Ultrasonic Bonding Interface Element Diffusion Concentration Prediction Method

Abstract

The present invention relates to a method for predicting the diffusion concentration of interface elements in ultrasonic bonding, which includes modifying the diffusion coefficient D value and the diffusion concentration C value in the atomic concentration distribution formula during the diffusion process of the ultrasonic Al-Au bonding interface diffusion couple according to the ultrasonic bonding process, and then establishing a quantitative correlation model between the atomic diffusion concentration, diffusion position at the ultrasonic Al-Au bonding interface and the ultrasonic bonding process condition parameters, so as to realize the prediction of the diffusion concentration of the bonding interface elements under the ultrasonic Al-Au bonding process parameter conditions; the correlation model of the present invention introduces ultrasonic bonding process parameters, which more accurately reflects the change law of atomic concentration during the ultrasonic bonding process, can accurately predict the distribution of atomic concentration during the ultrasonic bonding process, and uses the genetic algorithm to achieve the global optimal search of material parameters in ultrasonic bonding, thereby improving the accuracy of material parameters in the ultrasonic diffusion concentration prediction model of the ultrasonic bonding interface.

Description

Technical Field

[0001] The present invention relates to the technical field of ultrasonic bonding in microelectronic packaging, and particularly to a method for predicting the diffusion concentration of elements at the ultrasonic bonding interface. Background Art

[0002] Ultrasonic bonding is a process with instantaneous multi-energy domain input. Tiny bonding points are formed within dozens of milliseconds. Problems such as dynamic stress, strain, temperature rise, atomic diffusion at the metal interface, and the resulting microstructure in the bonding micro-region are all very complex. As is well known, the distribution of element concentrations in the interface region is an important factor affecting the quality of heterogeneous metal connections, thus affecting the service performance of components. Therefore, it is necessary to predict the diffusion concentration of elements at the interface under ultrasonic bonding process parameters to ensure the quality of metal connections.

[0003] The literature "Element Diffusion near the Diffusion Bonding Interface of Be / HR-1 Stainless Steel, Li Hui, Kong Jilan, Zhou Shangqi, Zhang Pengcheng, Rare Metals, 2012, 36(2):6" discloses a method for theoretically calculating the diffusion concentration distribution of elements in the diffusion bonding joint region of dissimilar materials based on Fick's second law. Based on Fick's second law and substituting boundary conditions, an element diffusion concentration distribution equation was established to predict the diffusion concentration distribution of elements in the hot isostatic pressing diffusion bonding joint region. Through experimental verification, it shows that this model can better reflect the distribution law of elements, laying a theoretical foundation for the formulation of hot isostatic pressing diffusion bonding process parameters. However, this method is difficult to apply to the theoretical calculation of the interface element concentration distribution during ultrasonic bonding. Specifically, the ultrasonic bonding process realizes the high-quality connection between the metal wire and the pad on the substrate under the combined action of ultrasonic vibration and pressure, while the existing method has advantages in calculating the element concentration distribution in the material connection joint region under the action of diffusion temperature, diffusion pressure, and time. Therefore, it has great limitations in calculating the diffusion concentration distribution of interface elements under the action of ultrasonic bonding power. Summary of the Invention

[0004] The purpose of the present invention is to avoid the deficiencies of the prior art and provide a method for predicting the diffusion concentration of elements at the ultrasonic bonding interface. By comprehensively considering the ultrasonic bonding power, ultrasonic bonding pressure, correcting the diffusion coefficient, and the concentration values at the start and end of atomic diffusion, a quantitative correlation model between the atomic diffusion concentration at the ultrasonic bonding interface and the ultrasonic bonding parameters and diffusion position is established, which can accurately predict the distribution of atomic concentration during the ultrasonic bonding process.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: A method for predicting the diffusion concentration of elements at the ultrasonic bonding interface, comprising the following steps:

[0006] Step 1. According to Fick's second law, obtain the atomic concentration distribution formula during the diffusion process of the ultrasonic Al-Au bonding interface element diffusion couple:

[0007]

[0008] In the formula, C is the atomic diffusion concentration value, with the unit of at.%; C1 is the concentration value at the beginning of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; D is the diffusion coefficient, with the unit of m 2 ·s -1 ; erf is the Gaussian error function; t is the diffusion time, with the unit of ms; x is the diffusion distance, with the unit of μm;

[0009] Step 2. Under the ultrasonic bonding process conditions of ultrasonic bonding power, pressure, and time, correct the diffusion coefficient D value in the atomic concentration distribution equation to obtain the correction formula for the diffusion coefficient D value:

[0010]

[0011] In the formula, P is the ultrasonic bonding power, with the unit of mW; F is the ultrasonic bonding pressure, with the unit of gf; Q is the diffusion activation energy, with the unit of kJ﹒mol -1 ; R is the gas constant 8.3145J﹒mol -1 ﹒K -1 ; T is the temperature during diffusion, with the unit of K; A0, A1, A2, A3, A4, and A5 are material parameters in the correction formula for the diffusion coefficient D value;

[0012] Step 3. Correct the diffusion concentration C1 and C2 values at the beginning and end of atomic diffusion in the atomic concentration distribution equation to obtain the correction formulas for the diffusion concentrations C1 and C2 of Al atoms at the beginning and end of diffusion:

