Preamplifying cantilever and applications thereof

Aspects of the invention are directed to piezoresponse force analysis of a material. A stimulus signal including a first frequency component is applied to a contact point on the material such that the stimulus signal actuates a portion of the material to experience a motion as a result of a piezoelectric effect. A resonant device is coupled to the contact point such that the resonant device experiences a resonant motion at the first frequency component in response to the motion of the material, the resonant motion having a greater displacement than a displacement of the motion of the material, and is substantially unaffected by mechanical properties of the material at the contact point. The resonant motion of the resonant device is detected and processed to produce a measurement representing the piezoresponse of the material at the contact point.

FIELD OF THE INVENTION

The invention relates generally to scanning probe microscopy and related applications, such as data storage, and, more particularly, to scanning probe microscopy techniques in which the sample surface is actuated to produce a motion to be measured, such as piezoresponse force microscopy apparatus and techniques, for example.

BACKGROUND OF THE INVENTION

Piezoresponse force microscopy (PFM) is a contact mode scanning probe microscopy (SPM) technique, which in its most basic form is used to measure out-of-plane and in-plane displacement response of ferroelectric and piezoelectric materials. For simplicity, hereinafter, the term piezoelectric will be used generally to denote materials having piezoelectric properties, including ferroelectric materials. The PFM technique is based on the reverse piezoelectric effect, where a piezoelectric material expands or contracts upon applying an electric field to the material. PFM is an example of the more general subset of SPM techniques that investigate surface motion of an actuated material that is actuated as part of the measurement technique.

PFM is described generally in Shijie Wu,Application Note: Piezoresponse Force Microscopy, Agilent Technologies (2007), which is incorporated by reference herein. In PFM, the scanning probe microscope probes a sample's mechanical response to an applied electric field. Both, contact, and non-contact techniques for PFM are known. PFM enables measurements and characterization of piezoelectric behavior of materials on the nanometer, and sub-nanometer scale. For instance, PFM can measure the electromechanical response of a material on the level of individual nanometer-scale grains. The PFM has been shown to delineate regions of different piezoresponse with sub-nanometer lateral resolution.

In PFM a micromachined probe is typically situated at the end of a cantilever. The probe tip used in PFM is usually made of, or is coated with, a conductive material, as this conductivity facilitates the electrical contact between the probe tip and the sample of material being analyzed. In contact mode PFM, an AC stimulus signal with an optional DC offset bias is applied to the probe tip, which is held in contact with the sample surface, and the piezoresponse of this sample is measured from the deflection of the cantilever using known detection techniques such as, for example, inferometry, scanning tunneling microscopy (STM) techniques, piezoelectric sensors, and optical beam techniques.

Vertical motion (i.e., perpendicular to the surface being measured), as well as lateral motion (i.e., parallel to the surface), can be detected. PFM can produce a topographic image of the surface of the sample, a piezoresponse image representing the piezoelectric properties of grains of piezoelectric material, and a phase image representing the polar orientation of the grains. PFM is particularly useful in investigating the nanometer-scale piezoelectric properties of ferroelectrics, which are the subject of intense research and development for their optoelectronic, sensor, and high-density memory applications. The lateral resolution of PFM provides highly localized information about the electromechanical behavior of thin ferroelectric films.

The amplitude and the phase of the motion are detected. This measurement technique permits the piezoresponse (PR) vector of the sample to be quantified. The displacement in the motion of the cantilever in response to PR of the sample of material is usually on the order of picometers per volt of applied AC stimulus. These displacements are detected and processed to produce the PFM measurement. Due to the very small displacements, and given the presence of electrical noise, which is unavoidably encountered in practice, conventional PFM suffers from poor signal-to-noise ratio (SNR). There are practical limits to increasing the amplitude of the AC stimulus to improve the SNR. For different materials, exceeding a certain voltage tends to re-polarize the piezoelectric domains, thereby altering the properties being measured. Accordingly, stimulation signal amplitudes must be kept low, typically necessitating the use of a lock-in amplifier. Indeed, certain materials exhibiting high re-polarization sensitivity to the stimulus signals are particularly difficult to measure using conventional techniques.

In conventional PFM techniques, the frequency of the applied AC stimulus signal has been designed to be far below the fundamental resonance frequency of the cantilever so as to avoid driving the cantilever into resonant oscillations. This is done mainly to facilitate signal processing, since the ability of the analysis system to amplify the signal representing the detected motion is determined by the signal's quality factor, Q. The Q of the contact mode measurement arrangement, with the sample being driven at a frequency far below the cantilever's first resonance, is equal to unity.

