CN115083542A - Method and device for predicting alloying service life of welding spot and computer equipment - Google Patents
Method and device for predicting alloying service life of welding spot and computer equipment Download PDFInfo
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Abstract
The application relates to a method and a device for predicting the alloying service life of a welding spot and computer equipment. The welding spot comprises a welding pad of a first metal and a welding flux layer of a second metal, and the welding pad and the welding flux layer are alloyed to generate an interface metal compound layer comprising the first metal and the second metal; the method comprises the following steps: obtaining a flux of the first metal in the pad, the solder layer, and the interfacial metal compound layer; obtaining the net flux of the first metal in the interface metallic compound layer and the relation between the net flux of the first metal and the growth rate of the interface metallic compound layer; establishing a growth model of the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer; and predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer. By adopting the method, the prediction preparation degree can be improved, and the time cost and the economic cost can be reduced.
Description
Technical Field
The present application relates to the field of microelectronic packaging, and in particular, to a method and an apparatus for predicting an alloying lifetime of a solder joint, and a computer device.
Background
With the development of microelectronic packaging technology, the prediction of the alloying life of the solder joint becomes an important index for evaluating the reliability of packaging interconnection. As the size of the solder joint is continuously reduced, the reliability of the device and even the whole system is seriously tested due to the influence of micro-size and large current density effect, and the improvement of the packaging I/O density is considered as an important way for improving the integration level of the high-performance microelectronic device. By taking the lead-free micro-soldering points as an example for illustration, the diameter of the lead-free micro-soldering points can reach below 30um, the intercept can be reduced to 20um, and the packaging I/O density is ultrahigh. However, lead-free micro solder joints are more easily alloyed into a Cu-Sn Interfacial Metal Compound (IMC) layer, reducing the alloying lifetime of the solder joint interconnect, which in turn creates a potential problem for the reliability of the device and hence the overall system.
Based on the prior art, the prediction method of IMC layer alloying degree is mainly suitable for the traditional large-volume interconnection welding spot structure, and the problems of complete alloying of salient points and interconversion between different types of IMC layers caused by reduction of the size of the quantified welding spot can not be realized.
Disclosure of Invention
In view of the above, it is desirable to provide a method, an apparatus, and a computer device for predicting an alloying lifetime of a solder joint, which can improve the degree of preparation for prediction and reduce time cost and economic cost.
In a first aspect, the present application provides a method for predicting an alloying lifetime of a solder joint, where the solder joint includes a pad of a first metal and a solder layer of a second metal, and the pad and the solder layer are alloyed to generate an interface metal compound layer including the first metal and the second metal; the method comprises the following steps:
obtaining a flux of the first metal within the pad, the solder layer, and the interfacial metal compound layer;
obtaining the net flux of the first metal in the interface metal compound layer and the relation between the net flux of the first metal and the growth rate of the interface metal compound layer;
establishing a growth model for the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
In one embodiment, the bonding pads comprise a first bonding pad and a second bonding pad, and the solder layer is positioned between the first bonding pad and the second bonding pad; the interface metal compound layer is located between the first pad and the solder layer and between the second pad and the solder layer, the interface metal compound layer comprises a first interface metal compound layer and a second interface metal compound layer, and the first interface metal compound layer and the second interface metal compound layer are reaction products of the first metal and the second metal.
It can be seen that the interface metal compound layer comprises the first interface metal compound layer and the second interface metal compound layer, rather than a single metal compound layer, so that the obtained growth model is more reasonable, the prediction of the alloying lifetime is more accurate, and the method has great significance for the reliability design of the supporting microelectronic device.
In one embodiment, the first pad comprises a cathode pad and the second pad comprises an anode pad; the first metal comprises copper and the second metal comprises tin; the obtaining the net flux of the first metal in the interfacial metallic compound layer and the relation of the net flux of the first metal to the growth rate of the interfacial metallic compound layer comprises: establishing the following relationship between the thickness variation of the first interfacial metallic compound layer and the second interfacial metallic compound layer between the first pad and the solder layer and the flux of the first metal in the first pad, the first interfacial metallic compound layer, the second interfacial metallic compound layer and the solder layer:
wherein, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metallic compound layer,
representing a thermal diffusion flux of copper from the first pad to the first interfacial metallic compound layer due to an atomic concentration gradient,
represents the thermal diffusion flux of copper from the first interfacial metallic compound layer to the second interfacial metallic compound layer due to the atomic concentration gradient,
represents the thermal diffusion flux of copper from the second interfacial metallic compound layer to the second metal due to the atomic concentration gradient,
for electromigration flux of copper in the first interfacial metallic compound layer caused by electron wind forces,
for electronic wind-force inductionThe second interfacial metallic compound layer.
Obtaining a net electromigration flux of the first metal in the first interfacial metal compound layer in the first pad based on the following equation:
wherein, C Cu/ε Represents the concentration of the copper atoms in the first interfacial metal compound layer, D Cu/ε Represents a thermal diffusion coefficient of the copper atoms in the first interfacial metallic compound layer,
is the effective charge number, rho, of the copper atoms in the first interfacial metallic compound layer ε K is a boltzmann constant, T is a kelvin temperature of a solder joint, e is a unit charge amount, and j is an average current density.
Obtaining a net electromigration flux of the first metal in the first pad in the second interfacial metallic compound layer based on the following equation:
wherein, C Cu/η Represents the concentration of the copper atoms in the second interfacial metal compound layer, D Cu/η Represents a thermal diffusion coefficient of the copper atoms in the second interfacial metallic compound layer,
is the effective charge number, rho, of the copper atoms in the second interfacial metallic compound layer η Is the resistivity of the second interfacial metal compound layer; k is the boltzmann constant, T is the kelvin temperature of the solder joint, e is the unit charge amount, and j is the average current density.
Obtaining a net thermal diffusion flux of the first metal in the first pad in the first interfacial metallic compound layer based on the following equation:
wherein, C Cu Is the copper atom concentration in the copper pad, D Cu/ε Is the thermal diffusion coefficient of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metallic compound layer.
Obtaining a net thermal diffusion flux of the first metal in the first pad in the second interfacial metallic compound layer based on the following equation:
wherein, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/Sn Concentration of copper atoms dissolved in Sn solder, D Cu/η Is the thermal diffusivity of copper atoms in the second interfacial metallic compound layer.
Establishing the following relationship between the thickness variation of the first interfacial metallic compound layer and the second interfacial metallic compound layer between the second pad and the solder layer and the flux of the first metal in the second pad, the first interfacial metallic compound layer, the second interfacial metallic compound layer and the solder layer:
wherein, C Cu/ε Represents a copper atom atConcentration in the first interfacial metal compound layer, C Cu/η Denotes a concentration of copper atoms in the second interfacial metallic compound layer, ε denotes a thickness of the first interfacial metallic compound layer, η denotes a thickness of the second interfacial metallic compound layer,
representing a thermal diffusion flux of copper from the second pad to the first interfacial metallic compound layer due to an atomic concentration gradient,
represents the thermal diffusion flux of copper from the first interfacial metallic compound layer to the second interfacial metallic compound layer due to the atomic concentration gradient,
represents the thermal diffusion flux of copper from the second interfacial metallic compound layer to the second metal due to the atomic concentration gradient,
for electromigration flux of copper in the first interfacial metallic compound layer caused by electron wind forces,
for electromigration flux of copper in the second interfacial metallic compound layer caused by electron wind,
a copper electromigration flux in the second metal layer caused by electron wind forces;
obtaining a net electromigration flux of the first metal in the first interfacial metallic compound layer in the second pad based on the following equation:
wherein, the first and the second end of the pipe are connected with each other,C Cu/ε represents the concentration of the copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of the copper atoms in the second interfacial metal compound layer; d Cu/ε Represents a thermal diffusion coefficient of the copper atom in the first interfacial metal compound layer, D Cu/η Represents a thermal diffusion coefficient of the copper atoms in the second interfacial metallic compound layer;
is the effective charge number of the copper atoms in the first interfacial metallic compound layer,
is the effective charge number of the copper atoms in the second interfacial metallic compound layer; rho ε Is the resistivity, p, of the first interfacial metal compound layer η Is the resistivity of the second interfacial metal compound layer; k is a Boltzmann constant, T is the Kelvin temperature of the solder joint, e is the unit charge amount, and j is the average current density;
obtaining a net electromigration flux of the first metal in the second interfacial metal compound layer in the second pad based on the following equation:
wherein, C Cu/Sn Represents the concentration of the copper atoms dissolved in the second metal layer, D Cu/Sn Represents a thermal diffusion coefficient of the copper atoms in the second metal layer,
is the effective charge number of the copper atoms in the second metal layer; ρ is a unit of a gradient Sn Is the resistivity of the second metal layer, k is the boltzmann constant, T is the kelvin temperature of the solder joint, e is the unit charge amount, j is the average current density;
obtaining a net thermal diffusion flux of the first metal in the first interfacial metallic compound layer in the second pad based on the following equation:
wherein, C Cu Is the copper atom concentration in the copper pad, D Cu/ε Is the thermal diffusion coefficient of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metallic compound layer;
obtaining a net thermal diffusion flux of the first metal in the second interfacial metallic compound layer in the second pad based on the following equation:
wherein, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/Sn Concentration of copper atoms dissolved in tin solder, D Cu/η Is the thermal diffusivity of copper atoms in the second interfacial metallic compound layer.
