阅读说明：本技术 非轻敲模式的散射式扫描近场光学显微镜系统及方法 (Non-tapping mode scattering type scanning near-field optical microscope system and method ) 是由 王浩民 徐晓纪 于 2019-01-22 设计创作，主要内容包括：用于实现峰值力散射扫描近场光学显微镜(PF-SNOM)的系统、装置和方法。传统的散射式显微镜(s-SNOM)技术使用轻敲模式操作和锁定检测,无法提供具有明确针尖-样品距离的直接层析成像信息。PF-SNOM使用峰值力散射式扫描近场光学显微镜,并结合峰值力轻敲模式和时间选通光检测,可以从样品表面直接分离垂直近场信号来进行三维近场成像和光谱分析。PF-SNOM还提供5nm的空间分辨率,并且可以同时测量机械和电气特性以及光学近场信号。(Systems, devices, and methods for implementing peak force scattering scanning near-field optical microscopy (PF-SNOM). Conventional scatter microscopy (s-SNOM) techniques using tap mode operation and lock-in detection fail to provide direct tomographic information with well-defined tip-sample distances. The PF-SNOM uses a peak force scattering scanning near field optical microscope in combination with peak force tapping mode and time gated light detection to directly separate the perpendicular near field signal from the sample surface for three dimensional near field imaging and spectroscopic analysis. PF-SNOM also provides 5nm spatial resolution and can measure both mechanical and electrical properties and optical near-field signals.)

1. An atomic force microscope circuit, comprising:

a probe having a cantilever ending at a tip, the probe configured to approach a set of samples on a sample stage, resulting in one or more vertical deflections of the cantilever;

a position sensor configured to detect vertical deflection of the cantilever;

a light source configured to direct light toward the sample;

an optical detector configured to detect light scattered from the sample; and

an analysis circuit configured to:

i) receiving a plurality of near-field scattering responses, the near-field scattering responses corresponding to a difference between a respective one of the plurality of near-field scattering responses and a background signal; and

ii) correlating the plurality of near field scattering responses with a plurality of tip-to-sample distances between the tip and the sample to create a near field response data map relating near field responses for different sample locations to corresponding tip-to-sample distances.

2. The afm circuit of claim 1, wherein the analysis circuit comprises a processor.

3. The atomic force microscope circuit of claim 1, wherein the analysis circuit further comprises a two-dimensional modeling circuit configured to generate a three-dimensional representation of the sample in response to a correlation.

4. The atomic force microscope circuit of claim 1, wherein the analysis circuit further comprises a three-dimensional modeling circuit configured to generate a three-dimensional representation of the sample in response to a correlation.

5. The atomic force microscope circuit of claim 1, further comprising: a piezoelectric region disposed on the sample stage and configured to oscillate within a frequency range.

6. The atomic force microscope circuit of claim 1, further comprising: an electrical sensor configured to determine a background signal when the needle tip is not sufficiently proximate to the sample to cause a short-range near-field interaction, and configured to determine a scattered light signal response due to the short-range near-field interaction of the needle tip with the sample.

7. The atomic force microscope circuit of claim 1, wherein the light source comprises a light source configured to generate a light signal from the group consisting of infrared light, visible light, and light in the terahertz range.

8. The afm circuit of claim 1, wherein the position sensor further comprises a voltage detector.

9. The afm circuit of claim 1, wherein the optical detector further comprises an interferometric optical detector.

10. The afm circuit of claim 1, wherein the tip comprises gold, platinum, iridium, or alloys thereof.

11. An atomic force microscope, comprising:

a sample stage for receiving a material sample;

a piezoelectric oscillation region configured to oscillate at an oscillation frequency;

a probe having a cantilever ending at a tip, the probe configured to approach a set of the samples on a sample stage, resulting in one or more vertical deflections of the cantilever;

a position sensor configured to detect vertical deflection of the cantilever;

a piezoelectric driver configured to drive the piezoelectric oscillation region at a frequency lower than a lowest resonance frequency of the cantilever of the probe;

a light source configured to direct light toward the sample;

an optical detector configured to detect light scattered from the sample; and

an analysis circuit configured to:

i) receiving a plurality of near-field scattering response signals corresponding to a difference between a respective one of the plurality of near-field scattering response signals and a background signal; and

ii) correlating the plurality of near field scattering response signals with a plurality of tip-to-sample distances between the tip and the sample to create a near field response data map relating near field responses at different sample locations to corresponding tip-to-sample distances.

12. The afm according to claim 11, wherem stage driver is further configured to drive the piezoelectric region at an oscillation frequency of 0.1kHz to 100.0 kHz.

13. The atomic force microscope of claim 11, further comprising: one or more parabolic mirrors configured to redirect a near-field scattering response.

14. The atomic force microscope of claim 13, further comprising: a beam splitter configured to combine a raw light source signal with the near-field scattering response signal.

15. The atomic force microscope of claim 14, further comprising: a homodyne retroreflector configured to distinguish the original light source signals.

16. A method of performing spectral imaging, the method comprising:

generating a signal configured to induce a motion in a sample, the motion comprising a periodic variation in a vertical distance between adjacent probes, wherein the probes comprise a tip disposed on a cantilever;

moving the tip towards the sample or moving the sample towards the tip to cause an interaction with the sample, the interaction comprising a vertical deflection of the cantilever causing dynamic contact of the tip with the sample;

detecting vertical deflection of the cantilever to determine a plurality of tip-to-sample distances corresponding to tip contact with the sample and cantilever deflection over time;

determining a plurality of near-field scattering responses from light focused on the sample at a tip contact region of the sample; and

correlating the plurality of near-field scattering responses with the plurality of tip-to-sample distances for each sample location to generate a near-field response data map for the sample.

17. The method of claim 16, further comprising: driving a piezoelectric driver configured to impart a periodically varying motion at a frequency of 0.1kHz to 100.0 kHz.

18. The method of claim 16, further comprising:

determining a background signal when the tip is not close enough to the sample to cause a short-range near-field interaction during the periodic variation;

approximating a linear response corresponding to the determined background signal; and

removing the approximated linear response from the plurality of near-field scattering responses.

19. The method of claim 16, wherein the correlating further comprises: associating a set of near-field scattering responses from the plurality of near-field scattering responses with a tip-sample distance for each sample location, wherein each set is associated with an equivalent tip-sample distance at the each sample location.

20. The method of claim 16, further comprising: generating a second near-field response data map of the sample using light of a different wavelength from the light source.

21. A method of measuring sub-micron region optical properties of a sample using an atomic force microscope, the method comprising:

allowing the probe to interact with the sample;

illuminating the sample with a beam of light from a radiation source such that the light is scattered from the probe-sample interaction region;

collecting scattered light from the probe-sample interaction region and a background region using a detector, the scattered light being a function of a distance between the probe and the sample; and

constructing a near-field signal in response to the collected scattered light relative to the distance.

22. The method of claim 21, wherein constructing the near-field signal further comprises:

extrapolating a linear function of distance-dependent scattered light response when the scattered light is dominated by scattered light from the background region of greater tip-sample distance; and

subtracting the extrapolated linear function from the scattered light when the scattered light is not dominated by scattered light from the background region of smaller tip-to-sample distance.

23. The method of claim 21, wherein constructing the near-field signal further comprises:

extrapolating a quadratic function of distance-dependent scattered light response when the scattered light is dominated by scattered light from the background region of greater tip-sample distance; and

subtracting the extrapolated quadratic function from the scattered light when the scattered light is not dominated by scattered light from the background region of smaller tip-to-sample distance.

24. The method of claim 21, wherein constructing the near-field signal further comprises:

extrapolating a polynomial function of a distance-dependent scattered light response when the scattered light is dominated by scattered light from the background region of greater tip-sample distance; and

subtracting the extrapolated polynomial function from the scattered light when the scattered light is not dominated by scattered light from the background region of smaller tip-to-sample distance.

25. The method of claim 21, further comprising: determining a tomographic section of a spatial near-field response map of the sample for a plurality of tip-sample distances for a plurality of locations of the sample.