More recently, techniques based on contact resonance PFM have been developed. The contact resonance frequency is the frequency at which a system comprising a scanning probe microscope (SPM) probe in contact with an oscillating surface reaches resonance. Contact resonance PFM has been used to amplify the out-of-plane response and also to measure higher order electromechanical coefficients of ferroelectric thin film materials, thereby increasing the SNR for these measurements.

While contact mode resonance techniques offer certain advantages, they also introduce certain limitations. These include the coupling of the cantilever inertia and elastic response of the sample into the measured signal. Additionally, contact resonance characteristics include complex vibration modes, which are affected by the contact area between the probe and the sample in addition to the geometry of the cantilever itself. Accordingly, the resonant frequency and the quality factor Q of the oscillation can vary significantly from point to point on even the same sample. The result, unfortunately, is the introduction of artifacts into the PFM measurement. These effects are difficult to physically quantify and correct, and hence present challenges when interpreting contact resonance PFM data.

Moreover, certain types of PFM analyses are simply not possible using known contact resonance techniques. For instance, contact resonance typically utilizes resonant frequencies of over 100 kHz, which makes contact resonance ill-suited for measuring in-plane motion of piezoelectric domains, since the probe tip does not remain with the surface at those frequencies.

In other applications of scanning probe microscopes, such as impact mode nanomechanical analysis, in particular, techniques have been developed to amplify higher-order harmonics while suppressing the excitation signal. In Turner et al., WIPO Publication No. WO 2007/095360, various preamplifying cantilevers are described for use with dynamic analysis of nanomechanical properties in which the sample material is repeatedly struck in a tapping mode by a probe tip at the end of an indentation cantilever or actuator operating in a tapping mode at a certain excitation frequency. The impacts generate higher-order oscillations, which the preamplifying cantilever of Turner et al. aims to amplify, while suppressing the excitation frequency. While Turner et al. achieve certain kinds of mechanical preamplification using principles of resonance, their approach does not address the challenges introduced by the coupling of the sample's mechanical properties into the measurement of PFM. To the contrary, the main applications discussed in Turner et al. are specifically aimed at measuring the sample's mechanical properties. Thus, Turner et al. provides little, if any, guidance on solving the problems specific to PFM and similar applications in which a de-coupling of the sample's mechanical properties from the measurement is desired.

In view of the challenges discussed above, an in view of other challenges of enhancing PFM performance, a more effective and efficient solution is needed for improving the accuracy and sensitivity of PFM.

SUMMARY OF THE INVENTION

One aspect of the invention is directed to conducting analysis of nanoscale surface motion of a material, such as piezoresponse force analysis. A stimulus signal including a first frequency component is applied to a contact point on the surface of the material such that the stimulus signal actuates a portion of the material to produce a motion as a result of a transduction by the material, such as by a piezoelectric effect, for instance. A resonant device is rigidly coupled to the contact point such that substantially all of the actuated motion of the material is transmitted to the resonant device (i.e. without any detectable damping or additional spring or resonant action) and such that that the resonant device experiences a resonant motion at the first frequency component in response to the motion of the material, the resonant motion having a greater displacement than a displacement of the motion of the material, and is substantially unaffected by mechanical properties of the material at the contact point. The resonant motion of the resonant device is detected and processed to produce a measurement representing the actuated motion of the material at the contact point.

Another aspect of the invention is directed to a preamplifying cantilever arrangement for use with a scanning probe microscope (SPM). The arrangement includes a main cantilever portion having a first operational length defined by a first end and a second end, with the first end being formed such that (when operably mounted in the PFM) the main cantilever portion is supported by the first end. The second end has a protruding tip adapted to contact a surface of a ferroelectric material. A resonator cantilever portion has a second operational length defined by a third end and a fourth end, with the third end being connected to the main cantilever portion.

The main cantilever portion is formed such that, when the preamplifying cantilever is used in a measurement arrangement in which the protruding tip is in contact with a rigid surface of the ferroelectric material, the main cantilever portion exhibits a first set of resonance characteristics that include a first set of fundamental frequencies and their overtones, and the resonator cantilever portion is formed such that it has a second set of resonance characteristics including a second set of fundamental frequencies and corresponding overtones, the second set of resonance characteristics being substantially distinct from any frequency of the first range of fundamental frequencies and at least a substantial portion of the overtones corresponding to first range of fundamental frequencies, such that resonant motion of the resonator cantilever is substantially un-coupled from any resonant motion of the main cantilever portion when the preamplifying cantilever is used in the measuring arrangement.

