Method for quantifying the influence of lift-off fluctuations on eddy current film thickness measurement error

Abstract

The application provides a method for quantifying the error of eddy current metal film thickness measurement caused by lift-off fluctuation, which quantifies the thickness error caused by lift-off fluctuation by calculating the influence of lift-off fluctuation on output voltage, and establishes the corresponding relationship between thickness error and measured film thickness and lift-off fluctuation; on this basis, the application faces the process of micro-nano metal film thickness detection, and takes lift-off reference and lift-off fluctuation as main influence parameters; according to the above corresponding relationship, the thickness error under any lift-off fluctuation can be calculated with high precision and high speed, so as to effectively evaluate the thickness measurement error caused by different lift-off references and lift-off fluctuations in practical application.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of micro-nano detection, and particularly relates to a method for quantifying the influence of fluctuation of lift-off on measurement error of metal film thickness by eddy current. BACKGROUND

[0002] The thickness of a metal film is a key parameter determining its performance, and accurate measurement of the thickness of a metal film is an important means to ensure high-precision manufacturing of the film. Current methods for measuring the thickness of a nanoscale film include optical method, four-probe method, ultrasonic method and eddy current method. Among them, the eddy current method can be used for online detection of the thickness of a metal film due to its advantages of non-contact, high stability and fast response speed. However, in the measurement process, factors such as mechanical vibration will cause the lift-off distance to change, thereby causing unavoidable thickness measurement error. Therefore, it is necessary to design a method for quantifying the measurement error of an eddy current sensor to accurately evaluate the influence of fluctuation of lift-off on the accuracy of measurement results. SUMMARY

[0003] To solve the above problems, the application provides a method for quantifying the influence of fluctuation of lift-off on measurement error of metal film thickness by eddy current, which can accurately evaluate the influence of fluctuation of lift-off on the accuracy of measurement results by eddy current.

[0004] A method for quantifying the influence of fluctuation of lift-off on measurement error of metal film thickness by eddy current, comprising the following steps:

[0005] S1: setting different lift-off references and corresponding lift-off fluctuation amplitudes, and determining the optimal parameter values of the eddy current detection coil under each lift-off reference;

[0006] S2: for each lift-off reference, obtaining the output voltage sequence of the sensor for the measurement thickness range under each lift-off distance, wherein the output voltage obtaining step is:

[0007] Under the current lift-off reference, the thickness of the measured film is measured by the eddy current sensor with the optimal coil parameters to obtain the output voltage reference value corresponding to each film thickness. Then, a plurality of amplitudes of lift-off fluctuation are introduced, and the maximum output voltage change of each film thickness measurement in the range under each amplitude of lift-off fluctuation is obtained in turn. The maximum output voltage change under each amplitude of lift-off fluctuation forms the output voltage change sequence of the corresponding film thickness under the current lift-off reference;

[0008] S3: obtaining the thickness error sequence under each amplitude of lift-off fluctuation according to the output voltage change sequence corresponding to each film thickness under each lift-off reference;

[0009] S4: fitting the corresponding relationship based on the thickness error sequence under different lift-off references, the thickness sequence and the lift-off fluctuation amplitude, to obtain the functional relationship among the thickness error, the thickness and the lift-off fluctuation amplitude;

[0010] S5: according to the functional relationship, the thickness measurement error of the measured metal film under the influence of the lift-off fluctuation amplitude can be calculated according to the current film thickness and the lift-off fluctuation amplitude in the actual measurement process.

[0011] Further, in steps S2 and S3, the corresponding thickness error sequence under any lift-off reference is obtained according to the output voltage change sequence corresponding to each film thickness under the lift-off reference, specifically:

[0012] S31: comparing the output voltage of each film thickness under the lift-off reference when affected by a certain lift-off fluctuation with the corresponding voltage reference value, obtaining the maximum output voltage change under the lift-off fluctuation amplitude, and sequentially obtaining the output voltage change sequence of each film thickness in the range under each lift-off fluctuation amplitude;

[0013] S32: taking the ratio of the output voltage change corresponding to each film thickness and the corresponding thickness sensitivity as the thickness error caused by the current lift-off fluctuation amplitude, and taking the thickness error of the thickness in the range caused by each lift-off fluctuation amplitude as the thickness error sequence under the current lift-off reference.

