NL2005687C2

NL2005687C2 - Method for determining a spring constant for a deformable scanning probe microscope element, and scanning probe microscope and calibration device arranged for determining a spring constant for a probe element.

Info

Publication number: NL2005687C2
Application number: NL2005687A
Authority: NL
Inventors: Johannes Frans Lodewijk Goosen; Adrianus Bossche; Patrick James French; Hamed Sadeghian; Chung-Kai Yang; Alfred Keulen
Original assignee: Tu Delft
Priority date: 2010-11-12
Filing date: 2010-11-12
Publication date: 2012-05-15
Also published as: WO2012064193A1

Description

Method for determining a spring constant for a deformable scanning probe microscope element, and scanning probe microscope and calibration device arranged for determining a spring constant for a probe element

5 TECHNICAL FIELD

The invention relates to a method for determining a spring constant k for a deformable scanning probe microscope element, to a calibration device for measuring the spring constant for the deformable scanning probe microscope element, and to a scanning probe microscope.

10 Furthermore, the invention relates to a computer program arranged to perform the proposed method, and a computer readable medium comprising such a computer program.

BACKGROUND

15 Scanning probe microscopy (SPM) is a branch of microscopy in which surface images are formed by scanning a probe element across a sample surface and measuring the probe-surface interaction as a function of position. SPM probes are basically elastically deformable cantilever structures with a sharp probe tip structure or projected portion at a free end. Atomic force microscopy (AFM) constitutes a specific SPM 20 application in which the positional dependence of the force acting on the cantilever structure is recorded. In AFM, the accuracy of the cantilever spring constant strongly influences the accuracy of the force ultimately registered by the cantilever probe. The spring constant of a typical rectangular AFM cantilever depends on its dimensions and material properties, and is theoretically calculated by k = Ebt3/413, where E is the elastic 25 modulus, b is the probe width, t is the probe thickness, and 1 is the probe length. The geometrical and material parameters are difficult to control during fabrication of the cantilever probe. Any deviation from nominal thickness and length values, as well as material defects and resulting changes in the elastic modulus, can introduce significant error in the theoretically calculated spring constant k, yielding inaccurate force 30 measurements. Furthermore, contaminations accumulated on the surface of the cantilever probe may also alter the value for the spring constant k. The uncertainty in the cantilever spring constant necessitates calibration of a SPM probe element, before it can be used in any scanning measurements.

2

The probe tip adds to the overall mass and also the spring constant of the cantilever probe. As a result, known resonance frequency based measurement methods do not yield sufficiently accurate SPM probe spring constant determinations.

In Rana et al, ref.[l], a method and device are described in which a calculated 5 electrostatic force is applied to an AFM cantilever probe having a probe tip at a free probe end. Electrostatic actuation of the cantilever probe is achieved by means of the fringing part of an inhomogeneous electric field that is laterally symmetric with respect to the cantilever probe. This electric field is generated by two actuation electrodes that are laterally displaced with respect to the cantilever probe. The horizontal configuration 10 of the actuation electrodes leaves open a space for free vertical movement of the cantilever probe. The vertical motion can be induced by varying the inhomogeneous electric field. Electrostatically actuated deflection of the cantilever probe may subsequently be measured by using a laser based deflection measurement device. The stable states of cantilever probe deflection are a result of the electromechanical 15 equilibrium maintained between the externally applied electrostatic forces and the restoring mechanical forces within the cantilever probe. The spring constant k is determined by correlating the probe deflection to the applied voltage to capacitance of the structure and the gap size.

A disadvantage of the device and method of Rana et al is that accurate 20 measurement of static cantilever displacement is required, which is hard to realize in practice. In particular, it requires accurate measurement of at least two states of cantilever displacement and exerted electrostatic force, in order to determine the cantilever spring constant k. Furthermore, strong electric fields are required for calibrating relatively stiff cantilever probes, for only the relatively small fringing 25 component of the electric field is responsible for the actuation.

SUMMARY

It is an object to provide a method of measuring or calibrating a spring constant of a SPM probe element including a probe tip, having improved calibration accuracy.

30 This object is achieved by providing a method according to claim 1.

Recently, the electrostatic pull-in instability (EPI) has been shown to be a robust and versatile method for characterizing mechanical properties of nanocantilevers within the framework of nanoelectromechanical systems (NEMS). In that particular framework, 3 EPI measurements have been introduced in order to improve the measurement accuracy of resonant cantilever based mass sensors. The details of this method are described for example in Sadeghian et al, ref. [2],

In the framework of scanning probe microscopy, a field in which the emphasis is 5 mainly on the mechanical properties of the devices, it is commonly considered that pull-in and stiction of the SPM probe element with respect to any surface (e.g. the scannable surface) should be avoided due to its destructive effect on the probe tip. This fact is for instance mentioned in the description of the method and device by Rana et al, ref.[l], where the necessary measures have been taken in order to avoid the occurrence 10 of pull-in. In particular, it can be observed that the device described in Rana et al employs an actuation electrode configuration with two laterally spaced electrode poles (similar to a horse-shoe) that cannot be used to create electrostatic pull-in instability for the deformable probe element, and therefore cannot be used to perform a method of measuring the spring constant k of the probe element based on EPI.

15 In Brugger et al, ref. [3], a SPM device is discussed comprising a cantilever probe with a probe tip and a probe electrode combined with an actuation electrode at a distance from the cantilever probe. Here, the spring constant k of the cantilever probe is assumed to be known in advance, and is not measured by the configuration presented. Deflection of the cantilever probe during force measurements is measurable by 20 determination of a varying capacitance between the respective electrodes. An electric source is provided for applying a bias potential difference between the probe electrode and the actuation electrode, in order to generate static or harmonic stable deflection states of the cantilever probe. Although the cantilever-electrodes system by Brugger et al would in principle allow EPI of the cantilever probe and snapping of the electrodes, 25 the configuration was not designed to have any calibration functionality, and again EPI is explicitly avoided here.

Bonaccurso et al, ref. [4] describe an AFM device also comprising a cantilever probe with a probe tip and a probe electrode. The cantilever probe can be deflected in the direction of the probe tip side of the cantilever and toward an actuation electrode 30 surface, as a result of an applied electrostatic potential difference between the electrodes. Calibration of the spring constant k of the cantilever probe is executed by analytic modeling of the balanced forces acting on the cantilever probe, yielding electromechanically stable states of deflection, but again avoiding EPI.

4

Due to the general conviction of avoiding pull-in in measuring SPM spring constants, the possibilities for using EPI measurement in SPM spring constant calibration have not been explored up till now.

Highly accurate spring constant determination of the EPI based measurement 5 method is enabled for SPM calibration by eliminating the detrimental effects (i.e. damage to the probe tip, stiction of the electrodes) by appropriate measures according to aspects of the invention. Advantageously, by deflecting the deformable probe element into a contacted state of the actuation electrode with only a contact portion of the tip-less area of the deformable probe element, the tip area is excluded from the 10 region of impact. As a result, the scanning probe tip is prevented from damaging on impact between the deformable probe element and the actuation electrode, and the EPI potential difference measurement can be employed for spring constant determination. Various configurations for preventing damage to the scanning probe tip are described hereafter. As the scanning probe tip remains intact during accurate calibration of the 15 spring constant, the scanning probe structure can subsequently be used in accurate SPM measurements.

According to an embodiment, the method comprises deflecting the deformable probe element out of the contacted state of the actuation electrode with only the contact 20 portion of the tip-less area, while measuring the EPI-potential difference Vpi.

Deflectional measurement on the deformable probe element starting from a contacted state will enable various method embodiments in which pull-in of the probe element into a contacted state can be alternated with release to a non-contacted state, leading to time-efficient sequences of EPI-potential difference measurements.

25

According to an embodiment, the method comprises providing the actuation electrode apart from and facing the first side of the deformable probe element, wherein the contact portion is located on the first side, and wherein the actuation electrode is provided with a saving space for accommodating the scanning probe tip of the 30 deformable probe element in the contacted state of the actuation electrode with only the contact portion, and deflecting the deformable probe element towards the first side into the contacted state of the actuation electrode with only the contact portion.

5

The method embodiment according to a configuration having an actuation electrode facing the first side of the deformable probe element on which the probe tip is located is particularly suitable for execution in a dedicated calibration device. In such a calibration device, the actuation electrode can be relatively large, and accurately 5 characterized and controlled.

According to an embodiment, the method comprises providing the actuation electrode apart from and facing a second side of the deformable probe element, the second side being opposite to the first side, wherein the contact portion is located on 10 the second side, and deflecting the deformable probe element towards the second side into the contacted state of the actuation electrode with only the contact portion.

The method embodiment according to a configuration having an actuation electrode facing the second side of the deformable probe element on which the probe tip is not located is particularly suitable for execution in an augmented scanning probe 15 microscope. The actuation electrode located above the deformable probe element does not interfere with a measurement sample present below the deformable probe element and its probe tip.

According to an embodiment in which the actuation electrode is spatially 20 separated from the probe electrode by an initial gap distance gO, the method comprises providing at least one of the actuation electrode and the deformable probe element with positioning means for controllably adjusting the initial gap distance gO; registering a first EPI-potential difference Vpil between the probe electrode and the actuation electrode separated by a first initial gap distance gl; adjusting the first initial gap 25 distance gl to a second initial gap distance g2; registering a second EPI-potential difference Vpi2 between the probe electrode and the actuation electrode separated by the second initial gap distance g2, and deriving the spring constant k for the deformable probe element, based on the first EPI-potential difference Vpil, the second EPI-potential difference Vpi2, the first initial gap distance gl and the second initial gap 30 distance g2.