26. The method of claim 21, further comprising: the wavelength of the radiation source is varied to determine a near-field spectrum corresponding to the wavelength dependence of near-field scattering.

27. The method of claim 21, further comprising: determining the time of pulsating contact t corresponding to a point-sample distance of zero_sAs a point of synchronization to enable predictive determination of the tip-sample distance from the probe deflection signal and correlation of the probe deflection signal with the scattered light signal.

28. The method of claim 21, further comprising: determining a separation time t corresponding to the point-sample distance no longer being zero_dAs a point of synchronization to enable predictive determination of the tip-sample distance from the probe deflection signal to correlate with the scattered light signal.

29. The method of claim 27, wherein the near field signal comprises a plurality of peak force tapping cycles that are synchronously averaged, thereby improving signal-to-noise ratio.

30. The method of claim 21, further comprising: the signal of the scattered light is interferometrically amplified at an optical detector using an optical interferometer.

31. The method of claim 21, wherein the wavelength of the light source comprises a range from ultraviolet wavelengths to far infrared wavelengths.

32. The method of claim 21, wherein the wavelength of the light source comprises a mid-infrared wavelength.

33. The method of claim 21, wherein interacting the probe with the sample further comprises interacting the probe with the sample in a peak force tapping mode.

Background

Scanning Near-Field Optical Microscopy (SNOM, also known as Near-Field Scanning Optical microscope-NSOM) is a microscopic technique for conducting nanostructure studies. In SNOM (described below), the laser is focused through an aperture having a diameter smaller than the wavelength excited by the laser, which results in an evanescent field (or near field) at the far side of the aperture. When the sample is scanned at a short distance below the aperture, transmitted or reflected light is captured and displayed by the display device with a spatial resolution below the diffraction limit.

In the SNOM application, a Scattering-type Scanning Near-Field Optical microscope (s-SNOM) is a special technique that has been developed to enable the study of various nanoscale phenomena that cannot be studied by far-Field spectra due to its Optical diffraction limit. s-SNOM has become a tool for studying graphene plasmons, surface phonon polarons, phase transitions of related electronic materials, compositions in heterogeneous materials, and chemical reactions. In s-SNOM, the elastic scattered light of a sharp metal tip operated by an Atomic Force Microscope (AFM) over a sample is measured by an optical detector. Near field interactions between the tip and the sample can alter the polarizability of the tip, thereby affecting elastic scattering of light. However, since elastic scattering does not change the wavelength of the scattered light, reflected or scattered photons from other parts of the AFM cantilever or the sample surface outside the tip region will also be recorded by the same optical detector and result in a background signal, which is the far field background from the background region outside the tip-sample interaction region. To distinguish between the far-field background and the near-field signal of the tip-sample interaction, one conventional approach is to oscillate the tip in tapping mode by mechanical resonance of the AFM cantilever and phase-lock demodulate or fourier analyze the scattered light at the non-fundamental of the tip oscillation frequency.

Despite the wide application and success of this method, there are limitations to phase lock detection in tap mode s-SNOM. First, because the phase-locked demodulated s-SNOM signal is a discrete value, conventional s-SNOM cannot provide direct information of the vertical extent of the tip-sample near-field interaction. This results in a complex and missing distance dependence of the tip-sample near-field interaction in the signal generation mechanism. Second, s-SNOM signals of different demodulation orders exhibit different signal shapes and cause the spatial pattern to be blurred. Furthermore, s-SNOM operating in tapping mode cannot be performed simultaneously with other AFM modes requiring robust tip-sample contact, such as measuring mechanical properties and conductivity. Tapping mode s-SNOM does not enable simultaneous and correlated measurements for near-field optical, mechanical and electrical signals.

Drawings

Embodiments of the presently disclosed subject matter will be described with reference to the accompanying drawings, in which:

FIG. 1 is a system diagram of a Peak Force Scattering-Type Near-Field Optical microscope (PF-SNOM) apparatus according to an embodiment of the presently disclosed subject matter;

FIG. 2A is a graph showing infrared detector signals of cantilever vertical deflection and scattered light from a tip recorded simultaneously by PF-SNOM technology according to an embodiment of the presently disclosed subject matter;

FIG. 2B is a graph showing the relationship between the optical detector signal and the tip-sample distance derived from the two waveforms in FIG. 2A, with the background signal preserved, according to an embodiment of the presently disclosed subject matter;

FIG. 2C is a graph showing a near-field-only signal with a well-defined tip-sample distance correlation obtained by subtracting the fitted linear background of FIG. 2B, according to an embodiment of the presently disclosed subject matter;

FIG. 2D is a graph showing the homodyne phase dependence of the PF-SNOM signal according to an embodiment of the presently disclosed subject matter;

FIG. 2E is a graph showing a 1000nm long line scan of boron nitride nanotubes versus one wavelength (1405 cm) in accordance with an embodiment of the presently disclosed subject matter^-1) A graph of different PF-SNOM signals for different tip-sample distances of (a);

FIG. 2F is a diagram of a boron nitride nanotube performing the line scan of FIG. 2E in accordance with an embodiment of the presently disclosed subject matter;

3A-3J are graphs showing PF-SNOM operations on boron nitride nanotubes and hexagonal boron nitride to reveal tip induced phonon polarization damping, 5nm spatial resolution, and associated mechanical-electrical and near-field imaging, according to embodiments of the presently disclosed subject matter;

FIG. 4 is a flow chart showing a method for implementing PF-SNOM technology in an AFM microscope according to an embodiment of the presently disclosed subject matter; and

fig. 5 is a diagram showing elements or components in a computer device or system configured to implement a method, process, function, or operation according to an embodiment.

It should be noted that the same numbers used in the present invention and the drawings denote similar components and features.

Detailed Description

The subject matter of the embodiments disclosed herein is described below to meet statutory requirements, but the description is not intended to limit the scope of the claims. The claimed subject matter may also be implemented in other ways, may include different elements or steps, and may be used in conjunction with other present or future technologies. The following description should not be construed as implying any particular order or arrangement between various steps or elements unless explicitly stated as such.

Embodiments will now be described more fully hereinafter with reference to the accompanying drawings, which form a part hereof, and in which are shown by way of illustration embodiments in which the systems and methods described herein may be practiced. The systems and methods may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable regulatory requirements and will fully convey the scope of the subject matter to those skilled in the art.

In summary, the systems and methods discussed herein can be used directly with Peak Force Scattering-Type Near-Field Optical Microscopy (PF-SNOM). Unlike conventional methods, the PF-SNOM technique avoids tapping mode operations that can cause subsequent information loss in lock detection. The new techniques discussed herein combine Peak Force Tapping (PFT) mode and time-gated detection (time-gated detection) of near-field scattered signals using a far-field background subtraction algorithm. In contrast to conventional tapping mode based s-SNOM, PF-SNOM enables tomographic sectioning of tip-sample near-field interactions at well-defined tip-sample distances and simultaneous performance of relevant near-field, mechanical, and electrical measurements with high spatial resolution well below the diffraction limit. These aspects, as well as advantages and other aspects, are explained in more detail in fig. 1-5 below.

Fig. 1 is a system diagram of a peak force (e.g., non-tapping mode) scattering near-field optical microscope (PF-SNOM) device 100, according to an embodiment of the presently disclosed subject matter. In this embodiment, the PF-SNOM device 100 includes an Atomic Force Microscope (AFM) 105 with a diode laser 110 (e.g., light source) to induce deflection of the AFM cantilever 115 by reflection at the back of the cantilever and detection by a deflection detector 119. The apparatus is configured to allow a beam from a laser source (e.g., a frequency tunable mid-infrared Quantum Cascade Laser (QCL) 128) to be focused onto a sample (not shown) that may be placed on a sample stage 117 having a piezoelectric oscillator 118. The light source 128 may be an infrared laser adapted to produce a beam of light having a wavelength in the infrared range, although other ranges may be used in other embodiments. Furthermore, the piezoelectric oscillator 118 arranged on the sample stage may be driven by a piezoelectric drive stage with a frequency between 0.1khz and 100.0khz, where 4.0khz is a typical drive frequency. In another embodiment, rather than oscillating the sample, the AFM cantilever can be oscillated at a non-resonant frequency between 0.1kHz and 100.0 kHz. An AFM cantilever 115 driven in oscillation at a non-resonant frequency does not retain kinetic energy (kinetic energy), unlike tapping mode AFMs that drive the AFM cantilever 115 at or near cantilever mechanical resonance.