In one embodiment, the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer comprises: obtaining a relationship between a net flux of the first metal in the first interfacial metallic compound layer between the first pad and the solder layer and a growth rate of the first interfacial metallic compound layer between the first pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/ε Represents the metal combination of copper atoms at the first interfaceConcentration in the layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metal compound layer, C Cu Is the copper atom concentration in the copper pad, D Cu/ε Is the thermal diffusivity of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number, rho, of copper atoms in the first interfacial metallic compound layer ε Is the resistivity of the first interface metal compound layer, k is the boltzmann constant, T is the kelvin temperature of the solder joint, e is the unit charge amount, j is the average current density;
obtaining a relationship between a net flux of the first metal in the second interfacial metallic compound layer between the first pad and the solder layer and a growth rate of the second interfacial metallic compound layer between the first pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, D Cu/Sn Is the thermal diffusivity of copper atoms in the solder layer,
represents the effective charge number of copper atoms in the solder layer, C Cu/Sn Represents the concentration of the copper atoms dissolved in the second metal layer, C Cu/η Denotes the concentration of copper atoms in the second interfacial metal compound layer, D Cu/ε Is the thermal diffusivity of copper atoms in the first interfacial metallic compound layer,
represents a copper atom inAn effective charge number of the first interfacial metallic compound layer,
represents the effective charge number, rho, of copper atoms in the second interfacial metallic compound layer ε Is the resistivity, p, of the first interfacial metal compound layer η Is the resistivity of the second interface metal compound layer, k is the boltzmann constant, T is the kelvin temperature of the solder joint, e is the unit charge amount, j is the average current density;
obtaining a relationship between a net flux of the first metal in the first interfacial metallic compound layer between the second pad and the solder layer and a growth rate of the first interfacial metallic compound layer between the second pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/η Denotes the concentration of copper atoms in the second interfacial metal compound layer, D Cu/η Is the thermal diffusion coefficient of copper atoms in the second interfacial metal compound layer, D Cu/ε Is the thermal diffusivity of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number of copper atoms in the first interfacial metal compound layer,
represents the effective charge number, rho, of copper atoms in the second interfacial metallic compound layer ε Is the resistivity, p, of the first interfacial metal compound layer η Is the resistivity of the second interfacial metallic compound layer, k is the Boltzmann constant, and T is the Kelvin temperature of the solder jointE is the unit charge amount, j is the average current density;
obtaining a relationship between a net flux of the first metal in the second interfacial metallic compound layer between the second pad and the solder layer and a growth rate of the second interfacial metallic compound layer between the second pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/Sn Is the concentration of copper atoms dissolved in the Sn solder, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, D Cu/η Is the thermal diffusion coefficient of copper atoms in the second interfacial metal compound layer, D Cu/Sn Is the thermal diffusivity of copper atoms in the solder layer,
represents the effective charge number of copper atoms in the second interfacial metallic compound layer,
represents the effective charge number, rho, of copper atoms in the solder layer η Is the resistivity, p, of the second interfacial metal compound layer Sn K is the boltzmann constant, T is the kelvin temperature of the solder joint, e is the unit charge amount, and j is the average current density.
In one embodiment, the modeling the growth of the interfacial metallic compound layer based on the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer comprises: obtaining the change of the thickness of the first interfacial metal compound layer and the thickness of the second interfacial metal compound layer with time under temperature stress based on the relation between the net flux of the first metal and the growth rate of the interfacial metal compound layer, wherein the formula of the change of the thickness of the first interfacial metal compound layer and the thickness of the second interfacial metal compound layer with time under the temperature stress is as follows:
wherein epsilon 0 Is the initial thickness, η, of the first interfacial metal compound layer 0 Is the initial thickness of the second interfacial metal compound layer. It can be seen that the method can yield Cu when Sn solder is not completely consumed under single temperature stress 3 Sn layer and Cu 6 Sn 5 The thickness growth relationship of the layers, so that the growth model is more reasonable, and the prediction of the alloying life is more accurate.
In one embodiment, the modeling the growth of the interfacial metallic compound layer based on the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer comprises: obtaining a formula of a change in thickness of the first interfacial metallic compound layer between the first pad and the solder under a temperature stress coupled current stress and a change in thickness of the second interfacial metallic compound layer between the first pad and the solder over time based on a relationship of a net flux of the first metal in the first interfacial metallic compound layer between the first pad and the solder layer and a relationship of a growth rate of the first interfacial metallic compound layer between the first pad and the solder layer and a relationship of a net flux of the first metal in the second interfacial metallic compound layer between the first pad and the solder layer and a relationship of a growth rate of the second interfacial metallic compound layer between the first pad and the solder layer:
wherein, C 1 The first bonding pad andintegral constant, C, related to initial thickness of the first interfacial metal compound layer between the solder layers 2 An integration constant related to an initial thickness of the second interfacial metallic compound layer between the first pad and the solder layer;
obtaining a formula of a change in thickness of the first interfacial metallic compound layer between the second pad and the solder under a temperature stress coupling current stress over time and a change in thickness of the second interfacial metallic compound layer between the second pad and the solder over time based on a relationship of a net flux of the first metal in the first interfacial metallic compound layer between the second pad and the solder layer and a relationship of a growth rate of the first interfacial metallic compound layer between the second pad and the solder layer and a relationship of a net flux of the first metal in the second interfacial metallic compound layer between the second pad and the solder layer and a growth rate of the second interfacial metallic compound layer between the second pad and the solder layer:
wherein, C' 1 And an integration constant, C ', related to the initial thickness of the first interfacial metallic compound layer between the second pad and the solder layer' 2 Is an integral constant related to an initial thickness of the second interfacial metallic compound layer between the second pad and the solder layer.
In one embodiment, the predicting the alloying lifetime of the solder joint based on the growth model of the interfacial metal compound layer comprises: predicting an alloying life of the solder joint when the second metal solder layer is depleted based on a growth model of the interfacial metal compound layer, comprising: and predicting the alloying life of the solder joint when the solder layer is exhausted based on the initial thickness of the solder layer, the initial thickness of the first interface metal compound layer and the initial thickness of the second interface metal compound layer, and the growth thickness of the first interface metal compound layer and the growth thickness of the second interface metal compound layer.
In one embodiment, the predicting the alloying lifetime of the solder joint based on the growth model of the interfacial metal compound layer comprises: predicting an alloying lifetime of the solder joint when the second interfacial metallic compound layer is completely converted to the first interfacial metallic compound layer based on a growth model of the interfacial metallic compound layer, comprising: predicting the alloying life of the solder joint when the second interfacial metallic compound layer is completely converted into the first interfacial metallic compound layer under the temperature stress based on the following formula:
wherein 0.68 is a conversion ratio relationship of thicknesses of the first interfacial metal compound layer and the second interfacial metal compound layer. Here,. epsilon 0 Represents the initial thickness, η, of the first interfacial metal compound layer when the solder is completely consumed 0 Representing the initial thickness of the second interfacial metallic compound layer when the solder is fully depleted.
Predicting the alloying life of the welding spot under the temperature stress coupling current stress when the second interface metal compound layer is completely converted into the first interface metal compound layer based on the following formula:
η＝η 0 -0.68×(ε Anode +ε Cathode )
wherein epsilon Cathode Is the thickness, epsilon, of the first interfacial metallic compound layer between the first pad and the solder layer when the solder is completely consumed Anode Is the thickness of the first interfacial metallic compound layer between the second pad and the solder layer when the solder is fully depleted.
Therefore, the method can solve the problem of mutual transformation among different types of IMC layers, and can accurately predict the alloying service life of the welding spot.
In a second aspect, the application further provides a device for predicting the alloying service life of the welding spot. The device comprises:
the welding spot comprises a welding pad of a first metal and a welding flux layer of a second metal, and the welding pad and the welding flux layer are alloyed to generate an interface metal compound layer comprising the first metal and the second metal; the device comprises:
an obtaining module, configured to obtain a flux of the first metal in the pad, the solder layer, and the interface metal compound layer;
a first processing module for obtaining the net flux of the first metal in the interfacial metallic compound layer and the relation between the net flux of the first metal and the growth rate of the interfacial metallic compound layer;
a second processing module for establishing a growth model of the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and the third processing module is used for predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
In a third aspect, the present application also provides a computer device. The computer device comprises a memory and a processor, wherein the memory stores a computer program, the processor realizes the following steps when executing the computer program, the welding spot mentioned in the following steps comprises a welding disc of a first metal and a welding flux layer of a second metal, and the welding disc and the welding flux layer are alloyed to generate an interface metal compound layer comprising the first metal and the second metal:
obtaining a flux of the first metal within the pad, the solder layer, and the interfacial metal compound layer;
obtaining the net flux of the first metal in the interface metal compound layer and the relation between the net flux of the first metal and the growth rate of the interface metal compound layer;
establishing a growth model for the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
In a fourth aspect, the present application further provides a computer-readable storage medium. The computer readable storage medium having stored thereon a computer program that when executed by a processor performs the steps of, where a solder joint includes a pad of a first metal and a solder layer of a second metal, the pad alloying with the solder layer to generate an interfacial metal compound layer including the first metal and the second metal:
obtaining a flux of the first metal within the pad, the solder layer, and the interfacial metal compound layer;
obtaining the net flux of the first metal in the interface metal compound layer and the relation between the net flux of the first metal and the growth rate of the interface metal compound layer;
establishing a growth model for the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
In a fifth aspect, the present application further provides a computer program product. The computer program product comprises a computer program, when executed by a processor, the computer program realizes the following steps, wherein a welding spot comprises a pad of a first metal and a solder layer of a second metal, and the pad is alloyed with the solder layer to generate an interface metal compound layer comprising the first metal and the second metal:
obtaining a flux of the first metal within the pad, the solder layer, and the interfacial metal compound layer;
obtaining the net flux of the first metal in the interfacial metallic compound layer and the relation between the net flux of the first metal and the growth rate of the interfacial metallic compound layer;
establishing a growth model for the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
The method, the device, the computer equipment, the storage medium and the computer program product for predicting the alloying service life of the welding spot, acquiring the net flux of the first metal and the relation between the net flux of the first metal and the growth rate of the interface metal compound layer according to the flux of the first metal, further, a growth model of the net flux of the first metal and the interface metal compound layer is obtained according to the growth rate, and the alloying service life of the welding spot is predicted based on the growth model, it can be seen that the growth model is obtained gradually based on the flux of the first metal, so that the prediction of the alloying life is more reasonable, thereby achieving the purpose of improving the prediction preparation degree, further, the time and the economic cost generated by a large number of service lives and failure analysis tests are reduced or avoided, and great economic benefits and social benefits are achieved.
