Novel EFM measuring system and method for measuring surface potential of two-dimensional material

Abstract

The invention discloses a novel EFM measurement system and a method for measuring the surface potential of a two-dimensional material, and belongs to the technical field of EFM measurement. The novel EFM measurement system is an improvement on a PI unit, and the improved PI unit module comprises a cantilever motion model (1), a mechanical acting force model (2), an electrostatic acting force model (3) and a material surface potential calculation model (4). According to the measurement method, the second modal amplitude of cantilever vibration is analyzed through combination of Fourier transform and improved wavelet transform, and the surface potential of a sample is quantitatively characterized. Firstly, Fourier transform is utilized to obtain second modal frequency and amplitude of a cantilever vibration signal, then improved wavelet transform is combined to accurately analyze the second modal amplitude, amplitude change of a second modal time domain reflects surface potential change of a sample, and through the relationship between two vibration signals and the surface potential of the sample, the surface potential of the sample is accurately analyzed. And transient characteristic analysis of the surface potential of the sample is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of EFM measurement, and more particularly to a new EFM measurement system with improved PI unit and a method for measuring surface potential of two-dimensional material using the new EFM measurement system. BACKGROUND

[0002] Electrostatic Force Microscope (EFM) is a kind of microscopic analysis instrument for characterizing and measuring the electrical properties of sample surface. The design and working principle of EFM instrument are based on Atomic Force Microscope (AFM), and the measurement is the electrostatic force between the conductive cantilever tip and the sample. EFM can directly measure the electrostatic force between the cantilever and the sample, and has been widely used. By controlling the electric field between the tip and the sample, EFM can measure various static or dynamic electrical properties of the sample with high spatial resolution, including surface contact potential difference, surface piezoelectric response, charge and decay time of photo-excited carriers, local activation energy of ion migration, etc.

[0003] Reference: Multifrequency electrostatic force microscopy in the repulsive regime, downloaded from the link of . As shown in Figure 1 , the first mode of the EFM cantilever is driven by a mechanical excitation signal, and the second mode is driven by an alternating current signal. By the difference in frequency, the mechanical interaction and electrostatic interaction between the cantilever and the sample are distinguished, and the scanning of a single process can obtain the topographic information and electrical property information of the sample at the same time. In Figure 1 , the PI unit (i.e. the motion control center of the EFM operation table) is used to control the motion of the EFM operation table.

[0004] Two-dimensional chip material is a planar material with atomic thickness, and its core feature is that the size is reduced to nanoscale or even single atomic layer thickness (usually less than 1 nanometer) in one dimension, while the continuity in the other two dimensions remains macroscopic scale. This unique structure makes it have completely different physical, electrical and optical properties from traditional three-dimensional bulk materials (such as silicon), such as high electron mobility, excellent gate control ability and low power consumption characteristics, and is considered as a key material to break through the physical limit of silicon-based chips. Among them, molybdenum disulfide (MoS2) as a two-dimensional material with excellent semiconductor performance, the surface potential distribution directly affects the device performance, so it is of great research value and application significance to accurately and dynamically characterize the surface potential of MoS2.

[0005] Since the difference and distribution of the surface potential / charge of the two-dimensional chip material are indirectly reflected when detected by EFM, the accurate absolute value cannot be directly obtained. This is because the traditional EFM measures the vibration signal of the cantilever under the combined action of mechanical force and electrostatic force, which reflects the size of the force rather than the potential itself. To overcome this limitation, with the aid of Figure 1 The application designs a new EFM measurement system by integrating the signal analysis module based on Fourier transform and improved wavelet transform. The system realizes high-precision analysis of the amplitude of the second mode of the cantilever vibration, and can directly and quantitatively represent the absolute size of the surface potential of the sample, avoiding the dependence on complex parameters such as the capacitance gradient and the quality factor of the traditional method, and significantly improving the accuracy, speed and practicability of the measurement. SUMMARY

[0006] In order to realize the quantitative characterization of the surface potential of the two-dimensional chip material sample by the EFM measurement system, the application adds a multi-frequency electrostatic force microscope electrostatic force analysis method based on Fourier transform and wavelet transform to the PI unit of the original EFM, that is, a new EFM measurement system is designed. The new EFM measurement system of the application models the cantilever beam of the traditional EFM measurement system by using the Simulink module in Matlab, and obtains the improved PI unit module as shown in Figure 2 The improved PI unit module includes a cantilever motion model (1), a mechanical force model (2), an electrostatic force model (3) and a material surface potential calculation model (4).