[0013] C1 = A6 + A7P + A8P 2 + A9P 3 + A 10 F + A 11 F 2 + A 12 F 3 ,

[0014] C2 = A 13 + A 14 P + A 15 P 2 + A 16 P 3 + A 17 F + A 18 F 2 + A 19 F3 ,

[0015] In the formula, C1 is the concentration value at the start of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; P is the ultrasonic bonding power, with the unit of mW; F is the ultrasonic bonding pressure, with the unit of gf; A6, A7, A8, A9, A 10 , A 11 , A 12 , A 13 , A 14 , A 15 , A 16 , A 17 , A 18 , A 19 are material parameters in the correction formula of the diffusion concentrations C1 and C2;

[0016] Step Four: Using the different ultrasonic bonding process conditions described in Step Two and the corresponding Al atom concentration state diagrams at different positions, and the concentration state diagrams of the start and end of Al atom diffusion described in Step Three, combined with the genetic algorithm, optimize and calculate the material parameters described in Step Two and Step Three to obtain the optimized values of all material parameters under the ultrasonic bonding process condition parameters;

[0017] Step Five: Establish a quantitative correlation model between the atomic diffusion concentration, diffusion position at the ultrasonic Al-Au bonding interface and the ultrasonic bonding process condition parameters, thereby realizing the prediction of the element diffusion concentration at the bonding interface under the ultrasonic Al-Au bonding process parameter conditions;

[0018] The quantitative correlation model is:

[0019]

[0020] In the formula, t is the ultrasonic bonding time, with the unit of ms; A0, A1, A2, A3, A4, A5, A6, A7, A8, A9, A 10 , A 11 , A 12 , A 13 , A 14 , A 15 , A 16 , A 17 , A 18 , A 19 are the optimized values of the material parameters obtained through the optimization calculation in Step Four.

[0021] Furthermore, the atomic concentration distribution equation during the diffusion process of the diffusion couple is obtained from the atomic concentration distribution equation of Fick's second law, and the atomic concentration distribution equation is:

[0022]

[0023] Set the initial conditions as: when t = 0,

[0024] The boundary conditions are: when t ≥ 0,

[0025] where C is the atomic diffusion concentration value, with the unit of at.%; C1 is the concentration value at the start of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; D is the diffusion coefficient, with the unit of m 2 ·s -1 ; t is the diffusion time; x is the diffusion distance;

[0026] Then, solve the atomic concentration distribution equation of the diffusion couple during the diffusion process according to Fick's second law.

[0027] Furthermore, in the second step, the ultrasonic Al-Au bonded specimen is subjected to an ultrasonic bonding process treatment to obtain the Al atomic concentration state diagrams at different positions of the Al-Au bonding interface under the influence of different ultrasonic bonding processes, and the diffusion coefficient D value in the atomic concentration distribution equation is corrected according to the Al atomic concentration state diagrams at different positions to obtain the correction formula for the diffusion coefficient D value;

[0028] In the third step, during the ultrasonic bonding process treatment of the ultrasonic Al-Au bonded specimen, the concentration state diagrams of the start and end of Al atomic diffusion at the Al-Au bonding interface under the influence of different ultrasonic bonding processes are also obtained, and the diffusion concentration C1 and C2 values at the start and end of atomic diffusion in the atomic concentration distribution equation are corrected according to the concentration state diagrams of the start and end of Al atomic diffusion to obtain the correction formulas for the diffusion concentration C1 and C2 at the start and end of Al atomic diffusion.

[0029] Furthermore, the specific steps for correcting the diffusion coefficient D value in the atomic concentration distribution equation in the second step and the diffusion concentration C1 and C2 values in the atomic concentration distribution equation in the third step include:

[0030] a. Obtain ultrasonic Al-Au bonding points through the ultrasonic bonding process, that is, use the ultrasonic Al-Au bonded specimen to carry out the ultrasonic bonding process treatment under the conditions of an ultrasonic bonding power of 65 - 85 mW, an ultrasonic bonding pressure of 19 - 27 gf, and an ultrasonic bonding time of 17 - 35 ms, and prepare at least 11 groups of ultrasonic Al-Au bonding points with different ultrasonic bonding process parameters under the ultrasonic bonding process conditions;

[0031] b. Micro-nano process the center position of the ultrasonic Al-Au bonding point to obtain the Al-Au bonding interface of the ultrasonic Al-Au bonding point. Subsequently, perform a line scan on the Al-Au bonding interface, and take the derivative of the line scan curve obtained from the line scan to obtain the initial position of the Al atom concentration diffusion at the Al-Au bonding interface;

[0032] c. Taking the initial position as the origin and the positive direction of the coordinate axis towards the Au layer, establish the Al atom concentration distribution diagrams of the Al-Au bonding interface under different ultrasonic bonding powers, pressures, and times;

[0033] d. According to the Al atom concentration distribution diagrams obtained in step c, obtain the Al atom concentration state diagrams at different positions of the Al-Au bonding interface under the influence of the ultrasonic bonding process. It can be obtained from the diagrams that the Al atom concentration at different positions of the Al-Au bonding interface has an approximate cubic function relationship with the ultrasonic bonding power, and an approximate quadratic function relationship with the ultrasonic bonding pressure. This is the corresponding relationship between the diffusion coefficient D and the ultrasonic bonding power and ultrasonic bonding pressure, and thus the value of the diffusion coefficient D is corrected;

[0034] e. According to the Al atom concentration distribution diagrams obtained in step c, obtain the state diagrams of the concentration C1 of Al atoms at the start of Al atom diffusion and the concentration C2 of Al atoms at the end of Al atom diffusion at the Al-Au bonding interface under the influence of the ultrasonic bonding process. It can be obtained from the diagrams that the concentration C1 of Al atoms at the start of atom diffusion and the concentration C2 of Al atoms at the end of atom diffusion have an approximate cubic function relationship with the ultrasonic bonding power, and an approximate cubic function relationship with the ultrasonic bonding pressure. This is the corresponding relationship between the concentration C1 of Al atoms at the start of atom diffusion and the concentration C2 of Al atoms at the end of atom diffusion and the ultrasonic bonding power and ultrasonic bonding pressure, and thus the diffusion concentrations C1 and C2 of Al atoms at the start and end of diffusion are corrected.

