A method for extracting surface potential signals from atomic force microscope topography images

Abstract

The present invention provides a method for extracting surface potential signals from atomic force microscope (AFM) topography images, comprising: using an AFM to detect the surface topography of a sample in an area with uneven surface potential, obtaining a topography image of the sample surface, and extracting a topography offset; establishing a quantitative relationship model between the surface potential signal and the topography offset based on a probe vibration model; and comparing the topography offset from step 1 with the quantitative relationship model from step 2 to obtain a surface potential signal. This method eliminates the need for additional detection modules, saving costs. Furthermore, due to the high resolution of topography detection, surface potential detection is free of signal distortion, resulting in a higher resolution than existing Kelvin force or electrostatic force detection technologies.

Description

Technical Field

[0001] The present invention relates to the field of scanning probe microscopy technology, and in particular but not limited to, to a method for extracting surface potential signals from atomic force microscope topography images. Background Art

[0002] Atomic force microscopy uses a nanometer-scale needle tip to detect the morphological information of the sample surface, and has the advantages of high imaging resolution and non-destructiveness. In recent years, people have developed Kelvin probe force microscopy and electrostatic force microscopy based on atomic force microscopy to detect the electrical properties of the sample surface. However, because the probe needs to be raised tens to hundreds of nanometers away from the sample surface during Kelvin force and electrostatic force detection, it leads to problems such as low imaging resolution and signal distortion. At present, there are some technical solutions that extract sample surface potential information from Kelvin probe force microscopy images and electrostatic force microscopy images through signal post-processing methods such as Wiener filtering, but these methods cannot improve imaging resolution, and the technical means are complex and rely on additional instrument detection modules.

[0003] In view of this, it is necessary to provide a new structure or control method to solve at least part of the above problems. Summary of the Invention

[0004] In response to one or more problems in the prior art, the present invention proposes a method for extracting surface potential signals from atomic force microscope topography images, which realizes the direct extraction of surface potential signals without the need for additional Kelvin force and electrostatic force detection modules, and has the same high resolution as topography detection.

[0005] The technical solutions for achieving the purpose of the present invention are:

[0006] A method for extracting surface potential signals from an atomic force microscope topography image comprises the following steps:

[0007] Step 1: Use an atomic force microscope to detect the surface morphology of the sample in an area with uneven surface potential, obtain a topographic image of the sample surface, and extract the topographic offset from it;

[0008] Step 2: Establish a quantitative relationship model between the surface potential signal and the topography offset based on the probe vibration model;

[0009] Step 3: Compare the topography offset in step 1 with the quantitative relationship model in step 2 to obtain the surface potential signal.

[0010] Furthermore, in the method of extracting surface potential signals from atomic force microscope topography images of the present invention, the probe vibration model in step 2 is:

[0011]

[0012] Where m is the effective mass of the probe, z(t) is the coordinate of the probe relative to its equilibrium position at time t, and are the first and second derivatives of z with respect to time, ω0, Q and k are the natural frequency, quality factor and stiffness coefficient of the probe, respectively. F d and ω are the driving force amplitude and frequency respectively, F ts and d are the force and average distance between the probe and the sample, respectively.

[0013] Furthermore, in the method of extracting surface potential signals from atomic force microscope topography images of the present invention, establishing a quantitative relationship model based on the probe vibration model in step 2 includes the following steps:

[0014] Step 2-1: Establish a relationship model between the probe force and amplitude based on the probe vibration model. The relationship model between the probe force and amplitude is:

[0015]

[0016] Where ω0, Q, and k are the natural frequency, quality factor, and stiffness coefficient of the probe, respectively; z is the coordinate of the probe relative to its equilibrium position; d is the average distance between the probe and the sample; A0 represents the amplitude when the probe is far away from the sample surface (d→∞); and A represents the amplitude when the probe is close to the sample surface (d→A);

[0017] Step 2-2: When the surface potential of the sample is 0, there is no long-range electrostatic force between the probe and the sample, so the force F between the probe and the sample is ts For: F ts =F vdw The formula for calculating the average distance d0 between the probe and the sample when the surface potential is 0 is:

[0018]

[0019] Among them, F vdw is the van der Waals force;

[0020] Step 2-3: When the sample surface potential is V s When there is a long-range electrostatic force between the probe and the sample, the force F between the probe and the sample is ts For: F ts (z+d)=F vdw (z+d)+F el (z+d,V s ), the average distance d between the probe and the sample changes to: d = d0 + Δd, and the surface potential signal V is established sThe quantitative relationship model between the morphology offset Δd is:

[0021]

[0022] Where Δd is the morphology deviation caused by the surface potential of the sample, F el Represents electrostatic force.

