Inversion method for elastic constants of metal single crystal micropillars in chip bonding layer compression test

Abstract

The present invention provides a chip bonding layer metal single crystal micro-column compression test elastic constant inversion method, which uses micro-column compression test, combined with n groups of micro-column compression data in different crystal directions, by establishing an accurate finite element model and setting reasonable boundary conditions, to provide a model basis and simulation support for elastic constant inversion calculation; by using a multi-objective optimization algorithm, the comprehensiveness and accuracy of the inversion result are improved; combined with the force-displacement curve simulation results of the finite element model, the elastic constants of the metal single crystal material consistent with the actual micro-column compression test results are obtained by inversion, and the optimal method is provided for determining the elastic constants of the metal single crystal of the chip bonding material. This method can effectively obtain the force-displacement curve of the metal single crystal micro-column during the compression process, and combined with the finite element model and the multi-objective optimization algorithm, accurately invert the elastic constants of the material, and provide a new technical means for material mechanical property testing in the field of electronic packaging.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic packaging mechanical testing, and in particular is an elastic constant inversion method for a chip bonding layer metal single crystal micro-column compression test. Background Art

[0002] In modern electronic packaging technology, the mechanical properties of the chip bonding layer play a vital role in the reliability and stability of the entire packaging structure. With the development of microelectronic devices, the microstructure and mechanical properties of the chip bonding layer are particularly important. Traditional macroscopic mechanical properties testing methods have certain limitations in micro-nanoscale material testing and are difficult to accurately reflect the true mechanical properties of materials. Especially in the bonding layer, such as single crystal mechanical properties testing of metal materials such as sintered silver and sintered copper, how to accurately obtain the elastic constants of the material single crystal has become an important research topic.

[0003] Metal materials such as silver and copper are widely used in chip bonding layer materials due to their excellent electrical and thermal conductivity and good mechanical properties. However, in the process of mechanical property testing and parameter inversion of single crystal microcolumn compression test of silver materials, there are problems such as difficulty in data acquisition, low test accuracy, and poor experimental repeatability. Traditional test methods and data analysis methods make it difficult to accurately use metal single crystal microcolumns in compression data to obtain material constitutive parameters, especially the accurate inversion of its elastic constants faces huge challenges.

[0004] As a powerful numerical calculation tool, finite element analysis can effectively simulate the mechanical behavior of anisotropic materials and perform parameter inversion in combination with experimental data. However, in micro-column compression tests, how to combine finite element models and experimental data to accurately invert the elastic constants of materials through optimization algorithms remains an unresolved problem.

[0005] In summary, in the prior art, the inversion method for the elastic constants of the metal single crystal micro-pillar compression test of the chip bonding layer is still a technical problem to be solved. Summary of the invention

[0006] The purpose of the present invention is to avoid the shortcomings of the prior art and provide a chip bonding layer metal single crystal micro-pillar compression test elastic constant inversion method, which obtains force-displacement curve data through a specific crystal orientation bonding layer metal material single crystal micro-pillar compression test and establishes a corresponding finite element model. Combined with a multi-objective optimization algorithm, the elastic constants of the metal single crystal material are accurately inverted, providing a new solution for the mechanical properties test in the field of electronic packaging, and effectively improving the accuracy and efficiency of the test.

[0007] To achieve the above object, the technical solution adopted by the present invention is: the elastic constant inversion method of the metal single crystal micro-pillar compression test of the chip bonding layer comprises the following steps:

[0008] Step 1: Conduct compression tests on metal single crystal micro-pillars in different crystal orientations in the chip bonding layer to obtain the corresponding metal single crystal micro-pillar compression test force-displacement curve data;

[0009] Step 2: Establish a finite element model of metal single crystal micro-column compression, including geometric model establishment, crystal orientation, boundary setting, mesh division, and obtain the finite element simulation results of the micro-column compression force-displacement curve by setting different elastic constants;

[0010] Step 3: Setting the multi-objective optimization problem of elastic constants of metal single crystals, including the determination of the objective function and the range of elastic constant parameters;

[0011] Step 4: Use a multi-objective optimization algorithm to solve the optimal metal single crystal elastic constants, thereby obtaining the metal single crystal material elastic constants inverted from the micro-pillar compression test data.

