Method for predicting and evaluating electromigration lifetime of low temperature interconnect sn-bi based alloy micro-joint and application

Abstract

The application provides a low-temperature interconnection Sn-Bi-based alloy micro-welding spot electromigration life prediction and evaluation method and application, and relates to the reliability evaluation field of advanced electronic packaging micro-welding spots. Based on the physical mechanism of electromigration failure, starting from the electronic wind-driven Bi atom directional migration theory, the correlation between atomic diffusion flux and beta-Sn / Bi two-phase separation, anode Bi layer growth and resistance evolution is revealed, the cross-scale systematic correlation of "microscopic atomic migration (Bi atom migration)-mesoscopic organization evolution (beta-Sn / Bi two-phase separation, anode Bi phase precipitation)-macroscopic weld failure (resistance growth)" is realized, the microstructure evolution of the Sn-Bi-based alloy micro-welding spot in the electromigration process is quantified, has reliable physical mechanism support, significantly reduces the parameter calibration workload (compared with the current electromigration life prediction commonly used empirical formula Black equation, reduces by 80%), and the prediction accuracy can reach more than 90%.

Description

Technical Field

[0001] This invention relates to the field of reliability evaluation of microscale solder joints in advanced electronic packaging, and more specifically, to a method and application for predicting and evaluating the electromigration lifetime of Sn-Bi-based alloy micro-solder joints for low-temperature interconnection. Background Technology

[0002] As electronic packaging technology continues to advance towards miniaturization and high performance, the size of interconnect solder joints is decreasing dramatically while the power density they carry is constantly increasing. Under the trend of miniaturization, the size of interconnect solder joints is gradually decreasing: the diameter of ball grid array (BGA) solder balls has decreased from 760 μm to 250 μm, flip chip interconnect solder joints have decreased to only 80–100 μm in diameter, and further to copper pillar bumps with diameters of only a few micrometers. With miniaturization, a reduction of one order of magnitude in solder joint diameter leads to a two-order-of-magnitude increase in current density through the solder joint; simultaneously, with the trend towards high performance, the power density carried by interconnect solder joints is significantly increased. Therefore, the electromigration (EM) reliability of micro-solder joints in advanced packaging technologies faces severe challenges.

[0003] Low-temperature soldering technology (<200℃) has attracted much attention in recent years in the fields of large-size chip packaging and consumer electronics due to its significant advantages such as reduced thermal stress, reduced substrate warpage, improved assembly yield, and energy saving and environmental protection. Currently, Sn-Bi-based lead-free solders (melting point 138–190℃) are the preferred material due to their lower melting point compared to traditional Sn-3Ag-0.5Cu (SAC305, melting point 217℃). However, the lower melting point of Sn-Bi-based solders leads to a significantly enhanced thermal activation effect at service temperatures, resulting in a substantial increase in the diffusion rate of metal atoms. Therefore, compared to traditional SAC305 alloy micro-solder joints, low-temperature Sn-Bi-based alloy micro-solder joints face a more severe challenge in terms of electromigration reliability during long-term service.

[0004] Unlike the traditional SAC305 alloy micro-solder joint electromigration failure mode characterized by cathode substrate dissolution and void / crack formation, the electromigration process of low-temperature Sn-58Bi eutectic alloy micro-solder joints exhibits the following characteristics: Bi atoms migrate directionally towards the anode under the influence of electron wind, leading to the separation of the β-Sn and Bi phases and the formation of a Bi-rich layer at the anode of the solder joint. Since the resistivity of the Bi-rich layer (1.290 μΩ·m) is significantly higher than that of eutectic Sn-58Bi solder (0.383 μΩ·m) and pure Sn (0.110 μΩ·m), the phase separation caused by electromigration and the thickening of the Bi-rich layer at the anode will increase the resistance of the micro-solder joint, ultimately leading to electromigration failure.

[0005] Currently, the Black equation is commonly used to assess the electromigration lifetime of micro-solder joints. This equation is used to predict the mean time to failure due to electromigration under accelerated experimental conditions.

[0006]

[0007] Where A is a material factor related to the conductivity of the material, such as density, resistivity, grain size, grain size distribution, ion mass, and geometry; n is the current density exponent; E a The activation energy (usually related to the diffusion path of metal atoms) is used. Researchers typically design five sets of electromigration experiments ("3j3T") (i.e., three current densities j and three electromigration temperatures T) to fit and calculate parameters n and E. a And A, to establish the corresponding electromigration lifetime prediction equation. The Black equation was originally used for predicting the electromigration lifetime of interconnect wires such as Al and Cu, and only considered the diffusion behavior of a single atom in the elemental metal. However, the electromigration process of Sn-Bi based alloy micro solder joints needs to comprehensively consider complex behaviors such as β-Sn / Bi two-phase separation, directional migration of Bi atoms, and the growth and thickening of the Bi-rich layer on the anode side. Therefore, the application of the Black equation in the electromigration lifetime of Sn-Bi based alloy micro solder joints lacks a reliable theoretical basis and is currently only used as an empirical formula for researchers' reference.