[0035] Further, in step a, a fully automatic ultrasonic silicon-aluminum wire bonder is used to perform the ultrasonic bonding process to form the ultrasonic Al-Au bonding point; in step b, a focused ion beam is used to perform micro-nano processing on the center position of the ultrasonic Al-Au bonding point. At the same time, a line scan function in an energy spectrometer is used to perform the line scan on the Al-Au bonding interface.

[0036] Further, step four is specifically as follows:

[0037] A. Select at least 9 groups of different ultrasonic bonding process parameters. After line scanning, select the Al atom concentrations at at least 7 different positions on the Al-Au bonding interface, with a total of at least 63 sets of Al atom concentration values as the sample data test values. At the same time, according to the different ultrasonic bonding process parameters, use the quantitative correlation model to predict the Al atom concentration values at different positions on the Al-Au bonding interface as the sample data calculated values.

[0038] B. Take the sum of squared residuals of the sample data calculated values and the sample data test values as the objective function for calculating the material parameters of the quantitative correlation model. The expression of the objective function is as follows:

[0039]

[0040] In the formula, f(A) is the sum of squared residuals of the calculated value and the test value of the atomic diffusion concentration. is the calculated value of the atomic diffusion concentration, with the unit of at.%. is the test value of the atomic diffusion concentration, with the unit of at.%. n represents the number of groups of ultrasonic bonding process parameters, and m represents different interface positions.

[0041] C. Use the genetic algorithm to calculate the material parameters in the quantitative correlation model. When the objective function in step B reaches the minimum value, select the A0 to A at this time 19 The material parameters are the optimized values of all the material parameters in the quantitative correlation model.

[0042] Further, the steps for verifying the accuracy of the quantitative correlation model obtained in step five are as follows:

[0043] Select at least 2 ultrasonic Al-Au bonding points with ultrasonic bonding process parameters different from the sample data, and select at least 3 different positions at the Al-Au bonding interface of each ultrasonic Al-Au bonding point, with a total of at least 6 groups of Al atom concentration values established as non-sample data test values. At the same time, under the conditions of the different ultrasonic bonding process parameters, use the Al atom concentration values calculated by the quantitative correlation model as non-sample data calculated values.

[0044] According to the non-sample data test values and non-sample data calculated values, establish a comparison table of the non-sample data test values and calculated values of the Al atom concentration in the Al-Au bonding interface to obtain the maximum relative error and the minimum relative error for verifying the prediction accuracy of the quantitative correlation model.

[0045] Further, the ultrasonic Al-Au bonding specimen includes an aluminum-1% silicon fine wire for bonding and a Au layer for bonding connection. The diameter of the aluminum-1% silicon fine wire is 0.013 - 0.1 mm, and the Au layer is deposited on the Si substrate by magnetron sputtering. The thickness of the Au layer is 700 - 800 nm.

[0046] The beneficial effects of the present invention are as follows: Based on the atomic concentration distribution equation, considering the influence of ultrasonic bonding power and ultrasonic bonding pressure, the diffusion coefficient D, the concentration value C1 at the beginning of atomic diffusion, and the concentration value C2 at the end of atomic diffusion are corrected. Thus, coupling the influence of ultrasonic bonding power, ultrasonic bonding time, ultrasonic bonding pressure, etc., an association model between the atomic diffusion concentration at the interface, ultrasonic bonding parameters, and diffusion position is established, which can accurately predict the distribution of atomic concentration during ultrasonic bonding; and the genetic algorithm is used to achieve the global optimal search of material parameters in ultrasonic bonding, thereby improving the accuracy of material parameters in the prediction model of element diffusion concentration at the ultrasonic bonding interface; in addition, ultrasonic bonding process parameters are introduced into the association model, which more accurately reflects the change law of atomic concentration during ultrasonic bonding, which is not available in other methods. Description of the Drawings

[0047] Figure 1 For the present invention, when the ultrasonic bonding power is 75 mW and the ultrasonic bonding time is 21 ms, the ultrasonic bonding pressure on the atomic concentration state diagram of the ultrasonic Al-Au bonding interface: (a) 19 gf; (b) 21 gf; (c) 23 gf; (d) 25 gf; (e) 27 gf;

[0048] Figure 2 The ultrasonic bonding process parameters on the Al atomic concentration state diagram at different positions of the Al-Au interface;

[0049] Figure 3 The ultrasonic bonding process parameters on the state diagram of the concentration C1 at the beginning of atomic diffusion and the concentration C2 at the end of atomic diffusion at the ultrasonic Al-Au bonding interface. Detailed Embodiments

[0050] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0051] To achieve the above object, the present invention provides the following specific embodiments:

[0052] Example 1: A method for predicting the element diffusion concentration at the ultrasonic bonding interface includes the following steps:

[0053] Step 1: According to Fick's second law, obtain the atomic concentration distribution formula during the diffusion process of the element diffusion couple at the ultrasonic Al-Au bonding interface:

[0054]

[0055] Wherein, C is the atomic diffusion concentration value, with the unit of at.%; C1 is the concentration value at the start of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; D is the diffusion coefficient, with the unit of m 2 ·s -1 ; erf is the Gaussian error function; t is the diffusion time, with the unit of ms; x is the diffusion distance, with the unit of μm;

[0056] The atomic concentration distribution equation of the diffusion couple during the diffusion process is obtained from the atomic concentration distribution equation of Fick's second law, and the atomic concentration distribution equation is:

[0057]

[0058] Set the initial condition as: when t = 0,

[0059] The boundary condition is: when t ≥ 0,

[0060] Wherein C is the atomic diffusion concentration value, with the unit of at.%; C1 is the concentration value at the start of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; D is the diffusion coefficient, with the unit of m 2 ·s -1 ; t is the diffusion time; x is the diffusion distance;

[0061] Then, the atomic concentration distribution equation of the diffusion couple during the diffusion process is solved from Fick's second law.

