APPLIED PHYSICS LETTERS 94, 173109 共2009兲

“Torsional tapping” atomic force microscopy using T-shaped cantilevers
Nic Mullin,1 Cvetelin Vasilev,2 Jaimey D. Tucker,2 C. Neil Hunter,2 Christa H. M. Weber,3and Jamie K. Hobbs1,3,a兲
1

Department of Physics and Astronomy, University of Sheffield, The Hicks Building, Hounsfield Road,Sheffield, South Yorkshire S3 7RH, United Kingdom
2Department of Molecular Biology and Biotechnology, University of Sheffield, Firth Court, Western Bank,Sheffield, South Yorkshire S10 2TN, United Kingdom
3Department of Chemistry, University of Sheffield, Sheffield, South Yorkshire S3 7HF, United Kingdom共Received 16 March 2009; accepted 8 April 2009; published online 29 April 2009兲
Torsional oscillation of atomic force microscope cantilevers has been shown to offer increased
optical lever sensitivity, quality factor, resonant frequency, and stiffness as compared to flexural
oscillation. In this letter, T-shaped cantilevers are oscillated torsionally to give a tapping motion at
the tip. This gives many of the advantages of small cantilevers, without the requirement forspecialized detection optics. In order to demonstrate the capability of this technique, high resolution
images of LH2 membrane protein crystal structures are presented. Reduced settle time andtip-sample force under error signal are also demonstrated. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3126047兴
Since the invention of atomic force microscopy 共AFM兲,1systems and methodologies have been employed to increase
the signal-to-noise ratio and the sensitivity of the techniquein order to measure smaller forces, reduce the force applied
to the sample by the tip, and increase the resolution obtainable. In oscillatory AFM techniques the force sensitivity has
been shown to depend critically upon the resonant frequency,
amplitude, quality factor 共Q兲, and stiffness of the cantileverused.2,3
Torsionally oscillating cantilevers have previously beenshown to have increased resonant frequency and Q (Refs. 4and 5兲 when compared to flexurally oscillating cantilevers.
Sahin et al.6 have utilized flexurally oscillating T-shaped cantilevers with laterally offset tips to give access to the higher
harmonics of the flexural oscillation via the increased bandwidth of the torsional mode. Various cantilever geometries
not conforming to the ubiquitous rectangular and triangularshapes commonly used for AFM 共see Ref. 7, for example兲
have also been reported, with the aim of increased resonant
frequency, reduced hydrodynamic damping, reduced spring
constant, increased deflection sensitivity, or all of the above.
Here, commercially available T-shaped cantilevers designed for Harmonix™ 共Ref. 8兲 imaging are driven in theirfirst torsional mode to give vertical oscillation at the tip. The
torsional amplitude is monitored and held constant by adjusting the tip-sample separation in the same way as the flexural
amplitude is used in tapping mode. Henceforth, in this letter,
this mode of operation will be referred to as “torsional tapping.” The advantages of this approach are outlined below.
The minimum force gradient that may be measured byslope detection has been shown to be3
2⬘ = 共2klkBTB/␻0Q具zosc
␦Fmin
典兲1/2 ,共1兲by assuming that thermal oscillation of the cantilever is thedominant noise source. Here ␦Fmin⬘ is the minimum detectable force gradient, kl is the cantilever spring constant, kB isBoltzmann’s constant, T is the absolute temperature, B is thea兲

Electronic mail: jamie.hobbs@shef.ac.uk.

0003-6951/2009/94共17兲/173109/3/$25.00

bandwidth of the measurement, ␻0 is the angular resonant2
典 is the meanfrequency, Q is the quality factor, and 具zosc
square oscillation amplitude. From Eq. 共1兲 it may be seenthat force sensitivity is reduced by increasing the spring constant and measurement speed, but increased by increasing theresonant frequency and quality factor. It has been previously
shown that the maximum possible measurement bandwidth
is3
Bmax = ␻0/2Q,