[0008] In summary, on the one hand, the Black equation, based on the diffusion behavior of a single atom, is difficult to use to evaluate the electromigration failure mode of Sn-Bi-based alloy micro-solder joints dominated by the "two-phase separation" phenomenon; on the other hand, the existing empirical formula Black equation requires at least five sets of electromigration experiments, each requiring a large number of electromigration experimental samples to statistically obtain the characteristic lifetime under those conditions, which is then used to fit the key parameters in the Black equation. This method suffers from problems such as lengthy experimental cycles and huge workloads. Therefore, there is an urgent need to develop an electromigration lifetime prediction model for Sn-Bi-based alloy micro-solder joints that is based on the physical nature of electromigration and requires less workload. Summary of the Invention

[0009] In view of the shortcomings of existing technologies, this invention provides a method and application for predicting and evaluating the electromigration lifetime of Sn-Bi-based alloy micro-solder joints at low temperatures. Based on the physical mechanism of electromigration failure in Sn-Bi-based alloy micro-solder joints, this invention starts from the theory of electron wind-driven directional migration of Bi atoms. By revealing the intrinsic relationship between atomic diffusion flux and the separation process of the β-Sn / Bi two-phase, the growth kinetics of the anodic Bi-rich layer, and the evolution of solder joint resistance during electromigration, it achieves a cross-scale systematic correlation of "microscopic atomic migration (Bi atom migration) - mesoscopic microstructure evolution (β-Sn / Bi two-phase separation, anodic Bi phase precipitation) - macroscopic solder joint failure (resistance growth)". Furthermore, this model significantly reduces the workload required for parameter calibration (by 80% compared to the commonly used empirical formula Black equation for electromigration lifetime prediction), and the prediction accuracy can reach over 90%.

[0010] The technical means employed in this invention are as follows:

[0011] A method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro solder joints, characterized by comprising the following steps:

[0012] Obtain the parameters of Sn-Bi based alloy micro-weld joints; obtain the experimental conditions and time intervals for electromigration;

[0013] The directional migration of Bi atoms with electron wind during the simulated electromigration process was used to construct the first differential equation characterizing the relationship between the thickness of the Bi-rich layer in the prototype theoretical anode and the diffusion flux of Bi atoms.

[0014] The theoretical growth rate of the Bi-rich anode layer in the early stage of electromigration is solved based on the first differential equation.

[0015] Electromigration experiments were conducted on Sn-Bi based alloy micro solder joints under electromigration experimental conditions to obtain the actual growth rate of the anodic Bi-rich layer in the early stage of electromigration.

[0016] The growth correction factor is determined based on the theoretical growth rate and the actual growth rate of the anolyte Bi-rich layer in the early stage of electromigration.

[0017] The first differential equation is modified based on the growth correction factor, thereby obtaining the second differential equation characterizing the relationship between the thickness of the Bi-rich layer in the prototype theoretical anode and the diffusion flux of Bi atoms.

[0018] Substituting the electromigration time interval into the second differential equation, we obtain a numerical solution for the Bi-rich layer thickness.

[0019] A solder joint structure model of Sn-xBi alloy and Bi-rich layer in series was constructed. Based on the solder joint parameters and the thickness of the Bi-rich layer, a third differential equation was established to characterize the relationship between the resistance change rate of Sn-Bi based alloy micro solder joint and the thickness of the Bi-rich layer.

[0020] Obtain the solder joint resistance change rate criterion for determining electromigration failure, substitute the solder joint resistance change rate criterion into the third differential equation, and solve to obtain the electromigration lifetime of Sn-Bi based alloy micro solder joints.

[0021] Furthermore, the first differential equation is:

[0022]

[0023] Where T(t) is the thickness of the Bi-rich anode layer, J total M represents the total diffusion flux of Bi atoms during electromigration, t represents the electromigration time, and M represents the total diffusion flux of Bi atoms during electromigration. Bi ρ is the molar mass of Bi atoms. Bi Let be the density of Bi.

[0024] Furthermore, the second differential equation is:

[0025]

[0026] Among them, z f The growth correction factor is calculated using the following formula:

[0027]

[0028] Where k1 is the theoretical growth rate of the anodic Bi-rich layer in the early stage of electromigration, and k2 is the actual growth rate of the anodic Bi-rich layer in the early stage of electromigration.

[0029] Furthermore, the third differential equation is:

[0030]

[0031] Where τ(t) is the resistance change rate of the Sn-Bi based alloy micro-solder joint, x(t) represents the function value of the composition x in the Sn-xBi alloy as a function of time, β(x(t)) is the function value of the resistivity as a function of x(t), L is the solder thickness, and β Bi Let D be the resistivity of Bi, D be the atomic diffusion coefficient of Bi, and Z be the resistivity of Bi. * Where is the effective charge number of Bi atoms, e is the unit charge, j is the current density, k is the Boltzmann constant, and T is the effective charge number of Bi atoms. c ρ is the electromigration temperature. Bi For the density of Bi, β solder The initial resistivity of the Sn-Bi based alloy.

[0032] Furthermore, the formula for calculating the total diffusion flux of Bi atoms during electromigration is as follows:

[0033] J total =z J ×JEM

[0034] Where z J J is the diffusion flux correction factor. EM The electromigration diffusion flux can be expressed as:

[0035]

[0036] Where ρ(x(t)) is the density of the Sn-xBi alloy, M Bi The molar mass of Bi atoms Z is the diffusion coefficient of Bi atoms in Sn-xBi alloy. * Let be the effective charge number of Bi atoms, e be the unit charge, j be the current density, β(x(t)) be the resistivity as a function of x(t), k be the Boltzmann constant, and T be the effective charge number of Bi atoms. c This is the electromigration temperature.

