Constant thermal stress sequential electrical stress test method

Abstract

The present invention relates to the field of stress testing technology, and specifically to a method for testing electrical stress using a constant thermal stress sequence. The method includes sample preparation and equipment calibration, applying linearly increasing electrical stress under constant thermal stress and monitoring failures in real time; calculating the electrical stress acceleration factor, equivalent time, and failure time; combining the test junction temperature with normal operating conditions to calculate the comprehensive acceleration factor and convert the failure time; and constructing a three-parameter Weibull distribution reliability model based on the converted data. The method uses maximum likelihood estimation and the Newton-Raphson algorithm to estimate parameters and obtain reliability indicators. The method can efficiently induce failures and accurately model reliability indicators under constant thermal stress conditions, thereby improving the efficiency, accuracy, and engineering practicality of reliability assessments.

Description

Technical Field

[0001] The present invention relates to the technical field of stress testing, and in particular to a constant thermal stress sequential electrical stress testing method. Background Art

[0002] In modern industrial manufacturing and product development, product reliability is an important indicator for measuring its performance stability and quality level. Thermal stress and electrical stress, as key environmental stress sources, have a significant impact on device performance and lifespan in multiple application fields. Therefore, establishing scientific and effective reliability assessment methods is of great significance for product design optimization and lifecycle management.

[0003] Existing reliability testing methods, such as long-term life tests under conventional working conditions, can more realistically reflect the degradation behavior of products in actual applications. However, they have problems such as long testing cycles, high costs, and large sample resource consumption. They are difficult to meet the needs of rapid development and iteration of modern products. Accelerated degradation testing, as an alternative, can improve testing efficiency, but the traditional constant stress acceleration method still has problems such as insufficient test time compression and limited failure data acquisition, which are particularly prominent in high-reliability scenarios such as electronic devices. Summary of the Invention

[0004] The present invention provides a constant thermal stress sequential electrical stress testing method to achieve accurate evaluation of product reliability, lifespan and failure rate, thereby effectively improving the efficiency of reliability testing and the engineering applicability of evaluation results.

[0005] The constant thermal stress sequential electrical stress test method comprises the following steps:

[0006] S1. Experimental preparation: Select 15 to 30 test samples and divide them into three batches of 5 to 10 samples each. Place the samples in a high-temperature test chamber stabilized at 125°C and connect them to a regulated power supply. Before the test, calibrate the test equipment to ensure that the temperature fluctuation of the high-temperature test chamber does not exceed ±0.5°C and the output accuracy of the regulated power supply reaches ±0.1V.

[0007] S2, stress application and failure monitoring: Control the regulated power supply to apply electrical stress according to the linear law. The electrical stress level is ,in, for The electrical stress level applied at any moment, The slope coefficient is used. The sample output signal is monitored in real time using monitoring equipment with a sampling frequency of no less than 10 Hz. When the current or voltage fluctuates abnormally, the sample is judged to have failed. The failure time and the corresponding electrical stress are recorded. At the same time, environmental parameters, including humidity and air pressure, are recorded.

[0008] S3, calculate the electrical stress acceleration factor: based on the electrical stress level experienced by the failed sample and yield stress Relationship, calculate the electric stress acceleration factor ;

[0009] S4, calculate the equivalent time integral: construct an integral expression according to the sequential stress application process, and perform analytical or numerical calculations to obtain the equivalent time of each sample;

[0010] S5, calculate equivalent failure time: calculate the equivalent failure time of each failed sample under the stress condition according to the equivalent time integral result;

[0011] S6, calculate the comprehensive acceleration factor: according to the junction temperature during the test , Temperature under normal working conditions and electrical stress levels , binding activation energy and the Boltzmann constant , calculate the comprehensive acceleration factor ;

[0012] S7, Failure time conversion: convert the equivalent failure time to normal working conditions through the comprehensive acceleration factor to obtain the converted failure time ;

[0013] S8, establish reliability model: use three-parameter Weibull distribution to model the reduced failure time and establish a reliability model;

[0014] S9, Parameter estimation and reliability index evaluation: Use the maximum likelihood estimation method combined with the Newton-Raphson algorithm to estimate the distribution parameters. By constructing the log-likelihood function and solving it iteratively, reliability evaluation indicators including reliability, median life and failure rate are obtained.

