Method for quantifying measurement error of lift-off fluctuation on eddy current type metal film thickness

Abstract

The invention provides a method for quantifying a measurement error of lift-off fluctuation on the thickness of an eddy current type metal film, which comprises the following steps of: calculating the influence of lift-off height fluctuation on output voltage, quantifying the thickness error caused by the lift-off fluctuation, and establishing a corresponding relationship between the thickness error and the measured film thickness as well as the lift-off fluctuation; on the basis, the thickness error under any lift-off fluctuation can be quickly calculated with high precision according to the corresponding relation by taking the lift-off reference and the lift-off fluctuation as main influence parameters in the micro-nano metal film thickness detection process; therefore, thickness measurement errors caused by different lift-off references and lift-off fluctuations can be effectively evaluated in practical application.

Description

Technical Field

[0001] The invention belongs to the field of micro-nano detection technology, and in particular relates to a method for quantifying the effect of lift-off fluctuations on eddy current metal film thickness measurement errors. Background Art

[0002] The thickness of metal films is a key parameter that determines their performance. Accurately measuring the thickness of metal films is an important means to ensure high-precision manufacturing of films. Currently, commonly used methods for measuring nanoscale film thickness 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 metal film thickness due to its advantages such as non-contact, high stability and fast response speed. However, during the measurement process, factors such as mechanical vibration will cause changes in the lift-off distance, resulting in inevitable thickness measurement errors. Therefore, in practical applications, it is necessary to design a quantitative evaluation method for the measurement error of eddy current sensors to accurately evaluate the impact of lift-off fluctuations on measurement accuracy. Summary of the invention

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

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

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

[0006] S2: For each lift-off reference, obtain the output voltage sequence of the sensor pair within the thickness measurement range at each lift-off distance, wherein the output voltage acquisition steps are:

[0007] Under the current lift-off reference, the thickness of the film to be measured is measured using an eddy current sensor with optimal coil parameters to obtain an output voltage reference value corresponding to each film thickness; then, lift-off fluctuations of various amplitudes are introduced to obtain the maximum output voltage variation of the sensor for each film thickness within the measuring range under each lift-off fluctuation amplitude; the maximum output voltage variation under each lift-off fluctuation amplitude is combined into an output voltage variation sequence corresponding to the film thickness under the current lift-off reference;

[0008] S3: Obtaining thickness error sequences under each lift-off fluctuation amplitude according to the output voltage variation sequences corresponding to each film thickness under each lift-off reference;

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

[0010] S5: According to the functional relationship, in the actual measurement process, 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.

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

[0012] S31: Compare the output voltage of each film thickness under the lift-off reference when it is affected by a lift-off fluctuation with the corresponding voltage reference value to obtain the maximum output voltage change under the lift-off fluctuation amplitude, and thereby obtain the output voltage change sequence of each film thickness within the measuring range under each lift-off fluctuation amplitude in turn;

[0013] S32: The ratio of the output voltage change corresponding to each film thickness to the corresponding thickness sensitivity is respectively used as the thickness error caused by the current lift-off fluctuation amplitude, and the thickness errors within the measuring range caused by each lift-off fluctuation amplitude are combined into a thickness error sequence under the current lift-off reference.

[0014] Furthermore, the thickness sensitivity is calculated as:

[0015] Obtain a voltage reference value sequence output by the eddy current sensor for each metal film thickness under a certain lift-off reference when there is no lift-off distance fluctuation;

[0016] A linear fit is performed on the voltage reference sequence, where the slope of the fitting line is the thickness sensitivity.

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

[0018]

[0019] Among them, k1~k6 are the 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] Furthermore, the coil parameters include the winding diameter, the inner diameter of the coil, the number of turns and the diameter-to-height ratio. The method for determining the optimal values ​​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 values ​​of the detection coil parameters are determined. When the winding diameter, coil inner diameter and diameter-to-height ratio are constant, the coil quality factor first increases 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, the coil quality factor increases with the increase of the diameter-to-height ratio, the output voltage sensitivity increases with the increase of the diameter-to-height ratio, and the output voltage linearity decreases with the increase of the diameter-to-height ratio; when the number of turns and the diameter-to-height ratio are larger, the coil volume is larger, and it is more difficult to meet the space constraint requirements.

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

[0023] Beneficial effects:

[0024] The present invention provides a method for quantifying the effect of lift-off fluctuation on the measurement error of eddy-current metal film thickness. By calculating the influence of lift-off fluctuation on the output voltage, the thickness error caused by lift-off fluctuation is quantified, and a corresponding relationship between the thickness error, the measured film thickness and the lift-off fluctuation is established. On this basis, the present invention is oriented to the thickness detection process of micro-nano metal films, with 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 quickly and with high precision, so as to effectively evaluate the thickness measurement error caused by different lift-off references and lift-off fluctuations in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 A simulation model diagram of the eddy current sensor provided by the present invention;

[0026] Figure 2 The overall flow chart of the eddy current thickness error quantitative evaluation method provided by the present invention;

[0027] Figure 3 Schematic diagram of the eddy current thickness error quantitative evaluation method provided by the present invention;

[0028] Figure 4 This is the thickness error quantization plane of the eddy current sensor provided by the present invention. DETAILED DESCRIPTION

[0029] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0030] The present invention proposes a thickness error quantification method suitable for different lift-off distances, which is aimed at the thickness detection of micro-nano metal films and can quantify the thickness measurement error caused by different lift-off fluctuations under different lift-off references. Figure 1 Schematic diagram of the eddy current sensor simulation model provided by the embodiment of the present invention. In this embodiment, the detection circuit signal conversion module takes the LC parallel resonant circuit as an example, including a coil (inductor L c and internal resistance R c ), series resistance R0 and coupling capacitance C0. Based on this, a method to quantify the effect of lift-off fluctuation on the eddy current metal film thickness measurement error is proposed. Figure 2 As shown, the following steps are included:

[0031] S1: setting different lift-off references and corresponding lift-off fluctuation amplitudes, and determining the optimal parameter value of the eddy current detection coil under each lift-off reference;

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

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

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

[0035] For example, in this embodiment, the winding diameter and the inner diameter of the coil are determined to be 100μm and 3.0mm respectively, the diameter-to-height ratio is fixed to 1, and the number of turns changes from 100 to 400, and the changes in the coil quality factor, the sensitivity and linearity of the output voltage of the LC resonant circuit under different numbers of turns are analyzed. With the continuous increase in 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 growth rate gradually slows down; the linearity of the output voltage gradually decreases; considering the quality factor, output voltage sensitivity and linearity, it is determined that the optimal value range of the number of turns is 150-170 turns, 200-220 turns and 300-320 turns when the lift is 1mm, 2mm and 3mm from the benchmark. After determining the optimal number of turns, the diameter-to-height ratio changes from 0.5 to 12, and the changes in the coil quality factor, the sensitivity and linearity of the output voltage of the LC resonant circuit under different diameter-to-height ratios are analyzed. As the diameter-to-height ratio increases, the coil quality factor increases gradually; the output voltage sensitivity increases gradually, but the growth rate slows down gradually; the output voltage linearity decreases gradually; at the same time, the larger the diameter-to-height ratio, the larger the outer diameter of the coil, which is not conducive to the miniaturization design of the sensor. Taking into account the coil quality factor, output voltage sensitivity, output voltage linearity and space constraints, the optimal range of the diameter-to-height ratio is determined to be 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 pair within the thickness measurement range at each lift-off distance, wherein the output voltage acquisition steps are:

[0037] Under the current lift-off reference, the thickness of the film to be measured is measured using an eddy current sensor with optimal coil parameters to obtain an output voltage reference value corresponding to each film thickness; then, lift-off fluctuations of various amplitudes are introduced, and the maximum output voltage variation of the sensor for each film thickness within the measuring range under each lift-off fluctuation amplitude is obtained in turn; the maximum output voltage variation under each lift-off fluctuation amplitude is combined into an output voltage variation sequence corresponding to the film thickness under the current lift-off reference;

[0038] S3: Obtaining thickness error sequences under each lift-off fluctuation amplitude according to the output voltage variation sequences corresponding to each film thickness under each lift-off reference;

[0039] Among them, according to the output voltage variation sequence corresponding to each film thickness under any lift-off reference, the corresponding thickness error sequence under the lift-off reference is obtained, specifically:

[0040] S31: Compare the output voltage of each film thickness under the lift-off reference when it is affected by a lift-off fluctuation with the corresponding voltage reference value to obtain the maximum output voltage change (absolute value) under the lift-off fluctuation amplitude, and thereby obtain the output voltage change sequence of each film thickness within the measuring range under each lift-off fluctuation amplitude in turn;

[0041] S32: taking the ratio of the output voltage change corresponding to each film thickness to the corresponding thickness sensitivity as the thickness error caused by the current lift-off fluctuation amplitude, and forming the thickness errors within the measuring range caused by each lift-off fluctuation amplitude into a thickness error sequence under the current lift-off reference;

[0042] That is to say, after determining the basic parameters of the coil, the present invention calculates the changes of the coil impedance and the output voltage under different lift-off references and different lift-off fluctuation amplitudes, and then calculates the thickness error according to the output voltage change as follows:

[0043]

[0044] Among them, Δt represents the thickness error, ΔU represents the voltage change, and k represents the slope of the output voltage fitting line when the base is lifted (i.e., when there is no lift-off fluctuation). Specifically, the method for setting the slope k is: obtain the voltage reference value output by the eddy current sensor under each lift-off base when there is no lift-off fluctuation amplitude disturbance; perform linear fitting on the voltage reference sequence curve, and the slope of the fitting line is the slope k, which is the thickness sensitivity.

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

[0046] Figure 4 The relationship plane between the thickness error and the copper film thickness and the lift-off fluctuation amplitude is shown; on the basis of the thickness error plane, the corresponding relationship is fitted, and the functional relationship between the thickness error and the copper film thickness and the lift-off fluctuation amplitude is obtained as follows:

[0047]

[0048] Among them, k1~k6 are the 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. According to the formula, the thickness error caused by any fluctuation within the lift-off fluctuation range of 150μm can be calculated under the lift-off reference of 1mm, 2mm and 3mm.

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

[0050] It can be seen that the present invention establishes a relationship surface between the thickness error and the current thickness value and the lift-off fluctuation amount, thereby fitting the thickness error calculation equation. According to the above equation, the thickness error caused by any lift-off fluctuation under different lift-off references can be calculated, thereby achieving accurate evaluation of the eddy current thickness sensor detection error caused by the lift-off fluctuation.

[0051] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may certainly make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for quantifying the effect of lift-off fluctuations on eddy current metal film thickness measurement error, characterized in that: The following steps are involved: S1: setting different lift-off references and corresponding lift-off fluctuation amplitudes, and determining the optimal parameter value of the eddy current detection coil under each lift-off reference; S2: For each lift-off reference, obtain the output voltage sequence of the sensor pair within the thickness measurement range at each lift-off distance, wherein the output voltage acquisition steps are: Under the current lift-off reference, the thickness of the film to be measured is measured using an eddy current sensor with optimal coil parameters to obtain an output voltage reference value corresponding to each film thickness; then, lift-off fluctuations of various amplitudes are introduced to obtain the maximum output voltage variation of the sensor for each film thickness within the measuring range under each lift-off fluctuation amplitude; the maximum output voltage variation under each lift-off fluctuation amplitude is combined into an output voltage variation sequence corresponding to the film thickness under the current lift-off reference; S3: Obtaining thickness error sequences under each lift-off fluctuation amplitude according to the output voltage variation sequences corresponding to each film thickness under each lift-off reference; S4: fitting the corresponding relationship between the thickness error sequence, thickness sequence and each lift-off fluctuation amplitude under different lift-off references to obtain the functional relationship between the thickness error, thickness and lift-off fluctuation amplitude; S5: According to the functional relationship, in the actual measurement process, 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.

2. A method for quantifying the effect of lift-off fluctuation on eddy current metal film thickness measurement error as claimed in claim 1, characterized in that: In steps S2 and S3, the corresponding thickness error sequence under any lift-off reference is obtained according to the output voltage variation sequence corresponding to each film thickness under the lift-off reference, specifically: S31: Compare the output voltage of each film thickness under the lift-off reference when it is affected by a lift-off fluctuation with the corresponding voltage reference value to obtain the maximum output voltage change under the lift-off fluctuation amplitude, and thereby obtain the output voltage change sequence of each film thickness within the measuring range under each lift-off fluctuation amplitude in turn; S32: The ratio of the output voltage change corresponding to each film thickness to the corresponding thickness sensitivity is respectively used as the thickness error caused by the current lift-off fluctuation amplitude, and the thickness errors within the measuring range caused by each lift-off fluctuation amplitude are combined into a thickness error sequence under the current lift-off reference.

3. A method for quantifying the effect of lift-off fluctuation on eddy current metal film thickness measurement error as claimed in claim 2, characterized in that: The thickness sensitivity is calculated as: Obtain a voltage reference value sequence output by the eddy current sensor for each metal film thickness under a certain lift-off reference when there is no lift-off distance fluctuation; A linear fit is performed on the voltage reference sequence, where the slope of the fitting line is the thickness sensitivity.

4. A method for quantifying the effect of lift-off fluctuation on eddy current metal film thickness measurement error as claimed in claim 1, characterized in that: When the thickness of the film to be measured is 100-1500nm, the corresponding relationship fitting is performed based on the thickness error sequence, thickness sequence and lift-off fluctuation amplitude under different lift-off references, and the functional relationship between the thickness error, thickness and lift-off fluctuation amplitude is obtained as follows: Among them, k1~k6 are the 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.

5. A method for quantifying the effect of lift-off fluctuation on eddy current metal film thickness measurement error as claimed in claim 1, characterized in that: The coil parameters include the winding diameter, the inner diameter of the coil, the number of turns and the diameter-to-height ratio. The method for determining the optimal values ​​of the eddy current detection coil parameters 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 values ​​of the detection coil parameters are determined. When the winding diameter, coil inner diameter and diameter-to-height ratio are constant, the coil quality factor first increases 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, the coil quality factor increases with the increase of the diameter-to-height ratio, the output voltage sensitivity increases with the increase of the diameter-to-height ratio, and the output voltage linearity decreases with the increase of the diameter-to-height ratio; when the number of turns and the diameter-to-height ratio are larger, the coil volume is larger, and it is more difficult to meet the space constraint requirements.

6. A method for quantifying the effect of lift-off fluctuation on eddy current metal film thickness measurement error as claimed in claim 1, characterized in that: Different lift-off references can be set to 1mm, 2mm and 3mm respectively; different lift-off fluctuation amplitudes can be set to 50μm, 100μm and 150μm respectively.

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