共2兲

where 2Q / ␻0 is the “ring down” time constant associatedwith transient oscillations of the cantilever, as may be causedby perturbations in the tip-sample force.
Increases in resonant frequency and Q while decreasingkl have previously been affected by reducing the size of cantilever sensors;9 however this has required the constructionof dedicated optical lever detection systems with small laser
spot sizes. The spring constant for torsional bending of thecantilevers used here 共Mikromasch TL01兲 is estimated to beapproximately 15 N/m.10,11 If the temperature, amplitude,and measurement bandwidth are held constant, and the resonant frequencies and quality factors from Figs. 1共b兲 and 1共c兲are inserted into Eq. 共1兲; the minimum force gradient detectable with this cantilever in air in torsional tapping is a factorof 0.6 smaller than could be detected by the same cantileverin flexural tapping under the same conditions. It has also
been shown that operating at higher tapping frequencies decreases the response time of the feedback electronics fortypical AFM systems.12
For the cantilevers used here, the resonant frequency of
the first torsional mode is typically increased by a factor of10, as compared to the first flexural mode and the Q by afactor of approximately 4.5 关see Figs. 1共b兲 and 1共c兲兴. As theincrease in frequency is larger than the increase in Q, Eq. 共2兲
states that the maximum available measurement bandwidth isincreased by a factor of 2.5. In order to verify this figure
experimentally, a T-shaped cantilever was driven into oscillation at resonance well above the sample surface using thesame setup described in Ref. 5. This comprises a homebuilt
cantilever holder incorporating two magnetostrictive actua-94, 173109-1© 2009 American Institute of Physics

Downloaded 08 May 2009 to 133.28.47.30. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

173109-2

Mullin et al.

FIG. 1. 共a兲 Scanning electron micrograph of T-shaped cantilevers used inthis work 共Mikromasch TL01兲, showing the cantilever length 共l兲 and tipoffset 共d兲. The dotted line marks the torsion axis. Scale bar 10 ␮m. 共b兲 The
first flexural and 共c兲 torsional resonances of a T-shaped cantilever. The resonant frequencies are 62.8 and 804 kHz and quality factors are 150 and 672,respectively.

tors under oppositely poled dc magnetic fields and a small
solenoid carrying an ac current at the drive frequency. The
cell was mounted in a Veeco Multimode AFM with a NanoScope IIIa controller, Extender electronics, and Signal Access Module. All data presented here were taken using theabove instrument. At time t = 0 the drive signal was switched
off and the resulting amplitude decay was recorded using ahigh speed analog-to-digital converter 共National Instruments
USB5133兲. The experiment was conducted separately forboth vertical and torsional excitation and the results are displayed in Fig. 2. For the cantilever used, the ring-down time
is a factor of approximately 3.5 less for the torsional mode,in agreement with Eq. 共2兲.
Further to the increase in force sensitivity and reduced
settle time, the optical lever detection system is more effective in torsion. This is due to the fact that the measured
deflection voltage at the photodiode is proportional to theangle through which the cantilever is deflected.13 Increase in
the cantilever deflection angle has been shown to give a linear increase in signal to noise ratio for optical lever systems,
regardless of the geometry of the optical beam path.14 For
flexural deflection in the small angle limit the deflection
angle of the cantilever may be approximated to the tip deflection divided by the length. In the case of a T-shaped
cantilever under torsional bending, the angle is given by thetip deflection divided by the tip offset from the torsion axis.
For the cantilevers used here, the ratio of the cantilever

FIG. 2. Amplitude decay of 共a兲 flexurally oscillating and 共b兲 torsionallyoscillating T-shaped cantilever after the drive signal is switched off at t = 0.
The times taken for the amplitudes to decay to 1 / e of their initial values areapproximately 1.4 and 0.4 ms, respectively. These values match the decay
time calculated from the resonant frequency and Q 共shown兲 of the respectivemode used.

Appl. Phys. Lett. 94, 173109 共2009兲

FIG. 3. Torsional tapping images of various test samples obtained in air. 共a兲
Height image of 2D crystals of the photosynthetic bacterial light harvesting
protein LH2 taken in air using a “whisker” probe. The scale bar represents
50 nm and the grayscale is 5 nm. 共b兲 Height image of C60H122 nanocrystal.
The scale bar represents 50 nm and the grayscale is 3 nm. 共c兲 Height 共second
order plane fitted to remove large scale curvature of the spherulite兲, 共d兲amplitude 共feedback error signal兲 and 共e兲 flexural deflection images of polyethylene spherulite crystals. Scale bar 2 ␮m, grayscale 共c兲 350 nm, 共d兲 1.5
V and 共e兲 50 mV.

