An optimized method for measuring the thickness of a metal film

Abstract

The application discloses an optimization method for measuring metal film thickness, comprising the following steps: creating a measurement model among input power, metal film thickness and process time; obtaining a first limit resistivity of the metal film according to vacuum coating theory; obtaining a corresponding relationship among the first limit resistivity, metal film material resistivity and metal film thickness; inputting the corresponding relationship and the first limit resistivity into the measurement model, converting the measurement model into an intermediate model; linearly fitting the metal film sheet resistance and the input power, obtaining parameters of the intermediate model, calibrating parameters of the measurement model by using the parameters of the intermediate model, and calculating the metal film thickness by using the calibrated measurement model. The application calibrates the parameters of the measurement model, guarantees the accuracy of the measurement model, calculates the metal film thickness by using the calibrated measurement model only by knowing the process time and the input power, omits the measurement of the metal film thickness, and greatly reduces the cost and improves the efficiency.

Description

Technical Field

[0001] This invention relates to the field of metal film thickness measurement technology, and in particular to an optimized method for measuring the thickness of metal films. Background Technology

[0002] In the manufacturing process of semiconductor integrated circuits, metal film growth processes are commonly used to form conductive metal interconnects on silicon wafers or substrates. The formation of metal interconnects generally includes metal film growth and metal film removal processes. Examples include physical vapor deposition (PVD) technology for titanium-platinum electrodes and the corresponding metal lift-off process. Measuring the thickness of the metal film becomes crucial during the formation of metal interconnects.

[0003] Currently, the industry uses the following methods to measure the thickness of metal films: contact-type four-point probe contact metal film thickness measurement method and probe-type profilometer step film thickness measurement method, eddy current non-contact metal film thickness measurement method and acoustic wave metal film thickness measurement method.

[0004] The four-point probe contact method for measuring metal film thickness requires knowledge of the resistivity of the thin metal film under a specific process to calculate the film thickness. However, the resistivity of the thin metal film is highly correlated with the process, leading to inaccuracies in the film thickness calculation. Using a probe-type profilometer to measure film thickness steps is susceptible to the effects of step burrs and film warping when measuring thicknesses at the hundred-nanometer level, often resulting in measurement deviations and inconsistencies exceeding 10%. Eddy current non-contact metal film thickness measurement offers lower accuracy for thin film layers. While acoustic wave metal film thickness measurement is mature and widely used in the industry, it presents significant technical barriers and requires sophisticated measuring instruments.

[0005] In addition, when using a probe-type profilometer to measure the thickness of stepped metal films, the measurement error is large when the metal film thickness is small (e.g., less than 1 micrometer), which cannot meet the market demand for metal film thickness measurement.

[0006] Therefore, overcoming the shortcomings of the existing technology is an urgent problem to be solved in this technical field. Summary of the Invention

[0007] The technical problem to be solved by the present invention is how to solve the problems of large error and poor consistency in the measurement of stepped metal film thickness using a probe-type profilometer when the metal film thickness is relatively small, and the measurement deviation caused by the lack of specific process thin metal film resistivity when using a four-probe tester to calculate the film thickness using the resistance method.

[0008] This invention provides an optimized method for measuring the thickness of a metal film, comprising:

[0009] Under preset process conditions, a measurement model is created to relate input power, metal film thickness, and process time.

[0010] Based on the vacuum deposition theory, the first limiting resistivity of the metal film is obtained.

[0011] Based on the electrical properties of the metal film, the corresponding relationship between the first limiting resistivity, the resistivity of the metal film material, and the thickness of the metal film is obtained.

[0012] The corresponding relationship and the first limiting resistivity are input into the measurement model, and the measurement model is converted into an intermediate model of sheet resistance of metal film and input power; wherein the parameters in the intermediate model are related to the parameters in the measurement model.

[0013] Linear fitting is performed on the sheet resistance of the metal film and the input power to obtain the parameters of the intermediate model. The parameters of the intermediate model are then used to calibrate the parameters of the measurement model, and the metal film thickness is calculated using the calibrated measurement model.

[0014] Preferably, obtaining the first limiting resistivity of the metal film based on vacuum deposition theory specifically includes:

[0015] Preparation of metal films;

[0016] When the thickness of the metal film is measured to be within the preset thickness range, the sheet resistance and thickness of the metal film are measured, and the first limiting resistivity of the metal film is calculated by defining the sheet resistance of the metal film.

[0017] Preferably, when the metal film thickness is measured to be within a preset thickness range, measuring the sheet resistance and resistivity of the metal film specifically includes:

[0018] Obtain the upper and lower limits of the thickness within the preset thickness range;

[0019] Obtain the difference between the upper and lower thickness limits, and divide the difference into equal parts according to a preset number to obtain the thickness gradient value of each metal film.

[0020] When the measured thickness of the metal film is equal to the corresponding gradient value of the metal film thickness, the sheet resistance of the metal film is measured, and the first limiting resistivity of each gradient value is calculated.

[0021] After the first limiting resistivity corresponding to all metal film thickness gradient values ​​has been calculated, the first limiting resistivity with the smallest value among all metal film thickness gradient values ​​is selected as the final first limiting resistivity of the metal film.

