WO1998008046A1

WO1998008046A1 - Atomic force microscopy apparatus and a method thereof

Info

Publication number: WO1998008046A1
Application number: PCT/GB1997/002232
Authority: WO
Inventors: Oleg Victor Kolosov; George Andrew Davidson Briggs
Original assignee: Isis Innovation Limited
Priority date: 1996-08-19
Filing date: 1997-08-19
Publication date: 1998-02-26
Also published as: AU4022597A; GB9617380D0

Abstract

The microscopy apparatus comprises a cantilever (10) having an atomically sharp tip (11) and a detector (15) which monitors the deflection of the tip (11) as a measure of the atomic force between the tip and a sample. A piezotransducer (12) is provided on the end of the cantilever (10) distant from the tip (11). The piezotransducer (12) generates high frequency vibrations which are applied to the cantilever. The vibrations transmitted to the tip (11) are modulated using means such as a second piezotransducer (20) in contact with the sample and the movement of the tip (11) is then sampled by the detector (15) at a much lower frequency. The microscopy apparatus and method described is able to maintain sensitivity to the properties of the sample whilst retaining sensitivity to the output of the apparatus. The apparatus and method is particularly suited of the study of time-dependent physico-chemical and physico-mechanical properties up to nanosecond and sub-nanosecond time resolution.

Description

ATOMIC FORCE MICROSCOPY APPARATUS AND A METHOD

THEREOF

The present invention relates to apparatus for and a method of imaging and studying surface and sub-surface characteristics of a sample at nanoscale resolution in dependence on the atomic force between the sample and a tip of the apparatus. Thus, the present invention relates to atomic force microscopy apparatus and a method thereof and it will be understood that in the context of this document reference to atomic force microscopy apparatus is intended as reference to any microscope or other apparatus which relies upon the detection and measurement of atomic force.

Essentially, an atomic force microscope consists of an arm or cantilever at the end of which is an atomically sharp tip which is held very close, for example a few Angstrom, from the surface of a sample to be studied. The cantilever is capable of deflection in a plane perpendicular to the surface of the sample and the characteristics of the sample are studied by monitoring the deflection of the tip as a result of the atomic force between the tip and the surface of the sample. The atomic force involved can be either of the van de Waals (attractive) or core (repulsive) type and is of the order of 10^"6 and 10^"12 N.

Recent developments in atomic force microscopes have involved the application of ultrasonic frequency (MHz to sub-GHz) vibrations to the sample under study and non-linearly detecting the deflection amplitude of the tip at the same high frequencies. With this arrangement, which is commonly identified as an ultrasonic force microscope and has been described in Japanese Appl. Phys. B (Letters) L1095 32_(1993) and in JP133878, the ultrasonic frequencies employed are much higher than the resonant frequency of the microscope cantilever. The microscope exploits the strongly non-linear dependence of the atomic force on the distance between the tip and the sample surface. Due to this non-linearity, when the surface of the sample is excited by an ultrasonic wave, the contact between the tip and the surface 'rectifies' the ultrasonic vibration with the cantilever on which the tip is mounted being dynamically rigid to the ultrasonic vibration. The ultrasonic force microscope enables the imaging and mapping of the dynamic surface and sub-surface viscoelastic properties of a sample and hence elastic and adhesion phenomena as well as local material composition which otherwise would not be visible using standard techniques at nanoscale resolution. Usually the sample is vibrated by means of a piezotransducer attached to the sample but this can be inconvenient and in some cases is impossible. Also, it requires the output of the microscope to be normalised with respect to the particular sample-piezotransducer attachment. Moreover, where the sample is particularly thick, has a very irregular surface or high ultrasonic attenuation only low surface vibration amplitude may be generated. In such circumstances the amplitude of vibration may be below the sensitivity threshold of the microscope in which case measurement is impossible.