length to the tip offset is eight. Hence the measured deflection voltage of the cantilever for a given displacement isincreased by the same factor in the torsional configuration.
The signal to noise ratio is also increased by the increase inoperating frequency due to a larger number of oscillation
cycles being averaged in the acquisition time for 1 pixel if
the measurement bandwidth is held constant 共this is the samefactor that gives the dependence of force sensitivity uponresonant frequency in Eq. 共1兲—the more oscillation cycles
that may be averaged per pixel, the lower the uncertainty inthe measurement兲.
In order to demonstrate the ability of this method to
produce high sensitivity, low noise images, two-dimensional
共2D兲 crystals of the photosynthetic bacterial light harvesting
protein LH2 were imaged under ambient conditions. Thesesamples have previously been extensively studied by contact
mode AFM under buffer solution.15 LH2 crystals were synthesized using a method similar to that outlined in Ref. 16
and prepared for imaging by pipetting approximately 10 ␮lof LH2 crystals in buffer solution onto a freshly cleaved
muscovite mica surface with 50 ␮l of tris-KCl buffer andallowed to bind for 10 min. The sample was then rinsed
thoroughly with buffer solution before washing with deionized water and drying under a stream of dry nitrogen.
The LH2 samples were imaged using Mikromasch TL01
Hi’Res cantilevers with diamondlike carbon “whiskers” 共radius of curvature ⬍1 nm兲 grown at the tip apex. Stable imaging was achieved with setpoint ratios varying at 50%–
95%. Figure 3共a兲 shows a membrane patch with LH2 protein
crystals, taken with a setpoint of approximately 90%. The
well characterized zigzag and rectangular packing reported
elsewhere17 is clearly visible, however the ringlike structureof the individual protein units reported when imaging in
buffer15–18 is not observed. This is consistent with the results
reported in Ref. 18 when imaging in air. As the rise and fall

Downloaded 08 May 2009 to 133.28.47.30. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

173109-3Appl. Phys. Lett. 94, 173109 共2009兲

Mullin et al.

