WO2004012201A2

WO2004012201A2 - Method of and apparatus for calibrating cantilevers

Info

Publication number: WO2004012201A2
Application number: PCT/GB2003/003358
Authority: WO
Inventors: John Gallop
Original assignee: The Secretary Of State For Trade & Industry Of Her Majesty's Britannic Government
Priority date: 2002-07-31
Filing date: 2003-07-31
Publication date: 2004-02-05
Also published as: WO2004012201A3; AU2003260713A8; AU2003260713A1; GB0217812D0

Abstract

A method of and apparatus for calibrating a cantilever (12) of a scanning probe microscope provide for applying radiation pressure to the cantilever so as to deflect the cantilever and measuring the deflection of the cantilever. Radiation pressure is provided by a focused beam of radiation, preferably a laser beam (14) and deflection of the cantilever is measured by measuring a reflection of the laser beam. Preferably, the laser light beam used for calibration is the same as that used for measurement of beam deflection in a scanning probe microscope. This provides an effective non-destructive calibration system which can be performed repeatedly without damaging the cantilever.

Description

METHOD OF AND APPARATUS FOR CALIBRATING CANTILEVERS

The present invention relates to a method of and apparatus for calibrating cantilevers, in particular cantilevers suitable for use in force microscopy.

Scanning probe microscopes (SPM) use a sharp tip that is scanned in close proximity to the surface to be measured. An example is shown in Figure 1. As the tip is moved across the surface, typically in a raster scan motion, a profile of the surface is built up, measured by the deflection of the tip.

The tip is connected to a cantilever; a beam with one fixed end and one moving end with the tip attached. The cantilever and tip are typically up to 0.5 mm long and grown from silicon or silicon nitride, though other materials have been used.

The bending of the cantilever corresponds to the tip deflection and is usually measured using a laser light reflecting off the tip surface of the cantilever, into a split photo detector.

Cantilevers of varying size and stiffness are used dependent on the type of surface to be measured. The cantilever stiffness is either assumed (from its dimensions) or calibrated using a number of techniques involving application of a variable force or by attaching weights to the pointer end. More specifically, the known thermal method is based on measurements of the brownian motion of the cantilever and the equipartition function. This method requires making contact with a mica surface and is applicable to almost all levers.

The Sader method is based on the measured plan dimensions of the lever and the resonant frequency and quality factor. This is a non-contact method and only applies to "diving board" levers with a length to width ratio greater than 5.

In the Reference Spring method the cantilever is pressed against a reference spring. The slope of the contact portion of the force depends on the relative compliance of the two levers. This method requires making contact with a mica surface and is applicable to almost all levers. The Cleveland (added mass) method, considered by many to be the "gold standard", requires the attachment of small masses to the end of the cantilever. The shift in resonance frequency is then used to calibrate the spring constant. This is considered a destructive measurement method which is applicable to almost all stiff cantilevers but is not appropriate for biological applications.

All these methods are either of relatively poor accuracy or require a high level of expertise and carefully controlled conditions to achieve reasonable results. Such methods are thus of limited value, particularly for the flexible cantilevers used in biological microscopy.

The present invention seeks to provide an improved method of calibrating cantilevers suitable for use in force microscopy.

According to an aspect of the present invention, there is provided a method of calibrating a cantilever including the steps of applying radiation pressure to the cantilever so as to deflect the cantilever and measuring the deflection of the cantilever.

Advantageously, radiation pressure is provided by a focused beam of radiation and the deflection of the cantilever is measured by measuring a reflection of said beam.

In the preferred embodiment, the radiation beam is a laser light beam.

The preferred embodiment makes use of the momentum of laser light itself to apply a small force to the cantilever. Such a light incident on the beam and of known power creates a force which can be easily calculated. This provides a method of accurately calibrating the cantilever force constant. Typical force constants to which this method is applicable are of the order of 0.001 to 10 Newtons/metre. In the preferred embodiments, the laser light beam used for calibration is the same as that used for the measurement of beam deflection in a scanning probe microscope. This provides a simple calibration facility incorporated within the instrument itself.

It will be apparent that the preferred method is a non-contact method which is unable to damage or permanently deform the cantilever.

According to another aspect of the present invention, there is provided apparatus for calibrating a cantilever including a source of radiation operative to apply radiation pressure to a cantilever so as to course the cantilever to deflect; and means for measuring deflection of the cantilever when subjected to radiation pressure from said source.

According to another aspect of the present invention, there is provided a scanning probe microscope including a cantilevered scanning tip and means for calibrating the cantilevered scanning tip as herein defined.

