A new detection system for extremely small vertically mounted

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A new detection system for extremely small vertically mounted cantilevers Article  in  Nanotechnology · September 2008 DOI: 10.1088/0957-4484/19/38/384002 · Source: PubMed

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A new detection system for extremely small vertically mounted cantilevers

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NANOTECHNOLOGY

Nanotechnology 19 (2008) 384002 (10pp)

doi:10.1088/0957-4484/19/38/384002

A new detection system for extremely small vertically mounted cantilevers M Antognozzi1, A Ulcinas1 , L Picco1 , S H Simpson1, P J Heard2 , M D Szczelkun3, B Brenner4 and M J Miles1 1

H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK Interface Analysis Centre, 121 St Michael’s Hill, Bristol BS2 8BS, UK 3 DNA–Protein Interactions Unit, Department of Biochemistry, University of Bristol, University Walk, Bristol BS8 1TD, UK 4 Molecular and Cell Physiology, Medical School Hanover, Hanover, Germany 2

Received 18 February 2008, in final form 17 March 2008 Published 12 August 2008 Online at stacks.iop.org/Nano/19/384002 Abstract Detection techniques currently used in scanning force microscopy impose limitations on the geometrical dimensions of the probes and, as a consequence, on their force sensitivity and temporal response. A new technique, based on scattered evanescent electromagnetic waves (SEW), is presented here that can detect the displacement of the extreme end of a vertically mounted cantilever. The resolution of this method is tested using different cantilever sizes and a theoretical model is developed to maximize the detection sensitivity. The applications presented here clearly show that the SEW detection system enables the use of force sensors with sub-micron size, opening new possibilities in the investigation of biomolecular systems and high speed imaging. Two types of cantilevers were successfully tested: a high force sensitivity lever with a spring constant of 0.17 pN nm−1 and a resonant frequency of 32 kHz; and a high speed lever with a spring constant of 50 pN nm−1 and a resonant frequency of 1.8 MHz. Both these force sensors were fabricated by modifying commercial microcantilevers in a focused ion beam system. It is important to emphasize that these modified cantilevers could not be detected by the conventional optical detection system used in commercial atomic force microscopes. (Some figures in this article are in colour only in the electronic version)

with a position-sensitive photodetector. A different detection system was required for scanning near-field optical microscopy (SNOM). In this case a vertically mounted optical fibre, with a sub-wavelength aperture, was used to collect the light from the sample or to illuminate the sample. The images obtained can have sub-wavelength information [4]. In this technique it is crucial to maintain a constant tip/sample distance and, for this purpose, the non-contact shear force interaction is used [5]. The probe is oscillated transversely and parallel to the sample surface. When the probe is approaching the sample surface from a distance of a few nanometres the oscillation amplitude begins to decrease and it continues to decrease as the probe approaches the surface. An accurate detection of the probe oscillation is critical and, ideally, would require the measurement of the x y -position of the very tip of the probe. Unfortunately, the SNOM probe has a cylindrical cross-section and is vertically mounted which makes it difficult to fulfil the previous requirements.

1. Introduction In scanning probe microscopy (SPM), the measurement of the position of the probe with respect to the specimen surface is a very critical operation. In scanning tunnelling microscopy (STM) it is possible to determine the distance (z ) between the tip and the sample surface by measuring the tunnelling current flowing in the gap [1]. The in-plane position (x y ) of the tip is inferred by the displacement of the positioning stage connected to the tip or to the sample. In an atomic force microscope (AFM) a horizontally mounted micro-cantilever with a sharp tip is used as a force sensor. The interaction force is measured via the detection of the cantilever’s vertical bending. Initially these measurements were obtained by positioning an STM probe on the back of the cantilever [2] but later an easier, optical lever detection method was introduced [3]. This method is commonly used in commercial AFMs and requires a focused laser beam to be directed onto the cantilever surface and the reflected beam direction to be measured 0957-4484/08/384002+10$30.00

1

© 2008 IOP Publishing Ltd Printed in the UK

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(FIB). The first is an extremely soft force sensor that is ideal for studies of the dynamic behaviour of biomolecular systems, while the second possesses a resonant frequency of more than a megahertz, making it well suited for high-speed SPM of soft samples. Both types were successfully detected and monitored, something which their small dimensions would prevent conventional optical detection methods from achieving. Although TIR microscopy has already been used to detect the position of colloidal particles [10] and to measure the vertical position of AFM cantilevers [11, 12] and other nanomechanical resonators [13], three important novelties are introduced in the present paper: (i) the use of evanescent em-field illumination in combination with vertically mounted probes. These probes can be conventional SNOM probes, as well as very small AFM cantilevers; (ii) the use of a foursector photodetector to detect the x y -position of the extreme end of the probe; and (iii) the use of an interference method to increase the lateral resolution of the detection system. The combination of these elements allows important technical advances in the use of very small force sensors.