[0022] Preferably, the formula corresponding to the measurement model is:

[0023] v = h / t = kP - c

[0024] Where v represents the metal film formation rate, h represents the metal film thickness, t represents the process time, P represents the input power, and k and c represent the slope and intercept of the formula, respectively, with both k and c being constants.

[0025] Preferably, the correspondence is as follows:

[0026]

[0027] Where p represents the electron mirror reflection coefficient, L represents the electron mean free path, and A is a conversion parameter. d represents the proportionality coefficient, which is a constant; F represents the first limiting resistivity of the metal film, which is a constant; ρ represents the resistivity of the metal film; and h represents the thickness of the metal film.

[0028] Preferably, the intermediate model is:

[0029]

[0030] Where F represents the first limiting resistivity of the metal film, t represents the process time, k represents the slope of the formula corresponding to the measurement model, c represents the intercept of the formula corresponding to the measurement model, d represents the proportionality coefficient in the corresponding relationship, and d is a constant. a and b represent the parameters of the intermediate model.

[0031] Preferably, after obtaining the correspondence between the first limiting resistivity, the resistivity of the metal film, and the thickness of the metal film, the method further includes verifying the obtained first limiting resistivity using the correspondence, specifically including:

[0032] By fitting the metal film thickness and resistivity using the aforementioned correspondence, the second limiting resistivity of the metal film is obtained;

[0033] Compare the first limiting resistivity with the second limiting resistivity;

[0034] If the first limiting resistivity and the second resistivity are outside the preset error allowable range, the verification fails, and the metal film is re-prepared and the first limiting resistivity of the metal film is measured.

[0035] The verification is successful when the first limiting resistivity is close to the second limiting resistivity and is within the allowable error range.

[0036] Preferably, after calibrating the parameters of the measurement model using the parameters of the intermediate model, the method further includes verifying the calibrated parameters of the measurement model, specifically including:

[0037] When the first limiting resistivity is close to the second limiting resistivity and is within the allowable error range, the corresponding reference coefficient is calculated using the second limiting resistivity, and the calculated reference coefficient is compared with the calibration value of the measurement model.

[0038] If the calculated reference coefficients are close to the calibration values ​​and within the allowable error range, it indicates that the calibrated parameters are reasonable.

[0039] If the calculated reference coefficient is close to the calibration value but outside the allowable error range, it indicates that the calibrated parameters are unreasonable, and the measurement model should be recalibrated.

[0040] Preferably, after verifying the parameters of the calibrated measurement model, the method further includes adjusting the parameters of the calibrated measurement model, specifically including:

[0041] Select the input power range of the metal film, and divide the input power range equally according to the preset power gradient value to obtain the first input power value, the second input power value, ..., the nth input power value, where the difference between adjacent input power values ​​is the preset power gradient value, n≥2, and is an integer;

[0042] Set the metal film formation process time and set the input power to the first input power value. Obtain m sets of step samples with respect to the first input power value, where m ≥ 2 and is an integer.

[0043] Set the input power to the second input power value and obtain m sets of step samples related to the second input power value;

[0044] Following a recursive approach, until the input power is set to the nth input power value, m sets of step samples are obtained for the nth input power value.

[0045] The thickness of the metal film in each step sample was measured, and the film formation rate in each step sample was calculated.

[0046] Take one data point from each of the step samples corresponding to the first input power value, the second input power value, ..., the nth input power value as a group, obtain m groups of data, and use the formula of the measurement model to fit and calculate the parameters corresponding to each group of data;

[0047] The parameters corresponding to each set of data are compared with the calibration values ​​to find the parameters that are closest to the calibration values, and the parameters of the measurement model are adjusted using the parameters.

[0048] Preferably, the step of finding the parameter closest to the calibration value and using the parameter to adjust the parameters of the calibrated measurement model specifically includes:

[0049] If the parameter closest to the calibration value is within the allowable error range, then the parameter is used to adjust the parameters of the calibrated measurement model.

[0050] If the parameter closest to the calibration value is not within the allowable error range, the step sample is remade until the parameter closest to the calibration value is within the allowable error range.

[0051] This invention utilizes vacuum deposition theory and the electrical properties of metal films to transform a measurement model for metal film thickness, which suffers from large measurement errors, into an intermediate model based on the sheet resistance of the metal film, which has smaller measurement errors, and the formula for calculating the limiting resistivity of the metal, both with relatively small calculation errors. The parameters in the intermediate model are related to those in the measurement model. By linearly fitting the sheet resistance of the metal film to the input power, the parameters of the intermediate model are obtained. These parameters are then used to calibrate the parameters of the measurement model, and the metal film thickness is calculated using the calibrated measurement model. This invention, by calibrating the parameters of the measurement model, ensures the accuracy of the measurement model. Knowing only the process time and input power, the metal film thickness can be calculated using the calibrated measurement model, eliminating the need for metal film thickness measurement, significantly reducing costs and improving efficiency. 。 Attached Figure Description

[0052] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0053] Figure 1 This is a flowchart of an optimized method for measuring the thickness of a metal film provided in an embodiment of the present invention;

[0054] Figure 2 It is a function of input power and metal film formation rate for different metal materials in an optimized method for measuring metal film thickness provided in an embodiment of the present invention;

[0055] Figure 3 This is a flowchart of a method for obtaining the first limiting resistivity within an optimized method for measuring the thickness of a metal film provided in an embodiment of the present invention.

