Method for measuring vibration modes of micro / nano electromechanical systems using distributed multi-electrode methods

Abstract

This invention discloses a method for measuring the vibration modes of micro / nano-electromechanical systems (MEMS) using distributed multi-electrodes, addressing the difficulty in accurately measuring the mode shapes and frequencies of MEMS in existing technologies. The method involves integrating distributed electrodes below a pre-set one-dimensional / two-dimensional MEMS vibration component, then using excitation electrodes to sweep the frequency of the vibration component to obtain its undetermined resonant frequency. Finally, the undetermined resonant frequency is used for fixed-frequency excitation, and the response signals at different locations of the vibration component are measured. The response signals are then subjected to a Fast Fourier Transform (FFT) and interpolation algorithms to accurately plot the frequencies and mode shapes of the vibration component, ultimately obtaining the first n vibration modes of the MEMS vibration component. This invention features low requirements for measurement equipment and environment, high precision, low cost, and low operational difficulty, making it suitable for widespread use in MEMS and nano-MEMS systems.

Description

Technical Field

[0001] This invention belongs to the field of micro / nano electromechanical systems technology, specifically relating to a method for measuring the vibration modes of micro / nano electromechanical systems using distributed multi-electrodes. Background Technology

[0002] In recent years, with the continuous development of micro and nanotechnology, micro / nano electromechanical systems (MEMS / NEMS) have developed rapidly, bringing significant impacts to various fields. MEMS / NEMS consists of structures ranging from micrometers to nanometers and can be used to manufacture various sensors, actuators, fast switches, etc. Due to their small size, low power consumption, high sensitivity, and short response time, MEMS / NEMS are widely used in biomedicine, energy, information technology, the Internet of Things, materials science, and other fields.

[0003] The dynamic characteristics of vibrating components within MEMS / NEMS directly determine the system's performance and stability; therefore, the acquisition and analysis of vibration modal information of MEMS / NEMS vibrating components are essential. However, due to factors such as small size and high vibration frequency, the measurement of micro- and nano-scale vibration modes faces significant challenges.

[0004] Currently, the vibration modal measurements of MEMS / NEMS generally employ the following methods:

[0005] 1. Laser Doppler Measurement: This method utilizes the Doppler effect to detect the velocity of vibrations in micro / nano electromechanical systems, thereby calculating the structural vibration frequency and amplitude. Multi-point scanning can yield the vibration mode information. While this method offers high accuracy, it requires sophisticated measurement equipment and cannot be integrated into MEMS / NEMS devices, significantly limiting its application.

[0006] 2. Mechanical Measurement Method: This method uses an atomic force microscope probe to perform non-contact displacement measurements on micro / nano electromechanical systems (MEMS) devices, thereby obtaining their vibration response. Due to the inherent frequency limitations of the atomic force microscope, this method has a relatively low upper limit for measurable frequencies and places high demands on both the equipment and the measurement process.

[0007] 3. Capacitive Sensing Method: This method uses a detection electrode to measure the change in capacitance of a MEMS / NEMS device during vibration, thereby obtaining the vibration response and further determining the structural vibration frequency. This method has advantages such as simple structure, high sensitivity, and ease of integration into MEMS / NEMS devices. However, current single-electrode methods cannot measure structural vibration modes. Summary of the Invention

[0008] To address the shortcomings of the existing technologies, the present invention aims to provide a method for measuring the vibration modes of micro / nano electromechanical systems using distributed multi-electrodes, thereby solving the problem of accurately measuring the mode shapes and frequencies of micro / nano electromechanical systems in the prior art. The present invention employs distributed electrodes to measure the response signals at different locations of the vibrating component, performs a Fast Fourier Transform on the response signals, and combines this with an interpolation algorithm to accurately plot the frequencies and mode shapes of the vibrating component.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] The present invention provides a method for measuring the vibration modes of micro / nano electromechanical systems using distributed multi-electrodes, comprising the following steps:

[0011] 1) Install the distributed multi-electrode capacitive sensor below the vibrating component of the micro / nano electromechanical system;

[0012] 2) By applying an alternating voltage to the excitation electrode to form an alternating electric field, the vibration component of the micro / nano electromechanical system is subjected to fixed-frequency excitation. After stabilization, the component is subjected to frequency sweep excitation. The capacitance change signals of one or more electrodes are received and frequency response curves are plotted to find the peak point. The peak points of multiple frequency response curves are combined for analysis to obtain the undetermined resonant frequency value.

