Method for representing thickness of metal film on surface of metal substrate through oscillator

Abstract

The invention discloses a method for representing the thickness of a metal film on the surface of a metal substrate through an oscillator, and the method comprises the steps: obtaining the thickness response data of the copper film on the surface of a double-layer metal substrate material through the oscillator based on known metal copper films with different thicknesses and the double-layer metal substrate material; and fitting a mathematical equation between the copper film thickness and the output data of the oscillator through a least square method algorithm. When a copper film with an unknown thickness is measured, firstly, a copper film material with a known thickness is used for calibration, an output value of a current oscillator is recorded, then data of the copper film with the known thickness is substituted into a fitting equation, and an output value of the fitting equation is solved; subtracting the current output value of the oscillator from the output value of the equation to obtain the difference value of the tiny drift; substituting the difference value into the fitting function to generate a new fitting equation after the tiny drift is eliminated; and finally, substituting the oscillator data of the copper film to be detected into the new fitting equation to invert the thickness of the unknown copper film.

Description

Technical Field

[0001] The present invention belongs to the technical field of metal film thickness detection, and more specifically, relates to a method for characterizing the thickness of a metal film on a metal substrate surface by using an oscillator. Background Art

[0002] As an important material, thin films are widely used in aerospace, electronics, nanotechnology, nuclear industry, oil and gas reservoirs, and chemical industries. The performance and characteristics of thin films, especially the thickness parameter, have a significant impact on their application. In terms of the degradation of some special materials, by characterizing the thickness of the metal film on the surface of the metal material, the degradation of the material can be reflected, so that timely material replacement and maintenance can be carried out. At the same time, in some special scenarios such as nuclear power plants, the thickness of the double-layer metal film on the surface of the metal nuclear fuel is crucial to the normal use of the nuclear fuel and the safety of the nuclear power plant. If the surface metal film is too thick or too thin, it may cause major safety accidents.

[0003] Therefore, how to detect the thickness of the metal film on the surface of the metal substrate without damaging the metal material is an issue that needs to be studied and solved urgently.

[0004] Although the current method of eddy current detection of metal films on metal substrates can detect the thickness of metal films on metal surfaces to a certain extent, the sensitivity of conventional electromagnetic sensors is not high enough. At the same time, there is little research on the thickness detection of metal films on metal substrates. It is also difficult to achieve more precise indicators for the thickness detection of metal films at the micron level. At the same time, conventional metal film thickness detection requires specific instruments, which is complex to operate and costly. Summary of the Invention

[0005] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a method for characterizing the thickness of a metal film on the surface of a metal substrate by an oscillator, thereby realizing rapid, quantifiable, high-precision non-destructive thickness detection of the metal film, which has the advantages of small size, high sensitivity and low power consumption.

[0006] To achieve the above-mentioned object of the invention, the present invention provides a method for characterizing the thickness of a metal film on a metal substrate surface by using an oscillator, characterized by comprising the following steps:

[0007] (1) Connect the oscillator to the oscillator circuit and signal conditioning circuit, and then connect it to the host computer to establish a signal acquisition and receiving system;

[0008] (2) Select n metal film specimens with different thicknesses. The thickness of each metal film specimen is known. The thickness of the i-th metal film specimen is recorded as d i ;

[0009] (3) Hang the oscillator in the air and collect the output signal of the oscillator through the signal acquisition and receiving system in the no-load state, which is recorded as X0;

[0010] Under the same test environment, the oscillator is placed on the surface of n metal thin film specimens in turn, and the output signal of the oscillator is collected by the signal acquisition and receiving system. The output signal collected by the signal acquisition and receiving system on the surface of the i-th metal thin film specimen is denoted as X i ;

[0011] (4) Calculate the output signal X by sliding window method i The peak-to-peak mean

[0012] (5) Calculate the peak-to-peak mean of the output signal X0 by sliding window method

[0013] (6) The thickness d of each metal film specimen i As variable x, The difference between the two is taken as the variable y, and n groups of data points (x1, y1), (x2, y2), ..., (x i ,y i ),…(x n ,y n ), and then perform polynomial fitting based on n sets of data points to obtain the fitting function: y=a0+a1x+a2x 2 +a3x 3 ;

[0014] (7) Change the test environment and perform drift correction on the fitting function. The real fitting function after eliminating the drift is: true =y+Δ;

[0015] (8) The metal film thickness of the metal film specimen to be tested is tested according to the true fitting function to obtain the metal film thickness.