[0037] Furthermore, the formula for calculating the density of the Sn-xBi alloy is:

[0038]

[0039] Where, ρ Sn Let Sn be the density.

[0040] Furthermore, the early stage of electromigration is the first 100 hours of electromigration.

[0041] Furthermore, the Sn-Bi-based alloy micro solder joint parameters include the micro solder joint type and the micro solder joint size; the micro solder joint type includes at least one of linear solder joints, ball grid arrays, flip chip interconnect solder joints, and copper pillar bumps; the micro solder joint size includes the length, width, height, solder joint diameter, pad diameter, and solder joint curvature of the micro solder joint.

[0042] Furthermore, the Sn-Bi-based solder alloy has a Bi atomic mass percentage of 20.0 wt.% to 58.0 wt.%, and contains trace elements Ag, Sb, In, Cu, Ni, Co, and Fe, with each trace element content ranging from 0 wt.% to 2.0 wt.%.

[0043] This invention also discloses the application of the method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro solder joints described in any one of the above-mentioned methods in the reliability evaluation of micro solder joints in electronic packaging.

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] 1. The low-temperature Sn-Bi-based alloy micro-weld joint electromigration lifetime prediction and evaluation method provided by this invention has reliable mechanistic support. The existing electromigration evaluation model, the Black equation, was originally an empirical formula for predicting the electromigration lifetime of single-element conductors. For the case of two-phase separation, it originally assumed constant material constants A and activation energy E during the electromigration process. a Parameters such as the current density exponent n are dynamically changing. This invention, by analyzing the intrinsic correlation between Bi atom diffusion flux and Bi-rich layer growth kinetics, resistivity evolution, and anodic segregation behavior, achieves a cross-scale systematic correlation of "microscopic atom migration (Bi atom migration) - mesoscopic structure evolution (β-Sn / Bi two-phase separation, anodic Bi phase precipitation) - macroscopic solder joint failure (resistivity growth)," which has reliable mechanistic support.

[0046] 2. The low-temperature Sn-Bi-based alloy micro-weld joint electromigration lifetime prediction and evaluation method provided by this invention reduces the workload required for parameter calibration. Existing electromigration evaluation models, such as the Black equation, require at least five sets of "3j3T" electromigration experiments. Each set of experiments requires a large number of samples to obtain the characteristic lifetime under those conditions, which is ultimately used to fit the key parameters n and E in the Black equation. a And A, to establish the corresponding electromigration lifetime prediction equation, the testing cycle is long and the workload is huge. This invention only needs to complete a set of "1j1T" electromigration experiments to fit and calculate the total correction factor z. f One parameter reduces parameter calibration workload by 80%.

[0047] 3. The prediction and evaluation method for the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro solder joints provided by this invention can achieve a prediction accuracy of over 90%. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of a method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro solder joints according to an embodiment of the present invention.

[0050] Figure 2 This is a schematic diagram of the diffusion flux of each atom within the Sn-Bi-based alloy micro-solder joint during the electromigration process according to an embodiment of the present invention.

[0051] Figure 3This is an embodiment of the present invention that requires inputting the relationship between the resistivity of the Sn-xBi alloy and the composition x.

[0052] Figure 4 This invention provides an embodiment of the theoretical thickness of the prototype Bi-rich anode layer obtained through calculation.

[0053] Figure 5 This invention provides an embodiment of the microstructure evolution of micro-solder joints during the early stage (first 100 hours) of electromigration, obtained through experiments. (a) represents the cathode microstructure at 20 hours; (b) represents the anode microstructure at 20 hours; (c) represents the cathode microstructure at 40 hours; (d) represents the anode microstructure at 40 hours; (e) represents the cathode microstructure at 60 hours; (f) represents the anode microstructure at 60 hours; (g) represents the cathode microstructure at 80 hours; (h) represents the anode microstructure at 80 hours; (i) represents the cathode microstructure at 100 hours; and (j) represents the anode microstructure at 100 hours.

[0054] Figure 6 This invention relates to an embodiment of the invention that experimentally obtained the growth kinetics of the anolyte Bi-rich layer in the early stage (first 100 hours) of electromigration.

[0055] Figure 7 One embodiment of the present invention obtains the thickness of the Bi-rich anode layer by calculation.

[0056] Figure 8 One embodiment of the present invention obtains the rate of change of solder joint resistance by calculation. Detailed Implementation

[0057] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0058] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0059] like Figure 1 As shown, this invention provides a method for predicting and evaluating the electromigration lifetime of Sn-Bi-based alloy micro-solder joints for low-temperature interconnection, comprising the following steps:

[0060] S1. Obtain the parameters of the Sn-Bi based alloy micro-weld joints; obtain the experimental conditions and time intervals for electromigration.

[0061] The solder joint parameters include solder joint type and solder joint assembly size. Optionally, the micro solder joint type includes at least one of linear solder joints, ball grid arrays, flip-chip interconnect solder joints, and copper pillar bumps. Optionally, the micro solder joint geometry includes the length, width, height, solder joint diameter, pad diameter, and solder joint curvature—geometric parameters necessary for constructing the geometric model. Optionally, the low-temperature Sn-Bi-based solder alloy composition includes Bi atomic mass percentages ranging from 20.0 wt.% to 58.0 wt.%. The low-temperature Sn-Bi-based solder alloy composition includes trace elements Ag, Sb, In, Cu, Ni, Co, and Fe, with each trace element content ranging from 0 wt.% to 2.0 wt.%.