[0013] 3) Using a certain undetermined resonant frequency as the alternating voltage frequency, the vibration component of the micro / nano electromechanical system is subjected to fixed-frequency excitation, and the time-domain signals of capacitance changes of all electrodes are received. After the capacitance changes stabilize, a stable time-domain signal is extracted and a fast Fourier transform is performed on the time-domain signal to obtain the frequency-domain signal. The frequency-domain signal obtained for each electrode is processed (for example, the frequency-domain signal of one electrode is taken). The maximum amplitude in the small frequency range corresponding to the excitation frequency is taken as the mode shape amplitude of the corresponding electrode, and the amplitude is assigned a sign according to the positive or negative phase corresponding to the excitation frequency. The mode shape diagram is plotted by associating the amplitude corresponding to each electrode with its coordinates. The mode shape diagram is used to determine whether the undetermined resonant frequency is a certain natural frequency. If it is, the complete modal information of the natural frequency is obtained and the corresponding modal information is stored; if not, the undetermined resonant frequency is discarded. Then, different undetermined resonant frequencies are selected and step 3) is repeated to obtain the complete modal information of different natural frequencies.

[0014] Further, step 1) specifically includes: preparing and cleaning a capacitive sensor substrate below a pre-set micro / nano electromechanical system vibration component; depositing a conductive material (such as silver, copper, etc.) on the substrate thin film using chemical vapor deposition (CVD) as a conductive layer (using the conductive layer as the lower electrode of the capacitor plate); fabricating a distributed multi-electrode structure on the conductive layer using photolithography or ion beam etching and creating an independent wire structure for each electrode (generally, a uniformly distributed multi-electrode structure is used unless there are special requirements; if it is necessary to know the vibration information of a certain part of the vibration component, the electrodes can be densified in that part, and the range of the distributed electrodes should completely cover the range of the vibration component); finally, preparing an insulating layer (such as silicon dioxide, aluminum nitrate, etc.) on the conductive layer using chemical vapor deposition, and then constructing other components of the micro / nano electromechanical system.

[0015] Further, step 2) specifically includes: applying a starting frequency to the excitation electrodes of the micro / nano electromechanical system integrating a distributed multi-electrode capacitive sensor for fixed-frequency excitation. After the capacitance change stabilizes, the vibrating component of the micro / nano electromechanical system is excited with a uniformly varying frequency (generally from low to high) (i.e., frequency sweep). (Note that the amplitude of the entire fixed-frequency and frequency sweep excitation process should not be large to avoid nonlinear response.) Frequency response data (i.e., the relationship between capacitance change signal and real-time frequency) of multiple electrodes at different positions are output in real time through independent wires of multiple electrodes, and frequency response curves are plotted. The frequency value corresponding to the k-th peak of the frequency response curve of different electrodes is found to be f. k1 f k2 f k3 ... f km , where f km To determine the k-th peak value on the m-th electrode, the k-th undetermined resonant frequency f is determined by combining different frequency values. k Then, the n undetermined resonance frequencies are rearranged in ascending order and denoted as f1, f2, f3, ..., f n , where f1 to f n This results in the final n undetermined resonant frequency values. (Note that the data from different electrodes are selected here to avoid the selected electrodes being located at nodes or nodal lines, resulting in a response at the corresponding frequency that is too small to identify the peak, thus missing the natural frequency of that order. The frequency values ​​corresponding to the peak values ​​of the frequency response curves of electrodes at different positions will have slight differences. When comparing multiple curves, the frequency values ​​obtained from different curves can be averaged.)

[0016] Furthermore, in step 2), the start and end frequencies of the frequency sweep are determined according to the size and shape of the vibration component of the micro / nano electromechanical system, and the frequency sweep speed cannot be too fast to avoid frequency response delay.

