modular apparatus for electrostatic actuation of common atomic force microscope cantilevers

Due to the small quality factor of the spurious mechanical resonances compared to the AFM cantilever, their contribution to the mo-tion of the cantilever tip can often be safely ignored;

Modular apparatus for electrostatic actuation of common atomic force microscope cantilevers

Christian J Long, and Rachel J Cannara

Citation: Rev Sci Instrum 86, 073703 (2015); doi: 10.1063/1.4926431

View online: http://dx.doi.org/10.1063/1.4926431

View Table of Contents: http://aip.scitation.org/toc/rsi/86/7

Published by the American Institute of Physics

Modular apparatus for electrostatic actuation of common atomic force

microscope cantilevers

Christian J Long1,2, a)and Rachel J Cannara1

1Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg,

Maryland 20899, USA

2Maryland Nanocenter, University of Maryland, College Park, Maryland 20742, USA

(Received 30 December 2014; accepted 25 June 2015; published online 27 July 2015)

Piezoelectric actuation of atomic force microscope (AFM) cantilevers often suffers from spurious

mechanical resonances in the loop between the signal driving the cantilever and the actual tip

motion These spurious resonances can reduce the accuracy of AFM measurements and in some

cases completely obscure the cantilever response To address these limitations, we developed a

specialized AFM cantilever holder for electrostatic actuation of AFM cantilevers The holder contains

electrical contacts for the AFM cantilever chip, as well as an electrode (or electrodes) that may be

precisely positioned with respect to the back of the cantilever By controlling the voltages on the AFM

cantilever and the actuation electrode(s), an electrostatic force is applied directly to the cantilever,

providing a near-ideal transfer function from drive signal to tip motion We demonstrate both static

and dynamic actuations, achieved through the application of direct current and alternating current

voltage schemes, respectively As an example application, we explore contact resonance atomic

force microscopy, which is a technique for measuring the mechanical properties of surfaces on the

sub-micron length scale Using multiple electrodes, we also show that the torsional resonances of

the AFM cantilever may be excited electrostatically, opening the door for advanced dynamic lateral

force measurements with improved accuracy and precision C 2015 Author(s) All article content,

except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported

License.[http://dx.doi.org/10.1063/1.4926431]

I INTRODUCTION

A wide variety of actuation methods have been explored

for the alternating current (AC) excitation and direct

cur-rent (DC) displacement control of atomic force microscope

(AFM) cantilevers Among these methods are piezoacoustic,1

magnetic,2 , 3 photothermal,4 , 5 and electrostatic excitation.6 9

Piezoacoustic excitation is by far the most frequently used

technique In piezoacoustic excitation, a piezoelectric

trans-ducer is used to shake the AFM cantilever chip Unfortunately,

this piezoelectric transducer also shakes other parts of the

AFM, most notably the tip holder assembly, exciting the

mechanical resonances of these other structures Due to the

small quality factor of the spurious mechanical resonances

compared to the AFM cantilever, their contribution to the

mo-tion of the cantilever tip can often be safely ignored; however,

when the quality factor of the cantilever is sufficiently small

(for example, in contact resonance measurements or

measure-ments in an aqueous environment), the spurious mechanical

resonances can completely obscure the mechanical resonance

of the cantilever, leading to a so-called “forest of peaks” in

the cantilever excitation spectrum.10Even in cases where the

cantilever resonance is not completely obscured, the resonance

peak is often distorted, which can affect the accuracy of certain

AFM techniques such as frequency modulation and phase

modulation imaging.11 – 13Further, the spurious resonances can

a) Author to whom correspondence should be addressed Electronic mail:

christian.long@nist.gov

drift with time, leading to instabilities in imaging conditions and generally reducing the accuracy of AFM measurements.11 These problems can largely be overcome using electro-static excitation In contrast to piezoacoustic actuation, elec-trostatic excitation only applies force to the AFM cantilever This localized excitation force removes the spurious mechan-ical resonances from the cantilever actuation transduction chain, providing a near-ideal transfer function from the canti-lever drive signal to the canticanti-lever displacement In order to take advantage of this fact, a variety of specialized cantilevers with integrated microelectrodes have been designed.8 , 14 – 16

Although this integrated device approach to electrostatic actu-ation works well, there has not been widespread adoption of these cantilevers This is likely due to the lack of variety in tip materials, cantilever geometries and spring constants, and the relatively high cost of probes with integrated microelectrodes

in comparison to more common cantilever designs In addition

to integrated microelectrodes, it has been shown that the opti-cal fiber in an interferometry-based AFM may be metallized

to allow for electrostatic excitation.6,17However, this type of AFM is less common than optical-lever based AFMs, and this configuration requires that the positioning of the laser used for optical detection coincides with the location of the electrostatic excitation electrode In this work, we introduce a cantilever holder that has an independent, micropositionable electrode

or electrodes near the back of the cantilever This module en-ables electrostatic excitation while maintaining compatibility with a wide variety of inexpensive, commercially available cantilevers

073703-2 C J Long and R J Cannara Rev Sci Instrum 86, 073703 (2015)

