Electromigration simulation method, electronic equipment, storage medium and program product

Abstract

The invention provides an electromigration simulation method, electronic equipment, a storage medium and a program product. The electromigration simulation method comprises the following steps: establishing a geometric model, and performing mesh generation on the model to generate a finite element model; setting initial conditions and boundary conditions of the finite element model, and performing multi-physics field coupling analysis on the finite element model; after multi-physics field coupling analysis, a life-death unit technology is introduced into a finite element model, and electromigration void evolution is simulated. The model is subjected to mesh generation to generate a finite element model, the welding spot electromigration failure is subjected to multi-physical field coupling analysis by adopting a finite element method, and electromigration cavity evolution is simulated by introducing a life-death element technology, so that the purpose of accurately predicting the welding spot electromigration failure position is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic device packaging, and in particular relates to an electromigration simulation method, electronic equipment, storage medium and program product. Background Art

[0002] As packaged chips transform towards multifunctionality, the density of solder joints of packaged chips gradually increases, while the spacing and size of solder joints gradually decrease, resulting in a higher current density inside the solder joints, which causes the metal atoms to migrate and diffuse along the direction of electron movement, i.e., electromigration. During the electromigration process, metal atoms will cause mass transport, resulting in the formation of voids near the cathode and hillocks near the anode. The formation of solder joint voids can easily lead to circuit breakages; while the formation of hillocks can easily lead to short circuits between solder joints and adjacent solder joints. Therefore, electromigration causes extremely serious reliability problems for electronic packaging devices.

[0003] Research shows that electromigration failure is not a single electrical migration mechanism. When a high current density passes through the solder joint, Joule heat will be generated, forming a temperature gradient, which will generate a driving force for thermal migration. At the same time, Joule heat will cause thermal stress in the structure. During the electromigration process, voids and hillocks will form in the solder joint, causing internal stress to be generated due to structural changes. The stress gradient formed by these stresses is the driving mechanism for stress migration of atoms. During the electromigration process, along with atomic migration, the atomic concentration distribution inside the solder joint is uneven, and the resulting atomic concentration gradient will cause chemical migration.

[0004] The inventors found in the process of implementing this embodiment that due to the various driving mechanisms of electromigration, it is difficult for existing electromigration testing methods to measure the distribution of these driving forces inside the solder joint, and thus it is impossible to accurately predict the electromigration failure position of the solder joint. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides an electromigration simulation method, electronic equipment, storage medium and program product, which at least partially solve the problem that the electromigration failure position of the solder joint cannot be accurately predicted in the prior art.

[0006] In a first aspect, an embodiment of the present disclosure provides an electromigration simulation method, comprising: Establish a geometric model and mesh the model to generate a finite element model; Set the initial conditions and boundary conditions of the finite element model and perform multi-physics coupling analysis on the finite element model; After multi-physics field coupling analysis, the birth-death cell technology is introduced into the finite element model to simulate the evolution of electromigration voids.

[0007] Optionally, the step of establishing a geometric model and meshing the model to generate a finite element model includes: Create a geometric model including copper plates and solder balls; Define the element type and material type in the finite element model.

[0008] Optionally, the setting of initial conditions and boundary conditions of the finite element model includes: Set the initial conditions and boundary conditions for the four physical fields of electricity, thermal, structure and diffusion.

[0009] Optionally, after the step of setting the initial conditions and boundary conditions of the finite element model, the following step is further included: Simulation results of the finite element model are extracted, including temperature, voltage, current density, hydrostatic stress, and atomic concentration.

[0010] Optionally, the method of introducing the birth-death unit technology into the finite element model after the physical field coupling analysis to simulate the evolution of the electromigration void includes: The electromigration failure life is obtained based on the ratio of the void area generated on the bottom surface of the solder joint in the finite element model to the set threshold.

[0011] Optionally, the set threshold is calculated based on the relationship between the resistance of the solder joint and the bottom surface area.

[0012] Optionally, the set threshold is 17%.

[0013] In a second aspect, an embodiment of the present disclosure further provides an electronic device, the electronic device comprising: at least one processor; and, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can perform any electromigration simulation method described in the first aspect.

[0014] In a third aspect, an embodiment of the present disclosure further provides a computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable a computer to execute any of the electromigration simulation methods described in the first aspect.

[0015] In a fourth aspect, an embodiment of the present disclosure further provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements any of the electromigration simulation methods described in the first aspect.

[0016] The present invention provides an electromigration simulation method, an electronic device, a storage medium and a program product, wherein the electromigration simulation method meshes the model to generate a finite element model, uses the finite element method to perform multi-physical field coupling analysis on solder joint electromigration failure, and simulates the evolution of electromigration voids by introducing the life-and-death unit technology, thereby achieving the purpose of accurately predicting the location of solder joint electromigration failure. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The above and other objects, features and advantages of the present disclosure will become more apparent through a more detailed description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present disclosure.