[0014] Further, the calculation method of the thickness sensitivity is:

[0015] The voltage reference value sequence output by the eddy current sensor for each metal film thickness without lift-off distance fluctuation under a certain lift-off reference is obtained.

[0016] Linear fitting is performed on the voltage reference sequence, and the slope of the fitting straight line is the thickness sensitivity.

[0017] Further, when the thickness of the measured film is 100-1500 nm, the corresponding relationship fitting is performed based on the thickness error sequence under different lift-off references, the thickness sequence and the lift-off fluctuation amplitude, to obtain the functional relationship among the thickness error, the thickness and the lift-off fluctuation amplitude as follows:

[0018]

[0019] Wherein, k1-k6 are fitting coefficients of the thickness error calculation equation, △t is the thickness error, t is the thickness of the measured film, and △l is the lift-off fluctuation amplitude.

[0020] Further, the coil parameters include winding diameter, coil inner diameter, number of turns and diameter-height ratio, and the determination method of the optimal value of the eddy current detection coil parameters under any lift-off reference is as follows:

[0021] According to the coil quality factor, output voltage sensitivity, output voltage linearity and space constraint requirements, the optimal value of the detection coil parameters is determined, wherein when the winding diameter, the coil inner diameter and the diameter-height ratio are fixed values, the coil quality factor increases first and then decreases with the increase of the number of turns, the output voltage sensitivity increases with the increase of the number of turns, and the output voltage linearity decreases with the increase of the number of turns; when the winding diameter, the coil inner diameter and the number of turns are fixed values, the coil quality factor increases with the increase of the diameter-height ratio, the output voltage sensitivity increases with the increase of the diameter-height ratio, and the output voltage linearity decreases with the increase of the diameter-height ratio; when the number of turns and the diameter-height ratio are larger, the coil volume is larger, and it is more difficult to meet the space constraint requirements.

[0022] Further, different lift-off references can be 1mm, 2mm and 3mm respectively; different lift-off fluctuation amplitudes can be 50μm, 100μm and 150μm respectively.

[0023] Beneficial effects:

[0024] The application provides a method for quantifying the error of eddy current metal film thickness measurement caused by lift-off fluctuation, which quantifies the thickness error caused by lift-off fluctuation by calculating the influence of lift-off fluctuation on output voltage, and establishes the corresponding relationship between thickness error and measured film thickness and lift-off fluctuation; on this basis, the application faces the process of micro-nano metal film thickness detection, and takes the lift-off reference and lift-off fluctuation as the main influencing parameters; according to the above-mentioned corresponding relationship, the thickness error under any lift-off fluctuation can be calculated with high precision and quickly, so that the thickness measurement error caused by different lift-off references and lift-off fluctuations can be effectively evaluated in practical application. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 A simulation model diagram of the eddy current sensor is provided for the application;

[0026] Figure 2 A general flowchart of the eddy current thickness error quantification evaluation method is provided for the application;

[0027] Figure 3 A principle diagram of the eddy current thickness error quantification evaluation method is provided for the application;

[0028] Figure 4 A thickness error quantification plane of the eddy current sensor is provided for the application. DETAILED DESCRIPTION

[0029] In order to enable the personnel in the technical field to better understand the scheme of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0030] The application provides a thickness error quantification method suitable for different lift-off distances, and is used for micro-nano metal film thickness detection. Figure 1 The application provides an eddy current sensor simulation model schematic diagram. c The detection circuit signal conversion module in the embodiment takes an LC parallel resonant circuit as an example, and includes a coil (inductor L c ), a series resistor R0 and a coupling capacitor C0. Based on this, a method for quantifying the lift-off fluctuation error of the eddy current type metal film thickness measurement is provided, as shown in the following formula (1). Figure 2 The method includes the following steps.