[0015] Optionally, the electrical stress acceleration factor is expressed as:

[0016]

[0017] in, represents the yield stress, is the stress acceleration index.

[0018] Optionally, the calculating of the equivalent time integral in S4 includes:

[0019] S41, construct the integral expression: For the failed sample, its yield stress The equivalent time integral under the condition is defined as:

[0020] ;

[0021] when hour, and is the linear growth expression of electric stress;

[0022] S42, substitute and simplify the expression: Substituting into the integral expression, it is expressed as:

[0023]

[0024] S43, variable substitution: Let ,but , ,when hour, ,when hour, ;

[0025] S44, complete the integral calculation: After the variables are substituted, the integral calculation is completed, which is expressed as:

[0026] .

[0027] Optionally, the comprehensive acceleration factor is expressed as:

[0028] .

[0029] Optionally, the converted expiration time is expressed as:

[0030] .

[0031] Optionally, the reliability model is expressed as:

[0032]

[0033] in, is a positional parameter, is the scale parameter, is the shape parameter.

[0034] Optionally, the parameter estimation and reliability index evaluation in S9 include:

[0035] S91, construct the maximum likelihood function: Assume that the failure time obeys the three-parameter Weibull distribution and construct the maximum likelihood function , expressed as:

[0036]

[0037] in, is the number of failed samples, For the The failure time of each failed sample is converted to the failure time under normal stress level;

[0038] S92, construct the log-likelihood function: take the logarithm to construct the log-likelihood function, expressed as:

[0039]

[0040] S93, find partial derivatives to construct the equation system: 、 、 Find the partial derivative and construct the system of equations, expressed as:

[0041]

[0042] S94, solve the nonlinear equations: take the minimum failure time as The initial value and mean value of 、1 is The initial value of , iteratively updates the parameters until the convergence condition is met and the estimated value is obtained;

[0043] S95, Calculate Reliability Indicators: Calculate reliability assessment indicators, including reliability, median life, and failure rate.

[0044] Optionally, the convergence condition is that the parameter change is less than .

[0045] Beneficial effects of the present invention:

[0046] The present invention applies linearly increasing electrical stress under constant thermal stress conditions and combines real-time failure monitoring, equivalent time integration, acceleration factor conversion and three-parameter Weibull distribution modeling. It can induce sample failure within a relatively short period, efficiently obtain failure data, and construct a reliability model suitable for actual working conditions through precise parameter estimation methods. Compared with traditional constant stress tests and long-cycle working condition tests, the present invention greatly shortens the test time, reduces the test cost, and improves data acquisition efficiency and modeling accuracy.

[0047] The present invention, through the established reliability model, can quantitatively evaluate the reliability function, median life and failure rate indicators of the device, assist in risk prediction and reliability verification of the product at different service time points, and provide data support for product reliability design optimization, fault prevention and maintenance cycle formulation. At the same time, it supports the flexible adaptation of numerical integration and iterative algorithms, and has good versatility and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only for the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0049] Figure 1 Schematic diagram of the electrical stress test process according to an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. It is also noted that, to provide a more detailed description, the following embodiments are best and preferred embodiments, and those skilled in the art may employ alternative methods for implementing certain known technologies. Furthermore, the accompanying drawings are intended only to provide a more detailed description of the embodiments and are not intended to limit the present invention.

[0051] It should be noted that references in the specification to "one embodiment," "an embodiment," "exemplary embodiments," "some embodiments," etc. indicate that the described embodiments may include specific features, structures, or characteristics, but not necessarily every embodiment will include such specific features, structures, or characteristics. Furthermore, when specific features, structures, or characteristics are described in conjunction with an embodiment, it is within the knowledge of persons skilled in the relevant art to implement such features, structures, or characteristics in conjunction with other embodiments (whether or not explicitly described).