[0062] Furthermore, the experimental conditions for electromigration include current density and electromigration temperature.

[0063] S2. Simulating the directional migration of Bi atoms along with the electron wind during electromigration, a first differential equation is constructed to characterize the relationship between the thickness of the Bi-rich layer at the anode and the diffusion flux of Bi atoms in the prototype theory. The first differential equation is:

[0064]

[0065] Where T(t) is the thickness of the Bi-rich anode layer, J total M represents the total diffusion flux of Bi atoms during electromigration, t represents the electromigration time, and M represents the total diffusion flux of Bi atoms during electromigration. Bi ρ is the relative atomic mass of Bi. Bi Let be the density of Bi.

[0066] S3. Solve the theoretical growth rate of the Bi-rich layer in the anode during the early stage of electromigration based on the first differential equation.

[0067] The differential equations were solved within a predetermined electromigration time interval to obtain the relationship between the theoretical thickness of the prototype Bi-rich anode layer and time. The theoretical thickness of the prototype Bi-rich anode layer in the early stage of electromigration (first 100 hours) was extracted, and the growth rate k1 of the early stage of electromigration Bi-rich anode layer was obtained by linear fitting.

[0068] S4. Electromigration experiments were conducted on Sn-Bi based alloy micro-solder joints under electromigration experimental conditions to obtain the actual growth rate of the anodic Bi-rich layer in the early stage of electromigration.

[0069] Experiments on the early stage of electromigration were carried out under defined experimental conditions. Through microstructural characterization, the actual growth rate k2 of the anodic Bi-rich layer in the early stage of electromigration was determined and fitted.

[0070] S5. The growth correction factor is determined based on the theoretical growth rate of the anolyte Bi-rich layer in the early stage of electromigration and the actual growth rate of the anolyte Bi-rich layer in the early stage of electromigration. The formula for calculating the growth correction factor is shown below.

[0071]

[0072] S6. Based on the growth correction factor, the first differential equation is modified to obtain the second differential equation characterizing the relationship between the thickness of the Bi-rich layer at the anode and the diffusion flux of Bi atoms in the prototype theory. The second differential equation is shown below.

[0073]

[0074] Among them, the total diffusion flux of Bi atoms during electromigration J total It can be represented as:

[0075] J total =J EM +J bm +J tm +J chem =z J ×J EM

[0076] J bm For the back stress gradient flux, J tm For temperature gradient flux, J chem Let z be the chemical potential gradient flux. J J is the diffusion flux correction factor. EM The electromigration diffusion flux can be expressed as:

[0077]

[0078] Where ρ(x(t)) is the density of the Sn-xBi alloy, M Bi The molar mass of Bi atoms Z is the diffusion coefficient of Bi atoms in Sn-xBi alloy. * denoted as Bi atom effective charge number, e as unit charge, j as current density (actual current density defined according to solder joint structure), β(x(t)) as resistivity as a function of x(t), k as Boltzmann constant, and T. c The electromigration temperature is calculated based on the JEDEC test standard JEP154A to obtain the actual electromigration temperature of the solder joint.

[0079] ρ(x(t)) can be expressed as:

[0080]

[0081] Where ρ Sn Let ρ be the density of Sn. Bi The density of Bi;

[0082] The diffusion coefficient of Bi atoms in the Sn-xBi alloy is characterized by... It can be represented as:

[0083]

[0084] in Let z be the diffusion coefficient of Bi atoms in pure Sn. D Diffusion coefficient correction factor. D It is difficult to obtain through calculation, but it can be eliminated in the subsequent equation simplification steps, and z can be obtained by inverse calculation through experimental fitting. f The value of can be used to perform the calculation according to the method of this application.

[0085] The resistivity β(x(t)) of Sn-xBi alloy is constructed by combining "cellular automata" and "Monte Carlo random numbers". The cellular elements in the Sn-Bi-based solder microstructure model matrix are similar to the elements in the finite element model. Furthermore, the direct conversion of the cellular automata model matrix (matrix cells 0 / 1 are mapped to β-Sn / Bi phase respectively) to Ansys Workbench is realized by APDL script, and the mapping relationship of "composition x-resistivity β(x(t))" is obtained by interpolation.

[0086] S7. Substitute the electromigration time interval into the second differential equation to obtain a numerical solution for the Bi-rich layer thickness.

[0087] S8. Construct a solder joint structure model of Sn-xBi alloy and Bi-rich layer in series, and establish a third differential equation characterizing the relationship between the solder joint resistance change rate of Sn-Bi based solder and the Bi-rich layer thickness based on solder joint parameters and Bi-rich layer thickness.

[0088] Simplifying the solder joint to a series structure of Sn-xBi alloy and Bi-rich layer, the resistance change rate of the Sn-Bi based solder joint can be expressed as:

[0089]

[0090] Where τ(t) is the rate of change of the solder joint resistance of the Sn-Bi based solder, R x (t) represents the resistance value of the Sn-xBi alloy, R Bi (t) represents the resistance value of the Bi-rich layer on the anode, and R0 represents the initial resistance value of the solder joint. Where R... x (t) can be represented as:

[0091]

[0092] Where β(x(t)) is the resistivity as a function of x(t), L is the solder thickness of the solder joint, and S is the cross-sectional area of ​​the solder joint.

