A siP device life test sampling optimization method based on multi-source data fusion

Abstract

This invention discloses a sampling optimization method for SiP device lifetime testing based on multi-source data fusion, comprising the following steps: Step 1: SiP product test profile equivalence; Step 2: SiP product structural similarity evaluation; Step 3: Historical data fusion based on Monte Carlo simulation; Step 4: Historical test data fusion based on Bayes' principle; Step 5: Establishing a sampling scheme design model based on SiP product reliability; Step 6: Sampling scheme design. This method, based on Bayes' data fusion theory and LTPD sampling theory, addresses the problem that insufficient batch sizes of SiP products cannot support qualification and quality consistency inspection tests. It conducts structural similarity analysis and data fusion method research on SiP products, establishes a sampling model based on SiP device reliability, and combines similarity analysis and data fusion to formulate a sampling method suitable for SiP devices, thereby reducing the sample size. This method belongs to the technical field of SiP device sampling optimization method research.

Description

Technical Field

[0001] This invention relates to a sampling optimization method for SiP device lifetime testing based on multi-source data fusion, belonging to the technical field of SiP device sampling optimization method research. Background Technology

[0002] With the rapid development of semiconductor manufacturing technology, lightweight, small, and portable electronic devices have become a requirement of the times. The integration level of semiconductor chips is gradually increasing, giving rise to the emergence and development of SiP (System-in-Package) products. SiP products assemble multiple active and passive components with different functions into a single standard package that can provide multiple functions. With the rapid development of aerospace electronics, military electronics, and other technologies, miniaturized, lightweight, high-density, and highly reliable system-in-package technology has been widely used.

[0003] Currently, there are no clear standards and methods for quality assurance of SiP products. It is usually achieved by referring to the relevant requirements in GJB2438B-2017 and GJB548B-2005. The methods contained in these standards have been thoroughly verified and can provide quality assurance for ordinary hybrid integrated circuits. However, compared with ordinary hybrid integrated circuits, SiP products have a more complex internal structure. Due to the integration of a large number of devices with different functions, a single SiP product can perform the functions that previously required a standalone device, thus resulting in a smaller demand. If experiments are conducted according to the statistical sampling method specified in GJB2438, the sample size may be insufficient. Therefore, there is an urgent need to optimize the sampling method by combining multi-source experimental data from the SiP product quality assurance process with the relevant principles of the LTPD statistical sampling method, and to establish a sampling method suitable for small-sample SiP products, providing theoretical guidance for engineering practice. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of existing technologies and provide a sampling optimization method for SiP device lifetime testing based on multi-source data fusion. This method considers historical test data from the SiP device quality assurance process and the requirements of traditional sampling methods specified in GJB2438B-2017 and GJB548B-2005. This method overcomes the shortcomings of traditional statistical sampling methods, which require large sample sizes, while SiP devices are produced in small batches and are insufficient to support Group C steady-state lifetime tests for device qualification and quality consistency verification. By fusing multi-source historical data to expand the sample size, the required sample size is reduced, providing theoretical guidance for the formulation of SiP device sampling schemes in engineering practice.

[0005] The technical solution of this invention is:

[0006] This invention discloses a sampling optimization method for SiP device lifetime testing based on multi-source data fusion, comprising:

[0007] Equivalent test profiles of SiP products were performed to obtain equivalent lifetimes under different test temperature conditions;

[0008] A similarity evaluation model based on fuzzy mathematics is established to obtain the similarity of SiP products;

[0009] System reliability simulation was performed using the Monte Carlo simulation method to obtain the lifetime distribution of SiP products.

[0010] Based on equivalent lifetime, SiP product similarity, and lifetime distribution, reliability distribution and historical test data are fused to obtain the posterior reliability distribution;

[0011] Based on the posterior distribution of reliability, a sampling scheme design model based on the reliability of SiP products is established, and the required sampling sample size is calculated.

[0012] Furthermore, in the above optimization method, the step of performing equivalent SiP product test profiles to obtain equivalent lifetimes under different test temperature conditions specifically involves:

[0013] ξ1=ξ0 / Af

[0014]

[0015] Where ξ1 is the equivalent test time at other test temperatures, and ξ0 is the steady-state life test holding time; A f The acceleration factor is the ratio of the steady-state life test temperature to the equivalent life at other test temperatures; T0 is the temperature under steady-state life test conditions, T1 is an arbitrary temperature, and E... A The activation energy is K, and K is the Boltzmann constant.

[0016] Furthermore, in the above optimization method, the establishment of a similarity evaluation model based on fuzzy mathematics to obtain the SiP product similarity specifically involves:

[0017] Determine the set of evaluation factors for SiP product similarity;

[0018] The membership function is used to obtain the SiP product similarity evaluation index matrix;

[0019] Based on the similarity evaluation factor set and evaluation index matrix, the analytic hierarchy process (AHP) is used to conduct a comprehensive evaluation of product similarity.