[0023] Furthermore, in the method of extracting surface potential signals from atomic force microscope topography images of the present invention, the van der Waals force F in step 2-2 vdw for:

[0024]

[0025] Where z is the coordinate of the probe relative to its equilibrium position, d is the average distance between the probe and the sample, H is the Hamaker constant, R is the radius of curvature of the probe, a0 is the critical position where the force reaches the minimum, and E is the equivalent Young's modulus between the probe and the sample.

[0026] Furthermore, in the method of extracting surface potential signals from atomic force microscope topography images of the present invention, the electrostatic force F in step 2-3 is el for:

[0027]

[0028] Where z is the coordinate of the probe relative to its equilibrium position, d is the average distance between the probe and the sample, R is the radius of curvature of the probe, ∈0 is the dielectric constant of vacuum, V s is the surface potential.

[0029] Furthermore, in the method of extracting surface potential signals from atomic force microscope topography images of the present invention, in step 1, the atomic force microscope detects the surface morphology of the sample in a tapping mode, and the driving force frequency in the tapping mode is equal to the probe's natural frequency.

[0030] Furthermore, in the method of extracting surface potential signals from atomic force microscope topography images of the present invention, in step 1, standard atomic force microscope image processing software is used to extract the topography offset.

[0031] Furthermore, in the method of extracting a surface potential signal from an atomic force microscope topography image of the present invention, step 3 of comparing the topography offset of step 1 with the quantitative relationship model of step 2 specifically includes:

[0032] The topographic offset of each sampling point in the topographic image of the sample surface is compared with the quantitative relationship model to obtain the surface potential signal of each sampling point. The surface potential signals of all sampling points in the topographic image are combined to construct a two-dimensional image of the sample surface potential signal distribution.

[0033] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0034] 1. Compared with existing non-contact Kelvin force or electrostatic force detection technologies, the method of the present invention for extracting surface potential signals from atomic force microscope topography images does not require the use of additional detection modules, thus saving costs.

[0035] 2. The method of extracting surface potential signals from atomic force microscope topography images of the present invention is based on the high resolution of topography detection, so that there is no signal distortion problem in detecting surface potential, and the resolution is higher than the existing Kelvin force or electrostatic force detection technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings are used to provide a further understanding of the present invention and, together with the description, to explain the embodiments of the present invention, but do not constitute a limitation of the present invention. In the accompanying drawings:

[0037] Figure 1 This is the surface morphology image of the nano-silicon floating gate structure detected by atomic force microscope tapping mode.

[0038] Figure 2 Schematic diagram of the principle of topography measurement offset due to surface potential signal.

[0039] Figure 3 This is a relationship curve diagram of the quantitative relationship model between the surface potential signal and the morphology offset.

[0040] Figure 4 This is the final extracted surface potential signal distribution image. DETAILED DESCRIPTION

[0041] In order to further understand the present invention, preferred embodiments of the present invention are described below in conjunction with examples. However, it should be understood that these descriptions are only for further illustrating the features and advantages of the present invention, rather than limiting the claims of the present invention.

[0042] The description in this section is based on typical embodiments only, and the present invention is not limited to the scope of the embodiments described. Combinations of different embodiments, replacement of certain technical features in different embodiments, and replacement of certain technical features in the embodiments with the same or similar prior art methods are also within the scope of the present invention.

[0043] A method for extracting surface potential signals from an atomic force microscope topography image comprises the following steps:

[0044] 1) Using an atomic force microscope in tapping mode, with the driving force frequency equal to the probe's natural frequency, probe the sample's surface topography in an area with uneven surface potential and record the image information. Use standard image processing software to extract the topography deviation signal.

[0045] 2) Based on the probe vibration model, a quantitative relationship model between the surface potential signal and the topography offset is established. The general model of probe vibration is as follows

[0046]

[0047] Where m is the effective mass of the probe, z(t) is the coordinate of the probe relative to its equilibrium position at time t, and are the first and second derivatives of z with respect to time, ω0, Q and k are the natural frequency, quality factor and stiffness coefficient of the probe (the inherent properties of the probe), respectively. d and ω are the driving force amplitude and frequency respectively, F ts and d are the force and average distance between the probe and the sample, respectively. According to the theory of simple harmonic vibration, the relationship between the stiffness coefficient and the natural frequency is as follows:

[0048]

[0049] The present invention only considers the case where the driving force frequency is consistent with the probe's natural frequency, that is, the case where ω=ω0.

