Metallic compound growth prediction method of lead-free micro-interconnection structure under temperature cycle

Abstract

The invention discloses a metal compound growth prediction method for a lead-free micro-interconnection structure under temperature circulation, and the method comprises the steps: building a function relation between the thermal diffusion net flux of target metal atoms in the lead-free micro-interconnection structure and the thickness growth rate of a metal compound layer, establishing a function relationship between the thickness growth rate and the thermal diffusion coefficient of the target metal atom; establishing a function relationship of the thermal diffusion coefficient of the target metal atom along with the temperature change; obtaining a thickness growth rate expression taking the temperature as a variable according to the function relationship of the thermal diffusion coefficient changing along with the temperature and the function relationship of the thickness growth rate and the thermal diffusion coefficient; time integration is carried out on a thickness growth rate expression with temperature as a variable, the thickness growth amount of the metal compound layer in a single temperature cycle period is obtained, and thickness growth prediction of the metal compound layer in multiple temperature cycle periods is achieved through accumulation calculation. According to the method, the growth prediction of the lead-free micro-interconnection interface metal compound under the temperature cycle working condition can be effectively realized.

Description

Technical Field

[0001] This invention belongs to the field of chip packaging, specifically relating to a method for predicting the growth of metal compounds in lead-free micro interconnect structures under temperature cycling. Background Technology

[0002] As chip manufacturing processes approach their physical limits, micro-interconnects in advanced packaging become crucial for reliability, with lead-free micro-interconnects gaining mainstream acceptance due to their environmental friendliness and mature technology. However, lead-free solders readily react with base metals (such as Cu and Ni) during service to form brittle intermetallic compounds (such as Cu6Sn5 and Cu3Sn). Excessive growth of these compounds can lead to interface embrittlement, voids, and cracks, severely weakening the mechanical integrity and fatigue resistance of the interconnect. Existing technologies have achieved growth prediction of interfacial metal compound layers in micro-interconnect structures from the perspectives of high-temperature stress and thermoelectric coupling stress, which are important methods for evaluating the reliability of micro-interconnects. However, existing technical solutions are all based on constant stress conditions, assuming that load parameters such as high temperature and current density remain constant during service. In real-world applications, chips often experience frequent power-on / off cycles or power fluctuations, resulting in cyclic temperature stress that causes the thermal load on the interface atoms to change periodically. Under temperature cycling conditions, atomic diffusion flux changes in real time with temperature, and key parameters such as diffusion coefficients are no longer constant. The growth kinetics of metal compounds differ significantly from those under constant stress. Existing growth prediction models cannot reflect the dynamic impact of periodic temperature changes on atomic migration patterns, and therefore cannot effectively predict the growth of interface metal compounds under temperature cycling conditions, making it difficult to accurately assess the actual service life of micro-interconnects under complex thermal loads. Therefore, there is an urgent need to establish a method for predicting the growth of lead-free micro-interconnect interface metal compounds suitable for temperature cycling conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a method, computer device, computer-readable storage medium, and computer program product for predicting the growth of metal compounds at the interface of lead-free micro interconnects under temperature cycling conditions, which can effectively predict the growth of metal compounds at the interface of lead-free micro interconnects under temperature cycling conditions.

[0004] To achieve the above objectives, one aspect of the present invention provides a method for predicting the growth of metal compounds in lead-free micro interconnect structures under temperature cycling, comprising: Step S1: Based on the type of interface metal compound layer in the lead-free micro interconnect structure, determine the target metal atoms, establish the functional relationship between the net thermal diffusion flux of the target metal atoms and the growth rate of the metal compound layer thickness, and then establish the functional relationship between the growth rate of the metal compound layer thickness and the thermal diffusion coefficient of the target metal atoms. Step S2: Based on atomic diffusion theory and the Arrhenius equation, establish the functional relationship between the thermal diffusion coefficient of the target metal atoms and temperature. Step S3: Based on the functional relationship between the thermal diffusivity of the target metal atom and temperature established in Step S2 and the functional relationship between the growth rate of the metal compound layer thickness and the thermal diffusivity of the target metal atom established in Step S1, the expression for the growth rate of the metal compound layer thickness with temperature as the variable is obtained. Step S4: By integrating the expression for the growth rate of the metal compound layer thickness with temperature as the variable over time, the thickness growth of the metal compound layer at different temperature change stages within a single temperature cycle is obtained. The thickness growth of the metal compound layer under multiple temperature cycles is predicted by cumulative calculation.