[0020] Furthermore, in the above optimization method, determining the SiP product similarity evaluation factor set specifically involves:

[0021] Based on the failure modes of SiP critical structures, similarity evaluation is performed on the structures affecting SiP product similarity during steady-state lifetime testing to obtain a set of SiP product similarity evaluation factors. The structures affecting SiP product similarity include active devices, wire bonding, and flip-chip bonding. The set of SiP product similarity evaluation factors includes chip performance, interconnect process design parameters, and product manufacturing process capabilities.

[0022] Furthermore, in the above optimization method, the step of using a membership function to quantify the SiP product similarity evaluation index matrix specifically involves:

[0023]

[0024] Where R is the SiP product similarity evaluation index matrix, r 1i Let r be the membership degree of the chip performance metric for the i-th module. 2i Let r be the membership degree of the interconnect process design parameter index for the i-th module. 3i Let be the membership degree of the manufacturing process index of the i-th module;

[0025] The membership function for chip performance metrics is as follows:

[0026]

[0027] The membership function of interconnect process design parameters is as follows:

[0028]

[0029] The membership function of manufacturing process indicators is as follows:

[0030]

[0031] Where λ0 is the failure rate of the target SiP device chip, λ is the failure rate of similar product chips; L0 is the bonding lifetime of the target SiP device, L T For similar products, bond life; C pk0 C represents the process capability index of each step in the process of the target SiP device. pk This refers to the process capability index for each step of similar products.

[0032] Furthermore, in the above optimization method, the step of using the analytic hierarchy process (AHP) to conduct a comprehensive evaluation of product similarity based on the similarity evaluation factor set and evaluation index matrix specifically involves:

[0033] S61. Based on expert experience, determine the fuzzy weights between each module and the fuzzy weights between each evaluation index, and construct the product module importance matrix AR1 and the evaluation index importance matrix AR2.

[0034] S62. Find the eigenvectors of the product module importance matrix AR1 and the evaluation index importance matrix AR2, and obtain the fuzzy weight vector K1 of the product module and the fuzzy weight vector K2 of the evaluation index respectively.

[0035] S63. Based on K1 and K2, the product similarity of similar products to the target SiP device is obtained, specifically as follows:

[0036] B = A·K2

[0037] A = R·K1

[0038] Where R is the SiP product similarity evaluation index matrix, A is the similarity matrix of similar SiP products, and B is the product similarity of similar products to the target SiP device.

[0039] Furthermore, in the above optimization method, step S61, constructing the product module importance matrix AR1 and the evaluation index importance matrix AR2, specifically involves:

[0040]

[0041]

[0042] Among them, a ij Let b be the importance of the i-th module to the j-th module. kl Let represent the importance of the k-th evaluation indicator to the l-th evaluation indicator.

[0043] Furthermore, in the above optimization method, system reliability simulation is performed based on the Monte Carlo simulation method to obtain the lifetime distribution of the SiP product, specifically:

[0044] According to component reliability theory, assuming that the component reliability follows an exponential distribution, and its failure rate λ is known and constant, the reliability of the unit that can still work normally when it is greater than or equal to t is:

[0045] R(t) = e -λt

[0046] The reliability of a cell is denoted as R by taking one sample from a population that follows a uniform distribution U(0,1).

[0047] The corresponding working hours are calculated as follows:

[0048]

[0049] By repeatedly sampling reliability values ​​and calculating the corresponding operating time, the lifetime distribution of each module within the SiP product can be obtained.

[0050] Furthermore, in the above optimization method, the method for fusing reliability distribution and historical test data based on equivalent lifetime to obtain posterior reliability distribution is as follows:

[0051]

[0052] p(x|R)=R n (1-R) f

[0053]

[0054]

[0055] Where π(R|x) is the posterior distribution, and p(x|R) is the likelihood function representing sample information. B is a mixed prior distribution; i Let F(R; n, f) be the similarity of the i-th information source; let F(R; n, f) be the distribution function of the reliability R; let n be the sample size of the experiment; and let f be the number of samples that failed in the experiment. x (n, f) is an incomplete beta function, and B(n, f) is a beta function.