[0016] The object of the invention of the present invention is achieved like this:

[0017] The present invention discloses a method for characterizing the thickness of a metal film on a metal substrate using an oscillator. The method first uses an oscillator to obtain the response data of the copper film thickness on the surface of the double-layer metal substrate material, based on known copper films of varying thicknesses and a double-layer metal substrate material. A least-squares algorithm is then used to fit a mathematical equation between the copper film thickness and the oscillator output data. When measuring a copper film of unknown thickness, the method first calibrates the film with a known copper film thickness, records the current oscillator output value, and then substitutes the data for the copper film of known thickness into the fitting equation to obtain the output value of the fitting equation. The current oscillator output value is then subtracted from the output value of the equation to obtain a difference in slight drift. This difference is then substituted into the fitting function to generate a new fitting equation that eliminates the slight drift. Finally, the oscillator data for the copper film to be tested is substituted into the new fitting equation to invert the thickness of the unknown copper film.

[0018] At the same time, the method of characterizing the thickness of the metal film on the surface of the metal substrate by using an oscillator of the present invention also has the following beneficial effects:

[0019] (1) Based on the LC resonance method, the thickness of the copper film on the surface of the double-layer metal substrate is characterized. The resonance maximizes the signal and makes the eddy current have the strongest penetrating power. For the thickness range of tens of microns to hundreds of microns, a relatively accurate characterization can be achieved.

[0020] (2) The drift problem of the oscillator and ordinary sensors is solved by combining the least squares method with a small drift compensation algorithm. The relationship between the copper film thickness and the oscillator output is reconstructed by refitting the equation through parameter calibration, thereby enhancing the robustness of the copper film thickness characterization and reducing the error of the copper film thickness characterization. The maximum error is <10μm, and a quantitative assessment of the copper film thickness with a precision of 10μm can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a flow chart of a method for characterizing the thickness of a metal film on a metal substrate surface by using an oscillator according to the present invention;

[0022] Figure 2 This is a schematic diagram of the principle of characterizing the thickness of a copper film on the surface of a double-layer metal substrate by an oscillator in the present invention;

[0023] Figure 3 This is the oscillator system block diagram;

[0024] Figure 4 This is the schematic diagram of the oscillator circuit;

[0025] Figure 5 It is the relationship curve between the copper film thickness and the oscillator output value;

[0026] Figure 6It is the function curve between the fitted copper film thickness and the oscillator output value;

[0027] Figure 7 is the overall fitting curve after taking the average value;

[0028] Figure 8 It is a graph showing the error between the measured copper film thickness and the true thickness. DETAILED DESCRIPTION

[0029] The following describes the specific embodiments of the present invention in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, such descriptions will be omitted here.

[0030] Example

[0031] Figure 1 This is a flow chart of a method for characterizing the thickness of a metal film on a metal substrate surface by using an oscillator according to the present invention.

[0032] In this embodiment, if Figure 1 As shown, taking a double-layer metal substrate specimen as an example, the thickness of the copper film on its surface is characterized and measured, which specifically includes the following steps:

[0033] (1) Figure 2 As shown, the oscillator is connected to the oscillator circuit and signal conditioning circuit, and then connected to the host computer to establish a signal acquisition and receiving system;

[0034] In this embodiment, if Figure 3 As shown, the oscillator is a three-dimensional coil, but it can also be a planar coil, such as a PCB planar coil or a planar flexible coil.