Advantageously, a change in gap distance gO during execution of the method will enable differential gap measurements in which at least two different values gl, g2 for the initial gap distance, and at least two corresponding values for the EPI-potential 6 difference Vpil, Vpi2 can be obtained. With this, the requirement of obtaining accurate knowledge of the initial gap distance gO in deriving the spring constant is avoided.

According to other aspects and in accordance with the advantages described 5 above, a scanning probe microscope and a calibration device according to claims 9 and 13 are provided.

According to an embodiment of the scanning probe microscope, the actuation electrode is spatially separated from the probe electrode by an initial gap distance gO, 10 and at least one of the actuation electrode and the deformable probe element is provided with positioning means for controllably adjusting the initial gap distance gO. This enables differential gap distance measurements, as described above, and also enables a pull-in measurement in which the value of the initial gap distance is swept until pull-in is achieved, instead of or in addition to controllably varying the potential 15 difference V between the probe electrode and the actuation electrode during the pull-in measurement.

According to an embodiment of the scanning probe microscope, the EPI deflection detector comprises an optical source for emitting a source beam of optical 20 radiation towards the deformable probe element, and an optical detector for receiving a return beam of optical radiation reflected by the deformable probe element, and wherein the actuation electrode is facing a second side of the deformable probe element and is positioned in-between the deformable probe element and the EPI deflection detector, the actuation electrode being a transparent actuation electrode that allows 25 transmission of the optical radiation.

Advantageously, by providing the actuation electrode on the second side of the deformable probe element on which the scanning probe tip is not present, a deflection of the deformable probe element towards the actuation electrode will leave the scanning probe tip out of the contact area, eliminating any chance of damage by 30 collision. The transparent actuation electrode enables transmission of the optical beam emitted by the optical source towards the deformable probe element, and enables transmission of the optical beam reflected by the deformable probe element back to the optical detector. This method embodiment is applicable to existing SPM cantilever 7 probes with an optically reflective surface for reflecting the optical deflection measurement beam. Therefore, by augmenting an existing SPM in accordance with the configuration described (or by providing a calibration device in an analogous configuration), the method according to the embodiments proposed above may be 5 efficiently executed without substantial alteration to the SPM probe.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols 10 indicate corresponding parts, and in which: FIG. la presents a schematic view of an embodiment of a scanning probe microscope capable of calibrating the spring constant of a SPM probe element; FIG. lb schematically shows a deformable probe element and an actuation electrode in a contacted state; 15 FIG.2 presents a schematic view of an embodiment of a calibration device for calibrating the spring constant of a SPM probe element; FIGs.3a-3d show flow charts for embodiments of a method of SPM probe spring constant determination; FIGs.4a-4e show several scanning probe element and actuation electrode 20 configurations, according to various embodiments of the scanning probe microscope and of the calibration device; FIG.5 presents a schematic block diagram of a computer arrangement.

The figures are only meant for illustration purposes, and do not serve as restriction of the scope or the protection as laid down by the claims.

25

DETAILED DESCRIPTION

The proposed spring constant calibration device, scanning probe microscope, and corresponding spring constant determination method will yield accurate spring constant calibration measurements.

30 Commonly, scanning probe microscopy is associated with the scanning of a surface area of a sample object by means of various physical interactions between the scanning probe and the sample surface. Nevertheless, the stiffness calibration device and determination method described here should not be conceived as being limited to 8 two/three-dimensional scanning applications. Instead, the stiffness calibration device and determination method described here are readily extendable to the applications of force spectroscopy and stiffness spectroscopy, which are inherently one-dimensional functions of a measured physical quantity. Modified SPM probes are commonly used 5 for such spectroscopy applications, and the inclusion of spectroscopy applications into the various aspects of the invention is implied here.

The pull-in effect

The term “electrostatic pull-in instability (EPI)” refers to the critical kinematic 10 state in which an initially electromechanically stable structure reverts to an unstable state. This EPI state or point of a structure is dictated by the geometrical and mechanical structure properties, as well as by the electric forces applied to the structure. The applied electric force may be associated with a potential difference applied between electrodes located on or near the structure. Above a corresponding 15 critical value Vpi of such an applied potential difference, also known as the “pull-in voltage Vpi” or the “EPI potential difference Vpi”, the structure becomes unstable and as a consequence will suddenly snap, buckle or otherwise deform, also referred to as “pull-in”. When an applied potential difference is increased from zero, the increasing electrostatic forces cause deflection with increasing mechanical restoring forces 20 attempting to balance the electrostatic force, until the EPI voltage is reached. Once the EPI voltage is reached, the mechanical restoring force can no longer compete with the electrostatic force and as a result, the structure will pull-in.

It is this description and accompanying drawings, values for the electric potential difference V and values for the EPI potential difference Vpi are defined as the positive 25 difference in electric potential measured between two points in an electric circuit. In case the potential difference is determined in a reversed (negative) order, then an appropriate change in any of the inequalities referred to in the description and the drawings is implied.

30 Scanning probe microscope

According to a first aspect, a functional scanning probe microscope design is added with components for determining a spring constant k for a deformable SPM probe element, e.g. by building an improved SPM or augmenting an existing SPM with 9 the components and functionality described below. With the proposed SPM, determination of the spring constant k of the deformable probe element may be executed prior to any SPM measurement.

FIG. la schematically shows a perspective view of an embodiment of a SPM 100, 5 provided with means for deriving the spring constant k of a deformable SPM probe element 102. In FIG. la, a SPM 100 is shown comprising a micro- or nano-electromechanical deformable probe element 102 having an outer surface area consisting of a tip area 112 and a tip-less area 113. The deformable probe element 102 comprises a scanning probe tip 104 for SPM scanning purposes. The scanning probe tip 10 104 is located on a first side 108 of the deformable probe element 102. This scanning probe tip 104 is mechanically connected to the deformable probe element 102 in the tip area 112 of the outer probe surface. In contrast, the tip-less area 113 covers the area of the outer probe surface that excludes the tip-area 112 in which the probe tip 104 is located.

15 In general, at least a part of the deformable probe element 102 will have some electrical charge retaining capability (i.e. electrical capacitance) or a non-uniform electrical charge distributive capability (electrical polarizability). This part of the deformable probe element 102 may function as a probe electrode 114. The deformable probe element 102 is therefore said to comprise a probe electrode 114. For example, the 20 deformable probe element 102 may be provided with an electrically conducting structure (e.g. a layer) that partially or completely covers the outer surface of the deformable probe element 102.

The deformable probe element 102 shown in FIG.la constitutes a cantilever probe 103 for which the main part of the mechanical structure consists of a cantilever 25 that is fixed at one end to a probe base 106, while the cantilever probe 103 is able to deform (e.g. deflect) in a free region. In the description below, reference is made to cantilever probes 103, which are commonly used probe element. Nevertheless, the method and features described below are equally applicable to cantilevers with integrated channels or perforations (e.g. for etching accessibility during cantilever 30 fabrication), or to deformable probe element 102 of different configuration, such as triangular probes, multi-legged probes, paddle probes, and doubly or multiply clamped beam probes.

10

As shown in FIG. la, the cantilever probe 103 is suspended above a scannable surface 101 of a sample, which surface structure is to be scanned by the SPM 100 during use. The sample with the scannable surface 101 is not necessarily part of the SPM 100. The probe electrode 114 and the cantilever probe 103 may be provided as 5 separate structures, or may alternatively be integrated into a single element. The probe electrode 114 is arranged to alter the deformation state of the cantilever probe 103 by means of electrostatic forces. For this purpose, the SPM 100 is provided with an actuation electrode 116 that is spatially separated from the probe electrode 114, at least for the cantilever probe 103 being in an initially non-actuated electromechanically 10 stable state. In general, the main function of the actuation electrode 116 is to provide electrostatic actuation of the deformable probe element 102. In the embodiment of FIG. la, the actuation electrode 116 is provided on a second side 110 of the cantilever probe 103.

The SPM 100 comprises an electrical source 120 for applying a potential 15 difference V between the probe electrode 114 and the actuation electrode 116.

Electrical terminals of the electrical source 120 are electrically connected to the probe electrode 114 and the actuation electrode 116, in order to convey the potential difference V. A strength for the applied potential difference V may be selected such that the deformable probe element 102 is forced into an electromechanically unstable 20 state, and deflected into a contacted state of the actuation electrode 116 with the deformable probe element 102.

Here, and in the entire specification, the “contacted state” refers to a mechanical state in which physical contact is established between at least a portion of the actuation electrode 116 and a further specified portion of the deformable probe element 102 25 particular to various aspects. In various embodiments, this physical contact may involve some intermediate structures located in-between the at least one portion of the actuation electrode 116 and a portion of the deformable probe element 102. The contacted state may also involve the establishment of electrical contact between portions of the probe electrode 114 and the actuation electrode 116, and/or of any of the 30 intermediate structures, although this is not required. In essence, the stationary contacted state represents a mechanical bound to electromechanically unstable EPI states of the deformable probe element 102, the non-actuated electromechanically stable state representing an opposite bound.