[0056] Furthermore, in the above optimization method, the specific method for establishing a sampling scheme design model based on SiP product reliability and calculating the required sampling size is as follows:

[0057]

[0058]

[0059] When the reliability R of SiP products L When R ≤ 1, determine the required sampling plan (n, f) that satisfies the acceptance criteria; where n is the number of samples to be sampled, and f is the number of invalid samples; R L β represents the lower limit of reliability specifications, and β represents the user's risk. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the implementation steps of the present invention;

[0061] Figure 2 This is a similarity evaluation tree for SiP products of the present invention;

[0062] Figure 3 This is a block diagram model of the reliability of SiP products in this invention;

[0063] Figure 4 This is a flowchart of the sampling scheme calculation process of the present invention. Detailed Implementation

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] like Figure 1 As shown, this invention provides a sampling optimization method for SiP device lifetime testing based on multi-source data fusion, comprising:

[0066] Step 1: Perform equivalent test profiles of SiP products to obtain equivalent lifetimes under different test temperature conditions;

[0067] Step 2: Establish a similarity evaluation model based on fuzzy mathematics to obtain the similarity of SiP products;

[0068] Step 3: Perform system reliability simulation based on Monte Carlo simulation to obtain the lifetime distribution of SiP products;

[0069] Step 4: Based on the equivalent lifetime, SiP product similarity, and lifetime distribution, the reliability distribution and historical test data are fused to obtain the posterior reliability distribution;

[0070] Step 5: Based on the posterior distribution of reliability, establish a sampling scheme design model based on the reliability of SiP products and calculate the required sampling size.

[0071] The following will provide a more detailed description of the SiP device lifetime test sampling optimization method based on multi-source data fusion based on the accompanying drawings. The specific steps are as follows:

[0072] Step 1: SiP Product Test Profile Equivalent

[0073] Because the historical data sources for SiP product quality assurance are extensive and diverse, to ensure data fusion consistency, an equivalent test profile of the SiP product must first be performed before data fusion. Under steady-state lifetime test conditions, SiP products are subjected to high-temperature stress, leading to device characteristic degradation or failure. Therefore, the Arrhenius model is used to transform the test profile, taking the degradation of the device's operating lifetime under different test temperatures as the equivalent condition, thereby obtaining the equivalent lifetime under different test temperatures. This equivalent lifetime is then used as the input for subsequent multi-source test data fusion.

[0074] According to the Arrhenius model, under certain temperature conditions, the reaction rate of the device is inversely proportional to the exponential of the activation energy and inversely proportional to the exponential of the reciprocal of the temperature, that is:

[0075]

[0076] Where M is the degradation amount of a certain characteristic of the product, dM / dt is the degradation rate of a certain characteristic of the product, A is the proportionality constant or "frequency factor" or pre-exponential factor, T is the absolute temperature, and K is the Boltzmann constant, 8.623 × 10⁻⁶. 5 eV / K, E A The activation energy is a constant that does not change with temperature.

[0077] Integrating the above equation with T constant, we get:

[0078]

[0079] Where t represents the product's lifespan starting from time M0.

[0080] Assuming T0 is the temperature condition under steady-state life test and T1 is an arbitrary temperature condition, after experiencing different times t0 and t1, a certain characteristic of the product exhibits the same amount of degradation, which can be obtained as follows:

[0081]

[0082] Therefore, we can conclude that:

[0083]

[0084] Let t0 / t1 be the acceleration coefficient A. f This refers to the ratio of the steady-state lifetime test temperature to the equivalent lifetime at other test temperatures. The acceleration factor can be determined based on the test temperature using the Arrhenius law formula:

[0085] ξ1=ξ0 / A f

[0086] Where ξ1 is the equivalent test time at other test temperatures, ξ0 is the steady-state lifetime test time, and A f This is the acceleration factor.

[0087] The device activation energy E was taken by transferring its room temperature test lifetime to 125℃ conditions. A =0.7eV, so the acceleration factor ξ0 = 260, that is, the acceleration factor of the device at 125℃ to 25℃ is 260. If the product life is 20 years at room temperature, then its equivalent life under steady-state life test conditions is 672h.

[0088] Step 2: SiP Product Structural Similarity Evaluation

[0089] SiP products from the same production line exhibit structural similarities, which can be used for data fusion. To ensure the consistency of the test object structure during experimental data fusion, a structural similarity evaluation of the relative SiP devices is required for SiP similar products and process capability domain assessment test carriers. The main content involves establishing a similarity evaluation model based on fuzzy mathematics, and establishing an evaluation factor set, a method for determining evaluation factor indicators, and a method for determining evaluation weights based on the structural characteristics of SiP products and their failure analysis. The final SiP product similarity will be used for subsequent experimental data fusion.

[0090] 1. Determination of key structures for SiP product similarity evaluation

[0091] Based on device structure, process characteristics, application conditions, and failure information of similar products, common failure modes of SiP products' key structures (bare die, interconnect, and substrate) include functional failure, open circuit, short circuit, parameter drift, and package leakage. The main failure modes affecting SiP reliability include: failures caused by active devices, wire bonding, device bonding, flip-chip bonding, package substrate, package shell failure, and other failures. The main failure modes, failure mechanisms, stress types, and related physical models are shown in Table 1.