[0062] Step 2: Under the ultrasonic bonding process conditions of ultrasonic bonding power, pressure, and time, perform ultrasonic bonding process treatment on the ultrasonic Al-Au bonding specimen, so as to obtain the Al atomic concentration state diagrams at different positions of the Al-Au bonding interface under the influence of different ultrasonic bonding processes, and correct the diffusion coefficient D value in the atomic concentration distribution equation according to the Al atomic concentration state diagrams at different positions, to obtain the correction formula for the diffusion coefficient D value:

[0063]

[0064] Wherein, P is the ultrasonic bonding power, with the unit of mW; F is the ultrasonic bonding pressure, with the unit of gf; Q is the diffusion activation energy, with the unit of kJ﹒mol -1 ; R is the gas constant 8.3145J﹒mol -1 ﹒K -1; T is the temperature during diffusion, in K; A0, A1, A2, A3, A4 and A5 are material parameters in the correction formula of the diffusion coefficient D value;

[0065] The specific steps of correcting the diffusion coefficient D value in the atomic concentration distribution equation in step 2 and the diffusion concentrations C1 and C2 values ​​in the atomic concentration distribution equation in step 3 include:

[0066] a. Obtaining ultrasonic Al-Au bonding points by ultrasonic bonding process, i.e., using ultrasonic Al-Au bonding sample to carry out ultrasonic bonding process under the conditions of ultrasonic bonding power 65-85mW, ultrasonic bonding pressure 19-27gf, and ultrasonic bonding time 17-35ms, and preparing at least 11 groups of ultrasonic Al-Au bonding points with different ultrasonic bonding process parameters under the ultrasonic bonding process conditions;

[0067] b. performing micro-nano machining on the center position of the ultrasonic Al-Au bonding point to obtain the Al-Au bonding interface of the ultrasonic Al-Au bonding point, then performing line scanning on the Al-Au bonding interface, and deriving the line scanning curve obtained by the line scanning to obtain the initial position of the Al atomic concentration diffusion at the Al-Au bonding interface;

[0068] c. With the initial position as the origin and the coordinate axis toward the Au layer as the positive direction, establish the Al atomic concentration distribution diagram of the Al-Au bonding interface under different ultrasonic bonding power, pressure and time conditions;

[0069] d. According to the Al atomic concentration distribution diagram obtained in step c, the Al atomic concentration state diagram at different positions of the Al-Au bonding interface under the influence of the ultrasonic bonding process is obtained. From the diagram, it is found that the Al atomic concentration at different positions of the Al-Au bonding interface is approximately a cubic function relationship with the ultrasonic bonding power, and is approximately a quadratic function relationship with the ultrasonic bonding pressure, that is, the diffusion coefficient D is the function of the ultrasonic bonding power and the ultrasonic bonding pressure.

[0070] The corresponding relationship between the combined pressures is used to correct the diffusion coefficient D value;

[0071] e. According to the Al atomic concentration distribution diagram obtained in step c, a state diagram of the concentration C1 at the beginning of Al atomic diffusion and the concentration C2 at the end of Al atomic diffusion at the Al-Au bonding interface under the influence of the ultrasonic bonding process is obtained. From the diagram, it can be obtained that the concentration C1 at the beginning of atomic diffusion and the concentration C2 at the end of atomic diffusion are approximately in a cubic function relationship with the ultrasonic bonding power, and are approximately in a cubic function relationship with the ultrasonic bonding pressure, that is, the correspondence between the concentration C1 at the beginning of atomic diffusion and the concentration C2 at the end of atomic diffusion and the ultrasonic bonding power and ultrasonic bonding pressure, thereby realizing the correction of the diffusion concentrations C1 and C2 values.

[0072] In step a, an automatic ultrasonic silicon-aluminum wire bonder is used for the ultrasonic bonding process to form the ultrasonic Al-Au bonding points. In step b, a focused ion beam is used for micro-nano processing of the center position of the ultrasonic Al-Au bonding points. At the same time, a line scan function in an energy spectrometer is used for line scanning of the Al-Au bonding interface.

[0073] Step 3: In the process of subjecting the ultrasonic Al-Au bonded specimen to the ultrasonic bonding process, concentration state diagrams of the start and end of Al atom diffusion at the Al-Au bonding interface under the influence of different ultrasonic bonding processes are also obtained. Based on the concentration state diagrams of the start and end of Al atom diffusion, the diffusion concentration values C1 and C2 at the start and end of atom diffusion in the atomic concentration distribution equation are corrected to obtain the correction formulas for the diffusion concentration C1 and C2 at the start and end of Al atom diffusion:

[0074] C1 = A6 + A7P + A8P 2 + A9P 3 + A 10 F + A 11 F 2 + A 12 F 3 ,

[0075] C2 = A 13 + A 14 P + A 15 P 2 + A 16 P 3 + A 17 F + A 18 F 2 + A 19 F 3 ,

[0076] In the formula, C1 is the concentration value at the start of atom diffusion, with the unit of at.%; C2 is the concentration value at the end of atom diffusion, with the unit of at.%; P is the ultrasonic bonding power, with the unit of mW; F is the ultrasonic bonding pressure, with the unit of gf; A6, A7, A8, A9, A 10 , A 11 , A 12 , A 13 , A 14 , A 15 , A 16 , A 17 , A 18 , A 19 are material parameters in the correction formulas for the diffusion concentrations C1 and C2;

[0077] Step 4: Use the different ultrasonic bonding process conditions described in Step 2 and the corresponding Al atom concentration state diagrams at different positions, and the concentration state diagrams of the start and end of Al atom diffusion described in Step 3. Combine the genetic algorithm to optimize and calculate the material parameters described in Steps 2 and 3 to obtain the optimized values of all material parameters under the ultrasonic bonding process condition parameters;

[0078] The specific content of Step 4 is as follows:

[0079] A. Select at least 9 groups of different ultrasonic bonding process parameters. After line scanning, select the Al atom concentrations at at least 7 different positions on the Al-Au bonding interface, totaling at least 63 groups of Al atom concentration values, as the sample data test values; at the same time, according to the different ultrasonic bonding process parameters, use the quantitative correlation model to predict the Al atom concentration values at different positions on the Al-Au bonding interface, as the sample data calculation values;

[0080] B. Take the sum of the squares of the residuals between the sample data calculation values and the sample data test values as the objective function for calculating the material parameters of the quantitative correlation model. The expression of the objective function is as follows:

[0081]

[0082] In the formula, f(A) is the sum of the squares of the residuals between the calculated value and the test value of the atomic diffusion concentration; is the calculated value of the atomic diffusion concentration, with the unit of at.%; is the test value of the atomic diffusion concentration, with the unit of at.%; n represents the number of groups of ultrasonic bonding process parameters; m represents different interface positions;

[0083] C. Use the genetic algorithm to calculate the material parameters in the quantitative correlation model. When the objective function in Step B reaches the minimum value, select A0 to A at this time 19 The material parameters are the optimized values of all material parameters in the quantitative correlation model.

[0084] Step 5: Establish a quantitative correlation model between the atomic diffusion concentration, diffusion position at the ultrasonic Al-Au bonding interface and the ultrasonic bonding process condition parameters, thereby realizing the prediction of the element diffusion concentration at the bonding interface under the ultrasonic Al-Au bonding process parameter conditions;

[0085] The quantitative correlation model is:

[0086]

[0087] In the formula, t is the ultrasonic bonding time, with the unit of ms; A0, A1, A2, A3, A4, A5, A6, A7, A8, A9, A 10, A 11 , A 12 , A 13 , A 14 , A 15 , A 16 , A 17 , A 18 , A 19 is the optimized value of the material parameters obtained by optimizing the calculation in the fourth step above.

[0088] Steps for verifying the accuracy of the quantitative correlation model obtained in the fifth step above:

[0089] Select at least 2 groups of ultrasonic Al-Au bonding points with ultrasonic bonding process parameters different from the sample data, and select at least 3 different positions at the Al-Au bonding interface of each ultrasonic Al-Au bonding point, and establish at least 6 groups of Al atomic concentration values as non-sample data test values in total; at the same time, under the conditions of the different ultrasonic bonding process parameters, the Al atomic concentration values calculated by using the quantitative correlation model are used as non-sample data calculated values;

[0090] According to the non-sample data test values and non-sample data calculated values, establish a comparison table of the non-sample data test values and calculated values of the Al atomic concentration in the Al-Au bonding interface, and obtain the maximum relative error and the minimum relative error, which are used to verify the prediction accuracy of the quantitative correlation model.

[0091] The ultrasonic Al-Au bonding specimen described above includes an aluminum-1% silicon fine wire for bonding and a Au layer for bonding connection. The diameter of the aluminum-1% silicon fine wire is 0.013 - 0.1 mm, and the Au layer is deposited on the Si substrate by magnetron sputtering, and the thickness of the Au layer is 700 - 800 nm.

[0092] Experimental example: As Figures 1-3 , taking the ultrasonic Al-Au bonding specimen as a specific implementation object, wherein, the diameter of the aluminum-1% silicon fine wire for bonding is 0.04 mm, and the Au layer is deposited on the Si substrate by magnetron sputtering, and the thickness of the Au layer is 700 - 800 nm.

[0093] (a) Carry out ultrasonic bonding process treatment by using a fully automatic ultrasonic silicon-aluminum wire bonder. Under the ultrasonic bonding conditions of ultrasonic bonding power of 65 - 85 mW, ultrasonic bonding pressure of 19 - 27 gf, and ultrasonic bonding time of 17 - 35 ms, prepare 11 groups of ultrasonic Al-Au bonding points with different ultrasonic bonding process parameters;

[0094] (b) Micro-nano machining was carried out on the central position of the ultrasonic Al-Au bonding point using a focused ion beam (FIB). Subsequently, the line scan function in an energy dispersive spectrometer (EDS) was used to differentiate the line scan curve obtained from the line scan, and the initial position of the Al atom concentration diffusion at the Al-Au bonding interface was obtained. According to Fick's second law, the atomic diffusion shows a parabolic relationship with time. Based on this, it was determined that the position with the largest change in atomic concentration is the initial position of interface diffusion.

[0095] (c) Taking the initial position of the Al atom concentration diffusion at the Al-Au bonding interface as the origin and the positive direction of the coordinate axis towards the Au layer, an influence diagram of ultrasonic bonding process parameters on the Al atom concentration at the Al-Au interface was obtained. Figure 1 It is an influence diagram of ultrasonic bonding pressure on the atomic concentration at the Al-Au interface when the ultrasonic bonding power is 75 mW and the ultrasonic bonding time is 21 m.