[0031] S1: different lift-off references and corresponding lift-off fluctuation amplitudes are set, and the optimal parameter value of the eddy current detection coil under each lift-off reference is determined.

[0032] For example, in the embodiment of the application, the lift-off references can be 1mm, 2mm and 3mm respectively, the lift-off fluctuation amplitudes can be 50μm, 100μm and 150μm respectively, the measured object is a copper film, and the thickness range can be 100-1500nm.

[0033] It should be noted that the coil parameters include the winding diameter, the coil inner diameter, the number of turns and the diameter-height ratio, and the determination method of the optimal value of the eddy current detection coil parameters under any lift-off reference is as follows.

[0034] According to the coil quality factor, the output voltage sensitivity, the output voltage linearity and the space constraint condition requirement, the optimal value of the detection coil parameters is determined, wherein when the winding diameter, the coil inner diameter and the diameter-height ratio are fixed values, the coil quality factor increases first and then decreases with the increase of the number of turns, the output voltage sensitivity increases with the increase of the number of turns, and the output voltage linearity decreases with the increase of the number of turns; when the winding diameter, the coil inner diameter and the number of turns are fixed values, the coil quality factor increases with the increase of the diameter-height ratio, the output voltage sensitivity increases with the increase of the diameter-height ratio, and the output voltage linearity decreases with the increase of the diameter-height ratio; when the number of turns and the diameter-height ratio are larger, the coil volume is larger, and it is more difficult to meet the space constraint requirement.

[0035] For example, in the present embodiment, the winding diameter and the inner diameter of the coil are determined as 100 μm and 3.0 mm, respectively, the fixed diameter-height ratio is 1, the number of turns is continuously changed from 100 to 400, and the changes in the coil quality factor, the sensitivity and the linearity of the output voltage of the LC resonant circuit under different numbers of turns are analyzed. With the continuous increase of the number of turns, the coil quality factor first increases and then decreases, and reaches the maximum value near 150 turns; the sensitivity of the output voltage gradually increases, but the speed gradually slows down; the linearity of the output voltage gradually decreases; considering the quality factor, the sensitivity and the linearity of the output voltage, the optimal range of the number of turns is determined as 150-170 turns, 200-220 turns and 300-320 turns under the lift-off reference of 1 mm, 2 mm and 3 mm, respectively. After determining the optimal number of turns, the diameter-height ratio is continuously changed from 0.5 to 12, and the changes in the coil quality factor, the sensitivity and the linearity of the output voltage of the LC resonant circuit under different diameter-height ratios are analyzed. With the continuous increase of the diameter-height ratio, the coil quality factor gradually increases; the sensitivity of the output voltage gradually increases, but the speed gradually slows down; the linearity of the output voltage gradually decreases; at the same time, the larger the diameter-height ratio, the larger the outer diameter of the coil, which is not conducive to the miniaturization design of the sensor. Considering the coil quality factor, the sensitivity and the linearity of the output voltage and the space constraint, the optimal range of the diameter-height ratio is determined as 4.5-4.7, 5.5-5.7 and 3.7-3.9.

[0036] S2: For each lift-off reference, obtain the output voltage sequence of the sensor under each lift-off distance for measuring the thickness range, wherein the output voltage obtaining step is:

[0037] Under the current lift-off reference, the thickness of the measured film is measured by using the eddy current sensor with the optimal coil parameters to obtain the output voltage reference value corresponding to each film thickness; then a plurality of amplitude lift-off fluctuations are introduced, and then the maximum output voltage change of the sensor for measuring each film thickness in the range under each lift-off fluctuation amplitude is obtained in turn; the maximum output voltage change under each lift-off fluctuation amplitude forms the output voltage change sequence of the corresponding film thickness under the current lift-off reference;

[0038] S3: Obtain the thickness error sequence under each lift-off fluctuation amplitude according to the output voltage change sequence corresponding to each film thickness under each lift-off reference;

