PHOTO-INDUCED FORCE MICROSCOPY AND RELATED TECHNIQUES

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application is entitled to the benefit of provisional U.S. Patent Application Serial Number 62/575,338, filed October 20, 2017, which is incorporated herein by reference.

BACKGROUND

[0002] Photo-induced Force Microscopy (PiFM) is based on an atomic force

microscopy (AFM) platform that includes an excitation light source. PiFM measures the dipole induced at or near the surface of a sample by the excitation light source by detecting the dipole-dipole force that exists between the induced dipole in the sample and the mirror image dipole in the metallic AFM tip. The accuracy of PiFM measurements is dependent on various frequencies that are used during different modes of operations, which may drift due to various factors. Thus, these frequency shifts should be compensated to ensure accurate PiFM measurements.

SUMMARY

[0003] A scanning probe microscope and method of operating the microscope, in which a cantilever with a tip of the microscope is driven to vibrate at a dither mode used for topographic imaging and a light source that irradiates an interface between the tip and the sample is modulated in a manner that excites vibration at a detection mode via mixing with the vibration frequency of the dither mode, adjusts modulation frequency of the light source during operation to keep the excitation of the detection mode tracking the resonant frequency of the detection mode.

[0004] A scanning probe microscope in accordance with an embodiment of the invention includes a cantilever with a tip, a light source to irradiate an interface between the tip and a sample, a dither control system coupled to the cantilever that vibrates the cantilever at a dither mode used for topographic imaging, and a modulation control system coupled to the dither control system and the light source to modulate the light source in a manner that excites vibration at a detection mode via mixing with the vibration frequency of the dither mode, and to adjust modulation frequency of the light source during operation to keep the excitation of the detection mode tracking the resonant frequency of the detection mode.

[0005] A method of operating a scanning probe microscope in accordance with an embodiment of the invention includes driving a cantilever with a tip of the scanning probe microscope to vibrate at a dither mode used for topographic imaging, modulating a light source that irradiates an interface between the tip and the sample in a manner that excites vibration at a detection mode via mixing with the vibration frequency of the dither mode, and adjusting modulation frequency of the light source during operation to keep the excitation of the detection mode tracking the resonant frequency of the detection mode.

[0006] Other aspects and advantages of embodiments of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrated by way of example of the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Fig. 1 is a block diagram of a frequency tracking Photo-induced Force

Microscopy (PiFM) system in accordance with an embodiment of the invention.

[0008] Fig. 2 is a flow diagram of a method of operating a scanning probe microscope, such as the PiFM system shown in Fig. 1, in accordance with an embodiment of the invention.

[0009] Throughout the description, similar reference numbers may be used to identify similar elements.

DETAILED DESCRIPTION

[0010] It will be readily understood that the components of the embodiments as generally described herein and illustrated in the appended figures could be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of various embodiments, as represented in the figures, is not intended to limit the scope of the present disclosure, but is merely representative of various embodiments. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated. [0011] The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by this detailed description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.

[0012] Reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the present invention should be or are in any single embodiment of the invention. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussions of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment.

[0013] Furthermore, the described features, advantages, and characteristics of the invention may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize, in light of the description herein, that the invention can be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the invention.

[0014] Reference throughout this specification to "one embodiment," "an

embodiment," or similar language means that a particular feature, structure, or characteristic described in connection with the indicated embodiment is included in at least one

embodiment of the present invention. Thus, the phrases "in one embodiment," "in an embodiment," and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment.

[0015] In Photo-Induced Force Microscopy (PiFM), two vibrational modes of the cantilever are excited. A first mode, referred to as the "dither" mode, is driven by a piezoelectric displacement transducer (the "dither" piezo) at a fraction of a nanometer (nm) amplitude up to as much as a few tens of nm. A second mode, referred to as the "detection" mode, is excited by Photo-Induced Force (PiF) acting between the tip and a sample stimulated by light from a modulated laser source, usually in the infrared (IR) or visible wavelength range. In the current state of the art, the detection mode is not directly excited by modulating the laser at the cantilever mode frequency, but instead is excited by mixing between the dither frequency and the laser modulation frequency. For example, if the dither frequency excites the second vibrational mode of the cantilever at 1.2 Mhz, and the first vibrational mode has a frequency of 0.2 Mhz, then the laser is modulated at the difference frequency of 1.0 Mhz.