11

In order to determine the EPI potential difference Vpi for the deformable probe element 102, the electrical source 120 may generate a range of voltage outputs V, preferably adjustable in a controlled fashion. The electrical source 120 is not necessarily an integral part of the scanning probe microscope 100, but may be a 5 separate unit connectable for spring constant measurement purposes. In general, both the actuation electrode 116 and the probe electrode 114 can be set at a bias potential difference V0. The selected polarity (positive/negative charge distribution) of the actuation electrode 116 and the probe electrode 114 is immaterial here.

10 FIG. lb schematically shows the deformable probe element 102 and the actuation electrode 116 in the contacted state, resulting from the EPI deflection of the deformable probe element 102 into the contacted state of the actuation electrode with only a contact portion 115 of the tip-less area 113 of the deformable probe element 102. In order to prevent the probe tip 104 from damaging on impact following EPI deflection, the 15 contacted state of the actuation electrode 116 with the deformable probe element 102 corresponds to a physical contact between at least a portion of the actuation electrode 116 and only the contact portion 115 of the tip-less area 113 of the deformable probe element 102.

By employing any of the spatial configurations shown in FIGs.l, 2, or 4a-4e (or 20 variations having interchanged elements as described with reference to FIGs. 4a-4e), the tip area 112 including the scanning probe tip 104 is effectively excluded from physical contact with the actuation electrode 116, when the deformable probe element 102 is in the contacted state.

25 According to FIG.la, the scanning probe microscope 100 may comprise an EPI

deflection detector 121 for detecting a deflection of the cantilever probe 103. For example, the EPI deflection detector 121 may be arranged for generating a displacement signal specific to a certain probe deflection w of the cantilever probe 103 from a non-actuated initial position. This probe deflection w may be caused in 30 particular by the applied potential difference V. As a minimum requirement, the EPI deflection detector 121 is able to generate an EPI detection signal once the cantilever probe 103 assumes an electromechanically unstable EPI state, and/or if the cantilever probe 103 reverts from an EPI state back to an electromechanically stable state. In this 12 way, the EPI deflection detector 121 is able to measure an EPI potential difference Vpi between the probe electrode 114 and the actuation electrode 116, although the measurement may be executed indirectly by generating a triggering signal for effectuating a sampling of the applied potential difference Y between the probe 5 electrode 114 and the actuation electrode 116 at the moment at which the EPI point is traversed. EPI deflection detection of the deformable probe element 102 will generally occur prior to or simultaneous with registering the EPI-potential difference Vpi between the probe electrode 114 and the actuation electrode 116.

The EPI deflection detector 121 for detecting an EPI deflection of the deformable 10 probe element 102 may be based on at least one of optical deflectional, optical interferometric, optical vibrometric, electrical capacitance, electrical potential, electric current, electric resistance, piezoresistive, piezoelectric, magnetomotive, and visual deflection sensing methods, implementations of which are described with reference to FIG’s.4a-4e.

15 In many atomic force based SPMs 100, a deflection measurement device that is based on detection of a laser beam reflected by the deformable probe element 102 is already present. This laser based deflection measurement device provides force induced probe deflection based sensing for scanning of the scannable surface 101. This laser based deflection measurement device may also be employed as EPI deflection detector 20 121 for detecting the moment of EPI deflection (i.e. “snapping”) of the deformable probe element 102 towards and in contact with the actuation electrode 116. In FIG.la, the EPI deflection detector 121 comprises an optical source 124 for emitting a source beam of optical radiation towards the deformable probe element 102, and an optical detector 126 for receiving a return beam of optical radiation reflected by the 25 deformable probe element 102. The actuation electrode 116 in FIG.la, which is facing the second side 110 of the deformable probe element 102, and which is positioned in-between the deformable probe element 102 and the deflection measurement device 121, essentially consists of optically transparent material, yielding a transparent actuation electrode 117 that allows transmission of the optical radiation emitted by the optical 30 source 124 and reflected towards the optical detector 126.

In general, the scanning probe microscope 100 shown in FIG. la further comprises a control unit 122 that is arranged to determine the spring constant k of the 13 deformable probe element 102 (e.g. cantilever probe 103), based on the registered EPI potential difference Vpi.

Calibration device 5 According to another aspect, a constant calibration device 200 is provided arranged for determining a spring constant k for a deformable probe element 102 of a scanning probe microscope 100. As a result, the measurement of the spring constant k of the deformable probe element 102 must be performed separately from SPM sample scanning measurements, but enables batch calibration procedures as described below.

10 FIG.2 schematically depicts an embodiment of a calibration device 200 for calibrating the spring constant k of a deformable SPM probe element 102. In the embodiment of FIG.2, the deformable probe element 102 comprises a scanning probe tip 104 on a first side 108 of the deformable probe element 102. The deformable probe element 102 further has a probe electrode 114. In addition, the calibration device 200 is 15 provided with an actuation electrode 116 that is spatially separated from the deformable probe element 102 with the probe electrode 114 by an initial gap distance gO.

The calibration device 200 shown comprises an electrical source 120 for applying a potential difference V between the probe electrode 114 and the actuation electrode 116. In order to deflect the deformable probe element 102 towards and in contact with 20 the actuation electrode 116. In the embodiment of FIG. 2, damage to the scanning probe tip 104 on contact of the deformable probe element with the actuation electrode 116 is (partially) realized by providing the actuation electrode 116 at a location facing the first side 108 of the deformable probe element 102. As a further contributor to preventing damage to the probe tip 104, the actuation electrode 116 is provided with a 25 saving space 210 for accommodating the scanning probe tip 104 on impact of the deformable probe element 102 with the actuation electrode 116.

The calibration device 200 comprises an EPI deflection detector 121 (not shown in FIG.2) for measuring an EPI-potential difference Vpi between the probe electrode 114 and the actuation electrode 116. According to the configuration shown in FIG.2, 30 the EPI deflection detector 121 may be implemented by means for measuring voltage, current, resistance or capacitance between the probe electrode 114 and the actuation electrode 116, or alternatively between the probe electrode 114 and an additional measurement electrode 218 provided on the actuation electrode 116. Electrical 14 separation of the actuation electrode 116 and the additional measurement electrode 218 requires an electrically insulating layer 219 between these electrodes 116, 218.

In FIG.2, the actuation electrode 116 of the calibration device 200 is further provided with positioning means 220 for controllably adjusting the initial gap distance 5 gO between the actuation electrode 116 and the deformable probe element 102, from a first initial gap distance value gl to a second initial gap distance value g2. This positioning means 220 enables various embodiments for the spring constant k determination method, as described with reference to FIGs.3b-3d.

Furthermore, the calibration device 200 comprises a control unit 122 arranged to 10 derive the spring constant k of the deformable probe element 102 based on the measured EPI-potential difference Vpi.

Control unit FIGs.la and 2 show that both the scanning probe microscope 100 or calibration 15 device 200 may comprise a control unit 122 that is communicatively coupled to the SPM 100 or calibration device 200. In the embodiments shown, the control unit 122 is arranged to control the voltage output of the electrical source 120. The control unit 122 may be integrally formed with the SPM 100 or calibration device 200, or may represent a spatially separated unit like a computer arrangement communicatively coupled to the 20 remaining components of the SPM 100 or calibration device 200. The computer arrangement may for example be communicatively coupled to the SPM 100 or calibration device 200 via a wired connection (e.g. wires, a cable, a wired local area network (LAN), etc.) or a wireless connection (e.g. a Bluetooth link, a wireless LAN, an infrared (IR) link, etc.). Details of a control unit 122 comprising a computer 25 arrangement are described below with reference to FIG.5.

Method: Measurement of EPI

FIGs.3a-3d show four flow charts representing embodiments of a method of determination of the spring constant k for a deformable SPM probe element 102.

30 Analogous to the description given with respect to the SPM 100 and the calibration device 200, the deformable probe element 102 according to the method generally has an outer probe surface area consisting of a tip area 112 and a tip-less area 113. The deformable probe element 102 comprises a scanning probe tip 104 for 15 scanning purposes, which is located on a first side 108 of the deformable probe element 102. This scanning probe tip 104 is mechanically connected to the deformable probe element 102 in the tip area 112 of the outer probe surface. Furthermore, the tip-less area 113 involves the area on the outer surface of the deformable probe element 102 that 5 excludes the tip-area 112. In general, at least part of the deformable probe element 102 has electrical capacitance to some extent, this part at least being able to act as a probe electrode 114. For example, the deformable probe element 102 may be provided with a structure e.g. a layer that partially or completely covers the outer surface of the deformable probe element 102. The method further comprises the provision of an 10 actuation electrode 116 that is spatially separated from the deformable probe element 102.

A first action of the method may be the obtainment of a probe parameter set S describing the physical probe parameters (e.g. probe shape, probe dimensions, electrical permittivity ε in the gap, effective electrostatic actuation area of the 15 deformable probe element, etc), indicated by action number 300 in FIGs.3a-3d.

Obtaining the probe parameter set S may involve separate prior measurement, or may imply advance knowledge of the respective values. The manner of obtaining the probe parameter set S (action 300) constitutes no limiting factor of the current method.

In general, the method comprises varying a potential difference Y applied 20 between the probe electrode 114 and the actuation electrode 116, an action indicated in FIGs.3a-3d by reference numbers 303 (increasing the potential difference V) and 304 (decreasing the potential difference). Variation of the voltage output of the electrical source 120 may be continuous, or may be executed in discrete steps.

The method generally comprises deflecting the deformable probe element 102 25 into a contacted state between the actuation electrode 116 and only a contact portion 115 of the tip-less area 113 of the deformable probe element 102.