[0096] (d) According to the influence law of ultrasonic bonding process parameters on the atomic concentration at the Al-Au interface obtained in step (c), the changes in the Al atom concentration at different positions of the Al-Au interface were analyzed. Figure 2 It is a state diagram of the Al atom concentration at different positions of the Al-Au interface with respect to ultrasonic bonding process parameters. It can be seen that the Al atom concentration at different positions shows an approximate cubic function relationship with the ultrasonic bonding power, and an approximate quadratic function relationship with the ultrasonic bonding pressure. Then, according to the state diagram of the Al atom concentration at different positions, the diffusion coefficient D value in the atomic concentration distribution equation was corrected to obtain the correction formula for the diffusion coefficient D value: Figure 2 In the formula, P is the ultrasonic bonding power, with the unit of mW; F is the ultrasonic bonding pressure, with the unit of gf; Q is the diffusion activation energy, with the unit of kJ﹒mol

[0097]

[0098] ; R is the gas constant 8.3145 J﹒mol -1 ; T is the temperature during diffusion, with the unit of K; A0, A1, A2, A3, A4, and A5 are material parameters in the correction formula for the diffusion coefficient D value. -1 ﹒K -1 ; T is the temperature during diffusion, with the unit of K; A0, A1, A2, A3, A4, and A5 are material parameters in the correction formula for the diffusion coefficient D value.

[0099] (e) According to the influence law of ultrasonic bonding process parameters on the atomic concentration at the Al-Au interface obtained in step (b), the relationship between the ultrasonic bonding power, ultrasonic bonding pressure and the initial concentration value C1 and the final concentration value C2 of Al atom diffusion at the Al-Au bonding point interface can also be obtained. Figure 3The influence of ultrasonic bonding process parameters on the C1 and C2 values at the Al-Au interface, that is, the concentration state diagrams of the start and end of Al atom diffusion at the Al-Au bonding interface under the influence of different ultrasonic bonding processes. It can be seen from the figure that C1 and C2 have an approximate cubic function relationship with the ultrasonic bonding power, and C1 and C2 have an approximate cubic function relationship with the ultrasonic bonding pressure. Then, according to the concentration state diagrams of the start and end of Al atom diffusion, the diffusion concentration C value in the atomic concentration distribution equation is corrected to obtain the correction formula for the diffusion concentration C value:

[0100] C1 = A6 + A7P + A8P 2 + A9P 3 + A 10 F + A 11 F 2 + A 12 F 3 ,

[0101] C2 = A 13 + A 14 P + A 15 P 2 + A 16 P 3 + A 17 F + A 18 F 2 + A 19 F 3 ,

[0102] In the formula, C1 is the concentration value at the start of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; P is the ultrasonic bonding power, with the unit of mW; F is the ultrasonic bonding pressure, with the unit of gf; A6, A7, A8, A9, A 10 , A 11 , A 12 , A 13 , A 14 , A 15 , A 16 , A 17 , A 18 , A 19 are the material parameters in the correction formulas for the diffusion concentrations C1 and C2;

[0103] (f) Establish a quantitative correlation model between the atomic diffusion concentration, diffusion position at the ultrasonic Al-Au bonding interface and the ultrasonic bonding process condition parameters, thereby realizing the prediction of the element diffusion concentration at the bonding interface under the ultrasonic Al-Au bonding process parameters;

[0104] The quantitative correlation model is:

[0105]

[0106] In the formula, t is the ultrasonic bonding time, and the unit is ms; A0, A1, A2, A3, A4, A5, A6, A7, A8, A9, A 10 、A 11 、A 12 、A 13 、A 14 、A 15 、A 16 、A 17 、A 18 、A 19 are the optimized values of the material parameters obtained through optimized calculation.

[0107] (g) Select 9 groups of ultrasonic bonding process parameters, and select 7 different positions at each process parameter interface, for a total of 63 groups of Al atomic concentration as sample data test values; at the same time, according to the different ultrasonic bonding process parameters described above, use the quantitative correlation model in step (f) to predict the Al atomic concentration values at different positions of the Al-Au bonding interface as sample data calculated values, and optimize the calculation of the material parameters in steps (d) and (e): specifically:

[0108] Take the sum of the squares of the residuals between the calculated values of the sample data and the test values of the sample data as the objective function for calculating the material parameters of the quantitative correlation model. The expression of the objective function is as follows:

[0109]

[0110] In the formula, f(A) is the sum of the squares of the residuals between the calculated value of the atomic diffusion concentration and the test value; is the calculated value of the atomic diffusion concentration, and the unit is at.%; is the test value of the atomic diffusion concentration, and the unit is at.%; n represents the number of groups of ultrasonic bonding process parameters; m represents different interface positions;

[0111] Use the genetic algorithm to calculate the material parameters in the quantitative correlation model. When the objective function reaches the minimum value, select A0 to A at this time 19 The material parameters are the optimized values of all the material parameters in the quantitative correlation model.

[0112] In this experimental example, Table 1 obtained by this method is the material parameters of the diffusion model of the Al-Au bonding interface obtained through optimized calculation:

[0113] Table 1

[0114]

[0115] (h) To verify the accuracy of the element diffusion concentration prediction model, two sets of ultrasonic bonding process parameters were selected, and three different positions were chosen under each process parameter. A total of six sets of Al atom concentrations were used as non-sample data for model verification. Table 2 shows the comparison between the experimental values and calculated values of partial non-sample data of Al atom concentrations at Al-Au bonding points. It can be seen from the table that the maximum relative error between the calculated values and experimental values of the non-sample data of Al atom concentrations is 6.38%, and the minimum relative error is 2.47%, indicating that the model has a high prediction accuracy.