[0056] Figure 4 This is a detailed flowchart of step 302 within an optimized method for measuring the thickness of a metal film provided in an embodiment of the present invention.

[0057] Figure 5This is a flowchart of a method for verifying the obtained first limiting resistivity using the aforementioned correspondence within an optimized method for measuring the thickness of a metal film provided in an embodiment of the present invention.

[0058] Figure 6 This is a flowchart of a method for verifying the parameters of a calibrated measurement model within an optimized method for measuring the thickness of a metal film provided in an embodiment of the present invention.

[0059] Figure 7 This is a flowchart of a method for adjusting parameters after calibration of a measurement model, which is part of an optimized method for measuring the thickness of a metal film provided in an embodiment of the present invention.

[0060] Figure 8 This is a data recording table of input power and film formation rate for 5 sets of stepped sample pieces provided in this embodiment of the invention;

[0061] Figure 9 This is a graph of the input power and film formation rate function corresponding to the data recording table of input power and film formation rate of 5 sets of stepped samples provided in the embodiments of the present invention;

[0062] Figure 10 This is a data recording table of fitting the sheet resistance and input power of 5 sets of stepped samples provided in this embodiment of the invention;

[0063] Figure 11 The data record table showing the fitting of sheet resistance and input power for the five sets of stepped samples provided in this embodiment of the invention corresponds to the function graph of input power and sheet resistance.

[0064] Figure 12 This is a data table of resistivity corresponding to different metal film thicknesses provided in the embodiments of the present invention. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0066] In the description of this invention, the terms "inner", "outer", "longitudinal", "lateral", "upper", "lower", "top", "bottom", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and do not require that this invention must be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0067] In this invention, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this application, unless otherwise stated, "a plurality of" means two or more.

[0068] In this application, unless otherwise expressly specified and limited, the term "connection" should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral part; it can be a direct connection or an indirect connection through an intermediate medium. Furthermore, the term "coupled" can refer to an electrical connection that enables signal transmission.

[0069] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0070] Example 1:

[0071] Embodiment 1 of the present invention provides an optimized method for measuring the thickness of a metal film, such as... Figure 1 As shown, it includes:

[0072] Step 201: Under preset process conditions, create a measurement model between input power, metal film thickness and process time.

[0073] In the metal film formation process, the process conditions need to be maintained within a suitable range, i.e., reasonable process conditions. Exceeding this suitable range can easily cause the metal film to blacken, leading to film formation failure; conversely, falling below the suitable range can prevent film formation altogether. The preset process conditions in this embodiment represent the suitable range for metal film formation. For different metal materials, the suitable range for film formation varies. The suitable range for metal film formation can be obtained experimentally by gradually increasing the input power and observing the shape, color, and electrical properties of the formed metal film to determine its suitability. Obtaining the preset process conditions for metal film formation is prior art and will not be elaborated upon here. Furthermore, the input power in this embodiment is typically DC.

[0074] In this embodiment of the invention, using an MS200-1 / EXW type metal thin film growth PVD equipment, during the magnetron sputtering deposition of metals with different power and process times, it was found that under preset process conditions, there is a linear relationship between the input power and the metal film deposition rate. Based on this, a measurement model is constructed between input power, metal film thickness, and process time. The formula corresponding to the measurement model is:

[0075] v = kP - c

[0076] Where v represents the metal film formation rate, h represents the metal film thickness, t represents the process time, P represents the input power, and k and c represent the slope and intercept of the formula, respectively, with both k and c being constants.

[0077] In the formula of the above measurement model, k and c are empirical constants. k describes the ease with which different metal materials can form films, and c measures the activation energy of the sputtering process in the metal. Figure 2 As shown, this represents the function of input power and metal film formation rate for different metal materials.

[0078] In the metal film deposition process, the metal film first grows on the substrate. After reaching a certain size, the metal film continues to grow across the substrate. During this process, since the substrate is usually made of silicon or silicon oxide, which are non-metallic materials, the rate of metal deposition on the substrate is different from the rate of deposition after the metal crosses the substrate. Furthermore, the deposition rate of the metal film remains essentially constant under the same process conditions after the diffusion stage across the substrate surface. Therefore, the formula corresponding to the above measurement model can be written as:

[0079] h / t=kP-c

[0080] Where h represents the thickness of the metal film and t represents the processing time.

[0081] To directly calculate the film thickness of metal films under different input powers and process times using a measurement model, the parameters k and c must first be calibrated. During calibration, precise knowledge of the input power, process time, and metal film thickness is required, followed by linear fitting to calibrate parameters k and c. However, current measurements of the metal film thickness in the above formula are based on the average value obtained after removing extreme values ​​from a large amount of probe-type profilometer step film thickness data. The biggest problem with using probe-type profilometers to measure film thickness is that the step film thickness data itself contains errors, leading to a lack of accuracy in the values ​​of parameters k and c in the formula fitting of the measurement model, and a lack of standards for measuring the accuracy of parameters k and c. Based on the above description, after calibrating parameters k and c in the measurement model using existing technology, inaccurate measurement of the metal film thickness (h) during the calibration process leads to inaccurate calibration of the parameters corresponding to the formula in the measurement model. Therefore, using the measurement model calibrated with existing technology to calculate the metal film thickness results in inaccurate measurements, especially for metal film thicknesses below 1 micrometer.