Conventionally, a laser beam diffraction method has been used [6]: a laser beam is directed perpendicularly to the probe at a certain distance from the tip and the resulting interference pattern is recorded by a two-sector photodetector. In this way a measurement of the oscillation of the probe in the direction perpendicular to the laser beam can be obtained. A system with two orthogonal detection lasers (transverse dynamic force microscope, TDFM) has been developed by the authors to measure the position of the probe in the sample x y -plane [7, 8]. Unfortunately, these optical methods (and similar techniques) do not allow one to directly measure the position of the very end of the probe and are not suitable when imaging in liquid. Alternatively, non-optical detection systems have also been employed and the use of a quartz tuning fork to excite and detect the oscillation of the probe has been particularly successful [9]. In this paper, a new method to measure the x y -position of conventional SNOM probes, as well as vertically mounted AFM cantilevers, is proposed. It is important to note that the x y -position of the probe tip is measured with respect to an equilibrium position of the tip and not with respect to the sample plane. This means that if the sample moves in the x or y direction the detection system will not measure the change in relative position of the tip and the sample. Furthermore, when using micro-fabricated AFM cantilevers the free end of the cantilever will be acting as the tip and not the pyramidal tip grown perpendicular to the sensor. Any reference to the cantilever tip will describe, therefore, the cantilever free end. The new detection system presented here requires an evanescent electromagnetic field just above the sample surface and uses objective-based total internal reflection (TIR) microscopy to generate it. When the tip of a vertically mounted force sensor enters the evanescent field, it causes part of this field to propagate. The scattered electromagnetic radiation is collected with the same objective lens and is projected onto a four-sector photodetector, where either an image of the tip or the interference pattern resulting from the combination of the scattered light from the tip and the reference beam, is in this way produced. This method has several advantages with respect to conventional optical detection: (i) it has the ability to detect accurately the position of the very end of the probe in the x y -plane; (ii) it is particularly suited for working in liquid; and (iii) it is not affected by the size of the probe due to the fact that only the last few tens of nanometres are interacting with the evanescent em-field. Taken together, these advantages enable this detection method to monitor very small cantilevers in ambient and liquid environments, a very important step in the ongoing development of both high-speed SPM and highsensitivity force spectroscopy. To estimate the amount of scattered light reaching the four-sector photodetector, the scattering function of a dielectric probe tip in an evanescent field has been calculated and compared to experimental curves. The detection system is also numerically simulated in order to improve its sensitivity. To demonstrate the potential of the detection system to measure the displacements from very small cantilevers two varieties of probes were produced by focused ion beam milling

2. Materials and methods 2.1. The force sensors Due to the novelty of this technique, there are currently no commercially available micro-cantilevers specially designed to be used in a vertical geometry. Conventional cantilevers do not normally terminate with a sharp tip and the only microfabricated cantilevers that can be used ‘out of the box’ with good resolution are silicon levers with triangular free ends (also known as ‘arrow shape’). For these silicon cantilevers the anisotropic etching produces edges that are not straight and the free end terminates approximately in a point. Because the tip lies in the axis of symmetry of the cantilever it does not experience any significant torsional force while interacting with the surface. Unfortunately, the silicon levers have a high stiffness (∼40 nN nm−1 ) and, ultimately, the success of the method will rely on the ideal properties of ad hoc levers. Table 1 lists the various probes that have been tested so far. In particular, conventional optical fibres (probe E) pulled using the Sutter 2000 puller (Sutter Instruments, USA) were successfully used for conventional shear force microscopy in ambient conditions (data not shown). Probes D are tipless tapping mode cantilevers (from NanosensorsTM , Switzerland) and were used to test the evanescent field above a glass surface and to image various samples in shear force microscopy in ambient conditions. The thermal power spectrum density (PSD) was recorded in ambient and liquid conditions using probes B. These levers were modified by a FIB from OBL biolever probes (probe A, see table 1), commercially available from Veeco Instruments Inc., USA. They have reduced dimensions resulting in very soft, highly force sensitive probes (0.17 pN nm−1 ). An image of the modified cantilever is shown in figure 1(a). Finally, a very small force sensor (probe C) was produced in the FIB (as shown in figure 1(b)), again by milling an OBL biolever probe. This cantilever has 2

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Figure 1. (a) The end of a rectangular cantilever (probe A in table 1, an OBL biolever) after been milled using a FIB to produce probe type B (see table 1). (b) A very small cantilever was milled at the end of an OBL biolever to produce probe type C (see table 1). The thickness and the width are comparable (∼200 nm). The structure surrounding the small cantilever is necessary to optically position the tip in the optical axis of the system.