The AFM 105 also includes a probe system having a drive 111 adapted to manipulate a cantilever 115, the cantilever 115 having a probe tip 116 (typically covered with a metal such as gold) at the end of the cantilever 115. Like most AFMs, the cantilever is flexible and vibrates when adjacent to a piezoelectric oscillator 118 disposed on the sample stage 117. In general, when cantilever 115 is in proximity to or in contact with a sample disposed on sample stage 117, cantilever 115 will deflect up and down when subjected to the mechanical forces generated by the sample on piezoelectric oscillator 118. Probe tip 116 can be placed near or in contact with a sample to measure the deflection of cantilever 115 over time using deflection detector 119, as will be described in more detail below. The deflection measurements may be input to the processor 130 to determine sample information (e.g., analysis circuitry for analyzing the collected data).

In addition, light from the mid-infrared quantum cascade laser 128 is directed to the beam splitter 121. The frequency of the mid-infrared quantum cascade laser can be tuned and can provide selective optical frequencies (e.g., vibrational transitions, polarization modes, or other resonance phenomena of molecules) that match the resonances in the sample. The light source may also be another laser source providing a resonant frequency, for example a nonlinear optical frequency converted laser radiation used in an optical parametric oscillator. A portion of the laser light is split by the beam splitter 121 into the reference light field 124 and another portion from the beam splitter 121 may be focused onto the probe tip 116 by the first parabolic mirror 120. The function of parabolic mirror 120 may be replaced by other types of light focusing optics, such as lenses. Light is scattered from the probe tip 116. The scattered light may be reflected off the sample. The first parabolic mirror 120 captures the direct scattered light and the secondary reflected light.

When the light is reflected, the first parabolic mirror 120 directs it to the beam splitter 121. In addition, a reference laser field 124 may also be added to the beam splitter 121 so that the signal may facilitate detection of the optical signal reflected by the needle tip by interferometric detection. To this end, the beam splitter 121 may direct the optical signal (combination of the reflected signal from the sample and the reference signal 124) to a second parabolic mirror 122 (or equivalent focusing element, e.g. a lens) and may be detected by an optical detector 123, e.g. a Mercury Cadmium Telluride (MCT) detector. It should be noted that the above-described setup comprising the light source (laser 128), beam splitter 121, light reference path 124, light path containing tip 116, and optical detector 123 for interferometric detection is a typical arrangement of s-SNOM and is an asymmetric Michelson interferometer. The detected optical signals (e.g., scatter signals) can be sent to processor 130 and used with the deflection detected by deflection detector 119 of cantilever 115 to determine various aspects of the sample disposed on sample stage 117. FIG. 2A shows the optical detector signal and the cantilever vertical deflection signal measured over time, as described below. Also, the specifics of these measurements will be discussed further below. Next, the operation and details of the apparatus shown in fig. 1 will be presented with reference to the components of the apparatus 100 of fig. 1.

FIG. 2A is a graph 200 of simultaneous recording of a vertical deflection 205 of cantilever 115 and a scattered signal 207 of scattered light from tip 116 detected by optical detector 123 via PF-SNOM technology according to an embodiment of the subject matter disclosed herein. During operation, the cantilever 115 may remain stationary while the sample on the sample stage 117 is vertically vibrated at a low frequency of a few kilohertz (defined as the PF-SNOM frequency) with a large amplitude (e.g., 300nm) by the piezoelectric oscillator 118. For each oscillation period, the maximum cantilever deflection (e.g., peak force) can be controlled and maintained at a set point under a negative feedback loop. When the tip 116 approaches the sample surface, intermolecular attraction forces cause the tip 116 to jump and contact the sample surface, a phenomenon known as snap-contact (also known as jump contact). The tip-sample contact time is predetermined, the bounce contact time t in FIG. 2A _s210 may be measured from the waveform of the cantilever deflection signal 205 and compared withThe minimum deflection coincides. In this example, the bouncing contact process (e.g., t)_sDarker band near 210) lasts from about 45 to 52 mus and the bouncing contact time t _s210 is 52 mus.

In FIG. 2A, the bouncing contact time t can be determined from the minimum and maximum deflection plots shown_s210, time of maximum peak force t _p212 and tip separation time t _d214. Cantilever 115 at the top of fig. 2A shows the corresponding tip-sample configuration for three phases of the PF-SNOM cycle, from left to right: the proximity of the tip to the sample 220, the bouncing contact 222, and dynamic tip-sample contacts 224 that allow other AFM modalities, such as electrical measurements 230 (here exemplified by the voltage applied between the tip and the sample). A graph 208 of the detector signal (207 in FIG. 2A) versus tip-sample distance (as shown in FIG. 2B. discussed below) can then be derived and given the contact time t in beats _s210 may be defined as the fact of zero. At the jump contact t_sBefore 210, the tip-sample distance may be a positive value. From after the jump contact to the tip at t _d214 before retracting from the sample, the distance remains zero.

FIG. 2B is a graph 240 showing the relationship between the optical detector signal 208 and the tip-sample distance derived from the two waveforms in FIG. 2A, wherein the far field background signal remains constant, according to an embodiment of the presently disclosed subject matter. In one embodiment, the cantilever vertical deflection waveform D (t)205 and the scattered light detector signal waveform S (t)207 (where t is time) in FIG. 2A are converted to a function S (d)208 as shown in FIG. 2B, where d is the tip-sample distance for tomographic imaging. In PFT mode, the sample piezo stage can be driven vertically in a sinusoidal oscillation at PFT frequency f. Vertical position d of the piezo-electric station_zCan be expressed as:

wherein A is the peak force amplitude,

is the oscillation phase of the piezo stage. In 205, the highest position of the piezo station also corresponds to time t_pMaximum cantilever vertical deflection (peak force set point). At t_pAt least one of

Calculating the phase of the piezoelectric station motion

To yield d_zIs then derived asThus, the vertical position d of the piezo-electric station_zComprises the following steps:

d_z(t)＝Acos(2πf(t-t_p))

in this example, the time t at which the maximum cantilever bending is identified from the cantilever vertical deflection signal waveform D (t)205_p. From the knowledge of the cantilever deflection sensitivity V, i.e. the correlation of the voltage or signal measured by the deflection sensor with the actual tip movement in nanometers (typically tens of nanometers), the tip-sample distance d (t) in the time domain is known as:

d(t)＝A-d_z(t)+V·D(t)

or

d(t)＝A-Acos(2πf(t-t_p))+V.D(t)

Due to contact time t of jumping_sAfter and separation time t_dPreviously, the tip-sample distance was almost zero (considering that the effect of the indentation in PF-SNOM is negligible, since the signal is not extracted in the indentation), so one d (t) can be defined as two regions and given a truncated sinusoidal shape:

all t can be identified from the original D (t) curve 205_p、t_sAnd t_d. In the current PF-SNOM operation, in each PFT cycle,only the bouncing contact time t is processed_sThe previous light scattering signal S (t) 207. Thus, t is measured according to calculated d (t) and synchronization<t_sS (t) of (a), the relation between the scattering signal and the tip-sample distance s (d)208 is derived.

A significant increase in scattered signal at the short tip-sample distance caused by the short range near field interaction can be observed in fig. 2B, along with a linear fit to the long range far field background 241 (dashed line). Since PF-SNOM techniques allow large amplitude oscillations of the tip-sample distance without loss of feedback stability, the far-field background 241 can be accurately linearly fitted in the region of the tip far from the sample, allowing accurate linear prediction of far-field background signals at short tip-sample distances. To obtain a near-field scatter signal, the far-field background signal of the background area can be removed from the scattered light signal, since at larger tip-sample distances the change in the detector signal is only responsive to changes in the far-field scatter of the cantilever axis and the sample surface. Because the laser wavelength is about 3-12 mu m, the change of dozens of nanometers of the vertical position of the sample stage is relatively small, and the change of the far-field scattering signal can be approximate to the linear change of the distance between the needle point and the sample. The fitted linear far-field background signal is then extrapolated to the short tip-sample distance region to be removed from the detector signal. The resulting difference (fig. 2C) provides a relationship between the near field signal and the tip-sample distance, thereby enabling accurate access to the perpendicular near field response.