[0082] Step 202: Based on the vacuum deposition theory, obtain the first limiting resistivity of the metal film.

[0083] According to vacuum deposition theory, the resistivity of magnetron sputtering coatings gradually approaches a constant after the film thickness exceeds 2000 nm. This constant is called the limiting resistivity, and its value is related to the material properties and the process. The limiting resistivity typically differs for different metals, but for the same metal, it can be considered the same under identical process conditions. Based on vacuum deposition theory, the first limiting resistivity of a metal film can be calculated using the definition of sheet resistance (thin film sheet resistance). The specific definition of sheet resistance is as follows:

[0084]

[0085] Where ρ is the resistivity of the metal film, R is the sheet resistance of the metal film material, and h is the thickness of the metal film.

[0086] Since the metal film thickness corresponding to the first limiting resistivity in this embodiment of the invention exceeds 2000 nm, the error caused by measuring the metal film thickness using a probe profilometer can be ignored (i.e., the metal film thickness measured using a probe profilometer is considered accurate in obtaining the first limiting resistivity of the metal film). The metal film thickness is measured, and then the sheet resistance of the metal film at this point is measured using a four-probe tester. The first limiting resistivity of the metal film at this point is calculated using the above formula. It is worth noting that, for ease of understanding, ρ in this embodiment of the invention represents the metal film resistivity, while the first limiting resistivity is actually the metal film resistivity after the metal film thickness exceeds 2000 nm, and the first limiting resistivity is a constant value; for ease of distinction, this embodiment of the invention uses F to represent the first limiting resistivity.

[0087] Step 203: Based on the electrical properties of the metal film, obtain the corresponding relationship between the first limiting resistivity, the resistivity of the metal film material, and the thickness of the metal film.

[0088] Theoretically, after the metal film is formed in the embodiments of the present invention, the metal film layers should be closely packed. Therefore, the relationship between the first limiting resistivity F and the resistivity of the metal film can be obtained through the electrical properties of the metal thin film:

[0089]

[0090] Where p represents the electron mirror reflection coefficient, L represents the electron mean free path (MBPS), since the MBPS of bulk materials remains constant at the same temperature, and the electron mirror reflection coefficient can be adjusted to keep the surface smoothness of the film constant; A is a conversion parameter. d represents the proportionality coefficient, which is a constant; F represents the first limiting resistivity of the metal film, which is a constant; ρ represents the resistivity of the metal film; and h represents the thickness of the metal film.

[0091] Step 204: Input the correspondence and the first limiting resistivity into the measurement model, and convert the measurement model into an intermediate model of sheet resistance of metal film and input power; wherein the parameters in the intermediate model are related to the parameters in the measurement model.

[0092] The first limiting resistivity and its corresponding relationship are input into the measurement model. Based on the definition of sheet resistance of a metal film, the scalar value of the metal film thickness h is eliminated from the measurement model, transforming it into an intermediate model of sheet resistance and input power. This intermediate model is:

[0093]

[0094] Where F represents the first limiting resistivity of the metal film, t represents the process time, k represents the slope of the formula corresponding to the measurement model, c represents the intercept of the formula corresponding to the measurement model, d represents the proportionality coefficient in the corresponding relationship, and d is a constant. a and b represent the parameters of the intermediate model.

[0095] In this embodiment of the invention, the parameters of the intermediate model are: From the expressions for parameters a and b, it can be seen that the parameters of the intermediate model are related to the parameters of the measurement model.

[0096] Step 205: Perform linear fitting between the sheet resistance of the metal film and the input power to obtain the parameters of the intermediate model, calibrate the parameters of the measurement model using the parameters of the intermediate model, and calculate the thickness of the metal film using the calibrated measurement model.

[0097] The intermediate model formula was fitted using sheet resistance data from a large number of metal coating processes with the same process time but different input power to obtain the specific values ​​of 'a' and 'b' in the intermediate model formula. Given the first limiting resistivity of the metal film, the process time, and the specific value of 'a', based on... The k value within the measurement model is calculated to complete the calibration of the measurement model parameter k. Then, this coefficient is used as a measure of the accuracy of the fitting of the input power and the metal film formation rate function. Among all the fitting functions within the range of the measured thickness h ± Δh (Δh is the maximum measurement error of the step thickness of the probe profilometer), the fitting function with the constant k value closest to the reference coefficient k' is the best fitting function. Then, the metal film thickness h and resistivity ρ can be obtained.

[0098] To illustrate the complete solution of the embodiments of the present invention, the details of the embodiments of the present invention will be described in detail below. The embodiments of the present invention obtain the first limiting resistivity of the metal film based on vacuum deposition theory, such as... Figure 3 As shown, it specifically includes:

[0099] Step 301: Prepare a metal film.

[0100] This invention uses the definition of sheet resistance of a metal film to calculate the first limiting resistivity. Based on this, in actual acquisition, it is necessary to fabricate a metal film with a thickness exceeding 2000 nm. Fabricating metal films with a thickness exceeding 2000 nm is prior art and will not be elaborated upon here.

[0101] Step 302: When the thickness of the metal film is measured to be within the preset thickness range, the sheet resistance and thickness of the metal film are measured, and the first limiting resistivity of the metal film is calculated by defining the sheet resistance of the metal film.

