Chip life prediction method based on PSO algorithm and markov grey model

Abstract

The application discloses a chip life prediction method based on a PSO algorithm and a Markov grey model, and belongs to the technical field of advanced packaging and reliability testing of integrated circuits. ω The method is aimed at a heterogeneous integrated packaging chip, a coupling analysis modeling of electrical degradation and mechanical failure of the chip is carried out, that is, an equivalent thermal mechanical stress calculated based on elastic parameters of packaging materials is introduced into a grey model as an interference term, and further optimization is carried out on a temperature, humidity and stress combination value through a PSO algorithm, after optimal parameter combination is determined, a residual error is further corrected by using a Markov method, and a PSO optimized prediction value is adjusted, so that accurate life prediction of the heterogeneous integrated packaging chip is realized, a reliable life prediction solution is provided for a high-density photoelectric co-packaging system, and the method is especially suitable for application scenarios, such as automobile electronics and high-performance computing, which have strict requirements on reliability.

Description

Technical Field

[0001] This invention relates to a chip lifetime prediction method based on the PSO algorithm and Markov grey model, belonging to the field of advanced integrated circuit packaging and reliability testing technology. Background Technology

[0002] As Moore's Law continues to evolve, the number of transistors integrated on a single chip has approached its physical limit, leading to a dramatic increase in chip design complexity, manufacturing costs, and power consumption. In the field of integration, DDR (Double Data Rate SDRAM) and FPGA (Field-Programmable Gate Array) are prime examples. Their integration facilitates module miniaturization and low power consumption, a key trend in chip packaging development. Against this backdrop, heterogeneous integration technology, particularly the System-in-Package (SIP) paradigm, has become an important path for the continued development of the semiconductor industry.

[0003] Existing chip lifetime prediction models primarily consider the chip's own electric field and uniform temperature field, neglecting the localized mechanical stress introduced during the packaging process. Under the current trend of heterogeneous chip integration packaging, accurate prediction of chip lifetime is impossible for several reasons: First, the mismatch in thermal expansion coefficients between the packaging material and the silicon chip generates significant residual stress within the chip. Specifically, the packaging process is typically accompanied by high temperature and high pressure (such as flip-chip bonding or thermoforming). When the equipment cools to room temperature, the packaging material forcibly "compresses" the silicon wafer, causing compressive or tensile stress within the wafer. Second, heterogeneous integration introduces more complex mechanical and thermal management issues. After heterogeneous integration, the power density difference between different locations can be several times, with extremely high heat flux density at local hotspots. Since heat is a crucial factor affecting chip lifetime, these thermal differences make lifetime prediction even more difficult. Third, heterogeneous integration technology also generates a thermo-mechanical coupling effect, further complicating prediction.

[0004] Chinese invention patent CN117828482A discloses a gray model chip lifetime prediction method based on chicken flock algorithm and Markov method. This method uses the phenomenon and time of disturbance of power chip as input of gray model and chicken flock algorithm to optimize the parameters of gray model. However, it does not consider the influence of packaging material on chip lifetime, so it still cannot accurately predict the lifetime of heterogeneous integrated packaged chips. Summary of the Invention

[0005] To achieve accurate prediction of the lifetime of heterogeneous integrated packaged chips, this invention provides a chip lifetime prediction method based on the PSO algorithm and Markov grey model. By coupling analysis and modeling of chip electrical degradation and mechanical failure, the problem of failure of pure data-driven models under changing operating conditions is avoided. Furthermore, by using the PSO algorithm and Markov correction, the model is made to adapt to different packaging structures and stress conditions, making the method widely applicable to the lifetime prediction of various heterogeneous integrated packaged chips.

[0006] A chip lifetime prediction method based on the PSO algorithm and Markov grey model includes: Step 1: Obtain lifetime degradation data and perform preprocessing. The lifetime degradation data refers to the equivalent resistance value of the chip interconnect structure. Step 2: Establish an initial grey model with interference terms, where the interference terms... oh The equivalent thermomechanical stress is calculated based on the elastic parameters of the packaging material; Step 3: Optimize the gray model parameters using the PSO algorithm. a , b , oh ), to obtain the optimal combination of temperature, humidity, and stress values ​​( a , b , oh ); Step 4: Correct the residuals of the grey model using the Markov method; Step 5: Use the modified grey model to perform rolling prediction of the packaged chip lifetime.