[0017] Furthermore, step 3) specifically includes: using a certain undetermined resonant frequency fi For a vibrating component of a micro / nano electromechanical system with a fixed input frequency for alternating voltage, the time-domain signals of capacitance changes at all electrodes are received in real time via independent wires for each electrode. After the capacitance changes stabilize, a stable time-domain signal is extracted from each electrode, and a Fast Fourier Transform (FFT) is performed on each extracted time-domain signal to obtain the frequency-domain information of the stable fluctuations of the capacitance signal corresponding to each electrode. Amplitude-frequency and phase-frequency curves are then plotted, thus obtaining the frequency-domain signal of each electrode. The amplitude-frequency curve corresponding to a specific electrode is then used, with f... i For the target frequency, the maximum amplitude within a small adjacent frequency range is taken as the mode shape amplitude of the corresponding electrode. Then, the amplitude is assigned a sign based on the phase sign of the target frequency on the phase-frequency curve. The obtained new amplitude is then correlated with the position information of the corresponding electrode. After processing all electrodes, interpolation is performed based on the electrode position and the new amplitude, and a mode shape diagram is plotted. The f-value is determined based on the mode shape diagram. i If it is a natural frequency, then obtain the complete modal information of that natural frequency and store the corresponding modal information; otherwise, discard it; then select different undetermined resonance frequencies and repeat step 3) to obtain the complete modal information of different natural frequencies.

[0018] The beneficial effects of this invention are:

[0019] This invention utilizes a distributed multi-electrode capacitive sensor to measure the modes of MEMS / NEMS devices, obtaining both frequency information and mode shape information for each frequency order, with repeatability. Compared to existing methods for MEMS / NEMS mode measurement, this invention features low requirements for measurement equipment and environment, high precision, low cost, and low operational difficulty, making it suitable for widespread use in microelectromechanical and nanoelectromechanical systems. Attached Figure Description

[0020] Figure 1 This is a schematic diagram illustrating a distributed multi-electrode mode acquisition example for a one-dimensional MEMS / NEMS device.

[0021] Figure 2 This is a schematic diagram illustrating a distributed multi-electrode mode acquisition example for a two-dimensional MEMS / NEMS device.

[0022] Figure 3 This is an example of the final vibration mode diagram obtained in the method of the present invention. Detailed Implementation

[0023] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0024] This invention is applicable to the measurement of vibrational natural modes of one-dimensional / two-dimensional MEMS / NEMS devices. Figure 1 and Figure 2 These are schematic diagrams of one-dimensional / two-dimensional devices given in connection with the method of the present invention. The following is in conjunction with... Figure 2 A method for measuring the vibrational natural modulus of a 50nm diameter circular plate-type nanoelectromechanical system using a distributed multi-electrode system is presented, with the following steps:

[0025] 1) Arrange a distributed multi-electrode capacitive sensor under the circular plate-shaped vibrating component to be tested; note that in practical applications, the distributed multi-electrode capacitive sensor is integrated into MEMS / NEMS, and the fabrication scheme of other MEMS / NEMS components depends on the application requirements, which will not be elaborated here;

[0026] 11) Prepare suitable substrate materials (such as silicon wafers or glass) and remove surface contaminants, oxide layers, and micro-defects using organic solvents and plasma cleaning methods; ensure the substrate surface is smooth and clean to ensure the quality of subsequent processing. Note that the substrate size must completely cover the circular plate vibrating component; for example, the medium substrate can be a 75*75nm square, placed directly below the circular plate vibrating component.

[0027] 12) Prepare a metal thin film (copper, silver, etc.) on the substrate surface using chemical vapor deposition. The film is the same size as the substrate and has a thickness of approximately 2-3 nm.

[0028] 13) Use micro / nano fabrication methods (photolithography, ion beam etching, etc.) to fabricate distributed electrodes and wire structures for each electrode. Note that the range of distributed electrodes needs to cover the vibrating component. The density of distributed electrodes can be determined according to the order of modal measurement. The higher the order, the higher the density required. Of course, the fabrication difficulty and cost will also be higher. In this example, a 10*10 square array distribution can be used to measure the first ten modal information well.

[0029] 14) Prepare an insulating material (silicon dioxide, aluminum nitrate, etc.) on a metal thin film, with the same size as the substrate and a thickness of approximately 30-50 nm. Note that the insulating layer is between the electrode and the vibrating component, but does not contact the vibrating component. This is to show the electrode distribution. Figure 1 and Figure 2 The insulating layer was not shown in the drawing.