[0102] The preset thickness range in this embodiment of the invention represents a metal film with a thickness exceeding 2000 nm. The metal film thickness is measured using a probe-type profilometer. When the thickness of the prepared metal film exceeds 2000 nm, the sheet resistance of the metal film is measured using a four-probe tester to obtain the sheet resistance R. The first limiting resistivity is calculated using the measured sheet resistance and the metal film thickness. It is worth noting that the use of a four-probe tester to measure the sheet resistance of the metal film in this embodiment of the invention is prior art and will not be elaborated upon here.

[0103] To avoid errors in the first limiting resistivity measurement process of this embodiment of the invention, when the measured thickness of the metal film is within a preset thickness range, the sheet resistance and resistivity of the metal film are measured. Figure 4 As shown, it specifically includes:

[0104] Step 401: Obtain the upper and lower limits of the thickness within the preset thickness range.

[0105] This invention calculates the first limiting resistivity by measuring the metal film thickness and sheet resistance. To avoid errors in measurement and calculation that could lead to inaccurate or large errors in the calculation of the first limiting resistivity, this invention calculates multiple values ​​of the first limiting resistivity by measuring the metal film thickness and sheet resistance multiple times, then removes the extreme values, and finally determines the value of the first limiting resistivity by taking the average value.

[0106] In obtaining the first limiting resistivity, this embodiment of the invention requires that the metal film thickness exceed 2000 nm. Therefore, the preset range in this embodiment can be, but is not limited to, set to 2.5 μm ± 500 nm, and the upper and lower limits of the preset thickness range are obtained. It is worth noting that the lower limit in this embodiment is a minimum of 2000 nm, and the upper limit is set according to actual conditions; for example, it can be, but is not limited to, set to 3000 nm.

[0107] Step 402: Obtain the difference between the upper and lower thickness limits, and divide the difference into equal parts according to a preset number to obtain the thickness gradient value of each metal film.

[0108] After obtaining the upper and lower thickness limits, the difference between the upper and lower thickness limits is obtained and divided equally to obtain the thickness gradient value of each metal film. For ease of understanding, a specific example is given below. For instance, the upper thickness limit is 3000 nm, the lower thickness limit is 2000 nm, and the difference between them is 1000 nm. This 1000 nm is divided into four equal parts, with each part spaced 250 nm apart. Therefore, all thickness gradient values ​​of the metal film are 2000 nm, 2250 nm, 2500 nm, 2750 nm, and 3000 nm. In this embodiment of the invention, the number of equal parts for dividing the upper and lower thickness limits is set according to actual conditions. For example, the difference of 1000 nm can be divided into four equal parts.

[0109] Step 403: When the measured metal film thickness is equal to the corresponding metal film thickness gradient value, measure the sheet resistance of the metal film and calculate the first limiting resistivity for each gradient value.

[0110] In this process, when the measured thickness of the metal film is equal to the set gradient value, the sheet resistance of the metal film is measured, and the first limiting resistivity for each gradient value is calculated. In actual measurement, due to errors in the manufacturing process and the measurement of the metal film thickness, a metal film with a thickness close to the gradient value is usually fabricated for the experiment. By measuring the actual thickness of the metal film and its sheet resistance, the value of the first limiting resistivity is calculated.

[0111] Step 404: After the first limiting resistivity corresponding to all metal film thickness gradient values ​​has been calculated, select the smallest first limiting resistivity among all metal film thickness gradient values ​​as the final first limiting resistivity of the metal film.

[0112] Among them, the formula relating the first limiting resistivity, the resistivity of the metal film, and the thickness of the metal film. It is known that the larger the value of h, the smaller ρ is. Theoretically, when h is "∞", ρ is at its minimum, which is the theoretical first limiting resistivity. Therefore, in this embodiment of the invention, the first limiting resistivity with the smallest thickness gradient among all metal film values ​​is selected as the final first limiting resistivity of the metal film.

[0113] After obtaining the correspondence between the first limiting resistivity, the resistivity of the metal film, and the thickness of the metal film, the method further includes using the correspondence to verify the obtained first limiting resistivity, such as... Figure 5 As shown, it specifically includes:

[0114] Step 501: Fit the metal film thickness and resistivity using the aforementioned correspondence to obtain the second limiting resistivity of the metal film; compare the first limiting resistivity with the second limiting resistivity.

[0115] In this embodiment of the invention, after obtaining the first limiting resistivity, it is necessary to verify the first limiting resistivity. This is achieved using the corresponding relationship. By fitting the metal film thickness h to the resistivity ρ, the second limiting resistivity of the metal film is obtained. It is worth noting that the resistivity ρ within this relationship can be derived from the definition of sheet resistance of a thin film. The calculation yielded the second limiting resistivity. Multiple metal film samples were fabricated, and their sheet resistance and film thickness were measured. The second limiting resistivity was then calculated through fitting. It is worth noting that the calculation of the second limiting resistivity in this embodiment of the invention actually involves the metal film deposition process. The second limiting resistivity is treated as a constant for fitting, and the final value of the second limiting resistivity is calculated. In obtaining the second limiting resistivity in this embodiment of the invention, the metal film thickness needs to be measured. At this time, the metal film thickness is not required to exceed 2000 nm. Measuring the metal film thickness introduces a large error, which affects the accuracy of the second limiting resistivity. Therefore, the second limiting resistivity in this embodiment of the invention can only be used to verify whether the first limiting resistivity is within the allowable error range.