[0007] The cantilever motion model (1) is used to obtain the interaction force information (23) between the scanning probe tip and the sample on the one hand, and to obtain the cantilever vibration information (30) by processing the interaction force information (23) by using the cantilever beam motion equation; on the other hand, the cantilever vibration information (30) is output to the surface potential calculation module (4), the mechanical force model (2) and the electrostatic force model (3).

[0008] The mechanical force model (2) is used to obtain the initial height information (11) between the probe and the sample on the one hand, and to obtain the mechanical force (21) by processing the initial height information (11) and the cantilever vibration signal (30) according to the Van der Waals force on the other hand; the third aspect outputs the mechanical force (21) generated by the mechanical force model (2), and the mechanical force (21) acts on the tip at the end of the cantilever.

[0009] The electrostatic force model (3) is used to obtain the initial height information (11) between the probe and the sample on one hand, to receive the cantilever vibration information (30) output by the cantilever motion model (1) on the other hand, to obtain the electrostatic driving force (12) of the EFM cantilever on the third hand, to obtain the sample surface potential (13) of the EFM cantilever on the fourth hand, to process the initial height information (11), the electrostatic driving force (12), the sample surface potential (13) and the cantilever vibration information (30) according to the combination of the capacitance gradient and the electrostatic force, and to obtain the electrostatic force (22); and the fifth hand outputs the electrostatic force (22) generated by the electrostatic force model (3), and the electrostatic force (22) acts on the needle tip at the end of the cantilever.

[0010] The calculation material surface potential model (4) is used to receive the cantilever vibration information (30) output by the cantilever motion model (1) on one hand, and to obtain the dynamic potential information (10) of the sample surface according to the electrostatic force analysis combined with the Fourier transform and the wavelet transform on the other hand, and to transmit the dynamic potential information (10) to a computer for visual demonstration.

[0011] In the present application, the electrostatic force analysis combined with the Fourier transform and the wavelet transform is the content of step four.

[0012] The measurement method of the surface potential of two-dimensional materials based on the novel EFM measurement system designed in the present application has the following measurement steps:

[0013] Step one, collecting the response of the cantilever beam under the sweep frequency signal;

[0014] In the present application, the Simulink module in Matlab is used to model and analyze the cantilever beam of the traditional EFM measurement system, the PXIe-6368 data acquisition card is used to collect signals, and the sampling rate is set to .

[0015] The response frequency-voltage curve of the cantilever beam under the continuous frequency signal excitation is collected, as shown in Figure 3 , the frequency of the first mode of the cantilever is analyzed from the frequency-voltage curve and recorded as , and the frequency of the second mode of the cantilever is recorded as .

[0016] Step two, setting the voltage signal for exciting the cantilever;

[0017] The first excited alternating voltage signal is recorded as , the frequency of the signal is recorded as , and the voltage amplitude is recorded as .

[0018] The second excited alternating voltage signal is recorded as The signal The frequency is denoted as The voltage amplitude is also .

[0019] In this invention, the voltage amplitudes of the two excitation voltage signals are equal (i.e., The frequency It is half the frequency of the second mode of the cantilever (i.e. The frequency The frequency is the same as that of the second mode of the cantilever (i.e. = ).

[0020] Step 3: Set the signal used to excite the first mode of the cantilever based on the frequency-voltage curve;

[0021] An auxiliary excitation signal with the same frequency as the first mode of the cantilever is set as follows: The signal Used to excite the first mode of vibration of the cantilever.

[0022] The sampling rate of the cantilever vibration signal is set as denoted as .

[0023] Step 4: Calculation of sample surface potential based on a combination of Fourier transform and wavelet transform;

[0024] See Figure 4 As shown, the cantilever vibration signal (30) is processed as follows:

[0025] (1) Perform a Fourier transform to obtain all frequency components. The frequency component with the largest amplitude is the first mode frequency. ,according to The relationship, in The second mode frequency is located nearby under the current excitation. .

[0026] (2) Based on the second mode frequency Calculate the second modal period Based on the second modal period The cantilever vibration signal (30) is segmented and aligned to obtain a two-dimensional data matrix; principal component analysis is performed on the two-dimensional data matrix, and the top 5 principal components with the highest cumulative contribution are selected for reconstructing the cantilever vibration signal; the reconstructed cantilever vibration signal retains the main components of the second mode vibration while suppressing noise, and subsequent analysis is based on the reconstructed cantilever vibration signal.