In an alternative arrangement two neighbouring ultrasonic high frequency vibrations have been applied to the sample. This mixing of two frequencies in the vibration applied to the sample causes the output of the microscope to be insensitive to the viscoelastic properties of the sample thereby preventing measurement of the dynamic behaviour of the material. Even more recently, it has been found that the cantilever of the microscope behaves as a waveguide and in a paper entitled "Contact imaging in the atomic force microscope using a higher order flexural mode combined with a new sensor" Appl. Phys. Lett. 68 (10), 1996 an ultrasonic force microscope is described in which the cantilever has a single common actuator and sensor which is caused to oscillate at ultrasonic frequencies which are the second and third harmonics of the cantilever. As mentioned previously, with the arrangements described above the cantilever is dynamically rigid to ultrasonic frequencies above its natural resonance. Although this rigidity makes the microscope sensitive to the viscoelastic properties of the sample, it significantly reduces the sensitivity of the output of the cantilever at these frequencies. Thus, greater sensitivity to the properties of the sample are gained at the loss of sensitivity to the output of the microscope with the above described atomic force microscopes.

In the context of this document reference herein to high frequency is intended as reference to frequencies greater than the resonance frequency of the cantilever whereas reference to low frequencies is intended as reference to frequencies below the resonance frequency of the cantilever.

The present invention seeks to provide apparatus and a method which maintain sensitivity to the properties of the sample whilst retaining sensitivity to the output of the microscope.

The present invention provides atomic force microscopy apparatus having a cantilever with a tip at a free end thereof, a vibration device for applying vibration to the cantilever at a first frequency greater than the resonance frequency of the cantilever and a detector for detecting movement of the tip in dependence on an atomic force between the tip and the surface of a sample characterised in that there is further provided an oscillation device for generating a modulation of the tip-surface interaction at a second frequency which is less than the resonance frequency of the cantilever and the detector includes sampling means whereby movement of the tip is detected at a frequency less than the resonance frequency of the cantilever.

Thus, with the present invention it has been realised that it is possible to benefit from the cantilever having the characteristics simultaneously of being effectively dynamically rigid for the purposes of high frequency vibration and exceptionally compliant and force sensitive for the detection of low frequency vibration. This is achieved through the frequency at which measurements are taken being different to the frequency of the applied vibration and also less than the resonance frequency of the cantilever. In a first embodiment the vibration device preferably includes a first signal generator and a vibration generator and the oscillation device is in the form of second signal generator which generates a low frequency signal whereby the output of the first signal generator is modulated by mixing of the output of the second signal generator and the modulated signal is supplied to the vibration generator mechanically coupled to the cantilever.

Preferably the detector is optical. Alternatively, the detector means may be in the form of a piezotransducer and the sampling means include the second signal generator so that the piezotransducer is in registration with the frequency of the second signal generator. Furthermore, the vibration generator may also be in the form of a piezotransducer.

The second signal generator may produce a frequency, amplitude or phase modulating signal.

In an alternative embodiment the vibration device is in the form of a first signal generator which supplies a high frequency signal to the vibration generator and the oscillation device is in the form of a second signal generator which supplies a high frequency signal to a second vibration generator arranged for mechanical coupling to the sample and the sampling means of the detector controls measurement of the tip-surface interaction at a frequency corresponding to the difference between the frequencies of the vibrations applied to the cantilever and sample.

With this alternative embodiment it is possible to recover phase information of the tip-surface mechanical interaction which allows measurement of viscoelastic properties and enables the application of acoustic holography algorithms for imaging nanoscale sized sub-surface defects.

In a similar manner to the first embodiment the vibration of the cantilever may be modulated by the action of the vibration of the sample either in frequency or in amplitude. Furthermore, the apparatus may alternatively or additionally include means for applying external forces to the sample such as electrostatic or electromagnetic etc. which may be constant or varied at frequencies greater than the resonance frequency of the cantilever.