[0093]

[0094] Where β Bi Let R0 be the resistivity of Bi.

[0095]

[0096] Where β solder Initial resistivity of Sn-Bi solder alloy.

[0097] The third differential equation is obtained by rearranging the equations as shown below.

[0098]

[0099] S9. Obtain the solder joint resistance change rate criterion for determining electromigration failure, substitute the solder joint resistance change rate criterion into the third differential equation, and solve to obtain the electromigration lifetime of Sn-Bi based solder joint.

[0100] The criterion for electromigration failure is the increase in solder joint resistance by t. fc (Growth percentage) is calculated using the following formula to obtain the electromigration lifetime of Sn-Bi based solder joints.

[0101] MTTF = τ -1 (t fc )

[0102] The present invention also provides an application of the method for predicting and evaluating the electromigration lifetime of Sn-Bi-based alloy micro solder joints for low-temperature interconnection as described in any of the above claims in the reliability evaluation of microscale solder joints in advanced electronic packaging.

[0103] The following specific embodiments further illustrate the solution and effects of the present invention.

[0104] Example 1

[0105] This embodiment describes a low-temperature Sn-58Bi linear solder joint with a predicted cross-sectional size of 300μm × 300μm and a solder thickness of 600μm, at a temperature of 90℃ and a current density of 1.0 × 10⁻⁶. 4 A / cm 2 Under electromigration conditions, the failure criterion is set as the electromigration lifetime when the solder joint resistance increases by 10%.

[0106] The flowchart of the method for electromigration lifetime of Sn-Bi based solder interconnect micro solder joints is as follows: Figure 1 As shown, the electromigration lifetime prediction method of this embodiment includes the following steps.

[0107] (1) Input the parameters and electromigration conditions of the Sn-58Bi solder linear solder joint sample: length 600μm, width 300μm, height 300μm, current density 1.0×10 4 A / cm 2 The temperature is 90℃.

[0108] (2) Figure 2 This diagram illustrates the atomic diffusion flux and microstructure evolution within a linear Sn-58Bi solder joint during electromigration. The growth of the Bi-rich phase at the anode during electromigration is controlled by four atomic diffusion fluxes: electromigration diffusion flux (J... EM ), concentration gradient flux (J) chem Temperature gradient flux (J) tm ) and back stress gradient flux (J bm ), where J chem J tm and J bm With J EM The directions are opposite. During electromigration, the microstructure of the solder joint can be simplified to a series structure of the Sn-xBi alloy and the anolyte Bi layer. Input the required relationships between the Sn-xBi alloy density and resistivity as a function of composition x, where the Sn-xBi alloy resistivity as a function of composition x is as follows: Figure 3 As shown.

[0109] (3) Establish the differential equation relating the pre-defined growth rate of the Bi-rich anode layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h. The results are as follows: Figure 4 As shown.

[0110] (4) The growth rate of the anolyte Bi-rich layer in the early stage of electromigration (first 100h) was extracted as k1 = 0.047 μm / h. The evolution of the microstructure of the micro-solder joints in the early stage of electromigration was analyzed (e.g., Figure 5 As shown), the actual growth rate of the Bi-rich anode layer in the early stage (first 100h) of electromigration obtained by fitting is k2 = 0.113 μm / h (as shown). Figure 6 (As shown), the total correction factor z is calculated. f =2.40.

[0111] (5) Construct the differential equation relating the growth rate of the anolyte Bi-rich layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h. The results are as follows: Figure 7 As shown.

[0112] (6) Calculate the resistance values ​​of Sn-xBi alloy and Bi-rich layer, and solve for the resistance change rate of solder joint. The results are as follows Figure 8 As shown;

[0113] (7) Input the resistance change rate of 10% into the relationship between the resistance change rate of the solder joint and time to obtain the corresponding solder joint electromigration life of 281h.

[0114] (8) Based on the experiment, the average electromigration lifetime of the solder joint under the same conditions was 294h, and the prediction accuracy reached 95.6%.

[0115] Example 2

[0116] This embodiment describes a low-temperature Sn-47Bi linear solder joint with a predicted cross-sectional size of 300μm × 300μm and a solder thickness of 200μm, at a temperature of 100℃ and a current density of 0.75 × 10⁻⁶. 4 A / cm 2 Under electromigration conditions, the failure criterion is set as the electromigration lifetime when the solder joint resistance increases by 20%.

[0117] The electromigration lifetime prediction method in this embodiment includes the following steps.

[0118] (1) Input the parameters and electromigration conditions of the Sn-47Bi solder linear solder joint sample: length 200μm, width 300μm, height 300μm, current density 0.75×10 4 A / cm 2 The temperature is 100℃.

[0119] (2) Construct a microstructure evolution model of the linear solder joint of Sn-47Bi solder during electromigration; input the relationship between the density and resistivity of Sn-xBi alloy and the composition x required for calculation.