In Sec.II, we describe the cantilever holder and the design

of the actuator electrode In Secs III and IV, we discuss

DC and AC biasing schemes for cantilever actuation,

respec-tively For DC biasing, we show that the electric field from the

actuator electrode is screened by the cantilever and does not

affect the tip-sample interaction For AC biasing, we show that

electrostatic excitation results in exceptionally clean cantilever

actuation spectra In Sec V, we apply electrostatic

excita-tion to demonstrate contact resonance spectroscopy and

imag-ing, which are typically difficult to perform using

piezoacous-tic actuation In Sec VIwe demonstrate torsional cantilever

excitation by two electrostatic excitation electrodes located

behind the cantilever Finally, in Secs.VIIandVIII, we discuss

the results and conclude All measurements are performed in

ambient air at room temperature

II CANTILEVER HOLDER FOR ELECTROSTATIC

ACTUATION

The electrostatic actuation cantilever holder is shown in

Fig 1 The actuation electrode is a platinum/iridium wire

that is held by friction within a stainless steel tube, making

replacement of the electrode simple The stainless steel tube is

mounted on a spring clip that has a positioning screw mounted

on it This positioning screw enables the actuation electrode to

be precisely positioned (±2 µm) with respect to the back of the

cantilever In practice, we find that the ideal gap size between

the cantilever and the actuation electrode is approximately

10 µm Making the cantilever-electrode gap larger reduces the

strength of the electrostatic force between the cantilever and the electrode, but making it smaller increases the damping of the cantilever due to squeeze-film damping in the gap between the cantilever and the actuation electrode

The end of the platinum iridium wire that is near the cantilever is either tapered (as in Fig 1(b)) or angled (as in Fig.1(d)), permitting optical access to the end of the cantilever This access is critical for sensing cantilever deflection, which

we accomplish using the typical optical beam-bounce and quadrant-photodiode detection scheme (Fig.2) The apex of the wire is polished to lie parallel to the cantilever plane In order to maximize electrostatic coupling to the fundamental flexural mode of the cantilever, the electrode surface should cover as much of the cantilever as possible while leaving

sufficient surface area exposed to accommodate the laser spot For optimal excitation of cantilever eigenmodes above the fundamental, the electrode should be centered at a displace-ment antinode of the eigenmode of interest, ideally covering one half-wavelength of the eigenmode The position of the cantilever chip in its spring-clip mount sets the location of the electrode along the long axis of the cantilever In addition, the area of overlap between the cantilever and the electrode can be adjusted by moving the cantilever chip laterally along a tapered electrode, as shown in Fig.1(d)

Electrical contact to the cantilever is made using a metal contact pad located on a printed circuit board (PCB), which

is visible in Figs.1(a),1(c), and1(d) The cantilever spring-clip pushes the back of the cantilever chip against this contact pad, providing a large contact area Alternatively, the metal

FIG 1 (a) shows a photograph of the tip holder detailing how the actuation electrode is mounted (b) shows a close-up view of a straight actuation electrode in proximity to the cantilever, demonstrating the ability to accommodate the optical path of the laser beam (c) A tilted view shows the L-shape of the electrode in this version of the module, corresponding to the holder shown in (a); the electrical connections to the cantilever and actuation electrode are schematized in blue and red, respectively In (d), a further close-up view of the actuation electrode and cantilever shows the tapered shape of the electrode, which allows the user to adjust the overlap area between the electrode and the cantilever.

FIG 2 Schematic of electrical connections to the sample, cantilever, and

actuator electrode V c is a common bias to both the cantilever and electrode,

while V d is a di fferential bias between the actuation electrode and the

can-tilever The connection of the sample to ground is optional, though it is useful

for conducting samples in order to establish a well-defined surface potential.

spring clip holding the cantilever chip can be used to make

electrical contact to the cantilever, though the contact area to

the cantilever chip is smaller in this case We typically use

cantilevers that have a metal backside (beam-bounce detector

side) coating that is contiguous between the cantilever and the

cantilever chip for connectivity between the PCB contacts and

cantilever However, we have had equal success with doped Si

cantilevers that have no metal coating

We find that the most challenging aspect of using the

electrostatic actuation module presented here is loading the

cantilever chip and aligning the actuation electrode with the

back of the cantilever With some practice, however, this

proce-dure has become routine and, in terms of cantilever loss, as

reliable as standard cantilever mounting procedures

The alignment is typically performed under a binocular

microscope with a working distance of approximately 10 cm

and a magnification ranging from 6.7× to 50× Low

magnifi-cation is used to align the electrode in the plane of the

canti-lever, and high magnification is used to set the gap between

the electrode and the cantilever To align the cantilever to the

actuator electrode, the electrode is first raised far enough above

the mounting plane of the cantilever chip to avoid risk of

breaking the cantilever The cantilever chip is then inserted

under the cantilever spring-clip, and the tip holder is placed

under a microscope (6.7× magnification) in plan view (tip

apex pointing towards the microscope objective) Next, the

electrode is aligned with the long axis of the cantilever by

adjusting the cantilever chip position with tweezers The tip

holder is then rotated to view the gap between the electrode

and the cantilever (at 50× magnification), and the electrode is

approached to the cantilever using the electrode positioning

screw until there is a gap of approximately 10 µm

Alternatively, a larger gap may be left in between the

cantilever and the electrode followed by a fine approach with

the tip holder mounted inside the AFM In this case, once

the cantilever holder is mounted inside the AFM, the

elec-trode positioning screw is used to approach the elecelec-trode to

the cantilever back while actuation spectra are continuously

acquired As the electrode nears the back of the cantilever, the strength of the actuation increases and the quality factor of the cantilever decreases due to squeeze-film damping of the air in between the electrode and the cantilever The decrease in the quality factor for a 10 µm electrode-cantilever gap depends

on the particular electrode and cantilever, but it is comparable

to that caused by the tip-sample interaction, as commercial cantilevers often have a tip that is approximately 10 µm long