[0116] Step 502: If the first limiting resistivity and the second resistivity are outside the preset error allowable range, the verification fails, and the metal film is re-prepared and the first limiting resistivity of the metal film is measured; if the first limiting resistivity and the second limiting resistivity are close and within the error allowable range, the verification passes.

[0117] By comparing the values ​​of the first limiting resistivity and the second resistivity, the error between the two can be indirectly determined. The magnitude of the error indicates whether the first limiting resistivity is accurate. The allowable error range in this embodiment can be set according to actual conditions; for example, but not limited to, the allowable error range can be set to 5%.

[0118] In practice, this invention typically involves first calibrating the parameter k within the measurement model, then substituting the calibrated k value into the measurement model, and further calibrating the c value using the calibrated k value to obtain the calibrated measurement model. Finally, the metal film thickness is calculated based on the calibrated measurement model. In this process, after calibrating the measurement model parameters using the intermediate model parameters as described in this invention, the calibrated parameters of the measurement model are also verified, such as... Figure 6 As shown, it specifically includes:

[0119] Step 601: When the first limiting resistivity is close to the second limiting resistivity and within the allowable error range, calculate the corresponding reference coefficient using the second limiting resistivity, and compare the calculated reference coefficient with the calibration value of the measurement model.

[0120] Among them, after verifying the accuracy of the first limiting resistivity through the second limiting resistivity, the second limiting resistivity is input to... Within this process, the corresponding reference coefficients are calculated. These reference coefficients are based on the second limiting resistivity. The calculated reference coefficients are then compared with the aforementioned reference coefficients based on the first limiting resistivity (corresponding to the calibration values ​​of the measurement model).

[0121] Step 602: If the calculated reference coefficient is close to the calibration value and within the allowable error range, it indicates that the calibrated parameters are reasonable; if the calculated reference coefficient is close to the calibration value but outside the allowable error range, it indicates that the calibrated parameters are unreasonable, and the measurement model should be recalibrated.

[0122] If the error between the reference coefficient calculated using the second limiting resistivity and the calibration value of the measurement model is within the allowable range, it indicates that the calibrated parameters are reasonable; otherwise, they are unreasonable and the measurement model needs to be recalibrated. It is worth noting that the allowable error range in this embodiment of the invention is set according to the actual situation; for example, the allowable error range can be, but is not limited to, set to 5%.

[0123] To make the calibrated measurement model of this invention more applicable to actual situations, after verifying the calibrated parameters of the measurement model as described in this embodiment, the invention also includes adjusting the calibrated parameters of the measurement model, such as... Figure 7 As shown, it specifically includes:

[0124] Step 701: Select the input power range of the metal film, and divide the input power range equally according to the preset power gradient value to obtain the first input power value, the second input power value, ..., the nth input power value, where the difference between adjacent input power values ​​is the preset power gradient value, n≥2, and is an integer.

[0125] The input power range in this embodiment of the invention needs to meet preset process conditions (see the explanation in step 201). Then, based on the input power range, the upper and lower limits of the power range are obtained, and then divided equally to obtain the corresponding first input power value, second input power value, ..., nth input power value. The process of dividing the input power range equally and obtaining the corresponding first input power value, second input power value, ..., nth input power value is the same as the method of obtaining the thickness gradient value of each metal film in step 402, and will not be described again here.

[0126] Step 702: Set the metal film formation process time and set the input power to the first input power value. Obtain m sets of step samples with respect to the first input power value, where m ≥ 2 and is an integer. Set the input power to the second input power value and obtain m sets of step samples with respect to the second input power value. Repeat this process until the input power is set to the nth input power value and m sets of step samples with respect to the nth input power value.

[0127] To facilitate understanding, specific examples will be used to illustrate steps 701-702 of the embodiment of the present invention. Assuming the value of n is 3, corresponding to the first input power value, the second input power value, and the third input power, and the value of m is assumed to be 4, then under the first input power value condition, 4 metal film step samples will be prepared; under the second input power value condition, 4 metal film step samples will be prepared; and under the third input power value condition, 4 metal film step samples will be prepared. A total of n×m=3×4=12 step samples need to be prepared.

[0128] Step 703: Measure the metal film thickness of each step sample and calculate the film formation rate within each step sample.

[0129] In this embodiment of the invention, each step sample of the metal film is prepared as an independent process, and continuous measurements cannot be performed based on a single step sample. The thickness of the metal film on the prepared step sample is measured using a probe profilometer, and then the film formation rate within each step sample is calculated using the known process time.

[0130] Step 704: Take one data point from each of the step samples corresponding to the first input power value, the second input power value, ..., the nth input power value as a group, obtain m groups of data, and use the formula of the measurement model to fit and calculate the parameters corresponding to each group of data.

[0131] For ease of understanding, this embodiment of the invention will use the example from step 702 to illustrate step 704. Assume the value of n is 3, the value of m is assumed to be 4, and the thicknesses of the four metal films prepared under the first input power condition are h, respectively. 1A h 1B h 1C and h 1D Under the second input power condition, the thicknesses of the four metal films measured were h, respectively. 2A h 2B h 2C and h 2D Under the third input power condition, the thicknesses of the four metal films measured were h respectively. 3A h 3B h 3C and h 36DThis is achieved by taking one data point from each of the first, second, and third input power values ​​as a group. For example, let the metal film thickness be h. 1B h 2A and h 3D As a group, data is selected sequentially, randomly paired within the three groups, and finally, m groups of data are obtained for fitting to calculate the parameters corresponding to each group of data. In addition, embodiments of the present invention can also calculate the parameters corresponding to the curve function by plotting the rate value of the metal film thickness and the input power using a line graph method (the measurement model is a linear relationship, and the calculated parameters are the slope and intercept of the measurement model relationship).