[0092] Table 1 Failure modes of key structures in SiP devices

[0093]

[0094]

[0095] In steady-state life tests, the stress on the device is high-temperature stress. Therefore, according to the table above, the structure that causes failure due to high-temperature stress is selected as the key structure for SiP product similarity evaluation, including active devices, wire bonding, and flip-chip bonding.

[0096] 2. Quantification of SiP Product Similarity Evaluation Indicators

[0097] The reliability differences among similar SiP products mainly stem from two aspects: firstly, product design factors, such as different chips, passive devices, and interconnect processes, which can lead to reliability variations; and secondly, manufacturing process factors, such as different production line levels and different production batches on the same production line, which can cause reliability fluctuations. Therefore, evaluation factors are categorized into design factors and process factors. The evaluation metrics for the parameterized layer are shown in Table 2. Product similarity evaluation metrics are defined as chip performance metrics, interconnect process design parameter metrics, and manufacturing process metrics, and membership functions are used to characterize the similarity of SiP products across these metrics.

[0098] Table 2. Evaluation Indicators for Parametric Layer Similarity

[0099]

[0100] 1) Membership function of chip performance indicators

[0101] SiP devices are manufactured from individual components through processes such as surface mounting, bonding, and sealing. The performance of the chips used in each module affects the reliability of the SiP system; therefore, chip performance is considered an important evaluation metric. Assuming that chips used in the same module have similar functions, and since failure rate can represent the chip's reliability level, the membership degree is quantified using the chip failure rate λ0 of the target SiP device as a benchmark. The chip performance metric membership function is as follows:

[0102]

[0103] 2) Membership function of interconnect process design parameters

[0104] There are various SiP interconnect methods, such as wire bonding, tape-based automated bonding, flip-chip bonding (FC), and through-silicon vias (TSV). Among these, wire bonding and flip-chip bonding are the most common interconnect methods. For devices using wire bonding, the bonding material is a crucial factor affecting device reliability. For example, at high temperatures, the formation of metal oxides leads to a decrease in bond strength, thus affecting device reliability. Furthermore, experiments have shown that the bonding wire diameter is also a significant factor influencing bond strength; at a given temperature, the reliable lifetime of the bond increases with increasing bonding wire diameter. For flip-chip devices, compared to wire bonding, the shorter signal transmission path makes the bonding material the primary factor affecting bond strength. Additionally, the solder joint size and arrangement also influence device reliability. Therefore, considering the above design parameters and bond strength, a membership function for the interconnect process design parameters is established based on the bond lifetime under steady-state lifetime test conditions.

[0105] The bonding lifetime L of the interconnect structure under steady-state lifetime test conditions was obtained through experiments and the Arrhenius model. T Based on the target SiP device bonding lifetime L0, the interconnect process design parameters are quantified using bonding lifetime as follows:

[0106]

[0107] 3) Membership function of manufacturing process indicators

[0108] Due to manufacturing process factors, different production lines or different production batches within the same production line can cause fluctuations in product reliability, thus increasing the differences between SiP products. Therefore, the impact of manufacturing process is considered an important indicator for similarity evaluation. In the SiP device quality assurance process, the production line C... pkMonitoring device performance level, passing review and analysis C pk Data is used to improve processes, and therefore, the process capability index can be used to evaluate the differences caused by the manufacturing process. Thus, the process capability index can reflect the impact of the manufacturing process on product reliability. The process capability index C of each process in SiP device manufacturing is used to analyze the process capability index. pk0 As a benchmark, the membership function of the manufacturing process index is determined using the process capability index, as follows:

[0109]

[0110] Based on the membership functions of the three similarity evaluation indicators mentioned above, an evaluation indicator matrix is ​​established, where the evaluation indicator matrix R represents the membership degree of each module of the product on each evaluation indicator:

[0111]

[0112] Where, r 1i r represents the membership degree of the chip performance metric for the i-th module. 2i r represents the membership degree of the interconnect process design parameter index of the i-th module. 3i This represents the membership degree of the manufacturing process index of the i-th module.

[0113] A SiP device was selected as the research object. The SiP device adopts metal-ceramic hermetically sealed packaging, single cavity, and contains one SoC chip, which is bonded by flip chip, two SRAM chips, which are bonded by wire bonding, and two FLASH chips, which are bonded by wire bonding.

[0114] There are similar products to this device, which use metal-ceramic sealed packaging, single cavity, and contain one SoC chip of different models, bonded by flip-chip, two SRAM chips, bonded by wire bonding, and one FLASH chip, bonded by wire bonding.

[0115] The SiP process capability domain evaluation test Class II test carrier structure is similar to the above products, adopts metal-ceramic sealed packaging, single cavity, contains SoC chip, bonding method is flip-chip, SRAM chip and FLASH chip, bonding method is wire bonding.