III DC DISPLACEMENT CONTROL IN COMMON AND DIFFERENTIAL MODES

For the electrode configurations shown in Figs.1and2, there are two DC-voltage biasing schemes that can be applied

In the first scheme, which we will call common mode, one applies a common bias voltage to both the actuation electrode and the cantilever (Vcin Fig.2) In practice, the bias in common mode is applied relative to a ground plane that may be the surface of a conducting sample, an electrode located below

an insulating sample, or a conductor located far from the tip (e.g., the AFM chassis) In the second mode, which we will call differential mode, one applies a potential difference between the actuation electrode and the cantilever (Vdin Fig.2) For comparison with these modes, we also discuss a simple tip-bias experiment where a DC voltage is applied

to a cantilever without an actuation electrode, as might be typical in piezoresponse force microscopy (PFM),18 elec-trostatic force microscopy (EFM),19 or kelvin probe force microscopy (KPFM).20In this case, it is well known that the force on the tip (Ft s) depends on the tip-sample capacitance (Ct s) gradient and may be modeled as Ft s= 1

2

∂Ct s

∂z Vt s2;21

here, z is the tip displacement (with the z-axis directed along the normal to the back of the cantilever), Vt s is the potential

difference between the tip and the sample, and we have taken

Vt s to include any applied tip bias and the contact potential difference between the tip and sample Qualitatively, the tip-sample electrostatic force in this case is attractive, increases

as the tip nears a sample surface, and scales quadratically with applied bias

This tip-sample distance-dependence and quadratic force-dependence may be seen in Fig.3(a), where we swept the

DC bias applied to a cantilever and measured the cantilever deflection for several tip-sample gap sizes The bias on the cantilever was applied with respect to a grounded conducting sample—here a piece of highly oriented pyrolytic graphite (HOPG) When the tip-apex was far from the sample (approx-imately 1 cm tip-sample gap, blue curve in Fig.3(a)), the tip-sample electrostatic force was relatively weak compared to when the tip-apex was near the sample (approximately 1 µm tip-sample gap, black curve in Fig.3(a)) We note that the offset

of the parabolas from zero bias was caused by a combination of analog offsets in the bias electronics and the contact potential

difference between the tip and sample materials

Applying a common mode bias using the electrostatic actuator (Fig 3(b), blue, red, and black curves) results in

a very similar force-distance and force-voltage behaviors as compared to a simple tip-bias without the electrostatic actu-ation electrode (Fig.3(a)) The primary difference is that the force on the cantilever is somewhat larger for common mode

073703-4 C J Long and R J Cannara Rev Sci Instrum 86, 073703 (2015)

FIG 3 Bias voltage and tip-sample distance dependence of electrostatic forces (a) shows bias parabolas for a cantilever (without an actuation electrode behind it) above a grounded HOPG sample (b) shows bias parabolas for di fferential mode (dotted lines, labeled DM) and common mode (solid lines, labeled CM) biasing schemes taken at di fferent heights above a grounded HOPG sample (c) shows bias parabolas with the same configuration as (b), except using a cleaved mica sample in place of HOPG (d) shows the approach part of force curves taken with the bias voltages marked with circles in (b) The same cantilever was used for (a) through (d); the cantilever was a model PPP-CONTR (Nanosensors, Neuchatel Switzerland)36that had a spring constant of approximately 0.27 N /m All bias parabolas were acquired using a triangular bias ramp with a period of 1 Hz The precision of the cantilever deflection given by a single standard deviation was less than the width of the plot lines The cantilever deflection was calibrated using the contact part of an approach curve, which we estimate results a relative accuracy of better than ±10%.

than for a simple tip-bias This is most readily visible by

comparing the bias parabolas for these modes when the

tip-apex is 1 µm from the surface (solid black curves in Figs

3(a) and3(b)) Between these two curves, the bias parabola

for common mode shows a moderately larger deflection per

voltage squared than the simple tip-bias We attribute this

increase in force to the addition of the electrode behind the

cantilever Physically, since the electrode is held at the same

potential as the cantilever in common mode operation, the

charge on the cantilever and the electrode will have the same

sign, resulting in a repulsive interaction between them and

increasing the force on the cantilever in the direction of the

sample

The increase in force available in common mode over

a simple tip-bias may be useful for applications such as 3D

lithography, where electrostatic forces between a cantilever

and a substrate have been used to control cantilever position

with exquisite precision.22 The primary drawbacks to using

common mode biasing for DC displacement control are that

the actuation force depends strongly on the tip-sample distance

and that the sample is immersed in the electric field from

the cantilever and tip Indeed, we find that the electric field

from the tip can be a problem for electrostatic actuation on

insulating samples, where surface charge redistribution can

change the sample’s surface potential Such a case is illustrated

in Fig.3(c), where charge redistribution on the surface of a mica sample results in hysteresis of the tip-sample electrostatic force when increasing and decreasing the common mode bias