[0120] (3) Establish the differential equation relating the pre-defined growth rate of the Bi-rich anode layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0121] (4) The growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration was extracted as k1 = 0.037 μm / h. Compared with the growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration obtained by fitting the actual electromigration experiment as k2 = 0.110 μm / h, the total correction factor z was calculated. f =2.97.

[0122] (5) Construct the differential equation relating the growth rate of the anolyte Bi-rich layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0123] (6) Calculate the resistance values ​​of Sn-xBi alloy and Bi-rich layer, and solve for the resistance change rate of solder joint.

[0124] (7) Input the resistance change rate of 20% into the relationship between the resistance change rate of the solder joint and time to obtain the corresponding solder joint electromigration life of 729h.

[0125] (8) Based on the experiment, the average electromigration lifetime of the solder joint under the same conditions was 693h, and the prediction accuracy reached 94.8%.

[0126] Example 3

[0127] This example demonstrates the application of low-temperature Sn-57Bi-1Ag solder for BGA solder joints with a predicted solder ball diameter of 250μm at a temperature of 70℃ and a nominal current density of 1.0×10⁻⁶. 4 A / cm 2 Under electromigration conditions, the failure criterion is set as the electromigration lifetime when the solder joint resistance increases by 30%.

[0128] The electromigration lifetime prediction method in this embodiment includes the following steps.

[0129] (1) Input the parameters and electromigration conditions of the Sn-57Bi-1Ag solder BGA solder joint sample: solder ball height 250μm, pad opening diameter 250μm. The maximum actual current density at the solder joint current inlet was obtained through numerical simulation as 3.9×10 4 A / cm 2 The electromigration temperature is 70℃.

[0130] (2) Construct a microstructure evolution model of Sn-57Bi-1Ag solder BGA solder joint during electromigration; input the relationship between Sn-xBi alloy density and resistivity as a function of composition x.

[0131] (3) Establish the differential equation relating the pre-defined growth rate of the Bi-rich anode layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0132] (4) The growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration was extracted as k1 = 0.023 μm / h. Compared with the growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration obtained by fitting the actual electromigration experiment as k2 = 0.106 μm / h, the total correction factor z was calculated. f =4.61.

[0133] (5) Construct the differential equation relating the growth rate of the anolyte Bi-rich layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0134] (6) Calculate the resistance values ​​of Sn-xBi alloy and Bi-rich layer, and solve for the resistance change rate of solder joint.

[0135] (7) Input the resistance change rate of 30% into the relationship between the resistance change rate of the solder joint and time to obtain the corresponding solder joint electromigration life of 1272h.

[0136] (8) Based on the experiment, the average electromigration lifetime of the solder joint under the same conditions was 1194h, and the prediction accuracy reached 93.5%.

[0137] Example 4

[0138] This example demonstrates the application of low-temperature Sn-40Bi-0.5Cu-0.05Ni solder for BGA solder joints with a predicted solder ball diameter of 600μm at a temperature of 100℃ and a nominal current density of 0.75×10⁻⁶. 4 A / cm 2Under electromigration conditions, the failure criterion is set as the electromigration lifetime when the solder joint resistance increases by 10%.

[0139] The electromigration lifetime prediction method in this embodiment includes the following steps.

[0140] (1) Input the parameters and electromigration conditions of the Sn-40Bi-0.5Cu-0.05Ni solder BGA solder joint sample: solder ball height 500μm, pad opening diameter 400μm. The maximum actual current density at the solder joint current inlet was obtained through numerical simulation as 2.9×10 4 A / cm 2 The electromigration temperature is 100℃.

[0141] (2) Construct a microstructure evolution model of Sn-40Bi-0.5Cu-0.05Ni solder BGA solder joint during electromigration; input the relationship between Sn-xBi alloy density and resistivity as a function of composition x.

[0142] (3) Establish the differential equation relating the pre-defined growth rate of the Bi-rich anode layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0143] (4) The growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration was extracted as k1 = 0.031 μm / h. Compared with the growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration obtained by fitting the actual electromigration experiment as k2 = 0.108 μm / h, the total correction factor z was calculated. f =3.48.

[0144] (5) Construct the differential equation relating the growth rate of the anolyte Bi-rich layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0145] (6) Calculate the resistance values ​​of Sn-xBi alloy and Bi-rich layer, and solve for the resistance change rate of solder joint.

[0146] (7) Input the resistance change rate of 10% into the relationship between the resistance change rate of the solder joint and time to obtain the corresponding solder joint electromigration life of 791h.

[0147] (8) Based on the experiment, the average electromigration lifetime of the solder joint under the same conditions was 819h, and the prediction accuracy reached 96.6%.

[0148] Example 5

[0149] This embodiment demonstrates the application of low-temperature Sn-40Bi-0.5Cu-0.05Ni solder for flip-chip interconnects with a predicted solder ball diameter of 80μm at a temperature of 80℃ and a nominal current density of 0.75×10⁻⁶. 4 A / cm 2 Under electromigration conditions, the failure criterion is set as the electromigration lifetime when the solder joint resistance increases by 20%.

[0150] The electromigration lifetime prediction method in this embodiment includes the following steps.

[0151] (1) Input the solder joint parameters and electromigration conditions for the Sn-40Bi-0.5Cu-0.05Ni flip-chip interconnect: solder ball height 60μm, pad opening diameter 60μm. The maximum actual current density at the solder joint current inlet was obtained through numerical simulation as 2.2×10 4 A / cm 2 The electromigration temperature is 80℃.