[0018] Figure 1a to Figure 1b A schematic diagram of a geometric model and a finite element model in the electromigration simulation method provided in an embodiment of the present disclosure; Figure 2a to Figure 2e In the electromigration simulation method provided in the embodiment of the present disclosure Cloud diagram of physical quantities of welding point at each moment; Figure 3a to Figure 3f A schematic diagram of void evolution during electromigration in an electromigration simulation method is provided for an embodiment of the present disclosure; Figure 4 A schematic diagram of solder ball voids when electromigration fails in an electromigration simulation method is provided for an embodiment of the present disclosure. DETAILED DESCRIPTION

[0019] The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.

[0020] It should be clear that the following embodiments of the present disclosure are described by specific specific examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that the following embodiments and features in the embodiments can be combined with each other in the absence of conflict. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present disclosure.

[0021] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0022] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present disclosure. The illustrations only show components related to the present disclosure rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0023] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.

[0024] This embodiment mainly considers four driving forces: electron wind force, hydrostatic stress gradient, temperature gradient and atomic concentration gradient. This embodiment considers the electromigration simulation method of multiple migration mechanisms, performs multi-physics field coupling analysis on solder joint electromigration, predicts the failure position and life, and provides an effective basis for improving solder joint reliability. At present, the life prediction of electronic packaging products mostly uses the Black equation. A large number of studies have shown that the Black equation only considers the influence of "electron wind force" and does not consider other driving force factors, and cannot accurately predict the electromigration failure life. This example adopts a multi-physics field coupling analysis method, comprehensively considering the four driving forces of electron wind force, hydrostatic stress gradient, temperature gradient and atomic concentration gradient, and simulates the evolution of electromigration voids by introducing the life and death unit technology to more accurately predict the electromigration failure position of the solder joint.

[0025] The multi-physics coupling analysis method is generally divided into two categories: indirect coupling and direct coupling. The indirect coupling method realizes multi-physics coupling analysis by using the result of the previous physical field analysis as the load excitation of the next physical field. This method is easy to converge, but the process is complicated. This embodiment uses the SOLID226 unit in ANSYS to activate the degrees of freedom of temperature, voltage, displacement and concentration. According to the direct coupling method, the coupling analysis of the four physical fields of electricity, heat, structure and diffusion can be performed at one time.

[0026] This embodiment discloses an electromigration simulation method, including: Establish a geometric model and mesh the model to generate a finite element model; A geometric model consisting of a copper plate and solder balls is established, the model is meshed to generate a finite element model, and the unit type and material type are defined.

[0027] Set the initial conditions and boundary conditions of the finite element model, and perform physical field coupling analysis on the finite element model; After multi-physics field coupling analysis, the birth-death cell technology is introduced into the finite element model to simulate the evolution of electromigration voids.

[0028] Optionally, the step of establishing a geometric model and meshing the model to generate a finite element model includes: Create a geometric model including copper plates and solder balls; Define the element type and material type in the finite element model.

[0029] Optionally, the setting of initial conditions and boundary conditions of the finite element model includes: Set the initial conditions and boundary conditions for the four fields: electrical, thermal, structural and diffusion.

[0030] Optionally, after the step of setting the initial conditions and boundary conditions of the finite element model, the following step is further included: Simulation results of the finite element model are extracted, including temperature, voltage, current density, hydrostatic stress, and atomic concentration.

[0031] Optionally, after the multi-physics field coupling analysis, the birth-death unit technology is introduced into the finite element model to simulate the evolution of electromigration voids, including: The electromigration failure life is obtained based on the ratio of the void area generated on the bottom surface of the solder joint in the finite element model to the set threshold.

[0032] A 20% increase in solder joint resistance is the electromigration failure criterion. Based on the relationship between the solder joint resistance and the bottom surface area, a 17% void area is generated on the bottom surface as the electromigration failure criterion to obtain the electromigration failure life.

[0033] In a specific implementation scenario, considering the electromigration simulation method of multiple migration mechanisms, this embodiment uses ANSYS APDL to write relevant programs, and the specific steps include: Step S1: The geometric model of this example consists of two copper layers and a solder ball. The geometric model is established and meshed to generate a finite element model, such as Figure 1a The geometric model is shown. Figure 1b It is a finite element model. The unit type is defined. SOLID226 unit is used. The material type is defined. The material parameters are shown in Tables 1 and 2. The electromigration parameters of the material are defined in Table 3.