Drawings
FIG. 1 is a schematic flowchart of a method for predicting an alloying lifetime of a solder joint according to an embodiment;
FIG. 2 is a schematic diagram of a solder joint in one embodiment;
FIG. 3 is a schematic diagram of yet another exemplary solder joint in one embodiment;
FIG. 4 is a schematic diagram of the structure of copper flux in a solder joint under temperature and current stress coupling conditions in one embodiment;
FIG. 5 is a graphical representation of a scenario illustrating a comparison of experimental results and predicted results for the growth thickness of an interfacial metal compound layer, according to one embodiment;
FIG. 6 is a graphical representation of a comparison of experimental results and predicted results for growth thickness of an interface metal compound layer according to an embodiment;
FIG. 7 is a schematic diagram of yet another exemplary solder joint structure;
FIG. 8 is a scenario diagram illustrating an alloying life prediction of a solder joint according to an embodiment;
FIG. 9 is a diagram of a solder joint alloying life prediction device in one embodiment;
FIG. 10 is a diagram showing an internal structure of a computer device according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description of the present application herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.
Hereinafter, although terms such as "first", "second", and the like may be used to describe various components, the components are not necessarily limited to the above terms. The above terms are only used to distinguish one component from another. It will also be understood that expressions used in the singular include expressions in the plural unless the singular has a significantly different meaning in the context.
A prediction method of welding spot alloying degree is based on numerical calculation of different atom migration fluxes between welding spot interfaces, and atom migration fluxes of copper welding pads, tin solder and interfaces between different IMCs under the conditions of temperature and current stress are simulated and calculated respectively. And converting the atomic flux obtained by theoretical calculation into the change of the interface position by combining the mass density relationship of conversion reaction among different structures, and further representing the function relationship of the IMC layer thickness along with the time change.
The other method for predicting the alloying degree of the welding spot is based on the mass transport conservation principle of copper atoms and is used for respectively simulating and calculating the copper welding disc, the tin solder and the Cu under the conditions of temperature and current stress 6 Sn 5 Net flux of copper atoms of the layer structure. And converting the migration flux of copper atoms into Cu based on theoretical calculation 6 Sn 5 Thickness variation of the layer, which in turn is used to characterize Cu 6 Sn 5 Layer thickness as a function of time.
However, in the first method, the calculation of the migration flux of atoms between interfaces needs to be based on a large amount of interface thermal diffusion and electromigration parameters, and at the present stage, the research work of the interface parameters is still in depth, and the acquisition of the relevant parameters and the accuracy of the parameters cannot be guaranteed. In addition, the method does not relate to the process prediction of complete alloying of the welding spot into an IMC layer or interconversion between the IMC layers as the lead-free welding spot is reduced in size, so that the alloying service life prediction of the welding spot cannot be realized.
In the second method, the IMC layer in the lead-free welding spot is simply considered, and only the lead-free welding spot Cu is considered 6 Sn 5 Growth effects of metal compounds, and therefore, Cu was not quantitatively characterized 3 The thickness of the Sn layer increases with the temperature and the current stress. In addition, the method does not relate to the process prediction of complete alloying of the welding spot into an IMC layer or interconversion between the IMC layers as the size of the lead-free welding spot is reduced, so that the alloying service life prediction of the lead-free welding spot cannot be realized.
Referring to fig. 1, fig. 1 is a schematic flow chart of a method for predicting an alloying lifetime of a solder joint in an embodiment, where the solder joint includes a pad of a first metal and a solder layer of a second metal, and the pad is alloyed with the solder layer to generate an interfacial metal compound layer including the first metal and the second metal, referring to fig. 2, fig. 2 is a schematic structural diagram of a solder joint in an embodiment, where the schematic structural diagram of the solder joint includes a pad 201 of the first metal and a solder layer 202 of the second metal, and in combination with the schematic structural diagram of the solder joint shown in fig. 2, the schematic flow chart of fig. 1 includes the following steps:
step 101, obtaining the flux of the first metal in the bonding pad, the solder layer and the interface metal compound layer.
The bonding pad 201 includes a first bonding pad and a second bonding pad, and the solder layer 202 is located between the first bonding pad and the second bonding pad; the interfacial metal compound layer is located between the first pad and the solder layer and between the second pad and the solder layer, the interfacial metal compound layer comprises a first interfacial metal compound layer and a second interfacial metal compound layer, and the first interfacial metal compound layer and the second interfacial metal compound layer both comprise a first metal and a second metal; the first pad includes a cathode pad, and the second pad includes an anode pad; the first metal includes copper, and the second metal includes tin.
For a detailed description, taking the first metal as copper and the second metal as tin as an example, please refer to fig. 3, and fig. 3 is a schematic structural diagram of another solder joint in an embodiment, where the schematic structural diagram includes a first pad 301, a solder layer 302, a first interfacial metal compound layer 303, and a second interfacial metal compound layer 304. The first pad 301 may include a copper pad, the solder layer 302 may include a tin layer, and the first interfacial metallic compound layer 303 may include Cu 3 The Sn layer, the second interfacial metallic compound layer 304 may include Cu 6 A layer of Sn 5. Flux of the above-described copper Cu in the first pad 301, the solder layer 302, and the first interfacial metallic compound layer 303 and the second interfacial metallic compound layer 304 is obtained, and the flux of Cu includes thermal diffusion flux of Cu, electromigration flux of Cu, and dissolution flux of Cu atoms.
Specifically, referring to fig. 4 in conjunction with fig. 2 and 3, fig. 4 is a schematic structural diagram of Cu flux in a solder joint under temperature and current stress coupling conditions in an embodiment.
J in FIG. 4 chem Represents the Cu thermal diffusion flux caused by the atomic concentration gradient, and the direction is always from the structure with high copper atomic concentration to the structure with low copper atomic concentration; flux J em Representing Cu electromigration flux caused by electron wind, and the direction is consistent with the electron flow direction; and flux J diss Which represents the dissolution flux of copper atoms, due to the unsaturated concentration of copper atoms caused by the migration of atoms under the action of an electric field, the dissolution flux is formed.
Among them, in FIG. 4
And
the Cu electromigration flux in the first pad 301, the first interfacial metallic compound layer 303, the second interfacial metallic compound layer 304, and the tin solder layer 302, respectively. Under current stress, the directional migration of copper atoms is a key factor in causing differences in the IMC layers in the cathode and anode of the solder joint. Wherein the first bonding pad 301 structure has good electromigration resistance
The flux can be ignored in the calculation, and Cu electromigration fluxes in the first interface metallic compound layer 303, the second interface metallic compound layer 304, and the solder layer 302 are collectively referred to as Cu electromigration flux
(i.e., the
Represents the above
Or
) And calculating according to a Huntington model to obtain:
in the formula, C Cu/Bulk And D Cu/Bulk Respectively, the concentration and diffusion coefficient of copper atoms in the tissue of the mobile body.
Is the effective charge number of the copper atom in the tissue of the mobile body. (for example,
represents the effective charge number of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number of copper atoms in the second interfacial metallic compound layer,
representing the effective charge number of copper atoms in the second metal solder layer), e is the unit charge amount, ρ Bulk It is the resistivity of the tissue of the migration volume, j is the average current density, k is the boltzmann constant, and T is the kelvin temperature of the weld spot.
In FIG. 4
And
the flux of dissolution of copper atoms in the first pad 301 toward the first interfacial metallic compound layer 303, the first interfacial metallic compound layer 303 toward the second interfacial metallic compound layer 304, and the second interfacial metallic compound layer 304 toward the solder layer 302, respectively. The dissolution flux of copper atoms is only related to the solubility of Cu when the temperature and current conditions are fixed, but the solubility of copper atoms in solid tissues is generally low, so that the formed dissolution flux can be ignored in the calculation.
Specifically, based on the numerical analysis of the Cu flux in step 201, in combination with the mass transport conservation principle of copper atoms, the net flux of copper atoms is established in relation to the change in the thickness of the first interface metal compound 303 layer and the second interface metal compound 304.