Fig. 2C is a graph 260 of a near-field-only signal 261 with a well-defined distance dependence obtained by subtracting the fitted linear background 241 from the detector signal 208 of fig. 2B, according to an embodiment of the presently disclosed subject matter. Subtracting the near linear far field background from the scattered signal yields a pure near field response as a function of distance. In one embodiment, the process for removing far-field signals includes analyzing the signals to linearly fit to the region s (d) of the large tip-sample distance d shown in fig. 2B (e.g., 20nm or more on the right side of the graph). In another embodiment, a general trend fit may be used to account for slight deviations from a linear trend. At larger tip-sample distances, the change in detector signal comes fromThe far field scattering changes (e.g., background area) at the cantilever axis and sample surface and can be fit to a linear far field background. The resulting difference (as discussed below with respect to FIG. 2C) provides a relationship S between the near-field signal and the tip-sample distance_NF(d)261, thereby enabling precise access to the vertical near field response.

In another embodiment, a fast background removal algorithm may be used to fit the far-field background signal directly from the scattered signal waveform in the time domain. The algorithm first begins with a bouncing contact time t_sA short period (e.g., 120 mus) of the nearby extraction laser signal waveform. Then at t_sIn the first short period (about 10 μ s), the near field scattered light increases significantly as the tip-sample distance decreases. This short period is defined as the signal region, which corresponds to a short distance of the tip-sample distance of substantially less than 5 nm. Before this signal region, the laser signal waveform exhibits a gradual and approximately linear increase due to the far field scattering background. A background trend fit (trend fit) can be made to this region and then extrapolated to the signal region. The trend fit may be a polynomial function, e.g., a quadratic function, or other function selected such that it substantially overlaps the scattering signal for large tip-sample distances, typically in the region above 10-20nm, below 80-100 nm. The extrapolated far-field background is then subtracted from the light scattering in the signal region to obtain a pure near-field response. After removing far field background, may be at t_sThe scattered signal is averaged over a previously specified time window and used as the PF-SNOM signal. This means that to improve the signal-to-noise ratio (e.g. for a fixed spatial position on the sample and a fixed wavelength), the near field response can be averaged with the tip-sample distance based on the arithmetic mean, i.e. the near field responses are summed and summed. In another embodiment, the scattered light signal may be averaged in the time domain before subtracting the background. In this case, the mean data may be synchronized, i.e. the scattered light signal s (t)207 of fig. 2A and the deflection signal d (t)205 of fig. 2A overlap in time at the synchronization reference point, which may be the time of the bouncing contact time t _s210. After overlapping data for each PFT cycle based on the time stamp, near field data or deflection may be appliedThe signals are averaged. From this simultaneous averaging data, according to the above steps, scattered light signals as a function of the distance S (d)208 can be obtained and after background removal, a true near field signal S depending on the tip-sample distance can be determined_NF(d)261。

Fig. 2C shows a near field response 260, which can be determined from the integration of the PF-SNOM signal corresponding to curve 261 at a particular tip-sample distance d. This is indicated by the dark grey bar 262. By varying the distance d over which the near field response is extracted, near field signals corresponding to different values of d (e.g., different gating distances) can be obtained, thereby capturing a well-defined perpendicular near field response between the tip and the sample. Thus, data may be acquired at different distances d along different locations of the sample to produce an overall tomographic image of the sample. An example of this is shown and discussed in fig. 3 below. Using the embodiment discussed with reference to fig. 1, a PF-SNOM image of 256 × 256 pixels can be generated in about 30 minutes. In PF-SNOM imaging, an average signal of 50 or 150 peak force tapping cycles can be used per pixel, depending on the signal strength. The PF-SNOM spectra shown in fig. 3A-3C are collected by the sweep frequency of the tunable qc laser 128, in this example, the piezoelectric frequency is held at 2 kHz. Each point in the PF-SNOM spectrum may be an average of about 400 PFT cycles. It should be noted that conventional tap-based s-SNOM cannot directly provide a distance dependent near-field signal because its lock detection at different harmonics of the tap frequency provides only discrete near-field signal values, and cannot provide the PF-SNOM tip-sample distance curve 261 (assuming that no more complex reconstruction process is used for the near-field response).

Fig. 2D is a graph 270 of the homodyne phase dependence of the PF-SNOM signal according to an embodiment of the disclosed subject matter. Like conventional s-SNOM, a homodyne reference field (reference 124 in FIG. 1) can be used for interferometric detection of the PF-SNOM signal, which can be used to enhance near-field signals and suppress background scatter in tap mode s-SNOM in general. Fig. 2D shows the PF-SNOM signal dependence at different homodyne phases 272 obtained by adjusting the position of the reference retroreflector (reference retro-reflector). The reference retroreflector is part of an asymmetric michelson-type interferometer commonly used in s-SNOM, which is explained in fig. 1. Again, in fig. 1, the QCL output beam is typically split by a beam splitter 121, so that the reference beam 124 is obtained by a QCL laser 128. When another portion of the laser output illuminates the parabolic mirror 120 and the tip 116, the reference beam 124 is reflected by a mirror or retroreflector and sent back to the beam splitter 121 and overlaps the tip-scattered light on the optical detector 123 after being focused by the focusing element 122. On the optical detector, the tip-scattered light, the reference light interfere, and the recorded signal intensity depends on the relative optical path length between the reference path and the tip-scattered path, i.e., the relative phase of the optical field. Intensity 271 in fig. 2D is the photodetector signal intensity when the homodyne phase 272 (i.e., the relative path length between the tip-scatter path and the reference path) is adjusted. The intensity is typically varied by changing the position of the retroreflector in the reference path to obtain clear signal minima and maxima as shown in fig. 2D that are not disturbed by the light field. In another embodiment, the optical path length of the tip-scattering path is varied relative to a fixed reference path. As with s-SNOM in tapping mode, the phase sensitive PF-SNOM can also be used to calculate the amplitude and phase of the near field signal and can extract the absorption and reflection of the sample therefrom.

FIG. 2E is a graph showing a 1000nm long line scan at one wavelength (1405 cm) of Boron Nitride Nanotubes (BNNT) according to an embodiment of the presently disclosed subject matter^-1) Graph 290 of different PF-SNOM signals relative to different tip-sample distances. The topography (e.g., three-dimensional representation) of the BNNTs is shown in FIG. 2F, and the zero point of the line scan begins at the end of the BNNT on the right side of the figure (near the label "1"). In this example plot, the response profiles of PF-SNOM extracted from the top surface of a Boron Nitride Nanotube (BNNT) sample are shown for different tip-sample distances d (for ease of comparison, the profiles of d-4, 8 and 12nm are magnified by 2, 4 and 8 times, respectively). Thus, images (e.g., two-dimensional representations) of different distances d may be extracted from this and other related maps of a 256 × 256 pixel area (or other suitable area). We can see that the near field distribution along the top surface of BNNT nanotubes is not only as good as it is when d is reduced from 12nm to 1nmIt showed a larger near field signal overall, but also more near field intensity near the end of the nanotube (near position "1" in FIG. 2F), indicating that the end of the BNNT has a stronger tip-sample interaction as the tip is closer to the surface. By using an empirical exponential decay function S (d) ═ A_NFe^(-d/b)Fitting the vertical decay activity of the near-field response, where S (d) is the near-field response depending on the tip-sample distance d, A_NFAnd b is a fitting coefficient representing the total amplitude of the near field response and the vertical attenuation range, based on the total amplitude of the near field A_NFAnd the attenuation range b of the needle point-sample characteristic 1/e, two new near-field signal representations can be obtained. Direct acquisition of the tip-sample interaction range is a unique advantage of the PF-SNOM method, which is lacking if no further reconstruction processing of the near-field response is performed for the tapping mode s-SNOM with single lock demodulation.