[0005] Another aspect of the present invention provides a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described above.

[0006] Another aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0007] Another aspect of the present invention provides a computer program product including a computer program that, when executed by a processor, implements the steps of the method described above.

[0008] The method, computer device, computer-readable storage medium, and computer program product for predicting the growth of metal compounds at the lead-free micro interconnect structure under temperature cycling conditions according to the above-described aspects of the present invention can effectively predict the growth of metal compounds at the lead-free micro interconnect interface under temperature cycling conditions. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort: Figure 1 This is a flowchart of a method for predicting the growth of metal compounds in lead-free micro interconnect structures under temperature cycling, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the thermal diffusion flux of Cu atoms in a Cu / Sn / Cu micro interconnect structure according to an embodiment of the present invention; Figure 3 This is an example diagram of temperature cycling stress conditions according to an embodiment of the present invention; Figure 4 This is a structural diagram of a computer device according to an embodiment of the present invention. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0011] One embodiment of the present invention provides a method for predicting the growth of metal compounds in lead-free micro interconnect structures under temperature cycling. In this embodiment, a common typical Cu / Sn / Cu lead-free micro interconnect structure is used as an example, combined with... Figure 1 The flowchart below provides a detailed explanation of each step in the metal compound growth prediction method of this invention.

[0012] Step S1: Based on the type of interface metal compound layer in the micro-interconnect structure, determine the target metal atoms (such as Cu, Ni, etc.), analyze the thermal diffusion flux of the target metal atoms in different metal compound layers, obtain the net thermal diffusion flux of the target metal atoms in each metal compound layer, and establish the relationship between the metal compound thickness growth rate and the thermal diffusion coefficient of the target metal atoms.

[0013] For the Cu / Sn / Cu lead-free micro interconnect structure, its composition is as follows: Figure 2 As shown, from left to right, there are Cu pads, Cu3Sn layer, Cu6Sn5 layer, Sn solder, Cu6Sn5 layer, Cu3Sn layer and Cu pads. The main metal compounds present are Cu6Sn5 and Cu3Sn layers. Cu atoms are important constituent atoms of the two metal compounds, and there is a lot of publicly reported data on the relevant thermal diffusion parameters. Therefore, they can be selected as the target metal atoms.

[0014] Figure 2 This is a schematic diagram of the thermal diffusion flux of Cu atoms in a Cu / Sn / Cu micro interconnect structure under certain temperature conditions. Figure 2 middle, , and These represent the thermal diffusion flux of Cu atoms from the Cu pad to the Cu3Sn layer, from the Cu3Sn layer to the Cu6Sn5 layer, and from the Cu6Sn5 layer to the Sn solder, respectively. By analyzing the thermal diffusion flux of Cu atoms in the Cu / Sn / Cu micro-interconnect structure, based on the principle of mass transport conservation of Cu atoms, the relationship between the net thermal diffusion flux of Cu atoms and the thickness of the Cu6Sn5 and Cu3Sn layers can be established.

[0015] This leads to the establishment of a relationship between the net thermal diffusion flux of Cu atoms and the growth rate of Cu6Sn5 and Cu3Sn layer thicknesses:

[0016] In the formula: and These represent the concentrations of Cu atoms in the Cu3Sn and Cu6Sn5 layers, respectively. and These represent the thicknesses of the Cu3Sn and Cu6Sn5 layers, respectively. and The thickness growth rates of Cu3Sn and Cu6Sn5 layers are represented, respectively. and The difference is the net thermal diffusion flux of Cu atoms in the Cu3Sn layer. and The difference is the net thermal diffusion flux of Cu atoms in the Cu6Sn5 layer. It can be expressed as:

[0017] In the formula, This refers to the concentration of Cu atoms in the Cu pad. This represents the concentration of Cu atoms dissolved in the Sn solder. and , respectively, are the thermal diffusivity coefficients of Cu atoms in the Cu3Sn and Cu6Sn5 layers.