[0052] In general, terms can be understood, at least in part, from their use in context. For example, depending at least in part on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in the singular sense, or can be used to describe a combination of features, structures, or characteristics in the plural sense. Additionally, the term "based on" can be understood as not necessarily intended to convey an exclusive set of factors, but can instead, depending at least in part on the context, allow for the presence of other factors that are not necessarily explicitly described.

[0053] like Figure 1 As shown, the constant thermal stress sequential electrical stress test method includes the following steps:

[0054] Step 1: Experimental preparation:

[0055] Select 15-30 test samples and divide them into three batches of 5-10 samples each. Place the samples in a high-temperature test chamber maintained at a stable temperature of 125°C. Connect a regulated power supply to ensure that it outputs voltage to the sample's collector-emitter according to the set rules. Before the test, the test equipment must be fully calibrated to ensure that the temperature fluctuation of the high-temperature test chamber is controlled within a very small range, such as ±0.5°C, and the output accuracy of the regulated power supply reaches ±0.1V, to ensure the stability and accuracy of thermal and electrical stress during the test.

[0056] Step 2: Apply electrical stress:

[0057] Control the regulated power supply according to The collector-emitter output voltage of the sample is determined by the law of for The electrical stress level applied at any moment, is the slope coefficient. The value of is crucial, as it directly affects the growth rate of electrical stress and the failure time of the sample. The value range of is determined according to the characteristics of the sample and the expected failure time range, usually in In between. Before the value is set, a preliminary test is required to Perform a preliminary analysis of the failure of samples under different values, and select the most appropriate value to ensure that the sample fails within a reasonable time, while avoiding adverse effects of electrical stress growth that is too fast or too slow on the test results.

[0058] Step 3: Failure monitoring and data recording:

[0059] Use high-precision monitoring equipment to monitor the output signal of each sample in real time. When the output signal of the sample is abnormal, such as the current or voltage value exceeds the normal range, the sample is judged to be failed. At the same time, the failure time of each sample is accurately recorded. And the electrical stress level corresponding to that moment To ensure the accuracy and reliability of monitoring data, the sampling frequency of the monitoring equipment should be no less than 10Hz, capable of promptly capturing even the slightest changes in the sample output signal and avoiding inaccurate failure time recording due to monitoring errors. Furthermore, during the test, relevant parameters of the test environment, such as humidity and air pressure, must be recorded to facilitate subsequent analysis of the impact of environmental factors on the test results.

[0060] Step 4: Calculate the electrical stress acceleration factor:

[0061] Calculate the sequential electrical stress level \(S(t)\) experienced by the sample before failure relative to The acceleration factor , the calculation formula is:

[0062]

[0063] Where, represents the yield stress, which is lower than No cumulative damage occurs; It is the stress acceleration index, which is related to the material and failure mechanism of the sample and is determined through preliminary tests or empirical data. In actual calculations, for samples of different materials and structures, the stress acceleration index The value of will be different. For example, for samples made of metal materials, under a specific failure mode, The value of may be between 2 and 4; and for samples of semiconductor materials, The value range of may be 3-6. In order to determine more accurately By collecting a large number of failure data of similar samples under different electrical stress levels, we can use statistical analysis methods to fit and calculate to obtain a more realistic value. value.

[0064] Step 5. Calculate the equivalent time integral:

[0065] Create samples in The equivalent time integral formula under To solve this integral, we need Substitute the expression and deduce it. hour, and , then the integral becomes:

[0066]

[0067] make ,but , .when hour, ;when hour, Substituting into the integral formula, we can get:

[0068]

[0069] In actual calculations, if complex sample structures or special failure mechanisms make it difficult to solve the integral, numerical integration methods such as trapezoidal integration method and Simpson integration method can be used for approximate calculations to improve the accuracy and efficiency of the calculation.