[0132] Step 705: Compare the parameters corresponding to each set of data with the calibration values, find the parameters that are closest to the calibration values, and use the parameters to adjust the parameters of the measurement model after calibration.

[0133] When comparing the parameters corresponding to each set of data with the calibration values, the parameter closest to the calibration value is found, and the parameters of the calibrated measurement model are adjusted using this parameter. If the parameter closest to the calibration value is within the allowable error range, the parameters of the calibrated measurement model are adjusted using this parameter; if the parameter closest to the calibration value is not within the allowable error range, the step sample is remade until the parameter closest to the calibration value is within the allowable error range.

[0134] This invention utilizes vacuum deposition theory and the electrical properties of metal films to transform a measurement model for metal film thickness, which suffers from large measurement errors, into an intermediate model based on the sheet resistance of the metal film, which has smaller measurement errors, and the formula for calculating the limiting resistivity of the metal, which also has smaller calculation errors. The parameters in the intermediate model are related to those in the measurement model. By linearly fitting the sheet resistance of the metal film to the input power, the parameters of the intermediate model are obtained. These parameters are then used to calibrate the parameters of the measurement model, and the metal film thickness is calculated using the calibrated measurement model. This invention, by calibrating the parameters of the measurement model, ensures the accuracy of the measurement model. Knowing only the process time and input power, the metal film thickness can be calculated using the calibrated measurement model, eliminating the need for metal film thickness measurement, significantly reducing costs and improving efficiency. 。

[0135] Example 2:

[0136] Embodiment 2 of this invention verifies the measurement model of Embodiment 1 using a specific example. Platinum, a metal with relatively stable film properties (thin film resistivity and thickness change little with external factors such as temperature and pressure), was selected for parameter calibration verification. A 200nm silicon oxide substrate was set as the substrate, and a 1200-second process with different powers ranging from 70W to 130W was used to fit the power-film deposition rate function and the power-sheet resistance function.

[0137] Five sets of stepped samples were prepared. The thickness of the metal film on each sample was measured using a probe profilometer. The formula of the measurement model was then fitted, and the corresponding data table and function graph are shown below. Figures 8-9 As shown.

[0138] For five sets of stepped samples, the sheet resistance of the sample was measured using a four-probe tester. A function fitting was then performed using the sheet resistance and input power. The data were recorded as follows: Figure 10 As shown, the graph of the function is as follows: Figure 11 As shown.

[0139] To obtain the theoretical resistivity of the material under this process, a thicker film was subsequently prepared by long-term deposition with the same power for film thickness and sheet resistance measurement. Within the film thickness range of 2.5 μm ± 500 nm, the resistivity of the platinum film remained basically stable between 15.56 and 15.68 μΩ·cm, with no significant change in resistivity. Therefore, the resistivity of the film material under this process can be approximated as the minimum value of all measured values, 15.56 μΩ·cm. Substituting this value into equation (5), the reference coefficient k' is obtained as 0.03010506. Compared with the constant of group AE, group C is the closest. Therefore, the theoretical optimal power-film formation rate function of the platinum film under this process condition is: v = 0.0298P - 0.3928.

[0140] Since the theoretical limiting resistance of the film material used above is only a reference value for relatively thick films, it needs to be verified. The formula h / t=kP-c of the measurement model is compared with the definition of sheet resistance of metal films. By combining the equations and substituting the parameters from group C, with a time of 1200s, the resistivity corresponding to different film thicknesses can be obtained as follows: Figure 12 As shown. Simultaneously, a variation of equation (4) is performed:

[0141]

[0142] The film thickness limiting resistivity parameter F' can be obtained by fitting the obtained relationship between film thickness and resistivity. This value is close to the minimum resistivity of 15.56 μΩ·cm within the previously selected film thickness range of 2.5 μm ± 500 nm. Substituting F' into equation (5), the reference coefficient k” is 0.0296808910570587. The obtained screening results are similar to those above, and the results are verified.

[0143] Embodiment 2 of the present invention verifies the measurement model after parameter calibration in Embodiment 1 through a specific example, so as to prove the accuracy of the measurement model after parameter calibration in Embodiment 1 of the present invention.