[0116] SiP product similarity evaluation levels, such as Figure 2 As shown, the similarity of SiP products is determined from the bottom up by the module similarity. The similarity of each module is evaluated using chip performance indicators, interconnect process design parameters, and manufacturing process indicators. It is known that gold wire bonding is used, and SnPb solder is used for flip-chip bonding. The design parameters for each product are as follows:

[0117] Compared to SiP devices, the performance similarity of the SiP similar product-level process capability domain evaluation test carrier SoC module chip is 0.67, the performance similarity of SRAM module chip is 1 and 0.6, and the performance similarity of FLASH module chip is 1.

[0118] Table 3. SiP Product Design and Process Data

[0119]

[0120]

[0121] Nonlinear fitting was performed on the tensile strength data of bonding wires with diameters of 20, 30, 35, and 38 μm to calculate the lifetime at the steady-state lifetime test temperature, and the results are shown in the table below:

[0122] Table 4. Bond tension fitting results

[0123]

[0124] The steady-state lifetime of wire bonding with arbitrary wire diameter can be obtained by fitting a cubic spline interpolation.

[0125] For wire bonding, the bonding process used in SiP products has a bonding lifetime of 12.86 years under steady-state lifetime test conditions, while the bonding lifetime of similar SiP products is 13.95 years. The bonding lifetime of the process capability domain evaluation test carrier, calculated based on the minimum bonding wire diameter, is 12.86 years. Therefore, the interconnect process similarity of similar products and process capability domain evaluation test carrier for SiP devices is 1.

[0126] Nonlinear fitting was performed on the shear strength data of weld joints with diameters of 0.6, 0.64, 0.68, and 0.76 mm to calculate the life at the steady-state life test temperature, and the results are shown in the table below:

[0127] Table 5. Fitting results of weld joint shear strength

[0128]

[0129] By fitting with cubic spline interpolation, the steady-state life of the solder joint under any size can be obtained.

[0130] For flip-chip bonding, the lifespan of the SiP product under steady-state life test conditions is 13.82 years, the lifespan of similar SiP products is 12.63 years, and the lifespan of the process capability domain evaluation test carrier calculated based on the minimum solder joint size is 12.86 years. Therefore, the interconnect process similarity of similar products and process capability domain evaluation test carrier for SiP devices is 0.91.

[0131] Compared to SiP devices, the process similarity of the SiP similar product-level process capability domain evaluation test carrier SoC module is 0.96 and 1, respectively; the process similarity of SRAM module chip is 0.93 and 0.94; and the process similarity of FLASH module is 0.97.

[0132] Based on the membership degree of each module to each evaluation index, the evaluation index matrix of the SiP similar product and process capability domain assessment test carrier can be obtained, as follows:

[0133]

[0134]

[0135] 3. Comprehensive evaluation of SiP product similarity

[0136] To determine the evaluation indicators and fuzzy weights for each key module, the Analytic Hierarchy Process (AHP) was used to quantify them based on expert judgment and the functions of each module in the SiP device. For key modules of SiP products, the AHP method was used to determine the fuzzy weights of chip performance indicators, interconnect process design parameters, and manufacturing process indicators. The product similarity of similar SiP products and process capability domain evaluation test carriers was calculated in conjunction with the evaluation indicator matrix.

[0137] First, based on expert experience, determine the fuzzy weights between each module and between each evaluation indicator. Construct the product module importance matrix AR1 and the evaluation indicator importance matrix AR2:

[0138]

[0139]

[0140] Among them, a ij Let b be the importance of the i-th module to the j-th module. kl Let represent the importance of the k-th evaluation indicator to the l-th evaluation indicator.

[0141] By normalizing and verifying the quality consistency of the above importance matrix, the fuzzy weight vector K1 of the product module and the fuzzy weight vector K2 of the evaluation index can be determined.

[0142] Then calculate the similarity matrix A of SiP similar products:

[0143] A = R·K1

[0144] Finally, the product similarity B of similar products for the target SiP device is obtained:

[0145] B = A·K2

[0146] Taking the above-mentioned SiP product as an example, based on expert experience, the product module importance matrix AR1 and the evaluation index importance matrix AR2 are constructed respectively:

[0147]

[0148]

[0149] The importance matrix above was normalized and its quality consistency was checked. The fuzzy weights of the product modules were determined to be K1 = [0.225, 0.459, 0.316]. T The fuzzy weights for the evaluation indicators are K2 = [0.361, 0.319, 0.320]. T .