[0018] Step S2: Based on atomic diffusion theory and the Arrhenius equation, establish the functional relationship between the thermal diffusion coefficient of the target metal atoms and temperature.

[0019] Thermal diffusivity of Cu atoms in Cu3Sn and Cu6Sn5 layers in equations (5) and (6) under temperature cyclic stress and The thermal diffusivity of atoms changes with temperature. Based on atomic diffusion theory and the Arrhenius equation, the specific calculation method for the atomic thermal diffusivity is as follows:

[0020] Where D is the thermal diffusivity of atoms, D0 is a constant factor independent of temperature, Q is the diffusion activation energy, and R is the universal gas constant with a value of 8.314 J / kJ. -1 mol -1 T is the Kelvin temperature.

[0021] Therefore, for and We can obtain the following respectively:

[0022] in, and These are constant factors for the thermal diffusivity of Cu atoms in the Cu3Sn and Cu6Sn5 layers, respectively. and The activation energies are the thermal diffusivity coefficients of Cu atoms in the Cu3Sn and Cu6Sn5 layers, respectively. The parameter values ​​in Table 1 below can be obtained by consulting publicly reported data.

[0023] Table 1. Parameter values ​​of Cu atomic thermal diffusivity

[0024] Step S3: Substitute the thermal diffusivity-temperature function relationship established in Step S2 into the metal compound thickness growth rate calculation relationship in Step S1 to obtain the thickness growth rate expression with temperature as the variable.

[0025] Substituting formula (8) into (3) and (4), the thickness growth rates of Cu3Sn and Cu6Sn5 layers under temperature cyclic stress are shown below:

[0026] Where A and B are constants, and the specific calculation method is as follows:

[0027] Step S4: By integrating over time, the formula for calculating the thickness growth of the metal compound in different temperature change stages within a single cycle is obtained. Based on the formula for calculating the thickness growth of the metal compound in different stages within a single cycle, the thickness growth in a single cycle is obtained. Combined with the number of temperature cycles, the thickness growth of the metal compound layer in the micro interconnect structure under multiple temperature cycles is predicted through cumulative calculation.

[0028] By integrating equations (9) and (10), the functional relationship between the thicknesses of the Cu6Sn5 and Cu3Sn layers under temperature cyclic stress and time can be obtained, as shown below.

[0029]

[0030] Figure 3 This is a curve showing the temperature versus time relationship under typical temperature cyclic stress conditions. Figure 3In the example, the initial temperature of the temperature cycle is set to -55℃, followed by a linear increase at a rate of approximately 12℃ / min. After 15 minutes, the temperature rises to 125℃ and remains at 125℃ for 15 minutes, forming a clear high-temperature stable phase. After the high-temperature stable phase, the temperature decreases linearly at a rate of 12℃ / min, and after 15 minutes, the temperature drops again to -55℃ and remains at -55℃ for 15 minutes, forming a clear low-temperature stable phase. This completes one high-low temperature cycle with a period of 60 minutes. After converting the time from minutes to hours, the formula for calculating the thickness growth of the metal compound in different temperature change stages within a single cycle is obtained by integrating the time. When the actual temperature cycle time is 0h ≤ s ≤ 0.25h:

[0031] When the actual temperature cycle time is 0.25h ≤ s ≤ 0.5h:

[0032] When the actual temperature cycle time is 0.5h ≤ s ≤ 0.75h

[0033] When the actual temperature cycle time is 0.75h ≤ s ≤ 1h

[0034] By appropriately adjusting variables such as temperature values, heating / cooling rates, and high / low temperature holding times in the above formulas, a thickness growth model for Cu6Sn5 and Cu3Sn layers within a single cycle under any temperature cycling condition can be obtained. Based on the obtained thickness growth in a single cycle, combined with the number of temperature cycles, the thickness growth of metal compound layers in micro-interconnect structures under multiple temperature cycling cycles can be predicted through cumulative calculation.