A measurement arrangement for actuated surface motion analysis of a surface of a material according to another aspect of the invention includes a signal generator, an electrical probe, a resonant cantilever, and a detection system. The signal generator is constructed to generate a stimulus signal having at least an alternating current component at a first frequency, with the stimulus signal adapted to actuate a portion of the surface of the material during measurement to create an actuated motion. The probe has a tip that contacts the surface of the material at a contact point, with the contact being achieved via a controlled probe-sample interaction. The resonant cantilever having a fixed end and a free end, is fixed to the contact point at the fixed end during measurement via a mechanical coupling having a sufficient rigidity such that substantially all of the actuated motion of the material is transmitted to the resonant cantilever. The detection system configured to detect motion of the resonant cantilever during measurement.

In another aspect of the invention, a system is provided for measuring a surface configuration of a material. A signal generator is constructed to generate a stimulus signal having at least an alternating current component at a first frequency, with the stimulus signal being adapted to actuate a portion of the surface of the material. A probe tip is adapted to contact the surface of the material at a positionable contact point established by a relative positioning of the probe tip and the material. The contact is defined based on a constant interaction force between the probe tip and the surface of the material. A positioning system operably couples the probe tip and the material, and is configured to control the interaction force between the probe tip and the surface of the material, and to adjust the relative positioning of the probe tip and the material to re-position the contact point.

A preamplifying cantilever is provided that has a supporting segment and a resonator segment; with the supporting segment being part of the positioning system and having a probe end comprising the probe tip; and the resonator segment being a distinct segment from the supporting segment and has resonant characteristics that substantially differ from resonant characteristics of the supporting segment, and having a first end coupled to the probe tip such that substantially all motion of the probe tip is transmitted to the resonator segment (i.e. without introducing damping or additional resonances). The preamplifying cantilever is electrically coupled to the signal generator such that the supporting segment facilitates a portion of the signal path, and a detector is configured to detect motion of the resonator segment. The system is constructed such that, in operation, the motion of the resonator segment is caused by the stimulus signal actuating the material at the contact point.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

One aspect of the invention is directed to a preamplifying cantilever design that is specifically adapted for enhancing measurement of surface motion of an actual material being subject to actuation that causes the surface motion. Further aspects are directed to techniques featuring the use of mechanical preamplification in the cantilever. Piezoresponse force microscopy (PFM) is one class of scanning probe microscopy (SPM) techniques that create and measure such surface motion and, for the sake of simplicity, the following description features embodiments utilizing that type of application as a representative example of the context in which the principles of the invention can be applied. However, the inventors contemplate applying the principles evident from these embodiments to other, related areas of scanning probe microscopy, in which benefits provided by aspects of the invention may also be applicable. For example, the invention may be applied using any of a variety of techniques for actuating the surface of the sample including, without limitation, techniques that produce a piezoelectric effect, a thermomechanical effect, an electromechanical effect, a magnetic effect, an electrorestrictive effect, or any combination thereof. Accordingly, the scope of the claimed invention is not limited to contact mode PFM implementations, unless such limitation is specifically stated in certain claims, in which case only those certain claims shall be so limited.

As examples of some conventional PFM techniques that can be modified based on principles of the invention, see A. Gruverman, O. Auciello and H. Tokumoto,Imaging And Control of Domain Structures in Ferroelectric Thin Films Via Scanning Force Microscopy” Annu. Rev. Mater. Sci. 1998. 28:101-123, incorporated by reference herein. Also, see C. Harnagea, A. Pignolet, M. Alexe and D. Hesse,Higher-Order Electromechanical Response of Thin Films by Contact Resonance Piezoresponse Force Microscopy, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 53, No. 12, pp. 2309-2322 (December 2006), also incorporated by reference herein. Principles of the invention may be applied to certain ones of those conventional PFM techniques (that are not incompatible with the invention), or to other compatible PFM techniques, to take advantage of one or more benefits provided by aspects of the invention, such as improved SNR, accuracy, and the ability to perform PFM analysis on particularly sensitive materials that were previously un-measurable using conventional technologies.