[0012] Furthermore, the method for obtaining the corresponding force-displacement curve data of the metal single crystal micro-pillar compression test in step 1 includes:

[0013] (1) Based on the results of electron backscatter diffraction (EBSD) of the metal cross section of the chip bonding layer, n metal grain regions with cross-sectional grain sizes greater than 20 μm and different crystal orientations are selected, and metal single crystal microcolumns are prepared using a focused ion beam (FIB). The diameter of the metal single crystal microcolumns is 5 to 10 μm, and the height is 10 to 20 μm, where n is a positive integer;

[0014] (2) Use a micro-indenter to perform compression tests on n metal single crystal micro-pillars. The test process is a quasi-static compression test. The pressing direction is the axial direction of the metal single crystal micro-pillars, and n sets of force-displacement data are obtained.

[0015] (3) Perform preliminary processing on the n sets of force-displacement data to obtain the force-displacement curve data. The processing process is as follows: take the data in the displacement range of 0 to 200 nm, use linear fitting to obtain the test slope of the force-displacement curve .

[0016] Furthermore, in the step 2, a metal single crystal micro-column compression finite element model is established to obtain a finite element simulation result of a micro-column compression force-displacement curve, specifically including:

[0017] (1) Use 3D modeling software to build a geometric model of a metal single crystal microcolumn, i.e., a cylindrical metal single crystal microcolumn, to ensure that the size and shape of the model are consistent with the actual sample;

[0018] (2) Setting the crystal orientation of n metal single crystal micropillars to ensure that the crystal orientation in the model is consistent with the actual metal single crystal micropillars;

[0019] (3) Setting boundary conditions: the bottom surface of the cylindrical metal single crystal microcolumn is fixed, and the top surface moves along the axial compression direction, and the displacement is not less than 50 nm;

[0020] (4) Set an appropriate grid density for meshing, and the grid size should not be larger than 10% of the microcolumn diameter;

[0021] (5) Based on the above finite element model, different elastic constants are set to calculate the compression force-displacement curve results of n metal single crystal micropillars, and the simulation slope of the force-displacement curve is obtained by linear fitting. .

[0022] Furthermore, in step 3, a multi-objective optimization problem of elastic constants of a metal single crystal is set, which specifically includes:

[0023] (1) The objective function of the multi-objective optimization problem of the elastic constants of metal single crystals is set as follows:

[0024] ,

[0025] in, is the metal single crystal elastic constant variable, that is, the variable vector to be optimized, For the The test slope, For the simulation slope;

[0026] (2) Setting the elastic constant parameter range, including setting a reasonable initial range of the elastic constant according to the physical properties of the metal material, and using this as a constraint condition for multi-objective optimization, as follows:

[0027] ,

[0028] in, For the Elastic constant The lower boundary of For the Elastic constant The upper boundary of .

[0029] Furthermore, in step 4, the multi-objective optimization algorithm is used to solve the optimal metal single crystal elastic constants, specifically including:

[0030] (1) Based on the multi-objective optimization problem, refer to the constraints of the multi-objective optimization in step 3 and randomly generate a group of elastic constant solution vectors as the initial population;

[0031] (2) Using the finite element model, simulate the force-displacement curve for each elastic constant solution in the population, calculate the simulation slope, and calculate the objective function value of each solution;

[0032] (3) Based on the objective function value, a multi-objective optimization algorithm is used to perform selection, crossover, and mutation operations to generate a new population;

[0033] (4) Repeat the above (2) and (3) until the preset number of iterations or convergence conditions are reached, and finally the optimal solution is obtained, which is used as the elastic constant of the metal single crystal material for inversion of the micropillar compression test data.

[0034] The beneficial effects of the present invention are as follows: the present invention provides a method for inverting the elastic constants of a metal single crystal micro-column compression test of a chip bonding layer, which can accurately obtain high-resolution and high-precision force-displacement curve data of micro-columns by using micro-column compression test, and can ensure the accuracy of the prediction of the elastic constants of metal single crystals by combining n groups of micro-column compression data of different crystal directions; by establishing an accurate finite element model and setting reasonable boundary conditions, a model basis and simulation support are provided for the inversion calculation of elastic constants; by using a multi-objective optimization algorithm, multi-objective functions can be optimized at the same time, thereby improving the comprehensiveness and accuracy of the inversion results; by combining the force-displacement curve simulation results of the finite element model, the elastic constants of metal single crystal materials that are consistent with the actual micro-column compression test results are inverted to obtain the optimal method for determining the elastic constants of metal single crystals of chip bonding materials. The present method can effectively obtain the force-displacement curve of metal single crystal micro-columns in the compression process, and by combining the finite element model and the multi-objective optimization algorithm, the elastic constants of the material can be accurately inverted, providing a new technical means for testing the mechanical properties of materials in the field of electronic packaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the present invention;

[0036] Figure 2 Schematic diagram of micro-column compression test in an embodiment of the present invention;