[0035] By repeatedly superimposing single-cycle models, growth models across multiple cycle time periods can be obtained. This was based on a review of publicly available literature. , and They are 0.84×10 23 0.31×10 23 and 0.52×10 23 at. / cm 3 Cu atoms have a maximum solubility of approximately 0.16 wt% in solid Sn solder, therefore, it can be calculated that... Approximately 0.11 × 10 21 at. / cm 3Substituting the relevant parameters into formula (11), we can obtain constants A and B as 1.033 and 1.690, respectively. Calculating formulas (13)-(16) yields the square increments of the thickness of Cu3Sn and Cu6Sn5 layers at different temperature stages, and the results are summarized in Table 2.

[0036] Table 2. Increment of the square of the thickness of Cu3Sn and Cu6Sn5 compound layers

[0037] Therefore, for a Cu / Sn / Cu lead-free interconnect microbump with an initial Cu6Sn5 layer thickness of 2.5 μm and a Cu3Sn layer thickness of 1 μm, based on the aforementioned temperature cycling stress conditions, and using 1000 temperature cycles as an example, the thicknesses of Cu6Sn5 and Cu3Sn can be predicted as follows:

[0038] Calculations showed that the Cu6Sn5 layer thickness increased from 2.5 μm to 3.51 μm, and the Cu3Sn layer thickness increased from 1 μm to 1.67 μm.

[0039] In summary, the method of this invention analyzes the thermal diffusion behavior of target metal atoms in different metal compound layers to obtain the net thermal diffusion flux of target metal atoms in different metal compounds. It then establishes a relationship between the metal compound thickness growth rate and the thermal diffusivity of the target metal atoms, obtains the functional relationship between the thermal diffusivity of the target metal atoms and temperature, and substitutes this into the metal compound thickness growth rate calculation relationship. Through integration, it obtains the calculation formula for the thickness growth of different metal compounds. Furthermore, based on actual temperature cycling conditions, it calculates the thickness increase of the metal compound within different temperature ranges in a single cycle, thereby enabling the prediction of metal compound layer growth under multiple temperature cycling cycles.

[0040] The method of this invention introduces the functional relationship between thermal diffusivity and temperature, and combines integral calculation to achieve cumulative prediction of metal compound thickness under periodic temperature change conditions. This effectively solves the technical gap that the existing technology can only be applied to constant stress conditions and cannot cover temperature cycling conditions, and provides a more accurate solution for reliability assessment of micro interconnect structures in advanced packaging.

[0041] The method described in this invention is not only universally applicable, but can also be widely used in micro-bump interconnect structures of different metal systems (such as Cu / Sn and Ni / Sn). Furthermore, it allows for flexible adjustment of calculation parameters based on actual temperature cycling profiles, enabling cumulative prediction from single cycles to multiple cycles. Engineers can use this invention to quickly assess the growth trend of metal compounds under temperature cycling conditions, optimize packaging structure design, or develop reliability screening criteria, effectively avoiding failure problems such as interface embrittlement and crack initiation caused by excessive growth of metal compounds.

[0042] In recent years, the industry has invested heavily in R&D resources in advanced packaging fields such as 2.5D / 3D packaging and chip integration. The long-term reliability of micro-interconnects has become a key bottleneck restricting the practical application of these technologies. This invention will facilitate the accurate assessment of the lifespan of micro-interconnects under real-world service conditions, accelerating the maturity and commercialization of advanced packaging technologies. Therefore, this invention has significant economic and social benefits.