[0035] In this embodiment, the structures and parameter values ​​of the oscillator circuit and the signal conditioning circuit are as follows: Figure 4 As shown;

[0036] In this embodiment, the oscillator output value is derived from the voltage signal between one end of the capacitor in the oscillator circuit and ground (GND). This voltage is a time-varying sinusoidal wave signal, whose frequency and amplitude vary with the thickness of the copper film. The oscillator's inductor, affected by the thickness of the copper film, experiences slight changes in its equivalent load and LC resonance, thereby altering the resonant characteristics at the capacitor, which is reflected in the peak-to-peak value variation of the voltage signal at that node. Therefore, measuring the amplitude of the sinusoidal signal at this node can indirectly indicate the thickness of the copper film.

[0037] (2) Five double-layer metal substrate specimens with different copper film thicknesses were selected. The copper film thickness of each specimen was known, namely d1 = 30 μm, d2 = 40 μm, d3 = 50 μm, d4 = 80 μm, and d5 = 100 μm.

[0038] (3) Hang the oscillator in the air and collect the output signal of the oscillator through the signal acquisition and receiving system in the no-load state, which is recorded as X0;

[0039] Under the same test environment, the oscillator is placed on the surface of 5 specimens in turn, and the output signal of the oscillator is collected by the signal acquisition and receiving system. The output signal collected by the signal acquisition and receiving system on the surface of the i-th specimen is denoted as X i , i=1,2,3,4,5;

[0040] In this embodiment, an oscillator is used to collect raw data on the surface of each specimen to obtain data on the thickness of each specimen. A total of 5 specimens with different thicknesses are used, and the experiment is repeated 6 times, obtaining a total of 5*6=30 pieces of thickness response data. The broken line relationship diagram of the raw data is shown in FIG. Figure 5 As shown;

[0041] (4) Calculate the output signal X by sliding window method i The peak-to-peak mean of

[0042] (4.1) Set a sliding window of length N; use the sliding window to i Perform sliding interception to obtain a sliding window signal of length N, where the sliding window signal of the jth sliding interception is recorded as W i,j ;

[0043] (4.2), statistical sliding window signal W i,j The maximum value Minimum Then calculate the peak-to-peak value

[0044] (4.3) To reduce the impact of accidental noise on peak-to-peak value calculation, a sliding average process can be performed on the peak-to-peak values ​​of multiple consecutive windows:

[0045]

[0046] Where M represents the output signal X i The number of sliding window signals intercepted in the filter is usually set to 3 to 5 to balance the response speed and filtering effect. In this embodiment, it is set to 4.

[0047] (5) Calculate the peak-to-peak mean of the output signal X0 according to step (4)

[0048] (6) Polynomial fitting;

[0049] (6.1), the copper film thickness d of each specimen i As variable x, The difference between the two is taken as the variable y, and n groups of data points (x1, y1), (x2, y2), ..., (x i ,y i ),…(x n ,y n );

[0050] (6.2) Construct the functional relationship of the copper film thickness on the specimen surface:

[0051] y=a0+a1x+a2x 2 +a3x 3

[0052] Among them, a0~a3 are coefficients to be fitted;

[0053] (6.3), construct the Vandermonde matrix X:

[0054]

[0055] (6.4), construct the objective function;

[0056]

[0057] (6.5) Optimize and solve the objective function using the least squares method;

[0058] According to n groups of data points, we can obtain the Vandermonde matrix X and the matrix Y = [y1, y2, ..., y n ] T ;

[0059] The coefficient matrix A = [a0, a1, a2, a3] T , Vandermonde matrix X and matrix Y are brought into the objective function, and the optimization solution is performed according to the least squares method to obtain the coefficient matrix A:

[0060] A=(X T X) -1 X T Y

[0061] Wherein, the superscript T indicates transposition;

[0062] Substitute the coefficient matrix A into the fitting function:

[0063] y=a0+a1x+a2x 2 +a3x 3

[0064] In this embodiment, if Figure 6As shown in FIG, a corresponding fitting curve can be fitted based on the data of 5 copper films with different thicknesses in each round; each round of experiments is repeated 6 times, thereby fitting more fitting curves about the relationship between the copper film thickness and the oscillator output value; finally, as shown in FIG. Figure 7 As shown, the overall cubic polynomial fitting method is used to fit the 6 experimental data into a curve, and its mathematical function expression is obtained;