[0070] Step 6. Calculate the equivalent failure time:

[0071] For each failed sample, calculate its corresponding Value. Due to the failure time of different samples Different, corresponding Different, so During the calculation process, the relevant parameters of each sample should be carefully checked to ensure the accuracy of the calculation results. At the same time, computer programming can be used to achieve batch calculations to improve calculation efficiency and data processing accuracy. For example, using Python language to write a calculation program, by importing test data, automatically calculate the The results are stored in the database for subsequent analysis and use.

[0072] Step 7. Calculate the comprehensive acceleration factor:

[0073] Calculate accelerated stress (junction temperature during the test), Relative to normal working stress level 、 The acceleration factor , the calculation formula is .in, is the activation energy, which reflects the energy barrier that needs to be overcome during the failure process of the sample, and its unit is ; is the Boltzmann constant, ; For normal operating temperature, is the normal operating electrical stress level. The activation energy can be determined by analyzing the microstructure of the sample material and calculating the thermal activation theory. For example, for a certain semiconductor material, the activation energy can be determined by measuring its conductivity or carrier mobility at different temperatures and fitting it using the Arrhenius equation. In practical applications, in order to improve the accuracy of calculations, a variety of experimental methods and theoretical models can be combined to determine value.

[0074] Step 8. Calculation of expiration time:

[0075] The equivalent failure time under accelerated stress is uniformly converted to the working stress level. The conversion formula is: Through this conversion, we get This provides a data foundation that meets actual operating conditions for the subsequent establishment of a reliability model. During the conversion process, attention should be paid to the consistency of units and the control of data accuracy. Furthermore, statistical analysis can be performed on the converted failure times, and a failure time distribution histogram can be plotted to observe the distribution characteristics of the data, providing a basis for selecting an appropriate reliability model.

[0076] Step 9: Establish reliability model:

[0077] Since the acceleration factor of each sample's failure stress level relative to the normal working stress level is different, the failure time converted to the normal stress level obeys a random variable with a certain distribution. Considering the yield stress of the sample, the three-parameter Weibull distribution is used to establish the sample reliability model. .in, is the position parameter, representing the starting time when the sample begins to fail; is a scale parameter, related to the average life span of the sample; is a shape parameter that reflects the temporal trend of the sample failure rate. When determining the parameters of the three-parameter Weibull distribution, various methods can be used, such as maximum likelihood estimation and least squares estimation. To improve the accuracy of parameter estimation, it is possible to combine multiple estimation methods for comparative analysis and select the optimal parameter estimates. For example, maximum likelihood estimation can be used to obtain a set of parameter estimates, which can then be verified and optimized using least squares estimation to ultimately determine the parameter values ​​that best reflect the actual situation.

[0078] Step 10: Use the maximum likelihood estimation method to estimate the unknown parameters in the three-parameter Weibull distribution 、 and . Construct the maximum likelihood function :

[0079]

[0080] in is the number of failed samples, For the The failure time of each failed sample is converted to the failure time under normal stress level. Taking the logarithm of the maximum likelihood function, we get the log likelihood function :

[0081]

[0082] respectively 、 and Find the partial derivatives and set them equal to 0 to obtain the system of equations:

[0083]

[0084] Solve the above equations using the Newton-Raphson algorithm and get 、 and When using the Newton-Raphson algorithm, it is necessary to select the initial value reasonably. The selection of the initial value can be set according to the statistical characteristics of the failure data and experience. For example, the minimum value of the failure time can be used as The initial estimate of , the mean of the failure time is taken as As the initial estimate of Then, through multiple iterations, the parameter values ​​are continuously updated until the convergence condition is met, such as the difference between the parameter values ​​obtained in two adjacent iterations is less than a preset threshold (such as ). Calculate the reliability of the device based on the estimated parameters , life expectancy (such as median life expectancy satisfy ), failure rate When calculating reliability, a reliability curve can be drawn according to actual needs to intuitively show the reliability of the product under different usage times; when calculating the median life, numerical calculation methods such as the dichotomy method can be used to quickly and accurately solve the problem that satisfies the requirements. When calculating the failure rate, the failure rate change trend over time can be analyzed to determine whether the product is in the early failure, accidental failure or wear and tear failure stage, providing a basis for product maintenance and replacement.