[0016] Typically, the two modes of the cantilever are chosen to be the first and second vibrational modes (the two lowest frequency modes of the cantilever). The lower of the two modes can be chosen as the detection mode, or it may be used as the dither mode; both approaches work.

[0017] The frequency of both modes (i.e., the dither mode and the detection mode) can shift due to force gradients acting between the tip and sample in the experiment. The dither mode is used to establish a constant distance between the tip and sample for purposes of mapping topography. The closed-loop servo control (either frequency modulation or amplitude modulation type) generally holds the frequency shift of the dither mode constant, thereby holding the tip-sample force gradient (arising from the van der Waals force between tip and sample) constant. This results in a constant tip-sample distance for topographic profiling.

[0018] Simultaneously, gradients in the PiF may cause additional frequency shifts to both vibrational modes. Additional shift in the dither mode frequency is automatically compensated by the closed-loop control of the dither vibration and tip-sample spacing. Shifts in the frequency of the detection mode, however, may not be automatically compensated, since the stiffness of the detection mode is different than the dither mode, and therefore the frequency shift is not proportional in frequency.

[0019] Because the sensitivity of PiFM sensing depends on how well the mixed frequency matches the resonant frequency of the detection mode, shifts in the detection mode frequency should be tracked and the laser modulation frequency adjusted to stay on resonance. This is particularly important when the Q of the cantilever vibration modes is high, such as when operating in vacuum, at reduced pressure, or with an atmosphere of a low viscosity gas such as helium.

[0020] In some of the prior art, PiFM does not include such frequency tracking and correction. At the beginning of the experiment, the tip is brought into close proximity (a fraction of a nm to several tens of nm) with the sample surface under the control of the closed loop dither system. Once stable operation has been established, the detection mode frequency is measured, and this fixed frequency is assumed for the duration of the experiment. Shifts in the detection mode frequency during the experiment result in lost PiFM sensitivity.

[0021] In other prior art (i.e., U.S. Patent No. 8,680,467 by Prater and Kjoller), the changing frequency of the detection mode is checked repeatedly either by performing a frequency sweep (while actively vibrating the cantilever) to generate a response curve and finding the frequency peak, or by finding the peak of a thermal response curve (without actively vibrating the cantilever). The modulation frequency of a light source is adjusted so that the frequency substantially overlaps the peak of the detection mode. Performing such frequency sweeps or thermal response curve analysis requires interrupting a measurement in progress, and therefore requires additional time to complete a measurement, and prevents continuous adjustment to the continuously changing mode frequency, resulting in some accumulation of frequency error between measurements.

[0022] As explained below, embodiments in accordance with the invention provide continuous tracking of the detection mode frequency shifts in a PiFM system, and actively correcting the laser modulation frequency on a continuous basis under closed-loop control during the experiment, to keep the PiFM sensing on resonance for best sensitivity at all times.

[0023] Fig. 1 shows a frequency-tracking PiFM system 100, which is a scanning probe microscope, in accordance with an embodiment of the invention. The PiFM system 100 is a scanning probe microscope The PiFM system 100 includes a tip 102 coupled to a cantilever 104, a modulated tunable laser 106 to irradiate an interface between the tip and a sample 108 with light, a dither control system 110 for establishing a fixed distance between the tip and the sample, and a laser modulation frequency control (LMFC) system 112 for tracking of the detection mode frequency shifts in the PiFM system and actively correcting the laser modulation frequency in response to the detection mode frequency shifts on a continuous basis under closed-loop control. In an embodiment, the modulated tunable laser 106 is an infrared (IR) laser.