[0007] Optionally, step 1 includes: The equivalent resistance values ​​of the chip interconnect structure measured at different time points or thermal cycles are recorded as the initial sequence. ; This represents the parameter value at the k-th time point or the k-th thermal cycle, where k = 1, 2, ..., n; n ≥ 4; A new sequence X is generated by accumulating the initial sequence in one step according to the following rule. (1) ; ; ; x (1) (k) represents the new sequence X (1) The k-th value in the matrix, x (0) (i) represents the i-th value in the initial sequence.

[0008] Optionally, step 2 includes: Step 21, based on the initial sequence X (0) and new sequence X (1)Establish the grey differential equation: ; Among them, the development coefficient a Ash action amount b In this model, temperature and humidity are function mappings under external environmental stress conditions, respectively, used to characterize the impact of environmental stress on the chip lifetime degradation rate; z (1) (k) is the nearest mean sequence, representing the sequence X generated by a single accumulation. (1) The average value between the (k-1)th and the kth time points is used to approximate the average level of chip degradation within this time interval; Step 22: Introduce interference terms oh The initial gray model is obtained as follows: ; Interference items oh The equivalent thermomechanical stress is calculated based on the elastic parameters of the packaging material. The calculation method is as follows: ; in, and These represent the coefficients of linear expansion of the two different materials in the packaging structure, used to characterize the thermal expansion mismatch of the materials. E(T,n) Let be the Young's modulus of the material. The Young's modulus of the material degenerates with temperature T and the number of thermal cycles n.

[0009] Optionally, step 3 includes: Step S31: Determine the parameters that need to be optimized in the gray model; Step S32: Construct the fitness function of the gray model, wherein the fitness function aims to minimize the average relative error; Step S33: Iteratively optimize using the following formula to obtain the optimal combination of "temperature, humidity, and stress": ; ; in, c 1 and c 2 is the learning factor. r 1 and r 2 is a random coefficient, with a value range of 0-1; For particles i The historical best position represents the optimal lifespan value under a certain operating condition. For particles i The global optimal position represents the most accurate life prediction result or key combination of operating conditions among all operating conditions under the overall assessment. For particles i The updated rate For particles i The current rate; particle i The updated location particle i The current position of the particle is defined as position( a , b , oh ( ), that is, the specific values ​​of "temperature, humidity, and stress" for a certain set of working conditions; Step S34: Determine if the maximum number of iterations has been reached. If the maximum number of iterations has been reached, the optimization ends, and the optimal life condition or minimum prediction error corresponding to a certain set of working conditions is output. The optimal life condition is denoted as (a opt , b opt ,ω opt Otherwise, return to step 33.

[0010] Optionally, step 4 includes: Step 41, the parameters after PSO optimization are (a opt , b opt , ω opt The grey model is used to make predictions, and the PSO optimized prediction value is obtained. The corresponding residual sequence E is then calculated. (0) ; Step S42: Construct the Markov state partitioning and transition matrix; Step S43: Correct the predicted value, using the state of the last value in the residual sequence as the initial state vector μ0, and then... t =μ0P t Predict the possible states of the future residual, P t Let be the transition probability at time t; Step S44: Based on the Markov state transition results, adjust the PSO optimized prediction value.

[0011] Optionally, in step 41, the residual sequence E (0) The calculation method is as follows: Subtracting the PSO-optimized predicted values ​​from the actual values ​​point by point yields the residual sequence:

[0012]

[0013] in, Represents the true value. This represents the PSO optimized prediction value.

[0014] Optionally, the adjusted PSO optimized prediction value in step 44 is:

[0015] in The sign (±1) is determined by the state probability; in the formula It is the predicted value of the grey model built on the residual sequence itself.

[0016] Optionally, the fitness function of the gray model in step S32 is the average relative error.

[0017] Optionally, the chip is packaged using a side-fill structure.

[0018] The beneficial effects of this invention are: This invention targets heterogeneous integrated packaged chips, and through coupled analysis and modeling of chip electrical degradation and mechanical failure, specifically the equivalent thermomechanical stress calculated based on the elastic parameters of the packaging material. oh The grayscale model is introduced as an interference term, and the PSO algorithm is used to further optimize the combined values ​​of temperature, humidity and stress. After determining the optimal parameter combination, the Markov method is used to correct the residuals and adjust the PSO optimization prediction value, thereby realizing the accurate prediction of the lifetime of heterogeneous integrated packaged chips. This provides a reliable lifetime prediction solution for high-density optoelectronic co-packaging systems, which is particularly suitable for application scenarios with stringent reliability requirements such as automotive electronics and high-performance computing. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.

[0020] Figure 1 This is an overall SIP package diagram in an embodiment of the present invention; Figure 2 This is a schematic diagram of a partial encapsulation structure using side-filling technology in an embodiment of the present invention; Figure 3 This is a flowchart of lifetime prediction using the PSO algorithm in an embodiment of the present invention; Figure 4 This is a flowchart of the gray model lifetime prediction using the Markov method; Among them, 200: PCB printed circuit board, 201: side filler structure, 202: solder ball, 203: FPGA chip, 204: through silicon via, 205: aluminum pad, 206: solder, 207: bottom bump metal layer, 208: copper pillar, 209: DDR chip, U1: FLASH RDL package structure, U2: FPGA package structure, U3: HBM package structure. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can also be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0022] Example 1: This embodiment provides a chip lifetime prediction method based on the PSO algorithm and Markov grey model. The method is designed for packaged chips and references... Figure 3 and Figure 4 The method includes: Step S1: Acquisition and preprocessing of lifetime degradation data; The initial sequence X (0) This is a time series of key degradation parameters of the chip measured at different time points or thermal cycles. The key degradation parameters are the equivalent resistance values ​​of the chip interconnect structure.

[0023] The equivalent resistance values ​​of the chip interconnect structure are used as the initial sequence, denoted as: ; in, This represents the parameter value at the k-th time point (or the k-th thermal cycle) (k=1,2,…,n). The resistance value used in this embodiment exhibits a monotonically changing trend with the accumulation of thermo-mechanical stress, consistent with the modeling assumption of the grey model GM(1,1). Specifically, when collecting data, considering that the grey model is suitable for small sample data, the sequence length is typically n≥4, meaning that failure data at at least four time points (or four thermal cycles) are recorded.

[0024] In this embodiment, the sequence length is 12, and the number of thermal cycles for failure handling can range from 200 to 2400. Here, it can be set to 200 iterations, requiring the number of iterations to meet the minimum data requirements of the grey model. Simultaneously, it must be ensured that the data is continuous, without missing data, and exhibits a monotonic trend, such as a certain quantity increasing with the number of cycles, to conform to the exponential growth assumption of the grey model.

[0025] More specifically, in a laboratory environment, chip parameters can be recorded periodically using high-precision measuring equipment, while environmental stress conditions such as temperature, humidity, and voltage are controlled to simulate actual operating conditions. Chip parameters refer to voltage, current, power consumption, and resistance, among others.

[0026] The data is preprocessed by accumulating the initial sequence in one step according to the following formula to generate a new sequence X. (1) : ; x (1) (k) represents the new sequence X (1) The k-th value in the matrix, x (0) (i) represents the i-th value in the initial sequence. Generate a new sequence X. (1) The aim is to mitigate random fluctuations and prepare for grey modeling: ; Step S2: Establish an initial gray model with interference terms; The aim is to construct the basic grey model GM(1,1) and introduce equivalent thermomechanical stress as an interference term. oh This enhances flexibility while avoiding the limiting factor that the fitted curve must pass through historical data points.

[0027] Step S21, based on the initial sequence X (0) and new sequence X (1) Establish the grey differential equation: ; Among them, the development coefficient a Ash action amount b In this model, temperature and humidity are function mappings under external environmental stress conditions, respectively. Temperature and humidity are externally controllable environmental parameters used to characterize the impact of environmental stress on the chip's lifetime degradation rate. Under different temperature, humidity, and thermal cycling conditions, the grey model parameters a and b are fitted, and the following mapping relationship is established using a multiple linear regression method:

[0028]

[0029] , , , as well as , , , All are regression coefficients, estimated using the least squares method from experimental data under multiple environmental conditions, used to characterize the sensitivity of each environmental variable to the development coefficient of the grey model. These regression coefficients can be recalibrated according to different packaging structures or material systems. and The intercept term represents the basic degradation trend of the system under standard reference conditions; and The temperature sensitivity coefficient of the material; and Humidity sensitivity coefficient; and is the stress coupling coefficient. T , H These refer to ambient temperature and humidity, respectively.

[0030] z (1) (k) is the nearest mean sequence, representing the sequence X generated by a single accumulation. ( ¹ ) The average value between the (k-1)th and kth time points is used to approximate the average level of chip degradation within that time interval.

[0031] Step S22: Introduce interference terms; Add stress values ​​to the time response equation oh The stress value oh The equivalent thermomechanical stress is calculated based on the elastic parameters of the packaging material. The calculation method is as follows: ; in, and These represent the coefficients of linear expansion of the two different materials in the packaging structure, used to characterize the thermal expansion mismatch of the materials. This represents the coefficient of linear expansion of the chip's main material. The equivalent coefficient of linear expansion of the packaging structure material or composite material that is in thermomechanical connection with the chip; E(T,n) This refers to the Young's modulus of the material, which degrades with temperature T and the number of thermal cycles n. The interference terms included in this application... oh pass and The position of the fitted curve is adaptively adjusted to better match the actual degradation trajectory, resulting in the initial gray model: ; At this point, the initial gray model has three parameters to be optimized: a , b , oh .

[0032] This application subsequently uses the PSO algorithm to optimize these three parameters. Using the PSO algorithm eliminates the need to consider constraints when utilizing the least squares method to optimize the development coefficients. a Ash action amount b Instead of performing parameter estimation, the parameter vector is obtained based on the algorithm's own optimization characteristics.

[0033] Step S3: Optimize the gray model parameters using the PSO algorithm ( a , b , oh ); In the PSO algorithm, the position of each particle not only represents a set of gray model parameters ( a, b, ω This also corresponds to a set of elastic degradation parameters for the encapsulation material. Random initialization is performed within a reasonable range, based on the initial degradation sequence. X (0) And the numerical ranges of ambient temperature, humidity, and equivalent thermomechanical stress, for a , b and oh Constraining the search interval in the particle swarm optimization algorithm avoids the decrease in search efficiency caused by parameter scale mismatch.

[0034] The purpose of using the PSO algorithm is to find the optimal combination of temperature, humidity, and stress. a , b , oh This aims to minimize the model's prediction error. To achieve this, a series of implementation steps are outlined: Step S31: Determine the parameters that need to be optimized for the gray model.

[0035] Set the number of test sample devices and the number of iterations to 100, and use PSO to try 100 different temperature and humidity conditions until the combination that can make the life prediction most accurate is found.

[0036] In the PSO algorithm, the inertia weight w represents the balance between global search capability and learning factor. c 1 and c 2 represents the degree to which the control sample approaches its own historical best operating condition and the group's global best operating condition, respectively. To balance local and global search, the learning factor is... c 1 and c 2 is set to 2.0. The stress parameters are... oh The parameters are obtained by the material Young's modulus evolution model, which includes an initial Young's modulus E0. These parameters are used as one of the optimization variables of the particle swarm optimization algorithm in the optimization process.

[0037] Step S32: Define a fitness function to evaluate the lifetime prediction accuracy under different operating conditions; By constructing a unified fitness function, the lifetime prediction results corresponding to different combinations of temperature, humidity, and stress in the particle swarm optimization algorithm are evaluated. The fitness function aims to minimize the mean relative error (MAPE). ; in This is the predicted value under the current parameters. For each particle, based on the individual optimal (p... best ) and global optimum (g bestThe update speed and location, i.e. the "temperature and humidity" conditions in this set of working conditions, will result in results such as stress = 100MPa, temperature = 85℃, voltage = 3.3V, etc.

[0038] Step S33: Iterative optimization using formulas: ; ; In this formula c 1 and c 2 is the learning factor. r 1 and r 2 is a random coefficient, ranging from 0 to 1, used to adjust the randomness of the particle's movement towards its individual optimal position and the global optimal position. For particles i The historical best position represents the optimal lifespan value under a certain operating condition. For particles i The global optimal position represents the most accurate life prediction result or key combination of operating conditions among all operating conditions under the overall assessment. For particles i The updated rate For particles i The current rate; particle i The updated location particle i The current position, defined in the formula as position ( a , b , oh ), which refers to the specific values ​​of "temperature, humidity, and stress" for a certain set of working conditions.

