APPLIED PHYSICS LETTERS 93, 023114 共2008兲

Cantilevers with integrated sensor for time-resolved force measurement
in tapping-mode atomic force microscopy
A. F. Sarioglua兲 and O. Solgaard
E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

共Received 7 June 2008; accepted 17 June 2008; published online 16 July 2008兲
We present a micromachined cantilever with an integrated high-bandwidth resonator for direct
measurement of tip-sample interaction forces in tapping-mode atomic force microscopy. Forcemeasurements are achieved by a diffraction grating that serves as a differential displacement sensor
for the tip motion relative to the cantilever body. Time-resolved tip-sample interaction force
measurement is demonstrated on a silicon sample following calibration of the probe structure. By
using lock-in detection, the harmonics of periodic tip-sample interaction have been utilized to obtainhigh-contrast, material specific images. The harmonic images of patterned silicon/silicon nitride
control samples and triblock copolymers are presented. © 2008 American Institute of Physics.
关DOI: 10.1063/1.2959828兴
Atomic force microscope1 共AFM兲 is widely used fornanoscale surface characterization. There is an increasing interest in its use for mapping of material specific surface properties. Quasistatic methods, such as nanoindentation,2 andseveral dynamic methods, such as ultrasonic force
microscopy,3 pulsed-force microscopy,4 and force modulation microscopy,5 have been developed for local stiffness
measurements. These techniques generally suffer from low
operational speeds and require large forces applied to thesurface under test, limiting their use on soft materials such as
biological samples.
Tapping-mode AFM6 is the preferred operational mode,
especially on soft samples. In tapping-mode, phase
information7 and higher harmonic signals8 can be used toobtain nanoscale maps of material characteristics. Measurement of tip-sample interaction forces is a more direct method
for material characterization. Recently, measurements of tipsample interaction have been demonstrated by specially designed probes.9,10
In this paper, we report a method for time-resolved measurement of tip-sample interaction forces by using a micromachined cantilever with an integrated high-bandwidth force
sensor. A small and stiff mechanical resonator on the cantilever provides the necessary temporal resolution for observing tip-sample interactions. The cantilever itself serves twopurposes. First, being softer, it limits the amount of repulsive
force applied to the surface. Secondly, it provides the necessary oscillation amplitude for the smaller sensor to interact
with the surface in a tapping-mode configuration. A scanningelectron microscope 共SEM兲 image of the micromachinedprobe is given in Fig. 1. The small resonator on the cantilever forms a phase sensitive diffraction grating that serves asa relative displacement sensor for tip motion. This type ofgrating has earlier been used to measure the displacement ofcantilevers in contact mode AFM.11
In operation, the cantilever is driven close to its fundamental resonance frequency. During a small fraction of theoscillation cycle, the tip interacts with the sample. The highbandwidth force sensor responds to the interaction force,
whereas the larger and softer cantilever cannot follow effia兲

Electronic mail: sarioglu@stanford.edu.

ciently because of its lower bandwidth. That causes the relative position of the diffractive grating fingers to change,
modifying the amount of light in the diffracted modes. By
measuring the light intensity variation in the diffracted
modes, the tip-sample interactions are observed.
Our cantilever has the advantage of achieving high temporal resolution by reducing the displaced mass rather thanpurely increasing the stiffness, which would cause lower
signal-to-noise ratio 共SNR兲. In addition, the use of interdigitated fingers provides completely differential interferometricmeasurement, minimizing crosstalk between cantilever oscillations and tip motion.
The design of cantilevers with force sensors requires
several specific considerations. First of all, the interdigitatedfingers of the differential sensor should be fabricated suchthat the adjacent fingers have ␭ / 8 offset, where ␭ is theillumination wavelength. This provides maximum sensitivity
and linearity for measuring weak tip-sample interaction thatcauses small relative displacements on the order of 1 nm orFIG. 1. SEM micrograph of a cantilever with integrated force sensor. Thecantilever is 370 ␮m long, 60 ␮m wide, and 2.5 ␮m thick. The gratingfingers of the interferometric force sensor are 3 ␮m wide and 70 ␮m long.