FIG. 1is a diagram illustrating a measurement arrangement100according to one embodiment of the invention. Measurement arrangement100utilizes a PFM technique in which sample102having certain piezoelectric properties, such as ferroelectric film, for example, is measured utilizing those piezoelectric properties. Probe104has a tip of nanoscale sharpness contacting the surface of the ferroelectric material at contact point105. In the context of SPM, contact implies some degree of interaction force between the material and the probe tip, which can be in the form of attractive and/or repulsive forces. In the context of some aspects of the invention, the contact between the probe tip and the sample is generally constant, and has sufficient interaction that the contact is effectively rigid, or quasi-static (i.e., substantially all of the surface motion is transmitted to the probe tip, with any damping or spring-like interaction being marginal or even undetectable). In one type of embodiment, tip104is so sharp that contact point105is smaller than a single piezoelectric domain of sample102. The tip of probe104is electrically coupled to signal generator106, and facilitates transmission of the output of signal generator106to contact point105. Signal generator106generates a stimulus signal, or excitation signal, which actuates sample102at contact point105.

The stimulus signal includes at least an AC signal component with a particular frequency and amplitude. In one embodiment, the amplitude is adjusted to be as large as practical without disturbing the polarization of the piezoelectric domains being studied. The amplitude is thus set according to the particular material of sample102. Typically, the amplitude is between 100 mV and 10 V; however, there may be applications where amplitudes outside this range may be used. Signal generator may also produce a DC component of the stimulus signal, as depicted at106′ inFIG. 1. The signal path of the stimulus signal from signal generator106includes sample102, probe104, and supporting cantilever108.

Besides providing a signal path for the stimulus signal, supporting cantilever108also supports probe104, and is part of the positioning system that controls the interaction of probe104and sample102. In one embodiment, probe104is integrally formed with supporting cantilever108such that probe104has its probe tip protruding from a surface of cantilever108. According to one type of embodiment, supporting cantilever108has a second end that is fixed. In another embodiment, supporting cantilever108is mounted or otherwise mechanically coupled to a positioning actuator such as the actuator depicted at110ainFIG. 1. When a PFM measurement is being made and probe104is in contact with sample102, the second end is held fixed, even if it is coupled to positioning actuator110a. Also, it should be understood that, in measuring arrangement100during measurement, supporting cantilever108is not technically a cantilever in the structural sense, since both ends are rigidly coupled to the sample and there is consequently no free end; however, consistent with common usage of the term “cantilever” in the SPM arts, the term shall be used to refer to element108even during measurement.

Actuator110acan be used for positioning and re-positioning of cantilever108relative to sample102(and therefore positioning probe104to different contact points105). In one embodiment, actuator110aincludes a Z-actuator for moving cantilever108in a direction perpendicular to the surface of sample102. In a related embodiment, actuator110aincludes a set of X-Y actuators to move cantilever108along directions parallel to the surface of sample102. Actuator110acan be in the form of a piezo tube, or can be any other suitable type of actuator such as piezo stacks, for example, or a combination of the two. Other types of actuators would certainly be well within the spirit of the invention.

In another type of embodiment, the relative positioning of probe108and sample102is accomplished using actuator110bmechanically coupled to the sample. Actuator110bmoves the sample, rather than cantilever108. Actuator110b, like actuator110acan include individual actuators for either the X-Y, or Z, directions, or any combination thereof, and the individual actuators can be of any suitable type. Actuators110aand110bcan also include both coarse and fine positioning actuators associated with separate control loops. In a related embodiment, system100can include a combination of actuators110aand110bsuch as, for example, X-Y motion provided by actuator110b, and Z motion provided by actuator110a. Positioning actuators110aand110bare controlled by positioning controller112, depicted as a proportional-integral controller according to one embodiment. Other types of positioning control can be used in various other embodiments.

When sample102is actuated by the stimulus signal, the piezoelectric domain or domains being excited cause motion of contact point105, thereby moving the probe104. The direction of the motion corresponds to the orientation of the piezoelectric domain(s) being probed. Unlike conventional non-resonance PFM techniques, which detect the motion of the probe tip, or contact resonance techniques, which use a stimulus signal to drive supporting cantilever108into resonant oscillation and detect the resonant motion at the apex of oscillating cantilever108, embodiments of the present invention may utilize a distinct component, resonator114, to amplify and measure the motion of probe104in response to actuation of contact point105. In one embodiment, resonator114is rigidly coupled to contact point105. For example, resonator114can be connected at or near probe104. The coupling is rigid in the sense that any effect on the motion of resonator114that is attributable to the coupling is negligible.

In one embodiment, the end of resonator114that is opposite the end which is at or near probe104is a free end (i.e. uncoupled to any other structure), such that the resonant motion of resonator114is uncoupled from any other motion besides that of contact point105. In a related embodiment, the motion of resonator114is generally unaffected by the mechanical properties of sample102or of the topographic features of the surface of sample102.

In one embodiment, the fundamental resonant frequency of resonator114is lower than the fundamental resonant frequency of supporting cantilever when probe104is in contact with sample102. In another related embodiment, the fundamental resonant frequency of resonator114is higher than the frequency associated with topographical features on sample102.