Embodiments of the present invention are described below, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 is a perspective view of the tip of a cantilevered scanning probe for a scanning probe microscope; _. . . . - -

Figure 2 shows a scanning probe tip and schematically a radiation beam from a laser source directed to the tip;

Figure 3 shows a perspective view of part of a preferred calibration instrument;

Figure 4 is a graph showing deflection of the beam as a function of distance from the fixed end of the cantilever; and

Figure 5 shows a graph of the resonant response of a cantilever. The embodiments described herein make use of radiation pressure produced by a source of radiation, typically a beam which is preferably a laser light beam, applied to the free end of the cantilever, typically at its tip, to cause the cantilever to deflect. In the preferred embodiment, a sensor is provided to measure a reflection of the radiation beam, which will change upon deflection of the tip. Knowledge of the force produced by the radiation beam is used to provide a calibration measurement of the cantilever. The calibration does not involve any mechanical contact with the tip and therefore does not damage the cantilever.

The calibration system can be incorporated into an instrument, typically a scanning probe microscope, such that the cantilever can be calibrated as often as desired by the user. It is envisaged that such calibration can be carried out automatically and periodically, for example, at fixed points in time, after a particular number of number of uses of the instrument or could be carried out before every use of the instrument.

There follows an explanation of the principles underlying the teachings disclosed herein.

Radiation Pressure

E mc²

For a particle of rest mass m and momentum p the correct expression is:

E² = p²c² + m²c⁴

For a photon m=0 so the above expression reduces to:

E = pc - hv

where v is the photon frequency and h is Planck's constant. The force F exerted by a stream of n particles/sec incident on an object and perfectly reflected of it is given by the rate of change of momentum:

F = dP = 2np = 2nE = 2! dt c c

(here I is the total radiation power (intensity) incident on the object).

Other methods (e.g. integrating the Lorentz force on carriers) agree:

For 1=1 W the force F is approx. 6nN

Thus a laser beam of measure intensity reflected from a cantilever provides a known force in the range pN-nN.

Referring now to Figure 2, there is shown in schematic form apparatus for calibrating a MΕMS or AFM cantilever. Such cantilevers could be considered analogous to a diving board which is fixed at one end and flexible. In an AFM a sharp tip is attached to the free end of the cantilever for surface detection. This lever can be used to detect optically displacements of less than one nanometre.

In Figure 2, the cantilever 10 shown has a sharp tip 12. A laser source 14 is located so as to provide a laser beam 16 which is directed to the tip 12 of the cantilever 10. A detector, in this embodiment a quadrant photodiode 18, is located so as to receive the reflected beam from the laser source 14. Any displacement of the tip 12 paused by the force of the laser beam 16 will cause a change in the reflected beam 20 and therefore a change in the output of the quadrant photodiode 18.

Referring now to Figure 3, there are shown the components of an example of a calibration system for calibrating MΕMS cantilevers. A silicon cantilever 22 is mounted on a piezoelectric mounting 24. There is provided a modulated diode laser 26 for resonant excitation of the mounting 24. The laser beam from the laser 26 is directed to an alignment mirror 28 which reflects the beam to the cantilever tip. The alignment mirror 28 provides a for accurate alignment of the laser beam onto the cantilever, requiring only coarse adjustment of the laser diode.

A calibration laser 14', in this case a CW diode laser, is located so as to produce a radiation beam 16 directed at the tip of the cantilever 22. Quadrant photodiode 18 is located so as to receive the reflected signal 20.

It has been found that this calibration method can give a sensitivity of around 950 V/m (using a voltage readout). Sensitivity can be calibrated by translating the photodiode over a known distance.

In an experiment, the measured displacement of a silicon cantilever by the means of a 3mW laser beam was 0.3 nanometres, which yields a force constant for that cantilever of k=0.06N/m. In this particular case, the force constant for the cantilever according to the manufacturer's figure was k=0.032 N/m.

In practice, the laser beam provides a known force in the range nanoNewtons to picoNewtons, in terms of radiation pressure from a measured light intensity. The first allows a MEMS cantilever, for example, to be calibrated and therefore used for reliable measurements of very low forces of the scale encountered in the interactions between single biomolecules. That reflected light of a measured intensity exerts a calculable force on any reflective surface on which it impinges. This force provides a quantum standard which is capable of calibrating a cantilever or other sensitive device.

For the avoidance of doubt, an explanation is now given as to what happens to the eigen frequencies of the cantilever if a force F is added to its free end.