The method also generally comprises registering or measuring an EPI-potential difference Vpi between the probe electrode 114 and the actuation electrode 116, an action indicated by reference numbers 316-318 in FIGs.3a-3b.

30 According to embodiments of the method, EPI deflection of the deformable probe element 102 may be initiated from an initially electromechanically stable non-contacted state of the deformable probe element 102, indicated by reference number 301 in FIGs.3a-3d. After EPI deflection, the deformable probe element 102 will be in the 16 (pulled-in) contacted state, for which the EPI-potential difference Vpi will be determined.

According to other embodiments of the method, registration of the EPI potential difference Ypi may be executed while releasing the deformable probe element 102 5 from an initially pulled-in (i.e. contacted) state in which the probe electrode 114 and actuation electrode 116 are touching. Here, EPI deflection or release of the deformable probe element 102 is initiated from an initially contacted state of the deformable probe element 102, indicated by reference number 302 in FIGs.3a-3d. After EPI release, the deformable probe element 102 will be in a final electromechanically stable non-10 contacted state, for which the EPI-potential difference Vpi will be determined. This in turn requires that the deformable probe element 102 has been previously deflected into a contacted state of the actuation electrode 116 with only a contact portion 115 of the tip-less area 113 of the deformable probe element 102. Therefore, according to various embodiments, the method further comprises deflecting the deformable probe element 15 102 out of the contacted state of the actuation electrode 116 with only the contact portion 115 of the tip-less area 113, while measuring the EPI-potential difference Vpi. Embodiments of the SPM 100 or calibration device 200 may allow for determination of the spring constant k based on any or both of deflection into pull-in and release from pull-in.

20 According to specific embodiments of the method, the EPI deflection of the deformable probe element 102 is to be detected, an action indicated in FIGs.3a-3d with reference numbers 310 (detecting EPI pull-in deflection) and 312 (detecting release from EPI pulled-in state). Therefore, the method may comprise providing an EPI deflection detector 121 for detecting an EPI deflection of the deformable probe element 25 102 based on at least one of optical reflectional, optical interferometric, optical vibrometric, electrical capacitance, electrical potential, electric current, electric resistance, piezoresistive, piezoelectric, magnetomotive, and visual deflection sensing methods, and subsequently detecting the EPI deflection 310, 312 of the deformable probe element 102. Detection of EPI deflection 310, 312 is to be executed prior to 30 registering the EPI-potential difference Vpi 316,317,318 between the probe electrode 114 and the actuation electrode 116.

According to embodiments of the method conforming to the calibration device shown in FIG.2, the deformable probe element 102 may be deflected towards the first 17 side 108. Here, the method may comprise the provision of the actuation electrode 116 apart from and facing the first side 108 of the deformable probe element 102, wherein the contact portion 115 is located on the first side 108, and wherein the actuation electrode 116 is provided with a saving space 210 for accommodating the scanning 5 probe tip 104 of the deformable probe element 102 in the contacted state of the actuation electrode 116 with only the contact portion 115. The method may then further comprise deflecting the deformable probe element 102 towards the first side 108 into the contacted state between the actuation electrode 116 and only the contact portion 115.

10 According to alternative specific embodiments of the method that conform to the embodiment of the SPM 100 shown in FIG. la, the deformable probe element 102 may be deflected towards the second side 110 opposite to the first side 108 (shown in FIG. lb). Here, the method may comprise the provision of the actuation electrode 116 apart from and facing the second side 110 of the deformable probe element 102, 15 wherein the contact portion 115 is located on the second side 110. The method may then further comprise deflecting the deformable probe element 102 towards the second side 110 into the contacted state of the actuation electrode 116 with only the contact portion 115.

Finally, the method generally comprises deriving the spring constant k for the 20 deformable probe element 102, based on the measured EPI-potential difference Vpi. This final action is indicated in FIGs.3a-3b by reference number 328.

The EPI potential difference is registered 316, 317, 318 by identifying the event that the probe electrode 114 and actuation electrode 116 snap together. At the EPI point 25 of the deformable probe element 102, which in general is a state in which the electrodes 114, 116 are not touching, a small motion of the deformable probe element 102 towards the actuation electrode 116 will result in a net force of attraction between the probe and actuation electrodes 114, 116. This attractive force will further decrease the distance between the electrodes. Once the EPI point is reached, the deformable probe element 30 102 can no longer maintain stability. The smallest disturbance will cause the electrodes to move closer together. When this pull-in effect occurs, the unbounded mechanical deflection of the deformable probe element 102 will eventually result in snapping i.e. establishment of physical contact between the probe and actuation electrode 114, 116.

18

As a consequence, the EPI point and corresponding EPI potential difference may be registered by increasing the applied potential difference and monitoring the current flowing between the first and actuation electrode 114, 116. For this purpose, an ammeter may be provided anywhere in series within the resulting current conducting 5 path, except in between and short circuiting the probe electrode 114 and actuation electrode 116. The EPI potential difference is identified by detecting a sudden current increase. Before snapping, the current I between the electrodes 114, 116 may be near to zero. After snapping, a sudden surge of current I flowing between the probe electrode 114 and actuation electrode 116 may be detected by monitoring the power output of the 10 electrical source 120 or by recording I-V curves. The current I generated by the electrical source 120 may be limited or even cut-off rapidly after snapping, in order to protect the components from overheating.

Alternatively, the potential difference V applied between the probe electrode 114 and the actuation electrode 116 may be monitored. For this purpose, a voltmeter (not 15 shown) may be provided anywhere in parallel in an (not necessarily closed) electrical circuit comprising the probe electrode 114, the actuation electrode 116, and the electrical source 120. By monitoring a steadily increasing adjustable potential difference V between the probe electrode 114 and actuation electrode 116, it is possible to measure the occurrence of pull-in by registering a temporary voltage drop, resulting 20 from the electrodes 114, 116 snapping together and establishing electrical contact. The potential difference V may be monitored between the probe electrode 114 and the actuation electrode 116. For safety reasons, an extra resistor component (not shown) may be adopted in the circuit, in order to protect the circuit from a strong short circuit current. The voltage drop indicates the traversal of the EPI-potential difference Vpi.

25 Alternatively, because the applied potential difference V is a controlled and known parameter, the measured current I may also be interpreted as a resistance R detection by applying Ohms law.

Other circuit configurations can be conceived by the skilled person for registering the EPI-potential difference Vpi by marking a sudden change in the electrical behavior 30 in the circuit comprising the probe electrode 114, the actuation electrode 116, and the electrical source 120.

Moreover, abrupt mechanical movement of the cantilever beam may indicate the occurrence of snapping. In this case, the measurement of the EPI-potential difference 19

Vpi may be realized by monitoring the bending of the deformable probe element 102 and detecting the characteristic abrupt change in the bending amplitude when the first and actuation electrodes 114, 116 snap together. In general, abrupt bending of the deformable probe element 102 may be determined using various deflection 5 measurement devices 121 and corresponding methods e.g. laser deflection, or piezoresistive, piezoelectric, capacitive or magnetomechanical based methods. Mechanical contact of the probe electrode 114 and actuation electrode 116 does not necessarily involve the establishment of electrical contact. For example, an electrically insulating layer 219 may be provided on at least one of the electrodes 114, 116, located 10 in-between the electrodes 114, 116.

Method: Basic EPI measurement. FIG.3a FIG.3a displays two alternative embodiments of the method, in which a pull-in measurement initiating from an electromechanically stable non-contacted state of the 15 deformable probe element 102 is shown on the left, and in which a release from pull-in measurement initiating from a contacted state of the deformable probe element 102 is shown on the right. As a first action, the probe parameter set S is obtained 300. The actuation electrode 116 is spatially separated from the probe electrode 114 by an initial gap distance gO. The method embodiments shown in FIG.3a may comprise the action 20 of measuring the initial gap distance gO, indicated by reference number 320.

Alternatively, the initial gap distance gO may be known in advance for example from a highly accurate manufacturing process. Analogously, an initial state of bending of the deformable probe element 102 with respect to the actuation electrode 116 (e.g. an initial bending angle: not shown) may be measured prior to the EPI potential difference 25 Vpi measurement, or may be known in advance.

In one of the alternative embodiments shown in the left branch of FIG.3a, an initial potential difference V0 applied between the probe electrode 114 and the actuation electrode 116 is below the expected EPI-potential difference Vpi, yielding the initially electromechanically stable state 301. The potential difference V is 30 subsequently increased 303, until the deformable probe element 102 is deflected to a contacted state of the actuation electrode 116 with only a contact portion 115 of the tipless area 113 of the deformable probe element 102. This EPI deflection into a pulled-in state is detected 310.

20

In the second of the alternative embodiments shown in the right branch of FIG.3a, an initial potential difference VO applied between the probe electrode 114 and the actuation electrode 116 is above the expected EPI-potential difference Vpi, yielding the initially electromechanically pulled-in state 302. The potential difference V is 5 subsequently decreased 302, until the deformable probe element 102 is deflected to a released state of the actuation electrode 116. This EPI deflection out of a pulled-in state is detected 312.

In both alternative embodiments shown in FIG. 3 a, the actions of registering the EPI-potential difference Vpi 316, and the optional intermediate actions of constructing 10 324 and solving 327 a differential equation based on the initial gap distance gO, the probe parameter set S, and the registered EPI-potential difference Vpi are executed. These optional intermediate actions for finding the spring constant k are explained below. Finally, derivation of the spring constant k 328 for the deformable probe element 102, based on the registered EPI-potential difference Vpi is executed.