[0085] The examples are as follows:

[0086] Taking a certain type of electronic component as an example, this component is sensitive to thermal stress and electrical stress during operation. In order to evaluate its reliability, a test method based on constant thermal stress and progressive electrical stress is carried out.

[0087] Step 1: Experimental preparation:

[0088] Twenty components were randomly sampled from a batch of products and divided into four batches of five components each. The components were placed in a high-temperature test chamber maintained at a stable temperature of 125°C and connected to a regulated power supply. Before testing, the chamber was calibrated to ensure good temperature uniformity and temperature fluctuations within ±0.5°C. The regulated power supply was also precision-tested to ensure an output accuracy of ±0.1V. The operating status of the monitoring equipment was also checked to ensure a sampling frequency of at least 10Hz to accurately capture changes in the component output signal.

[0089] Step 2: Apply electrical stress:

[0090] Based on preliminary test results and component characteristics, the slope coefficient (K = 2V / s) is determined. The regulated power supply is controlled to output voltage to the component collector-emitter according to the rule (S(t) = 2t). During the electrical stress application process, the power supply output is monitored in real time to ensure that the electrical stress strictly follows the set rule.

[0091] Step 3: Failure monitoring and data recording:

[0092] During the test, monitoring equipment monitored component output signals in real time. If the component's output current or voltage fluctuated abnormally, exceeding the normal operating range, the component was deemed to have failed. The moment of failure and the corresponding electrical stress value were accurately recorded. Environmental parameters during the test were also recorded, such as humidity maintained at 50% ± 5% and air pressure maintained at standard atmospheric pressure.

[0093] Step 4: Calculate the electrical stress acceleration factor:

[0094] By consulting the component material data and previous test experience, the yield stress of the component is determined. , stress acceleration index For component 1, calculate the electrical stress acceleration factor at different times before its failure. hour, ,because , according to the formula ;when Assume that we continue to calculate the acceleration factor at this moment for demonstration purposes). ,

[0095] .

[0096] Step 5. Calculate the equivalent time integral:

[0097] Using the formula Calculate the equivalent time integral of element 1. , , , Substituting into the formula, we can get

[0098] .

[0099] Step 6. Calculate the equivalent failure time of each sample:

[0100] According to the above method, the equivalent failure time of each failed component is calculated. For example, if component 2 fails at 250s, , we can calculate its . The values ​​are recorded and prepared for subsequent calculations.

[0101] Step 7. Calculate the comprehensive acceleration factor:

[0102] The normal operating temperature of the component is known (Converted to Kelvin temperature ), normal working electrical stress , the junction temperature when component 1 fails during the test (Converted to Kelvin temperature , activation energy ). According to the formula , the comprehensive acceleration factor of computing element 1 is:

[0103]

[0104] Step 8. Calculation of expiration time:

[0105] According to the formula , calculate the failure time of component 1 converted to normal working stress level The same method is used to calculate the other components. values ​​and organize the data.

[0106] Step 9: Establish reliability model:

[0107] Collect all failed components Data, the reliability model is established using the three-parameter Weibull distribution First, Perform preliminary statistical analysis on the data and calculate the mean, variance and other statistics. Assume that the calculated mean is , the variance is Based on these statistics and experience, it is preliminarily estimated that , , as the initial value.

[0108] Step 10: Parameter estimation and indicator evaluation:

[0109] The maximum likelihood estimation method combined with the Newton-Raphson algorithm is used to estimate the model parameters. Substitute the data into the log-likelihood function\ , calculate the partial derivatives and construct the equation system. Use the Newton-Raphson algorithm to iteratively solve. After multiple iterations (such as 10 iterations), when the difference between the parameter values ​​obtained in two adjacent iterations is less than When , more accurate parameter estimates are obtained , , .