[0027] (3) Based on the current cantilever second mode frequency Sampling rate and the center frequency of the wavelet mother function Calculate the corresponding scale ,in Based on scale Construct a frequency-domain generalized Morse wavelet and perform frequency analysis on the current cantilever second mode frequency. The single-scale continuous wavelet transform is used to extract the values ​​from the wavelet transform at different scales. and Maximum amplitude of wavelet transform of the second mode under excitation and and extract the The corresponding time point is The The corresponding time point is .

[0028] (4) , Centered on a time window, a windowed Fourier transform is performed on the signal segment within the window to obtain the actual maximum amplitude of the second mode. , .

[0029] To avoid the transient signal characteristics being averaged out due to an excessively long time window, the selected time window should not be too wide or too narrow. In this invention, the time window is set to 0.05 milliseconds before and after the time point of the maximum amplitude. For example, if the time point corresponding to the maximum amplitude is the 8th millisecond, then the window is 7.95 milliseconds to 8.05 milliseconds.

[0030] (5) Calculate the ratio of the maximum amplitude of the wavelet transform to that of the Fourier transform. , Using ratio and The amplitude obtained from the single-scale continuous wavelet transform is calibrated to obtain the calibrated second mode amplitude. and .

[0031] (6) The surface potential is calculated using the following formula: Calculate the surface potential of the sample, where The potential of the sample surface is... The amplitude of the alternating current signal applied to the cantilever. In the signal The amplitude of the second mode under excitation, In the signal The amplitude of the second mode under excitation.

[0032] In this invention, amplitude and amplitude It is obtained by combining Fourier transform and wavelet transform.

[0033] Step 5: Visualize the dynamic potential change process of the sample surface in the computer.

[0034] The dynamic potential changes on the sample surface include response frequency-voltage curves, surface potential-time curves, and second mode amplitude-time curves.

[0035] The novel EFM measurement system of this invention overcomes the limitation of existing EFM systems, which can only indirectly characterize the sample surface potential. It achieves quantitative characterization of the sample surface potential and visually displays the characterization results using computer visualization technology, such as... Figure 5 , Figure 6 and Figure 7 As shown.

[0036] The novel EFM measurement system designed in this invention uses two voltage signals of different frequencies ( , The second mode of the cantilever is excited, and the first mode of the cantilever is excited to generate a vibration signal (30). In the processing based on the combination of Fourier transform and wavelet transform (set in the calculation material surface potential model (4)), (1) the Fourier transform of the cantilever vibration signal (30) is first performed to obtain the frequency components of all cantilever vibrations, and the frequency component with the largest amplitude is identified as the first mode. Furthermore, based on the characteristic that the second mode frequency is approximately 6.27 times the first mode frequency ( ), at the first modal frequency The second modal frequency is approximately 6.27 times that of the previous one. (2) Based on the second mode frequency Calculate its period , in a cycle The cantilever vibration signal (30) is segmented and aligned to obtain a two-dimensional data matrix; principal component analysis is performed on the two-dimensional data matrix, and the top 5 principal components with the highest cumulative contribution are selected for reconstructing the cantilever vibration signal; (3) the center frequency of the selected wavelet mother function is used to reconstruct the cantilever vibration signal. Sampling rate and the second mode frequency Calculate the corresponding scale Construct a frequency-domain generalized Morse wavelet and perform frequency analysis on the current cantilever second mode frequency. The single-scale continuous wavelet transform is used to extract the values ​​from the wavelet transform at different scales. and Maximum amplitude of wavelet transform of the second mode under excitation and and extract the The corresponding time point is The The corresponding time point is (4) with , Centered on a time window, a windowed Fourier transform is performed on the signal segment within the window to obtain the actual maximum amplitude of the second mode. , (5) Calculate the ratio of the maximum amplitude of the wavelet transform to that of the Fourier transform. , Using ratio and The amplitude obtained from the single-scale continuous wavelet transform is calibrated to obtain the calibrated second mode amplitude. and (6) In the calculation model (4) of the material surface potential, the formula for the relationship between the amplitude of the second mode of the two vibration signals and the surface potential of the sample is used. The change of sample surface potential over time was obtained, thus achieving quantitative characterization of sample surface potential.

[0037] In this invention, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the EFM measurement method.

[0038] In this invention, a computer program product is provided, comprising a computer program; when the computer program is executed by a processor, it implements the steps of the EFM measurement method.