15

Method: Differential gap EPI measurement. FIG.3b FIG.3b shows yet another embodiment of the method, in which pull-in measurement is initiated for a deformable probe element 102 in an electromechanically stable state. As a first action, the probe parameter set S is obtained 300. Here, the first 20 value for the initial gap distance gl between the actuation electrode 116 and the probe electrode 114 may be unknown. Instead, a change in the initial gap distance gO may be exploited in order to derive a value for the spring constant k. For enabling a differential gap distance measurement, a positioning means 220 may provided on at least one of the actuation electrode 116 and the deformable probe element 102. According to an 25 embodiment, the method then comprises measuring a first EPI-potential difference Vpil between the probe electrode 114 and the actuation electrode 116 separated by a first initial gap distance gl. Subsequently, the method comprises adjusting the first initial gap distance gl to a second initial gap distance g2, measuring a second EPI-potential difference Vpi2 between the probe electrode 114 and the actuation electrode 30 116 separated by the second initial gap distance g2, and deriving the spring constant k for the deformable probe element 102 based on the first EPI-potential difference Vpil, the second EPI-potential difference Vpi2, the first initial gap distance gl and the second initial gap distance g2. As only a differential gap distance Ag between the 21 second initial gap distance g2 and the first initial gap distance gl may be obtainable, this differential gap distance Ag alone may suffice to execute this method embodiment.

The loop shown in FIG.3b starts in a first iteration (indicated by x = 1). The initial potential difference YO in FIG.3b is below the expected EPI-potential difference 5 Vpi, yielding the initially electromechanically stable state 301. The potential difference V is subsequently increased 303, until the deformable probe element 102 is deflected to a contacted state of the actuation electrode 116 with only a contact portion 115 of the tip-less area 113 of the deformable probe element 102. This EPI deflection into a pulled-in state is detected 310. The first EPI potential difference Vpil is registered 316. 10 The left branch of the loop shown in FIG.3b is traced backwards by a second iteration (indicated by x = 2). Here, the probe is released from a pulled in state 314 by decreasing the potential difference V to a value that is assumed to be lower than a value of a second EPI-potential difference Vpi2 that is expected for a probe configuration with a second initial gap distance g2 that differs by an amount Ag with respect to the 15 first initial gap distance gl. Subsequently, the initial gap distance is changed by Ag. It may be increased by Ag 321 or decreased by Ag 323. The potential difference V is again subsequently increased 303, until the deformable probe element 102 is again deflected into the contacted state between the actuation electrode 116 and only the contact portion 115 of the tip-less area 113 of the deformable probe element 102. This 20 EPI deflection into the pulled-in state is again detected 310. The second EPI potential difference Vpi2 is subsequently registered 317.

The loop in FIG.3b traversed only once, but in principle the loop can be executed with as many iterations (x = 2, 3, 4, ...) as desired, and the obtained values for the differential gap distance Agx and the registered EPI-potential difference Vpix may be 25 stored by the control unit 122 that may be present in the SPM 100 or calibration device 200 as described.

The iterations may be followed by the optional intermediate action of constructing a differential equation 325 based on the differential gap distance Ag, the probe parameter set S, and the registered EPI-potential differences Vpil, Vpi2. This 30 differential equation may be solved 327, and the spring constant k for the deformable probe element 102 is derived 328.

Method: Differential gap EPI measurement. FIG.3c 22 FIG.3c shows two alternative embodiments of the method, in which a differential gap measurement is executed in an efficient manner. The left branch and the right branch in FIG.3c are complementary: The left branch starts with a pull-in measurement initiating from an electromechanically stable state of the deformable probe element 5 102, and the right branch starts with a release from pull-in measurement initiating from a contacted pulled-in state of the deformable probe element 102. The actions in each branch are traversed in complementary order with respect to the other branch. Only the left branch is explained below.

As a first action, the probe parameter set S is obtained 300. The efficient 10 differential gap measurement in the left branch of FIG.3c shows the initial potential difference Y0 to be below the expected first EPI-potential difference Vpil, yielding the initially electromechanically stable state 301 for the deformable probe element 102.

The potential difference V is subsequently increased 303, until the deformable probe element 102 is deflected to a contacted state of the actuation electrode 116 with only a 15 contact portion 115 of the tip-less area 113 of the deformable probe element 102. This EPI deflection into a pulled-in state is detected 310. The first EPI potential difference Vpil is then registered 316. Advantageously, the initial gap distance is now decreased 323 by a (measurable) differential gap distance Ag, keeping the deformable probe element 102 and the actuation electrode 116 in the contacted state. Subsequently, the 20 potential difference V is decreased 304, until release deflection of the deformable probe element 102 from the pulled-in state is detected 312. The second EPI potential difference Vpi2 is subsequently registered 317, followed by the derivation of the spring constant 328. The latter may require the optional intermediate actions of constructing 325 and solving 327 of a differential equation that is based on the differential gap 25 distance Ag, the probe parameter set S, and the registered EPI-potential differences Vpil, Vpi2.

Method: Decreasing gap EPI measurement. FIG.3d

According to embodiments of the method, the action of varying the potential 30 difference Y 303, 304 may be efficiently substituted by actions wherein the initial gap distance gO is decreased instead, until pull-in of the deformable probe element 102 is achieved. For this purpose, at least one of the actuation electrode 116 and the deformable probe element 102 of the SPM 100 or the calibration device 200 may be 23 provided with positioning means 220 for controllably adjusting the initial gap distance go.

As a first action, the probe parameter set S is obtained 300. Optionally, the first value for the initial gap distance gl may be determined 320. According to the 5 embodiment shown in FIG.3d, a non-zero initial potential difference VO starts out below an expected first EPI-potential difference Vpil corresponding to the first value for the initial gap distance gl, yielding an initially electromechanically stable state 301 for the deformable probe element 102. Subsequently, the initial gap distance gO is decreased 322 (using the positioning means 220), until the deformable probe element 10 102 is deflected by the non-zero initial potential difference V0 to a contacted state of the actuation electrode 116 with only a contact portion 115 of the tip-less area 113 of the deformable probe element 102. This EPI deflection into a pulled-in state is detected 310. The second value for the initial gap distance g2 corresponding to pull-in may be determined 320’ by direct measurement, or by relating the (total) differential gap 15 distance Ag to the initial value for the initial gap distance gl. The non-zero initial potential difference V0 is registered 318, with V0 now corresponding to the EPI-potential difference Vpi for the reduced gap. This is followed by the derivation of the spring constant 328, possibly requiring the optional intermediate actions of constructing 326 and solving 327 of a differential equation that is based on the differential gap 20 distance Ag, the probe parameter set S, and the registered EPI-potential difference Vpi = V0.

Summarizing, the embodiment of the method shown in FIG.3d comprises adjusting the initial gap distance from a first initial gap distance value gl to a second initial gap distance value g2, while applying the potential difference V between the 25 probe electrode 114 and the actuation electrode 116. Alternatively, the potential difference V may be varied also, but is preferably kept at a constant non-zero value V0, while the initial gap distance is varied to the second initial gap distance value g2. In this way, a constant non-zero potential difference V0 applied between the probe electrode 114 and the actuation electrode 116 will be identical to the final EPI-potential 30 difference Vpi that corresponds to the critical value for the initial gap distance gO at which EPI-deflection occurs and the electrodes 114, 116 snap.

24

Any of the proposed actions given above with reference to FIGs.3a-3d may be efficiently combined into new embodiments of the method for determining a spring constant k for the deformable SPM probe element 102. For example, the pull-in measurement shown in the left branch of FIG.3a may be followed by a re-initialization 5 of the initial potential difference VO, and by a subsequent decreasing gap measurement described with reference to FIG.3d. Many other combinations from the proposed set of options in FIGs.3a-3d are conceivable.

Method: Construction of the governing equations 10 In an embodiment of the method, the spring constant k of the deformable probe element 102 may be derived from the measurement of the EPI potential difference Vpi by extracting the spring constant k from solving a mathematical relation between the measured EPI-potential difference Vpi and geometrical and material properties of the deformable probe element 102. In principle, the spring constant k may be extracted by 15 solving an equation involving elementary functions, or by solving a carefully selected differential equation. In general, elementary functions provide rough estimations, while construction and solution of an appropriate differential equation will enable refinement by higher order effects.

In deriving the value for the spring constant k of the deformable probe element 20 102, the method may comprise finding an approximate solution of the following equation:

r - IM

ρι V 21 εΑ

Where gO is the initial gap distance, ε is the permittivity of the material inside the volume created by the initial gap (usually vacuum or air), and A is a surface area of the 25 deformable probe element on which the electrostatic force is exerted i.e. the effective surface area that contributes to the electrostatic load.

Alternatively, the method may comprise finding a solution to an equation that takes the curvature and non-uniform gap distance into account. An example of such an equation is found in ref. [6],

Method: Construction of a differential equation 30 25

Alternatively, the spring constant k of the deformable probe element 102 may be derived by using a non-linear differential equation describing the electromechanical behavior of the deformable probe element 102 with electrodes system subjected to the electrostatic and mechanical forces, together with the appropriate boundary conditions.

5 This differential equation constitutes a mathematical relation between the applied potential difference V and geometrical and material properties of the deformable probe element 102.