[0152] (2) Construct a microstructure evolution model of Sn-40Bi-0.5Cu-0.05Ni solder flip chip interconnect solder joint during electromigration; input the relationship between Sn-xBi alloy density and resistivity as a function of composition x.

[0153] (3) Establish the differential equation relating the pre-defined growth rate of the Bi-rich anode layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0154] (4) The growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration was extracted as k1 = 0.012 μm / h. Compared with the growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration obtained by fitting the actual electromigration experiment as k2 = 0.069 μm / h, the total correction factor z was calculated. f =5.75.

[0155] (5) Construct the differential equation relating the growth rate of the anolyte Bi-rich layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0156] (6) Calculate the resistance values ​​of Sn-xBi alloy and Bi-rich layer, and solve for the resistance change rate of solder joint.

[0157] (7) Input the resistance change rate of 20% into the relationship between the resistance change rate of the solder joint and time to obtain the corresponding solder joint electromigration life of 1393h.

[0158] (8) Based on the experiment, the average electromigration lifetime of the solder joint under the same conditions was 1523h, and the prediction accuracy reached 91.5%.

[0159] Example 6

[0160] This embodiment describes the application of low-temperature Sn-42Bi-1Sb solder for flip-chip interconnects with a predicted solder ball diameter of 100μm at a temperature of 100℃ and a nominal current density of 1.5×10⁻⁶. 4 A / cm 2 Under electromigration conditions, the failure criterion is set as the electromigration lifetime when the solder joint resistance increases by 30%.

[0161] The electromigration lifetime prediction method in this embodiment includes the following steps.

[0162] (1) Input Sn-42Bi-1Sb solder flip-chip interconnect solder joint parameters and electromigration conditions: solder ball height 80μm, pad opening diameter 60μm. The maximum actual current density at the solder joint current inlet is obtained as 4.2×10 through numerical simulation. 4 A / cm 2 The electromigration temperature is 100℃.

[0163] (2) Construct a microstructure evolution model of Sn-42Bi-1Sb solder flip chip interconnect solder joint during electromigration; input the relationship function of Sn-xBi alloy density and resistivity as a function of composition x required for calculation.

[0164] (3) Establish the differential equation relating the pre-defined growth rate of the Bi-rich anode layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0165] (4) The growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration was extracted as k1 = 0.018 μm / h. Compared with the growth rate of the Bi-rich layer on the anode in the early stage (first 100h) of electromigration obtained by fitting the actual electromigration experiment as k2 = 0.089 μm / h, the total correction factor z was calculated. f =4.94.

[0166] (5) Construct the differential equation relating the growth rate of the anolyte Bi-rich layer to the diffusion flux of Bi atoms. Numerical solutions were obtained for the variation of the Bi-rich layer thickness of the anode with electromigration time within a preset electromigration time of 6000 h.

[0167] (6) Calculate the resistance values ​​of Sn-xBi alloy and Bi-rich layer, and solve for the resistance change rate of solder joint.

[0168] (7) Input the resistance change rate of 10% into the relationship between the resistance change rate of the solder joint and time to obtain the corresponding solder joint electromigration life of 1430h.

[0169] (8) Based on the experiment, the average electromigration lifetime of the solder joint under the same conditions was 1329h, and the prediction accuracy reached 92.4%.

[0170] Comparative Example 1

[0171] This comparative example uses the currently used empirical formula, Black's equation, under five sets of experimental conditions of "3j3T" (current densities of 0.75, 1.0, 1.5 × 10⁻⁶). 4 A / cm 2 The temperatures were 90, 100, and 110℃ respectively, and the electromigration experiment duration for a single solder joint exceeded 1500 hours. The parameters of the fitted equation fluctuated with changes in the failure criterion: when the failure criterion was set as a 10-30% increase in resistance, the current density exponent n fluctuated by 33.5% (1.61-2.15), and the activation energy E... a The value fluctuated by 55.6% (0.54–0.84 eV). This parameter fluctuation means that the currently used empirical formula, the Black equation, cannot accurately predict the electromigration lifetime of Sn-Bi based alloy micro-solder joints. In contrast, this invention only requires completing one set of "1j1T" electromigration experiments to fit and calculate the total correction factor z. f With one parameter, the parameter calibration workload is reduced by 80% compared to the Black equation, and the total electromigration experiment time does not exceed 100 hours, resulting in a significant reduction in workload.

[0172] Comparative Example 2

[0173] This comparative example uses the currently used empirical formula, the Black equation, to predict the failure of a low-temperature Sn-58Bi linear solder joint with a cross-sectional area of ​​300μm × 300μm and a solder thickness of 600μm, when the failure criterion is set at a 30% increase in solder joint resistance. The result is achieved at a temperature of 110℃ and a current density of 0.75 × 10⁻⁶. 4 A / cm 2 Electromigration lifetime under certain conditions.