[0110] Based on these parameters, the reliability, life and failure rate of the components are calculated. Reliability ; Calculate median life expectancy ,make ,Right now , solved by bisection, in the interval The inner iteration calculation finally gets Calculate failure rate ,when hour, Through these indicators, the reliability performance of the component model is comprehensively evaluated, providing data support for component quality improvement and reliability enhancement.

[0111] The present invention encompasses any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention. To provide a thorough understanding of the present invention, specific details are described in detail below in connection with the preferred embodiments of the present invention, but those skilled in the art will be able to fully understand the present invention without these detailed descriptions. Furthermore, to avoid unnecessary confusion regarding the essence of the present invention, well-known methods, processes, procedures, components, and circuits have not been described in detail.

[0112] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. Constant thermal stress sequential electrical stress test method, characterized in that: The following steps are involved: S1, Experimental preparation: Select the test sample, place the test sample in the high temperature test chamber, and connect the stabilized power supply; S2, stress application and failure monitoring: Control the regulated power supply to apply electrical stress, monitor the sample output signal in real time, and determine the sample as failed when the current or voltage fluctuates abnormally, and record the failure time. and corresponding electrical stress , while recording environmental parameters; S3, calculate the electrical stress acceleration factor , and calculate the equivalent time integral , according to the equivalent time integral result, calculate the equivalent failure time of each failed sample under the stress condition; S4, calculate the comprehensive acceleration factor , and perform failure time conversion, including converting the equivalent failure time to normal working conditions through the comprehensive acceleration factor to obtain the converted failure time , the three-parameter Weibull distribution is used to model the reduced failure time and establish a reliability model ; S5, by constructing the log-likelihood function and solving it iteratively, the reliability evaluation indicators including reliability, median life and failure rate are obtained; In S3, an integral expression is constructed according to the sequential stress application process, and analytical or numerical calculation is performed to obtain the equivalent time of each sample, specifically including: S31, construct the integral expression: For the failed sample, its yield stress The equivalent time integral under the condition is defined as: ； in, for The level of electrical stress applied at all times; when hour, and is the linear growth expression of electric stress, where is the slope coefficient, is the stress acceleration index, represents the yield stress, Lower than No cumulative damage occurs; S32, substitute and simplify the expression: Substituting into the integral expression, it is expressed as: S33, variable substitution: Let ,but , ,when hour, ,when hour, ; S34, complete the integral calculation: After the variables are substituted, the integral calculation is completed, which is expressed as: ； The S4 is based on the junction temperature during the test , Temperature under normal working conditions and electrical stress levels , binding activation energy and the Boltzmann constant , calculate the comprehensive acceleration factor , expressed as: ； The converted failure time is expressed as: 。 2. The constant thermal stress sequential electrical stress testing method according to claim 1, characterized in that: The electrical stress level experienced by the failed sample in S3 is and yield stress Relationship, calculate the electric stress acceleration factor , expressed as: in, represents the yield stress, is the stress acceleration index.

3. The constant thermal stress sequential electrical stress testing method according to claim 2, characterized in that: The reliability model is expressed as: in, is a positional parameter, is the scale parameter, is the shape parameter.

4. The constant thermal stress sequential electrical stress testing method according to claim 3, characterized in that: The parameter estimation and reliability index evaluation in S5 include: S51, construct the maximum likelihood function: Assume that the failure time obeys the three-parameter Weibull distribution and construct the maximum likelihood function , expressed as: in, is the number of failed samples, For the The failure time of each failed sample is converted to the failure time under normal stress level; S52, construct the log-likelihood function: take the logarithm to construct the log-likelihood function, expressed as: S53, find partial derivatives to construct the equation system: 、 、 Find the partial derivative and construct the system of equations, expressed as: S54, solve the nonlinear equations: take the minimum failure time as The initial value and mean value of 、1 is The initial value of , iteratively updates the parameters until the convergence condition is met and the estimated value is obtained; S55, Calculate reliability indicators: Calculate reliability assessment indicators, including reliability, median life and failure rate.

5. The constant thermal stress sequential electrical stress testing method according to claim 4, characterized in that: The convergence condition is that the parameter change is less than .

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