The differential equation may already be available, or may be constructed by analysis of the system properties of the deformable probe element 102 with electrodes 10 system, as is represented by actions 324, 325, 326 in FIGs. 3a-3d. The structure of this differential equation is determined by the geometrical properties of the deformable probe element 102, as well as by the way in which the deformable probe element 102 actually deforms. A generic form of a differential equation describing the behavior of a cantilever probe 103 is given by 15 k d = aV2F(gO - w(x),b) ax wherein x is the distance from the probe base 106 along the length direction of the cantilever probe 103, w is the probe deflection, b is the probe width, gO is the initial gap distance between the probe electrode 114 and the actuation electrode 116, a is a 20 constant, and F is a function of the gap distance g = gO - w and of b.

Accordingly, in various embodiments of the SPM 100 and the calibration device 200, the deformable probe element 102 is a cantilever probe 103, and the control unit 122 is arranged to extract the spring constant k for the cantilever probe 103 from a solution of this differential equation having the general form stated above.

25 As an example, the differential equation may have an inverse quadratic dependency of the gap distance function g = gO - w, and may involve a first order correction for the fringing character of the electrostatic field along the width direction near the edges of the cantilever probe 103: 30 frfA-y), sv'b L^gO-.d)' dxA 2[g0-vv(x)] ^ b ) 26

Here, ε is the permittivity of the material inside the volume created by the initial gap (usually vacuum or air). The origin of this differential equation is further explained in Sadeghian et al, ref. [5]. The known geometrical properties of the cantilever probe 103 and the permittivity ε serve as input to the differential equation.

5

Method: Solution of the differential equation

Solution of the non-linear differential equation 328 may proceed in closed form, or the solutions may be approximated by any suitable numerical solution method. In a numerical method, the differential equation may be solved for any of the values of the 10 potential difference V in the range between 0 Volt and the EPI-potential difference Vpi. The measured EPI potential difference Vpi may then be compared to instable solutions for specific EPI potential difference values corresponding to iterated values for the k-parameter. By iteratively solving the differential equation for various values of the spring constant k, the error resulting from a comparison of the calculated EPI-potential 15 difference and the actually measured EPI-potential difference may be minimized.

The generalized differential quadrature method (GDQM) may be used as an approximation scheme. The application of the GDQM in approximating the description of EPI behavior of electro-statically actuated structures is described in Sadeghian et al, ref. [5]. In principle, any computer arrangement with proper coding can be used for 20 finding such approximate solutions. After a solution or approximate solution to the differential equation is found 328, the spring constant k of the cantilever probe 103 may be extracted, represented by action 328 in FIGs. 3a-3d.

Further embodiments 25 According to embodiments of the method of measuring the spring constant k, the method comprises detection of EPI deflection of the deformable probe element 102, prior to measuring the EPI-potential difference Vpi between the probe electrode 114 and the actuation electrode 116. An EPI deflection detector 121 is provided in the SPM 100 or calibration device 200 for the purpose of detecting an EPI deflection of the 30 deformable probe element 102, based on at least one of optical deflectional, optical interferometric, optical vibrometric, electrical capacitance, electrical potential, electric current, electric resistance, piezoresistive, piezoelectric, magnetomotive, and visual deflection sensing methods. In addition, the a gap determination device 406 may be 27 provided in the SPM 100 or calibration device 200, for measuring an initial gap distance gO between the actuation electrode 116 and the probe electrode 114, based on at least one of optical deflectional, optical interferometric, optical vibrometric, and electrical capacitance observation methods.

5 In FIGs.4a - 4e, various configurations for the deformable probe element 102 and the actuation electrode 116 provided with an EPI deflection detector 121 and/or a gap determination device 406 are shown, according to various embodiments of the scanning probe microscope 100 and of the calibration device 102.

FIG.4a shows a configuration in which the deformable probe element 102, which 10 is on one end fixed to a probe base 106, is provided with a layer of electrically conductive material forming the probe electrode 114 located on an upwards facing second side 110 of the deformable probe element 102. The actuation electrode 116 is located above and at a distance from this second side 110. The electrical source 120 for applying the potential difference V between the respective electrodes 114, 116 is not 15 shown. The deformable probe element 102 will be deflected upwards as a result of an increasing potential difference V between the respective electrodes 114,116, corresponding to the pulled-in state shown in Fig.lb. The deflection is directed away from a downward facing first side 108 of the deformable probe element 102, on which the scanning probe tip 104 is attached. An initial gap distance gO is present between a 20 lower side of the actuation electrode 116 and the second side 110 of the deformable probe element 102 with the probe electrode 114. The actuation electrode 116 is on the lower side provided with an anti-stiction structure 408 at a location on which the deformable probe element 102 will physically contact the actuation electrode 116 in a contacted state. The anti-stiction structure 408 presents a minimum contact pattern.

25 FIG. 4b shows an alternative configuration, in which the deformable probe element 102, which is on one end fixed to a probe base 106, is provided on an upward facing second side 110 with a layer of electrically conductive material forming the probe electrode 114. The scanning probe tip 104 is attached on an other end of the deformable probe element 102 on a downward facing first side 108 of the deformable 30 probe element 102. Located below and at a distance from the first side 108 is the actuation electrode 116. The electrical source 120 for applying the potential difference V between the respective electrodes 114, 116 is again not shown. As a result of an increasing potential difference V between the respective electrodes 114, 116, the 28 deformable probe element 102 will be deflected downwards in a direction corresponding to the first side 108. The initial gap distance gO is present between an upper side of the actuation electrode 116 and the first side 108 of the deformable probe element 102. Not shown is the result of the deflection of the deformable probe element 5 102 into a contacted state between the actuation electrode and only a contact portion 115 of the tip-less area 113 of the deformable probe element 102. This contacted state is a result of the deformable probe element 102 having been previously forced into an electromechanically unstable (EPI) state. According to known SPM/AFM implementations, the deformable probe element 102 may be provided with piezo-10 resisitve or piezo-electric layers (or even a magnetostriction based sensor) constituting electro/magnetomechanical detection means 410 for detecting or measuring deflection of the deformable probe element 102. According to FIG.4b, a piezo layer and conductive connections may be provided, forming the electromechanical detection means 410. This electro/magnetomechanical detection means 410 may be employed as 15 the EPI deflection detector 121 for detecting the occurrence of EPI-deflection of the deformable probe element 102. A saving space 210 is provided for accommodating the scanning probe tip 104 in case the deformable probe element 102 and the actuation electrode 116 are in the contacted state. The actuation electrode 116 may on an upper side be provided with an anti-stiction structure 408. In FIG.4b, the anti-stiction 20 structure 408 stretches over an area larger than only the location where the deformable probe element 102 physically contacts the actuation electrode 116 in a contacted state.

FIG.4c shows yet another configuration, which is similar to the configuration shown in FIG.4a, but here the actuation electrode 116 and the deformable probe element 102 are each provided with positioning means 220 for controllably adjusting 25 the initial gap distance gO between the actuation electrode 116 and the deformable probe element 102 (from a first initial gap distance value gl to a second initial gap distance value g2). In general, any one or both of the actuation electrode 116 and the deformable probe element 102 may be provided with positioning means 220. Such positioning means 220 may for example be formed by a piezoelectric actuator capable 30 of changing the relative distance between the actuation electrode 116 and the deformable probe element 102 by several nanometers. The provision of positioning means 220 enables differential gap based EPI-potential difference measurements, as well as changing gap with constant potential difference V based EPI-potential 29 difference measurements, as described with reference to FIGs.3b-3d. Shown in FIG.4c is an additional measurement electrode 218 provided on the lower side of the actuation electrode 116. The additional measurement electrode 218 is electrically separated from the actuation electrode 116 by an intermediate electrically insulating layer 219. The 5 pair consisting of the probe electrode 114 and the measurement electrode 218 represent a capacitor structure or current conducting switch, that may be used as EPI deflection detector 121 for measuring an EPI-potential difference Vpi between the probe electrode 114 and the actuation electrode 116, or as a gap determination device 406 for detecting a change in the initial gap distance gO between the actuation electrode 116 and the 10 deformable probe element 102.

FIG. 4d shows yet another configuration that is identical to the configuration shown in FIG.la, as was earlier described.

FIG. 4e shows yet another configuration that is similar to the configuration shown in FIG.4a. Here, the actuation electrode 116 is provided with optical waveguides 15 412 that are at least partially located inside bores that run through the actuation electrode 116. The configuration in FIG.4e further comprises at least one optical source 124, and at least one optical detector 126. At least one such optical waveguide 412 may serve as a transmission line for the electromagnetic radiation emitted by the optical source 124. The electromagnetic radiation emitted by the optical source 124 is coupled 20 into the optical waveguides 412 by known methods and is transmitted through the optical waveguide 412 towards the deformable probe element 102. At the lower side of the actuation electrode 116, the electromagnetic radiation is coupled out of the optical waveguides 412, and directed towards the second side 110 of the deformable probe element 102. There, the electromagnetic radiation is reflected by the probe electrode 25 114 having an electromagnetically (optically) reflective top surface. Reflected electromagnetic radiation is again coupled into at least one of the optical waveguides 412 and transmitted there through towards the optical detector 126. A beam splitter 414 located within the paths of the electromagnetic radiation emitted by the optical source 124 and the reflected electromagnetic radiation enables interferometry based 30 measurement of a deflection of the deformable probe element 102. The resulting interferometer may be employed as an EPI deflection detector 121 for detecting a sudden EPI deflection of the deformable probe element 102, as well as a gap 30 determination device 406 for detecting a change in the initial gap distance gO between the actuation electrode 116 and the deformable probe element 102.