[0065] (7) Drift correction;

[0066] (7.1) Change the test environment, suspend the oscillator, and collect the oscillator's output signal through the signal acquisition and receiving system in the no-load state, and record it as

[0067] Under the same test environment, the oscillator is placed on the surface of a double-layer metal substrate specimen with a known copper film thickness d, and the oscillator's output signal X is collected by the signal acquisition and receiving system;

[0068] (7.2), calculate the output signal X, The peak-to-peak mean

[0069] (7.3), The difference is taken as the measured value y' of the oscillator;

[0070] (7.4), the copper film thickness d of the double-layer metal substrate specimen is substituted into the fitting function as the variable x, and the fitting value y is calculated;

[0071] (7.5) Calculate the drift value Δ: Δ = y' - y;

[0072] (7.6) Correct the fitting function according to the drift value Δ to obtain the true fitting function after eliminating the drift:

[0073] y true =y+Δ

[0074] (8) Detection of copper film thickness of double-layer metal substrate specimens;

[0075] Under the same test environment, the signal acquisition and receiving system collects the output signals of the oscillator when it is suspended in the air and when it is placed on the surface of a double-layer metal substrate specimen with an unknown copper film thickness.

[0076] Calculate the peak-to-peak value of both output signals according to step (4), and then use the difference between the peak-to-peak values ​​as the measurement value of the oscillator.

[0077] The measured value Substitute the true fitting function y after eliminating drift true, and thus calculate the copper film thickness x on the surface of the double-layer metal substrate specimen.

[0078] Example verification

[0079] Because the average value of the data collected from six rounds of experiments was ultimately used as input for the calibration curve or surface, the copper film thickness inferred from the calibration curve for each specific point in the data set may deviate from the actual copper film thickness. This example analyzes this deviation to assess the accuracy of the calibration method.

[0080] In this embodiment, the five copper films tested are all standard 99.9% pure copper. The data of each test piece is measured in order of thickness, and the experimental process is repeated 6 times to obtain the function fitting curve after the average value. Finally, the final calibration fitting curve is obtained through drift correction, as shown in FIG. Figure 7 As shown, the functional relationship expression is:

[0081] y=-0.0002x 3 +0.0442x 2 -1.8193x+132.26

[0082] Furthermore, the error inverted by the fitting curve equation according to the S6 process is shown in Table 1. The table describes in detail the 6 rounds of experimental data corresponding to each specimen, and records its error by subtracting the true thickness from the thickness inverted from the measured value.

[0083] Table 1. Error between measured and true thickness of copper film.

[0084]

[0085] Table 1

[0086] Figure 8 This is the error diagram between the measured copper film thickness and the actual thickness based on Table 1. It can be seen from the figure and Table 1 that the maximum error is 8.3um, indicating that this method has high accuracy and sensitivity and can achieve accurate thickness measurement characterization with an error of <10um.

[0087] In summary, this invention proposes a method for characterizing the thickness of a copper film on a double-layer metal substrate using an oscillator, enabling rapid, quantifiable, and highly accurate nondestructive thickness measurement of copper films. Unlike conventional eddy current testing, this method offers higher sensitivity and accuracy, and employs a more precise algorithmic compensation for minor drift.

[0088] Furthermore, the present invention proposes an oscillator-based hardware design method for measuring copper film thickness, including the design of the oscillator circuit's LC parameters and the design of the circuit hardware PCB. This oscillator method not only utilizes the eddy current effect of electromagnetic sensors, as used in conventional methods, but also leverages the LC oscillation effect to minimize resonant impedance, thereby obtaining a signal with the highest sensitivity and accuracy. By integrating the LC physical effect with algorithm fitting and drift compensation, the present invention significantly reduces errors in copper film thickness detection.

[0089] Although the above describes the illustrative specific embodiments of the present invention to facilitate understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concepts of the present invention are protected.