[0039] Wherein, the thickness error sequence under any lift-off reference is obtained according to the output voltage change sequence corresponding to each film thickness under the lift-off reference, and the specific process is as follows:

[0040] S31: comparing the output voltage of each film thickness under the influence of the lift-off fluctuation with the corresponding voltage reference value to obtain the maximum output voltage variation (absolute value) under the lift-off fluctuation amplitude, and then obtaining the output voltage variation sequence of each film thickness in the range under each lift-off fluctuation amplitude;

[0041] S32: taking the ratio of the output voltage variation corresponding to each film thickness and the corresponding thickness sensitivity as the thickness error caused by the current lift-off fluctuation amplitude, and taking the thickness error of the thickness in the range caused by each lift-off fluctuation amplitude to form a thickness error sequence under the current lift-off reference;

[0042] That is, after determining the above-mentioned coil basic parameters, the variations of the coil impedance and the output voltage under different lift-off references and different lift-off fluctuation amplitudes are calculated, and then the thickness error is calculated according to the output voltage variation as follows:

[0043]

[0044] Where Δt represents the thickness error, ΔU represents the voltage variation, k represents the slope of the output voltage fitting straight line under the lift-off reference (i.e. without lift-off fluctuation), and specifically, the setting method of the slope k is as follows: obtaining the voltage reference value of the eddy current sensor output under each lift-off reference without lift-off fluctuation amplitude disturbance; linear fitting is performed on the voltage reference sequence curve, and the slope of the fitting straight line is the slope k, that is, the thickness sensitivity.

[0045] S4: fitting the corresponding relationship based on the thickness error sequence under different lift-off references, the thickness sequence and each lift-off fluctuation amplitude to obtain the mapping relationship between the thickness error, the thickness and the lift-off fluctuation amplitude;

[0046] Figure 4 A thickness error and copper film thickness and lift-off fluctuation relationship plane is shown; based on the thickness error plane, the corresponding relationship is fitted to obtain the functional relationship between the thickness error, the copper film thickness and the lift-off fluctuation amplitude as follows:

[0047]

[0048] Where k1-k6 are fitting coefficients of the thickness error calculation equation, Δt is the thickness error, t is the thickness of the measured film, and Δl is the lift-off fluctuation amplitude. According to the formula, the thickness error caused by any fluctuation within the lift-off fluctuation range of 150 μm under the lift-off references of 1 mm, 2 mm and 3 mm can be calculated.

[0049] S5: according to the mapping relationship, the thickness measurement error of the measured metal film under the influence of the current lift-off fluctuation can be quickly calculated according to the current film thickness and the lift-off fluctuation amplitude in the actual measurement process, such asFigure 3 is shown.

[0050] Therefore, the application establishes the relationship surface between the thickness error and the current thickness value and the lift-off fluctuation, thereby fitting the thickness error calculation equation, and the thickness error caused by the lift-off fluctuation under different lift-off references can be calculated according to the above equation, and the accurate evaluation of the detection error of the eddy current thickness sensor caused by the lift-off fluctuation is realized.

[0051] Of course, the application can also have other various embodiments, and those skilled in the art can certainly make various corresponding changes and modifications according to the application without departing from the spirit and essence of the application, but these corresponding changes and modifications shall all belong to the protection scope of the claims attached to the application.