The features of the configurations described above may be interchanged in order 5 to obtain various embodiments for the SPM 100 or the calibration device 200. The embodiments may be provided with any or all compatible combinations of electric capacity based EPI deflection detection means, electric potential based EPI deflection detection means, electric current based EPI deflection detection means, electric resistance based EPI deflection detection means, electromechanical based EPI 10 deflection detection means, magnetomechanical based EPI deflection detection means, optical interferometry based EPI deflection detection means, optical reflection based EPI deflection detection means, as well as electric capacity based gap determination means, optical interferometry based gap determination means, optical reflection based gap determination means, and differential gap determination means.

15

The SPM deformable probe element 102 may be constructed from Si, SiN or SiC. Optionally, it may be coated with extra layers of selected materials. In AFM applications for example, the backside (i.e. the second side 110) of the deformable probe element 102 is often coated with an optically reflective metal layer (e.g. gold).

20 In general, deformable probe elements 102 made of softer materials (e.g. SiN) are preferably made shorter and/or thinner than deformable probe elements 102 made of harder materials (e.g. Si). The cantilever probe 103 presented in the embodiments of FIGs.4a-4e, can be easily designed as a long, thin and very small structure. Probe dimensions of commercially available Si cantilever probes 103 may typically range 25 from 70 - 540 micrometers for the length, 20 - 55 micrometers for the width, and 800 -10200 nanometers for the thickness. Probe dimensions of commercially available SiN cantilever probes 103 may typically range from 30 - 120 micrometers for the length, 1.6-36 micrometers for the width, and 140 - 1000 nanometers for the thickness.

Other sizes like nanometer sized deformable probe elements 102 and/or materials 30 are possible.

Cantilever probes 103 are often used in AFM (SPM) applications, because they allow for relatively simple force measurement as well as mathematical analysis.

31

However, it is to be understood that many different micro- or nanoelectromechanical deformable probe elements 102 suffice for SPM measurements, and consequently for carrying out the invention. In alternative embodiments of the method, the calibration device 200, and/or the SPM 100, the deformable probe element 102 may comprise an 5 arbitrarily shaped patch of elastic material, being held by a plurality of supports, the remainder of the patch being allowed to deform. The deformable probe element 102 may for example comprise a double cantilever with a connected free end, having improved sensitivity for torques and resulting torsional deflection about a central axis along the length direction of the double cantilever. Also, the deformable probe element 10 102 may be a multiply clamped beam, held in place by multiple supporting structures.

A beam-shaped deformable probe element 102 incorporating paddles is also possible.

Different geometries, materials require different mathematical expressions relating the EPI potential difference to the spring constant k. A person skilled in the art will be able to derive or approximate these expressions. Inevitably, the sensitivity, 15 measurement range, and reliability of the SPM 100 will change with differing geometric and material properties of the probe element 102 used.

Computer arrangement

In FIG. 5, a block diagram is given of a computer arrangement 500 that may be 20 employed to carry out the method according to the invention. The computer arrangement 500 shown is spatially separated and in communication with the other components of the SPM 100 or the calibration device 200.

The computer arrangement 500 may comprise at least one processor 502, a volatile memory 504, and a non-volatile memory 506. The computer arrangement 500 25 may also include one or more I/O devices 508.

The processor 502 is arranged for carrying out arithmetic operations. The volatile memory 504 may include, for example, a random access memory (RAM). The nonvolatile memory 506 may include, for example, one or more of a hard disk (HD), a read only memory (ROM), an erasable programmable ROM (EPROM), an electrically 30 erasable programmable ROM (EEPROM), a CD ROM, a DVD, a flash memory, etc. Not all of these memory types need necessarily be provided. Moreover, these memory components need not be located physically close to the processor 502 but may be located remote from the processor 502.

32

The processor 502, the volatile memory 504, the non-volatile memory 506 and I/O devices 508 may be interconnected via one or more address/data buses 518. The volatile memory 504, the non-volatile memory 506 and I/O devices 508 may be coupled to the processor 502 via one or more separate address/data buses (not shown), 5 and/or via separate interface devices (not shown) coupled directly to the processor 502.

The computer arrangement 500 may also include input units 510 for inputting instructions, data, etc. by a user. These units may comprise one or more of a keyboard 511, a mouse 512, a tracker ball, a touch pad, a touch screen, a voice converter, etc. Other known input units may also be provided.

10 The computer arrangement 500 may comprise one or more visible output units, like a printer 516 for printing output data on paper. Furthermore, the computer arrangement may comprise at least one graphical display unit 515 like a monitor or LCD (Liquid Crystal Display) screen, a plasma display panel, or any other type of display.

15 The processor 502 may be connected to a communication network 520, for instance, the Public Switched Telephone Network (PSTN), a Local Area Network (LAN), a Wide Area Network (WAN), the Internet, etc. by means of the I/O unit 508. The processor 502 may be arranged to communicate with other communication arrangements through the network 520.

20 The non-volatile memory 506 may be represented by a computer readable medium 522. Exemplary computer readable media 522 are a compact disk (CD), a floppy disk, a tape, a digital versatile disk (DVD), a Blu Ray disk, or a memory stick. Other types of computer readable media 522 may be used.

The computer arrangement may be provided with a reading unit 524 that is 25 connected to the processor 502, and is arranged to read data from and possibly write data on the computer readable medium 522.

In some embodiments, the EPI potential difference Vpi collected by the SPM 100 or the calibration device 200 may first be stored on the computer readable medium 522 and then transferred to the computer arrangement 500 via the computer readable 30 medium 522.

It is to be understood that the computer arrangement 500 shown in FIG. 5 is merely one example of a computing arrangement 500 that may be employed. Many other types of computer devices may be used as well. In general, the computer 33 arrangement 500 may comprise, for example, an analogue circuit, a digital circuit, a mixed analogue and digital circuit, and/or a processor with associated memory. The computer arrangement 500 may for example refer to a desktop computer, a laptop computer, a workstation, a server, a mainframe, a tablet PC, a personal digital assistant 5 (PDA), a telephone, a navigation device, a car radio, etc.

Method execution

Execution of the method may be implemented in part or in whole via a computer program product for execution by the processor 502. Any of the memory units 504, 10 506, 522 may be provided with the computer program product comprising instructions and data arranged to be read by the processor 502 and, after being read, allowing the processor 502 to perform a method in accordance with the embodiments. Such a computer program product may then be loaded in one of the memory components 504, 506. However, such computer program product may, alternatively, be downloaded via 15 the telecommunication network 520. A person skilled in the art will readily appreciate that the entire computer program product or parts thereof may alternatively be executed by a device other than the processor 502 and/or be incorporated in firmware and/or dedicated hardware in a known manner.

The computer arrangement 500 may be provided with a database 526 stored in 20 one or several of the memory units 504, 506. The database 526 may contain for example thermal expansion coefficient values representative for the materials contained by the deformable probe element 102, in order to predict and compensate for the changing probe dimensions due to an ambient temperature. Also, values for electric permittivity ε may be contained by the database 526 in order to tailor the executed 25 calculations to the medium located in-between the electrodes 114, 116 and generate an accurate prediction of the electrostatic field resulting from the applied potential difference V. Furthermore, the database 526 may contain specifics of predefined deformable probe elements 102 (e.g. the physical probe parameter set S) as well as specifics of pre-defined actuation electrodes 116.

30 The processor 502 may be implemented as standalone system, or as a plurality of parallel operating processors each arranged to carry out subtasks of a larger computer program, or as one or more main processors with several sub-processors. Parts of the 34 functionality of the invention may even be carried out by remote processors communicating with processor 502 through the network 520.

Furthermore, one or more of the method actions referred to in FIGs.3a-3d may alternatively be implemented by other types of devices, such as an analog circuit, a 5 digital circuit, a mixed analog and digital circuit, etc.

Batch spring constant measurement

Under conditions described hereafter, the proposed method may be used in batch spring constant k measurement/calibration procedures. In batch measurements, 10 parallelism in the actuation and EPI-detection of a plurality of deformable probe elements 102 is employed. AFM deformable probe elements are typically fabricated on semiconductor wafers, and then mechanically separated to be distributed individually. The proposed batch stiffness calibration may be implemented on the wafer level by subjecting the wafer containing the plurality of deformable probe elements 102 to an 15 actuation stage. In the actuation stage, an increasing potential difference Y may be applied over the electrodes 114, 116 of each of the plurality of deformable probe elements 102, until all probe elements are pulled-in (or until a maximum protection value is reached). The initial gap distance gO may be measured at different regions of the wafer. Alternatively, determination of the initial gap distance gO may be avoided by 20 using the differential gap measurement method as described. During increase of the potential difference V, the EPI-deflection and corresponding EPI-potential difference Vpi may be registered for each of the plurality of deformable probe elements 102. A plurality of EPI deflection detectors 121 that is required may employ optical means, requiring for example an array of laser beams. The plurality of EPI deflection detectors 25 121 may alternatively employ electrical means, requiring for example an array of electrical wire connections, possibly with a matrix addressing system, to the plurality of probe electrodes 114 and the plurality of actuation electrodes 116. Alternatively, a multiplexing method for EPI detection may be employed, in which the plurality of deformable probe elements 102 may consist of a number of units that is an integer 30 multiple of a further number of units in the plurality of EPI deflection detectors 121.