In contrast, these drawbacks are largely resolved by using

differential mode

In differential mode, the gap between the electrode and the cantilever does not depend on the tip-sample distance, eliminating the variation in actuation force with tip-sample distance Figure 3(b)shows a comparison of bias parabolas for common mode and differential mode that were measured with different tip-sample gaps with the common mode bias set

to 0 V The most obvious difference between these modes is that for differential mode, the cantilever is pulled away from the sample surface (towards the actuation electrode), while for common mode, the cantilever is pulled towards the sample surface More importantly, for differential mode, there is very little variation in the bias parabolas at different tip-sample gap sizes (dotted curves with purple, green and cyan coloring in Figs 3(b) and3(c)), while for common mode (solid curves with blue, red, and black coloring in Figs.3(b)and3(c)) and simple tip biasing (solid curves with blue, red, and black color-ing in Fig.3(a)), there is a strong dependence on the tip-sample gap size This behavior is consistent with our expectation that

for differential mode, the electric fields are largely contained

in the gap between the actuation electrode and the cantilever,

while for common mode, the electric fields are located below

the tip and therefore show a strong dependence on the

tip-sample distance This also provides some evidence that in

differential mode, the stray electric field from the actuation

electrode does not affect tip-sample forces

In order to verify that the stray electric fields in differential

mode do not interfere with the tip-sample interaction even

when the tip is very near the sample, we took force curves using

both common mode and differential mode biasing schemes, as

shown in Fig.3(d) For these force curves, the applied di

fferen-tial mode bias was set to zero when taking force curves in

com-mon mode, and vice versa For both modes, the out-of-contact

deflection of the cantilever shifts with applied bias, which

is consistent with the bias dependence shown in Fig 3(b)

Again as expected, the cantilever was displaced away from

the sample for differential mode, while for common mode, the

displacement was towards the sample The most interesting

behavior occurs as the tip nears the surface: in common mode

operation, the long-range electrostatic force between the

tip-apex and the sample causes the cantilever to bend towards the

surface just before snap-in (red and black curves in Fig.3(d));

however, for differential mode, the deflection is completely

flat until the snap-in point These observations imply that

for differential mode, the bias on the actuation electrode is

screened by the (grounded) cantilever and therefore does not

interfere with the tip-sample interaction This screening effect

is consistent with the behavior of AFM probes containing an

integrated electrostatic shield.23

By combining both the common mode and differential

mode biasing schemes, the net electrostatic force on the

canti-lever can be either positive or negative, essentially doubling

the range of cantilever positions that can be obtained when

compared to traditional tip-sample based electrostatic

actu-ation Alternatively, the electrostatic interaction between the

tip and sample can be nulled using a common mode bias (as

in KPFM), while the position of the cantilever can still be

controlled by applying a differential mode bias

IV DYNAMIC EXCITATION

In order to excite the cantilever for dynamic AFM modes,

we introduce a biasing scheme that has an AC component in

addition to a DC component To avoid electrostatic tip-sample

interactions, we consider operation in differential mode (Vc

= 0) and apply a differential bias that contains both an AC and

a DC component,

Vd= VDC+ VACsin(ωt), (1)

where VDCincludes the work function difference between the

cantilever and the actuation electrode as well as an externally

applied voltage In order to estimate the force on the cantilever

in differential mode, we approximate the cantilever-electrode

gap as a parallel plate capacitor with capacitance Cd and

take the force (Fd) on the cantilever to be Fd=1

2

∂Cd

∂z Vd2 The resulting force on the cantilever can be written as

F= FDC+ Fω+ F2ω, where

FDC= 1 2

∂Cd

∂z

(

VDC2 +1

2V

2 AC

)

Fω= ∂Cd

∂z VDCVACsin(ωt) , (3) and

F2ω= −1

4

∂Cd

∂z VAC2 cos(2ωt) (4) The DC component of the force adds an offset to the equilibrium position of the cantilever and is trivially ignored

in experimental operation This leaves two frequency compo-nents, one at angular frequency ω and another at angular fre-quency 2ω For single frefre-quency operation, one would ideally apply a DC bias such that VDC= 0, thus nulling the actuation force at angular frequency ω One could then measure the cantilever response at 2ω However, exactly nulling the analog

offsets in the bias electronics and accounting for the surface potential difference between the actuator electrode and the cantilever can entail significant effort In practice, we have found that it is often sufficient to apply a DC bias between the cantilever and the actuation electrode such that VDC≥ VACand then match the AC drive frequency to the resonance frequency

of the cantilever In this case, since Fω is at the resonance frequency of the cantilever and F2ω is above the resonance, the cantilever response is primarily at angular frequency ω, with negligible actuation at the second harmonic The degree to which VDCshould exceed VACdepends on the quality factor of the cantilever resonance, where low quality factor resonances require a larger ratio of VDC to VAC in order to effectively suppress the cantilever excitation at the second harmonic

A comparison of cantilever actuation spectra using elec-trostatic and piezoacoustic actuation appears in Fig.4 Figure

4(a)shows an example cantilever actuation spectrum taken using our electrostatic actuator The electrostatic actuation spectrum is ideal in the sense that it only shows the resonances corresponding to the first two flexural modes of the cantilever The accuracy of the actuation is highlighted by the excellent agreement between the measured actuation spectrum (red) and

a curve fit to a damped harmonic oscillator model for the fundamental eigenmode of the cantilever (black) Figure4(b)

shows an example actuation spectrum taken using the common

“tip shaker” (a standard cantilever holder on a Cypher AFM, Asylum Research/Oxford Instruments, Santa Barbara, CA) as well as a curve fit to a damped harmonic oscillator model for the fundamental eigenmode The piezoacoustic actuation spectrum exhibits multiple spurious resonances with ampli-tudes comparable to the flexural modes of the cantilever, re-sulting in poor agreement between the measured actuation spectrum and a damped harmonic oscillator model Figure4(c)

shows the thermal motion of the cantilever in the absence of an external actuator The thermal spectrum exhibits peaks at the same frequencies as the electrostatically actuated spectrum, clearly identifying these resonances as the flexural modes of the cantilever