[0039] Step S34: Determine whether the maximum number of iterations has been reached.

[0040] If the target is reached, the optimization process ends; otherwise, return to step 33.

[0041] Output the optimal life condition (a) corresponding to a certain set of operating conditions. opt , b opt , ω opt Or the minimum prediction error. Substituting the optimal parameters into the grey model, a preliminary prediction sequence is obtained. Obtain the optimized prediction value of PSO.

[0042] Compared to other algorithms, PSO has fewer parameters, converges faster, and is easy to parallelize, making it suitable for handling continuous optimization problems.

[0043] Step S4: Markov method to correct residuals; The purpose is to reduce the residual accumulation effect of the grey model and improve the fit.

[0044] Step S41, the parameters after PSO optimization are (a opt , b opt , ω opt The grey model is used to make predictions, the predicted values ​​are obtained, and the corresponding residual sequence E is calculated. (0) ; Optimize PSO predictions Compared with the true value By subtracting point by point, we obtain the residual sequence: ; ; Step S42: Markov state partitioning and transition matrix construction.

[0045] Divide the residual sequence into positive and negative states, and calculate the state transition probability matrix P; the state transition probability matrix is ​​the probability of transitioning from a positive state to a negative state or from a negative state to a positive state.

[0046] A positive residual sequence indicates that the actual value is greater than the predicted value; a negative residual sequence indicates that the actual value is less than the predicted value. The transition probabilities can be calculated based on historical residual data using the state transition matrix. ,

[0047] Where M hj M is the number of times state h transitions to state j. h It is the total number of times state h occurs. State h and state j are the two states, positive and negative.

[0048] Step S43: Correct the predicted value, using the state of the last value in the residual sequence as the initial state vector μ0, and then... t =μ0P t Predict the possible states of the future residual, P t Let m be the transition probability at time t. The state with the highest probability is selected to determine the correction symbol m. (0) (k) is +1 or -1.

[0049] Step S44: Based on the Markov state transition results, adjust the PSO optimized prediction values:

[0050] Where m (0) (k) is the sign (±1), determined by the state probability. In the formula... This is the grey model prediction value built on the residual sequence itself. This step can effectively adjust the trend of the prediction curve.

[0051] Step S5: Model validation and lifetime prediction. Rolling predictions are performed using the modified model, and the accuracy is evaluated using metrics such as mean relative error.

[0052] In one implementation, the residual states can be physically divided according to the degree of degradation of the material's Young's modulus. S1, S2, and S3 represent different states of encapsulation, respectively.

[0053] S1: E>0.9E0, elasticity intact S2: 0.9E0 > E > 0.7E0 Mild fatigue S3: Crack initiation occurs when E < 0.7E0 The Markov transition probability reflects the statistical characteristics of the evolution of the elastic degradation state of a material with thermal cycling.

[0054] Step S51: Model Validation.

[0055] Calculate the final predicted sequence With the original sequence X (0) The accuracy is quantitatively assessed using indicators such as average relative error and root mean square error. After correction using this method, the average relative error can be reduced to a lower level.

[0056] Table 1. Model Validation Comparison Data

[0057] Using experimentally obtained chip degradation data as the true values, the prediction results of using only the grey model and those using "PSO + Markov correction" were compared. The results show that, under the same training data conditions, the average relative error before correction was approximately 3.93%, while after Markov residual correction, the average relative error decreased to 0.14%, verifying the effectiveness of this method in improving lifetime prediction accuracy.

[0058] Step S52: Perform lifetime prediction.

[0059] Using existing data as the training set, the established optimized model is used to predict chip performance parameters for future time points k=n+1, n+2,… Structural failure is defined as a 20% increase in package resistance. When the resistance value of a sample exceeds this failure threshold, the corresponding MTTF (Mean Transmission Time To Value) is the predicted chip lifetime. Chip degradation data obtained from accelerated aging experiments are used as the true lifetime indicator to compare and validate different models. Lifetime predictions are performed on chips at different time points, and the results are shown in the table below.

[0060] Table 2 Comparison of lifetime prediction results of different models

[0061] The results show that, under the same training data conditions, the average relative error of the traditional prediction method is 7.3001%, while the error of this model is reduced to 2.0201%.