[0150] By combining the evaluation index matrix, the similarity matrices of similar products and process capability domain assessment test vehicles can be calculated as follows:

[0151] A1=R1·K1=[0.871, 0.978, 0.991] T

[0152] A2=R2·K1=[0.884, 0.891, 0.991] T

[0153] Compared to SiP devices, the product similarity of SiP similar products and process capability domain evaluation test carriers are as follows:

[0154] B1 = A1·K2 = 0.944

[0155] B² = A²·K² = 0.920

[0156] Step 3: Fusion of historical data based on Monte Carlo simulation

[0157] SiP devices contain a large amount of failure rate data for their bare chips. Using this historical information for multi-source data fusion allows SiP devices to be treated as complex systems, enabling system reliability simulation based on the Monte Carlo method. The basic principle is to simulate failure events that occur during system operation. Failures of system components will directly or indirectly affect the normal operation of the system, and the system reliability level is calculated based on the impact of these events. This method uses random numbers for computer simulation. It employs a random number generator to randomly sample the system, and by statistically analyzing the sample values, the sampling method for the operating time of the system under study is obtained.

[0158] If a SiP product is viewed as being composed of numerous components and elements arranged in a certain manner, its reliability block diagram is as follows: Figure 3 As shown. The failure rates of the five devices are 2 × 10⁻⁶. -6 / hour, 3×10-6 / hour, 3×10 -6 / hour, 5×10 -6 / hour, 5×10 -6 / time. According to the component reliability model, assuming that the component reliability follows an exponential distribution and its failure rate λ is constant, the reliability of the unit that can still work normally at a time greater than or equal to t is:

[0159] R(t) = e -λt

[0160] The reliability of a cell is denoted as R by taking one sample from a population that follows a uniform distribution U(0,1).

[0161] The corresponding working hours are calculated as follows:

[0162]

[0163] Based on 1000 Monte Carlo sampling results, the number of failures of SiP products at the end of the steady-state life test was 56.

[0164] Step 4: Fusion of historical experimental data based on Bayesian principle

[0165] For historical data of SiP products and similar products, as well as process capability domain assessment test vehicles, this method utilizes Bayes theory to fuse the obtained reliability distributions. The reliability portions obtained from test data from various sources are fused based on product similarity to form a pre-approval distribution for Bayes data fusion. Then, a likelihood function is constructed using field test data, and the reliability distributions are fused according to the Bayes fusion method to obtain the post-approval reliability distribution.

[0166] 1. Confidence distribution determination

[0167] In a steady-state life test, the sample size is n, and the failure rate is f. Then, the reliability R of this batch of products at the end of the test follows a beta distribution β(s, f), with the following probability density function:

[0168]

[0169] For the case where there are no failures in the experiment, the lower confidence limit of the reliability at confidence level α can be obtained as R using the experimental data. L :

[0170]

[0171] Where n is the experimental sample size, and t is the end time of the experiment. This represents the total test time.

[0172] Reliability confidence distribution of the device under its test information:

[0173]

[0174]

[0175] The second-moment method is used to approximate the β distribution. First, the first two moments of f(R) are calculated and equal to the first two moments of the undetermined β distribution, thus simulating success-failure data and obtaining an approximate reliability confidence distribution. Let μ1 and μ2 be the first and second moments of f(R), respectively, then:

[0176]

[0177]

[0178] Let μ1 and μ2 be equal to the parameters of the beta distribution, respectively:

[0179]

[0180] f0=n-(n+1)μ1

[0181] The distribution of the lower confidence limit of the reliability R of the SiP product at the end of the test is β(R; n0, f0), and the distribution of the reliability R at the end of the test is taken as β(R; n0+0.5, f0+0.5).

[0182] For a product with a test sample size of n and a failure sample size of f, the probability density function of the reliability R is:

[0183]

[0184]

[0185] The distribution function of reliability R is:

[0186]

[0187] 2. Construction of Mixed Prior Distributions

[0188] According to step two, B i Let be the similarity of the i-th information source, then The mixed prior distribution is:

[0189]

[0190] For the field test data of SiP products, the test sample size is n, the failure sample size is f, and the sample size of each historical test is n. i The number of failed samples is f i Then the likelihood function containing sample information is:

[0191] p(x|R)=R n (1-R) f

[0192] 3. Posterior distribution determination

[0193] According to Bayes' formula, the posterior reliability distribution, which integrates field test data and historical process data, is as follows:

[0194]

[0195] Table 6 shows the existing test data for each SiP product in the quality assurance and process capability domain assessment stage. Based on the similarity assessment of SiP products, reliability data fusion is performed using the Bayes hybrid method.

[0196] Table 6 Steady-state life test data for SiP products

[0197]

[0198]

[0199] Based on the similarity assessment test vehicle data of SiP similar products and process capability domains, as well as their steady-state life test data, the prior reliability distribution of the SiP product after integrating historical data from each stage of SiP product quality assurance can be obtained as follows:

[0200] π(r) = 16.32r 3.49 (1-r) 0.75 +29.97r 6.5 (1-r) 0.64 +52.22r 10.5 (1-) 0.59

[0201] Step 5: Establish a sampling scheme design model based on SiP product reliability.