[0039] Technical effects of the present invention:

[0040] (A) In the process of calculating the sample surface potential based on the combination of Fourier transform and wavelet transform, Fourier transform is first used to locate the frequency of the second mode, and then wavelet transform is performed on the specific frequency. This eliminates the need to use a logarithmic interval scale to cover the frequency range, thus improving the data processing speed of the new EFM measurement system (e.g., Figure 8 (As shown, it improved by 3 orders of magnitude) and accuracy.

[0041] (B) The novel EFM measurement system designed in this invention improves the PI unit and analyzes the amplitude change of the second mode of the cantilever vibration signal (30) under two voltage excitations. It can achieve high-precision quantitative characterization of the sample surface potential simply and efficiently without measuring complex parameters such as quality factor and capacitance gradient.

[0042] (C) The novel EFM measurement system designed in this invention uses Fourier transform and wavelet transform to analyze cantilever vibration data in the calculation of the material surface potential model (4), which replaces the traditional multi-frequency EFM system for analyzing data and reduces hardware costs. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of a traditional EFM system.

[0044] Figure 2 This is a structural diagram of the PI unit based on the improved EFM system of this invention.

[0045] Figure 3 This is the frequency-voltage response curve of a cantilever beam.

[0046] Figure 4 This is a flowchart of the surface potential calculation of the present invention.

[0047] Figure 5 It is the second mode amplitude calculated by wavelet transform under the first voltage (235kHz) signal excitation.

[0048] Figure 6 It is the second modal amplitude calculated by wavelet transform under the excitation of the second voltage (470kHz) signal.

[0049] Figure 7 It is a graph showing the change of the sample surface potential over time.

[0050] Figure 8 This is a comparison chart of the calculation speeds of single-scale continuous wavelet transform and continuous wavelet transform. Detailed Implementation

[0051] The present invention will now be described in further detail with reference to the accompanying drawings. The examples of the parameters listed are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0052] The novel EFM measurement system designed in this invention was applied to the Park XE-100E system, using a PPP-EFM probe and a PXIe-6368 data acquisition card to acquire signals at a sampling rate of 14 MS / s. The first modal excitation signal frequency was 71.1224 kHz, and the amplitude was 4.5 nm. The first excitation voltage frequency was set to 229.178 kHz, and the amplitude was set to 4 V. The second driving voltage frequency was set to 458.357 kHz, and the amplitude was set to 4 V. The initial height between the probe and the sample was set to 120 nm. The cantilever beam vibration was modeled using the Simulink module in Matlab, and data analysis was performed using PyCharm. Computer hardware configuration: Intel Core I5 ​​2.0 GHz or higher processor; 4 GB or more of memory; at least 10 GB of hard disk space; Windows 7 or later operating system; Matlab 2022; PyCharm 2023.

[0053] like Figure 3As shown, information is collected in the novel EFM measurement system where the first and second modes of the cantilever are excited synchronously. The vibration amplitude of the first mode directly reflects the change in the distance between the probe and the sample, characterizing the sample's surface morphology. Simultaneously, two voltage excitations of different frequencies are applied to the cantilever to induce its second mode vibration: the first excitation uses half the second mode frequency as the driving frequency, and the measured second mode amplitude at this time mainly reflects the influence of parameters such as the system's capacitance gradient and quality factor; the second excitation directly uses the second mode frequency for driving, and the measured second mode amplitude at this time includes the combined influence of parameters such as capacitance gradient and quality factor, as well as the sample surface potential. By calculating the ratio of the two second mode amplitudes, the measurement of complex parameters such as capacitance gradient and quality factor can be avoided, thus allowing for a simple and accurate calculation of the sample surface potential.

[0054] See Figure 2 The present invention proposes a novel EFM method for measuring the surface potential of two-dimensional materials. This method is embedded in a PI unit, that is, the PI unit is equipped with at least a model for calculating the surface potential of materials (4).

[0055] Two-dimensional material surface potential measurement based on the material surface potential model (4):

[0056] First, the initial height information (11) between the probe and the sample is set, and the initial height information (11) is synchronously input into the mechanical force model (2) and the electrostatic force model (3).

[0057] Subsequently, the electrostatic driving force signal (12) and the sample surface potential signal (13) are configured and transmitted to the electrostatic force model (3).

[0058] The mechanical force model (2) outputs the initial mechanical force (21) based on the initial height information (11) and the combination of mechanical excitation, mechanical contact force and van der Waals force. Meanwhile, the electrostatic force model (3) outputs the initial electrostatic force (22) based on the initial height information (11) and the combination of electrostatic driving force signal (12) and sample surface potential signal (13).