[0050] First, a relationship model between the probe vibration amplitude and the force is established. When the probe tip is far away from the sample surface, the force between the probe and the sample can be ignored, that is, F ts = 0, so the vibration equation is simplified to the following forced vibration equation including damping

[0051]

[0052] The tentative solution z(t) = A0cos(ω0+φ0) is adopted, where the undetermined parameters A0 and φ0 are the amplitude and phase of the forced vibration respectively. Substitute it into formula (3) and multiply both sides of the equal sign by And integrate it within a time period, and then use formula (2) to get

[0053] 0=F d cos(φ0) (4)

[0054] Similarly, multiply both sides of the equal sign in formula (3) by And within a time period, you can get

[0055]

[0056] Combining formulas (4) and (5), we can get

[0057]

[0058] On the other hand, when the probe tip is close to the sample surface, the force between the probe and the sample needs to be considered, and the vibration equation is:

[0059]

[0060] The tentative solution z(t) = Acos(ω0t+φ) is adopted, where the unknown parameters A and φ are the amplitude and phase, and after substituting them into formula (7), multiply both sides of the equal sign by And integrate within a period T, we can get

[0061]

[0062] Similarly, multiply both sides of the equal sign in formula (7) by And integrate within a period T, we can get

[0063]

[0064] Combine formula (8) and (9) to eliminate φ, and then combine formula (6) and the variable substitution identity The relationship model between the probe force and amplitude is as follows

[0065]

[0066] In the tapping mode of the atomic force microscope, the amplitude A remains unchanged and the integral in formula (10) is a constant.

[0067] On this basis, a quantitative relationship model between the surface potential signal and the morphology offset is established. If the surface potential of the sample is 0, there is no long-range electrostatic force, and the force F between the probe and the sample is ts Equal to van der Waals force F vdw , defined as

[0068]

[0069] Where z is the coordinate of the probe relative to its equilibrium position, d is the average distance between the probe and the sample, H is the Hamaker constant, R is the radius of curvature of the probe, a0 is the critical position where the force reaches the minimum, and E is the equivalent Young's modulus between the probe and the sample. Combining formulas (10) and (11), the average distance d0 between the probe and the sample when the surface potential is 0 can be calculated by numerical calculation, that is, solving the following equation

[0070]

[0071] If the surface potential of the sample is V s(not equal to 0), there is a long-range electrostatic force between the probe and the sample. The present invention uses a flat plate capacitor model to describe this electrostatic force F el ,Right now

[0072]

[0073] Where V s is the surface potential value, z is the coordinate of the probe relative to its equilibrium position, d is the average distance between the probe and the sample, R is the probe curvature radius, and ∈0 is the vacuum dielectric constant. At this time, the force between the probe and the sample needs to be corrected to: F ts (z+d)=F vdw (z+d)+F el (z+d,V s ), which will cause the average distance between the probe and the sample to change, that is, d = d0 + Δd, where Δd is the morphology offset caused by the surface potential of the sample. According to formula (10), Δd and V s The relationship model is as follows:

[0074]

[0075] This is about Δd and V s The implicit function form of Δd and V can be obtained by conventional numerical calculation s The quantitative relationship model between the sample surface potential signal and the morphology deviation is established through formulas (11) to (14).

[0076] 3) Compare and analyze the surface morphology information Δd obtained in step 1 with the detection model in step 2 to obtain the surface potential signal V s .

[0077] Example 1

[0078] A method for extracting surface potential signals from an atomic force microscope topography image comprises the following steps:

[0079] Step 1. Use an atomic force microscope (Bruker Nanoscope III-D) in tapping mode to test the sample and record the image information. The test sample is a nano-silicon floating gate storage structure with storage function on a p-type single crystal silicon substrate (resistivity 1.5–3Ω-cm). The central area stores charge, so the surface potential distribution is uneven. The probe model used in the test is SCM-PIT (made of silicon material), the driving force frequency is equal to the probe's natural frequency (about 75kHz), the scanning rate is 1Hz, the side length of the scanning area is 2 microns, and the number of sampling points is 512×512. According to the probe manual and the set conditions during the test, the relevant parameters involved in the detection model are listed in Table 1. The morphological image obtained by the test is shown in the attached figure. Figure 1As shown in the figure, due to the influence of the stored charge at the center, there is an obvious morphological shift in the central area. Using conventional atomic force microscope image processing software, the original morphological image can be further decomposed into the real morphological image and the additional signal image caused by the surface potential. The decomposition results are shown in the attached figure. Figure 1 As shown, the average topography offset in the central area is about 1.5 nm.