[0037] In the figure, 1. Micro-indenter; 2. Micro-column specimen cut by FIB;

[0038] Figure 3 The force-displacement curve and linear fitting diagram of the micro-column compression test of Example No. 1 of the present invention;

[0039] Figure 4 The force-displacement curve and linear fitting diagram of the micro-column compression test of Example No. 2 of the present invention;

[0040] Figure 5 The force-displacement curve and linear fitting diagram of the micro-pillar compression test of Example No. 3 of the present invention;

[0041] Figure 6 Schematic diagram of the micropillar compression finite element geometric model, crystal orientation and boundary conditions in an embodiment of the present invention;

[0042] Figure 7 It is a scatter plot of the multi-objective optimization target and the number of iterations with sequence number 1 in the embodiment of the present invention;

[0043] Figure 8 It is a scatter plot of multi-objective optimization target and iteration number with sequence number 2 in an embodiment of the present invention;

[0044] Fig. 9 This is a scatter plot of the multi-objective optimization target and the number of iterations with sequence number 3 in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0046] like Figure 1 As shown, the elastic constant inversion method of the chip bonding layer metal single crystal micro-pillar compression test comprises the following steps:

[0047] Step 1: Conduct compression tests on metal single crystal micro-pillars in different crystal orientations in the chip bonding layer to obtain the corresponding metal single crystal micro-pillar compression test force-displacement curve data;

[0048] Step 2: Establish a finite element model of metal single crystal micro-column compression, including geometric model establishment, crystal orientation, boundary setting, mesh division, and obtain the finite element simulation results of the micro-column compression force-displacement curve by setting different elastic constants;

[0049] Step 3: Setting the multi-objective optimization problem of elastic constants of metal single crystals, including the determination of the objective function and the range of elastic constant parameters;

[0050] Step 4: Use a multi-objective optimization algorithm to solve the optimal metal single crystal elastic constants, thereby obtaining the metal single crystal material elastic constants inverted from the micro-pillar compression test data.

[0051] Furthermore, the method for obtaining the corresponding force-displacement curve data of the metal single crystal micro-pillar compression test in step 1 includes:

[0052] (1) Based on the electron backscatter diffraction (EBSD) results of the metal cross-section of the chip bonding layer, n metal grain regions with cross-sectional grain sizes greater than 20 μm and different crystal orientations were selected, and metal single crystal microcolumns were prepared using a focused ion beam (FIB). The metal single crystal microcolumns had a diameter of 5 to 10 μm and a height of 10 to 20 μm.

[0053] (2) Use a micro-indenter to perform a compression test on n metal single crystal micro-pillars. The test process is a quasi-static compression test. The pressing direction is the axial direction of the metal single crystal micro-pillar. Obtain n sets of force-displacement data, where n is a positive integer.

[0054] (3) Perform preliminary processing on the n sets of force-displacement data to obtain the force-displacement curve data. The processing process is as follows: take the data in the displacement range of 0 to 200 nm, use linear fitting to obtain the test slope of the force-displacement curve .

[0055] Furthermore, in the step 2, a metal single crystal micro-column compression finite element model is established to obtain a finite element simulation result of a micro-column compression force-displacement curve, specifically including:

[0056] (1) Use 3D modeling software to build a geometric model of a metal single crystal microcolumn, i.e., a cylindrical metal single crystal microcolumn, to ensure that the size and shape of the model are consistent with the actual sample;

[0057] (2) Setting the crystal orientation of n metal single crystal micropillars to ensure that the crystal orientation in the model is consistent with the actual metal single crystal micropillars;

[0058] (3) Setting boundary conditions: the bottom surface of the cylindrical metal single crystal microcolumn is fixed, and the top surface moves along the axial compression direction, and the displacement is not less than 50 nm;

[0059] (4) Set an appropriate grid density for meshing, and the grid size should not be larger than 10% of the microcolumn diameter;

[0060] (5) Based on the above finite element model, different elastic constants are set to calculate the compression force-displacement curve results of n metal single crystal micropillars, and the simulation slope of the force-displacement curve is obtained by linear fitting. .

[0061] Furthermore, in step 3, a multi-objective optimization problem of elastic constants of a metal single crystal is set, which specifically includes:

[0062] (1) The objective function of the multi-objective optimization problem of the elastic constants of metal single crystals is set as follows:

[0063] ,

[0064] in, is the metal single crystal elastic constant variable, that is, the variable vector to be optimized, For the The test slope, For the simulation slope;

[0065] (2) Setting the elastic constant parameter range, including setting a reasonable initial range of the elastic constant according to the physical properties of the metal material, and using this as a constraint condition for multi-objective optimization, as follows:

[0066] ,

[0067] in, For the Elastic constant The lower boundary of For the Elastic constant The upper boundary of .