[0043] Embodiments of the present invention also provide a computer device, which may be a server, and its internal structure diagram may be as follows: Figure 4 As shown. The computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores operating parameter data for various components. The network interface communicates with external terminals via a network connection. When executed by the processor, the computer program implements the steps of the method according to embodiments of the present invention.

[0044] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0045] Embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method of the embodiments of the present invention.

[0046] Embodiments of the present invention also provide a computer program product, including a computer program that, when executed by a processor, implements the steps of the method of the embodiments of the present invention.

[0047] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the growth of metal compounds in lead-free micro-interconnect structures under temperature cycling, characterized in that, include: Step S1: Based on the type of interface metal compound layer in the lead-free micro interconnect structure, determine the target metal atoms, establish the functional relationship between the net thermal diffusion flux of the target metal atoms and the growth rate of the metal compound layer thickness, and then establish the functional relationship between the growth rate of the metal compound layer thickness and the thermal diffusion coefficient of the target metal atoms. Step S2: Based on atomic diffusion theory and the Arrhenius equation, establish the functional relationship between the thermal diffusion coefficient of the target metal atoms and temperature. Step S3: Based on the functional relationship between the thermal diffusivity of the target metal atom and temperature established in Step S2 and the functional relationship between the growth rate of the metal compound layer thickness and the thermal diffusivity of the target metal atom established in Step S1, the expression for the growth rate of the metal compound layer thickness with temperature as the variable is obtained. Step S4: By integrating the expression for the growth rate of the metal compound layer thickness with temperature as the variable over time, the thickness growth of the metal compound layer at different temperature change stages within a single temperature cycle is obtained. The thickness growth of the metal compound layer under multiple temperature cycles is predicted by cumulative calculation.

2. The method as described in claim 1, characterized in that, The lead-free micro interconnect structure includes Cu pads, Cu3Sn layers, Cu6Sn5 layers, and Sn solder, wherein the metal compound layers are Cu6Sn5 and Cu3Sn layers, and the target metal atom is Cu.

3. The method as described in claim 2, characterized in that, In step S1, the functional relationship between the net thermal diffusion flux of Cu atoms and the growth rate of the Cu6Sn5 and Cu3Sn layers is established: in, and These represent the concentrations of Cu atoms in the Cu3Sn and Cu6Sn5 layers, respectively. and These represent the thicknesses of the Cu3Sn layer and the Cu6Sn5 layer, respectively. and These represent the thickness growth rates of Cu3Sn and Cu6Sn5 layers, respectively. , and These represent the thermal diffusion flux of Cu atoms from the Cu pad to the Cu3Sn layer, from the Cu3Sn layer to the Cu6Sn5 layer, and from the Cu6Sn5 layer to the Sn solder, respectively. This represents the net thermal diffusion flux of Cu atoms in the Cu3Sn layer. Net thermal diffusion flux of Cu atoms in the Cu6Sn5 layer: in, This refers to the concentration of Cu atoms in the Cu pad. This represents the concentration of Cu atoms dissolved in the Sn solder. and , respectively, are the thermal diffusivity coefficients of Cu atoms in the Cu3Sn and Cu6Sn5 layers.

4. The method as described in claim 3, characterized in that, In step S2, the thermal diffusivity of Cu atoms varies with temperature as follows: ， ， in, and These are constant factors for the thermal diffusivity of Cu atoms in the Cu3Sn and Cu6Sn5 layers, respectively. and R and T are the diffusion activation energies of the thermal diffusion coefficient of Cu atoms in Cu3Sn and Cu6Sn5 layers, respectively, where R is the gas constant and T is the Kelvin temperature.

5. The method as described in claim 4, characterized in that, In step S3, the growth rate expressions for the thickness of the Cu3Sn layer and the Cu6Sn5 layer, with temperature as the variable, are as follows: Where A and B are constants, 。 6. The method as described in claim 5, characterized in that, In step S4, time integration is performed to obtain the thickness growth amounts of the Cu6Sn5 and Cu3Sn layers as follows: Where t is time.

7. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

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