[0144] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An optimized method for measuring the thickness of a metal film, characterized in that, include: Under preset process conditions, a measurement model is created to relate input power, metal film thickness, and process time. Based on the vacuum deposition theory, the first limiting resistivity of the metal film is obtained. The method for obtaining the first limiting resistivity of a metal film based on vacuum deposition theory includes: preparing a metal film; when the metal film thickness is measured to be within a preset thickness range, measuring the sheet resistance and thickness of the metal film, and calculating the first limiting resistivity of the metal film using the definition of sheet resistance; specifically, measuring the sheet resistance and resistivity of the metal film when the metal film thickness is measured to be within a preset thickness range includes: obtaining an upper and lower thickness limit within the preset thickness range; obtaining the difference between the upper and lower thickness limits, and dividing the difference equally according to a preset number to obtain each metal film thickness gradient value; when the metal film thickness is equal to the corresponding metal film thickness gradient value, measuring the sheet resistance of the metal film, and calculating the first limiting resistivity for each gradient value; after calculating the first limiting resistivity for all metal film thickness gradient values, selecting the smallest first limiting resistivity among all metal film thickness gradient values ​​as the final first limiting resistivity of the metal film. Based on the electrical properties of the metal film, the corresponding relationship between the first limiting resistivity, the resistivity of the metal film material, and the thickness of the metal film is obtained. The corresponding relationship and the first limiting resistivity are input into the measurement model, and the measurement model is converted into an intermediate model of sheet resistance of metal film and input power; wherein the parameters in the intermediate model are related to the parameters in the measurement model. Linear fitting is performed on the sheet resistance of the metal film and the input power to obtain the parameters of the intermediate model. The parameters of the intermediate model are then used to calibrate the parameters of the measurement model, and the metal film thickness is calculated using the calibrated measurement model.

2. The optimized method for measuring the thickness of a metal film according to claim 1, characterized in that, The formula corresponding to the measurement model is: in, Indicates the metal film formation rate. Indicates the thickness of the metal film. Indicates process time. Indicates input power. and These represent the slope and intercept of the formula, respectively. and All are constants.

3. The optimized method for measuring the thickness of a metal film according to claim 2, characterized in that, The correspondence is as follows: in, The electron's mirror reflection coefficient is represented by L, which represents the electron's mean free path. For conversion parameters, , Represents the proportionality coefficient. It is a constant. This represents the first limiting resistivity of the metal film. It is a constant. Represents the resistivity of a metal film. This indicates the thickness of the metal film.

4. The optimized method for measuring the thickness of a metal film according to claim 3, characterized in that, The intermediate model is: in, This represents the first limiting resistivity of the metal film. Indicates process time. This represents the slope of the formula corresponding to the measurement model. This represents the intercept of the formula corresponding to the measurement model. This represents the proportionality coefficient within the corresponding relationship. It is a constant. , , and This represents the parameters of the intermediate model.

5. The optimized method for measuring the thickness of a metal film according to claim 1, characterized in that, After obtaining the correspondence between the first limiting resistivity, the resistivity of the metal film, and the thickness of the metal film, the method further includes verifying the obtained first limiting resistivity using the correspondence, specifically including: By fitting the metal film thickness and resistivity using the aforementioned correspondence, the second limiting resistivity of the metal film is obtained; Compare the first limiting resistivity with the second limiting resistivity; If the first limiting resistivity and the second resistivity are outside the preset error allowable range, the verification fails, and the metal film is re-prepared and the first limiting resistivity of the metal film is measured. The verification is successful when the first limiting resistivity is close to the second limiting resistivity and is within the allowable error range.

6. The optimized method for measuring the thickness of a metal film according to claim 5, characterized in that, After calibrating the parameters of the measurement model using the parameters of the intermediate model, the method further includes verifying the calibrated parameters of the measurement model, specifically including: When the first limiting resistivity is close to the second limiting resistivity and is within the allowable error range, the corresponding reference coefficient is calculated using the second limiting resistivity, and the calculated reference coefficient is compared with the calibration value of the measurement model. If the calculated reference coefficients are close to the calibration values ​​and within the allowable error range, it indicates that the calibrated parameters are reasonable. If the calculated reference coefficient is close to the calibration value but outside the allowable error range, it indicates that the calibrated parameters are unreasonable, and the measurement model should be recalibrated.

7. The optimized method for measuring the thickness of a metal film according to claim 6, characterized in that, After verifying the parameters of the calibrated measurement model, the process further includes adjusting the calibrated parameters, specifically including: Select the input power range of the metal film, and divide the input power range equally according to the preset power gradient value to obtain the first input power value, the second input power value, ..., the nth input power value, where the difference between adjacent input power values ​​is the preset power gradient value, n≥2, and is an integer; Set the metal film formation process time and set the input power to the first input power value. Obtain m sets of step samples with respect to the first input power value, where m ≥ 2 and is an integer. Set the input power to the second input power value and obtain m sets of step samples related to the second input power value; Following a recursive approach, until the input power is set to the nth input power value, m sets of step samples are obtained for the nth input power value; The thickness of the metal film in each step sample was measured, and the film formation rate in each step sample was calculated. Take one data point from each of the step samples corresponding to the first input power value, the second input power value, ..., the nth input power value as a group, obtain m groups of data, and use the formula of the measurement model to fit and calculate the parameters corresponding to each group of data; The parameters corresponding to each set of data are compared with the calibration values ​​to find the parameters that are closest to the calibration values, and the parameters of the measurement model are adjusted using the parameters.

8. The optimized method for measuring the thickness of a metal film according to claim 7, characterized in that, The process of finding the parameter closest to the calibration value and using that parameter to adjust the parameters of the calibrated measurement model specifically includes: If the parameter closest to the calibration value is within the allowable error range, then the parameter is used to adjust the parameters of the calibrated measurement model. If the parameter closest to the calibration value is not within the allowable error range, the step sample is remade until the parameter closest to the calibration value is within the allowable error range.

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