For the cathode:
for the anode:
in the formula, C Cu/ε And C Cu/η Each represents a copper atom in Cu 3 Sn 303(ε phase) and Cu 6 Sn 5 304(η phase), and ∈ and η denote the thicknesses of the first interface metallic compound layer 303 and the second interface metallic compound layer 304, respectively; in equations (2) to (5)
And
the difference is the net flux of thermal diffusion of copper atoms in the first interfacial metal compound layer 303, which can be equivalent to the diffusion process of copper atoms in the first interfacial metal compound layer 303 caused by the difference of atomic concentration in the first pad 301 and the second interfacial metal compound layer 304,
and
the difference is the net flux of thermal diffusion of copper atoms in the second interfacial metal compound layer 304, which can be equivalent to the diffusion process of copper atoms in the second interfacial metal compound layer 304 caused by the difference between the atomic concentrations in the second interfacial metal compound layer 304 and the Sn solder.
The net thermal diffusion flux of copper atoms in the above-described first interfacial metallic compound layer 303 is obtained based on the following formula:
the net thermal diffusion flux of copper atoms in the above-described second interfacial metal compound 304 layer is obtained based on the following formula:
wherein, C Cu Is the copper atom concentration, C, in the first pad 301 Cu/Sn Is the concentration of Cu atoms dissolved in the solder layer 302. D Cu/ε And D Cu/η Are the thermal diffusion coefficients of copper atoms in the above-described first interfacial metallic compound layer 303 and second interfacial metallic compound layer 304, respectively.
The mathematical relationship between the growth rate of the thicknesses of the first interface metallic compound layer 303 and the second interface metallic compound layer 304 of the cathode and the anode of the lead-free welding spot and the net flux of Cu can be obtained by jointly solving the formulas (2) to (7), which is specifically shown as follows:
for the cathode:
for the anode:
wherein:
in the formula (I), the compound is shown in the specification,
and
the effective charge numbers of the copper atoms in the first interfacial metallic compound layer 303 and the second interfacial metallic compound layer 304 are shown, respectively. Rho ε And ρ η The resistivities of the first interface metallic compound layer 303 and the second interface metallic compound layer 304 in the IMC layer, respectively.
Step 203, establishing a growth model of the interfacial metallic compound layer based on the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer.
(1) Growth model of IMC layer under single temperature stress:
when no current stress acts, the electromigration flux of copper atoms in the lead-free welding spot structure does not exist, and the thickness of the first interface metal compound layer and the thickness of the second interface metal compound layer under temperature stress are obtained according to the relation between the net flux of the first metal and the growth rate of the interface metal compound layer; therefore, N in the formulas (8) to (11) ε ＝N η ＝N' ε ＝N' η 0. By solving equations (8), (9) and (10), (11) by integration, the thickness of the first interface metal compound layer 303 and the second interface metal compound layer 304 as a function of time under a single temperature stress is obtained.
In the formula, epsilon 0 And η 0 Respectively, a first interfacial metal compound layer 303 (Cu) 3 Sn layer) and a second interfacial metal compound layer 304 (Cu) 6 Sn 5 Layer) of the substrate. Under temperature stress, the growth of IMC layers at two ends of the lead-free welding spot has no obvious polarity difference, so the formula(13) The method can be applied to a thickness growth model for characterizing the first interface metal compound layer 303 and the second interface metal compound layer 304 under single temperature stress and when the solder layer 302 is not completely exhausted.
(2) IMC layer growth model with temperature, current stress coupling:
when temperature, current stress are coupled, N ε ≠N η ≠N' ε ≠N' η And 0, obtaining a change with time in a thickness of the first interface metallic compound layer between the first pad and the solder under the temperature stress and the current stress and a change with time in a thickness of the second interface metallic compound layer between the first pad and the solder under the temperature stress and the current stress based on a relationship between a net flux of the first metal in the first interface metallic compound layer between the first pad and the solder layer and a growth rate of the first interface metallic compound layer between the first pad and the solder layer and a relationship between a net flux of the first metal in the second interface metallic compound layer and the growth rate of the first interface metallic compound layer between the first pad and the solder layer and a relationship between a net flux of the first metal in the second interface metallic compound layer between the first pad and the solder layer and a growth rate of the second interface metallic compound layer between the first pad and the solder layer, and obtaining a change with time in a net flux of the first metal in the first interface metallic compound layer between the second pad and the solder layer and the second pad and the solder layer based on the net flux of the first metal A relationship between a growth rate of the first interfacial metallic compound layer between the solder layers and a relationship between a net flux of the first metal in the second interfacial metallic compound layer between the second pad and the solder layers and a growth rate of the second interfacial metallic compound layer between the second pad and the solder layers, obtaining a change in thickness of the first interfacial metallic compound layer between the second pad and the solder over time and a change in thickness of the second interfacial metallic compound layer between the second pad and the solder over time under temperature stress and current stress; specifically, the functional relationship of the thicknesses of the first interfacial metal compound layer 303 and the second interfacial metal compound layer 304 with the stress time can be obtained by solving the equations (8), (9), (10), (11) by integration:
for the cathode:
for the anode:
in the formula, C 1 、C 2 、C' 1 And C' 2 The integral constants are respectively related to the initial thickness of the IMC layer, so that the formulas (14) and (15) respectively quantify and represent thickness growth models of the first interface metallic compound layer 303 and the second interface metallic compound layer 304 along with the temperature and the current stress time under the temperature and current stress coupling condition and when the solder layer 302 is not completely exhausted.
To verify the accuracy of the growth model, reported experimental data and Cu under temperature and current stress in the present case were used 6 Sn 5 Layer, Cu 3 The results of the thickness growth predictions of the Sn layers were compared. Referring to table 1, table 1 shows some material parameters required for numerical calculation of a prediction method:
TABLE 1 partial material parameters required for the numerical calculation of the prediction method
C Cu 、C Cu/η And C Cu/ε Are respectively 0.84 multiplied by 10 23 、0.31×10 23 And 0.52X 10 23 at./cm 3 ，c Sn About 0.11X 10 21 at./cm 3 . The necessary parameters are substituted into equation (13) and compared to published literature data.
The growth model was verified based on some of the material parameters in table 1. Referring to FIG. 5, FIG. 5 is a graph showing a test junction for thickness growth of an interfacial metal compound layer according to an embodimentAs can be seen from FIG. 5, under the single temperature conditions of 155 deg.C (fig. 5 (a)) and 180 deg.C (fig. 5 (b)) the Cu/Sn/Cu lead-free solder joint structure 3 Sn layer and Cu 6 Sn 5 The results of the layer growth experiments and the predicted results show that Cu 3 Sn layer and Cu 6 Sn 5 The thickness of the layer shows good consistency with the temperature stress action time.
Referring to FIG. 6, FIG. 6 is a schematic diagram illustrating a comparison between a predicted and a test result of a growth thickness of an interface metal compound layer according to an embodiment, and it can be seen from FIG. 6 that a current density of 0.53 × 10 is applied at a temperature of 155 deg.C 4 A/cm 2 Under the conditions, Cu at the anode terminal (figure 6 (a)) and the cathode terminal (figure 6 (b)) of the Cu/Sn/Cu lead-free solder joint structure 6 Sn 5 Layer and Cu 3 The growth thickness verification and comparison results of the Sn layer show that the anode Cu is under the coupling action of the temperature and the current stress of 40h 6 Sn 5 The predicted maximum deviation result of the layer is about 1.3um, Cu 6 Sn 5 The maximum deviation of the layers is also only 1.1 um. Thereby obtaining Cu of positive and negative poles of welding spot 6 Sn 5 Layer and Cu 3 The growth tendency of the Sn layer and the model results showed good consistency.
Therefore, the comparison results of fig. 5 and fig. 6 show that the prediction method of the present application document can accurately calculate the Cu in the lead-free solder under different temperature and current stresses, no matter under the condition of single temperature stress or under the condition of temperature and current coupling stress 6 Sn 5 Layer and Cu 3 And a growth model of the thickness of the Sn layer along with the stress time can be used for accurately predicting the alloying life of the welding spot according to the growth model.
And 203, predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
(1) Alloying life when tin solder is exhausted:
predicting the alloying life of the welding spot when the solder layer is exhausted based on the growth model of the interface metal compound layer, which comprises the following steps:
predicting the alloying life of the solder joint when the solder layer is depleted based on the initial thickness of the solder layer, the initial thickness of the first interfacial metal compound layer and the initial thickness of the second interfacial metal compound layer, the growth thickness of the first interfacial metal compound layer and the growth thickness of the second interfacial metal compound layer; specifically, as the temperature and the current stress time are prolonged, the IMC layer continues to grow in the lead-free solder according to the relationships of the formulas (13) to (15). When the solder layer 302 is completely consumed, i.e., the solder layer 302 is completely transformed into the first interfacial metallic compound layer Cu 3 Sn 303 and a second interfacial metal compound layer Cu 6 Sn 5 304 layers. Based on the initial thickness of the solder layer 302, the initial thickness of the first interface metal compound layer 303 and the initial thickness of the second interface metal compound layer 304, the growth thicknesses of the first interface metal compound layer 303 and the second interface metal compound layer 304 can be used to determine whether the solder is completely depleted and transformed at the current moment, and the determination criterion can be determined based on the thickness transformation relationship among the solder layer 302, the second interface metal compound layer 304 and the first interface metal compound layer 303, as shown in the following:
a. consuming 1um of solder layer 302, which translates to about 2.14um of first interfacial metal compound layer 303;
b. consuming 1um of solder layer 302 can translate to about 1.4um of second interfacial metal compound layer 304.
The criterion relationship is determined based primarily on the molar mass, density, and transformation ratio relationships of the solder layer 302, the first interfacial metallic compound layer 303, and the second interfacial metallic compound layer 304.