[0024] The dither control system 110 includes a dither drive unit 114, a dither piezo device 116 coupled to the cantilever 104, a position feedback laser 118, a photo position detector 119, a first lock-in detector or amplifier 120, a sample Z servo controller 122, and a sample Z piezo device 124. For the example of amplitude modulation (AM) detection (also called "slope detection"), the dither drive unit 114 is configured to provide a signal with a desired drive frequency to the dither piezo device 116, which causes the cantilever 104 to vibrate. The photo position detector 119 optically measures the vibration of the cantilever 104 using light from the position feedback laser 118 reflected off the cantilever. The signal from the photo position detector 119 is input to the first lock-in amplifier 120, which provides amplitude error signal to the sample z servo controller 122. The amplitude error signal indicates that the spacing between the tip 102 and the sample 108 has deviated from desired spacing. In response, the sample z servo controller 122 provides a control signal to the sample z piezo device 124 so that the spacing between the tip 102 and the sample 108 can be adjusted. In particular, the dither frequency is fixed at a point slightly above the resonance frequency of the dither vibrational mode of the cantilever 104. If the tip- sample spacing falls below the target value, the dither mode frequency shifts downward, effectively moving the dither drive frequency further above resonance, resulting in decreased dither amplitude (and vice versa). The sample Z servo controller 122 determines the amplitude error and applies a correction to the voltage on the sample Z piezo device 124 to bring the tip-sample spacing back to the target value. As the sample 108 is raster scanned relative to the tip 102, topography data is obtained at the output for the sample Z servo controller 122, and mechanical phase data (relating to sample mechanical stiffness and damping) is provided at the phase output of the lock-in amplifier 120.

[0025] The dither control system 110 could be replaced with a frequency modulation (FM) detection scheme, with no impact on the rest of the PiFM system 100. When operating with very high cantilever Q, FM may be preferred, since the control loop response speed, and therefore the imaging speed, can be too slow with an AM approach.

[0026] The laser modulation frequency control (LMFC) system 112 is a phase-locked loop (PLL) which includes a second lock-in detector or amplifier 126, mathematical calculation units 128 and 130 (a multiplier 128 and a summing unit 130 in the example shown) acting on the lock- in amplitude outputs, a center voltage source 132, which sets the nominal center modulation frequency of the laser 106, a voltage controlled oscillator (VCO) 134 that modulates the laser 106, and an optional mixer 136 that generates a mixer product, for example, a difference frequency of the dither frequency and the laser modulate frequency (LMF) to serve as the reference for the second lock-in amplifier 126. The mathematical calculation units 128 and 130 may be implemented using analog circuitry or may be implemented digitally using a digital signal processor with appropriate software and firmware or using a field programmable gate array with appropriate software and firmware.

[0027] To understand the operation of the LMFC 112, first consider the case where there is a strong PiFM signal at all times. Ignoring the amplitude output of the second lock- in amplifier 126 (treating it as constant for now), the behavior is as follows: At the beginning of the experiment, after establishing closed-loop dither control as described above, the frequency of the detection mode is measured (either by measuring its thermal excitation frequency or by sweeping the laser modulation frequency through a range of frequencies and determining the frequency at which the PiFM response is maximum, and therefore on resonance). The center voltage from the center voltage source 132 is set so that the VCO 134 produces a laser modulation frequency (LMF) that results in on-resonance cantilever vibration at the detection mode frequency. The laser excites the sample 108, and by virtue of mixing with the dither frequency, the cantilever 104 is excited at the detection mode resonant frequency. The signal from the photo position detector 119 is provided to the second lock- in amplifier 126, which has as its reference a signal generated by mixing the VCO frequency and the dither frequency and selecting the difference frequency. At resonance under this condition, the phase output of the lock-in amplifier 126 is set to zero. For now, it is assumed that the amplitude is constant, so the multiplier 128 output is zero, which is in turn added to the center frequency (for no shift) and everything is in balance.

[0028] If an interaction occurs that shifts the frequency of the PiFM mode so that the system 100 is out of resonance, then the phase output of the lock- in amplifier 126 will shift to a negative value if the LMF is too high, or to a positive value if the LMF is too low, which will be reflected in the output voltage of the multiplier 128. This non-zero phase value may be referred to as a phase error. This error voltage is added to the center frequency by the summing unit 130 to bring the system 100 back to resonance. It is understood that the VCO 134 has an adjustable frequency control gain that is set for stable closed-loop control of the LMF in this system.