[0034] Table 1. Material parameters Material <![CDATA[Resistivity (Ωm) × 10 -8 > Thermal conductivity (W / (mK)) <![CDATA[Coefficient of thermal expansion (1 / K) × 10 -6 > Specific heat capacity (J / (kg.K)) <![CDATA[Density (kg / m 3 )]]> <![CDATA[Elastic modulus (Pa) × 10 9 > Poisson's ratio <![CDATA[Yield stress (Pa) × 10 6 > Cu 1.75 401 16.5 384.6 8960 128 0.34 400 SAC305 12 36 28 130 7400 39.5 0.3 — Table 2. Viscoplastic ANAND characteristics of solder Deformation resistance saturation value s0 (Pa) <![CDATA[1.0665×10 6 ]]> Activation energy (Q / T) 10413 Pre-exponential factor / constant A (1 / s) <![CDATA[8.25×10 7 ]]> Stress coefficient δ 2.55 Strain rate sensitivity factor m 0.14145 Hardening constant h0 (Pa) <![CDATA[5.0239×10 7 ]]> Deformation resistance saturation coefficient Ŝ (Pa) <![CDATA[2.03×10 7 ]]> Strain rate sensitivity factor n for resistance to deformation 0.03 Strain rate sensitivity factor a of anti-hardening 1.12 Table 3. Electromigration parameters of materials Electromigration parameters Cu SAC305 <![CDATA[Initial self-diffusion coefficient D0 (m 2 ) / s]]> <![CDATA[7.8×10 -5 ]]> <![CDATA[4.1×10 -5 ]]> <![CDATA[Activation energy E a > <![CDATA[2.1×10 5 J / (K.mol)]]> 0.8 eV <![CDATA[Atomic volume Ω (m 3 ).]]> <![CDATA[1.182×10 -29 ]]> <![CDATA[2.71×10 -29 ]]> Transfer heat Q (eV) — 0.0094 Effective charge -4 -23

[0035] Step S2: Set the initial conditions and boundary conditions of the four fields of electricity, heat, structure, and diffusion. The ambient temperature is 25°C, and the convection heat transfer coefficient is 12.5 W / (m 2 .℃), the initial concentration is 1, one end of the copper lead is grounded, and a current of 2.5A is applied to the other end. The Z displacement of the top and bottom surfaces of the model is constrained, and the X displacement is restricted at the lower left end of the copper plate. Then, a multi-physics coupling analysis is performed.

[0036] Step S3: Extract cloud maps of temperature, voltage, current density, hydrostatic stress, atomic concentration, etc., such as Figure 2a is the temperature, Figure 2b is the voltage, Figure 2c is the current density, Figure 2d is the hydrostatic stress, Figure 2e is the atomic concentration. Temperature is the temperature field, voltage and current density are the electric field, hydrostatic stress is the structural field, and atomic concentration is the diffusion field.

[0037] Step S4: Introduce the birth and death cell technology to simulate the evolution process of electromigration voids, such as Figure 3a 2.28×10 6 s moment, Figure 3b for time, Figure 3c for time, Figure 3d for time, Figure 3e for time, Figure 3f for time.

[0038] Step S5: The bottom surface produces a 17% void area as the electromigration failure criterion, and the electromigration failure life is obtained as 4.7×10 6 s, the schematic diagram of the void at failure time is as follows Figure 4 shown.

[0039] In this embodiment Figure 1a to Figure 1b , Figure 2a to Figure 2e , Figures 3a to 3f and Figure 4 The text in the description does not affect the clarity and completeness of the description.

[0040] This implementation comprehensively considers various migration driving mechanisms to conduct multi-physics field coupling analysis, and simulates the evolution of voids by introducing the life and death unit technology to more accurately predict the electromigration failure location and failure life.

[0041] The electronic device disclosed in this embodiment includes a memory and a processor. The memory is used to store non-temporary computer-readable instructions. Specifically, the memory may include one or more computer program products, and the computer program product may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, a random access memory (RAM) and / or a cache memory (cache), etc. The non-volatile memory may include, for example, a read-only memory (ROM), a hard disk, a flash memory, etc.

[0042] The processor may be a central processing unit (CPU) or other forms of processing units with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the present disclosure, the processor is used to run the computer-readable instructions stored in the memory, so that the electronic device performs all or part of the steps of the electromigration simulation method of each embodiment of the present disclosure.

[0043] Those skilled in the art should be able to understand that in order to solve the technical problem of how to obtain a good user experience, the present embodiment may also include well-known structures such as a communication bus and an interface, and these well-known structures should also be included in the protection scope of the present disclosure.

[0044] An electronic device may include a processing device (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) or a program loaded from a storage device into a random access memory (RAM). In the RAM, various programs and data required for the operation of the electronic device are also stored. The processing device, ROM, and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0045] Typically, the following devices can be connected to the I / O interface: input devices such as sensors or visual information acquisition devices; output devices such as display screens; storage devices such as magnetic tapes and hard disks; and communication devices. The communication device can allow the electronic device to communicate with other devices (such as edge computing devices) wirelessly or by wire to exchange data.