Another advantage of PF-SNOM over traditional tapping mode s-SNOM is the ability to directly acquire near-field scattered signals and tip-sample vertical distance dependence (e.g., gated sampling) at different distances. This capability allows for the collection of tomographic near field images, which can reveal more microseconds of tip-sample interaction than traditional s-SNOM techniques. As will be discussed below with reference to fig. 3A-3F, line width broadening (linewidth polarization) and resonance frequency shift of Phonon polaron (PhP) resonances in boron nitride materials are observed using PF-SNOM over tip-sample distances of less than 10nm, whereas for tapping mode s-SNOM it is difficult to distinguish over this range due to the required oscillation amplitude of the tip, typically 25-60nm, and the subsequent complex signal (resonant signal). Since a direct and quantitative elastic scattering signal can be obtained by PF-SNOM, the tip-induced PhP relaxation characteristics can be determined.

Since the PF-SNOM signal is proportional to the near field signal, the computational complexity required for numerical modeling of the PF-SNOM signal is much lower than for the tapping mode s-SNOM, where additional steps are required to interpret the tip oscillation and lock-in demodulation to reproduce the s-SNOM signal. Although the method of reconstructing s-SNOM by Fourier synthesis is used in tapping mode s-SNOM to vertically reconstruct the tip-sample near-field response, the bandwidth of the reconstructed s-SNOM is limited by the harmonic demodulation times in Fourier synthesis and the amplitude of the tip oscillation. For example, even if 18 th harmonic demodulation is used altogether, the vertical resolution in reconstructing the s-SNOM is only 8.3nm for a tip oscillation amplitude of 150 nm. A vertical resolution of 8.3nm does not capture the short range near field interaction features below 10nm that are achievable with the system and technique of the present invention, much less to record the 18 th harmonic simultaneously without the expensive high-end multi-channel lock-in amplifier. In contrast, the vertical resolution of the PF-SNOM is related to the bandwidth, PFT amplitude and PFT frequency of the infrared detector, and these parameters can be easily adjusted or satisfied to improve the vertical resolution. In our PF-SNOM device, the vertical resolution is estimated to be 0.12nm, so the near field resolution of PF-SNOM in the vertical direction is more accurate than the existing tapping mode s-SNOM technique. A large number of tomographic images over a wide range of tip-sample distances can be obtained directly by PF-SNOM. This advantage can be used to reveal the three-dimensional near-field distribution of the plasmonic nanoantenna. Furthermore, since spatial resolution depends on the lateral limits of field enhancement, PF-SNOM with high vertical accuracy can achieve the most stringent field limits in gap mode (gap mode) by acquiring at short tip-sample distances and provide excellent 5nm lateral spatial resolution of the signal profile as shown in fig. 3I. Whereas in the tapping mode s-SNOM beyond 10-20nm the magnitude of the field confinement varies with the vertical oscillation of the tip, resulting in impaired lateral field confinement.

The tomographic near field image and the SiC spectrum of BNNTs by PF-SNOM are very significant for scattering near field optical microscopy. s-SNOM is widely used for characterization of near-field response of polarized materials. There is little concern that the tip of an AFM will alter the near field activity of a sample. In PF-SNOM, the near field response of the short tip-sample distance was directly extracted and the change in PhP spectral activity could be clearly observed. The metal tip not only detects scatterers of the near field, but also acts as a damper (damper) at short tip-to-sample distances. This means that the spatial pattern obtained by a scattering near-field optical microscope should generally be carefully treated, since the measuring tip may affect the near-field response being measured. Since PF-SNOM is able to obtain responses at different tip-sample distances, its measurements are particularly useful in interpreting the actual near-field response.

As previously mentioned, peak force tapping can not only enable topographical imaging, but also nanomechanical mapping and electrical imaging of sample properties (such as modulus or adhesion), for example to determine nanoscale conductivity of a sample. In PF-SNOM, this method can be combined with near field mapping to obtain correlation images of many sample properties. The ability to derive a perpendicular near-field response from real-time measurement of near-field scattered signals and the compatibility of PF-SNOM with electromechanical simultaneous measurements is achieved by well-defined tip-sample contact in PFT mode. Since the AFM tip cantilever remains stationary, unless pushed up during dynamic contact, the kinetic energy stored in the cantilever is almost zero. The cantilever thus responds very sensitively to intermolecular forces between the probe and the sample and thus gives a well-defined bouncing contact time t from the tip-sample zero distance reference point_s. In contrast, the tapping mode AFM cantilever is vibrated by external actuation. Intermolecular forces between the probe and the sample cause a significant shift in the vibrational phase of the cantilever relative to the externally driven oscillation. Although the phase shift in tapping mode AFM is informative and serves as a phase imaging mode, large phase shifts can make it difficult to determine the instantaneous tip-sample contact time for other AFM modes. PF-SNOM can accurately determine the tip-sample distance over time, whereas the oscillatory phase shift in tap mode AFM leads to difficulties in implementing a time gated detection scheme compared to PF-SNOM.

In tapping mode AFM, repulsion, attraction, and especially adhesion between the probe and the sample, cause nonlinear dynamics of cantilever vibration, which are exhibited even when high order lock demodulation is performed by anharmonic far-field scattering. In contrast, PF-SNOM measures the scattered signal directly from the side close to the PFT period where there is no effect on the adhesion between the rear tip and the sample, thus avoiding the mechanical effects that may be produced by a sticky surfaceAnd (5) deforming. In this respect, PF-SNOM is more adaptable to rough and sticky samples than tapping mode s-SNOM. It should be noted that in another embodiment, a retraction curve (retract curve) may be used to obtain near field information, i.e., at point t of curve 205 in fig. 2A_dThe scattered signal is then analyzed as the tip separates from the surface. This can be achieved when the possible mechanical deformations are small or can be corrected.

PF-SNOM is a complement to the existing Peak Force Infra Red (PFIR) microscope that measures laser induced photothermal expansion in peak force tapping mode. PF-SNOM optical detection of near-field scattered signals from the tip and sample, which are determined by the tip-sample polarizability and the propagating surface waves; while PFIR performs mechanical detection based on the results of local optical absorption and subsequent dissipation of energy as heat. Compared to PFIR microscopy, which is suitable for soft materials with large coefficients of photothermal expansion, PF-SNOM inherits the advantages of s-SNOM in measuring rigid and polarized materials with spatial contrast derived from differences in dielectric functions.

The PF-SNOM enables simultaneous mechanical, electrical and optical near-field characterization of a sample. The three aspects of sample performance obtained by one measurement of PF-SNOM would be very helpful in studying the nanoscale activities of functional materials, such as metal-insulator transitions of related electronic materials, and nanoscale opto-mechanical structures and devices. The general compatibility of PF-SNOM makes it a more perfect scattering type near-field optical microscope platform.

FIG. 3 shows an example of valuable information that can be obtained using tip-sample distance dependent near field spectroscopy of PF-SNOM. Fig. 3A-3I show exemplary sets of data analyzing resonance peak positions and spectral peak widths of phonon polarons of Boron Nitride Nanotubes (BNNTs) and their tip-sample distance dependence according to embodiments of the herein disclosed subject matter. The PF-SNOM signal was measured as a function of the laser wavelength at three different spatial locations on the same BNNT nanotube (fig. 3A- 3C show 1, 2, 3, respectively, in fig. 2F) for three different tip-sample distances d. For example, FIG. 3A shows the scattered near field response to a first location on a BNNT at tip-sample distances of multiple wavelengths of the light source (x-axis 306)(y-axis 305) (1 nm 310, 3.5nm 311, and 6.5nm 312 in this example). Lorentzian fits (Lorentzian fits) of the central peak regions are shown as solid lines for the respective distance group sets. The inset shows the resonance peak ω fitted at three different values of d_pFull width transition at full-width at half-maximum (FWHM). It can be observed that ω is decreased with d_pThe line width of (a) increases.