[0202] Based on the statistical sampling methods and hypothesis testing principles specified in GJB2438B-2017 and GJB548B-2005, the sampling method based on product nonconforming rate is transformed into a sampling method based on product reliability. Statistical hypotheses are proposed for product reliability, thereby establishing a sampling plan design model based on SiP product reliability.

[0203] The lower limit of product reliability is specified as R. L According to the reliability probability distribution, when the product reliability R ≤ R L In this case, the acceptance probability L(R) is the area of ​​the region filled by the product reliability probability distribution. The user risk β is calculated as follows:

[0204]

[0205] Typically, the user's maximum risk is limited to a given value β. Therefore, developing a reliability-based sampling inspection plan involves solving the following equation:

[0206]

[0207] Step Six: Sampling Plan Design

[0208] An inspection plan outlines the number of samples to be drawn from a batch of products, the size of each sample, and the rules for determining whether to accept the entire batch based on the sample inspection results. Therefore, the sample size and the allowable number of failures are two crucial aspects in determining the sampling plan. According to the sampling method specified in GJB2438 General Specification for Hybrid Integrated Circuits, the unknowns in calculating the sampling plan are the sample size *n* and the batch allowable number of failures *c*. In this embodiment, the sampling plan is determined by taking the batch allowable number of failures *c* = 0, 1, 2, ..., thereby calculating the corresponding required sample size *n*. Based on Bayes data fusion theory and LTPD sampling theory, this study addresses the challenges of SiP devices' high functional integration and small production batches, while traditional integrated circuits require large sample sizes for assurance testing. The insufficient batch sizes of SiP products to support partial qualification and quality consistency verification tests necessitate structural similarity analysis and data fusion methods for SiP products, similar products, and process capability domain assessment test carriers. Furthermore, a sampling model based on SiP device reliability is established, and a suitable sampling method for SiP devices is developed by combining similarity analysis and data fusion to reduce the sample size.

[0209] 1. Sampling condition transformation

[0210] For sampling scheme design with reliability as the quality objective, it is necessary to specify the user's risk β and the lower limit of reliability R for SiP products. L Under these conditions, determine the sampling quantity and the acceptance conditions for the batch of products.

[0211] Regarding the user risk in sampling, the statistical sampling method specified in GJB2438 General Specification for Hybrid Integrated Circuits is to conduct sampling tests with the minimum sample size at a 90% confidence level. That is, the user risk β specified in the sampling is 10%, and the user risk specified in the standard is used as the user risk of the new sampling plan.

[0212] For the lower limit of reliability R of sampling L According to the sampling scheme specified in GJB2438 General Specification for Hybrid Integrated Circuits, the reliability of the next batch of products under this scheme is evaluated, and the reliability lower limit R of the new sampling scheme is used as the basis for evaluation. LThis allows for the design of a sampling plan by combining experimental results with historical information on the availability of SiP products.

[0213] 2. Sampling Plan

[0214] Following the design principles of the Less Permissible Nonconforming Rate (LTPD) sampling inspection plan, and based on the acceptance quality level, manufacturer risk, and user risk, the sampling plan meets the specified design requirements. The user risk β0 is defined, and the lower limit of batch product reliability R is calculated according to the original sampling plan. L Combined with user risk β0 and batch product reliability lower limit R L The sampling plan is formulated based on the sample size n. The flowchart for the plan formulation is as follows: Figure 4 As shown.

[0215] Taking the user's risk β0 = 10%, adopting Figure 4 The illustrated process uses Python for calculations. When n=11, the user risk β=0.109; while when n=12, the user risk β=0.091. Therefore, the sample size required to meet the sampling plan requirement of user risk not exceeding 10% is 12. Compared with GJB2438B-2017 and GJB548B-2005, the required steady-state life test sample size is reduced from 22 to 12, resulting in a significant reduction in the required sampling quantity.

[0216] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

[0217] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A sampling optimization method for SiP device lifetime testing based on multi-source data fusion, characterized in that, include: Equivalent test profiles of SiP products were performed to obtain equivalent lifetimes under different test temperature conditions; A similarity evaluation model based on fuzzy mathematics is established to obtain the similarity of SiP products; System reliability simulation was performed using the Monte Carlo simulation method to obtain the lifetime distribution of SiP products. Based on equivalent lifetime, SiP product similarity, and lifetime distribution, reliability distribution and historical test data are fused to obtain the posterior reliability distribution; Based on the posterior distribution of reliability, a sampling scheme design model based on the reliability of SiP products is established, and the required sampling sample size is calculated. The establishment of a similarity evaluation model based on fuzzy mathematics to obtain the similarity of SiP products is as follows: Determine the set of evaluation factors for SiP product similarity; The membership function is used to obtain the SiP product similarity evaluation index matrix; Based on the similarity evaluation factor set and evaluation index matrix, the analytic hierarchy process (AHP) is used to conduct a comprehensive evaluation of product similarity. The membership function is used to quantify the SiP product similarity evaluation index matrix, specifically as follows: Where R is the SiP product similarity evaluation index matrix. Let be the membership degree of the chip performance metric for the i-th module. Let the membership degree be the interconnect process design parameter index of the i-th module. Let be the membership degree of the manufacturing process index of the i-th module; The membership function for chip performance metrics is as follows: The membership function of interconnect process design parameters is as follows: The membership function of manufacturing process indicators is as follows: in, The failure rate of the target SiP device chip. Failure rate of chips for similar products; L 0 represents the target SiP device bonding lifetime. L T For similar products, the bond life; C pk0 This refers to the process capability index of each step in the target SiP device manufacturing process. C pk This refers to the process capability index for each step of similar products.