[0068] Furthermore, in step 4, the multi-objective optimization algorithm is used to solve the optimal metal single crystal elastic constants, specifically including:

[0069] (1) Based on the multi-objective optimization problem, refer to the constraints of the multi-objective optimization in step 3 and randomly generate a group of elastic constant solution vectors as the initial population;

[0070] (2) Using the finite element model, simulate the force-displacement curve for each elastic constant solution in the population, calculate the simulation slope, and calculate the objective function value of each solution;

[0071] (3) Based on the objective function value, a multi-objective optimization algorithm is used to perform selection, crossover, and mutation operations to generate a new population;

[0072] (4) Repeat the above (2) and (3) until the preset number of iterations or convergence conditions are reached, and finally the optimal solution is obtained, which is used as the elastic constant of the metal single crystal material for inversion of the micropillar compression test data.

[0073] In a specific implementation, the chip bonding layer takes sintered copper as an example, and the metal single crystal takes copper single crystal as an example.

[0074] Based on the results of electron backscatter diffraction (EBSD) of the metal cross section of the chip bonding layer, three metal grain regions with cross-sectional grain sizes greater than 20 μm and different crystal orientations were selected, and metal microcolumns were prepared using a focused ion beam (FIB). The schematic diagram is shown in Figure 2 As shown, v is the downward direction of the indenter, 1 is the micro indenter, 2 is the micro-column sample cut out by FIB, and the collected data of micro-column crystal orientation, micro-column diameter d, and micro-column height h are shown in the following table.

[0075]

[0076] A micro-indenter was used to perform compression tests on three copper single crystal micro-pillars. The pressing direction was the axial direction of the metal micro-pillars, and three sets of force-displacement curve data were obtained. The data diagram is shown in Figure 3-5 As shown;

[0077] The three sets of force-displacement curve data were preliminarily processed to obtain the elastic segment data of the force-displacement curve. The displacement data was taken from 0 to 200 nm, and the test slope k of the force-displacement curve was obtained by linear fitting. 1 = 15.027 nm / μN, k 2 = 9.2763 nm / μN, k 3 = 27.496 nm / μN.

[0078] Using the micro-pillar crystal orientation, micro-pillar height and micro-pillar diameter in the above table, the geometric model of three metal single crystal micro-pillars is established using 3D modeling software, and the crystal orientation EA of the three metal single crystals is set. The schematic diagram of micro-pillar No. 1 is shown in Figure 6 As shown in the figure; set the boundary conditions, the bottom surface of the cylinder is fixed, the top surface moves along the axial compression direction, and the displacement is 50 nm; set the appropriate grid density for grid division, and the grid size is 0.5μm; based on the above finite element model, set different elastic constants. Since the copper single crystal is FCC isotropic, the elastic modulus E, Poisson's ratio v, and shear modulus G are taken as the elastic constants to be inverted. In the example, the elastic constant is taken = E, = v, = G, the micro-pillar compression force-displacement curve results of three metal single crystals can be calculated, and the simulation slope of the force-displacement curve can be obtained by linear fitting. .

[0079] The objective function of the multi-objective optimization problem of the elastic constants of metal single crystals is set as follows:

[0080] ,

[0081] in, is the crystal elastic constant variable, that is, the variable vector to be optimized, is the simulation slope of the first microcolumn, is the simulated slope of the second microcolumn, is the simulated slope of the third microcolumn.

[0082] Setting the elastic constant parameter range includes setting a reasonable initial range of the elastic constant according to the physical properties of the metal material, which is used as a constraint condition for multi-objective optimization as follows:

[0083] ,

[0084] The multi-objective optimization algorithm used is NSGA II, which is as follows:

[0085] Based on the multi-objective optimization problem, 30 sets of elastic constant solution vectors are randomly generated with reference to the constraints as the initial population; the finite element model is used to simulate the force-displacement curve of each elastic constant solution in the population, and the simulation slope is calculated, and the objective function value of each solution is calculated; according to the objective function value, a multi-objective optimization algorithm such as NSGA II is used, and the algorithm performs selection, crossover and mutation operations to generate 30 new populations; the above process is repeated until the preset number of iterations or convergence conditions are reached. Here, the number of iterations is set to 30 times. It can be seen that the three objective functions decrease with the increase of the number of iterations, such as Figure 7-9 As shown, the optimal solution is finally obtained, and the final elastic constant is = E = 59337.33 MPa, = v =0.32689, = G = 10175.70, and the absolute values ​​of the slope errors between the corresponding three groups of micro-pillar compression simulations and tests are 0.0172, 0.00386, and 0.0146, respectively, which are used as the elastic constants of the metal single crystal material for the inversion of the micro-pillar compression test data.