Table 1. List of micro-cantilevers and their properties as described in the text. Resonance frequency

Spring constant (nN nm−1 )

L = 100 μm W = 30 μm T = 0.18 μm L = 68.5 μm W = 0.48 μm T = 0.18 μm

13 kHz

0.006

32 kHz

0.000 17

L = 10.3 μm W = 0.2 μm T = 0.18 μm

1.8 MHz

0.05

L = 125 μm W = 30 μm T = 4 μm L = 3 mm R = 0.062 μm

340 kHz

40

12 kHz

1

Code

Model

Type

Shape

Dimensions

A

OBL Biolever Veeco FIB milled OBL Biolever

Si3 N4

Rectangular

Si3 N4

Rectangular, reduced size to decrease spring constant Rectangular, reduced size to increase resonant frequency Rectangular with triangular end Cylindrical with tapered end

B

C

FIB milled OBL Biolever

Si3 N4

D

Tipless Nanosensors

Si

E

Pulled glass probe

Glass

the small sensor, but it confined the detection to the last few tens of nanometres of the free end.

a resonance frequency of 1.85 MHz and a spring constant of 37 pN nm−1 , as calculated from its dimensions. To the authors’ knowledge this sensor has the highest resonance– stiffness ratio ever achieved for an optically detected cantilever. The natural future applications of these sensors will be high-speed imaging using shear force feedback, as will be reported in upcoming publications. In the present work, the ability to detect (and therefore to use) cantilevers of this size is described. The resonance frequency of the sensor described in figure 1(b) was recorded, as well as the signal produced when the sensor is displaced by nanometre-size in-plane movements. It should be emphasized, that, due to its very small width (200 nm), this cantilever could not be detected using the conventional AFM optical lever method. The detection system here described was not only able to monitor the movements of

2.2. The scattered evanescent wave (SEW) detection system An evanescent electromagnetic wave is produced above a transparent surface by using a totally internally reflected laser beam. When a dielectric particle enters the evanescent field it disrupts the em-field causing light to propagate and therefore become ‘visible’ to a photodetector or a CCD camera. The diagram of the system is shown in figure 2. In this setup the evanescent wave is produced by focusing (using lens L ) a 10 times expanded laser beam (Nd:YAG 532 nm, 30 mW from Coherent) on the back focal plane of a high numerical aperture lens (Nikon 1.49 NA, 100× magnification, infinity corrected). The glass cube after lens L is used to translate 3

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Figure 2. Complete diagram of the SEW detection system as described in the text. The only elements not shown here are related to the positioning of the probe and the sample. A piezo-stack controls the vertical position of the probe and a x y -stage is connected to the sample.

transversally oscillated at its first resonant frequency, the SEW detection system was used to measure the oscillation amplitude, while the feedback loop adjusted the tip–sample separation in order to maintain a constant shear force interaction. In the configuration described in figure 2 the tip–sample separation is controlled by moving the probe while the sample is translated in the conventional raster scan. The scanning stage used was the x y -stage P-734.2CL from Physik Intrumente. To demonstrate the potential of this new instrument, DNA molecules deposited onto mica were successfully imaged in air. When imaging DNA molecules on a mica substrate some attention should be paid to the substrate preparation. After negative results using thick mica substrates (thickness ∼100 μm) the best results were obtained by gluing a thin layer of mica on a glass coverslip. Care must be taken to prevent the overall thickness of the substrate from exceeding the working distance of the objective lens (200 μm). This was achieved by depositing a small amount of low-viscosity UV glue (Bohle, Germany) onto a clean coverslip, applying and pressing firmly a mica disk in order to produce a very thin layer of glue (less than 10 μm), curing the glue under a UV source for 5 min and finally removing the bulk of the mica to leave only a few layers attached to the glue film. To confirm that this substrate is suitable for TIRF microscopy, its transmission spectrum is shown in figure 3, indicating that the presence of the glass, glue and mica only reduces the transmission of light by 10% (the biggest contributor actually being the glass).