According to one embodiment, resonator114is designed such that its fundamental resonant frequency and its overtones do not coincide with, and are not close to, the resonant frequency and overtones of supporting cantilever108when probe104is at contact point105. Thus, the resonant characteristics of resonator114are unaffected by the mechanical properties of sample102. Also, with resonator being distinct from the positioning system of measurement arrangement100, the resonant characteristics of resonator114are advantageously unaffected by the mechanical structure of supporting cantilever108and any of the rest of the mechanics of measurement arrangement100.

In a related embodiment, the design of resonator114takes into account the fact that a variety of different materials having correspondingly different nanomechanical properties might be measured by measurement arrangement100. Since the nanomechanical properties of the sample being measured affect the characteristics of contact resonance, it is expected that the resonance characteristics of supporting cantilever108when probe104is at contact point105, would actually constitute a range of frequencies for the fundamental frequency, and a range of frequencies for each of the overtones, with the ranges being defined based on the general range of nanomechanical properties associated with the sample materials that might be measured. Hence, in this embodiment, resonator114is constructed such that its resonant characteristics are well outside of those frequency ranges for the materials for which measurement arrangement100is designed to work.

For the type of embodiment in which resonator114has a free end, its resonant characteristics are relatively simple, being modeled as a simple harmonic oscillator for out-of-plane (i.e., flexural) motion. Advantageously, for this type of embodiment, the geometry and shape of only the resonator affects the resonant characteristics. Thus, for various applications, the resonance frequency can be designed by selecting only the geometry corresponding to the desired resonant frequency, while keeping the overall shape the same.

A second mode of oscillation, torsional oscillation, is also available for resonator114. This mode of oscillation is useful for detecting in-plane motion for piezoelectric domains polarized parallel to the surface of sample102. Thus, measurement arrangement100, in some embodiments, includes signal generator106that produces a first frequency component intended to drive resonator114flexurally, and a second frequency component that is intended to drive resonator114torsionally. The resonant characteristics of resonator114can therefore include each fundamental resonant frequency for flexural and torsional motion, as well as their respective overtones. Since supporting cantilever108also has a torsional resonance, the design of resonator114according to one embodiment avoids the range of frequencies corresponding to torsional resonance of supporting cantilever108and its overtones. In a related embodiment, multiple lock-in frequencies are utilized in lock-in amplifier118corresponding to the different modes of oscillation of resonator114.

In measurement arrangement100, according to one aspect of the invention, the frequency or frequencies at which sample102is actuated are selected to coincide with the fundamental resonant frequency, or frequencies, of resonator114. Accordingly, resonator114responds to actuation of sample102at the contact point with its own motion of a greater displacement than the displacement of the actuated motion of sample102. Additionally, the motion of resonator114is proportional to the actuated motion of sample102at that frequency or frequencies. In this way, resonator114provides a form of mechanical preamplification of the piezoresponse of sample102. In embodiments where both, in-plane, and out-of-plane motion of sample102are analyzed, the flexural and torsional motions of resonator114each provide mechanical amplification.

Motion of resonator114is detected by detection system116. Detection system116, can be embodied by any suitable arrangement. Examples of conventional technologies that form the state of the art and that could be utilized include, without limitation, inferometry, scanning tunneling microscopy (STM) techniques, piezoelectric sensors on the resonator, and optical beam techniques, such as the technique diagrammed inFIG. 1. For instance, in an example of the latter technique, a laser is aimed at the end of resonator114, which in a corresponding embodiment, has a reflective target for the laser formed at its end opposite contact point105. The laser reflects from resonator114onto a photodetector array, the output of which is processed using lock-in amplifier118to produce a measurement corresponding to the piezoresponse corresponding to contact point105of sample102.

Piezoresponse amplitude data, as well as phase data (indicating the relative orientation of the piezoelectric domain of contact point105), is obtained. As sample102is scanned from one contact point105to another, piezoresponse amplitude and phase images of its surface can be constructed of the scanned area of sample102. The output of detection system116is also fed to positioning controller112via low pass filtering120. Hence, the motion of resonator114is also used in the control loop for adjusting the relative positioning of probe104and sample102. The output of positioning controller112comprises driving signals for either actuator110aor110b, or for both. Additionally, the output of low pass filtering120can form an image of the topography of the scanned area of sample102.