[0062] Example 2 This embodiment focuses on the chipplet packaging structure for chip-to-wafer bonding, and uses the chip lifetime prediction method provided in Embodiment 1 for prediction. In this embodiment, the sidefill structure in the chipplet packaging structure changes the equivalent Young's modulus of the packaging structure by altering the packaging material combination and edge constraint conditions. This equivalent Young's modulus further affects the equivalent thermomechanical stress generated under thermal cycling conditions, and the equivalent thermomechanical stress is used as an interference term in the gray model. oh The input is fed into the particle swarm optimization process, thereby achieving coupling between structural parameters and lifetime prediction models.

[0063] Please refer to Figure 1 Overall SIP package diagram and Figure 2 A partial encapsulation structure diagram of sidefill technology, in which... Figure 2 The structure shown is Figure 1 The U2 part in it.

[0064] Figure 1 The overall SIP package structure is divided into U1, U2, and U3, which are FLASH RDL, FPGA, and HBM, respectively. Taking the U2 structure as an example, the package structure parameters are as follows: chip size is 1.4mm×1mm×0.1mm, microbump height is 0.035mm, first-level interconnect height is 0.06mm, BGA solder ball height is 0.180mm, and the number of solder balls is 10.

[0065] Specifically, a polymer-based sidefill material is applied to the edge of the package to implement the sidefill adhesive technology. The specific configuration includes material properties and CTE (Coefficient of Thermal Expansion) characteristics. The sidefill application mode uses either "4L" full-edge filling or "2U" four-corner filling; in this embodiment, the filling shape is simplified to a triangle. Different sidefill methods change the equivalent Young's modulus E of the chip-substrate-sidefill composite structure. eq Different sidefill structures correspond to different stress level ranges. During the search for optimal parameters, the particle swarm optimization algorithm can adaptively reflect the impact of the sidefill structure on the lifespan.

[0066] More specifically, in the lifetime prediction experiment, samples with and without filler were compared, and the method described in Example 1 was used for evaluation. Environmental temperature cycling tests from -40°C to 125°C were used as boundary conditions, with a cycle time of 1 hour; the solder constitutive model used was the generalized Garofalo creep model.

[0067] More specifically: Step 1: Acquire and preprocess the lifespan degradation data.

[0068] Chip parameters, including voltage, current, power consumption, and resistance, can be recorded periodically using high-precision measuring equipment. Simultaneously, multi-source failure data, such as threshold voltage drift and leakage current changes, can be collected during temperature cycling tests of the chip.

[0069] Step 2: Establish an initial grey model with disturbance terms, incorporating the function mapping values ​​of temperature and humidity as development coefficients and grey action quantities into the grey differential equation form. Introduce equivalent thermomechanical stress as a disturbance term. oh This constitutes the initial gray model.

[0070] Step 3: Use the PSO algorithm to optimize the grey model. Based on the algorithm's selection characteristics, find the optimal sample lifetime predicted under different operating conditions. Set the number of test sample devices to 100 and the number of iterations to 100. Set the learning factor. c 1 = c 2 = 2.0 is used to balance local and global searches. Through continuous iteration of the algorithm model, the optimal operating conditions are found, and lifetime prediction is performed on different samples.

[0071] Step 4: Use the Markov method to correct the residuals to improve the fit. Calculate the residual sequence, construct the transition matrix, and then correct the predicted values ​​to finally obtain the fitted curve for lifetime prediction.

[0072] Under the same test conditions, the packaged samples with and without side filler showed a longer TTF (time to failure) and improved reliability.

[0073] Table 3 Comparison of life predictions with and without side packing

[0074] Side fillers can effectively alleviate thermal mismatch stress in the packaging structure, thereby reducing the intensity of the equivalent thermomechanical stress ω, slowing down the degradation rate, and improving the reliable lifespan of the chip. The method of this invention can accurately reflect the influence of the side filler structure on the stress-lifespan relationship and has good engineering applicability.

[0075] Some steps in the embodiments of the present invention can be implemented using software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk.