the laser beam with respect to the optical axis of the lens and in this way obtaining total internal reflection at the sample surface. The evanescent field occupies a circular area of 25 μm in diameter at the sample plane. The vertical position of the probe is controlled using a piezo-stack (P-239 from Physik Instrumente, Germany), not shown in figure 2. When the probe tip enters the evanescent field, it scatters the light and the image of the tip is projected onto a four-sector photodetector, after passing through the tube lens (10× magnification) and a further 100× objective lens. To increase the sensitivity of the detection system, 50% of the parallel laser beam exiting the beam expander (see figure 2) is realigned with the optical axis of the tube lens and interferes with the scattered light from the probe tip at the image plane of the tube lens. The interference pattern is projected by the second objective lens onto the detector plane. This method is similar to the back focal plane detection used in optical tweezers set-ups as described by Pralle et al [14] and Allersma et al [15]. The intensity of the evanescent wave above the sample was measured by collecting the scattered light from the free end of a tipless tapping mode cantilever (probe D in table 1) at different tip–sample separations. These silicon cantilevers terminate in a very sharp tip and are ideal for scattering measurements. The cantilever was not oscillating and the propagating light was recorded using a CCD camera (Ixon from Andor). To calibrate the detection system a nanometre-size displacement was applied in the x (or y ) direction using the dither piezo shown in figure 2 and the corresponding detector signal recorded. The piezo element was previously characterized using a laser vibrometer and had a strain ˚ V−1 . Usual calibration constants for coefficient of (6 ± 1) A the SEW detection system are between 100 and 1000 nm V−1 .

3. Theory The theory underlying the detection system here described requires the calculation of the scattered intensity of an evanescent wave by the free end of the force sensor and the interference of these spherical waves with a reference laser beam. In this discussion it is assumed that the geometry of the system is similar to the experimental set-up described in

2.3. The implementation of the SEW detection in a shear force microscope The SEW detection system was tested as part of a complete scanning probe microscope. A vertically oriented probe was 4

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Figure 3. Transmission spectrum of glass, glue and mica blanked against air. In order to use mica as a substrate a thin layer of this material is glued onto a glass coverslip. Here, the transmission spectrum of this substrate is reported to confirm its suitability for fluorescence investigation, due to its low adsorption coefficient.

figure 4. A laser beam (incident beam) with wavelength (in vacuum) λ travels upwards into the glass (objective lens) and reaches the glass/air (or glass/water) interface at an angle θ greater than the critical angle, and an evanescent em-field is generated above the glass/air (or glass/water) interface. The electric field above the interface is non-propagating and decays exponentially with distance above the surface with a decay length, δ , given by:

δ=

1 ; kz

(1)

where k z is the modulus of the complex component of the wavevector in the direction perpendicular to the interface (z ) and is given by:   2 n1 k z = k2 sin θ − 1; (2) n2

Figure 4. A diagram of the optical path of the scattered light from the probe and of the reference beam as used in the SEW detection system. With respect to figure 2, the position of some optical elements is slightly modified for clarity. The light beam related to the evanescent field is shown in grey. The objective lens in front of the detector plane is not shown in this diagram because it was not considered for the numerical simulation of the SEW system. The effect of this lens is only to adjust the size of the diffraction pattern in order to match the detector’s area.

with k2 = 2πn 2 /λ the wavenumber of the transmitted beam, n 1 is the refractive index of the medium (glass) containing the incident laser beam and n 2 is the refractive index of the medium (air or water) where the evanescent field is created. If the direction of the incident beam is contained in the x z plane, as shown in figure 4, the evanescent field will have a phase component depending on the x -position, according to equation (3). n1 φ(x) = k2 sin(θ )x. (3) n2

by the tube lens in its focal plane. At the same time, part of the parallel incident laser beam is redirected and recombined with the scattered light exiting the high NA lens. This second beam is parallel and coaxial with the tube lens and it will also be focused in the focal plane of the tube lens. This point defines the origin of the reference system x  y  z  (r = 0) and the two spherical waves propagating out of the focal plane will be, in the far-field (r  rs ), approximated by:

The evanescent electric field will therefore depend on the distance from the interface and on the position along the x -axis as shown in the following equation:

ˆ E(x, z) = E 0 exp(−k z z + iφ(x))

exp(ikr ) ; kr exp(ik | r − rs |) E s (r ) = As f s (ϑ, ϕ) . k | r − rs |

E r (r ) = Ar f r (ϑ, ϕ)

(4)

with E 0 the electric field at z = x = 0. The phase of the evanescent field is not varying with y . As shown in figure 4, the scattered light from the cantilever tip is first collected with the high numerical aperture objective lens and then refocused

(5)

The subscripts ‘r’ and ‘s’ refer to the reference waves and the scattered waves, respectively. k is the wavenumber in air and it is given by k = 2πn 0 /λ, with n 0 the refractive index of air. 5

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Figure 5. (a) The electric field intensity across the detector plane as described in figure 4. The simulation considers a laser wavelength of 532 nm, an objective focal length of 2 mm and a numerical aperture of 1.49 and a displacement of the probe in the x -direction of +5 nm from the optical axis. The phase difference is between the reference and the scattered beams and it is calculated when the probe is in the optical axis. The tube lens has a focal length of 180 mm. (b) Signal produced by the detector as a function of the probe x -position. The signal is calculated by integrating the electric field intensity in the two areas of the detector for different tip x -positions. The dashed line highlights the position of the probe used to calculate the two curves in (a).

r is the modulus of the vector r from the origin of the system x  y  z  . The angular function f (ϑ, ϕ) takes into consideration the Gaussian shape of the beams, whereas the terms Ar and As are two complex numbers describing the amplitude of the two waves and their relative phase ( A j = |A j |eiξ j , with j = r, s). In particular, the amplitude of As is proportional to the amplitude of the electric field calculated in equation (4). The phase of As is controlled by equation (3) and, obviously, by the cantilever tip position. After the tube lens focal plane, the two waves interfere in the far-field in a direction described by the polar coordinates (ϑ, ϕ). The objective lens in front of the detector shown in figure 2 is not included in the calculation because it does not affect the general solution presented here. The position of the cantilever tip is inferred by the signal detected by the photodetector as shown in figure 4. More precisely, the movement of the tip (assumed for simplicity) in the x direction is measured by integrating the intensity of the electric field in the semi-area D1 of the detector and subtracting the integrated intensity of the field on the semi-area D2 . In general terms the intensity of the interference is given by:

to the interference between the two beams and can be simply rewritten using equation (5):       Re E r E s∗ dσ = Re E r ( r )E s∗ (r − rs ) dσ Dj

Dj







|E r |2 dσ +

Sj = Dj

( j = 1, 2).

|E s |2 dσ +2 Dj

Dj

f r (ϑ, ϕ) fs∗ (ϑ, ϕ)

eik(r−|r −rs |) dσ . (8) × 2 k r |r − rs | It is clear that any constant multiplying S j will also multiply S , therefore linearly increasing the detector signal. The simplest way to maximize the signal S requires one to increase the intensity of the reference beam |Ar | (or the scattered beam |As |). A more effective way to maximize S is to adjust the phase difference between the reference beam and the scattered beam to obtain: (ξr − ξs ) = 90◦ . This is due to the last integral in equation (8), where its real part is symmetric in x  (i.e. across the detector) and therefore does not contribute significantly when computing S . On the other hand, the complex part of this integral is anti-symmetrical in x  and, when combined with a phase difference of (ξr −ξs ) = 90◦ , gives its maximal contribution to S j and therefore to S . A numerical calculation of the interference pattern as a function of the tip position confirms these considerations and it can be used to understand better the effect of the relative phase between the reference and the scattered beam. When the probe is aligned with the optical axis (x = y = 0) the two Gaussian beams are concentric and the interference pattern on the detector is symmetric, producing a null signal ( S = 0). Figure 5(a) shows how the intensity of the electric field (calculated using equation (8)) varies across the detector when the probe is displaced by +5 nm from the centre in the x direction. As predicted, a phase difference of 90◦ , between the reference and the scattered beams, produces a non-symmetric intensity profile across the detector and results, therefore, in a more intense signal S . A phase difference of 0◦ , produces a symmetric intensity profile and will not contribute significantly to the signal S . This analysis is confirmed in figure 5(b) where the signal S from the detector is computed (using equation (7)) as a function of the tip position (between −10 and 10 nm) for two different phases (0◦ and 90◦ ).