Measurement arrangement100, in one type of application, is part of a SPM system such as an atomic force microscope, in which sample102is subject to study. In another application, measurement arrangement100is implemented as part of a data storage system, in which sample102is the medium on which data is stored. In a related application, measurement arrangement100constitutes a part of an array of PFM probes, with each probe having a probe104, an associated resonator114, detection system116, etc.

FIG. 2is a perspective view diagram illustrating a preamplifying cantilever (PAC)200according to one embodiment of the invention. PAC200can be used with a measurement arrangement for conducting PFM of sample202as shown, or for conducting other SPM techniques that would benefit from the mechanical preamplification and other characteristics offered by PAC200. PAC200is a compound cantilever situated along operational axis220. At one end of PAC200, probe tip204protrudes downward, as illustrated. At the other end of PAC220is formed a base209used for handling PAC200and for affixing PAC200to a measurement arrangement (such as to an actuator or to a point of fixation, neither of which is shown inFIG. 2). Resonator214is rigidly connected to probe tip204at one end of resonator beam217, and has a target215at the other end of beam217facilitating optical beam detection methods for detecting motion of resonator214. In the embodiment shown, target215has a surface that reflects a major portion of laser216utilized in an optical beam motion detector. Together, beam217and target215of resonator214have a general paddle-like shape. It should be understood, however, that the shape and geometry of resonator214can take any suitable form within the spirit of the invention, including shapes that do not utilize a target for optical beam motion detection.

The main cantilever portion of PAC220includes beams208aand208barranged in a generally triangular fashion with probe tip204being at the triangle's apex. Beams208aand208bare situated symmetrically about operational axis220in the embodiment shown. Principles of the invention could be used with other suitable arrangements of the main cantilever portion. For example,FIG. 3is a plan view diagram illustrating PAC300according to another embodiment, in which the main cantilever portion consists of a pair of beams,308aand308b, both of which run parallel to operational axis320. Resonator314is situated such that it can oscillate perpendicular to the place defined by beams308aand308b. Other alternative arrangements will be described below, but it is to be understood that those examples are not an exhaustive presentation of the possible configurations for a PAC according to embodiments of the invention.

Turning back toFIG. 2, in PAC200, resonator214is integrally formed with the rest of the cantilever, including main cantilever beams218aand208b, probe tip204, and base209. The fabrication techniques for constructing PAC200are generally known. PAC200can be fabricated using conventional processing steps used for constructing existing SPM cantilevers. For example, the fabrication techniques described in Turner et al., WIPO Publication No. WO 2007/095360, the contents of which are incorporated herein by reference, can be used.

FIG. 4is a graph illustrating the resonant enhancement of the output amplitude of resonator214. The ordinate of the graph is the logarithmic amplitude signal measured at resonator214, and the abscissa of the graph is the drive frequency of the input signal at probe tip204. Curve402represents two orders of magnitude or more improvement measured at resonator214when the resonator is in resonance. In contrast, curve404represents the signal measured at the tip end of cantilever200(on the top surface-opposite the tip) instead of at resonator214.

FIG. 5represents a specific application of the PAC200for piezoresponse force microscopy (PFM). Curve502shows the amplitude of the signal measured on two oppositely polarized domains. Curve504represents the amplitude of the signal measured on the same domains with contact resonance PFM. As described above, inherent challenges with contact resonance PFM include coupling of the mechanical properties of both the sample and the probe into the PFM measurements. Curve506represents the amplitude of the signal measured with regular PFM. Curve508represents the background signal measured for purposes of correcting out the floor noise.

The method of operation of PAC200for the characterization of its amplification, and comparisons to contact resonance-PFM were developed using samples of periodically poled lithium niobate (PPLN). The choice of this material was based on its two characteristics, viz., smooth surface (roughness of <1 nm) and well distinguished ferroelectric domains with vertically up and downward oriented PR vectors of equal amplitude. Thus, one PPLN domain oscillates in phase with the electric field, the other out of phase with it. To make the comparison with contact resonance PFM operation, commercially available cantilevers, of a type known as metal coated etched silicon probe (MESP) (marketed under the trade name Veeco Probes), having nominal length of 225 um, and a spring constant of 2-5 N/m, were chosen because of their accepted general use for PFM studies. The PR vector amplitudes were compared when the applied ac bias frequency was equal to the paddle resonance frequency for PAC200with contact resonance PFM operation of a MESP cantilever, providing a one-to-one comparison. The PR vector amplitudes can be expressed in picometer per volt of applied ac bias by converting the measured signal in mV to picometer using the static displacement sensitivity, also known as the inverse optical lever sensitivity.