Claims

1. A method of quantifying the error in eddy current metal film thickness measurement due to lift-off fluctuations, comprising: The method comprises the following steps: S1: setting different lift-off references and corresponding lift-off fluctuation amplitudes, and determining the optimal value of the parameter of the eddy current detection coil under each lift-off reference; S2: for each lift-off reference, obtaining the output voltage variation sequence of the eddy current sensor under each lift-off fluctuation amplitude within the measurement thickness range, wherein the output voltage variation sequence obtaining step is: Under the current lift-off reference, the thickness of the measured film is measured by the eddy current sensor with the optimal coil parameter to obtain the output voltage reference value corresponding to each film thickness; then a plurality of lift-off fluctuation amplitudes are introduced, and the maximum output voltage variation of the eddy current sensor for measuring each film thickness within the range under each lift-off fluctuation amplitude is obtained in turn; the maximum output voltage variation under each lift-off fluctuation amplitude is combined to form the output voltage variation sequence of the corresponding film thickness under the current lift-off reference; S3: obtaining the thickness error sequence under each lift-off fluctuation amplitude according to the output voltage variation sequence corresponding to each film thickness under each lift-off reference; S4: fitting the corresponding relationship based on the thickness error sequence, the thickness sequence and each lift-off fluctuation amplitude under different lift-off references to obtain the functional relationship between the thickness error, the thickness and the lift-off fluctuation amplitude; S5: according to the functional relationship, the thickness measurement error of the measured film under the influence of the lift-off fluctuation amplitude can be calculated according to the current film thickness and the lift-off fluctuation amplitude in the actual measurement process.

2. The method of claim 1, wherein the eddy current measurement is a metal film thickness measurement. In step S3, the thickness error sequence under each lift-off fluctuation amplitude is obtained according to the output voltage variation sequence corresponding to each film thickness under any lift-off reference, and specifically: Under each lift-off fluctuation amplitude, the ratio of the output voltage variation corresponding to each film thickness to the corresponding thickness sensitivity is taken as the thickness error caused by each lift-off fluctuation amplitude; Each thickness error of the thickness within the range caused by each lift-off fluctuation amplitude is combined to form the thickness error sequence under each lift-off fluctuation amplitude.

3. A method of quantifying the error in eddy current film thickness measurements due to lift-off, as claimed in claim 2, wherein, The calculation method of the thickness sensitivity is: Obtain the voltage reference value sequence of the eddy current sensor output for each film thickness without lift-off fluctuation amplitude under a certain lift-off reference; Linear fitting is performed on the voltage reference value sequence, and the slope of the fitting straight line is the thickness sensitivity.

4. The method of claim 1, wherein the step of quantifying the error in the eddy current measurement of the metal film thickness is performed by the steps of: When the thickness of the measured film is 100-1500 nm, the functional relationship between the thickness error, the thickness and the lift-off fluctuation amplitude is obtained by fitting the corresponding relationship based on the thickness error sequence, the thickness sequence and the lift-off fluctuation amplitude under different lift-off references as follows: ​ wherein are fitting coefficients of the functional relationship between the thickness error, the thickness, and the lift-off fluctuation amplitude, is the thickness error, is the thickness of the measured thin film, is the lift-off fluctuation amplitude.​ 5. The method of claim 1, wherein the step of quantifying the error in the eddy current measurement of the metal film thickness due to lift-off wave motion comprises the steps of: determining the lift-off wave motion of the metal film; and determining the error in the eddy current measurement of the metal film thickness due to the lift-off wave motion. The coil parameters include the winding diameter, the coil inner diameter, the number of turns and the diameter-height ratio, and the determination method of the optimal value of the parameter of the eddy current detection coil under any lift-off reference is as follows: According to the coil quality factor, output voltage sensitivity, output voltage linearity and space constraint requirements, the optimal value of the detection coil parameters is determined, wherein when the winding diameter, coil inner diameter and diameter-height ratio are constant values, the coil quality factor increases first and then decreases with the increase of the number of turns, the output voltage sensitivity increases with the increase of the number of turns, and the output voltage linearity decreases with the increase of the number of turns; when the winding diameter, coil inner diameter and number of turns are constant values, the coil quality factor increases with the increase of the diameter-height ratio, the output voltage sensitivity increases with the increase of the diameter-height ratio, and the output voltage linearity decreases with the increase of the diameter-height ratio; when the number of turns and the diameter-height ratio are larger, the coil volume is larger, and it is more difficult to meet the space constraint requirements.

6. A method of quantifying the error in eddy current film thickness measurements due to lift-off, as recited in claim 1, wherein, Different lift-off references are set to be 1 mm, 2 mm and 3 mm respectively; different lift-off fluctuation amplitudes are 50 μm, 100 μm and 150 μm respectively.

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