[0030] 2) Sweep the frequency of the vibrating component to find the undetermined resonant frequency value;

[0031] 21) Apply a sinusoidal alternating voltage with linearly varying frequency to the excitation electrode. Where U is the applied real-time voltage value, and A is the alternating amplitude value. Let ω(t) be the initial phase, t be time, and ω(t) be the angular frequency of the alternating voltage as a function of time. Specifically, Where f start with f endThese are the start and end frequencies of the frequency sweep, respectively, and T is the total sweep time. Note that in actual operation, to minimize the influence of nonlinear vibrations, the value of A should be as small as possible, generally a few microvolts. start with f end The value needs to be determined based on the approximate range of the inherent frequency of the specific device. The inherent frequency of MEMS devices is generally in the kHz or even MHz range, while that of NEMS devices is usually around the GHz range. For example, in this case, which falls under the category of NEMS devices, a frequency sweep of 1GHz to 200GHz can be used. However, the actual sweep frequency needs to be determined based on the actual device structure and environment. The total sweep time T should not be too short to avoid frequency response delay due to excessively fast sweep speed.

[0032] 22) Compare the frequency response curves of electrodes at different locations. Combine multiple amplitude-frequency curves of different electrodes to statistically analyze the frequency values ​​corresponding to the peak values ​​of each curve and compare them to obtain the undetermined resonant frequency. For example, the frequency values ​​corresponding to the kth peak of the frequency response curves of different electrodes are fk, ... k1 f k2 f k3 ... f km , where f km To determine the k-th peak value on the m-th electrode, the average of these different frequency values ​​is taken to determine the k-th undetermined resonant frequency, i.e. Then, the n undetermined resonance frequencies are rearranged in ascending order and denoted as f1, f2, f3, ..., f n This yields a new undetermined resonant frequency value.

[0033] 3) Excite the vibrating component with the undetermined resonant frequency obtained in step 2), and after the capacitance change stabilizes, extract the time domain signal of each electrode and perform a fast Fourier transform (FFT) on it to obtain the amplitude frequency diagram and phase frequency diagram.

[0034] 31) Make the frequency of the excitation electrode ω(t) = 2πf i Let i = 1, 2, 3, ..., n. After the vibration stabilizes, a stable time-domain signal segment is extracted. Note that the signal acquisition interval Δt should not exceed 1 / 2 of the vibration period. To ensure the accuracy of the Fast Fourier Transform, it is generally taken as 1 / 10 of the vibration period or smaller. The indicator of reaching steady-state vibration can be determined by observing the stability of the time-domain signal output by the electrodes in real time.

[0035] 32) Perform Fast Fourier Transform on the steady-state time-domain signal values ​​of each electrode to obtain amplitude frequency information and phase frequency information.

[0036] 33) For using f i The amplitude and phase frequency information of each electrode obtained from the excitation is used to find the f in the amplitude-frequency curve of each electrode. iThe corresponding amplitude A xy Corresponding to the planar position (x,y) of the electrode, the amplitude information (x,y,A) of the electrode is constituted. xy );

[0037] 34) Locate f in the phase frequency curves of each electrode. i The corresponding phase sign, if positive, will not change the amplitude information of the electrode; if negative, the amplitude information will be modified to (x, y, -A). xy Or conversely, change the sign for positive values ​​and leave it unchanged for negative values;

[0038] 35) After obtaining the amplitude information of all electrodes, the final amplitude is interpolated with respect to position to obtain more continuous and smooth amplitude information. The interpolation method used is biharmonic spline interpolation.

[0039] 36) Draw the mode shape diagram based on the final obtained amplitude information, i.e., the frequency f. i The corresponding mode shape diagram. And determine f based on the mode shape diagram. i If the frequency is a natural frequency, obtain and store the complete modal information (frequency and mode shape) for that frequency; otherwise, discard it; then change the fixed-frequency excitation f. i Repeat step 3) for the value, and the final ten mode shapes obtained in this example are as follows. Figure 3 As shown.