Fig. 3B and 3C show similar curves for different positions relative to the sample. Thus, data corresponding to a 256x256 position matrix (e.g., pixels) may be collected to ultimately generate a tomographic image based on the collected PF-SNOM data. Fig. 3D contains the fitting parameters for the lorentz fit of fig. 3A-3C. Fig. 3E shows simulated spectra and dielectric functions of Boron Nitride (BN) based on image dipole models with d ═ 1, 3.5, and 6.5 nm. FIG. 3E illustrates ω for different values of d_pThe offset 320 occurs and is shown by the oblique vertical line. Similar shifts can be seen from the experimental data summarized in fig. 3D. Accurate measurement of plasmon resonance and displacement based on tip-sample interaction provides a more accurate estimate of nanostructure resonance, which improves the assessment of the spectral properties of chemical sensors based on poled materials.

3F-3G are diagrams of tomographic images that may be created from data collected by the PF-SNOM technique according to an embodiment of the presently disclosed subject matter. In the figure, one set of data corresponds to a near-field response with a single wavelength of light from a light source (e.g., 1390cm in this example)^-1) Is correlated (e.g., d 1nm in fig. 3F and d 4nm in fig. 3G). As previously mentioned, surface phonon polarons (phps) are surface electromagnetic modes formed by the collective oscillation of optical phonons and the electric field associated with the surface. It is known that a polar material such as silicon carbide (SiC) or Boron Nitride (BN) supports the surface PhP. The PF-SNOM is capable of probing PhP in both lateral and vertical directions of the sample surface. Fig. 3A-3I show an example of data collection, measurement and image construction for Boron Nitride Nanotubes (BNNTs) using a PF-SNOM microscope.

The spatial resolution of the PF-SNOM can be estimated from the edges of the BNNT. Fig. 3H shows an enlarged PF-SNOM image taken at d ═ 1 nm. Fig. 3I shows a profile cross section of the PF-SNOM image along the white line 350 in fig. 3H, which achieves a spatial resolution of 5 nm. In contrast, the radius of the metal tip used in this example was estimated to be 30 nm. The spatial resolution of PF-SNOM is greatly improved over the tip radius because of the enhancement of the gap mode (gap-mode) formed at the short tip-sample distance of 1nm due to the highly non-uniform spatial distribution of the optical field, which is tightly confined in the lateral dimension to a range much smaller than the tip radius.

The spectral response of BNNTs also shows a dependence on the tip-sample distance d. FIGS. 3A-3C show the scattering spectra of PF-SNOM at three positions on BNNT at three different d values of 1, 3.5 and 6.5nm, frequency of 1370cm^-1To 1440cm^-1. The fitting parameters for PF-SNOM spectra from three locations and three tip-sample distances are listed in FIG. 3D, where it can be found that as the probe location gets farther and farther from the nanotube end (from locations 1 to 3 in FIG. 2F), the central resonance frequency ω of PhP red-shifted (redshift) is_pAnd its peak linewidth becomes narrow (in terms of full width at half maximum (FWHM)). This is likely caused by interference between the PhP emitted by the tip and the PhP reflected by the end. PhP excited by lower frequencies has a longer polarization wavelength and lower losses. This lower frequency PhP propagates further and therefore is more prominent at locations away from the tip. On the other hand, since a lower polaron loss means a longer lifetime, correspondingly, the resonance peak ω_pAlso narrower.

In FIG. 3D, there are two special features related to the tip-sample distance that can only be shown by PF-SNOM. First, at the same location on BNNT, the resonance frequency ω of PhP decreases with decreasing tip-sample distance d_pA small red shift occurred. This offset can be qualitatively explained by a large dipole model based on the dielectric function of boron nitride. Fig. 3E shows a simulated relationship between the maximum of the polarization resonance spectrum and the tip-sample distance d according to an image dipole model with a 30nm radius tip coated with gold (Au). In the figureIn 3E, omega was observed as the tip-sample distance d decreased from 6.5 to 1nm_p1cm of light emission^-1Small displacement of (2). Since the spatial frequency of PhP depends on the frequency of the light source, ω_pThe shift in PhP indicates that the spatial pattern of PhP changes at different measurement distances in the high dispersion region of PhP.

The second feature of FIG. 3D is that ω is the decrease of the tip-sample distance at the same probing location_pThe line width of BNNT-PhP becomes wider, indicating that the lifetime of BNNT-PhP decreases as the tip approaches the surface. The decrease in lifetime is likely due to the presence of the highly confined gap mode creating more relaxation channels, which will greatly increase the optical density of the state between the BNNT tip and the surface. Thus, although the stronger field enhancement of the gap mode excites more PhPs, relaxation of PhPs is advantageous and the resonance linewidth is widened. This enhanced relaxation effect is conceptually similar to the Cyseoul effect (Purcell effect), which is a fluorophore coupled to the cavity and the tip to enhance relaxation.

With the atomic force microscope system described above, many advantages are realized by this novel PF-SNOM method and system. Particularly, PF-SNOM can rapidly measure three-dimensional near-field response. PF-SNOM allows for the measurement of multiple near field signals from multiple tip-sample distances. Thus, a three-dimensional near-field response cube (e.g., a three-dimensional map) may be constructed by stacking PF-SNOM images at different tip-sample distances into a data cube, or by aggregating near-field responses at different tip-sample distances from a set of two-dimensional lateral positions. In contrast, the current tapping mode s-SNOM can only achieve this operation at a sufficient speed if highly complex algorithms are applied. Therefore, three-dimensional data mapping using conventional s-SNOM systems and methods is not feasible.

Another advantage over conventional solutions is that the ability to measure near field signals at tip-sample distances equal to or less than 2nm can improve spatial resolution. In PF-SNOM, the tip-sample distance can be accessed when the tip is very close to the sample (e.g., less than 2 nm). Thus, near field signals with tip-sample distances of less than 2nm can be readily obtained. The minimum tip-sample distance possible is limited only by the detector response time. Measurements at a tip-sample distance of 1nm were demonstrated in the examples discussed above.

In contrast, in conventional tapping mode s-SNOM, the oscillation amplitude of an arbitrarily small AFM tip cannot be achieved because conventional tapping mode AFM requires at least a moderate oscillation amplitude for AFM topography feedback. Typical conventional tapping mode AFM tips oscillate at 25-60 nm. The signal from the tapping mode s-SNOM cannot provide a near field signal between the tip and the sample over a small tip-sample distance. In contrast, PF-SNOM near field images at a tip-sample distance of 1nm with high spatial resolution are provided herein.

Another advantage is that the PF-SNOM amplifies near field signals and increases signal strength by gap mode enhancement. PF-SNOM allows for conventional access gap pattern enhancement. That is, when a metal tip is close to a conductor, or generally to a sample whose real part of the dielectric function is negative, the electric field in the gap between the tip and the sample is greatly enhanced. The gap mode enhancement results in electric field amplification and results in a stronger near field signal. PF-SNOM can measure near-field scattered signals when the tip-sample is very close (e.g., less than 2 nm). The close range of distances allows for the collection of near field signals from gap mode enhancement without mixing with near field scattered signals lacking gap mode enhancement. The gap mode enhancement technique can highly localize the excitation field and increase the spatial resolution of PF-SNOM to about 5nm using an AFM tip with a radius of about 30 nm. In contrast, conventional tapping mode s-SNOM provides spatial resolution in excess of 10 nm.

Another advantage is that the PF-SNOM uses synchronized data acquisition, which allows for the simultaneous averaging of multiple tip-sample approaches/retractions over multiple events, thereby improving signal-to-noise ratio. In PF-SNOM, data acquisition is synchronized with changes in tip-sample distance to the moment just before tip-sample contact. Synchronous detection, also known as gated detection (gatedetection), averages the near-field signal, thereby improving the signal-to-noise ratio.