  |E|2 = (E r + E s )(E r + E s )∗ = |E r |2 + |E s |2 + 2 Re E r E s∗ ; (6) where the values for E r and E s at the detector plane are given by equations (5) and the symbol ‘*’ stands for complex conjugate. The signal produced by the photodetector is given by: S = S1 − S2 ; with:

Dj

  = |Ar | |As | Re ei(ξr −ξs )

  Re E r E s∗ dσ ; (7)

The first integral calculates the intensity produced by the reference beam; ideally it is the same in S1 and S2 and it does not affect S . The second integral calculates the intensity of the scattered beam and gives rise to the basic signal due to the displacement of the cantilever tip. The third part is due 6

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Finally, it should be noted that the present system allows the relative phase between the two Gaussian beams to be adjusted to maximize the signal output. This is performed by translation of one of the mirrors that is responsible for steering the reference beam. It is this additional flexibility that sets the detection system described here apart from conventional back focal plane detection used in optical tweezers, that operates at fixed phase [14].

4. Results and analysis The first step in the characterization of the SEW detection system was to measure the intensity of the scattered light from the tip of a vertically mounted cantilever (probe D) as it enters the evanescent field above a glass coverslip. One of the first measurements of evanescent field intensity using SNOM was obtained by Marti et al [16]. The measurements here presented were first performed in ambient conditions, the cantilever was then withdrawn and a small amount of distilled water (20 μl) added onto the surface and the measurement repeated. Figure 6(a) shows two moments captured by the CCD camera when the tip of the cantilever is just outside the evanescent field (left) and when it is well inside the field scattering light from a very well defined area (right). Two typical curves, measured by integrating the signal collected by the CCD camera at different tip–sample separation, are plotted in figure 6(b). They show a clear exponential decay with a decay length of 143 ± 10 nm in water and 64 ± 10 nm in air. This agrees, within the experimental errors, with equation (1) when using a laser wavelength of 532 nm the refractive index for water 1.33, for air 1, and for glass 1.53, and an incident angle θ of 66◦ (the same for both measurements). The second step was to test the sensitivity of the SEW detection system by measuring the thermal PSD of a rectangular micro-cantilever (probe B) shown in figure 1(a). The length and width of the milled cantilever were 68.5 μm and 480 nm respectively as measured from the FIB image. The thickness of the probe was assumed to be within the range specified for the unmodified OBL cantilever from which it was milled (between 140 nm and 220 nm). The resonant frequency and spring constant were calculated from this knowledge of the dimensions and material properties of the cantilever to be 32.5 kHz and 0.15 pN nm−1 . As in the previous case, the cantilever was mounted vertically and free to oscillate in the x direction (as described in figure 2). When lowered into the evanescent field, the end of the cantilever scattered the evanescent field and produced a bright spot on the detector (when the reference laser beam is temporarily stopped). To avoid shear force interaction, care was taken to ensure that the free end of the cantilever was at least 20 nm away from the glass surface. The detection sensitivity (i.e. calibration constant) was measured at this particular tip–surface distance and the position of the tip was recorded as the cantilever was thermally driven. The procedure was repeated after placing the cantilever in the water, for which special care had to be taken to avoid bending of the cantilever due to the surface tension of water. The signal was converted into actual displacement and the PSD was calculated (shown in figure 7). The two

Figure 6. (a) left, a tipless cantilever (probe D) is positioned just above the evanescent field and imaged using a CCD camera mounted at the detector position (see figure 2). The dark shadow is produced by illuminating the cantilever laterally using a conventional light source. The white dots are produced by dust particles on the glass surface scattering the evanescent field. (a) right, once the cantilever tip is lowered inside the evanescent field, it becomes a scattering point and the very tip of the cantilever becomes visible to the CCD camera. (b) The light intensity collected by the CCD camera is plotted as the probe approaches the glass surface in two different media (water and air). The experimental data are fitted using an exponential function with decay length given by equation (2).

experimental curves refer to the same cantilever but in different environments: ambient (a) and liquid conditions (b). The Lorentzian curve in equation (9) is fitted to the experimental data (in air) to estimate the quality factor Q , the spring constant k and the resonant frequency νn of the cantilever. Once the spring constant of the cantilever in air is obtained, the fitting of the spectrum in liquid is calculated adjusting only Q and νn .

x 2 (ν) 2k B T 1 = 

.

