nm , � = 0:11 min , and � = 0:048 nm =min .

E. Experimental Results

The following results were obtained on the AutoProbe AFMwith a sharp tip in dynamic mode, imaging, and manipulatinggold nanoparticles with nominal diameters of 15 nm, depositedon a mica surface, covered with poly-L-lysine, in air, at roomtemperature and humidity. Filter parameters were selected at thenominal values computed as explained above.

In order to assess the tracking capability of the filter, we con-ducted two experiments. In the first experiment, we measuredthe drift with the method explained in Section III-A at time inter-vals 30 s apart. At specific time instants, several minutes apart,we switched the filter from a measurement state (in which themeasurements are used to update the drift estimate) to a predic-tion state (in which the measurements are ignored and the stateis updated by prediction only), and vice-versa. Fig. 9(a) depictsthe measured values of drift in the direction. Note that overa period of 160 min, the total drift was more than 500 nm ornearly 40 times the diameter of the particles being manipulated.The variance of the residuals, defined as the difference betweenthe estimates and the measurements during the measurement pe-riods, is about 1.14 nm . The drift error (residual) is plotted inFig. 9(b), which shows a growing error once the filter is switchedto the prediction state. This deviation depends on the amountof measurement time before the prediction and on the drift be-havior. However, the prediction error does not grow faster than


Fig. 9. (a) Drift measurements in the x direction with a 30-s sampling period.(b) Drift error in the x direction, defined as the difference between estimatedand measured values. The measurements are used to estimate the state of driftduring the time intervals labeled “Measurement State” at the bottom of thefigure, whereas during “Prediction State” intervals, the estimates are predictionsonly.

0.5 nm/min while the speed of the drift in the same experimentcan be as high as 6 nm/min. This implies an order of magnitudeimprovement in drift speed in a pure prediction mode.

In the second experiment, we used the drift compensatorfor the automatic nanomanipulation of particles. Manipulationneeds accurate estimates for the position of particles, especiallywhen their diameters are below 15 nm. The procedure forintegrating the drift compensator and the automatic manipulatoris the following. We first scan and choose an appropriate areain the sample. The desired particles and their destinations aremarked in the acquired sample area. The drift compensatorstarts with a default sampling time (30 s) and it continuesrunning until it reaches a stable condition (typically after5 min–10 min). Then, the AFM starts the manipulation processby using the prediction states provided by the Kalman filter. Themanipulation process is terminated once the uncertainty in thedrift estimate exceeds a certain limit, and new measurementsare performed. Manipulation continues after the measurementsand so on.

Fig. 10 shows the automatic manipulation of particles usingthe drift compensator. In this experiment, the drift measure-ments are only carried out before the manipulation of each setof five nanoparticles. Before each manipulation, the tip waitsabout 30 s (to combat the effects of creep) at the approximatelocation of a particle computed using the drift value predicted bythe filter. Then, it searches for the center of the particle (using thecenter-search procedure discussed in Section III-A and Fig. 3) in

Fig. 10. Manipulation of 15-nm Au particles using the drift compensator andan automatic manipulation procedure. The drift measurements are only carriedout before the manipulation of each set of five nanoparticles. The sampling timefor the measurements is 30 s and the manipulation of each particle takes about 40s, which includes waiting time to combat creep, plus time for the particle-centersearch. The left panel is the initial and random configuration, and the right panelis the final structure proposed in [17] for a QCA inverter.

an area comparable to the size of the particle. After that, the par-ticle is manipulated. Since large-distance manipulation motionsare typically less accurate than short ones, we ran the wholeprocess of manipulation twice—the first for a gross displace-ment of particles and the second for accurately placing the par-ticles at their target positions. The final result is the structureproposed in [17] for a Quantum-dot cellular automaton (QCA)inverter. Similar experiments without drift compensation failed:particles were missed or moved to the wrong locations.

The computational time for the filter operation in these ex-periments is associated primarily with scanning of the trackingwindow (about 8 s for a 64 64 pixel window) and processingof the resulting image (less than 2 s). The compensator is ca-pable of predicting the drift state with an error of less than0.5 nm/min for at least 10 min. Therefore, drift compensationcan be run as a background process while the AFM executesother tasks, such as the manipulation of nanoobjects.

V. CONCLUSION

Drift is a major cause of spatial uncertainty in AFMs. It causesdistortion in AFM images, and it has even more deleteriouseffects on nanomanipulation, where it is often responsible forthe outright failure of desired operations. Drift compensation intoday’s instruments is done primarily through user interaction.

This paper presents a Kalman filtering approach to drift es-timation. The filter updates the origin of the AFM coordinates,scheduling measurements when the covariance of the error ex-ceeds a given threshold. AFM tip motions are always executedin the updated coordinate system and become largely immuneto drift.

Sequential manipulation of nanoparticles over a relativelylong period of time without user intervention is demonstratedexperimentally. By using drift compensation, it will be possible,for the first time, to perform manipulation tasks that last severalhours without a user in the loop, and to construct, with AFMmanipulation, nanostructures that are more complex and usefulthan those which have been built until now.

Future work in this area includes more accurate drift measure-ment methods (e.g., by removing the effect of tip convolutionfrom the images), and compensation for other sources of spatial


uncertainty, such as creep and hysteresis. Coupling the results ofthis research with high-level planning algorithms, such as thosein [18], will lead to the fully automatic construction of complexnanoassemblies.

REFERENCES

[1] A. A. G. Requicha, “Nanorobots, NEMS and nanoassembly,” Proc.IEEE, vol. 91, no. 11, pp. 1922–1933, Nov. 2003.

[2] , “Nanorobotics,” in Handbook of Industrial Robotics, 2nd ed, S.Nof, Ed. New York: Wiley, 1999, pp. 199–210.

[3] (2005). Asylum Research, Santa Barbara, CA. [Online]http://www.asy-lumresearch.com/.

[4] V. Y. Yurov and A. N. Klimov, “Scanning tunneling microscope calibra-tion and reconstruction of real image: drift and slope elimination,” Rev.Sci. Inst., vol. 65, no. 5, pp. 1551–1557, May 1994.

[5] R. Staub, D. Alliata, and C. Nicolini, “Drift elimination in the calibra-tion of scanning probe microscopes,” Rev. Sci. Inst., vol. 66, no. 3, pp.2513–2516, Mar. 1995.

[6] J. T. Woodward and D. K. Schwartz, “Removing drift from scanningprobe microscope images of periodic samples,” J. Vac. Sci. Technol. B,vol. 16, no. 1, pp. 51–53, Jan./Feb. 1998.

[7] S. H. Huerth and H. D. Hallen, “Quantitative method of image anal-ysis when drift is present in a scanning probe microscope,” J. Vac. SciTechnol. B, vol. 21, no. 2, pp. 714–718, Mar. 2003.

[8] K. J. Ito, Y. Uehara, S. Ushioda, and K. Ito, “Servomechanism forlocking scanning tunneling microscope tip over surface nanostruc-tures,” Rev. Sci. Inst., vol. 71, no. 2, pp. 420–423, Feb. 2000.

[9] R. Haralick and L. Shapiro, Computer and Robot Vision. Reading,MA: Addison-Wesley, 1993, vol. 2.

[10] A. Gelb, Applied Optimal Estimation. Cambridge, MA: MIT Press,2001.

[11] Y. Bar-Shalom and X. Rong Li, Estimation With Application to Trackingand Navigation. New York: Wiley, 2001.

[12] R. A. Singer, “Estimating optimal tracking filter performance formanned maneuvering targets,” IEEE Trans. Aerosp. Electron. Syst., vol.AES-6, no. 4, pp. 473–483, Jul. 1970.

[13] A. A. G. Requicha, C. Baur, A. Bugacov, B. C. Gazen, B. Koel, A.Madhukar, T. R. Ramachandran, R. Resch, and P. Will, “Nanoroboticassembly of two-dimensional structures,” in Proc. IEEE Int. Conf.Robotics Automation, Leuven, Belgium, May 16–21, 1998, pp.3368–3374.

[14] W. Förstner and E. Gülch, “A fast operator for detection and preciselocations of distinct points, corners, and centers of circular features,” inProc. Intercommission Conf. Fast Processing of Photogrammetric Data,1987, pp. 281–305.

[15] R. K. Mehra, “On the identification of variances and adaptive Kalmanfiltering,” IEEE Trans. Autom. Control, vol. AC-15, no. 2, pp. 175–184,Apr. 1970.

[16] , “On-Line identification of linear dynamic systems with applica-tions to Kalman filtering,” IEEE Trans. Autom. Control, vol. AC-16, no.1, pp. 12–21, Feb. 1971.

[17] C. S. Lent et al., “Quantum cellular automata,” Nanotechnology, vol. 4,pp. 49–57, Jan. 1993.

[18] J. H. Makaliwe and A. A. G. Requicha, “Automatic planning of nanopar-ticle assembly tasks,” in Proc. IEEE Int. Symp. Assembly Task Planning,Fukuoka, Japan, May 28–30, 2001, pp. 288–293.

Babak Mokaberi (S’05) received the B.S. degreein electrical engineering from Isfahan Universityof Technology, Isfahan, Iran, in 1995 and the M.S.degree in electrical engineering from Sharif Univer-sity of Technology, Tehran, in 1998. He is currentlypursuing the Ph.D. degree in electrical engineeringfrom the University of Southern California (USC),Los Angeles.

He is currently with the Laboratory for MolecularRobotics, USC. His research interests include dy-namical system control of atomic force microscopesfor the manipulation of nanometer-scale objects.

Aristides A. G. Requicha (F’92) was born in MonteEstoril, Portugal, in 1939. He received the Engen-heiro Electrotécnico degree from the Instituto Supe-rior Técnico, Lisbon, Portugal, in 1962, and the Ph.D.degree in electrical engineering from the Universityof Rochester, Rochester, NY, in 1970.

Currently, he is the Gordon Marshall Professorof Computer Science and Electrical Engineering,Laboratory for Molecular Robotics, University ofSouthern California, Los Angeles, where he is alsoDirector. He has authored 170 scientific papers and

has served in numerous conference program committees and journal editorialboards. His past research focused on geometric modeling of three-dimensionalsolid objects and spatial reasoning for intelligent engineering systems. He iscurrently working on the robotic manipulation of nanometer-scale objects usingscanning probe microscopes; nanorobot components and nanorobotic systemintegration; fabrication of nanostructures by robotic self-assembly; sensor/ac-tuator networks; and applications in nanoelectromechanical systems (NEMS)and nanobiotechnology. The long-term goals are to build, program, and deploynanorobots and networks of nanoscale sensors/actuators for applications in theenvironment and health-care fields.

Dr. Requicha co-chairs the Micro/Nano Robotics and Automation TechnicalCommittee of the IEEE Robotics and Automation Society. He is also a memberof the American Association for Artificial Intelligence (AAAI), American As-sociation for the Advancement of Science (AAAS), Association for ComputerMachinery (ACM), American Vacuum Society (AVS), Computer Graphics Pi-oneers, Sigma Xi, and the Society of Manufacturing Engineers (SME).

Drift compensation for automatic nanomanipulation with scanning probe microscopes

Documents

Transcript of Drift compensation for automatic nanomanipulation with scanning probe microscopes