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A. F. Sarioglu and O. Solgaard

FIG. 2. 共Color online兲 Oscilloscope traces of individual tapping events on aSi sample.

less. Secondly, the coupling between flexural resonances of
the cantilever and the force sensor should be minimized sothat the force sensor can be modeled as a simple harmonic
oscillator. This is achieved by designing the reference fingers
and fingers connected to the tip to have equal resonance frequencies. The fingers connected to the tip have additionalmass, so their resonance frequency will be lower if no balancing is performed. The resonance frequencies of adjacentfingers are equalized by designing the outer fingers to be
shorter by incorporating thick support regions around thefingers.
The cantilevers are fabricated with standard optical lithography in a four-mask process that requires wafer bonding. The process starts with silicon on insulator 共SOI兲 wafers
with 10 ␮m device layers. First, the offset between grating
fingers is defined using local oxidation of silicon. A 40 nm
thick SiO2 layer is grown, followed by an 80 nm Si3N4 deposition. The nitride layer is patterned and followed by an oxidation process that removes silicon from areas that are notcovered with silicon nitride without affecting the surface
roughness. After removal of nitride and oxide layers, anothersilicon wafer with thermal oxide is fusion bonded to the SOI
device layer. The substrate of the SOI wafer is removed using tetramethylammonium hydroxide. The tips and the support regions are patterned in the oxide layer using 6:1 buffered oxide etch 共BOE兲 and formed by undercutting SF6
plasma etching. The tips are oxide sharpened at 950 ° C. The
cantilever outline with sensor gratings is patterned in aplasma etch. The top surface is covered with tetraethyl orthosilicate and silicon nitride. The handle wafer is etched using
KOH through a nitride mask from the backside. Finally, thestructures are released in a nitride plasma etch followed by a
6:1 BOE etch.
We performed time-resolved interaction force measurements with a commercial AFM12 combined with a custom
photodetector circuit. The cantilever was excited close to its
fundamental resonance frequency at 22 kHz. The resonancefrequency of the force sensor was measured to be 672 kHz.
A 690 nm laser light was focused to a 30⫻ 30 ␮m2 spot on
the integrated diffraction grating force sensor on the cantilever. The zeroth and first modes of the diffraction pattern wereplaced on each half of an external dual-cell photodiode. The
individual cell outputs were subtracted from each other andlow-pass filtered with a 1 MHz bandwidth. The measured
signal is presented in Fig. 2. The ringing that is apparent in
the trace is due to the resonance of the small force sensor andcoupling of the force sensor to cantilever resonances. TheAppl. Phys. Lett. 93, 023114 共2008兲

FIG. 3. 共Color online兲 Time-resolved tip-sample interaction force curve obtained on a Si sample. The maximum attractive forces on approach andduring retraction are 4.93 nN and 19.97 nN, respectively. The maximumrepulsive force is 41.26 nN. The tip-sample interaction corresponds to 6% of
the cantilever oscillation period.