[0029] Note that PiFM can be done via "direct drive" in which the LMF equals the detection mode frequency, rather than the difference frequency between the two modes. This approach is simpler, but has known experimental disadvantages. If the system is operated in this manner, the mixer 136 which generates the reference signal for the second lock-in amplifier 126 can be omitted, and the VCO frequency alone serves as the lock-in reference.

[0030] The prior art described in U.S. patent 8,680,467 by Prater and Kjoller uses direct drive, and does not anticipate the embodiment here which uses frequency mixing.

Furthermore, this prior art does not use a PLL to continuously adjust the laser modulation frequency, but rather interrupts the measurement process to perform a frequency sweep or thermal peak measurement to update the detection mode resonance frequency and the laser modulation frequency.

[0031] Now consider the purpose of the multiplier 128 in the illustrated embodiment. In an actual experiment, the amplitude of the PiFM signal may not be constant. In fact, since PiFM is mainly produced when the wavelength of the tunable laser 106 is set to coincide with an absorption peak in the sample, the PiFM signal is quite specific to the wavelength and the local sample material, and therefore there are many conditions when the PiFM signal is small or zero. When the PiFM signal is too weak, the phase output of the second lock- in amplifier 126 is noisy (in the case of a weak signal) or completely random (in the total absence of signal). Making frequency adjustments to the LMF under weak or no-signal conditions results in instability of the LMFC 112. Therefore, in the absence of an adequately strong PiFM signal, the multiplier 128 has the effect of making the correction voltage to the center frequency very small or zero. The system 100 naturally reverts to the center frequency in the absence of a PiFM signal. If the PiFM signal is strong, the multiplier 128 provides a larger correction factor to the center frequency, which drives the LMFC loop to keep the LMF on resonance. The lock-in amplitude can be viewed as a "confidence level," with faster correction applied when the signal is strong, and no correction applied in the case of no signal.

[0032] An alternative to the use of a multiplier 128 with the amplitude and phase signals of the lock-in amplifier 126 is to use a quadrature output of the second lock-in amplifier. In addition to having amplitude and phase channels, a lock-in amplifier can also have an in-phase (or "X axis") output and a quadrature (or "Y axis") output. On a continuous basis, the X output is proportional to the in-phase component of the signal and the Y output is proportional to the quadrature component. The X output is the PiFM amplitude data. An analysis of the behavior of the Y output shows that it is qualitatively very similar to the product of the amplitude and phase as described above. If the phase of the lock-in amplifier 126 is zeroed when the system 100 is on resonance as described above, then the Y output is zero on resonance. Below resonance the Y output will be proportional to the signal amplitude and the sine of the phase offset from resonance. Above resonance, the Y output will be similar, but have opposite sign. For small phase offsets, the sine of the phase offset is approximately equal to the phase offset, making the output approximately the same as the product of the amplitude and phase as described above. An inverting amplifier may be needed to generate the correct sign of control signal for a stable control loop. Therefore, the second lock-in amplifier 126 and multiplier 128 as shown in Fig. 1 may be replaced with a lock-in amplifier with a Y-axis output and an optional inverting amplifier, with the output driving the voltage controlled oscillator 134 via the summing unit 130.

[0033] In other embodiments, the multiplier 128 could be replaced with a simple threshold detector, set so that if the PiFM signal is weak or zero, there is no correction to the center voltage, and if the signal is above a threshold, the phase is passed directly as a correction to the center voltage (i.e., multiply by zero if amplitude below threshold; multiply by 1 or a fixed constant above threshold). Other mathematical calculations can also be used, such as a nonlinear curve. Whatever replaces the multiplier 128, it will generally be monotonic, starting a zero with no signal amplitude, and reaching a positive value at some larger signal amplitude.