[0059] The initial mechanical force (21) and the initial electrostatic force (22) together constitute the force signal (23) between the scanning probe tip and the sample.

[0060] The force signal (23) is transmitted to the cantilever motion model (1), which in turn generates the vibration signal (30) of the cantilever. The vibration signal (30) is fed back to the mechanical force model (2) and the electrostatic force model (3) to calculate the force signal at the next moment. On the other hand, it is sent to the surface potential calculation module (4) for dynamic potential analysis of the two-dimensional material.

[0061] See Figure 4 The flowchart shown illustrates the calculation of the surface potential of molybdenum disulfide (MoS2) in the surface potential calculation module (4) and its visualization in a computer.

[0062] (1) Perform a Fourier transform to obtain all frequency components, and identify the frequency component with the largest amplitude as the first mode frequency. ( =71.1224kHz), according to The relationship, in The second mode frequency is located nearby under the current excitation. ( =458.357kHz). For example... Figure 3 As shown.

[0063] (2) Based on the second mode frequency Calculate the second modal period Based on the second modal period The cantilever vibration signal (30) is segmented and aligned to obtain a two-dimensional data matrix. Principal component analysis is then performed on the two-dimensional data matrix, and the top 5 principal components with the highest cumulative contribution are selected to reconstruct the cantilever vibration signal. The reconstructed cantilever vibration signal retains the main components of the second mode vibration while suppressing noise. Subsequent analyses are all based on the reconstructed cantilever vibration signal.

[0064] (3) Based on the current cantilever second mode frequency Sampling rate =14MS / s and the center frequency of the wavelet mother function =0.2995Hz, calculate the corresponding scale. ,in Based on scale Construct a frequency-domain generalized Morse wavelet and perform frequency analysis on the current cantilever second mode frequency. The single-scale continuous wavelet transform is used to extract the values ​​from the wavelet transform at different scales. and Maximum amplitude of wavelet transform of the second mode under excitation =0.9592nm and =0.005117nm, and extract the... The corresponding time point is =11.0036ms, the The corresponding time point is =11.9784ms.

[0065] (4) respectively with , Centered on the signal, time windows of 10.9536 ms to 11.0536 ms and 11.9284 ms to 12.0284 ms were selected. Windowed Fourier transforms were performed on the signal segments within these windows to obtain the actual maximum amplitude of the second mode. =0.1322nm =0.001177nm.

[0066] (5) Calculate the ratio of the maximum amplitude of the wavelet transform to that of the Fourier transform. =7.2562、 =4.3476, using the ratio and The amplitude obtained from the single-scale continuous wavelet transform is calibrated to obtain the calibrated second mode amplitude. and ,like Figure 5 and Figure 6 As shown.

[0067] (6) Calculation formula based on surface potential Obtain as Figure 7 The representation shown.

[0068] Constructing the frequency domain generalized Morse wavelet:

[0069] Discrete frequency points defined by the Discrete Fourier Transform (Where m = 0, 1, ..., N-1, and N is the signal length) The construction scale is... The generalized Morse wavelet is .in, To control the parameters of wavelet time-domain symmetry, To control the parameters of wavelet frequency domain attenuation rate, and The shape parameters of the generalized Morse wavelet control the time-domain symmetry and frequency-domain attenuation rate of the wavelet, respectively, in the calculations of this invention. , .

[0070] Single-scale continuous wavelet transform:

[0071] Let the frequency domain spectrum of the discrete Fourier transform of the cantilever vibration signal be... ,Will Complex conjugate of frequency domain generalized Morse wavelet Perform pointwise multiplication, then perform inverse Fourier transform to obtain the result at scale. wavelet coefficients , where IFFT represents the inverse Fourier transform, n=0,1,...,P-1, and P is the time-domain index. model Indicates instantaneous amplitude, reflecting single-scale The amplitude of the corresponding frequency changes over time.

[0072] Cantilever motion model (1)

[0073] The cantilever motion model (1) is used to obtain the force information (23) between the scanning probe tip and the sample, and to process the force information (23) using the cantilever beam motion equation to obtain the cantilever vibration information (30); on the other hand, the cantilever vibration information (30) is output to the surface potential calculation module (4), the mechanical force model (2) and the electrostatic force model (3) respectively.

[0074] In this invention, the equation of motion for the cantilever beam is based on Equation 1 from KPFM (Kelvin Force Microscopy), published in ACS Nano, author Liam Collins, August 6, 2017.