time of the features observed on the sample surface is considerably less than the inner diameter of the LH2 ring, ringstructures should be clearly resolved if they are present. The
absence of rings may indicate that the conformation of theindividual proteins is different in air to in liquid environments. Hexacontane 共C60H122兲 nanocrystals were also imaged in torsional tapping using whisker tips. Thin films wereprepared by spin casting on HOPG substrates from a saturated toluene solution, followed by annealing at 150 ° C for
one hour. Imaging was performed at a setpoint of approximately 95%. Figure 3共b兲 shows a height image of such acrystal. Individual lamellae are clearly resolved, as previously reported.19
Finally, in order to demonstrate the ability of this technique to track the surface of highly topographic samples,polyethylene 共PE兲 spherulite semicrystalline aggregates wereimaged using torsional tapping under ambient conditions.
The samples were prepared by dissolving PE 共molecularweight: 60 kDa兲 in p-xylene at 120 ° C and a concentrationof 0.5% 共w/w兲, then pipetting the solution onto a clean silicon wafer. The solvent was evaporated at 160 ° C and thesample was quenched to room temperature. Mikromasch
TL01 cantilevers with conventional silicon tips were usedwith a setpoint ratio of approximately 85% and an amplitude
of around 10 nm. Figures 3共c兲–3共e兲 are the height, amplitude,
and flexural deflection 共respectively兲 of the cantilever captured during a scan of a spherulite crystal. As can be seenfrom Figs. 3共c兲 and 3共d兲, the flexural deflection of the cantilever correlates well with the amplitude 共feedback error signal兲. This indicates that under error signal, the cantilever isdeflected flexurally, thus limiting the maximum force applied
between the tip and the sample. Hence, the torsional configuration allows stiff, high frequency cantilevers to be usedwhile maintaining a low spring constant in the Z direction.
The maximum peak-to-valley deflection in Fig. 3共d兲 is approximately 35 mV, corresponding to a variation in force ofapproximately 3 nN. The dc component of the torsional deflection signal was also recorded, but showed no measurable
variation above the noise level.
In summary, T-shaped cantilevers have been excited andmonitored torsionally to give tapping mode imaging under adifferent geometry. Due to the increased Q and resonant frequency outweighing the increase in torsional spring constantfor this configuration, the minimum force gradient detectablein dynamic AFM is decreased while increasing the available
measurement bandwidth. The geometry of the T-shaped cantilever also improves the sensitivity of the optical lever detection system over conventional cantilevers. Hence torsional
tapping offers an increase in force sensitivity and signal tonoise ratio over conventional cantilevers but does not require
specialized detection optics. Alternatively, small tapping amplitudes can be used without a significant decrease in signalto-noise ratio, due to the increased optical lever sensitivity.
An obvious application of this technique is for high reso-lution dynamic mode imaging in liquid, upon which we hope
to report in the near future.
This configuration also offers an advantage of having a
low force constant in the Z direction when compared to thecantilevers usually used in tapping mode in air, thus decreasing the likelihood of tip or sample damage when the feedback error signal is large and negative. Further to the acquisition of high resolution, high sensitivity images at increased
scan rates it would also be possible to reduce the Q via
electronic Q control20 in order to acquire images with thesame force sensitivity as typically obtainable in conventional
tapping-mode AFM but at higher scan rates.
It should be noted that the cantilevers used here weredesigned for use in Harmonix™ imaging and not optimizedfor torsional tapping in any way. It is conceivable that cantilevers specifically designed for this application could yieldconsiderably better results.
G. Binnig, C. F. Quate, and Ch. Gerber, Phys. Rev. Lett. 56, 930 共1986兲.
Y. Martin, C. C. Williams, and H. K. Wickramasinghe, J. Appl. Phys. 61,4723 共1987兲.
3
T. R. Albrecht, P. Grütter, D. Horne, and D. Rugar, J. Appl. Phys. 69, 668
共1991兲.
4
L. Huang and C. Su, Ultramicroscopy 100, 277 共2004兲.
5
N. Mullin and J. Hobbs, Appl. Phys. Lett. 92, 053103 共2008兲.
6O. Sahin, S. Magonov, C. Su, C. F. Quate, and O. Solgaard, Nat. Nanotechnol. 2, 507 共2007兲.
7A. Beyder and H. Sachs, Ultramicroscopy 106, 838 共2006兲.
8
Harmonix imaging is commercially available on Veeco AFM systems:
www.veeco.com.
9T. E. Schäffer, J. P. Cleveland, F. Ohnesorge, D. A. Walters, and P. K.
Hansma, J. Appl. Phys. 80, 3622 共1996兲.
10
Two methods were used to calculate this figure: the torsional Sadermethod 共Ref. 11兲 allows the calculation of the spring constant 共in units of
newton-metres per radian兲 for a rectangular cantilever of the same dimensions, but without the crossbar. This may then be converted into a spring
constant in newtons per metre by multiplying by the square of the tip
offset. This method would be expected to underestimate the spring constant. The cantilever may also be treated as two springs in series. Assuming that there is minimal cross-talk between the torsional and flexural
deflection signals, and that the inverse optical lever sensitivity is determined by the geometry of the cantilever, it is possible to calculate thespring constants by taking an approach curve while monitoring the verticaland lateral photodiode signals. Estimates from these two methods are inbroad agreement.
11C. P. Green, H. Lioe, J. P. Cleveland, R. Proksch, P. Mulvaney, and J. E.
Sader, Rev. Sci. Instrum. 75, 1988 共2004兲.
12
T. Sulchek, G. G. Yaralioglu, C. F. Quate, and S. C. Minne, Rev. Sci.
Instrum. 73, 2928 共2002兲.
13
G. Meyer and N. M. Amer, Appl. Phys. Lett. 53, 2400 共1988兲.
14C. A. J. Putman, B. G. De Grooth, N. F. Van Hulst, and J. Greve, J. Appl.
Phys. 72, 6 共1992兲.
15
S. Scheuring, F. Reiss-Husson, A. Engel, J. L. Rigaud, and J. L. Ranck,EMBO J. 20, 3029 共2001兲.
16
M. Chami, G. Pehau-Arudet, O. Lambert, J. L. Ranck, D. Levy, and J. L.
Rigaud, J. Struct. Biol. 133, 64 共2001兲.
17
S. Bahatyrova, R. N. Frese, K. O. van der Werf, C. Otto, C. N. Hunter, andJ. D. Olsen, J. Biol. Chem. 279, 21327 共2004兲.
18
A. Stamouli, S. Kafi, D. C. G. Klein, T. H. Oosterkamp, J. W. M. Frenken,R. J. Cogdell, and T. J. Aartsma, Biophys. J. 84, 2483 共2003兲.
19
S. N. Magonov and N. A. Yerina, Langmuir 19, 500 共2003兲.
20
T. Sulchek, R. Hsieh, J. D. Adams, G. G. Yaralioglu, S. C. Minne, C. F.
Quate, J. P. Cleveland, and A. Atalar, Appl. Phys. Lett. 76, 1473 共2000兲.
1
2

Downloaded 08 May 2009 to 133.28.47.30. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp