A metal film thickness measurement method for reducing parasitic capacitance effects
By combining a single-coil sensor with a differential evolution algorithm to fit the feature slope method, the error problem caused by the parasitic capacitance effect in eddy current measurement was solved, and high-precision measurement of the thickness of nanoscale metal thin films was achieved.
Patent Information
- Application Number
- CN202411955399.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-28
- Publication Date
- 2025-11-07
- Estimated Expiration
- 2044-12-28
AI Technical Summary
Traditional eddy current measurement methods suffer from parasitic capacitance effects when measuring the thickness of nanoscale metal thin films, resulting in large measurement errors and failing to meet high-precision requirements.
A characteristic slope method combining a single-coil sensor and differential evolution algorithm fitting is used to reduce parasitic capacitance effect and improve measurement accuracy by measuring impedance changes.
This method enables the measurement of metal film thickness with nanometer-level resolution, significantly reduces the influence of parasitic capacitance effects, and improves the sensitivity and stability of the measurement system.
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Figure CN119803263B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of measurement, and particularly relates to a metal film thickness measurement method for reducing parasitic capacitance effect. BACKGROUND
[0002] With the rapid development of integrated circuit and semiconductor manufacturing technology, metal thin film materials play an increasingly important role in precision manufacturing. Especially in the process of integrated circuit interconnection, packaging and component manufacturing, the precise control of metal thin film thickness is directly related to the performance and reliability of the device. Nanoscale metal thin films are widely used in conductive layers, shielding layers and other functional layers inside the chip. Accurate measurement of the thickness of these metal thin films is crucial to ensure the performance and quality of the product. However, traditional thickness measurement methods such as mechanical contact probes and optical interference methods have low measurement accuracy and reliability when facing complex curved surfaces or small sizes.
[0003] The eddy current measurement method utilizes the electromagnetic interaction between the coil and the metal thin film, and calculates the thickness of the metal thin film by measuring the change of the induced impedance. Compared with traditional measurement methods, the eddy current measurement method can quickly and non-contactly obtain the thickness data of the metal thin film, and can effectively cope with the measurement challenges of high frequency, complex topography and small size.
[0004] However, in practical applications, the eddy current measurement technology still faces many challenges. Parasitic capacitance effect, signal noise interference and complexity of circuit design can all affect the measurement accuracy. Especially in the measurement of nanoscale metal thin films, the existence of parasitic capacitance can significantly reduce the resonant frequency, thereby affecting the accuracy of the measurement. Therefore, how to overcome the parasitic effect in eddy current measurement and improve the sensitivity and stability of the measurement system has become an important research topic. SUMMARY
[0005] The present application proposes a metal film thickness measurement method for reducing parasitic capacitance effect, which takes a single-coil sensor system as the core part, and uses a characteristic slope method combined with a differential evolution algorithm for fitting to obtain nanoscale thickness resolution and significantly reduce parasitic capacitance effect.
[0006] The present application adopts the following technical solutions.
[0007] A metal film thickness measurement method for reducing parasitic capacitance effect, the device used in the method comprises a sensor coil, a pre-signal processing module, a data acquisition module, a communication module and an upper computer, the method inputs an alternating voltage into the sensor coil and the pre-signal processing circuit through the crystal oscillator in the signal generator, the pre-signal processing circuit outputs a measurement impedance value corresponding to the metal film thickness, the impedance value is input into the upper computer through the data acquisition module and the communication module, fitting operation is performed in the upper computer, and a corresponding metal film thickness characteristic value is calculated, comprising the following steps:
[0008] Step one: install the data acquisition module, the communication module and the upper computer, and ensure that they work normally.
[0009] Step two: input a sweep excitation signal to both ends of the sensor coil through the signal generating circuit.
[0010] Step three: place a wafer coated with a metal thin film on the wafer support, and measure the sweep value of the wafer at each lift-off height by changing the lift-off height multiple times.
[0011] Step four: calculate the parasitic capacitance value, fit the real impedance value at each frequency using the differential evolution algorithm, and obtain the characteristic slope value. The characteristic slope absolute value and the film thickness product are used to obtain the calibration curve. Multiple characteristic slope values of wafer coated with films of different thicknesses can also be obtained by repeating step three.
[0012] Step five: repeat the above steps to complete the calibration curve of the thin film of other metal materials, and store the calibration curve in the upper computer.
[0013] Step six: take the wafer to be measured with a known surface material, measure and fit to obtain the characteristic slope value S, and compare it with the calibration curve of the corresponding material film obtained in step four, that is, according to the mapping relationship of table S-c, the metal film thickness is calculated.
[0014] The sensor coil is a single-coil eddy current sensor.
[0015] The single-coil eddy current sensor is an eddy current sensor fixed by a clamp, and the lead is connected to the pre-circuit of the pre-signal processing module.
[0016] In step one, the sensor coil is located above and adjacent to the wafer support, and in step two, the sweep excitation signal is sent to the sensor coil, so that the metal thin film adjacent to the sensor coil generates eddy current.
[0017] In step two, the sweep range of the sweep excitation signal is 0.01MHz-50MHz.
[0018] In step three, the lift-off height is changed multiple times in the range of 0mm-3mm, and the sweep values of at least two lift-off heights are measured.
[0019] In step three, the lift-off height is changed multiple times, and the difference between each lift-off height is as large as possible, so as to measure at least one thickness of the plated wafer.
[0020] The single-coil sensor is used to excite and measure the impedance change caused by different metal film thicknesses. In the case where other measurement environmental parameters remain unchanged, the impedance change measured by the single-coil sensor and the metal film thickness have a one-to-one correspondence. When the parasitic capacitance is not considered, the actual impedance value between the two ends of the coil is:
[0021] Z=R+jωL Formula 1;
[0022] When the parasitic capacitance exists between the two ends of the coil due to the existence of the coil lead in the experimental measurement, the measured impedance value at this time is:
[0023]
[0024] When it is necessary to minimize the influence of parasitic capacitance to accurately measure the film thickness, it is necessary to obtain the actual impedance value of the coil, and the characteristic slope method is derived through the formula:
[0025]
[0026] Formula 4 is the analytical solution of the impedance change amount. When the phase term and the amplitude term in the analytical solution can be separated; and compared with other parts of the integral function, the change rate of α is very small, and When the characteristic frequency α0 reaches the maximum value; the approximation of the solution is calculated at α0 and the phase term of the impedance change outside the integral is only determined by The phase term includes the conductivity, thickness, and magnetic permeability of the metal film. After approximation and simplification, the following is obtained:
[0027]
[0028] At this time, the peak frequency is:
[0029] The change of α0 caused by the change of the lift-off height is
[0030]
[0031] The change amount of the peak frequency is:
[0032] Further obtained:
[0033]
[0034] The ratio of the peak frequency variation and the lift-off height variation is inversely proportional to the film thickness, and the ratio is the characteristic slope S.
[0035] In step three, the frequency value corresponding to the maximum inductance imaginary part variation in the sweep mode is taken as the peak frequency, and the formula is defined as:
[0036]
[0037] In order to obtain the accurate inductance imaginary part value, the accurate value at the corresponding frequency, i.e. the actual value of the coil impedance real part variation, needs to be obtained,
[0038] From the above formula, when other conditions remain unchanged, the characteristic slope is inversely proportional to the film thickness c; when measuring the nanoscale metal film thickness, the corresponding peak frequency is high, and the existence of the parasitic capacitance reduces the resonance frequency, making the measurement error larger, so the influence of the parasitic capacitance needs to be reduced; when the peak frequency is obtained by changing the lift-off height, the change of the lift-off height can cause a larger change of the peak frequency, and a peak frequency-lift-off height relationship curve with excellent linearity can be obtained;
[0039] When the skin effect exists, the electric eddy current intensity in the conductor decreases exponentially with the increase of the depth into the conductor, in order to accurately measure the metal film thickness, the skin depth at the corresponding working frequency f needs to be greater than the metal film thickness, i.e. the electromagnetic field needs to completely penetrate the metal film; for non-magnetic materials, the calculation formula of the skin depth is as follows:
[0040]
[0041] In order to reduce the influence of the parasitic capacitance, the intelligent optimization algorithm is used to fit the real impedance value of the coil at each frequency. First, the resonance frequency of the coil in the air is measured, and the inductance value of the coil is measured at low frequency, and then the parasitic capacitance value is obtained through the following formula:
[0042]
[0043] After the measurement impedance value at the corresponding film thickness and different frequencies is measured, such as formula 2 and formula 3, the parallel capacitance value, frequency, measured real part and imaginary part value are known at a certain frequency, and at this time, two fitting output parameters R and L, i.e. the actual value of the coil impedance, can be obtained.
[0044] When fitting, a global optimization algorithm needs to be selected, and the differential evolution algorithm is used for fitting in this method.
[0045] The specific steps of the differential evolution algorithm are as follows:
[0046] xi,0 = (R i,0 , L i,0 ) Equation 13;
[0047] R i,0 and L i,0 are resistance and inductance values of the i-th individual in the initial population, generated by random initialization:
[0048] R i,0 = R min + rand(0, 1) · (R max - R min ) Equation 14;
[0049] L i,0 = L min + rand(0, 1) · (L max - L min ) Equation 15;
[0050] where R min and R max are lower and upper bounds of resistance, L min and L max are lower and upper bounds of inductance, rand(0, 1) is a uniform random number between [0, 1];
[0051] The mutation operation is to generate a new individual by amplifying the difference of individuals; for each individual x i,G = (R i,G , L i,G ), three different individuals x r1,G = (R r1,G , L r1,G ), x r2,G , x r3,G are randomly selected from the population, a new mutation vector v i,G is generated:
[0052] v i,G = (R v,i,G L v,i,G ) = (R r1,G , L r1,G ) + F · ((R r2,G , L r2,G ) - (R r3,G , L r3,G )) Equation 16;
[0053] where F is a scaling factor, which controls the amplitude of mutation;
[0054] The vector generated by the mutation operation is crossed with the current individual; for each individual x i,G = (R i,G , Li,G Generate a new test vector u. i,G =(R u,i,G L u,i,G ):
[0055]
[0056] L u,i,G The generation of R u,i,G Similarly; crossover probability C r The proportion of parameters inherited from the mutation vector is determined, and j is a random index that guarantees at least one component is selected from the mutation vector;
[0057] The selection step is used to determine whether to use the trial vector u. i,G Replacement of the original individual x i,G Moving to the next generation; selection is based on the fitness function value, i.e., the objective function value. The algorithm is optimized through multiple iterations until the termination condition is met, such as reaching the maximum number of iterations or meeting the convergence condition; the error function is set as the difference between the actual impedance measurement value and the impedance value obtained from the fitted model, i.e., formulas 2 and 3, as shown in formulas 18 and 19 below. The objective function, formula 20, is the sum of the squares of the real part error and the imaginary part error. The relative error of the objective function value is set to reach 10. -6 The fitting process stops at the specified level.
[0058] error_real=Z_measured_real-real(Z) Formula 18;
[0059] error_imag=Z_measured.imag-imaag(Z) Formula 19;
[0060] error_sum=error_real^2+error_imag^2 Formula 20.
[0061] This invention can achieve nanometer-level thickness resolution and significantly reduce parasitic capacitance effects.
[0062] The method of the present invention can obtain a large change in peak frequency by changing the lift-off height, and can obtain a peak frequency-lift-off height relationship curve with excellent linearity. Attached Figure Description
[0063] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:
[0064] Appendix Figure 1 This is a schematic diagram of the equivalent circuit at both ends of a single-coil sensor circuit when no capacitor is present;
[0065] Appendix Figure 2is a schematic diagram of the equivalent circuit of the single-coil sensor loop when there is a capacitance present;
[0066] attached Figure 3 is a schematic diagram of the optimization steps of the differential evolution algorithm;
[0067] attached Figure 4 is a schematic diagram of the measured impedance real part and the fitted value when measuring a 315nm copper film by sweeping frequency at the same lift-off height;
[0068] attached Figure 5 is a schematic diagram of the fitted R value and the actual resistance value;
[0069] attached Figure 6 is a schematic diagram of the relative error of the fitting result;
[0070] attached Figure 7 is a schematic diagram of the inductance imaginary part-frequency relationship curve after fitting for different film thicknesses at the same lift-off height;
[0071] attached Figure 8 is a schematic diagram of the relationship curve between the peak frequency obtained after fitting and the lift-off height for measuring a 315nm copper film;
[0072] attached Figure 9 is a schematic diagram of the relationship curve between the absolute value of the characteristic slope and the film thickness;
[0073] attached Figure 10 is a schematic diagram of the flow of the measurement method of the present application;
[0074] attached Figure 11 is a schematic diagram of the hardware connection used in the present application. DETAILED DESCRIPTION
[0075] As shown in the figure, a metal film thickness measurement method for reducing the parasitic capacitance effect, the device used in the method includes a sensor coil, a pre-signal processing module, a data acquisition module, a communication module and a host computer, the method inputs an alternating voltage to the sensor coil and the pre-signal processing circuit through the crystal oscillator in the signal generator, respectively, the pre-signal processing circuit outputs a measurement impedance value corresponding to the metal film thickness, the impedance value is input to the host computer through the data acquisition module and the communication module, fitting operation is performed in the host computer, and the corresponding metal film thickness characteristic value is calculated, including the following steps.
[0076] Step one: install the data acquisition module, the communication module and the host computer, and ensure that they work normally;
[0077] Step two: pass a sweep excitation signal through the signal generation circuit to both ends of the sensor coil;
[0078] Step three: Place the wafer coated with metal film on the wafer holder, and measure the sweep value of the wafer at each lift-off height by changing the lift-off height multiple times.
[0079] Step four: Calculate the parasitic capacitance value, and use the differential evolution algorithm to fit the real impedance value at each frequency to obtain the characteristic slope value. The characteristic slope absolute value and the film thickness are multiplied to obtain the calibration curve. Multiple characteristic slope values of different thicknesses of coated wafers can also be obtained by repeating step three.
[0080] Step five: Repeat the above steps to complete the calibration curve of other metal material films, and store the calibration curve in the upper computer.
[0081] Step six: Take the wafer to be measured with a known surface material, measure and fit to obtain the characteristic slope value S, and compare it with the calibration curve of the corresponding material film obtained in step four. According to the mapping relationship of table S-c, the thickness of the metal film is calculated.
[0082] The sensor coil is a single-coil eddy current sensor.
[0083] The single-coil eddy current sensor is an eddy current sensor fixed by a clamp, and the lead is connected to the pre-circuit of the pre-signal processing module.
[0084] In step one, the sensor coil is located above and adjacent to the wafer holder. In step two, a sweep excitation signal is sent to the sensor coil, causing the metal film of the wafer adjacent to the sensor coil to generate eddy current.
[0085] In step two, the sweep range of the sweep excitation signal is 0.01MHz-50MHz.
[0086] In step three, the lift-off height is changed multiple times in the range of 0mm-3mm, and the sweep values of at least two lift-off heights are measured.
[0087] In step three, when the lift-off height is changed multiple times, the lift-off height difference of each time is as large as possible to measure at least one thickness of the coated wafer.
[0088] The single-coil sensor is used to excite and measure the impedance change caused by different metal film thicknesses. In the case where other measurement environmental parameters remain unchanged, the impedance change measured by the single-coil sensor and the metal film thickness have a one-to-one correspondence. When the parasitic capacitance is not considered, the actual impedance value across the coil is:
[0089] Z=R+jωL Formula 1;
[0090] When there is a parasitic capacitance across the coil due to the presence of the coil lead in the experimental measurement, the measured impedance value at this time is:
[0091]
[0092]
[0093] When the influence of parasitic capacitance needs to be minimized to accurately measure the film thickness, the actual impedance value of the coil needs to be obtained, and the characteristic slope method is derived by formula:
[0094]
[0095] Formula 4 is the analytical solution of the impedance change, when the phase term and amplitude term in the analytical solution can be separated; and compared with other parts of the integral function, The rate of change of α is very small, and When the characteristic frequency α0 reaches the maximum value; the solution is calculated at α0 And outside the integral, the phase term of the impedance change is only determined by The phase term includes the conductivity, thickness, and permeability of the metal film, and after approximation and simplification, we get:
[0096]
[0097] At this time, the peak frequency is: The change of α0 caused by the change of lift-off height is
[0098]
[0099] The change of the peak frequency is: Further obtained:
[0100]
[0101] That is, the ratio of the change of the peak frequency to the change of the lift-off height is inversely proportional to the film thickness, and the ratio is the characteristic slope S.
[0102] In step three, in the sweep mode, the frequency value corresponding to the maximum change of the inductance imaginary part is taken as the peak frequency, and the formula is defined as:
[0103]
[0104] In order to obtain the accurate inductance imaginary part value, the accurate value corresponding to the frequency is obtained, that is, the actual value of the change of the coil impedance real part,
[0105] From the above formula, it can be seen that when other conditions remain unchanged, the characteristic slope is inversely proportional to the film thickness c. When measuring the thickness of a nanoscale metal film, the corresponding peak frequency is relatively high, but the presence of parasitic capacitance reduces the resonant frequency, which increases the measurement error. Therefore, it is necessary to reduce the influence of parasitic capacitance. This is to ensure that when changing the lift-off height to obtain the peak frequency, the change in lift-off height can cause a large change in the peak frequency, and a peak frequency-lift-off height relationship curve with excellent linearity can be obtained.
[0106] When the intensity of eddy currents in a conductor decreases exponentially with increasing depth due to the skin effect, the skin depth at the corresponding operating frequency f needs to be greater than the metal film thickness to ensure accurate measurement of the metal film thickness, allowing the electromagnetic field to completely penetrate the metal film. For non-magnetic materials, the formula for calculating the skin depth is as follows:
[0107]
[0108] To reduce the impact of parasitic capacitance, an intelligent optimization algorithm is used to fit the true impedance value of the coil at each frequency. First, the resonant frequency of the coil in air should be measured, and the inductance value of the coil should be measured at low frequencies. Then, the parasitic capacitance value is obtained using the following formula:
[0109]
[0110] After measuring the impedance values at different frequencies corresponding to the film thickness, as shown in Formulas 2 and 3, at a certain frequency, the parallel capacitance value, frequency, and the measured real and imaginary parts are known. At this time, two fitting output parameters R and L can be obtained, which are the actual values of the coil impedance.
[0111] A global optimization algorithm should be used for fitting; this method uses the differential evolution algorithm for fitting.
[0112] The specific steps of the differential evolution algorithm are shown in the following formula:
[0113] x i,0 =(R i,0 L i,0 ) Formula 13;
[0114] R i,0 and L i,0 These are the resistance and inductance values of the i-th individual in the initial population, generated through random initialization:
[0115] R i,0 =R min +rand(0,1)·(R) max -R min ) Formula 14;
[0116] Li,0 = L min + rand(0, 1) · (L max - L min ) Formula 15;
[0117] where R min and R max are the lower and upper bounds of resistance, L min and L max are the lower and upper bounds of inductance, rand(0, 1) is a uniform random number between [0, 1];
[0118] The mutation operation is to generate new individuals by amplifying the difference of individuals; for each individual x i,G = (R i,G , L i,G ), three different individuals x r1,G = (R r1,G , L r1,G ), x r2,G , x r3,G are randomly selected from the population, a new mutation vector v i,G is generated:
[0119] v i,G = (R v,i,G L v,i,G ) = (R r1,G , L rl,G ) + F · ((R r2,G , L r2,G ) - (R r3,G , L r3,G )) Formula 16;
[0120] where F is a scaling factor, which controls the amplitude of mutation;
[0121] The vector generated by the mutation operation is crossed with the current individual; for each individual x i,G = (R i,G , L i,G ), a new trial vector u i,G = (R u,i,G , L u,i,G ) is generated:
[0122]
[0123] The generation of L u,i,G is similar to R u,i,G ; the crossover probability C r determines the proportion of parameters inherited from the mutation vector, j is a random index to ensure that at least one component is selected from the mutation vector;
[0124] In the selection step for deciding whether to use the trial vector u i,G Instead of the original individual x i,G Enter the next generation; selection is made according to the fitness function value, i.e., the objective function value, and the algorithm is optimized through multiple iterations until the termination condition is met, such as reaching the maximum number of iterations or meeting the convergence condition; the error function is set as the difference between the actual impedance measurement value and the impedance value obtained from the fitting model, i.e., formula 2 and formula 3, as shown in the following formula 18 and formula 19, and the objective function formula 20 is the sum of the squares of the real part error and the imaginary part error, and the relative error of the objective function value is set to 10 -6 times the error when stopping fitting.
[0125] error_real = Z_measured.real - real(Z) formula 18;
[0126] error_imag = Z_measured.imag - imag(Z) formula 19;
[0127] error_sum = error_real^2 + error_imag^2 formula 20.
[0128] Embodiment:
[0129] The method in this example uses a differential evolution algorithm for fitting, and the key steps of the differential evolution algorithm are as shown in Figure 3
[0130] When other conditions remain unchanged, the characteristic slope is inversely proportional to the film thickness c. When measuring nanoscale metal film thickness, the corresponding peak frequency is relatively high, and the existence of parasitic capacitance reduces the resonance frequency, making the measurement error larger, so it is necessary to reduce the impact of parasitic capacitance. This method changes the lift-off height to obtain the peak frequency, and the change in lift-off height can cause a large change in peak frequency, and a peak frequency-lift-off height relationship curve with excellent linearity can be obtained.
[0131] Due to the skin effect, the electric eddy current intensity in the conductor decreases exponentially with the increase of the depth into the conductor, in order to accurately measure the metal film thickness, the skin depth at the corresponding working frequency f needs to be greater than the metal film thickness, that is, the electromagnetic field completely penetrates the metal film.
[0132] Figure 4 The measured impedance real part when the 315 nm film thickness is measured by sweeping frequency at the same lift-off height and the fitted R value; Figure 5 The fitted R value at each frequency and the actual resistance value, it can be seen that the curves basically coincide; Figure 6 The relative error of the R value obtained by the algorithm fitting and the actual resistance value, it can be seen that the relative error is very small (in the order of 10-11 The fitting effect is very good.
[0133] Figure 7 The fitting effect is very good.
[0134] The fitting effect is very good. Figure 8 ;
[0135] The fitting effect is very good. Figure 9 The fitting effect is very good.
[0136] The fitting effect is very good. Figure 11 The fitting effect is very good.
[0137] The fitting effect is very good.
[0138] Step one: install the eddy current sensor through the clamp, connect the lead to the pre-circuit, and ensure that the data acquisition module, communication module, and host computer work normally.
[0139] Step two: pass the sweep excitation signal through the signal generation circuit to both ends of the coil, and the sweep frequency range is usually 0.01MHz-50MHz.
[0140] Step three: place a wafer coated with a metal film on the wafer support, change the lift-off height from 0mm to 3mm, measure the sweep frequency value of at least two lift-off heights, and the measurement interval should be as large as possible. Measure at least one thickness of the coated wafer.
[0141] Step four: calculate the parasitic capacitance value, use the differential evolution algorithm to fit the impedance real value at each frequency, and obtain the characteristic slope value. The product of the absolute value of the characteristic slope and the film thickness can obtain the calibration curve, or multiple characteristic slope values of different thickness coated wafers can be obtained by repeating step three.
[0142] Step five: repeat the above steps to complete the calibration curve of other metal thin films, and store the calibration curve in the host computer.
[0143] Step six: take a wafer of known surface material to be measured, measure and fit to get the characteristic slope value S, and compare with the corresponding material film calibration curve obtained in step four, that is, according to the mapping relationship of table S-c, the thickness of the metal film is calculated.
[0144] The flowchart of the measurement method is shown in Figure 10 .
Claims
1. A method of measuring the thickness of a metal film with reduced effects of parasitic capacitance, comprising: The device used in the method comprises a sensor coil, a pre-signal processing module, a data acquisition module, a communication module and an upper computer, the method inputs an alternating voltage into the sensor coil and a pre-signal processing circuit of the pre-signal processing module through a crystal oscillator in a signal generator, outputs a measurement impedance value corresponding to a metal film thickness from the pre-signal processing circuit, inputs the impedance value into the upper computer through the data acquisition module and the communication module, performs fitting operation in the upper computer, and calculates a corresponding metal film thickness characteristic value, comprising the following steps. Step one: install the data acquisition module, the communication module and the upper computer to ensure their normal operation; Step two: input a sweep excitation signal to both ends of the sensor coil through a signal generating circuit of the signal generator; Step three: place a wafer coated with a metal thin film on a wafer support, and measure the sweep values of the wafer at various lift-off heights by changing the lift-off height multiple times; Step four: calculate the parasitic capacitance value, fit the real impedance value at each frequency by using the differential evolution algorithm, and obtain the characteristic slope value; Obtain the calibration curve by the product of the absolute value of the characteristic slope and the film thickness, or obtain the characteristic slope values of multiple different thickness coated wafers by repeating step three; Step five: repeat the above steps to complete the calibration curve of other metal thin films, and store the calibration curve in the upper computer; Step six: take a wafer to be measured with a known surface material, measure and fit to obtain a characteristic slope value S, compare it with the calibration curve of the corresponding material thin film obtained in step four, that is, calculate the metal thin film thickness according to the mapping relationship of table S-c; The sensor coil is used to excite and measure the impedance change caused by different metal film thicknesses, and in the case that other measurement environmental parameters remain unchanged, the impedance change measured by the sensor coil and the metal film thickness have a one-to-one correspondence, and when the parasitic capacitance is not considered, the actual impedance value between the two ends of the coil is: Z=R+jωL Formula 1: When the parasitic capacitance exists between the two ends of the coil due to the existence of the coil lead in the experimental measurement, the measurement impedance value at this time is: When it is necessary to minimize the influence of parasitic capacitance to accurately measure the film thickness, the actual impedance value of the coil needs to be obtained, and the characteristic slope method is derived through the formula: Equation 4 is the analytical solution of the impedance change amount, the phase term and the amplitude term in the analytical solution can be separated; and compared with other parts of the integral function, The change rate of a is very small, and When the characteristic frequency a0reaches the maximum value; the approximation of the solution is calculated at a0 And the phase term of the impedance change outside the integral sign is only determined by The phase term includes the conductivity, thickness and permeability of the metal film, and after approximation and simplification, the following equation is obtained: The peak frequency at this time is: The change of α0 caused by the change of lift-off height is The amount of change in peak frequency is: Further obtained: That is, the ratio of the change of the peak frequency and the change of the lift-off height is inversely proportional to the film thickness, and the ratio is the characteristic slope S.
2. The method of claim 1, wherein: The sensor coil is a single-coil eddy current sensor.
3. The method of claim 2, wherein: The single-coil eddy current sensor is an eddy current sensor fixed by a clamp, and the lead is connected to the pre-circuit of the pre-signal processing module.
4. The method of claim 1, wherein: In step one, the sensor coil is located above and adjacent to the wafer support, and in step two, the sweep excitation signal is sent to the sensor coil, so that the metal thin film of the wafer adjacent to the sensor coil generates eddy current.
5. The method of claim 1, wherein: In step two, the sweep range of the sweep excitation signal is 0.01MHz-50MHz.
6. The method of claim 5, wherein: In step three, the lift-off height is changed multiple times in the lift-off height range of 0mm-3mm, and the sweep values of at least two lift-off heights are measured.
7. The method of claim 6, wherein: In step three, the lift-off height is changed multiple times, and the lift-off height difference of each time is made as large as possible to measure the at least one thickness of the coated wafer.
8. The method of claim 1, wherein: In step three, the peak frequency is defined as the frequency value corresponding to the maximum change in the inductance imaginary part in the sweep mode. In order to obtain an accurate inductance imaginary part value, an accurate value at the corresponding frequency, i.e., the actual value of the change in the inductance real part, is obtained, From the above formula, when other conditions remain unchanged, the characteristic slope value is inversely proportional to the film thickness c; when measuring the nanoscale metal film thickness, the corresponding peak frequency is high, and the existence of the parasitic capacitance reduces the resonance frequency, which increases the measurement error, so it is necessary to reduce the influence of the parasitic capacitance; when the lift-off height is changed to obtain the peak frequency, the change in the lift-off height can cause a large change in the peak frequency, and a peak frequency-lift-off height relationship curve with excellent linearity can be obtained; When the skin effect exists, the electric eddy current intensity in the conductor decreases exponentially with the increase of the depth into the conductor, in order to accurately measure the metal film thickness, the skin depth at the corresponding working frequency f needs to be greater than the metal film thickness, i.e., the electromagnetic field completely penetrates the metal film; for non-magnetic materials, the calculation formula of the skin depth is as follows: In order to reduce the influence of the parasitic capacitance, a smart optimization algorithm is used to fit the real impedance value of the coil at each frequency, first, the resonance frequency of the coil in the air is measured, and the inductance value of the coil is measured at low frequency, then the parasitic capacitance value is obtained through the following formula: After measuring the measurement impedance value at the corresponding film thickness and different frequencies, such as formula 2 and formula 3, the parallel capacitance value, frequency, measurement real part and imaginary part value are known at a certain frequency, at this time, two fitting output parameters R and L, i.e., the actual value of the coil impedance, are obtained. In the fitting process, a differential evolution algorithm is used for fitting.
9. The method of claim 8, wherein: The specific steps of the differential evolution algorithm are as follows: x i,0 = (R i,0 , L i,0 ) Equation 13; R i,0 and L i,0 are the resistance and inductance values of the i-th individual in the initial population, generated by random initialization: R i,0 = R min + rand(0, 1) · (R max - R min ) Equation 14; L i,0 = L min + rand(0, 1) - (L max - L min ) Equation 15; where R min and R max are the lower and upper bounds of the resistance, L min and L max are the lower and upper bounds of the inductance, and rand(0, 1) is a uniform random number between [0, 1]; The mutation operation is to amplify the difference of individuals and generate new individuals; for each individual x i,G = (R i,G , L i,G ), three different individuals x r1,G = (R r1,G , L r1,G ), x r2,G , x r3,G are randomly selected from the population, and a new mutation vector v i,G is generated: v i,G = (R v,i,G , L v,i,G ) = (R r1,G , L r1,G ) + F · ((R r2,G , L r2,G ) - (R r3,G , L r3,G )) Equation 16; Where F is the scaling factor, which controls the amplitude of variation; The vector generated by the mutation operation is crossed with the current individual; for each individual x i,G = (R i,G ; L i,G ), a new trial vector u i,G = (R u,i,G , L u,i,G ) is generated: L u,i,G is generated similarly to R u,i,G ; the cross probability C r determines the proportion of parameters inherited from the mutation vector, and j is a random index that ensures at least one component is chosen from the mutation vector. In the selection step for deciding whether to use the trial vector u i,G Instead of the original individual x i,G Into the next generation; according to the fitness function value, i.e. the objective function value, the algorithm is optimized through multiple iterations until the termination condition is met, such as reaching the maximum number of iterations or meeting the convergence condition; set the error function as the difference between the actual impedance measurement value and the impedance value obtained by the fitting model, i.e. formula 2, formula 3, as shown in the following formula 18, formula 19, the objective function is the sum of the squares of the real part error and the imaginary part error as shown in formula 20, and the relative error of the objective function value is set to 10 -6 When the fitting is stopped; error_real=Z_measured.real-real(Z) Formula 18; error_imag=Z_measured.imag-imag(Z) Formula 19; error_sum=error_real^2+error_imag^2 Formula 20.
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