[0080] Table 1 Probe attribute related parameter list

[0081]

[0082]

[0083] Step 2: Establish a quantitative relationship model between the surface potential signal and the topography deviation based on the probe vibration model. This invention only considers the case where the driving force frequency is consistent with the probe's natural frequency. The relationship model between the force and amplitude between the probe and the sample is as follows (refer to formula (10)):

[0084]

[0085] Where ω0, Q and k are the natural frequency, quality factor and stiffness coefficient of the probe respectively, F ts and d are the force and average distance between the probe and the sample, respectively. z is the coordinate of the probe relative to its equilibrium position. A0 represents the amplitude when the probe is far away from the sample surface (d→∞), and A represents the amplitude when the probe is close to the sample surface (d→A). In the tapping mode of the atomic force microscope, the set values ​​of A0 and A are also listed in Table 1.

[0086] On this basis, the quantitative relationship between the surface potential signal and the topography offset is obtained by the following method. First, the average distance d0 between the probe and the sample when the surface potential is 0 is calculated by numerical calculation, that is, the following equation is solved (refer to formula (12)):

[0087]

[0088] The van der Waals force F vdw The definition is as follows:

[0089]

[0090] Where z is the coordinate of the probe relative to its equilibrium position, d is the average distance between the probe and the sample, H is the Hamaker constant, R is the radius of curvature of the probe, a0 is the critical position where the force is minimized, and E is the equivalent Young's modulus between the probe and the sample. Using the probe parameters in this example (see Table 1), numerical calculations show that the average distance d0 between the probe and the sample when the surface potential is zero is: d0 = 16.183616 nm.

[0091] Next, consider the sample surface potential to be V s (not equal to 0), there is still a long-range electrostatic force between the probe and the sample. The present invention uses a flat plate capacitor model to describe this electrostatic force F el :

[0092]

[0093] Where V s is the surface potential value, z is the coordinate of the probe relative to its equilibrium position, d is the average distance between the probe and the sample, R is the radius of curvature of the probe, and ∈0 is the dielectric constant of vacuum. At this time, the force between the probe and the sample is corrected to F ts (z+d)=F vdw (z+d)+F el (z+d,V s ), which will cause the average distance between the probe and the sample to change, that is, d = d0 + Δd, where Δd is the morphology offset caused by the surface potential of the sample. Figure 2 Given the detection principle involved in the present invention, the sample surface potential V s The existence of will make the probe move upward as a whole by displacement Δd, and Δd is related to V s The relationship is as follows (refer to formula (14)):

[0094]

[0095] This is about Δd and V s The implicit function form of the probe is numerically calculated using the parameter values ​​of the probe in Table 1 to obtain Δd and V s The relationship curve is as follows Figure 3 As shown in Figure 3, when the morphology shifts by 1.5 nm, the corresponding surface potential is approximately 0.32 V.

[0096] Step 3: Figure 1 Each sampling point of the two-dimensional image of the additional signal (i.e., the topography offset) is Figure 3 By comparing, a two-dimensional image of the sample surface potential can be constructed. The extraction results of this example are shown in the attached figure. Figure 4 As shown, it is proved that this method is feasible.

[0097] The description and application of the present invention here are illustrative and are not intended to limit the scope of the present invention to the above-mentioned embodiments. The relevant descriptions of the effects or advantages involved in the specification may not be reflected in the actual experimental examples due to the uncertainty of specific condition parameters or other factors, and the relevant descriptions of the effects or advantages are not used to limit the scope of the invention. Variations and changes to the embodiments disclosed here are possible, and the replacement of the embodiments and various equivalent components are well known to those of ordinary skill in the art. It should be clear to those skilled in the art that, without departing from the spirit or essential characteristics of the present invention, the present invention can be implemented in other forms, structures, arrangements, proportions, and with other components, materials and parts. Without departing from the scope and spirit of the present invention, other variations and changes can be made to the embodiments disclosed here.