effect of sensor resonance can be compensated by inverse
filtering the displacement signal.10,13,14 In our experiments,
the transfer function of the force sensor is modeled as adamped, simple harmonic oscillator. The resonance frequency and the quality factor of the sensor are determined
experimentally by sweeping the cantilever driving frequency.
This lets us observe the sensor resonance, because a small
mismatch between the resonance frequencies of the stationary and moving grating fingers causes relative displacement
when the cantilever is driven close to the sensor resonancefrequency. The accuracy of the calibration parameters is confirmed by observing tip-sample rupture events. In addition to
inverse filtering, nonlinear least square fitting was performedon the signal for the time periods in which the tip is not in
contact with the sample. During this process, the harmonics
of the driving signal were used as the basis set. Together withinverse filtering, this lets us remove the errors caused bymisplacement of the photodiode, photodetector nonlinearity,and coupling between flexural resonances of the cantilever
and the force sensor.
The force constant of the cantilever is estimated by finite
element analysis to be 0.74 N / m. The force calibration of
the integrated force sensor is performed by pressing the cantilever on a hard surface. The total force acting on the tip iscalculated by multiplying the piezotube displacement withthe estimated spring constant of the cantilever. The resulting
change in the photodiode signal is measured. The timeresolved force signal following calibration and signal processing is given in Fig. 3. The attractive, repulsive, and adhesive phases of the tip-sample interaction can be identified
with ␮s time resolution. The hysteresis in tip-sample interaction is also apparent from the measurements.
Our cantilever can be used in commercial AFMs in twoways. One is to align one of the diffracted modes to thecenter of the quadrant photodiode and block the others. In
this setting, the vertical displacement of the spot corresponds
to cantilever oscillations and the total power on the quadrant
photodiode corresponds to relative tip displacement due tointeraction with the sample. The other scheme is to align two
adjacent diffracted modes onto the left and right halves of thequadrant photodiode such that they are vertically centered. In
this setting, the vertical difference signal corresponds to cantilever oscillations and the lateral difference signal gives thetip displacement relative to the cantilever body. We chose theDownloaded 19 Mar 2009 to 133.28.47.30. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

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Appl. Phys. Lett. 93, 023114 共2008兲

A. F. Sarioglu and O. Solgaard

FIG. 4. 共Color online兲 Topography 共left兲 and simultaneously acquired 28th
harmonic image 共right兲 of Si3N4 stripes on a Si substrate imaged with ourprobe. 共Scan size: 10⫻ 10 ␮m2.兲

second method for the images reported in this paper. In thissetting, differential measurement minimizes common modenoise due to laser diode intensity and wavelength instabilities
and two spatially separated diffraction modes on the photodiode eliminate crosstalk between vertical and lateral signals
in tapping-mode operation.
In tapping-mode AFM, the tip-sample interaction is quasiperiodic and the frequency spectrum consists of harmonics
of the cantilever excitation frequency. The tip-sample interaction depends on material parameters, so the amount of signal power at each harmonic is a function of sample
properties.15 This provides a contrast mechanism for obtaining material specific AFM images.
We performed imaging on a Si sample with 3 ␮m wide,
670 nm high low-stress Si3N4 lines with our cantilevers in acommercial AFM.12 By use of a lock-in amplifier, the signal
power at the 28th harmonic is recorded as the harmonic image data signal. The topography image and the 28th harmonic image are shown in Fig. 4. The harmonic image
shows contrast between Si and Si3N4 surfaces and the material boundaries are very clearly observed. Moreover, the harmonic image clearly shows the roughness of the Si surfaces,
caused by reactive ion etching of Si3N4.
We also used our probes on thin films of polystyreneblock-polybutadiene-block-polystyrene 共SBS兲 triblock copolymer in a commercial AFM.16 At room temperature, thepolybutadiene blocks are above their glass transition temperature, whereas the polystyrene blocks are in glassy state.
This results in local stiffness variations on length scales
around 50 nm.17 Figure 5 shows the topography and 17th
harmonic image of the sample. The microphase separation isrevealed by the harmonic image. The bright and dark regionsin the 17th harmonic image correspond to stiff polystyrene
blocks and compliant polybutadiene blocks respectively.
In summary, we have designed and fabricated cantilevers
that have integrated force sensors for observing tip motion

FIG. 5. 共Color online兲 Topography 共left兲 and simultaneously acquired 17th
harmonic image 共right兲 of thin film of SBS triblock copolymer imaged withour probe. 共Scan size: 1 ⫻ 1 ␮m2.兲

relative to the cantilever body. This let us observe tip-sample
interactions with high SNR. We demonstrated time-resolved
measurement of tip-sample interaction forces in tappingmode AFM, and we used our probes to obtain harmonic images of samples containing materials with different mechanical properties.
The authors would like to thank Maozi Liu of Agilent
Technologies for the polymer sample. This work was supported by NSF PHY-0425897, DARPA under Grant No.
HR0011-06-1-0049, and Boeing under Contract No. SPO#33130.
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