(2)Cu 6 Sn 5 304 is completely converted into a first interfacial metal compound layer 303 (Cu) 3 Sn layer) alloying life:
after the solder layer 302 is completely depleted, the structure of the solder joint structure is changed, and a schematic diagram of the flux of copper atoms is specifically shown in fig. 7 below, and fig. 7 is a schematic diagram of a structure of another solder joint according to an embodiment, which includes a first pad 301, a first interfacial metal compound layer 303, and a second interfacial metal compound layer 304.The alloying stage is that the second interfacial metal compound layer 304 will be towards Cu 3 Sn transformation, the thickness of the second interfacial metallic compound layer 304 decreases with stress time, and the specific transformation relationship is as follows:
9Cu+Cu6Sn5→5Cu3Sn (16)
specifically, after the solder layer 302 is completely depleted, the net flux of copper atoms in the first interfacial metallic compound layer 303 is not changed, and therefore, the growth of the thickness of the first interfacial metallic compound layer 303 can still be performed with reference to equations (13) to (15), while the thickness of the second interfacial metallic compound layer 304 can be determined in conjunction with the molar mass, density, and the like of the second interfacial metallic compound layer 304 and the first interfacial metallic compound layer 303 with reference to the conversion relationship of equation (16) because the net flux of copper atoms is changed in the second interfacial metallic compound layer 304.
Predicting the alloying life of the welding spot when the second interface metal compound layer 304 is completely converted into the first interface metal compound layer 303 based on the growth model of the interface metal compound layer, wherein the predicting comprises the following steps:
the alloying life of the solder joint at the time of complete conversion of the second interfacial metallic compound layer 304 into the first interfacial metallic compound layer 303 under temperature stress is predicted based on the following formula:
in the formula, 0.68 is a conversion ratio relationship between the thicknesses of the first interfacial metallic compound layer 303 and the second interfacial metallic compound layer 304. Here,. epsilon. 0 And η 0 It indicates the initial thickness of the first interfacial metallic compound layer 303 and the second interfacial metallic compound layer 304, respectively, after the solder layer 302 is fully alloyed.
The alloying life of the solder joint under the temperature-coupled current stress when the second interfacial metallic compound layer 304 is completely converted into the first interfacial metallic compound layer 303 is predicted based on the following formula:
η＝η 0 -0.68×(ε Anode +ε Cathode ) (18)
wherein epsilon Cathode And ε Anode The thicknesses of the cathode and anode first interfacial metal compound layers 303, respectively, can be alternatively characterized by the epsilon parameter in equations (14) and (15), respectively. Based on the conversion relationship of the equations (17) and (18), the alloying life when the second interfacial metallic compound layer 304 is completely converted into the first interfacial metallic compound layer 303 in the lead-free solder joint can be determined.
Since the accuracy of the growth model described above has been verified in fig. 5 and 6, the alloying life prediction will be made from the growth model described above and by the specific solder joint structure.
Specifically, a Cu/Sn/Cu lead-free solder joint structure is selected, the thickness of the tin solder layer 302 in the initial state is 13um, and the Cu is 6 Sn 5 Layer and Cu 3 The total thickness of the Sn layer is 8um and 4um respectively, and evenly distributed at two ends of the welding spot, and the alloying service life is predicted based on the lead-free welding spot structure.
Referring to fig. 8, fig. 8 is a schematic view illustrating a scenario of predicting an alloying lifetime of a solder joint in an embodiment, and as can be seen from fig. 8, fig. 8 (a), (b), (c), and (d) show a coupling current density of 1.0 × 10 at 155 ℃ and a coupling current density at 155 ℃ respectively 5 A/cm 2 High temperature of 180 ℃ and high temperature of 180 ℃ coupling current density of 1.0 multiplied by 10 5 A/cm 2 Under the condition of Cu 6 Sn 5 Layer and Cu 3 The variation relation of the thickness of the Sn layer and the total IMC layer along with the stress time, wherein the growth curve of the IMC layer is divided into three stages: in stage I, Cu is added when tin solder is not completely consumed 6 Sn 5 Layer and Cu 3 The thickness of the Sn layer keeps growing along with the stress action; stage II, complete exhaustion of tin solder and Cu 6 Sn 5 Layer direction Cu 3 At the time of Sn layer conversion, Cu 6 Sn 5 Layer thickness decrease with stress time, Cu 3 The thickness of the Sn layer continues to rise along with the stress time; stage III, Cu 6 Sn 5 Complete conversion of the layer to Cu 3 The thickness of the Sn layer and the IMC layer in the welding spot basically does not change any more, and is based on Cu in figure 8 6 Sn 5 Layer and Cu 3 The change relationship of the thickness of the Sn layer and the total IMC layer along with the stress time is obtainedThe alloying life of the lead-free solder joint is shown in the following table 2, and the table 2 is a prediction result of the alloying life of the solder joint.
TABLE 2 results of prediction of alloyed lifetime of solder joints
As can be seen from the above process, Cu is obtained by quantifying the flux of copper atoms under temperature and current stress 3 Sn layer and Cu 6 Sn 5 The net flux of copper atoms in the layers is converted into a growth model which can be used for representing the IMC layers in different alloying stages based on the proportional relation of copper atom concentrations in different IMC layers, and further the alloying service life prediction of the lead-free welding spot is realized, so that the alloying service life prediction is more reasonable, the prediction preparation degree can be improved, a large amount of time and economic cost generated by a service life and failure analysis test are reduced or avoided, and the economic benefit and the social benefit are huge.
The present document has a high general applicability, and taking the example of the consumption of the covering solder layer 302, the complete conversion of the solder into the second interfacial metal compound layer 304 and the first interfacial metal compound layer 303, and the complete conversion of the second interfacial metal compound layer 304 into the first interfacial metal compound layer 303 to perform the full life cycle phase prediction, it is of great significance to the reliability design for supporting high performance microelectronic devices.
It should be understood that, although the steps in the flowcharts related to the embodiments described above are sequentially displayed as indicated by the arrows, the steps are not necessarily performed sequentially as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a part of the steps in the flowcharts related to the above embodiments may include multiple steps or multiple stages, which are not necessarily performed at the same time, but may be performed at different times, and the execution order of the steps or stages is not necessarily sequential, but may be performed alternately or alternately with other steps or at least a part of the steps or stages in other steps.
Based on the same inventive concept, the embodiment of the application also provides a welding spot alloying life prediction device for realizing the welding spot alloying life prediction method. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the method, so that specific limitations in the following embodiment of the device for predicting the alloying lifetime of one or more welding spots can be referred to the limitations of the method for predicting the alloying lifetime of the welding spot, and are not described herein again.
In one embodiment, as shown in fig. 9, fig. 9 is an embodiment of a solder joint alloying life prediction apparatus 900, the apparatus comprising: an obtaining module 901, a first processing module 902, a second processing module 903, and a third processing module 904, wherein:
an obtaining module 901, configured to obtain a flux of the first metal in the pad 201, the solder layer 202, and the interface metal compound layer;
a first processing module 902, configured to obtain a net flux of the first metal in the interfacial metallic compound layer and a relationship between the net flux of the first metal and a growth rate of the interfacial metallic compound layer;
a second processing module 903, configured to establish a growth model of the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and a third processing module 904 for predicting the alloying lifetime of the solder joint based on the growth model of the interfacial metal compound layer.
All or part of each module in the welding spot alloying service life prediction device can be realized by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as shown in fig. 10. The computer device includes a processor, a memory, and a network interface connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The database of the computer device is used to store the flux, net flux, growth rate, growth model and related calculation methods. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a method for predicting an alloying life of a solder joint. The welding spot comprises a welding pad of a first metal and a welding flux layer of a second metal, and the welding pad and the welding flux layer are alloyed to generate an interface metal compound layer comprising the first metal and the second metal; the method comprises the following steps:
obtaining a flux of the first metal in the pad, the solder layer, and the interfacial metal compound layer;
obtaining the net flux of the first metal in the interface metallic compound layer and the relation between the net flux of the first metal and the growth rate of the interface metallic compound layer;
establishing a growth model of the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
In one embodiment, the bonding pad includes a first bonding pad and a second bonding pad, and the solder layer is located between the first bonding pad and the second bonding pad; the interfacial metal compound layer is located between the first pad and the solder layer and between the second pad and the solder layer, the interfacial metal compound layer includes a first interfacial metal compound layer and a second interfacial metal compound layer, and the first interfacial metal compound layer and the second interfacial metal compound layer both include a first metal and a second metal.
It can be seen that the interface metal compound layer includes the first interface metal compound layer and the second interface metal compound layer, rather than a single metal compound layer, so that the obtained growth model is more reasonable, the prediction of the alloying lifetime is more accurate, and the method has great significance for supporting the reliability design of a high-performance device.
In one embodiment, the first pad comprises a cathode pad and the second pad comprises an anode pad; the first metal comprises copper 301, the second metal comprises tin 302; the obtaining the net flux of the first metal in the interfacial metallic compound layer and the relation between the net flux of the first metal and the growth rate of the interfacial metallic compound layer includes:
establishing the following relationship between the thickness variation of the first interfacial metal compound layer and the second interfacial metal compound layer between the first pad and the solder layer and the flux of the first metal in the first pad, the first interfacial metal compound layer, the second interfacial metal compound layer and the solder layer:
wherein the content of the first and second substances,
in the formula, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer，C Cu/η Represents the concentration of copper atoms in the second interfacial metallic compound layer,
indicating a thermal diffusion flux of Cu from the first pad to the first interfacial metallic compound layer due to an atomic concentration gradient,
represents a heat diffusion flux of Cu from the first interfacial metallic compound layer to the second interfacial metallic compound layer due to an atomic concentration gradient,
represents the heat diffusion flux of Cu from the second interface metal compound layer to the second metal due to the atomic concentration gradient,
for the Cu electromigration flux in the first interfacial metallic compound layer described above,
is the Cu electromigration flux, C, in the second interfacial metallic compound layer Cu/ε Represents the concentration of the copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of the copper atoms in the second interfacial metal compound layer, D Cu/ε Represents a diffusion coefficient of the copper atom in the first interfacial metal compound layer, D Cu/η Represents a diffusion coefficient of the copper atoms in the second interfacial metallic compound layer,
is the effective charge number of the copper atoms in the first interfacial metallic compound layer,
is the effective charge number of the copper atoms in the second interfacial metallic compound layer,e is the unit charge amount, ρ ε Is the resistivity, p, of the first interfacial metal compound layer η J is the average current density, k is the boltzmann constant, and T is the kelvin temperature of the solder joint.
Establishing the following relationship between the thickness variation of the first interfacial metal compound layer and the second interfacial metal compound layer between the second pad and the solder layer and the flux of the first metal in the second pad, the first interfacial metal compound layer, the second interfacial metal compound layer and the solder layer:
wherein the content of the first and second substances,
in the formula, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Denotes the concentration of copper atoms in the second interfacial metallic compound layer, ∈ denotes the thickness of the first interfacial metallic compound layer, η denotes the thickness of the second interfacial metallic compound layer,
indicating a thermal diffusion flux of Cu from the first pad to the first interfacial metallic compound layer due to an atomic concentration gradient,
represents a heat diffusion flux of Cu from the first interfacial metallic compound layer to the second interfacial metallic compound layer due to an atomic concentration gradient,
represents a heat diffusion flux of Cu from the second interfacial metallic compound layer to the second metal due to an atomic concentration gradient,
for the Cu electromigration flux in the first interfacial metallic compound layer described above,
for the Cu electromigration flux in the second interfacial metallic compound layer described above,
is the Cu electromigration flux in the second metal layer, C Cu/ε Represents the concentration of the copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of the copper atoms in the second interfacial metal compound layer, C Cu/Sn Represents the concentration of the copper atoms in the second metal layer, D Cu/ε Represents a diffusion coefficient of the copper atom in the first interfacial metal compound layer, D Cu/η Represents a diffusion coefficient of the copper atom in the second interfacial metal compound layer, D Cu/Sn Represents a diffusion coefficient of the copper atoms in the second metal layer,
is the effective charge number of the copper atoms in the first interfacial metallic compound layer,
is the effective charge number of the copper atoms in the second interfacial metallic compound layer,
is the effective charge number of the copper atoms in the second metal layer, e is the unit charge amount, ρ ε Is the resistivity, p, of the first interfacial metal compound layer η Is the firstResistivity, rho, of two interfacial metal compound layers Sn And j is the resistivity of the second metal layer, j is the average current density, k is the Boltzmann constant, and T is the Kelvin temperature of the solder joint.
Obtaining a net thermal diffusion flux of the first metal in the first interfacial metallic compound layer in the first pad based on the following formula:
wherein, C Cu Is the copper atom concentration in the Cu bonding pad, D Cu/ε Is a thermal diffusion coefficient of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metal compound layer.
Obtaining a net thermal diffusion flux of the first metal in the second interfacial metallic compound layer in the second pad based on the following formula:
wherein, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/Sn Concentration of copper atoms dissolved in tin solder, D Cu/η Is the thermal diffusion coefficient of copper atoms in the second interfacial metal compound layer.
And solving the formula to obtain the relation between the net flux of the first metal and the growth rate of the interface metal compound layer.
In one embodiment, the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer comprises: obtaining a relationship between a net flux of the first metal in the first interfacial metallic compound layer between the first pad and the solder layer and a growth rate of the first interfacial metallic compound layer between the first pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/ε Denotes the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metal compound layer, C Cu Is the copper atom concentration in the Cu pad, D Cu/ε Is a thermal diffusion coefficient of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number, rho, of copper atoms in the first interfacial metal compound layer ε Is the resistivity of the first interfacial metal compound layer; obtaining a relationship between a net flux of the first metal in the second interfacial metallic compound layer between the first pad and the solder layer and a growth rate of the second interfacial metallic compound layer between the first pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metal compound layer, C Cu/Sn The concentration of copper atoms dissolved in the tin solder, D Cu/ε Is a thermal diffusion coefficient of copper atoms in the first interfacial metallic compound layer,
represents a copper atom in the above-mentioned secondThe effective charge number of an interfacial metal compound layer,
represents the effective charge number, rho, of copper atoms in the second interfacial metallic compound layer ε Is the resistivity, p, of the first interfacial metal compound layer η Is the resistivity of the second interfacial metal compound layer;
obtaining a relationship between a net flux of the first metal in the first interfacial metallic compound layer between the second pad and the solder layer and a growth rate of the first interfacial metallic compound layer between the second pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metal compound layer, C Cu/Sn The concentration of copper atoms dissolved in the tin solder, D Cu/ε Is a thermal diffusion coefficient of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number of copper atoms in the first interfacial metal compound layer,
represents the effective charge number, rho, of copper atoms in the second interfacial metallic compound layer ε Is the resistivity, rho, of the first interfacial metal compound layer η Is the resistivity of the second interfacial metal compound layer; obtaining the second boundary of the first metal between the second pad and the solder layer based on the following formulaA net flux in the surface metallic compound layer and a growth rate of said second interfacial metallic compound layer between said second pad and said solder layer:
wherein the content of the first and second substances,
in the formula, C Cu/Sn The concentration of copper atoms dissolved in the tin solder, D Cu/Sn Is the thermal diffusivity of copper atoms in the above-mentioned solder layer,
c represents the effective charge number of copper atoms in the solder layer Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, D Cu/η Is a thermal diffusion coefficient of copper atoms in the above-mentioned second interfacial metallic compound layer,
represents the effective charge number, rho, of copper atoms in the second interfacial metallic compound layer η Is the resistivity, rho, of the second interfacial metal compound layer Sn Is the resistivity of the solder layer.
In one embodiment, the modeling the growth of the interfacial metallic compound layer based on the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer includes: obtaining a change with time of the thickness of the first interfacial metallic compound layer and the thickness of the second interfacial metallic compound layer under a temperature stress based on a relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer, wherein a formula of the change with time of the thickness of the first interfacial metallic compound layer and the thickness of the second interfacial metallic compound layer under the temperature stress is:
wherein epsilon 0 Is the initial thickness, η, of the first interfacial metal compound layer 0 Is the initial thickness of the second interfacial metal compound layer. It can be seen that the thickness growth relationship between the first interface metal compound layer 303 and the second interface metal compound layer 304 can be obtained by the method when the solder layer 302 is not completely consumed under a single temperature stress, so that the growth model is more reasonable, and the alloying life is more accurately predicted.
In one embodiment, the modeling the growth of the interfacial metallic compound layer based on the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer includes: obtaining a formula of a change with time of a thickness of the first interface metallic compound layer between the first pad and the solder under a temperature stress coupling current stress and a change with time of a thickness of the second interface metallic compound layer between the first pad and the solder based on a relationship of a net flux of the first metal in the first interface metallic compound layer between the first pad and the solder layer and a growth rate of the first interface metallic compound layer between the first pad and the solder layer and a relationship of a net flux of the first metal in the second interface metallic compound layer between the first pad and the solder layer and a growth rate of the second interface metallic compound layer between the first pad and the solder layer:
wherein, C 1 Is an integral constant related to the initial thickness of the first interfacial metal compound layer between the first pad and the solder layer, C 2 An integral constant related to an initial thickness of said second interfacial metal compound layer between said first pad and said solder layer;
obtaining a formula of a change with time of a thickness of the first interface metallic compound layer between the second pad and the solder under a temperature stress coupling current stress and a change with time of a thickness of the second interface metallic compound layer between the second pad and the solder based on a relationship of a net flux of the first metal in the first interface metallic compound layer between the second pad and the solder layer and a relationship of a growth rate of the first interface metallic compound layer between the second pad and the solder layer and a relationship of a net flux of the first metal in the second interface metallic compound layer between the second pad and the solder layer and a growth rate of the second interface metallic compound layer between the second pad and the solder layer:
wherein, C' 1 And an integral constant, C ', relating to an initial thickness of the first interfacial metal compound layer between the second pad and the solder layer' 2 An integral constant related to an initial thickness of said second interfacial metal compound layer between said second pad and said solder layer;
in one embodiment, the predicting the alloying lifetime of the solder joint based on the growth model of the interfacial metal compound layer includes: predicting the alloying life of the welding spot when the solder layer is exhausted based on the growth model of the interface metal compound layer, which comprises the following steps: and predicting the alloying life of the solder joint when the solder layer is depleted based on the initial thickness of the solder layer, the initial thickness of the first interfacial metal compound layer and the initial thickness of the second interfacial metal compound layer, the growth thickness of the first interfacial metal compound layer and the growth thickness of the second interfacial metal compound layer.