The fourth boundary condition of the free cantilever is modified thus:

u(0,t) = 0 Su(O.t) = 0

6x

& (LS) = 0 at²

-EI dⁱu(L,t) = F dx³

h the above, E is young's modulus, I is a specific moment of inertia and L is length. The skilled reader will appreciate that this is the Bernoulli Euler equation and that it provides an expression for the displacement of the cantilever, which can be given as:

y(x) = (F/6EI)x^Λ2(3L-x)

If a force F is applied at the free end, there exists an analytical solution for the deflection as a function of distance from the fixed end. Figure 4 shows a graph of the deflection of the beam as a function of the distance from the fixed end.

Figure 5 shows the resonant frequency response of the cantilever. By sweeping the frequency of laser modulation through a resonance, it is possible to see a much enhanced oscillation amplitude at the point of resonance. In the example given, the Q of a cantilever in air is about 100. There are, as will be noted, other resonant modes of cantilever.

It will thus be apparent, as it has been discovered, that this method can provide accurate, reliable and repeatable calibration of a cantilever of the type used in scanning probe microscopes. The system is such that calibration can be carried out substantially automatically and therefore without specialist personnel to carry out calibration. Indeed, calibration can be carried out without specific operator input.

For example, the cantilever of an atomic force microscope is often made from highly reflective single crystal silicon. A "diving board" structure is used in which one end of the cantilever is clamped. It is advantageous to know the spring constant of the cantilever, that is the force which, when applied to the free end of the cantilever, produces unit deflection. When this is known the cantilever deflection can be used to measure the force between any molecule attached to the end of the cantilever and a surface over which it is passed. In this way accurate and reproducible values for the interaction between, for example, two biomolecules may be measured. This is potentially very important for understanding protein folding and functional operation of genes and so on.

The accuracy of the system can be improved by reducing the spot size of the laser beam and also by operating the system in a vacuum. Similarly, using multi-layer thin film reflection coatings it may be possible to use more intense light to reflect from the cantilever, allowing higher values of force to be applied (up to perhaps 10 nanoNewtons) without heating the cantilever significantly. The device can be directly incorporated within an atomic force microscope to allow on-line calibration or even the application of controlled nanoforces to bring about movement or interaction.

The main advantages of the described embodiment are the simplicity and traceability of the method which makes it unique in this range of force. It is also a quantum method, based on a fundamental constant (the velocity of light) and straightforward measurements of conventional quantities (light intensity). It may be readily incorporated into existing instrument designs (e.g. an atomic force microscope).

The teachings herein could be used to calibrate cantilever probes other than those used in a scanning probe microscope and could be used for calibrating any cantilever structure, particularly a MEMS or AFM structure.

The disclosures in British patent application no. 0217812.7, from which this application claims priority, and in the abstract accompanying this application are incorporated herein by reference.

Claims

1. A method of calibrating a cantilever including the steps of applying radiation pressure to the cantilever so as to deflect the cantilever and measuring the deflection of the cantilever.

2. A method according to claim 1, wherein radiation pressure is provided by a focused beam of radiation.

3. A method according to claim 2, wherein deflection of the cantilever is measured by measuring a reflection of said beam of radiation.

4. A method according to claim 2 or 3, wherein the radiation beam is a laser light beam.

5. A method according to claim 4, wherein the laser light beam used for calibration is the same as that used for measurement of beam deflection in a scanning probe microscope.

6. A method according to any preceding claim, wherein the radiation pressure is of the order of 0.001 to 10 Newtons/metre.

7. A method according to any preceding claim, wherein the cantilever is a cantilever probe of the type used in a scanning probe microscope.

8. Apparatus for calibrating a cantilever including a source of radiation operative to apply radiation pressure to a cantilever so as to course the cantilever to deflect; and means for measuring deflection of the cantilever when subjected to radiation pressure from said source.

9. Apparatus according to claim 8, wherein the source of radiation provides a focused beam of radiation.

10. Apparatus according to claim 9, wherein measuring means is operable to measure deflection of the cantilever by measuring a reflection of said beam of radiation.

11. Apparatus according to claim 9 or 10, wherein the radiation beam is a laser light beam.

12. Apparatus according to claim 11, wherein the laser light beam used for calibration is the same as that used for measurement of beam deflection in a scanning probe microscope.

13. Apparatus according to any one of claims 8 to 12, wherein the radiation pressure is of the order of 0.001 to 10 Newtons/metre.

14. Apparatus according to any one of claims 8 to 13, wherein apparatus is designed to calibrate a cantilever probe of the type used in a scanning probe microscope.

15. A scanning probe microscope including a cantilevered scanning tip and calibration apparatus according to any one of claims 8 to 14.

16. A scanning probe microscope calibrated by a method according to any one of claims 1 to 7.