[0116] Table 2

[0117]

[0118]

[0119] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for predicting the diffusion concentration of ultrasonic bonding interface elements, characterized in that It includes the following steps: Step 1: Obtain the atomic concentration distribution formula during the diffusion process of the ultrasonic Al-Au bonding interface element diffusion couple according to Fick's second law: Wherein, C is the atomic diffusion concentration value, with the unit of at.%; C1 is the concentration value at the start of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; D is the diffusion coefficient, with the unit of m 2 ·s -1 ; erf is the Gaussian error function; t is the diffusion time, with the unit of ms; x is the diffusion distance, with the unit of μm; Step 2: Under the ultrasonic bonding process conditions of ultrasonic bonding power, pressure, and time, correct the diffusion coefficient D value in the atomic concentration distribution equation to obtain the corrected formula for the diffusion coefficient D value: Wherein, P is the ultrasonic bonding power, with the unit of mW; F is the ultrasonic bonding pressure, with the unit of gf; Q is the diffusion activation energy, with the unit of kJ﹒mol -1 ; R is the gas constant 8.3145J﹒mol -1 ﹒K -1 ; T is the temperature during diffusion, with the unit of K; A0, A1, A2, A3, A4, and A5 are material parameters in the diffusion coefficient D value correction formula; Step 3: Correct the diffusion concentration C1 and C2 values at the beginning and end of atomic diffusion in the atomic concentration distribution equation to obtain the corrected formulas for the diffusion concentration C1 and C2 of Al atoms at the beginning and end of Al atom diffusion: C1 = A6 + A7P + A8P 2 + A9P 3 + A 10 F + A 11 F 2 + A 12 F 3 , C2 = A 13 + A 14 P + A 15 P 2 + A 16 P 3 + A 17 F + A 18 F 2 + A 19 F 3 , Wherein, C1 is the concentration value at the start of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; P is the ultrasonic bonding power, with the unit of mW; F is the ultrasonic bonding pressure, with the unit of gf; A6, A7, A8, A9, A 10 、A 11 、A 12 、A 13 、A 14 、A 15 、A 16 、A 17 、A 18 、A 19 are material parameters in the correction formula for the diffusion concentrations C1 and C2; Step 4: Use the different ultrasonic bonding process conditions described in Step 2 and the corresponding Al atom concentration state diagrams at different positions, and the concentration state diagrams of the start and end of Al atom diffusion described in Step 3. Combine the genetic algorithm to optimize and calculate the material parameters described in Step 2 and Step 3 to obtain the optimized values of all material parameters under the ultrasonic bonding process condition parameters: Step 5: Establish a quantitative correlation model between the atomic diffusion concentration, diffusion position at the ultrasonic Al-Au bonding interface and the ultrasonic bonding process condition parameters, thereby realizing the prediction of the diffusion concentration of the bonding interface elements under the ultrasonic Al-Au bonding process parameter conditions: The quantitative correlation model is: In the formula, t is the ultrasonic bonding time, with the unit of ms; A0, A1, A2, A3, A4, A5, A6, A7, A8, A9, A 10 、A 11 、A 12 、A 13 、A 14 、A 15 、A 16 、A 17 、A 18 、A 19 are the optimized values of the material parameters obtained through the optimization calculation in the fourth step.

2. The ultrasonic bonding interface element diffusion concentration prediction method according to claim 1, characterized in that The atomic concentration distribution equation during the diffusion process of the diffusion couple is obtained from the atomic concentration distribution equation of Fick's second law, and the atomic concentration distribution equation is: Set the initial conditions as: when t = 0, The boundary conditions are: when t ≥ 0, Where C is the atomic diffusion concentration value, with the unit of at.%; C1 is the concentration value at the start of atomic diffusion, with the unit of at.%; C2 is the concentration value at the end of atomic diffusion, with the unit of at.%; D is the diffusion coefficient, with the unit of m 2 ·s -1 ; t is the diffusion time; x is the diffusion distance; Then, the atomic concentration distribution equation during the diffusion process of the diffusion couple is solved by Fick's second law.

3. The ultrasonic bonding interface element diffusion concentration prediction method according to claim 1, wherein In Step 2, the ultrasonic Al-Au bonding specimen is subjected to ultrasonic bonding process treatment to obtain the Al atom concentration state diagrams at different positions of the Al-Au bonding interface under the influence of different ultrasonic bonding processes, and the diffusion coefficient D value in the atomic concentration distribution equation is corrected according to the Al atom concentration state diagrams at different positions to obtain the corrected formula for the diffusion coefficient D value: In Step 3, during the ultrasonic bonding process treatment of the ultrasonic Al-Au bonding specimen, the concentration state diagrams of the start and end of Al atom diffusion at the Al-Au bonding interface under the influence of different ultrasonic bonding processes are also obtained, and the diffusion concentration C1 and C2 values at the start and end of atomic diffusion in the atomic concentration distribution equation are corrected according to the concentration state diagrams of the start and end of Al atom diffusion, thereby obtaining the corrected formulas for the diffusion concentration C1 and C2 of Al atoms at the start and end of Al atom diffusion.