We note that the vertical axes are in voltage (mV) rather than distance (nm) for Figs 4(a) and 4(b) and in V/√Hz for Fig.4(c) because the optical lever sensitivity differs for

073703-6 C J Long and R J Cannara Rev Sci Instrum 86, 073703 (2015)

FIG 4 Measured cantilever actuation spectra for several different actuation

mechanisms, with the first two flexural modes of the cantilever highlighted

in gray (a) A frequency spectrum showing the cantilever’s response to the

electrostatic drive (red), the level of detector noise with the actuator turned

o ff (blue), and a fit of an ideal damped harmonic oscillator to the cantilever

response (black) (b) A frequency spectrum showing the cantilever’s response

to a commercial piezoelectric actuator located behind the cantilever chip

(red), the level of detector noise with the actuator turned o ff (blue), and

a damped harmonic oscillator fit (black) (c) Power spectral density (PSD)

spectrum showing thermal motion of the cantilever at ambient temperature

(red) and detector noise with the laser spot on a rigid surface (blue) The

electrostatic drive in (a) does not exhibit the spurious resonances that are

apparent when using tip piezo-drive in (b) The cantilever used here was a

model DCP-11 (NT-MDT, Moscow, Russia) that had a spring constant of

approximately 11 N /m.

the first and second flexural modes of the cantilever For the

fundamental mode (at ≈151 kHz), the optical lever sensitivity

was approximately 40 nm/V For piezoacoustic actuation, the

amplitude of the drive voltage was 100 mV; for electrostatic

actuation, the drive amplitude was 1 V with an additional DC

bias of 1 V between the actuator electrode and the cantilever

Although the drive voltage was higher for electrostatic

actu-ation than for piezoacoustic actuactu-ation, it was still well within

the ±10 V range that is typical for auxiliary voltage sources on

AFM instruments

The dynamic electrostatic actuation response

demon-strated here enables exceptionally clean cantilever excitation

that does not depend on the electrical properties of the sample

or require a specialized cantilever

V CONTACT RESONANCE MICROSCOPY

Contact resonance spectroscopy and imaging are

mechan-ical property characterization techniques that can

non-destructively probe the elastic storage moduli and viscoelastic

loss moduli of materials on the nanometer length scale.24 , 25For

contact resonance spectroscopy, the elastic properties of the

sample are probed by measuring the resonance frequency and

quality factor of a cantilever while it is free and then measuring

them again while it is in contact with a sample of interest.26For

contact resonance imaging, the contact resonance frequency

is tracked in real time while the tip is scanned over a sample

surface in contact mode.27,28

In general, by applying suitable models for the cantilever

beam dynamics and the tip-sample contact mechanics, one

can use the measured free and contact resonance

frequen-cies to obtain quantitative values for the elastic modulus of

a sample A variety of different modeling approaches have been used for this purpose and have been applied with a great deal of success to both hard materials and to soft materials that exhibit viscoelastic behavior.23,29In this work, we confine ourselves to demonstrating the utility of electrostatic actu-ation for measuring contact resonance frequencies, without emphasizing any particular modeling approach for extracting quantitative mechanical property information from the contact resonance observables

For contact resonance measurements, the cantilever reso-nance is often strongly damped when the tip is brought into contact with the sample, making the quality factor of the relevant eigenmodes comparable to or even smaller than the quality factors of the spurious mechanical resonances of the AFM In order to avoid exciting these spurious resonances, contact resonance measurements are often performed using a piezoelectric sample actuator instead of piezoacoustic actua-tion of the tip.23Sample actuators for contact resonance tend to

be mechanically simpler than a tip shaker, as well as more me-chanically damped Thus, the use of sample actuators reduces the probability of exciting spurious mechanical resonances in the AFM but does not eliminate them Sample actuators also typically require that the sample be glued to (and later removed from) the actuator surface to minimize unwanted mechan-ical resonances Thus, compared to piezoelectric actuation

of the tip or sample, electrostatic actuation provides several advantages: it provides direct cantilever excitation to elimi-nate spurious mechanical resonances, it does not require any special sample preparation, and it is compatible with small-sample AFMs, where adding a bulky small-sample actuator can be challenging

In order to demonstrate contact resonance spectroscopy and imaging by electrostatic actuation, we explored a sample consisting of patterned titanium squares on a silicon substrate Contact resonance spectra and images of this sample are shown

in Fig.5 Figure5(c)shows contact resonance spectra for the free cantilever (black), the cantilever in contact with the tita-nium (red), and the cantilever in contact with the silicon (blue) Since the electrostatic actuator only excites the resonance of the cantilever, the resonance peaks are straightforward to iden-tify and have the expected damped harmonic oscillator shape The clean transfer function from excitation signal to force

on the cantilever also greatly simplifies contact resonance imaging, because there are no spurious resonance peaks for the frequency feedback loop to mistakenly follow, even when

it deviates significantly from the true resonance frequency Figure5(b)shows a contact resonance image obtained on the titanium-on-silicon sample using dual-amplitude resonance tracking,24 which is a technique for tracking the resonance frequency of the cantilever as the tip is scanned in contact with

a sample surface The observed contact resonance frequency for titanium is lower than for silicon, which is consistent with the fact that titanium is the more compliant material