[0034] It should be understood that the VCO control loop could be more sophisticated that the very simple case described here. For example, a conventional PID ("proportional- integral-differential") control could be used, or a complex digital control loop could be used, such as one including a finite impulse response (FIR) filter.

[0035] Although the various embodiments of the invention above are described in terms of discrete functional blocks of analog circuitry (such as a lock-in amplifier, a multiplier, etc.), it should be understood that equivalent digital implementations may be used to provide the necessary functionality. Popular methods of implementation include the use a digital signal processor with appropriate software and firmware, or the use of a field programmable gate array with appropriate software and firmware.

[0036] Operating a PiFM system with the LMFC of this invention maximizes the PiFM sensitivity, and equally important, keeps the PiFM sensitivity of the system constant, providing for better quantitative analysis of the PiFM signal. For example, by keeping the PiFM constantly on resonance while sweeping the wavelength of the tunable laser, a quantitative absorption spectrum can be obtained at any location on the sample.

Quantitatively correct absorption spectra should correlate well with spectra obtained by conventional techniques such as FTIR (Fourier Transform Infrared spectroscopy) on bulk samples. Since good libraries of FTIR data are readily obtainable, correlation between PiFM spectra and FTIR spectra can provide chemical mapping at the nm-scale with high

confidence.

[0037] In an embodiment, the cantilever and the sample are operated in a vacuum, a reduced pressure atmosphere, or an atmosphere of a low viscosity gas (such as helium) or a low viscosity gas mixture, so that the Q of the cantilever vibrational modes is high.

[0038] A method of operating a scanning probe microscope, such as the PiFM system 100, in accordance with an embodiment of the invention is described with reference to a flow diagram of Fig. 2. At block 202, a cantilever with a tip of the scanning probe microscope is driven to vibrate at a dither mode used for topographic imaging. As an example, this may be achieved using the dither control system 110 of the PiFM system 100 and the tunable IR laser 106 as the light source. At block 204, a light source that irradiates an interface between the tip and the sample is modulated in a manner that excites vibration at a detection mode via mixing with the vibration frequency of the dither mode. At block 206, modulation frequency of the light source is adjusted during operation to keep the excitation of the detection mode tracking the resonant frequency of the detection mode.

[0039] Reference throughout this specification to "one embodiment," "an

embodiment," or similar language means that a particular feature, structure, or characteristic described in connection with the indicated embodiment is included in at least one

embodiment of the present invention. Thus, the phrases "in one embodiment," "in an embodiment," and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment.

[0040] Although the operations of the method(s) herein are shown and described in a particular order, the order of the operations of each method may be altered so that certain operations may be performed in an inverse order or so that certain operations may be performed, at least in part, concurrently with other operations. In another embodiment, instructions or sub-operations of distinct operations may be implemented in an intermittent and/or alternating manner.

[0041] It should also be noted that at least some of the operations for the methods may be implemented using software instructions stored on a computer useable storage medium for execution by a computer. As an example, an embodiment of a computer program product includes a computer useable storage medium to store a computer readable program that, when executed on a computer, causes the computer to perform operations, as described herein.

[0042] Furthermore, embodiments of at least portions of the invention can take the form of a computer program product accessible from a computer-usable or computer-readable medium providing program code for use by or in connection with a computer or any instruction execution system. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.

[0043] The computer-useable or computer-readable medium can be an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system (or apparatus or device), or a propagation medium. Examples of a computer-readable medium include a semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disc, and an optical disc. Current examples of optical discs include a compact disc with read only memory (CD-ROM), a compact disc with read/write (CD-R/W), a digital video disc (DVD), and a Blu-ray disc.

[0044] In the above description, specific details of various embodiments are provided. However, some embodiments may be practiced with less than all of these specific details. In other instances, certain methods, procedures, components, structures, and/or functions are described in no more detail than to enable the various embodiments of the invention, for the sake of brevity and clarity.

[0045] Although specific embodiments of the invention have been described and illustrated, the invention is not to be limited to the specific forms or arrangements of parts so described and illustrated. The scope of the invention is to be defined by the claims appended hereto and their equivalents.