In one embodiment, the predicting the alloying lifetime of the solder joint based on the growth model of the interfacial metal compound layer includes: predicting an alloying lifetime of the solder joint when the second interfacial metal compound layer is completely converted into the first interfacial metal compound layer based on the growth model of the interfacial metal compound layer, comprising: predicting the alloying life of the solder joint under the temperature stress when the second interface metal compound layer is completely converted into the first interface metal compound layer based on the following formula:
where 0.68 is the conversion ratio of the thicknesses of the first interfacial metallic compound layer 303 and the second interfacial metallic compound layer 304. Here,. epsilon 0 Represents the initial thickness, η, of the first interfacial metal compound layer when the tin solder is completely consumed 0 Which represents the initial thickness of the second interfacial metal compound layer described above when the solder is completely depleted.
Predicting the alloying life of the welding spot under the temperature stress coupling current stress when the second interface metal compound layer is completely converted into the first interface metal compound layer based on the following formula:
η＝η 0 -0.68×(ε Anode +ε Cathode )
wherein epsilon Cathode The thickness of the first interface metal compound layer of the cathode at the time of complete depletion of the solder material,. epsilon Anode Is the thickness of the first interfacial metal compound layer in the anode when the solder is completely consumed.
Therefore, the method can solve the problem of mutual transformation among different types of IMC layers, and can accurately predict the alloying service life of the welding spot.
The method, the device, the computer equipment, the storage medium and the computer program product for predicting the alloying service life of the welding spot, obtaining the net flux of the first metal and the relation between the net flux of the first metal and the growth rate of the interface metal compound layer according to the flux of the first metal, further, a growth model of the net flux of the first metal and the interface metal compound layer is obtained according to the growth rate, and the alloying life of the welding spot is predicted based on the growth model, it can be seen that the growth model is obtained gradually based on the flux of the first metal, so that the prediction of the alloying life is more reasonable, thereby improving the prediction preparation degree, further, the time and the economic cost generated by a large number of service lives and failure analysis tests are reduced or avoided, and great economic benefits and social benefits are achieved.
Those skilled in the art will appreciate that the architecture shown in fig. 10 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In one embodiment, a computer device is further provided, which includes a memory and a processor, the memory stores a computer program, and the processor implements the steps of the above method embodiments when executing the computer program.
In an embodiment, a computer-readable storage medium is provided, on which a computer program is stored which, when being executed by a processor, carries out the steps of the above-mentioned method embodiments.
In an embodiment, a computer program product is provided, comprising a computer program which, when being executed by a processor, carries out the steps of the above-mentioned method embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above may be implemented by hardware instructions of a computer program, which may be stored in a non-volatile computer-readable storage medium, and when executed, may include the processes of the embodiments of the methods described above. Any reference to memory, database, or other medium used in the embodiments provided herein may include at least one of non-volatile and volatile memory. The nonvolatile Memory may include Read-Only Memory (ROM), magnetic tape, floppy disk, flash Memory, optical Memory, high-density embedded nonvolatile Memory, resistive Random Access Memory (ReRAM), Magnetic Random Access Memory (MRAM), Ferroelectric Random Access Memory (FRAM), Phase Change Memory (PCM), graphene Memory, and the like. Volatile Memory can include Random Access Memory (RAM), external cache Memory, and the like. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM), among others. The databases referred to in various embodiments provided herein may include at least one of relational and non-relational databases. The non-relational database may include, but is not limited to, a block chain based distributed database, and the like. The processors referred to in the embodiments provided herein may be general purpose processors, central processing units, graphics processors, digital signal processors, programmable logic devices, quantum computing based data processing logic devices, etc., without limitation.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above examples only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.
Claims (12)
1. The method for predicting the alloying service life of the welding spot is characterized in that the welding spot comprises a welding pad of a first metal and a welding flux layer of a second metal, and the welding pad and the welding flux layer are alloyed to generate an interface metal compound layer comprising the first metal and the second metal; the method comprises the following steps:
obtaining a flux of the first metal within the pad, the solder layer, and the interfacial metal compound layer;
obtaining the net flux of the first metal in the interface metal compound layer and the relation between the net flux of the first metal and the growth rate of the interface metal compound layer;
establishing a growth model for the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
2. The method of claim 1, wherein the pad comprises a first pad and a second pad, wherein the solder layer is between the first pad and the second pad, wherein the interfacial metal compound layer is between the first pad and the solder layer and between the second pad and the solder layer, wherein the interfacial metal compound layer comprises a first interfacial metal compound layer and a second interfacial metal compound layer, and wherein the first interfacial metal compound layer and the second interfacial metal compound layer are reaction products of the first metal and the second metal.
3. The method of claim 2, wherein the first pad comprises a cathode pad, the second pad comprises an anode pad, the first metal comprises copper, the second metal comprises tin, and the obtaining the net flux of the first metal in the interfacial metallic compound layer and the relationship of the net flux of the first metal to the growth rate of the interfacial metallic compound layer comprises:
establishing the following relationship between the thickness variation of the first interfacial metallic compound layer and the second interfacial metallic compound layer between the first pad and the solder layer and the flux of the first metal in the first pad, the first interfacial metallic compound layer, the second interfacial metallic compound layer and the solder layer:
wherein, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metallic compound layer,
representing a thermal diffusion flux of copper from the first pad to the first interfacial metallic compound layer due to an atomic concentration gradient,
represents the thermal diffusion flux of copper from the first interfacial metallic compound layer to the second interfacial metallic compound layer due to the atomic concentration gradient,
represents the thermal diffusion flux of copper from the second interfacial metallic compound layer to the second metal due to the atomic concentration gradient,
for electromigration flux of copper in the first interfacial metallic compound layer caused by electron wind forces,
a copper electromigration flux in the second interfacial metallic compound layer due to electron wind forces;
obtaining a net electromigration flux of the first metal in the first interfacial metal compound layer in the first pad based on the following equation:
wherein, C Cu/ε Represents the concentration of the copper atoms in the first interfacial metal compound layer, D Cu/ε Represents a thermal diffusion coefficient of the copper atoms in the first interfacial metallic compound layer,
is the effective charge number, rho, of the copper atoms in the first interfacial metallic compound layer ε Is the resistivity of the first interface metal compound layer, k is the boltzmann constant, T is the kelvin temperature of the solder joint, e is the unit charge amount, j is the average current density;
obtaining a net electromigration flux of the first metal in the first pad in the second interfacial metallic compound layer based on the following equation:
wherein, C Cu/η Represents the concentration of the copper atoms in the second interfacial metal compound layer, D Cu/η Represents a thermal diffusion coefficient of the copper atoms in the second interfacial metallic compound layer,
is the effective charge number, rho, of the copper atoms in the second interfacial metallic compound layer η Is the resistivity of the second interfacial metal compound layer; k is a Boltzmann constant, T is the Kelvin temperature of the solder joint, e is the unit charge amount, and j is the average current density;
obtaining a net thermal diffusion flux of the first metal in the first pad in the first interfacial metallic compound layer based on the following equation:
wherein, C Cu Is the copper atom concentration in the copper pad, D Cu/ε Is the thermal diffusion coefficient of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metallic compound layer;
obtaining a net thermal diffusion flux of the first metal in the first pad in the second interfacial metallic compound layer based on the following equation:
wherein, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/Sn Concentration of copper atoms dissolved in tin solder, D Cu/η Is the thermal diffusivity of copper atoms in the second interfacial metallic compound layer;
establishing the following relationship between the thickness variation of the first interfacial metallic compound layer and the second interfacial metallic compound layer between the second pad and the solder layer and the flux of the first metal in the second pad, the first interfacial metallic compound layer, the second interfacial metallic compound layer and the solder layer:
wherein, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Denotes a concentration of copper atoms in the second interfacial metallic compound layer, ε denotes a thickness of the first interfacial metallic compound layer, η denotes a thickness of the second interfacial metallic compound layer,
representing a thermal diffusion flux of copper from the second pad to the first interfacial metallic compound layer due to an atomic concentration gradient,
represents the thermal diffusion flux of copper from the first interfacial metallic compound layer to the second interfacial metallic compound layer due to the atomic concentration gradient,
represents the thermal diffusion flux of copper from the second interfacial metallic compound layer to the second metal due to the atomic concentration gradient,
for electromigration flux of copper in the first interfacial metallic compound layer caused by electron wind forces,
for electromigration flux of copper in the second interfacial metallic compound layer caused by electron wind,
a copper electromigration flux in the second metal layer caused by electron wind forces;
obtaining a net electromigration flux of the first metal in the first interfacial metallic compound layer in the second pad based on the following equation:
wherein, C Cu/ε Represents the concentration of the copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of the copper atoms in the second interfacial metal compound layer; d Cu/ε Represents a thermal diffusion coefficient of the copper atom in the first interfacial metal compound layer, D Cu/η Represents a thermal diffusion coefficient of the copper atoms in the second interfacial metallic compound layer;
is the effective charge number of the copper atoms in the first interfacial metallic compound layer,
is the effective charge number of the copper atoms in the second interfacial metallic compound layer; rho ε Is the resistivity, p, of the first interfacial metal compound layer η Is the resistivity of the second interfacial metal compound layer; k is a boltzmann constant, T is a kelvin temperature of a welding spot, e is a unit charge quantity, and j is an average current density;
obtaining a net electromigration flux of the first metal in the second interfacial metal compound layer in the second pad based on the following equation:
wherein, C Cu/Sn Represents the concentration of the copper atoms dissolved in the second metal layer, D Cu/Sn Represents a thermal diffusion coefficient of the copper atoms in the second metal layer,
is the effective charge number of the copper atoms in the second metal layer; rho Sn K is the resistivity of the second metal layer and is BohrThe Zeeman constant, T is the Kelvin temperature of the welding spot, e is the unit charge amount, and j is the average current density;
obtaining a net thermal diffusion flux of the first metal in the first interfacial metallic compound layer in the second pad based on the following equation:
wherein, C Cu Is the copper atomic concentration in the copper pad, D Cu/ε Is the thermal diffusion coefficient of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metallic compound layer;
obtaining a net thermal diffusion flux of the first metal in the second interfacial metallic compound layer in the second pad based on the following equation:
wherein, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/Sn Concentration of copper atoms dissolved in tin solder, D Cu/η Is the thermal diffusivity of copper atoms in the second interfacial metallic compound layer.