The present invention also provides in a second aspect a method of monitoring the atomic force between a tip mounted on a cantilever and the surface of a sample comprising applying a first signal having a frequency greater than the resonance frequency of the cantilever to a vibration generator mechanically coupled to the cantilever, generating a modulation of the tip-surface interaction at a second frequency less than the resonance frequency of the cantilever and detecting movement of the tip at a frequency less than the resonance frequency of the cantilever, the movement of the tip being representative of the atomic force between the tip and the surface of the sample.

Embodiments of the present invention will now be described by way of example with reference to the accompanying drawings, in which: Figure 1 is a schematic diagram of atomic force microscopy apparatus in accordance with the present invention;

Figure 2 shows a driving signal for the apparatus of Figure 1 ; and Figure 3 shows the non-linear response of the cantilever with the driving signal of Figure 2.

The atomic force microscopy apparatus shown in Figure 1 is generally conventional in design and comprises a cantilever 10 having at its free end a probe or tip 11. The radius of curvature of the tip 11 is made to be as small as possible so as to maximise the resolution of the apparatus. The end of the cantilever 10 opposite to the tip 11 is supported in a mount (not shown). At the end of the cantilever attached to the mount an ultrasonic vibration generator 12 is also provided mechanically coupled to the cantilever so that the cantilever may function as a waveguide. The vibration generator 12 is either directly attached to the cantilever or may be attached through a support member 13, as shown in Figure 1. The vibration generator 12 may be in the form of a piezotransducer or other generator of high frequency vibration. The vibration generator 12 is, in turn, connected to a controller 14 which provides the signal for driving the vibration of the generator. A detector 15 is also provided, separate from the cantilever, for detecting movement of the tip 11. The detector 15 is conventional in design and is arranged to detect vibration of the tip 11. As shown in Figure 1 the detector may comprise a laser and a light sensitive reader which is arranged to receive light reflected from off the head of the tip 1 1. Alternatively, the detector 15 may be in the form of a piezoelectric detector.

The controller 14 has a high frequency first signal generator 16, a low frequency second signal generator 17 and a modulation device 18 which modulates the high frequency signal from the first signal generator 16 with a low frequency signal from the second signal generator 17. Thus, the vibration generator 12 is driven by a modulated signal supplied by the controller 14. It will of course be appreciated that the high frequency signal either may be frequency modulated or amplitude modulated as desired.

Additionally, a lock-in amplifier 19 is provided between the controller 14 and detector 15 so that the frequency at which the detector 15 operates is in registration with the frequencies of the controller 14. Any alternative frequency registration device may of course be employed instead of a lock- in amplifier. It will be seen from Figure 1 that the lock-in amplifier 19 is connected to the low frequency second signal generator 17 and it is this low frequency, which is less than the resonance frequency of the cantilever, at which the detector 15 operates. It will of course be understood that the detector 15 need not be in registration with the modulation in which case the lock-in amplifier may be omitted.

Hence, with the atomic force microscopy apparatus shown in Figure 1 , the waveguide properties of the cantilever are employed with the cantilever 10 being caused to vibrate at a frequency greater than its resonance frequency and the vibration modulated with a frequency less than the resonance frequency of the cantilever. The resultant deflection of the tip 11 is then measured by the detector 15 at substantially the same frequency used to modulate the vibration frequency of the cantilever. The atomic force microscopy apparatus may be used in a scanning mode in which the tip and the surface of the sample move relative to one another and spatially resolved information on the surface of the sample is collected. Alternatively, the apparatus may be used for point measurement of the sample to gain temporally resolved information for example where fluctuations in the characteristics of a region of the surface or sub-surface of the sample are to be measured.