ν πνn Qk 1 − ν 2 2 + ν 2 νn νn Q

(9)

The value of the spring constant was also calculated using Sader’s method [17] (using Q and k from the spectrum in air) to check the accuracy of the calibration procedure. Sader’s method, in fact, does not rely on a calibrated PSD as in the case of equation (9). In this particular case the spring constant of the cantilever was measured to be 0.17 pN nm−1 , this agrees well with the calculated value derived from the cantilevers geometry. We note that it was not possible to record the displacement of this cantilever using a commercial AFM since it is too small to be detected by a conventional optical lever method. 7

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Figure 7. The power spectrum density is calculated after recording the position of the cantilever (probe B) for a few seconds with a 300 kHz sampling rate; (a) the cantilever is in ambient conditions, (b) the cantilever is immersed in water. The grey lines are fitting curves obtained using equation (9). The quality factor of the cantilever is 1.3 (air) and 0.03 (water) and the spring constant is 0.17 pN nm−1 .

Figure 8. (a) Frequency spectrum in air of the very small cantilever shown in figure 1(b), detected using the SEW detection system. The resonance frequency is 1.8 MHz and the Q factor is ∼10 as calculated using the driven harmonic oscillator model (solid line). (b) The top curve shows the recorded signal in volts, when a square wave lateral displacement (bottom curve) is applied to the cantilever used in (a). The resolution of the SEW detection for this cantilever is ∼1 nm.

resonance peak (1.8 MHz), while figure 8(b) shows the recorded signal when the cantilever is displaced in the x direction by applying a square voltage wave to a dither piezo, resulting in 6 nm steps (peak-to-peak). Both resonant frequency and displacement step are clearly detected, thus

The final step in the characterization of the SEW detection method was to show the possibility of using a very small cantilever which has a high resonant frequency (probe C). Figure 8(a) shows the frequency spectrum recorded by driving the cantilever with a sweeping frequency around its first 8

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Figure 9. (a) Image under ambient conditions of λ-DNA molecules deposited onto mica. The image was taken using shear force feedback. The cantilever used was probe type D (see table 1), with a resonance frequency of 340 kHz in air and a spring constant of 40 nN nm−1 . The scan rate was 1 line per second and the image is 400 × 400 pixels over a 2 μm × 2 μm area. (b) A line profile correspondent to the white horizontal line in (a) shows that the height of the DNA molecules measured using this technique is ∼1 nm; this value is consistent with conventional shear force microscopy images of DNA molecules [8].

confirming that the SEW detection system can resolve the position of the cantilever tip with nanometre resolution. This result is an important landmark in the use of smaller and faster force sensors. At the present, the lack of large scale production of smaller cantilevers is the only obstacle preventing their use in exciting areas such as molecular biology and high-speed SPM imaging. The last part of this section shows the application of the SEW detection system in a complete scanning probe microscope using shear force interaction as the separation control. Figure 9 shows double stranded λ-DNA molecules deposited onto a mica surface and imaged in air. The image was obtained using a tipless Si cantilever (probe D) at a scan rate of 1 line per second and 400 points per line. The performance is expected to improve further as probes specifically designed for operation in vertical orientation become available. The operation of the SEW detection system combined to shear force microscopy is affected by the scattering properties and the relative size of the deposited sample. Biomolecules deposited onto mica do not interfere

with the SEW detection system and the resolution limit in this case is controlled by the tip size. Gold nanoclusters smaller than 50 and 20 nm polystyrene spheres can be reliably imaged (data not shown) without significant cross-talk between the light scattered by the particles and the probe. Height measurements of 20 nm polystyrene spheres are within 10% of the manufacturer specifications. Sample features with higher aspect-ratio are not considered because clearly outside the range of samples suitable for the system here presented.

5. Conclusions From the results presented here, it is evident that the use of the SEW detection system, combined with adequate vertically oriented micro-fabricated cantilevers, has the following advantages. (i) The position of the very end of the probe is detected in the x and y direction simultaneously. (ii) The size of the cantilever is much less critical than with conventional optical detection methods. This means that 9

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extremely small cantilevers (probably even less than 1 μm long) can be accurately detected. (iii) The force sensitivity of the cantilever (in the plane of the sample) is not limited by adhesion effects because the vertical geometry ensures very high vertical stiffness of the cantilever. (iv) Imaging in water does not interfere with the detection system, as it does in the case of conventional optical methods.

for very helpful discussions concerning the SEW detection system. AU gratefully acknowledges the support of Unilever Research plc.