4. The method of claim 3, wherein the relationship between the net flux of the first metal in the interfacial metallic compound layer and the growth rate of the interfacial metallic compound layer comprises:
obtaining a relationship between a net flux of the first metal in the first interfacial metallic compound layer between the first pad and the solder layer and a growth rate of the first interfacial metallic compound layer between the first pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metal compound layer, C Cu Is the copper atomic concentration in the copper pad, D Cu/ε Is the thermal diffusivity of copper atoms in the first interfacial metallic compound layer,
representing the effective charge number of copper atoms in the first interface metallic compound layer, rho epsilon is the resistivity of the first interface metallic compound layer, k is a Boltzmann constant, T is the Kelvin temperature of a welding spot, e is a unit charge amount, and j is an average current density;
obtaining a relationship between a net flux of the first metal in the second interfacial metallic compound layer between the first pad and the solder layer and a growth rate of the second interfacial metallic compound layer between the first pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, C Cu/η Represents the concentration of copper atoms in the second interfacial metal compound layer, D Cu/Sn Is the thermal diffusivity of copper atoms in the solder layer,
represents the effective charge number of copper atoms in the solder layer, C Cu/Sn Represents the concentration of the copper atoms dissolved in the second metal layer, D Cu/ε Is the thermal diffusivity of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number, rho, of copper atoms in the second interfacial metallic compound layer ε Is the resistivity, p, of the first interfacial metal compound layer η Is the resistivity of the second interface metal compound layer, k is the boltzmann constant, T is the kelvin temperature of the solder joint, e is the unit charge amount, j is the average current density;
obtaining a relationship between a net flux of the first metal in the first interfacial metallic compound layer between the second pad and the solder layer and a growth rate of the first interfacial metallic compound layer between the second pad and the solder layer based on the following formula:
wherein, the first and the second end of the pipe are connected with each other,
in the formula, C Cu/η Represents the concentration of copper atoms in the second interfacial metal compound layer, D Cu/η Is the thermal diffusion coefficient of copper atoms in the second interfacial metal compound layer, D Cu/ε Is the thermal diffusivity of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number of copper atoms in the first interfacial metallic compound layer,
represents the effective charge number, rho, of copper atoms in the second interfacial metallic compound layer ε Is the resistivity, p, of the first interfacial metal compound layer η K is a boltzmann constant, T is a kelvin temperature of a welding spot, e is a unit charge amount, and j is an average current density;
obtaining a relationship between a net flux of the first metal in the second interfacial metallic compound layer between the second pad and the solder layer and a growth rate of the second interfacial metallic compound layer between the second pad and the solder layer based on the following formula:
wherein the content of the first and second substances,
in the formula, C Cu/Sn The concentration of copper atoms dissolved in the tin solder layer, D Cu/Sn Is the thermal diffusivity of copper atoms in the solder layer,
represents the effective charge number of copper atoms in the solder layer, C Cu/ε Represents the concentration of copper atoms in the first interfacial metal compound layer, D Cu/η Is the thermal diffusivity of copper atoms in the second interfacial metallic compound layer,
represents the effective charge number, rho, of copper atoms in the second interfacial metallic compound layer η Is the resistivity, p, of the second interfacial metal compound layer Sn Is the resistivity of the solder layer.
5. The method of claim 4, wherein modeling the growth of the interfacial metallic compound layer based on the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer comprises:
obtaining the change of the thickness of the first interface metal compound layer and the thickness of the second interface metal compound layer with time under temperature stress based on the relation between the net flux of the first metal and the growth rate of the interface metal compound layer, wherein the formula of the change of the thickness of the first interface metal compound layer and the thickness of the second interface metal compound layer with time under temperature stress is as follows:
wherein epsilon 0 Is the initial thickness, η, of the first interfacial metal compound layer 0 Is the initial thickness of the second interfacial metal compound layer.
6. The method of claim 5, wherein modeling the growth of the interfacial metallic compound layer based on the relationship between the net flux of the first metal and the growth rate of the interfacial metallic compound layer comprises:
obtaining a formula of a change in thickness of the first interfacial metallic compound layer between the first pad and the solder under a temperature stress coupled current stress and a change in thickness of the second interfacial metallic compound layer between the first pad and the solder over time based on a relationship of a net flux of the first metal in the first interfacial metallic compound layer between the first pad and the solder layer and a relationship of a growth rate of the first interfacial metallic compound layer between the first pad and the solder layer and a relationship of a net flux of the first metal in the second interfacial metallic compound layer between the first pad and the solder layer and a relationship of a growth rate of the second interfacial metallic compound layer between the first pad and the solder layer:
wherein, C 1 An integral constant, C, related to an initial thickness of the first interfacial metallic compound layer between the first pad and the solder layer 2 An integration constant related to an initial thickness of the second interfacial metallic compound layer between the first pad and the solder layer;
obtaining a formula of a change in thickness of the first interfacial metallic compound layer between the second pad and the solder under a temperature stress coupling current stress over time and a change in thickness of the second interfacial metallic compound layer between the second pad and the solder over time based on a relationship of a net flux of the first metal in the first interfacial metallic compound layer between the second pad and the solder layer and a relationship of a growth rate of the first interfacial metallic compound layer between the second pad and the solder layer and a relationship of a net flux of the first metal in the second interfacial metallic compound layer between the second pad and the solder layer and a growth rate of the second interfacial metallic compound layer between the second pad and the solder layer:
wherein, C' 1 And an integration constant, C ', related to the initial thickness of the first interfacial metallic compound layer between the second pad and the solder layer' 2 Is an integral constant related to an initial thickness of the second interfacial metal compound layer between the second pad and the solder layer.
7. The method of claim 6, wherein predicting the alloying life of the solder joint based on the growth model of the interfacial metal compound layer comprises: predicting an alloying life of the solder joint when the second metal solder layer is depleted based on a growth model of the interfacial metal compound layer, comprising:
based on the initial thickness of the second metal solder layer, the initial thickness of the first interfacial metal compound layer and the initial thickness of the second interfacial metal compound layer, the grown thickness of the first interfacial metal compound layer and the grown thickness of the second interfacial metal compound layer predict an alloying life of the solder joint when the second metal solder layer is depleted.
8. The method of claim 7, wherein predicting the alloying life of the solder joint based on the growth model of the interfacial metal compound layer comprises: predicting an alloying lifetime of the solder joint when the second interfacial metal compound layer is completely converted into the first interfacial metal compound layer based on a growth model of the interfacial metal compound layer, comprising:
predicting the alloying life of the solder joint when the second interfacial metallic compound layer is completely converted into the first interfacial metallic compound layer under the temperature stress based on the following formula:
wherein 0.68 is a conversion ratio of thicknesses of the first interfacial metal compound layer and the second interfacial metal compound layer, where ε 0 Represents the initial thickness, η, of the first interfacial metal compound layer when the solder is completely consumed 0 Represents the initial thickness of the second interfacial metal compound layer when the solder is completely depleted;
predicting the alloying life of the welding spot under the temperature stress coupling current stress when the second interface metal compound layer is completely converted into the first interface metal compound layer based on the following formula:
η＝η 0 -0.68×(ε Anode +ε Cathode )
wherein epsilon Cathode Is the thickness of the first interfacial metal compound layer between the first pad and the solder layer when the solder is completely consumed Anode Is the thickness of the first interfacial metallic compound layer in between the second pad and the solder layer when the solder is fully depleted.
9. The device for predicting the alloying service life of the welding spot is characterized in that the welding spot comprises a welding spot of a first metal and a welding flux layer of a second metal, and the welding spot and the welding flux layer are alloyed to generate an interface metal compound layer comprising the first metal and the second metal; the device comprises:
an obtaining module, configured to obtain a flux of the first metal in the pad, the solder layer, and the interface metal compound layer;
a first processing module for obtaining the net flux of the first metal in the interfacial metallic compound layer and the relation between the net flux of the first metal and the growth rate of the interfacial metallic compound layer;
a second processing module for establishing a growth model of the interfacial metallic compound layer based on a relationship between a net flux of the first metal and a growth rate of the interfacial metallic compound layer;
and the third processing module is used for predicting the alloying life of the welding spot based on the growth model of the interface metal compound layer.
10. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the method of any of claims 1 to 8.
11. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 8.
12. A computer program product comprising a computer program, characterized in that the computer program realizes the steps of the method of any one of claims 1 to 8 when executed by a processor.
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| PCT/CN2022/104383 WO2023226168A1 (en) | 2022-05-24 | 2022-07-07 | Method and device for predicting alloying service life of welding spot and computer device |
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| CN101984442A (en) * | 2010-10-29 | 2011-03-09 | 北京工业大学 | Method for predicting fatigue life of lead-free solder joint in electronic packaging |
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