VI TORSIONAL EXCITATION

Next, we demonstrate torsional excitation of the cantilever using electrostatic forces Torsional excitation has applications

FIG 5 Contact resonance images of patterned titanium metal on a silicon

substrate (a) shows the topography of the sample, which consists of

ap-proximately 280 nm thick titanium islands (b) shows the contact resonance

frequency as the tip is scanned across the surface (c) shows contact resonance

spectra for the free cantilever (tip located approximately 100 nm above the

sample surface) and for the cantilever in contact with the titanium and silicon

surfaces at a normal load of (300 ± 30) nN Peaks labeled Mode 1 correspond

to the fundamental flexural mode of the cantilever, while Mode 2 refers to

the first flexural overtone The main source of uncertainty in the cantilever

amplitude in (c) was given by the detector noise, which contributed a root

mean square amplitude noise of less than 0.2 (arbitrary unit) at all

mea-surement frequencies The cantilever was a model PPP-NCLR (Nanosensors,

Neuchatel Switzerland) that had a spring constant of (25.3 ± 2.5) N /m The

spring constant was calibrated using the thermal spectrum method 37 The

uncertainties in the spring constant correspond to ±10% relative error, which

is considered to be a conservative estimate of the relative accuracy of this

technique.38

in tribology, nanomechanical characterization, and force

spec-troscopy In the past, excitation of torsional cantilever modes

has most frequently been performed with a split piezoelectric

actuator, which shakes the cantilever chip in a rocking

mo-tion.30,31Torsional excitation has also been performed using

a shear-wave piezoelectric sample transducer32and using the

(non-split) piezoacoustic tip actuator that is typically

pres-ent in most AFMs.33 Unfortunately, piezoacoustic actuation

of the torsional mode is susceptible to the same “forest of

peaks” as piezoacoustic excitation of the flexural cantilever

modes, again making electrostatic actuation an attractive

alter-native

Here, the torsional modes of a cantilever are excited using

two electrodes that are offset laterally with respect to the long

axis of the cantilever A schematic of this configuration is

shown in Fig.6(b), and an image of a dual-electrode actuator is

shown in Fig.6(c) In torsional excitation mode, the two

elec-trodes carry a common DC bias, while the AC bias is driven

180◦ out-of-phase between the two electrodes This biasing

scheme causes one electrode to increase the force on one side

of the cantilever while the force due to the other electrode

decreases, causing the cantilever to undergo a torque The two

electrodes may also be used to perform flexural excitation by

driving the AC bias on both electrodes in-phase, as shown in

Fig.6(a) Figure6(d)shows cantilever actuation spectra

ob-tained using this dual-electrode actuator for both the torsional

FIG 6 Excitation of flexural and torsional cantilever modes using multiple electrodes (a) shows a schematic in which both actuation electrodes are driven in-phase to excite the flexural modes of the cantilever In (b), the actuation electrodes are driven with a common DC bias but with an out-of-phase AC bias to excite torsional modes of the cantilever (c) shows an optical microscope image of a dual-electrode electrostatic actuator with a cantilever aligned to the electrodes (d) The flexural and torsional actuation spectra are shown for the setup in (c) The cantilever is a model RC800PSA (Olympus, Tokyo, Japan) For both flexural and torsional excitations, a DC bias of 4 V and an AC bias of 4 V were applied to the electrodes.

and flexural excitation schemes Of course, it is also possible

to excite both a flexural resonance and a torsional resonance simultaneously In this case, the electrodes are driven in-phase

at the fundamental flexural mode frequency (ωf) and have an additional out-of-phase component at the torsional resonant frequency (ωt)

We note that for the dual-electrode configuration, it is

difficult to perfectly align the centerline between the electrodes

to the long axis of the cantilever This imperfect alignment causes some cross talk between the torsional and flexural exci-tation schemes outlined above This cross talk appears in Fig

6(d)as small peaks in the flexural excitation spectrum, which correspond to torsional resonances, and vice versa To avoid this cross talk, we have found that it is possible to measure the excitation spectrum for each electrode independently and then adjust the drive voltage on each electrode to obtain equal forces

VII DISCUSSION

In addition to providing a clean transfer function, electro-static actuation has applications that cannot be achieved us-ing piezoelectric actuators These expanded applications arise from the location of the driving force on the cantilever For piezoacoustic excitation, the force is applied at the base of the cantilever, while for electrostatic actuation, the force is applied

at or near the end of the cantilever, without relying on a sample actuator that functions solely in contact (or very near contact) with a surface