References [1] Binnig G, Rohrer H, Gerber C and Weibel E 1982 Tunneling through a controllable vacuum gap Appl. Phys. Lett. 40 178–80 [2] Binnig G, Quate C F and Gerber C 1986 Atomic force microscope Phys. Rev. Lett. 56 930–3 [3] Meyer G and Amer N M 1988 Novel optical approach to atomic force microscopy Appl. Phys. Lett. 53 1045–7 [4] Betzig E, Trautman J K, Harris T D, Weiner J S and Kostelak R L 1991 Breaking the diffraction barrier—optical microscopy on a nanometric scale Science 251 1468–70 [5] Betzig E, Finn P L and Weiner J S 1992 Combined shear force and near-field scanning optical microscopy Appl. Phys. Lett. 60 2484–6 [6] Froehlich F F and Milster T D 1994 Minimum detectable displacement in near-field scanning optical microscopy Appl. Phys. Lett. 65 2254–6 [7] Antognozzi M, Haschke H and Miles M J 2000 A new method to measure the oscillation of a cylindrical cantilever: ‘the laser reflection detection system’ Rev. Sci. Instrum. 71 1689–94 [8] Antognozzi M, Szczelkun M D, Round A N and Miles M J 2002 Comparison between shear force and tapping mode AFM—high resolution imaging of DNA Single Mol. 3 104–9 [9] Karrai K and Tiemann I 2000 Interfacial shear force microscopy Phys. Rev. B 62 13174–81 [10] Prieve D C 1999 Measurement of colloidal forces with TIRM Adv. Colloid Interface Sci. 82 93–125 [11] Clark S C, Walz J Y and Ducker W A 2004 Atomic force microscopy colloid-probe measurements with explicit measurement of particle–solid separation Langmuir 20 7616–22 [12] McKee C T, Clark S C, Walz J Y and Ducker W A 2005 Relationship between scattered intensity and separation for particles in an evanescent field Langmuir 21 5783–9 ¨ u M S, [13] Karabacak D M, Ekinci K L, Gan C H, Gbur G J, Unl¨ Ippolito S B, Goldberg B B and Carney P S 2007 Diffraction of evanescent waves and nanomechanical displacement detection Opt. Lett. 32 1881–3 [14] Pralle A, Prummer M, Florin E L, Stelzer E H K and Horber J K H 1999 Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light Microsc. Res. Tech. 44 378–86 [15] Allersma M W, Gittes F, deCastro M J, Stewart R J and Schmidt C F 1998 Two-dimensional tracking of ncd motility by back focal plane interferometry Biophys. J. 74 1074–85 [16] Marti O, Bielefeldt H, Hecht B, Herminghaus S, Leiderer P and Mlynek J 1993 Near field optical measurement of the surface plasmon field Opt. Commun. 96 225–8 [17] Sader J E, Larson I, Mulvaney P and White L R 1995 Method for the calibration of atomic-force microscope cantilevers Rev. Sci. Instrum. 66 3789–98

Although this innovative detection system has been presented here in combination with conventional scanning probe microscopy it is fairly straightforward to extend this technique to force spectroscopy methods. In this case the probe is not scanning the surface to obtain an image but is used to sense the interaction force at different tip–sample separations. Indeed, probe B, with its sub-piconewton spring constant is an excellent example of a force spectroscopy probe that would be unusable with a conventional optical detection system. However, because the SEW detection method can measure the deflection of these probes one can therefore envisage performing force spectroscopy with cantilevers possessing similar force sensitivities to optical tweezers while also achieving greater temporal resolution. Clearly, this new technique is particularly suited for the investigation of biomolecules on flat, transparent substrates and it is therefore presented here as a complementary probe microscopy method. As an imaging tool, it is limited to low scattering and small aspect-ratio features on a flat surface; 20 nm polystyrene sphere and 50 nm gold nanoclusters were indeed successfully observed (data not shown). More importantly, it has been demonstrated that the SEW detection system described here allows the use of smaller cantilevers, which in turn permit access to greater temporal resolution and force sensitivity. It should be emphasized that by combining high force resolution (smaller than 1 pN nm−1 ) with high time resolution (in the μs range), these types of cantilevers fulfil the basic requirement for high-speed SPM and for the characterization of dynamic biomolecular systems. The method here presented could have the merit to accelerate this natural evolution of probe microscopy towards more sensitive and faster force sensors.

Acknowledgments The authors would like to acknowledge Mr David Engledew and Mr Ray Blyth for their contributions to the design of the microscope and their overall technical assistance. They also wish to thank Professor John Hannay and Dr Peter Dunton

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