[0075] In the experiment, the intensity of the first and second mode responses of the cantilever jointly determines the validity of the measurement. The amplitude of the first mode directly reflects the change in distance between the probe and the sample, and is used for high-resolution topographic imaging; therefore, its response must be sufficiently strong and stable to ensure the clarity and reliability of the topographic signal. Meanwhile, the second mode is excited by the applied AC voltage, and its amplitude reflects the electrostatic force between the tip and the sample. The experiment must also ensure that the second mode response has sufficient intensity to achieve accurate resolution of the surface potential. Because...

[0076] The first mode is directly mechanically driven by piezoelectric ceramics, resulting in high excitation efficiency. The second mode, however, relies on a weak electrostatic force between the tip and the sample for indirect driving. Therefore, the amplitude of the first mode is typically much larger than that of the second mode. In the experimentally acquired cantilever vibration signal, the amplitude of the first mode is the largest among all frequency components, and thus it is used to locate the frequency of the second mode.

[0077] Mechanical force model (2)

[0078] The mechanical force model (2) is used to obtain the initial height information (11) between the probe samples on the one hand, and to receive the cantilever vibration signal (30) output by the cantilever motion model (1) on the other hand. The initial height information (11) and the cantilever vibration signal (30) are processed according to the van der Waals force to obtain the mechanical force (21). The mechanical force (21) generated by the mechanical force model (2) is output on the third aspect, and the mechanical force (21) is applied to the tip of the needle at the end of the cantilever.

[0079] In this invention, the mechanical force model (2) is divided into three parts: mechanical excitation force, van der Waals force and mechanical contact force.

[0080] The mechanical excitation force provides the mechanical drive for the multi-frequency electrostatic force microscope system, and the drive frequency is the same as the first mode frequency of the cantilever. The van der Waals force is the interatomic force reflected by the Lennard-Jones potential. Since the multi-frequency EFM system operates in the long-range van der Waals force range, the repulsive force can be ignored.

[0081] The mechanical contact force was modeled using the DMT model proposed by Derjaguin, Muller, and Toporov.

[0082] In the experiment, the initial height between the probe and the sample was set at 120 nanometers. This distance takes into account both the strength of the electrostatic force signal and the safety of the measurement. If the distance is too small, the system will enter the short-range region of van der Waals forces. This not only increases the attractive force dramatically, easily leading to uncontrollable contact between the probe tip and the sample, damaging both the sample and the probe, but also introduces complex nonlinear mechanical effects. If the distance is too large, the capacitance gradient between the probe tip and the sample will decrease sharply, resulting in an excessively weak electrostatic force signal, a significant decrease in the signal-to-noise ratio, and an inability to accurately extract potential information.

[0083] Electrostatic force model (3)

[0084] The electrostatic force model (3) is used to obtain the initial height information (11) between the probe samples on the one hand, and to receive the cantilever vibration information (30) output by the cantilever motion model (1) on the other hand. It also obtains the electrostatic driving force (12) of the EFM cantilever on the third hand, and the sample surface potential (13) of the EFM cantilever on the fourth hand. The initial height information (11), electrostatic driving force (12), sample surface potential (13) and cantilever vibration information (30) are processed according to the combination of capacitance gradient and electrostatic force to obtain electrostatic force (22). The electrostatic force (22) generated by the electrostatic force model (3) is output on the tip of the needle at the end of the cantilever on the fifth hand.

[0085] The key to accurately measuring the surface potential of molybdenum disulfide (MoD) lies in applying voltage excitation at two different frequencies, ensuring that the height between the tip and the sample remains constant during both excitations, thus maintaining a constant capacitance gradient between the tip and the sample. The first excitation frequency is set to half the frequency of the second mode. The amplitude of this second mode primarily reflects parameters such as capacitance gradient and quality factor. With the tip-sample distance remaining constant, this amplitude appears as a straight line in the time domain. The second excitation uses the same frequency as the second mode, and its amplitude simultaneously incorporates the contributions of capacitance gradient, quality factor, and the MoD surface potential. Finally, by combining Fourier transform and wavelet transform analysis of the cantilever second mode amplitude under the two voltage excitations, the weak second mode signal can be effectively extracted from the noise, allowing direct calculation of the MoD surface potential and its dynamic changes. This avoids the need for measuring complex parameters while achieving quantitative characterization of the sample surface potential.