2. The method for sampling optimization of SiP device lifetime testing based on multi-source data fusion according to claim 1, characterized in that: The equivalent lifespan under different test temperature conditions by performing SiP product test profile equivalence is as follows: in, For equivalent test time at other test temperatures, The holding time for steady-state life testing; The acceleration factor is the ratio of the steady-state life test temperature to the equivalent life at other test temperatures; T0 is the temperature under steady-state life test conditions, T1 is an arbitrary temperature, and E... A The activation energy is K, and K is the Boltzmann constant.

3. The method for optimizing SiP device lifetime testing sampling based on multi-source data fusion according to claim 1, characterized in that: The determination of the SiP product similarity evaluation factor set specifically includes: Based on the failure modes of SiP critical structures, similarity evaluation is performed on the structures affecting SiP product similarity during steady-state lifetime testing to obtain a set of SiP product similarity evaluation factors. The structures affecting SiP product similarity include active devices, wire bonding, and flip-chip bonding. The set of SiP product similarity evaluation factors includes chip performance, interconnect process design parameters, and product manufacturing process capabilities.

4. The method for sampling optimization of SiP device lifetime testing based on multi-source data fusion according to claim 1, characterized in that: The process of comprehensively evaluating product similarity using the analytic hierarchy process (AHP) based on the similarity evaluation factor set and evaluation index matrix is ​​as follows: S61. Based on expert experience, determine the fuzzy weights between each module and the fuzzy weights between each evaluation index, and construct the product module importance matrix AR1 and the evaluation index importance matrix AR2. S62. Find the eigenvectors of the product module importance matrix AR1 and the evaluation index importance matrix AR2, and obtain the fuzzy weight vector K1 of the product module and the fuzzy weight vector K2 of the evaluation index respectively. S63. Based on K1 and K2, the product similarity of similar products to the target SiP device is obtained, specifically as follows: Where R is the SiP product similarity evaluation index matrix, A is the similarity matrix of similar SiP products, and B is the product similarity of similar products to the target SiP device.

5. The method for sampling optimization of SiP device lifetime testing based on multi-source data fusion according to claim 4, characterized in that: In step S61, constructing the product module importance matrix AR1 and the evaluation index importance matrix AR2 specifically involves: in, Let i be the importance of the i-th module to the j-th module. Let represent the importance of the k-th evaluation indicator to the l-th evaluation indicator.

6. The method for optimizing SiP device lifetime testing sampling based on multi-source data fusion according to claim 1, characterized in that: System reliability simulation was performed using the Monte Carlo simulation method to obtain the lifetime distribution of the SiP product, as follows: According to component reliability theory, assuming that the component reliability follows an exponential distribution, and its failure rate λ is known and constant, the reliability of the unit that can still work normally when it is greater than or equal to t is: The reliability of a cell is denoted as R by taking one sample from a population that follows a uniform distribution of U(0,1). The corresponding working time is calculated as follows: By repeatedly sampling reliability values ​​and calculating the corresponding operating time, the lifetime distribution of each module within the SiP product can be obtained.

7. The method for sampling optimization of SiP device lifetime testing based on multi-source data fusion according to claim 1, characterized in that: The reliability distribution is obtained by fusing reliability distribution and historical test data based on equivalent lifetime, SiP product similarity, and lifetime distribution. The specific method is as follows: in, For the posterior distribution, Let be the likelihood function representing the sample information. B is a mixed prior distribution; i For the first i Similarity between information sources; Let be the distribution function of the reliability R; n be the test sample size; f be the number of samples that failed during the test; It is an incomplete beta function. It is a β function.

8. The method for optimizing the sampling of SiP device lifetime testing based on multi-source data fusion according to claim 1, characterized in that: The specific method for establishing a sampling scheme design model based on SiP product reliability and calculating the required sampling size is as follows: When SiP product reliability When the conditions for acceptance are met, the required sampling plan (n, f) is determined; where n is the number of samples to be sampled and f is the number of invalid samples. β represents the lower limit of reliability specifications, and β represents the user's risk.

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