[0076] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A chip lifetime prediction method based on the PSO algorithm and Markov grey model, characterized in that, The method includes: Step 1: Obtain lifetime degradation data and perform preprocessing. The lifetime degradation data refers to the equivalent resistance value of the chip interconnect structure. Step 2: Establish an initial gray model with interference terms, where the interference terms are the equivalent thermomechanical stress calculated based on the elastic parameters of the packaging material; Step 3: Optimize the gray model parameters using the PSO algorithm. a , b , ω ), to obtain the optimal combination of temperature, humidity, and stress values ​​( a , b , ω ); Step 4: Correct the residuals of the grey model using the Markov method; Step 5: Use the corrected grey model to perform rolling prediction of the packaged chip lifetime; Step 2 includes: Step 21, based on the initial sequence X (0) and new sequence X (1) Establish the grey differential equation: ； Among them, the development coefficient a Ash action amount b In this model, temperature and humidity are function mappings under external environmental stress conditions, respectively, used to characterize the impact of environmental stress on the chip lifetime degradation rate; z (1) (k) is the nearest mean sequence, representing the sequence X generated by a single accumulation. (1) The average value between the (k-1)th and the kth time points is used to approximate the average level of chip degradation within this time interval; Step 22: Introduce interference terms ω The initial gray model is obtained: ； Interference items ω The equivalent thermomechanical stress is calculated based on the elastic parameters of the packaging material. The calculation method is as follows: ； in, and These represent the coefficients of linear expansion of the two different materials in the packaging structure, used to characterize the thermal expansion mismatch of the materials. E(T,n) Let be the Young's modulus of the material. The Young's modulus of the material degenerates with temperature T and the number of thermal cycles n.

2. The method according to claim 1, characterized in that, Step 1 includes: The equivalent resistance values ​​of the chip interconnect structure measured at different time points or thermal cycles are recorded as the initial sequence. ; This represents the parameter value at the k-th time point or the k-th thermal cycle, where k = 1, 2, ..., n; n ≥ 4; A new sequence X is generated by accumulating the initial sequence in one step according to the following rule. (1) ; ； ； x (1) (k) represents the new sequence X (1) The k-th value in the matrix, x (0) (i) represents the i-th value in the initial sequence.

3. The method according to claim 2, characterized in that, Step 3 includes: Step S31: Determine the parameters that need to be optimized in the gray model; Step S32: Construct the fitness function of the gray model, wherein the fitness function aims to minimize the average relative error; Step S33: Iteratively optimize using the following formula to obtain the optimal combination of "temperature, humidity, and stress": ； ； in, c 1 and c 2 is the learning factor. r 1 and r 2 is a random coefficient, with a value range of 0-1; For particles i The historical best position represents the optimal lifespan value under a certain operating condition. For particles i The global optimal position represents the most accurate life prediction result or key combination of operating conditions among all operating conditions under the overall assessment. For particles i The updated rate For particles i The current rate; particle i The updated location particle i The current position of the particle is defined as position( a , b , ω ( ), that is, the specific values ​​of "temperature, humidity, and stress" for a certain set of working conditions; Step S34: Determine if the maximum number of iterations has been reached. If the maximum number of iterations has been reached, the optimization ends, and the optimal life condition or minimum prediction error corresponding to a certain set of working conditions is output. The optimal life condition is denoted as (a opt , b opt , ω opt Otherwise, return to step 33.

4. The method according to claim 3, characterized in that, Step 4 includes: Step 41, the parameters after PSO optimization are (a opt , b opt , ω opt The grey model is used to make predictions, and the PSO optimized prediction value is obtained. The corresponding residual sequence E is then calculated. (0) ; Step S42: Construct the Markov state partitioning and transition matrix; Step S43: Correct the predicted value, using the state of the last value in the residual sequence as the initial state vector μ0, and then... t =μ0P t Predict the possible states of the future residual, P t Let be the transition probability at time t; Step S44: Based on the Markov state transition results, adjust the PSO optimized prediction value.

5. The method according to claim 4, characterized in that, In step 41, the residual sequence E (0) The calculation method is as follows: Subtracting the PSO-optimized predicted values ​​from the actual values ​​point by point yields the residual sequence: ； ； in, Represents the actual value. This represents the PSO optimized prediction value.

6. The method according to claim 5, characterized in that, The adjusted PSO prediction value in step 44 is: in The sign (±1) is determined by the state probability; in the formula It is the predicted value of the grey model built on the residual sequence itself.

7. The method according to claim 6, characterized in that, In step S32, the fitness function of the gray model is the average relative error.

8. The method according to claim 1, characterized in that, The chip is packaged using a side-fill structure.

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