[0086] The novel EFM measurement system designed in this invention is used to calculate the surface potential of two-dimensional materials. First, initial parameters are set for the system, including mechanical driving force, electrostatic driving force, and initial height between the probe and sample. A first-mode mechanical excitation and a first-stage AC voltage excitation are simultaneously applied to the cantilever, exciting two modes of vibration. The vibration signal data is acquired at high speed and converted into digital signals by a data acquisition card. The acquired vibration data is then transmitted to a model for calculating the surface potential of the material. Through a joint analysis process of Fourier transform and improved wavelet transform, the vibration amplitude of the second mode under the first voltage excitation is extracted. Subsequently, a first-mode mechanical excitation and a second-stage AC voltage excitation are simultaneously applied to the cantilever, and the same operation is performed to extract the vibration amplitude of the second mode under the second voltage excitation. Based on the derived amplitude-potential relationship formula, the dynamic change of the sample surface potential is calculated, achieving quantitative characterization.

[0087] In this invention, to verify the computational efficiency advantage of the single-scale continuous wavelet transform method used in this invention, a 7 ms cantilever vibration signal was processed and compared at a sampling rate of 14 MS / s. Traditional continuous wavelet transform requires calculating multiple scales with logarithmic intervals to cover the entire frequency band, resulting in high computational overhead and a time consumption of 34.0861 seconds. In contrast, the single-scale continuous wavelet transform method of this invention, whose computation time mainly includes: quickly locating the second modal frequency using FFT, constructing and transforming a generalized Morse wavelet for this single frequency, and subsequent amplitude calibration, has a computation time of 0.1559 seconds. This process does not require full-scale calculation. The comparison process does not include the processing time for principal component analysis denoising. The comparison results show that the single-scale continuous wavelet transform method is significantly faster than the traditional continuous wavelet transform. Specifically, the comparison is as follows: Figure 8 As shown, this effectively improves the data processing efficiency of the new EFM measurement system.

Claims

1. A novel EFM measurement system, characterized by incorporating a multi-frequency electrostatic force analysis method based on a combination of Fourier transform and wavelet transform into the PI unit of an electrostatic force microscope. The EFM measurement system includes: The cantilever motion model (1) acquires the force information (23) between the scanning probe tip and the sample, and processes the force information (23) using the cantilever beam motion equation to obtain the cantilever vibration information (30); on the other hand, it outputs the cantilever vibration information (30) to the surface potential calculation module (4), the mechanical force model (2) and the electrostatic force model (3) respectively. The mechanical force model (2) acquires the initial height information (11) between the probe samples on the one hand, and receives the cantilever vibration signal (30) output by the cantilever motion model (1) on the other hand. It processes the initial height information (11) and the cantilever vibration signal (30) according to the van der Waals force to obtain the mechanical force (21); and outputs the mechanical force (21) generated by the mechanical force model (2) on the third hand. The mechanical force (21) acts on the tip of the needle at the end of the cantilever. The electrostatic force model (3) acquires the initial height information (11) between the probe samples on the one hand, and receives the cantilever vibration information (30) output by the cantilever motion model (1) on the other hand. It also acquires the electrostatic driving force (12) of the EFM cantilever on the third hand, and the sample surface potential (13) of the EFM cantilever on the fourth hand. The initial height information (11), electrostatic driving force (12), sample surface potential (13) and cantilever vibration information (30) are processed according to the combination of capacitance gradient and electrostatic force to obtain electrostatic force (22). The electrostatic force (22) generated by the electrostatic force model (3) is output on the tip of the needle at the end of the cantilever on the fifth hand. The material surface potential model (4) is calculated. On the one hand, it receives the cantilever vibration information (30) output by the cantilever motion model (1); on the other hand, it obtains the dynamic potential information (10) of the sample surface based on the electrostatic force analysis combining Fourier transform and wavelet transform, and transmits the dynamic potential information (10) to the computer for visualization demonstration.

2. The EFM measurement system according to claim 1, characterized in that: In the model for calculating the surface potential of materials (4), the combination of Fourier transform and wavelet transform is used at the discrete frequency points defined by the discrete Fourier transform. Above, the structural scale is The generalized Morse wavelet is ;in, To control the parameters of wavelet time-domain symmetry, Parameters for controlling the wavelet frequency domain attenuation rate; Let the frequency domain spectrum of the discrete Fourier transform of the cantilever vibration signal be... ,Will Complex conjugate with frequency domain generalized Morse wavelet Perform point-by-point multiplication, then perform inverse Fourier transform to obtain the result at a single scale. wavelet coefficients Where IFFT stands for Inverse Fourier Transform. model Indicates instantaneous amplitude, reflecting single-scale The amplitude of the corresponding frequency changes over time.