4. The ultrasonic bonding interface element diffusion concentration prediction method according to claim 3, wherein The specific steps for correcting the diffusion coefficient D value in the atomic concentration distribution equation in Step 2 and the start and end diffusion concentrations C1 and C2 in the atomic concentration distribution equation in Step 3 include: a. Obtain ultrasonic Al-Au bonding points through an ultrasonic bonding process, that is, use ultrasonic Al-Au bonding specimens to perform ultrasonic bonding process treatment under the conditions of ultrasonic bonding power of 65 - 85 mW, ultrasonic bonding pressure of 19 - 27 gf, and ultrasonic bonding time of 17 - 35 ms, and prepare at least 11 groups of ultrasonic Al-Au bonding points with different ultrasonic bonding process parameters under the above ultrasonic bonding process conditions; b. Perform micro-nano processing on the central position of the ultrasonic Al-Au bonding point to obtain the Al-Au bonding interface of the ultrasonic Al-Au bonding point. Subsequently, perform line scanning on the Al-Au bonding interface, and take the derivative of the line scanning curve obtained from the line scanning to obtain the initial position of the Al atom concentration diffusion at the Al-Au bonding interface; c. Taking the above initial position as the origin and the positive direction of the coordinate axis towards the Au layer, establish the Al atom concentration distribution maps of the Al-Au bonding interface under different ultrasonic bonding powers, pressures, and times; d. According to the Al atom concentration distribution maps obtained in step c, obtain the Al atom concentration state maps at different positions of the Al-Au bonding interface under the influence of the ultrasonic bonding process. It can be obtained from the maps that the Al atom concentration at different positions of the Al-Au bonding interface has an approximate cubic function relationship with the ultrasonic bonding power, while having an approximate quadratic function relationship with the ultrasonic bonding pressure. This is the corresponding relationship between the diffusion coefficient D and the ultrasonic bonding power and ultrasonic bonding pressure, and thus the value of the diffusion coefficient D is corrected; e. According to the Al atom concentration distribution maps obtained in step c, obtain the state maps of the concentration C1 of Al atoms at the start of Al atom diffusion and the concentration C2 of Al atoms at the end of Al atom diffusion at the Al-Au bonding interface under the influence of the ultrasonic bonding process. It can be obtained from the maps that the concentration C1 of Al atoms at the start of diffusion and the concentration C2 of Al atoms at the end of diffusion have an approximate cubic function relationship with the ultrasonic bonding power, while having an approximate cubic function relationship with the ultrasonic bonding pressure. This is the corresponding relationship between the concentration C1 of Al atoms at the start of atom diffusion and the concentration C2 of Al atoms at the end of atom diffusion and the ultrasonic bonding power and ultrasonic bonding pressure, and thus the values of the diffusion concentrations C1 and C2 of Al atoms at the start and end of diffusion are corrected.

5. The ultrasonic bonding interface element diffusion concentration prediction method according to claim 4, characterized in that In step a, a fully automatic ultrasonic silicon-aluminum wire bonder is used to perform the ultrasonic bonding process to form the ultrasonic Al-Au bonding points; in step b, a focused ion beam is used to perform micro-nano processing on the central position of the ultrasonic Al-Au bonding point. At the same time, the line scanning function in the energy spectrometer is used to perform line scanning on the Al-Au bonding interface.

6. The ultrasonic bonding interface element diffusion concentration prediction method according to claim 1, wherein The specific content of step four is as follows: A. Select at least 9 groups of different ultrasonic bonding process parameters. After line scanning, select the Al atom concentrations at at least 7 different positions on the Al-Au bonding interface, totaling at least 63 groups of Al atom concentration values, as sample data test values; at the same time, according to the above different ultrasonic bonding process parameters, use the quantitative correlation model to predict the Al atom concentration values at different positions of the Al-Au bonding interface, as sample data calculated values; B. Take the sum of the squared residuals between the calculated values of the sample data and the experimental values of the sample data as the objective function for calculating the material parameters of the quantitative correlation model. The expression of the objective function is as follows: Where f(A) is the sum of squared residuals between the calculated value and the experimental value of atomic diffusion concentration; is the calculated value of atomic diffusion concentration, with the unit of at.%; is the experimental value of atomic diffusion concentration, with the unit of at.%; n represents the number of groups of ultrasonic bonding process parameters; m represents different interface positions; C. Calculate the material parameters in the quantitative correlation model by using a genetic algorithm. When the objective function in step B reaches the minimum value, select A0 to A at this time 19 The material parameters are the optimized values of all the material parameters in the quantitative correlation model.

7. The ultrasonic bonding interface element diffusion concentration prediction method according to claim 1, characterized in that Steps for verifying the accuracy of the quantitative correlation model obtained in step 5: Select at least 2 ultrasonic Al-Au bonding points with ultrasonic bonding process parameters different from the sample data, and select at least 3 different positions at the Al-Au bonding interface of each ultrasonic Al-Au bonding point, and establish at least 6 sets of Al atomic concentration values in total as non-sample data experimental values; at the same time, under the conditions of the different ultrasonic bonding process parameters, the Al atomic concentration values calculated using the quantitative correlation model are used as non-sample data calculated values; According to the non-sample data experimental values and non-sample data calculated values, establish a comparison table of the non-sample data experimental values and calculated values of the Al atomic concentration in the Al-Au bonding interface, and obtain the maximum relative error and the minimum relative error for verifying the prediction accuracy of the quantitative correlation model.

8. The ultrasonic bonding interface element diffusion concentration prediction method according to any one of claims 1-7, characterized in that, The ultrasonic Al-Au bonding specimen includes aluminum-1% silicon fine wires for bonding and a Au layer for bonding connection. The diameter of the aluminum-1% silicon fine wires is 0.013 - 0.1 mm. The Au layer is deposited on the Si substrate by magnetron sputtering, and the thickness of the Au layer is 700 - 800 nm.

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