Claims

1. A method for characterizing the thickness of a metal film on a metal substrate by an oscillator, characterized in that: The following steps are involved: (1) Connect the oscillator to the oscillator circuit and signal conditioning circuit, and then connect it to the host computer to establish a signal acquisition and receiving system; (2) Select n metal film specimens with different thicknesses. The thickness of each metal film specimen is known. The thickness of the i-th metal film specimen is recorded as d i ; (3) Hang the oscillator in the air and collect the output signal of the oscillator through the signal acquisition and receiving system in the no-load state, which is recorded as X0; Under the same test environment, the oscillator is placed on the surface of n metal thin film specimens in turn, and the output signal of the oscillator is collected by the signal acquisition and receiving system. The output signal collected by the signal acquisition and receiving system on the surface of the i-th metal thin film specimen is denoted as X i ; (4) Calculate the output signal X by sliding window method i The peak-to-peak mean (4.1) Set a sliding window of length N; use the sliding window to i Perform sliding interception to obtain a sliding window signal of length N, where the sliding window signal of the jth sliding interception is recorded as W i,j ; (4.2), statistical sliding window signal W i,j The maximum value Minimum Then calculate the peak-to-peak value (4.3) Calculate the mean of the peak-to-peak values ​​of multiple sliding window signals; Where M represents the output signal X i The number of sliding window signals intercepted in ; (5) Calculate the peak-to-peak mean of the output signal X0 according to step (4) (6) Obtaining the fitting function through polynomial fitting; (7) Obtain the true fitting function after drift elimination through drift correction; (8) Detection of metal film thickness of metal film specimens; Under the same test environment, the signal acquisition and receiving system collects the output signals of the oscillator when it is suspended in the air and when it is placed on the surface of a metal film specimen of unknown thickness; Calculate the peak-to-peak value of the output signal according to step (4), and then use the difference between the peak-to-peak value and the average value as the measurement value of the oscillator The measured value Substitute the true fitting function y after eliminating drift true , thereby calculating the metal film thickness x of the metal film specimen.

2. The method for characterizing the thickness of a metal film on a metal substrate surface by using an oscillator according to claim 1, characterized in that: The polynomial fitting process of the fitting function in step (6) is: (2.1), the thickness d of each metal film specimen i As variable x, The difference between the two is taken as the variable y, and n groups of data points (x1, y1), (x2, y2), ..., (x i ,y i ),…(x n ,y n ); (2.2) Construct the functional relationship of the film thickness on the surface of the metal film specimen: y=a0+a1x+a2x 2 +a3x 3 Among them, a0~a3 are the coefficients to be fitted; (2.3) Construct the Vandermonde matrix X: (2.4), construct the objective function; (2.5) Optimize and solve the objective function using the least squares method; According to n groups of data points, we can obtain the Vandermonde matrix X and the matrix Y = [y1, y2, ..., y n ] T ; The coefficient matrix A = [a0, a1, a2, a3] T , Vandermonde matrix X and matrix Y are brought into the objective function, and the optimization solution is performed according to the least squares method to obtain the coefficient matrix A: A=(X T X) -1 X T Y Wherein, the superscript T indicates transposition; Substitute the coefficient matrix A into the fitting function: y=a0+a1x+a2x 2 +a3x 3 。 3. The method for characterizing the thickness of a metal film on a metal substrate surface by using an oscillator according to claim 1, characterized in that: The specific process of drift correction in step (7) is as follows: (3.1) Change the test environment, hang the oscillator in the air, and collect the output signal of the oscillator through the signal acquisition and receiving system in the no-load state, which is recorded as Under the same test environment, the oscillator is placed on the surface of a metal film specimen with a known thickness d, and the oscillator's output signal X is collected by the signal acquisition and receiving system; (3.2), respectively calculate the output signal X, The peak-to-peak mean (3.3), The difference is taken as the measured value y' of the oscillator; (3.4), the thickness d of the metal film specimen is substituted into the fitting function as the variable x, and the fitting value y is calculated; (3.5) Calculate the drift value Δ: Δ = y' - y; (3.6) Correct the fitting function according to the drift value Δ to obtain the true fitting function after eliminating the drift: and true =y+Δ。

Images