For comparison, the method of operation for PAC200was developed analogous to contact resonance-PFM of a MESP. The laser was aligned on target215of PAC200and positioned on the center of a four-quadrant photodiode detector. The probe was then approached to the PPLN sample, and the surface was scanned by maintaining tip-sample force enough to track the surface. An AC bias of 1 V amplitude (2 V peak-to-peak) was applied to the sample. A frequency sweep of the ac bias was performed to measure the first resonance of resonator214. Similarly, for the MESP probe, the laser was aligned at the apex of the cantilever and, once on the PPLN sample, the contact resonance frequency was determined by sweeping the AC bias frequency. The static displacement sensitivities were then determined for both a PAC and a MESP cantilever to convert the response in mV to picometer. Finally, in order to normalize the data the PR vector was converted into picometer (or nanometer) per volt of applied ac bias.

FIG. 6shows the measured PR vector amplitude as a function of frequency for a MESP cantilever operating at its contact resonance (curve602), along with the PR vector amplitude with the laser aligned on target215for PAC200(curve604). The maximum response of MESP cantilever operating in contact resonance-PFM was measured to be about 700 pm/V, whereas the maximum response of PAC200at resonance was measured to be 3000 pm/V. The maximum amplitude reached will depend on the time for which the oscillator was allowed to “ring up.” In order to ensure an equivalent comparison, both MESP and PAC cantilevers were allowed to ring up for the same amount of time. As can be inferred from the measured PR vector amplitudes, the amplitude response of PAC200at resonance is as good as or better than the MESP cantilevers in contact resonance PFM. When comparing amplitudes away from resonance, versus at resonance, at least an order of magnitude improvement (˜3000 pm compared to ˜100 pm) in the signal was measured.

Next, the PR imaging performance of PAC200was evaluated in comparison with that of MESP cantilevers in contact resonance PFM. Data representing the height, PR amplitude, and PR phase scans of the PPLN surface obtained with a MESP cantilever operating at its contact resonance at 338.1 kHz when 1 V amplitude AC bias was applied to the sample, was obtained. Additionally, data representing height, PR amplitude, and PR phase scans were obtained with PAC200operating at a resonator214resonance of 104.5 kHz for the same applied sample bias. The scan velocity was maintained at 70 um/s and the static displacement sensitivity for both MESP as well as PAC was about 78 nm/V. Analysis of the surface scan with the laser aligned on the paddle clearly demonstrated that good topographical imaging is possible using PAC200. Because PAC200is designed such that the frequency of the topographical features is to be much smaller than the paddle resonance of 104 kHz, the height signal had a unity gain for the dc deflection signal with the laser aligned on the paddle.

The domains on the PPLN surface were also clearly distinguishable in the PR amplitude data. A phase difference of 180° was measured between adjacent oppositely polarized ferroelectric domains. In order to compare the response amplitudes and to understand the SNR during scanning, section the analysis as shown inFIG. 7was performed. Curve702denotes the PR amplitude of PAC200, whereas curve704denotes the MESP's PR amplitude. PAC200shows at least three times as much signal as the MESP cantilever, validating the frequency response data fromFIG. 6. Thus the out-of-plane PR vector was completely measured and quantified using PAC200with signals at least as good as, and generally superior to, commonly used MESP cantilevers in contact resonance mode.

In other embodiments of PACs according to aspects of the invention, the arrangement of the resonator relative to other parts of the PAC can vary substantially.FIG. 8is a spring mass diagram illustrating various alternative configurations according to other embodiments. The main spring M and/or M′ is attached to the base B on one end and to a mass Maon the other end. The input signal is measured locally at mass Ma. The resonator spring-mass combinations could be in multiple positions denoted by P, Q, R, S and T, respectively, attached to masses Mp, Mq, Mr, Ms, and Mt, respectively. In one type of embodiment, that the main spring-mass and resonator spring-mass systems are not perpendicular to each other, as illustrated by position T.

Thus, referring briefly toFIG. 2, the resonator can be along the operational axis of the PAC.FIG. 9illustrates another embodiment, in which resonator914of PAC900is situated on the opposite side of the probe tip compared to the configuration of PAC200. If the resonator is mounted parallel to the main cantilever (as R and P inFIG. 8) the flexural resonance of the resonator will be driven by the out-of-plane motion of the sample, and the torsional resonance of the resonator will be driven by the in-plane motion of the sample.