[0040] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A method for measuring the vibration modes of micro / nano electromechanical systems using distributed multi-electrode methods, characterized in that, The steps are as follows: 1) Install the distributed multi-electrode capacitive sensor below the vibrating component of the micro / nano electromechanical system; 2) By applying an alternating voltage to the excitation electrode to form an alternating electric field, the vibration component of the micro / nano electromechanical system is subjected to fixed-frequency excitation. After stabilization, the component is subjected to frequency sweep excitation. The capacitance change signals of one or more electrodes are received and frequency response curves are plotted to find the peak point. The peak points of multiple frequency response curves are combined for analysis to obtain the undetermined resonant frequency value. 3) Using a certain undetermined resonance frequency as the alternating voltage frequency, the vibration component of the micro / nano electromechanical system is subjected to fixed-frequency excitation, and the time-domain signals of capacitance changes of all electrodes are received. After the capacitance changes stabilize, a stable time-domain signal is extracted and a fast Fourier transform is performed on the time-domain signal to obtain the frequency-domain signal. The frequency-domain signal obtained for each electrode is processed, and the maximum amplitude in the small frequency range corresponding to the excitation frequency is taken as the mode amplitude of the corresponding electrode. The amplitude is assigned a sign according to the positive or negative phase corresponding to the excitation frequency. The mode diagram is plotted by associating the amplitude corresponding to each electrode with its coordinates. The mode diagram is used to determine whether the undetermined resonance frequency is a certain natural frequency. If it is, the complete modal information of the natural frequency is obtained and the corresponding modal information is stored. If not, the undetermined resonance frequency is discarded. Then, different undetermined resonance frequencies are selected and step 3) is repeated to obtain the complete modal information of different natural frequencies.

2. The method for measuring the vibration modes of micro / nano electromechanical systems using distributed multi-electrodes according to claim 1, characterized in that, Step 1) specifically includes: preparing and cleaning a capacitive sensor substrate below a pre-set micro / nano electromechanical system vibration component; depositing a conductive material as a conductive layer on the substrate thin film using chemical vapor deposition; fabricating a distributed multi-electrode structure on the conductive layer using photolithography or ion beam etching and creating an independent wire structure for each electrode; preparing an insulating layer on the conductive layer using chemical vapor deposition; and then constructing other components of the micro / nano electromechanical system.

3. The method for measuring the vibration modes of micro / nano electromechanical systems using distributed multi-electrodes according to claim 1, characterized in that, Step 2) specifically includes: On a micro / nano electromechanical system integrating a distributed multi-electrode capacitive sensor, the excitation electrodes are subjected to a fixed-frequency excitation at an initial frequency. After the capacitance change stabilizes, the vibrating components of the micro / nano electromechanical system are excited with an alternating voltage of uniformly varying frequency. Frequency response curves are plotted, and the frequency values ​​corresponding to the k-th peak of the frequency response curves for different electrodes are found to be fk. k1 f k2 f k3 ... f km , where f km To determine the k-th peak value on the m-th electrode, the k-th undetermined resonant frequency f is determined by combining different frequency values. k Then, the n undetermined resonance frequencies are rearranged in ascending order and denoted as f1, f2, f3, ..., f n , where f1 to f n These are the final n undetermined resonance frequency values.

4. The method for measuring the vibration modes of micro / nano electromechanical systems using distributed multi-electrodes according to claim 1, characterized in that, In step 2), the start and end frequencies of the frequency sweep are determined according to the size and shape of the vibration component of the micro / nano electromechanical system, and the frequency sweep speed cannot be fast.

5. The method for measuring the vibration modes of micro / nano electromechanical systems using distributed multi-electrodes according to claim 1, characterized in that, Step 3) specifically includes: using a certain undetermined resonance frequency f i For a vibrating component of a micro / nano electromechanical system with a fixed input frequency for alternating voltage, the time-domain signals of capacitance changes at all electrodes are received in real time via independent wires for each electrode. After the capacitance changes stabilize, a stable time-domain signal is extracted from each electrode, and a Fast Fourier Transform is performed on each extracted time-domain signal to obtain the frequency-domain information of the stable fluctuation of the capacitance signal corresponding to each electrode. Amplitude-frequency and phase-frequency curves are then plotted, thus obtaining the frequency-domain signal of each electrode. The amplitude-frequency curve corresponding to a specific electrode is then taken, and f... i For the target frequency, the maximum amplitude within a small adjacent frequency range is taken as the mode shape amplitude of the corresponding electrode. Then, the amplitude is assigned a sign based on the phase sign of the target frequency on the phase-frequency curve. The obtained new amplitude is then correlated with the position information of the corresponding electrode. After processing all electrodes, interpolation is performed based on the electrode position and the new amplitude, and a mode shape diagram is plotted. The f-value is determined based on the mode shape diagram. i If it is a natural frequency, then obtain the complete modal information of that natural frequency and store the corresponding modal information; otherwise, discard it; then select different undetermined resonance frequencies and repeat step 3) to obtain the complete modal information of different natural frequencies.

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