Another advantage over conventional s-SNOM is that PF-SNOM techniques utilize peak force tapping mode rather than conventional tapping mode. In peak force tapping mode, the distance between the tip and the sample is predictable because the AFM cantilever does not store kinetic energy. In contrast, in conventional tapping mode s-SNOM, the cantilever oscillates at a resonant frequency. Kinetic energy is stored in the AFM cantilever motion (Kinetic energy). The intermolecular force interaction between the tip and the sample results in unpredictable shifts in oscillation phase in tapping mode AFM. The change in the phase of the tapping mode AFM oscillation means that the closest time instant of the tip and the sample cannot be predicted and depends on the sample surface. This makes it difficult to acquire a time synchronization signal because the tip-sample distance cannot be predicted without knowing the basic sample profile to be measured.

PF-SNOM is not affected by this. In contrast, PF-SNOM accounts for tip-sample distance deviations due to intermolecular forces between the AFM tip and the sample. Intermolecular forces within the short tip-sample distance range cause the tip-sample distance to change during approach and retraction from the cantilever. In PF-SNOM, the cantilever deflection is dynamically measured in synchronism with the near field signal. Cantilever deflection is used to correct the reading of the tip-sample distance. In contrast, conventional tapping mode s-SNOM cannot correct for real-time tip-sample distance perturbations by using a lock-in amplifier.

Another advantage of PF-SNOM is the ability to simultaneously measure near field signals, mechanical responses and electrical signals in one mode of AFM operation and without the need for switching. In conventional s-SNOM, joint measurements of near field and mechanical mapping are done in turn. That is, the peak force tapping mode can be used to determine mechanical information, but near field imaging is collected using the conventional s-SNOM in the conventional tapping mode. Joint measurements are very time consuming. In PF-SNOM, both near field measurements and mechanical measurements are done in peak force tapping mode. In addition, conductivity measurements may also be made in one mode of operation along with near field imaging and mechanical mapping. Fig. 3J shows relevant measurements of sample morphology, mechanical modulus, contact current, and near field response of a hexagonal boron nitride wafer on a semiconductor silicon substrate. Hexagonal boron nitride in comparison to silicon substrateHas higher modulus and lower conductivity. Is shown at 1530cm^-1The near-field response of phonon polarons in hexagonal boron nitride under the infrared illumination frequency.

In another advantage, the PF-SNOM provides a higher signal-to-noise ratio per unit tip-sample oscillation period than conventional tapping mode s-SNOM. In PF-SNOM, the near field signal can be restored to the integral of the near field signal over a range of tip-sample distances. This can provide more data points than single value lock-in demodulation. Thus, fewer periods of tip oscillation are required compared to conventional tapping mode s-SNOM.

Another advantage is that the peak force tapping mode based on PF-SNOM is widely applicable to a range of samples. Tapping mode atomic force microscopy provides poor or unstable feedback on a sticky or rough sample surface. Therefore, the tapping mode s-SNOM cannot be applied to these sample surfaces. Peak force tapping mode AFM does not so much limit the adhesion or roughness of the sample surface. Thus, PF-SNOM inherits the broad applicability of peak force tapping mode and can be applied to non-ideal sample surfaces.

Fig. 4 is a flow chart 400 illustrating a method suitable for implementing PF-SNOM techniques for AFM microscopy according to an embodiment of the subject matter disclosed herein. The method may begin at step 410 by placing a sample on a sample stage of an AFM and initiating a PF-SNOM scan cycle at step 410. In one embodiment, the sample may be BNNTs, as described above. When the PF-SNOM process is initiated, the piezoelectric drive stage may generate a signal configured to cause a motion on the sample stage that is a periodic variation in the vertical distance between the proximity tip/cantilever arrangement and the sample. The tip may then be manipulated 415 toward the sample to a particular location (e.g., pixel location). This will cause an interaction between the tip and the sample and a vertical deflection of the cantilever, resulting in dynamic contact of the tip with the sample at the oscillation frequency of the piezoelectric material in the sample stage. As mentioned above, this frequency is typically between 0.1kHz and 100.0 kHz.

As the tip interacts with the sample, the method determines near-field responses (e.g., gated discrete range responses) for various ranges in step 420. A plurality of tip-to-sample distances are determined by detecting vertical deflection of the cantilever, the tip-to-sample distances corresponding to the tip in contact with the sample and deflection of the cantilever over a period of time. That is, as the maximum deflection moves away from the rest position, the bouncing contact may be determined within a certain time interval. By this determination, a plurality of near-field scattering responses can be determined from light focused on the sample at the tip contact region of the sample. Furthermore, when the tip is not close enough to the sample to cause a short-range near-field interaction during the cyclic variation, any background signal may be removed from the response signal initially determined to be representative of the background signal. Then, a linear or nonlinear response may correspond to the background signal, and when the sample induces a deflection in the cantilever through the induced interaction, then the approximate linear or nonlinear response may be removed from the plurality of near-field scattering responses.

These scans can be done at different wavelengths. Thus, in step 430, an interrogation is provided that scans at another frequency. If the pixel location is to be scanned at an additional frequency, the method returns to step 420 after adjusting the wavelength of the light source in step 440 and records the scattered near field response again using the new wavelength. If there are no more wavelengths at this location for which response data can be collected for the sample, the method proceeds to query 445 to determine if more pixel locations are to be analyzed. If so, the method returns to step 415 and moves the tip to the new pixel location. If there are no more pixel locations at query step 445, the method moves to step 460 where all of the collected data may be used to generate one or more tomographic images of the underlying sample at step 460. This may be accomplished by correlating multiple near-field scattering responses to multiple tip-to-sample distances for each sample location to generate a near-field response data map for the sample. The correlation function may further include: a set of near-field scattering responses from the plurality of near-field scattering responses is associated with the tip-sample distance for each sample location, wherein each set is associated with an equivalent tip-sample distance for each sample location of d 1 to n nanometers. Furthermore, this correlation may be achieved at different wavelengths used to analyze the sample. Fig. 4 depicts different examples, such as near-field mapping/imaging of constant wavelength, near-field point spectra of various wavelengths at a single spatial location, and near-field spectra of various wavelengths at different spatial locations (e.g., a 256x256 pixel line scan or hyperspectral map, where a full spectrum is recorded at each pixel).

Conventional s-SNOM based tapping mode AFM operation requires a continuous-wave (cw) or quasi-cw light source, i.e. if a pulsed light source, a sufficiently high repetition rate, typically in the MHz range of 10s, e.g. 80MHz, is required. The reason for this is that the near field signal is obtained by demodulating the tip scattered signal at the higher harmonics (typically 2-4 th harmonics) of the tip oscillation frequency (typically 200-. The repetition frequency of the light source in the range 100kHz to 1MHz is typically lower than the Nyquist sampling rate (Nyquist sampling rate) required to reveal the higher harmonics of the tip oscillation frequency, and so demodulation using a lock-in amplifier, typically in s-SNOM, will not be satisfactory. In order for a conventional s-SNOM to work with a low repetition rate laser, a more complex signal reconstruction must be performed. The PF-SNOM has less stringent requirements for the light source. Since the scattered signal in PF-SNOM is usually only around the beat contact time t_sExtraction within a few tens of microseconds before establishing tip-sample contact (see fig. 2A and 2B), it is sufficient to illuminate the sample only during this time interval. This means that in the extreme case, the laser need only emit during approximately 50us during a PET cycle of 2kHz PFT frequency, which can typically last 500 us. In this example, a 10% reduction in duty cycle may be beneficial to prevent overheating of sensitive samples. Furthermore, light source pulses in the range from kHz up to MHz still allow extraction of PF-SNOM data. Since the tip position in the PFT cycle is known and well-defined at each instant, the optical detector signal can be referenced to a specific tip position. For a PFT cycle frequency sequential low laser repetition rate (e.g., 2kHz), only a very few pulses (e.g., only 1) are recorded with the tip position per cycle. This may be achieved by collecting data over multiple PFT cyclesSufficient data points of the scatter signal versus tip-sample distance s (d) so that the curve 208 in fig. 2B, which consists of discrete data points, can be interpolated and analyzed. The laser repetition rate and PFT frequency may be synchronized with each other so that a scattered signal at a certain fixed tip-sample distance (e.g. d ═ 1nm) may be obtained in each PFT period. In this particular case of synchronizing the PFT period and the laser repetition frequency, once the shape of the background signal is determined, the PF-SNOM signal minus the background signal can be inferred by measuring only a single photodetector signal during a single PFT period. This means that the entire curve of the scattering signal s (d) in relation to the tip-sample distance does not need to be determined and a low kHz pulsed laser can be used. It requires knowledge of the background signal, which can be obtained by measuring the scatter signal versus tip sample distance (curve 208 in fig. 2B), for example, by moving the relative time between the synchronized laser pulse and the PFT period, or by operating out of synchronization, thereby collecting enough data points to interpolate and reconstruct curve 208 in fig. 2B. As previously described, a subsequent linear or non-linear fit will produce a background curve. This also requires that the background shape does not change between different sample locations in the image or spectrum.