In other embodiments, such as positions Q, S, and T ofFIG. 8, the resonator can be situated off-axis. In the embodiment illustrated inFIG. 10, resonator1014of PAC1000is situated 90 degrees off-axis, as in positions Q and S ofFIG. 8. In this type of perpendicular arrangement, the torsional resonance of resonator is driven by the out-of-plane motion of the sample, and the flexural resonance of the resonator will be driven by the in-plane motion of the sample. In the embodiment ofFIG. 11, corresponding to position T ofFIG. 8, resonator1114of PAC1100is situated at an angle to the operational axis of the cantilever. In this type of arrangement, either flexural or torsional resonances can be excited by in-plane or out-of-plane sample motion depending on the frequency of the sample motion.

In other types of embodiment, as illustrated in combined form inFIG. 12, the resonator can be out of the plane of the main cantilever. For instance, resonators1214band1214care each situated in a plane that is distinct from the plane in which resonator1214ais situated. Accordingly, the flexural motions of each of the cantilevers will respond to correspondingly different vectors of motion of the probe tip due to movement of the sample's surface. The different planes can be orthogonal, as illustrated for PAC1200, or non-orthogonal.

Another type of embodiment shown inFIG. 12is one where more than one resonator is present on a PAC. The multiple resonators can be situated in the same plane, or in different planes, as illustrated for PAC1200. The corresponding measurement arrangement has a separate motion detection system for each resonator. In one embodiment, different types of motion detection systems are used for different resonators. In various embodiments having multiple resonators, the different resonators have the same resonant frequency or, alternatively, different resonant frequencies, depending on the desired application.

FIGS. 13A and 13Billustrate an example embodiment of resonator1300that is designed for increased sensitivity to torsional motion. Resonator1300includes a protruding feature1319that is asymmetrical about a reference plane in which the surface of target1315is defined. In the embodiment depicted inFIGS. 13A and 13B, protruding feature1319is in the form of a tail that projects from the bottom side of the resonator (opposite the surface of target1315). As shown inFIG. 13B, the resulting cross-section is T-shaped. When subjected to forces caused by in-plane motion of the sample during PFM measurement, protruding feature1319enhances the tendency of resonator1300to move torsionally.

Another aspect of the invention is directed to further improving the performance of PFM and other SPM techniques incorporating a dedicated resonator. Embodiments according to this aspect of the invention arise from the challenge presented by electrostatic effects experienced when analyzing or measuring certain types of materials. When scanning a material during PFM, there can be a non-uniform charge distribution of the surface being scanned. This condition is present in periodically poled lithium niobate (PPLN) domains, for example. In cases where the resonator has an intrinsic charge, there can be different DC electric potentials between the resonator and the sample as the resonator passes over different PPLN domains. Since these conditions result in additional forces acting on the resonator, the resonator's resonant frequency can vary during the scan.

Accordingly, in one type of embodiment, the measurement arrangement (such as measurement arrangement100ofFIG. 1) includes an electrostatic charge correction arrangement. In one embodiment of this type, the electrostatic correction arrangement includes a DC bias signal such as DC component106′ (FIG. 1).FIG. 14diagrammatically illustrates a technique for applying DC bias to compensate for the electrostatic effects according to one embodiment.

Other embodiments of an electric charge corrections include preventing static electric fields between the sample and the resonator. In one such embodiment, the air between the resonator and the sample is ionized. Any suitable techniques may be used for ionizing the air, such as using an alpha radiation source. Similarly, in another embodiment, the measuring arrangement provides a polar fluid between the resonator and the sample. In both of these approaches, the static electric field is dissipated through the conductive medium surrounding the resonator and sample. In another embodiment, the electrostatic correction arrangement includes a shielding arrangement positioned between the sample and the resonator. In another embodiment, the measurement arrangement is constructed such that spacing between the resonator and the surface of the sample is so large that the electrostatic effects are marginalized. In a further embodiment, provisions are made to reduce surface charging of the resonator, such as, for example, turning off the laser when the motion of the resonator is not being measured. In yet another embodiment, the sample is coated to reduce its resistance. According to a further embodiment, a resonator that is entirely or substantially non-conductive is utilized.

The embodiments above are intended to be illustrative and not limiting. Additional embodiments are within the claims. In addition, although aspects of the present invention have been described with reference to particular embodiments, those skilled in the art will recognize that changes can be made in form and detail without departing from the spirit and scope of the invention, as defined by the claims.

Persons of ordinary skill in the relevant arts will recognize that the invention may comprise fewer features than illustrated in any individual embodiment described above. The embodiments described herein are not meant to be an exhaustive presentation of the ways in which the various features of the invention may be combined. Accordingly, the embodiments are not mutually exclusive combinations of features; rather, the invention may comprise a combination of different individual features selected from different individual embodiments, as understood by persons of ordinary skill in the art.