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for inverting elastic constants of metal single crystal micro-pillars in a chip bonding layer compression test, characterized in that: The following steps are involved: Step 1: Conduct compression tests on metal single crystal micropillars in different crystal orientations in the chip bonding layer to obtain the corresponding metal single crystal micropillar compression test force-displacement curve data, including: (1) Based on the electron backscatter diffraction results of the metal cross section of the chip bonding layer, n metal grain regions with cross-sectional grain sizes greater than 20 μm and different crystal orientations are selected, and metal single crystal microcolumns are prepared using a focused ion beam, wherein the diameter of the metal single crystal microcolumns is 5 μm to 10 μm, and the height is 10 μm to 20 μm, where n is a positive integer; (2) Using a micro-indenter to perform compression tests on n metal single crystal micro-pillars, the test process is a quasi-static compression test, the pressing direction is the axial direction of the metal single crystal micro-pillar, and n sets of force-displacement data are obtained; (3) Perform preliminary processing on the n sets of force-displacement data to obtain force-displacement curve data. The processing process is as follows: take the displacement range of 0 to 200 nm, use linear fitting to obtain the force-displacement curve test slopes k1, ..., k i , ..., k n ; Step 2: Establish a finite element model of metal single crystal micro-column compression, including geometric model establishment, crystal orientation, boundary setting, mesh division, and obtain the finite element simulation results of the micro-column compression force-displacement curve by setting different elastic constants, including: (1) Use 3D modeling software to establish a geometric model of a metal single crystal microcolumn, i.e., a cylindrical metal single crystal microcolumn, to ensure that the size and shape of the model are consistent with the actual sample; (2) Setting the crystal orientation of n metal single crystal micropillars to ensure that the crystal orientation in the model is consistent with the actual metal single crystal micropillars; (3) Setting boundary conditions: the bottom surface of the cylindrical metal single crystal microcolumn is fixed, and the top surface moves along the axial compression direction, and the displacement is not less than 50 nm; (4) Setting an appropriate grid density for grid division, where the grid size is no larger than 10 percent of the diameter of the metal single crystal microcolumn; (5) Based on the above finite element model, different elastic constants are set to calculate the compression force-displacement curve results of n metal single crystal micropillars, and the simulation slopes of the force-displacement curves k'1, ..., k' are obtained by linear fitting. i , ..., k' n ; Step 3: Set the multi-objective optimization problem of the elastic constants of metal single crystals, including the determination of the objective function and the range of elastic constant parameters, specifically including: (1) The objective function of the multi-objective optimization problem of the elastic constants of metal single crystals is set as follows: Where x=(x1,x2,...,x m ) is the metal single crystal elastic constant variable, that is, the variable vector to be optimized, k i is the slope of the ith trial, k' i is the ith simulation slope; (2) Setting the elastic constant parameter range, including setting a reasonable initial range of the elastic constant according to the physical properties of the metal material, and using this as a constraint condition for multi-objective optimization, as follows: l1≤x1≤u1 l2≤x2≤u2 … l i ≤x i ≤u i … l m ≤x m ≤u m , Among them, l i is the i-th elastic constant x i The lower boundary of u i is the i-th elastic constant x i The upper boundary of Step 4: Use a multi-objective optimization algorithm to solve the optimal metal single crystal elastic constants, thereby obtaining the metal single crystal material elastic constants inverted from the micro-pillar compression test data.

2. The chip bonding layer metal single crystal micro-pillar compression test elastic constant inversion method according to claim 1, characterized in that: In the step 4, a multi-objective optimization algorithm is used to solve the optimal metal single crystal elastic constant, which specifically includes: (1) Based on the multi-objective optimization problem, referring to the constraints of the multi-objective optimization in step 3, a group of elastic constant solution vectors are randomly generated as the initial population; (2) Using the finite element model, simulate the force-displacement curve for each elastic constant solution in the population, calculate the simulation slope, and calculate the objective function value of each solution; (3) Based on the objective function value, a multi-objective optimization algorithm is used to perform selection, crossover, and mutation operations to generate a new population; (4) Repeat the above (2) and (3) until the preset number of iterations or convergence conditions are reached, and finally the optimal solution is obtained, which is used as the elastic constant of the metal single crystal material for inversion of the micro-pillar compression test data.

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