In Figure 2 the type of vibration which can be applied to the cantilever using an ultrasonic piezotransducer is shown, the high frequency signal has a frequency of 7.504 MHz with a peak-to-peak amplitude of 0.8 V and has been 100% modulated with a saw tooth signal at a frequency of 2.781 kHz (the cantilver resonance frequency is taken to be 39 kHz). In Figure 3 the non-linear response of the caVitilever is shown

The effective stiffness K_π of the cantilever at the tip end may be estimated using the model of vibration of a free end cantilever. The effective stiffness K_n and effective mass M_n of the cantilever for the n-th flexural vibration mode can be related with the mode frequency ω_n by the simple point mass oscillator equation ω _n≡(K_n/M_n) ².The higher the mode number n (and, correspondingly, the number of vibration nodes), the lower is the effective mass M_n between the nodes which is coupled to this vibration in inverse proportion to the wavenumber of the mode K_n-M_n≡1/K_n (because the mass of vibrating part of the cantilever between the stationary nodes becomes proportionally smaller). At the same time, the vibration frequency of the n-th mode is proportional to the square of the wavenumber ω_n≡(K_n)². From this it can be found that the effective rigidity K_ns(ω_n)2M_n=(K_n)³. The approximation of K_n for higher n gives K^K^I .δn and, therefore,

K_n/K₁=(K_n)³=4(n)³ (1)

Thus, this confirms the strong dependence of K_n on the mode number n which drastically increases the effective rigidity of the cantilever at high frequency vibration. For example, for the 8^th flexural mode of the cantilever vibration ( with frequency ω₈ approximately 150 times higher than frequency of the main cantilever resonance ω^, the effective rigidity K₈ is about 2x103 times higher than cantilever rigidity on its first resonance. Therefore, a frequency increase of the cantilever vibration causes a strong increase of the dynamic high frequency rigidity of the cantilever which could greatly exceed the tip-surface contact compliance. At the same time, the low frequency cantilever constant remains unchanged which allows one to effectively preserve the high force sensitivity of the compliant cantilever. The essence of the method and apparatus described herein is thus to simultaneously excite high frequency vibration of the cantilever and detect the resulting low frequency cantilever displacement (utilising strong force-distance non-linearity of the tip-surface interaction).

In an alternative arrangement a third signal generator 20 is mechanically coupled to the sample so that the sample can be vibrated at a frequency higher than the resonance frequency of the cantilever. This is shown in dotted lines in Figure 1. The first signal generator 16, which also generates a signal at a frequency greater than the resonance frequency of the cantilever, but at a frequency which is different to the vibration frequency applied to the sample, remains connected to the vibration generator 12 and the detector 15 may or may not be brought into registration with the combined vibration frequencies. With this arrangement as the tip-surface interaction is non-linear, it is reasonable to assume that with a high frequency ω_t vibration applied to the cantilever and an adjacent frequency ω_s applied to the sample, the cantilever should vibrate at a difference frequency ω,-ω_s.

Considering a simple model of the tip-surface force non-linearity F(z)=K_s(Z_t-Z_s)+χ_s(Z,-Z_s)² where Z_t and Z_sare the instantaneous displacements of the tip and the surface, vibrating at frequencies ω_tand ω_s respectively, with a phase delay of surface vibration (modelling sample relaxation, resonance or other time dependent phenomena) φ=ω_s ^*τ such as Z,=a,cos(ω_st) and Z_s=a_tcos(ω_st+ω_s ^*τ). Performing simple calculations and preserving only the low frequency terms in the atomic force cantilever response, it is possible to show that the additional force due to the high frequency vibration of the tip and surface (and, consequently, the resulting cantilever deflection) will be:

F=χ_s{a,²/2-a_sa_tcos[(ω_t-ω_s)t-ω_sτ]+a_s ²/2} (2)

The first term in parentheses is responsible for the non-linear detection of the cantilever vibration, the last term describes the non-linear detection of the sample vibration and the middle term describes the heterodyne mixing of two frequencies.

It can be seen from equation (2) that it is only the middle term which is sensitive to the phase of the high frequency vibration of the sample and the relaxation phenomena of the sample material. Even very small relaxation times τ of the fraction of the period of the high frequency vibration will cause a very strong phase shift in the resulting non-linear low frequency cantilever response proportional to ω_sτ. Therefore, if the phase of the low frequency vibration is measured, for example with a 1 kHz cantilever vibration giving a precision of 1 degree and with the high frequency vibration of the order of 10 MHz, relaxation times of the order of 1 ns can be achieved.