3. The EFM measurement system according to claim 1, characterized in that: The formula for calculating the surface potential of a material (4) is based on the relationship between the amplitude of the second mode of the two vibration signals and the surface potential of the sample. The change of sample surface potential over time was obtained, thus achieving quantitative characterization of sample surface potential; among which The potential of the sample surface. The amplitude of the alternating current signal applied to the cantilever. In the signal The amplitude of the second mode under excitation, In the signal The amplitude of the second mode under excitation.

4. The EFM measurement system according to claim 1, characterized in that: The EFM measurement system uses two voltage signals of different frequencies ( , The second mode of the cantilever is excited, and the first mode of the cantilever is excited to generate a vibration signal (30).

5. The EFM measurement system according to claim 1, characterized in that: The EFM measurement system is applied to the Park XE-100E system, using the PPP-EFM probe and the PXIe-6368 data acquisition card to acquire signals.

6. A measurement method for implementing the measurement system according to any one of claims 1-4, characterized in that... The measurement steps include the following: Step 1: Acquire the response of the cantilever beam under the swept frequency signal; The response frequency-voltage curve of the cantilever beam was acquired under continuous frequency signal excitation, and the first mode and the second mode of the cantilever were obtained from the frequency-voltage curve. The frequency of the first mode of the cantilever was denoted as . The frequency of the second mode of the cantilever is denoted as ; Step 2: Set the voltage signal used to excite the cantilever; The AC voltage signal of the first excitation is denoted as... The signal The frequency is denoted as The voltage amplitude is denoted as ; The AC voltage signal of the second excitation is denoted as... The signal The frequency is denoted as The voltage amplitude is also ; The voltage amplitudes of the two excitation voltage signals are equal; The frequency It is half the frequency of the second mode of the cantilever; The frequency The frequency is the same as that of the second mode of the cantilever; Step 3: Set the signal used to excite the first mode of the cantilever based on the frequency-voltage curve; An auxiliary excitation signal with the same frequency as the first mode of the cantilever is set as follows: The signal Used to excite the first mode of vibration of the cantilever; The sampling rate of the cantilever vibration signal is set as denoted as ; Step four, the processing of the cantilever vibration signal (30) is based on the calculation of the sample surface potential by combining Fourier transform and wavelet transform; (1) Perform a Fourier transform to obtain all frequency components. The frequency component with the largest amplitude is the first mode frequency. ,according to The relationship, in The second mode frequency is located nearby under the current excitation. ; (2) Based on the second mode frequency Calculate the second modal period Based on the second modal period The cantilever vibration signal (30) is segmented and aligned to obtain a two-dimensional data matrix; and principal component analysis is performed on the two-dimensional data matrix to select the top 5 principal components with the highest cumulative contribution to reconstruct the cantilever vibration signal. (3) Based on the current cantilever second mode frequency Sampling rate and the center frequency of the wavelet mother function Calculate the corresponding scale ,in ; Based on scale Construct a frequency-domain generalized Morse wavelet and perform frequency analysis on the current cantilever second mode frequency. The single-scale continuous wavelet transform is used to extract the values ​​from the wavelet transform at different scales. and Maximum amplitude of wavelet transform of the second mode under excitation and and extract the The corresponding time point is The The corresponding time point is ; (4) , Centered on a time window, a windowed Fourier transform is performed on the signal segment within the window to obtain the actual maximum amplitude of the second mode. , ; (5) Calculate the ratio of the maximum amplitude of the wavelet transform to that of the Fourier transform. , Using ratio and The amplitude obtained from the single-scale continuous wavelet transform is calibrated to obtain the calibrated second mode amplitude. and ; (6) The surface potential is calculated using the following formula: Calculate the surface potential of the sample; Step 5: Visualize the dynamic potential change process of the sample surface in the computer.

7. The EFM measurement method according to claim 1, characterized in that: The time window is set to 0.05 milliseconds before and after the time point of the maximum amplitude.

8. The EFM measurement method according to claim 1, characterized in that: The dynamic potential changes of the sample surface visualized in the computer include response frequency-voltage curves, surface potential-time curves, and second mode amplitude-time curves.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the steps of an EFM measurement method according to any one of claims 6-8.

10. A computer program product, comprising a computer program; characterized in that: When executed by a processor, the computer program implements the steps of an EFM measurement method according to any one of claims 6-8.

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