Applying forces at the end of the cantilever allows one

to dynamically balance the tip-sample force during approach,

effectively eliminating snap-in and snap-off instabilities.34

Applying forces at the end of the cantilever also enables more

073703-8 C J Long and R J Cannara Rev Sci Instrum 86, 073703 (2015)

accurate measurement of the tip displacement because one

does not need to account for the displacement of the base of the

cantilever, as in piezoacoustic excitation This is particularly

important when shaking the cantilever well below or above its

resonance frequency, where the motion of the cantilever base

induced by piezoacoustic excitation can be comparable to or

larger than the motion of the tip

Electrostatic actuation of AFM cantilevers, as described

here, may be used to image any type of material, including both

conducting and insulating samples, and is compatible with a

wide variety of cantilever materials However, there are some

considerations to be made when choosing a cantilever For

example, the electrode can obscure the beam-bounce optical

path when placed directly above a relatively small cantilever

To minimize this effect, we find it simplest to use cantilevers

that are longer than 100 µm However, for cantilevers smaller

than this, it may be possible to use a transparent actuator

electrode or an electrode that is located above the plane of the

cantilever but offset slightly from the space directly above the

cantilever In addition to long cantilevers, we prefer cantilevers

for which electrical contacts are easily made, as is the case for

doped silicon cantilevers or cantilevers with a metal coating on

either the tip-side or the backside Ideally, this metal coating

should be contiguous between a cantilever and its chip This

demand for electrical contact to the cantilever may preclude

the use of some cantilevers For example, performing

elec-trostatic actuation on silicon nitride cantilevers with no metal

backside coating could be challenging However, in this case,

actuation may still be possible through dielectrophoretic forces

or by embedding charge in the cantilever body before loading

it into the tip holder

Finally, although the current design of our electrostatic

actuator is optimized for actuation in air, it has recently

been demonstrated that electrostatic actuation may be

per-formed in aqueous environments through the application of

an amplitude-modulated high-frequency bias voltage.35When

combined with an actuation electrode behind the cantilever,

such a biasing scheme removes yet another limit on

elec-trostatic actuation, enabling it to be utilized in vacuum, air,

or aqueous environments, with any sample and with a broad

variety of commercially available cantilevers

VIII CONCLUSION

The electrostatic actuation module presented here

pro-vides an exceptionally clean mechanism for actuating many

types of common AFM cantilevers, making it possible to bring

the accuracy of electrostatic actuation to bear on wide variety

of cantilever geometries and tip materials Our approach is

compatible with both conducting and insulating samples, is

relatively inexpensive, and may be adapted to retrofit

exist-ing AFM systems We have shown that electrostatic

actua-tion is particularly useful in contact resonance measurements,

where tip-sample damping may lead to reduced quality

fac-tors, thereby diminishing the ability to distinguish cantilever

resonances from spurious ones Using multiple electrodes, we

have also shown that it is possible to excite the torsional modes

of a common AFM cantilever directly, opening the door for

improved dynamic lateral force measurements

ACKNOWLEDGMENTS

The authors are grateful to Fred Sharifi, Donna Hurley, and Jason Killgore for insightful and invaluable discussions and feedback on this work We also thank Donna Hurley and Gene Hilton for providing the Ti/Si sample used for contact resonance measurements C.J.L acknowledges support under the Cooperative Research Agreement between the University

of Maryland and the National Institute of Standards and Tech-nology, Center for Nanoscale Science and TechTech-nology, Award

No 70NANB10H193, through the University of Maryland

1 V B Elings and J A Gurley, “Jumping probe microscope,” U.S patent

5266801 (30 November 1993).

2 S P Jarvis, H Yamada, S.-I Yamamoto, and H Tokumoto, “A new force controlled atomic force microscope for use in ultrahigh vacuum,” Rev Sci Instrum 67, 2281 (1996).

3 S Lindsay, “Controlled force microscope for operation in liquids,” U.S patent US5515719 A (14 May 1996).

4 G C Ratcli ff, D A Erie, and R Superfine, “Photothermal modulation for oscillating mode atomic force microscopy in solution,” Appl Phys Lett.

72, 1911 (1998).

5 A Labuda, K Kobayashi, Y Miyahara, and P Grütter, “Retrofitting an AFM with photothermal excitation for a clean cantilever response in low

Q environments,” Rev Sci Instrum 83, 053702 (2012).

6 J W Hong, Z G Khim, A S Hou, and S Park, “Tapping mode atomic force microscopy using electrostatic force modulation,” Appl Phys Lett.

69, 2831 (1996).

7 N Kato, I Suzuki, H Kikuta, and K Iwata, “Force-balancing microforce sensor with an optical-fiber interferometer,” Rev Sci Instrum 68, 2475 (1997).

8 T Yagi and S Yasuda, “Electrostatic actuator, probe using the actuator, scan-ning probe microscope, processing apparatus, and recording /reproducing apparatus,” U.S patent US5753911 A (19 May 1998).

9 S Jeffery, A Oral, and J B Pethica, “Quantitative electrostatic force measurement in AFM,” Appl Surf Sci 157, 280 (2000).

10 T E Schä ffer, J P Cleveland, F Ohnesorge, D A Walters, and P K Hansma, “Studies of vibrating atomic force microscope cantilevers in liquid,” J Appl Phys 80, 3622 (1996).

11 A Labuda, K Kobayashi, D Kiracofe, K Suzuki, P H Grütter, and H Ya-mada, “Comparison of photothermal and piezoacoustic excitation methods for frequency and phase modulation atomic force microscopy in liquid environments,” AIP Adv 1, 022136 (2011).

12 R Proksch and S V Kalinin, “Energy dissipation measurements in frequency-modulated scanning probe microscopy,” Nanotechnology 21,

455705 (2010).

13 A Labuda, Y Miyahara, L Cockins, and P H Grütter, “Decoupling conser-vative and dissipative forces in frequency modulation atomic force micros-copy,” Phys Rev B 84, 125433 (2011).