With the first apparatus described non-linear detection of the cantilever vibration is provided without the need for vibration to be applied to the sample. This is clearly of benefit where the sample is not suitable for the attachment of a piezotransducer for example or where the sample is too thick for the vibration to be transmitted through the sample. With the alternative apparatus where heterodyne mixing of two high frequency vibrations is employed, nanosecond and sub-nanosecond time scale phase information on the tip-surface mechanical interaction can be obtained, for example acoustic wave propagation and material mechanical viscoelastic properties. This phase information may also be utilised in acoustic holographic algorithms for imaging nanoscale sized sub-surface defects.

With the apparatus described above other external forces may be applied to the sample to enable various properties of the sample to be monitored. For example, electrostatic or electromagnetic forces may be applied to the sample or thermal expansion effects may be examined. In any of these cases the external forces may be constant or may be varied at frequencies greater than the resonance of the cantilever. The detection of the resulting cantilever response with or without reference to the modulation frequencies of tip vibration or the combination frequencies of spectral components of tip vibration or the combination frequencies of spectral components of tip vibration with the spectral components of the variation of additional physical forces should reveal local physico-chemical and physico-mechanical properties of the sample such as carrier concentration or optoelastic constants as well as sensing time-dependent phenomena such as relaxation or oscillations up to nanosecond and sub- nanosecond time resolution.

The apparatus could also be employed in nanofabrication techniques where the application of bursts of high frequency vibration at high amplitude could produce plastic deformation of the sample with low amplitude vibration being used for sample imaging.

Claims

1. Atomic force microscopy apparatus having a cantilever with a tip at a free end thereof, a vibration device for applying vibration to the cantilever at a first frequency greater than the resonance frequency of the cantilever and a detector for detecting movement of the tip in dependence on an atomic force between the tip and the surface of a sample characterised in that there is further provided an oscillation device for generating a modulation of the tip-surface interaction at a second frequency which is less than the resonance frequency of the cantilever and the detector includes sampling means whereby movement of the tip is detected at a frequency less than the resonance frequency of the cantilever.

2. Atomic force microscopy apparatus as claimed in claim 1 , wherein the vibration device includes a first signal generator and a vibration generator mechanically coupled to the cantilever.

3. Atomic force microscopy apparatus as claimed in either of claims 1 or 2, wherein the oscillation device for generating a modulation of the tip- sample interaction includes a second signal generator which generates a signal having a frequency less than the frequency of the signal from the first generator.

4. Atomic force microscopy apparatus as claimed in claims 2 and 3, wherein a modulating device is provided which mixes the signals from the outputs of the first and second signal generators and drives the vibration generator with the modulated signal.

5. Atomic force microscopy apparatus as claimed in claim 3, wherein the output of the second signal generator is connected to means for subjecting the sample to a variable externally applied physical phenomena.

6. Atomic force microscopy apparatus as claimed in claim 5, wherein the variable physical phenomena is one of the following: a magnetic field, electric field, electrostatics, thermal, electromagnetic radiation or physical vibration.

7. A method of monitoring the atomic force between a tip mounted on a cantilever and the surface of a sample comprising applying a first signal having a frequency greater than the resonance frequency of the cantilever to a vibration generator mechanically coupled to the cantilever, generating a modulation of the tip-surface interaction at a second frequency less than the resonance frequency of the cantilever and detecting movement of the tip at a frequency less than the resonance frequency of the cantilever, the movement of the tip being representative of the atomic force between the tip and the surface of the sample.

8. A method as claimed in claim 7, wherein a modulation of the tip-surface interaction is generated by adding a second signal having a frequency less than the first signal to the first signal to generate a modulation of the first signal having a frequency less than the resonance frequency of the cantilever.

9. A method as claimed in claim 7, wherein a modulation of the tip-surface interaction is generated by applying a vibration to the sample at a frequency less than the frequency of the first signal.

10. A method as claimed in any one of claims 7 to 9, further including scanning the tip over the sample.