[0174] Electromigration experiments were conducted to obtain linear solder joints with Sn-58Bi solder at a temperature of 110℃ and a current density of 0.75 × 10⁻⁶. 4 A / cm 2 The electromigration lifetime under the given conditions is 285 hours. Based on the Black equation parameters obtained in Comparative Example 1, when the failure criterion is set as a 30% increase in solder joint resistance, the value of n is 2.15, and the activation energy E... a The value is 0.84 eV. The Black equation prediction for a linear solder joint with Sn-58Bi solder at low temperature is obtained at 110℃ and a current density of 0.75 × 10⁻⁶ eV.4 A / cm 2 Under the given electromigration conditions, the lifetime was 530 hours, with a prediction accuracy of 14.0%. This invention calculated the lifetime of the linear solder joint with Sn-58Bi solder under these electromigration conditions to be 292 hours, with a prediction accuracy of 97.5%, significantly better than the Black equation.

[0175] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro-solder joints, characterized in that, Includes the following steps: Obtain the parameters of Sn-Bi based alloy micro-weld joints; Obtain the experimental conditions and time intervals for electromigration; The directional migration of Bi atoms with electron wind during the simulated electromigration process was used to construct the first differential equation characterizing the relationship between the thickness of the Bi-rich layer in the prototype theoretical anode and the diffusion flux of Bi atoms. The first differential equation is: ; in, T(t) The thickness of the Bi-rich layer at the anode is [missing information]. J total This represents the total diffusion flux of Bi atoms during electromigration. t For electromigration time, M Bi The molar mass of Bi atoms, ρ Bi The density of Bi; The theoretical growth rate of the Bi-rich anode layer in the early stage of electromigration is solved based on the first differential equation. Electromigration experiments were conducted on Sn-Bi based alloy micro solder joints under electromigration experimental conditions to obtain the actual growth rate of the anodic Bi-rich layer in the early stage of electromigration. The growth correction factor is determined based on the theoretical growth rate and the actual growth rate of the anolyte Bi-rich layer in the early stage of electromigration. The first differential equation is modified based on the growth correction factor, thereby obtaining the second differential equation characterizing the relationship between the thickness of the Bi-rich layer in the prototype theoretical anode and the diffusion flux of Bi atoms. The second differential equation is: ; in, z f The growth correction factor is calculated using the following formula: ; in, k 1 This represents the theoretical growth rate of the Bi-rich layer at the anode during the early stages of electromigration. k 2 This represents the actual growth rate of the Bi-rich anode layer during the early stages of electromigration. Substituting the electromigration time interval into the second differential equation, we obtain a numerical solution for the Bi-rich layer thickness. A solder joint structure model of Sn-xBi alloy and Bi-rich layer in series was constructed. Based on the solder joint parameters and the thickness of the Bi-rich layer, a third differential equation was established to characterize the relationship between the resistance change rate of Sn-Bi based alloy micro solder joint and the thickness of the Bi-rich layer. The third differential equation is: ; in, τ(t) The resistance change rate of Sn-Bi based alloy micro-solder joints. x ( t () indicates the composition of Sn-xBi alloy x The function value changes over time. β(x(t)) For resistivity as x ( t The changing function value of ) L For the thickness of the brazing filler metal, β Bi Let Bi be the resistivity. D The diffusion coefficient of Bi atoms, Z * The effective charge number of Bi atoms, e For unit charge, j For current density, k Boltzmann's constant, T c For electromigration temperature, ρ Bi For the density of Bi, β solder The initial resistivity of the Sn-Bi based alloy; Obtain the solder joint resistance change rate criterion for determining electromigration failure, substitute the solder joint resistance change rate criterion into the third differential equation, and solve to obtain the electromigration lifetime of Sn-Bi based alloy micro solder joints.

2. The method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro-solder joints according to claim 1, characterized in that, The formula for calculating the total diffusion flux of Bi atoms during electromigration is as follows: ; in, z J This is the diffusion flux correction factor. J EM Let the electromigration diffusion flux be expressed as: ; in, ρ(x(t)) The density of Sn-xBi alloy, MBi The molar mass of Bi atoms, The diffusion coefficient of Bi atoms in the Sn-xBi alloy is given. Z * The effective charge number of Bi atoms, e For unit charge, j For current density, β(x(t)) For resistivity as x ( t The changing function value of ) k Boltzmann's constant, T c This is the electromigration temperature.

3. The method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro-solder joints according to claim 2, characterized in that, The formula for calculating the density of Sn-xBi alloys is: ; in, ρ Sn Let Sn be the density.

4. The method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro-solder joints according to claim 1, characterized in that, The early stage of electromigration is the first 100 hours of electromigration.

5. The method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro-solder joints according to claim 1, characterized in that, The Sn-Bi-based alloy micro solder joint parameters include the micro solder joint type and the micro solder joint size; the micro solder joint type includes at least one of linear solder joints, ball grid arrays, flip chip interconnect solder joints, and copper pillar bumps; the micro solder joint size includes the length, width, height, solder joint diameter, pad diameter, and solder joint curvature of the micro solder joint.

6. The method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro-solder joints according to claim 1, characterized in that, The Sn-Bi-based solder alloy has a Bi atomic mass percentage of 20.0 wt.% to 58.0 wt.%, and contains trace elements Ag, Sb, In, Cu, Ni, Co, and Fe, with each trace element content ranging from 0 wt.% to 2.0 wt.%.

7. The application of a method for predicting and evaluating the electromigration lifetime of low-temperature interconnect Sn-Bi-based alloy micro solder joints as described in any one of claims 1-6 in the reliability evaluation of micro solder joints in electronic packaging.

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