14 A G Onaran, M Balantekin, W Lee, W L Hughes, B A Buchine, R O Guldiken, Z Parlak, C F Quate, and F L Degertekin, “A new atomic force microscope probe with force sensing integrated readout and active tip,”

Rev Sci Instrum 77, 023501 (2006).

15 S Rana, P M Ortiz, A J Harris, J S Burdess, and C J McNeil, “An electrostatically actuated cantilever device capable of accurately calibrating the cantilever on-chip for AFM-like applications,” J Micromech Microeng.

19, 045012 (2009).

16 E Sarajlic, M H Siekman, H Fujita, L Abelmann, and N Tas, “A novel electrostatically actuated AFM probe for vibroflexural mode operation,”

in Proceedings of IEEE 24th International Conference on Micro Electro Mechanical Systems (MEMS) (IEEE, 2011), p 537.

17 V Yakimov and R Erlandsson, “Electrostatic force-feedback sensor incor-porated in an ultrahigh vacuum force microscope,” Rev Sci Instrum 71,

133 (2000).

18 S Hong, J Woo, H Shin, J U Jeon, Y E Pak, E L Colla, N Setter, E Kim, and K No, “Principle of ferroelectric domain imaging using atomic force microscope,” J Appl Phys 89, 1377 (2001).

19 P Girard, “Electrostatic force microscopy: Principles and some applications

to semiconductors,” Nanotechnology 12, 485 (2001).

20 M Nonnenmacher, M P O’boyle, and H K Wickramasinghe, “Kelvin probe force microscopy,” Appl Phys Lett 58, 2921 (1991).

21 S Hudlet, M Saint Jeana, C Guthmann, and J Berger, “Evaluation of the

capacitive force between an atomic force microscopy tip and a metallic

surface,” Eur Phys J B 2, 5 (1998).

22 D Pires, J L Hedrick, A De Silva, J Frommer, B Gotsmann, H Wolf,

M Despont, U Duerig, and A W Knoll, “Nanoscale three-dimensional

patterning of molecular resists by scanning probes,” Science 328, 732

(2010).

23 P Pingue, V Piazza, P Baschieri, C Ascoli, C Menozzi, A Alessandrini,

and P Facci, “Demonstration of an electrostatic-shielded cantilever,” Appl.

Phys Lett 88, 043510 (2006).

24 U Rabe, S Amelio, E Kester, V Scherer, S Hirsekorn, and W Arnold,

“Quantitative determination of contact sti ffness using atomic force acoustic

microscopy,” Ultrasonics 38, 430 (2000).

25 P A Yuya, D C Hurley, and J A Turner, “Contact-resonance atomic force

microscopy for viscoelasticity,” J Appl Phys 104, 074916 (2008).

26 D C Hurley, in Applied Scanning Probe Methods Vol XI, edited by B.

Bhushan and H Fuchs (Springer-Verlag, Berlin, 2009), Chap 5, pp 97–138.

27 B J Rodriguez, C Callahan, S Kalinin, and R Proksch, “Dual-frequency

resonance-tracking atomic force microscopy,” Nanotechnology 18, 475504

(2007).

28 S Jesse and S V Kalinin, “Band excitation scanning probe microscopy:

Sines of change,” J Phys D: Appl Phys 44, 464006 (2001).

29 U Rabe, in Applied Scanning Probe Methods Vol II, edited by B Bhushan

and H Fuchs (Springer, Berlin, 2006), Chap 2, pp 37–90.

30 M Reinstädtler, T Kasai, U Rabe, B Bhushan, and W Arnold, “Imaging

and measurement of elasticity and friction using the TRmode,” J Phys D:

Appl Phys 38, R269 (2005).

31 C Su and R C Daniels, “Method and apparatus of driving torsional resonance mode of a probe-based instrument,” U.S patent US7168301 B2 (30 January 2007).

32 M Reinstädtler, U Rabe, V Scherer, U Hartmann, A Goldade, B Bhushan, and W Arnold, “On the nanoscale measurement of friction using atomic-force microscope cantilever torsional resonances,” Appl Phys Lett 82,

2604 (2003).

33 O Pfei ffer, R Bennewitz, A Baratoff, E Meyer, and P Grütter, “Lateral-force measurements in dynamic “Lateral-force microscopy,” Phys Rev B 65, 161403 (2002).

34 M P Goertz and N W Moore, “Mechanics of soft interfaces studied with displacement-controlled scanning force microscopy,” Prog Surf Sci 85,

347 (2010).

35 K Umeda, K Kobayashi, K Matsushige, and H Yamada, “Direct actu-ation of cantilever in aqueous solutions by electrostatic force using high-frequency electric fields,” Appl Phys Lett 101, 123112 (2012).

36 The full description of the procedures used in this article requires the identification of certain commercial products and their suppliers The inclusion of such information should in no way be construed as indicating that such products or suppliers are endorsed by NIST or are recommended

by NIST or that they are necessarily the best materials, instruments, software, or suppliers for the purposes described.

37 J L Hutter and J Bechhoefer, “Calibration of atomic force microscope tips,”

Rev Sci Instrum 64, 1868 (1993).

38 K H Chung, G A Shaw, and J R Pratt, “Accurate noncontact calibration of colloidal probe sensitivities in atomic force microscopy,” Rev Sci Instrum.

80, 065107 (2009).