Claims

1. A method for extracting surface potential signals from atomic force microscope topography images, characterized in that: The steps include: Step 1: Use an atomic force microscope to detect the surface morphology of the sample in an area with uneven surface potential, obtain a topographic image of the sample surface, and extract the topographic offset from it; Step 2: Establish a quantitative relationship model between the surface potential signal and the topography offset based on the probe vibration model. The quantitative relationship model is: Where ω0, Q and k are the natural frequency, quality factor and stiffness coefficient of the probe respectively, A represents the amplitude when the probe is close to the sample surface, A0 represents the amplitude when the probe is far away from the sample surface, F vdw is the van der Waals force, z is the coordinate of the probe relative to its equilibrium position, d0 is the average distance between the probe and the sample when the surface potential is 0, Δd is the topography offset, and F el represents the electrostatic force, V s is the sample surface potential; Step 3: Compare the topography offset in step 1 with the quantitative relationship model in step 2 to obtain the surface potential signal.

2. The method for extracting surface potential signals from atomic force microscope topography images according to claim 1, characterized in that: The probe vibration model in step 2 is: Where m is the effective mass of the probe, z(t) is the coordinate of the probe relative to its equilibrium position at time t, and are the first and second derivatives of z with respect to time, ω0, Q and k are the natural frequency, quality factor and stiffness coefficient of the probe, respectively. F d and ω are the driving force amplitude and frequency respectively, F ts and d are the force and average distance between the probe and the sample, respectively.

3. The method for extracting surface potential signals from atomic force microscope topography images according to claim 2, characterized in that: In step 2, establishing a quantitative relationship model based on the probe vibration model includes the following steps: Step 2-1: Establish a relationship model between the probe force and amplitude based on the probe vibration model. The relationship model between the probe force and amplitude is: Where ω0, Q, and k are the natural frequency, quality factor, and stiffness coefficient of the probe, respectively; z is the coordinate of the probe relative to its equilibrium position; d is the average distance between the probe and the sample; A0 represents the amplitude when the probe is far away from the sample surface; and A represents the amplitude when the probe is close to the sample surface. Step 2-2: When the surface potential of the sample is 0, there is no long-range electrostatic force between the probe and the sample, so the force F between the probe and the sample is ts For: F ts =F vdw The formula for calculating the average distance d0 between the probe and the sample when the surface potential is 0 is: Among them, F vdw is the van der Waals force; Step 2-3: When the sample surface potential is V s When there is a long-range electrostatic force between the probe and the sample, the force F between the probe and the sample is ts For: F ts (z+d)=F vdw (z+d)+F el (z+d,V s ), the average distance d between the probe and the sample is: d = d0 + Δd, and the surface potential signal V is established. s The quantitative relationship model between the morphology offset Δd is: Where Δd is the morphology deviation caused by the surface potential of the sample, F el Represents electrostatic force.

4. The method for extracting surface potential signals from atomic force microscope topography images according to claim 3, characterized in that: Van der Waals force F in step 2-2 vdw for: Where z is the coordinate of the probe relative to its equilibrium position, d is the average distance between the probe and the sample, H is the Hamaker constant, R is the radius of curvature of the probe, a0 is the critical position where the force reaches the minimum, and E is the equivalent Young's modulus between the probe and the sample.

5. The method for extracting surface potential signals from atomic force microscope topography images according to claim 3, characterized in that: The electrostatic force F in steps 2-3 el for: Where R is the probe curvature radius and ∈0 is the vacuum dielectric constant.

6. The method for extracting surface potential signals from atomic force microscope topography images according to claim 1, characterized in that: In step 1, the atomic force microscope detects the surface morphology of the sample in a tapping mode, and the driving force frequency in the tapping mode is equal to the natural frequency of the probe.

7. The method for extracting surface potential signals from atomic force microscope topography images according to claim 1, characterized in that: In step 1, standard atomic force microscope image processing software is used to extract the topography offset.

8. The method for extracting surface potential signals from atomic force microscope topography images according to claim 1, characterized in that: In step 3, the comparison of the topography offset in step 1 with the quantitative relationship model in step 2 specifically includes: The topographic offset of each sampling point in the topographic image of the sample surface is compared with the quantitative relationship model to obtain the surface potential signal of each sampling point. The surface potential signals of all sampling points in the topographic image are combined to construct a two-dimensional image of the sample surface potential signal distribution.

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