Then, the plurality of EPI deflection detectors 121 may be grouped and operated to register EPI deflection of corresponding further numbers of deformable probe elements 102 in sequence.

35

The descriptions above are intended to be illustrative, not limiting. It will be apparent to the person skilled in the art that alternative and equivalent embodiments of the invention can be conceived and reduced to practice, without departing from the scope of the claims set out below.

5

REFERENCES

[1] S. Rana, P.M. Ortiz, A.J. Harris, J.S. Burdess, C.J. McNeil, “An electrostatically actuated cantilever device capable of accurately calibrating the cantilever on-chip for 10 AFM-like applications”, J. Micromech. Microeng. 19, pp.1-11, 2009 [2] H. Sadeghian, J. F. L. Goosen, A. Bossche, F. van Keulen “Application of electrostatic pull-in instability on sensing adsorbate stiffness in nanomechanical resonators”, Thin Solid Films 518, pp. 5018-5021, 2010 15 [3] J. Brugger, N. Blanc, Ph. Renaud, N.F. Rooij, “Mircolever with combined integrated sensor/actuator function for scanning force microscopy, Sensors and Actuators A 43, pp. 339-345, 1993 20 [4] E. Bonaccurso, F. Schönfeld, H. Butt, “Electrostatic forces acting on Tip and

Cantilever in Atomic Force Microscopy”, Phys. Rev. B 74 (085413), 2006

[5] H. Sadeghian, G. Rezazadeh, P. M. Osterberg, “Application of the Generalized Differential Quadrature Method to the Study of Pull-in Phenomena of MEMS

25 Switches.” J. Microelectromech. Syst. 16, pp. 1334-1340, 2007.

[6] H. Yuh-Chung, “Closed form solutions for the pull-in voltage of micro curled beams subjected to electrostatic loads”, J. Micromech. Microeng. 16 (3), p.648, 2006.

30

Claims

A method for determining a spring constant k for a deformable probe element (102) of a scanning probe microscope (100), wherein the deformable probe element (102) comprises: 5. a probe electrode (114) ); an outer surface consisting of a needle area (112) on a first side (108) of the deformable probe element (102), and a needle-free area (113); a field probe needle (104) in the needle region (112); wherein the method comprises: 10. providing a drive electrode (116) spatially separated from the deformable probe element (102); varying a potential difference V applied between the probe electrode (114) and the drive electrode (116); characterized by 15. deflecting the deformable probe element (102) into a contacting state of the driving electrode (116) with only a contact portion (115) of the needleless region (113) of the deformable probe element (102) ; registering an EPI potential difference Vpi between the probe electrode (114) and the drive electrode (116); 20. deriving the spring constant k for the deformable probe element (102) based on the recorded EPI potential difference Vpi.

2. Method according to claim 1, comprising: deflecting the deformable probe element (116) from the contacting state of the drive electrode (116) with only the contact portion (115) of the needleless region (113), prior to the registering the EPI potential difference Vpi.

The method of claim 1 or 2, comprising: 30. providing the drive electrode (116) separated from and directed to the first side (108) of the deformable probe element (102), the contact area (115) being located on the first side (108), and wherein the driving electrode (116) is provided with a recess (210) for accommodating the field probe (104) of the deformable probe element (102) in the tangent state; 5. deflecting the deformable probe element (102) toward the first side (108) into the tangent state between the drive electrode (116) and only the contact portion (115).

The method of claim 1 or 2, comprising: providing the drive electrode (116) separated from and directed to a second side (110) of the deformable probe element (102), the second side (110) facing the first side (108), the contact area (115) being located on the second side (110); diverting the deformable probe element (102) toward the second side (110) into the tangent state between the drive electrode (116) and only the contact portion (115).

5. Method as claimed in any of the claims 1-4, comprising: providing an EPI deflection detector (121) for detecting an EPI deflection of the deformable probe element (102) based on at least one of optical reflective, optically interferometric, optically vibrometric, electrically capacitive, electric potential, electric current, electric resistance, piezo-resistive, piezoelectric, magnetomotor, and visual perception methods; detecting the EPI deflection (310,312) of the deformable probe element (102), prior to registering the EPI potential difference Vpi (316, 317) between the probe electrode (114) and the drive electrode (116) ;

The method of any one of claims 1 to 5, wherein the drive electrode (116) is spatially separated from the probe electrode (114) by an initial gap distance g0, the method comprising: providing a gap determination device (406) for measuring the initial gap distance g0 based on at least one of optically reflective, optically interferometric, optically vibrometric, and electrically capacitive observation methods; 5. determining the initial gap distance g0 (320) prior to deflecting the deformable probe element (102) into the tangent condition between the driving electrode (116) and only the contact portion (115) of the deformable probe element (102).

The method of any one of claims 1-5, wherein the drive electrode (116) is broadly separated from the probe electrode (114) by an initial gap distance g0, the method comprising: providing at least one of the drive electrode (116) ) and the deformable probe element (102) with positioning means (220) for controllably adjusting the initial gap distance g0; registering a first EPI potential difference Vpil (316) between the probe electrode (114) and the drive electrode (116) separated by a first initial gap distance g1; adjusting the first initial gap distance g1 to a second initial gap distance g2 (322); registering a second EP1 potential difference Vpi2 (317) between the probe electrode (114) and the drive electrode (116) separated by the second initial gap distance g2; deriving the spring constant k (328) for the deformable probe element 25 (102), based on the first EPI potential difference Ypi 1, the second EPI potential difference Vpi2, the first initial gap distance g1 and the second initial gap distance g2.

8. Method as claimed in any of the foregoing claims, wherein the deformable probe element (102) is a cantilever probe (103), and wherein deriving the spring constant k for the cantilever probe (103) comprises: dissolving a differential equation (327) of the general form k - Mx), b) dx where x is the distance from the probe base along a probe length direction, w the probe deflection from initial position, b the probe width, gO the initial gap, α a 5 constant, and F a function of the gap distance g = gO - w and of b.

A scanning probe microscope (100), comprising: a deformable probe element (102) having an outer surface consisting of a needle area (112) and a needle-free area (113), the deformable probe element (102) having a probe electrode ( 114), and further comprising a field probe (104) on a first side (108) in the needle region (112); a driving electrode (116) spatially separated from the deformable probe element (102); an electrical source (102) for applying a potential difference V between the probe electrode (114) and the drive electrode (116) for deflecting the deformable probe element (102) into a tangent state between the drive electrode ( 116) and only a contact area (115) of the needleless area (113) of the deformable probe element (102); characterized in that the scanning probe microscope (100) comprises: 20. an EPI deflection detector (121) for detecting an EPI deflection of the deformable probe element (102), and for registering an EPI potential difference Ypi between the probe electrode (114) and the drive electrode (116), and a control unit (122) adapted to derive a spring constant k for the deformable probe element (102), based on the recorded EPI-25 potential difference Ypi between the probe electrode (114) and the drive electrode (116). 1 Screen probe microscope (100) according to claim 9, comprising an anti-dictation structure (408) located on a surface part (118) of the driving electrode (116) facing the deformable probe element (102), the anti-constitution structure (408) is adapted to reduce stiction between the driving electrode (116) and only a contact area (115) of the deformable probe element (102) in a tangent state.

The field probe microscope (100) according to any of claims 9-10, wherein the drive electrode (116) is spatially separated from the probe electrode (114) by an initial gap distance g0, wherein at least one of the drive electrode (116) and the deformable probe element (102) is provided with positioning means (220) for controllably adjusting the initial gap distance g0.

A scanning probe microscope (100) according to any of claims 9-11, wherein the EPI deflection detector (121) comprises an optical source (124) for transmitting a source beam of optical radiation to the deformable probe element (102), and an optical detector (126) for receiving a return beam of optical radiation reflected by the deformable probe element (102), and wherein the driving electrode (116) is directed to a second side (110) of the deformable probe element ( 102) and is disposed between the deformable probe element (102) and the EPI deflection detector (121), the drive electrode (116) being a transparent drive electrode (117) that allows transmission of the optical radiation.

A calibration device (200) for calibrating a spring constant k of a deformable probe element (102) of a scanning probe microscope (100), wherein the deformable probe element (102) has an outer surface consisting of a needle region (112) on a first side (108) of the deformable probe element (102) and a needleless area (113), the deformable probe element (102) comprising a probe electrode (114), and a field probe needle (104) in the needle area (112), wherein the calibration device (200) comprises: - a probe holder (202) for holding the deformable probe element (102); - a driving electrode (116) spatially separated from the deformable probe element (102) if present; 30. an electrical source (120) for applying a potential difference Y between the probe electrode (114) and the drive electrode (116) for deflecting the deformable probe element (102) into a tangent state between the drive electrode (116) and only a contact portion (115) of the needleless region (113) of the deformable probe element (102); characterized in that the calibration device (200) comprises: 5. an EPI deflection detector (121) adapted to detect an EPI deflection of the deformable probe element (102) and to register an EPI potential difference Ypi between the probe electrode (114) and the drive electrode (116); - a control unit (122) adapted to derive the spring constant k on the basis of the registered EPI potential difference Vpi; 10. wherein the calibration device (200) is adapted to perform the method steps according to any of claims 1-8.

A computer program product configured to provide instructions for performing a method according to any of claims 1-8 when loaded on a computer arrangement (400).

Computer readable medium (422) comprising a computer program product according to claim 14. 25