There are several advantages to PF-SNOM in being able to use a continuous wave light source like a conventional tap mode s-SNOM. As described above, if the sample is sensitive to light or heat, the duty cycle and time during which the sample is illuminated can be minimized. This avoids the sample being destroyed or unnecessarily modified. Furthermore, PF-SNOM can use more light sources than s-SNOM, since the repetition frequency range is more flexible. For example, s-SNOM cannot use 1-100kHz optical parametric amplifier systems in the mid-infrared region, while PF-SNOM can.

In alternative embodiments, the PF-SNOM can employ a wider range of wavelengths outside the mid-infrared spectral region, such as the ultraviolet, visible, near infrared, and terahertz or far infrared ranges. QCLs, Optical Parametric Oscillators (OPOs) and amplifiers exist as pulsed and continuous wave light sources in the infrared. Ultraviolet, visible and near infrared are covered by laser sources such as solid state lasers, diode lasers, fiber lasers, OPO or gas lasers, and by laser sources based on nonlinear frequency conversion including optical parametric generation, sum frequency generation, harmonic generation, frequency combs and related methods. In the terahertz spectral region, terahertz quantum cascade lasers have emerged, and terahertz gas lasers, terahertz antennas, or free electron lasers have existed to cover this range.

Another embodiment is adapted to perform near-field spectroscopy using a broadband light source, such as a laser driven plasma source, a silicon carbide rod (globar), a supercontinuum source, or a synchrotron. These light sources may cover several hundred cm at a time^-1And QCLs typically provide narrow laser lines of about 1cm in width^-1. Tens to hundreds cm supplied by a broadband optical parametric oscillator or amplifier^-1The pulse of (2) is also sufficient. When the laser is replaced with a broadband light source, the setup is the same as in fig. 1. But now a PF-SNOM near field interferogram is obtained. This is achieved by varying the relative optical path length between reference arm 124 and the arm comprising tip 116 in the asymmetric michelson interferometer of figure 1. Typically, this is accomplished by moving (e.g., using a motorized stage) the retroreflector in the reference path 124. And extracting the PF-SNOM signal according to the steps while changing the relative path length. In one embodiment, the path length is varied stepwise, and after each step, a PF-SNOM signal is obtained at a specific tip-sample distance d (e.g., d ═ 1nm), and possibly an average of a specific number of PFT cycles. The resulting data set contains interferograms, i.e. the PF-SNOM signal at a certain distance d is a function of the relative path lengths of the two interferometer arms. The subsequent fourier transform yields the PF-SNOM near field spectrum as a function of wavelength. This process can be used to acquire spectra from a broadband source. In various embodiments, the path length is continuously varied rather than stepwise.

In the above PF-SNOM embodiment, the distance between the AFM tip and the sample is periodically oscillated by adjusting the sample position, and in addition to this, the same distance oscillation effect can be obtained by oscillating the position of the AFM tip. In this embodiment, the position of the AFM tip can be driven externally at a frequency below the mechanical resonance of the cantilever, and the related near-field signal and tip-sample distance measurements can be performed using PF-SNOM. It should be noted that the tip motion in this embodiment is different from the resonant oscillation of the cantilever in the tapping mode s-SNOM. In PF-SNOM, driving the position oscillation of the AFM tip at the resonance frequency of the AFM cantilever is avoided. Under PF-SNOM operation, the cantilever does not store kinetic energy in the form of resonant oscillations. In contrast, in s-SNOM in tapping mode, the cantilever is driven into oscillation at the resonant frequency of the cantilever. As a result, the cantilever vibration undergoes a phase change upon interaction with the sample, which makes it difficult to determine the tip-sample distance in a given time.

Fig. 5 is a diagram showing elements or components that may be present in a computer device or system configured to implement a method, process, function, or operation according to an embodiment. In accordance with one or more embodiments, the systems, apparatus, methods, procedures, functions and/or operations for configuring and efficiently presenting a user interface to a user based on previous behavior of the user may be implemented, in whole or in part, in the form of a set of instructions executed by one or more programmed computer processors (e.g., a Master Control Unit (MCU), a Central Processing Unit (CPU), or a microprocessor). Such processors may be incorporated into devices, servers, clients, or other computing or data processing devices that are operated by or in communication with other components of the system. By way of example, fig. 5 is a diagram showing elements or components that may be present in a computer device or system 600 for implementing a method, process, function or operation according to an embodiment. The subsystems shown in fig. 5 are interconnected by a system bus 602. Additional subsystems include a printer 604, a keyboard 606, a fixed disk 608, and a display 610 coupled to a display adapter 612. Peripheral devices and input/output (I/O) devices coupled to I/O controller 614 may be connected to the computer system by any number of means known in the art, such as serial port 616. For example, serial port 616 or external interface 618 may be used to connect computer device 600 to other devices and/or systems not shown in FIG. 5, including a wide area network such as the Internet, a mouse input device, and/or a scanner. The interconnection via system bus 602 allows one or more processors 620 to communicate with each subsystem and to control the execution of instructions stored in system memory 622 and/or fixed disk 608, as well as the exchange of information between subsystems. The system memory 622 and/or the fixed disk 608 may include tangible computer-readable media.

In this embodiment, the AFM 105 may also be coupled to the bus 602 via an interface (not shown). Thus, the above-described operations and processes may be initiated and performed using the processor 620 of the overall computing system 600 or on-board the processor 621 of the AFM 105. Further, the data determined and collected by the AFM 105 may be stored in the memory 622 of the computing system 600 or may be stored in a local memory 623 associated with the AFM 105.

It should be understood that the present disclosure as described above may be implemented in the form of control logic using computer software in a modular or integrated manner. Based on the disclosure and teachings provided herein, a person of ordinary skill in the art will appreciate other ways and/or methods to implement the present disclosure by hardware as well as by combining hardware and software.

Any of the software components, processes, or functions described herein may be implemented as software code executable by a processor using any suitable computer language (e.g., assembly language Java, JavaScript, C + +, or Perl) and using, for example, conventional or object-oriented techniques. The software code may be stored as a series of instructions or commands on a computer readable medium, such as a Random Access Memory (RAM), a Read Only Memory (ROM), a magnetic medium such as a hard drive or floppy disk, or an optical medium such as a CD-ROM. Any such computer-readable media may reside on or within a single computing device, and may exist on or within different computing devices within a system or network.

All references, including publications, patent applications, and issued patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and/or were set forth in its entirety herein.

The use of The terms "a" and "an," "The," and similar referents in The specification and The appended claims is to be construed to cover both The singular and The plural, unless otherwise indicated herein or clearly contradicted by context. Unless otherwise indicated, the terms "having," "including," "containing," and similar language in the specification and appended claims are to be construed as open-ended terms (e.g., meaning "including, but not limited to"). Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., "such as") provided herein, is intended merely to better illuminate embodiments and does not pose a limitation on the scope of the disclosure unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to each embodiment of the disclosure.

May have a different arrangement of parts than those shown in the drawings or described above, and may have parts and steps not shown or described. Similarly, some features and subcombinations may be of benefit and may be employed without reference to other features and subcombinations. The examples are given by way of illustration only and not for purposes of limitation, and alternative examples will become apparent to the reader of this patent. Accordingly, the present subject matter is not limited to the embodiments described above or depicted in the drawings, and various modifications may be made to the embodiments without departing from the scope of the appended claims.