[0046] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a non-transitory computer-readable medium, and the computer program contains program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication device, or installed from a storage device, or installed from a ROM. When the computer program is executed by a processing device, all or part of the steps of the electromigration simulation method of the embodiment of the present disclosure are executed.

[0047] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0048] The computer-readable storage medium disclosed in this embodiment stores non-transitory computer-readable instructions, and when the non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the electromigration simulation method of each embodiment of the present disclosure are executed.

[0049] The above-mentioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or mobile hard disk), media with built-in rewritable non-volatile memory (e.g., memory card) and media with built-in ROM (e.g., ROM box).

[0050] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0051] The basic principles of the present disclosure are described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, effects, etc. mentioned in the present disclosure are only examples and not limitations, and it cannot be considered that these advantages, strengths, effects, etc. are required by each embodiment of the present disclosure. In addition, the specific details disclosed above are only for the purpose of illustration and ease of understanding, and are not limitations. The above details do not limit the present disclosure to the necessity of adopting the above specific details to be implemented.

[0052] In the present disclosure, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. The block diagrams of the devices, devices, equipment, and systems involved in the present disclosure are only illustrative examples and are not intended to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagram. As will be appreciated by those skilled in the art, these devices, devices, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including", "comprising", "having", etc. are open words, referring to "including but not limited to", and can be used interchangeably with them. The words "or" and "and" used here refer to the words "and / or" and can be used interchangeably with them, unless the context clearly indicates otherwise. The words "such as" used here refer to the phrase "such as but not limited to", and can be used interchangeably with them.

[0053] Additionally, as used herein, "or" used in a list of items beginning with "at least one" indicates a separate list, so that, for example, a list of "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not mean that the example described is preferred or better than other examples.

[0054] It should also be noted that in the system and method of the present disclosure, each component or each step can be decomposed and / or recombined. Such decomposition and / or recombination should be regarded as equivalent solutions of the present disclosure.

[0055] Various changes, substitutions, and modifications of the techniques described herein may be made without departing from the teachings defined by the appended claims. Furthermore, the scope of the claims of the present disclosure is not limited to the specific aspects of the processes, machines, manufactures, compositions of events, means, methods, and actions described above. Currently existing or later to be developed processes, machines, manufactures, compositions of events, means, methods, or actions that perform substantially the same functions or achieve substantially the same results as the corresponding aspects described herein may be utilized. Thus, the appended claims include such processes, machines, manufactures, compositions of events, means, methods, or actions within their scope.

[0056] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present disclosure. Therefore, the present disclosure is not intended to be limited to the aspects shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0057] The above description has been given for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present disclosure to the forms disclosed herein. Although multiple example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, changes, additions and sub-combinations thereof.

Claims

1. An electromigration simulation method, characterized in that: include: Establish a geometric model and mesh the model to generate a finite element model; Set the initial conditions and boundary conditions of the finite element model and perform multi-physics coupling analysis on the finite element model; After multi-physics field coupling analysis, the birth-death cell technology is introduced into the finite element model to simulate the evolution of electromigration voids.

2. The electromigration simulation method according to claim 1, characterized in that: The step of establishing a geometric model and meshing the model to generate a finite element model includes: Create a geometric model including copper plates and solder balls; Define the element type and material type in the finite element model.

3. The electromigration simulation method according to claim 1, characterized in that: The setting of the initial conditions and boundary conditions of the finite element model includes: Set the initial conditions and boundary conditions for the four physical fields of electricity, thermal, structure and diffusion.

4. The electromigration simulation method according to claim 3, characterized in that: After the step of setting the initial conditions and boundary conditions of the finite element model, the method further includes: Simulation results of the finite element model are extracted, including temperature, voltage, current density, hydrostatic stress, and atomic concentration.

5. The electromigration simulation method according to claim 4, characterized in that: After the multi-physics field coupling analysis, the birth and death unit technology is introduced to simulate the evolution of electromigration voids, including: The electromigration failure life is obtained based on the ratio of the void area generated on the bottom surface of the solder joint in the finite element model to the set threshold.

6. The electromigration simulation method according to claim 5, characterized in that: The set threshold is calculated based on the relationship between the resistance of the solder joint and the bottom surface area.

7. The electromigration simulation method according to claim 5, characterized in that: The set threshold is 17%.

8. An electronic device, characterized in that: The electronic device comprises: at least one processor; and, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the electromigration simulation method according to any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the electromigration simulation method according to any one of claims 1 to 7.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the electromigration simulation method according to any one of claims 1 to 7 is implemented.

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