A method for predicting trends in integrated circuit burn-in test data

Abstract

The present application relates to the technical field of integrated circuit testing, and in particular to a kind of integrated circuit aging test data trend prediction method.The method comprises: collecting various performance parameters of integrated circuit in aging test, and any one performance parameter is regarded as target performance parameter, and target performance parameter sequence is obtained;According to the residual cumulative distribution function of target performance parameter in a local period of a time and standard normal distribution function, the residual random disturbance degree of the time is obtained by integration;According to the continuous change of the residual of target performance parameter at each time in a local period of a time, the residual one-way continuous drift degree of the time is obtained;Further, the residual feedback weight value at each time is obtained;The target performance parameter at the current time is predicted using the residual feedback weight value at each time and target performance parameter sequence combined with ARIMA model.The present application can effectively predict the data of integrated circuit aging test.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit testing technology, and more specifically to a method for predicting trends in integrated circuit aging test data. Background Technology

[0002] The core purpose of trend prediction in integrated circuit aging test data is to extrapolate and evaluate the performance degradation trend of devices over future operating time based on historical test data, thereby enabling the prediction of failure time points, lifetime assessment, and reliability level determination. By continuously collecting key performance parameters of devices under accelerated stress conditions (such as high-temperature operation, bias stress, and cyclic loading), a degradation data sequence over time is obtained. The industry typically uses time series modeling methods, including the Autoregressive Moving Average (ARIMA) model, for analysis. By performing differential stabilization on historical observation data and combining autoregressive and moving average terms, the temporal correlation and historical prediction errors of the data are modeled, thereby enabling the extrapolation and prediction of performance parameters at future time points. This provides a data foundation and decision-making basis for device reliability analysis and lifetime assessment.

[0003] The residual feedback mechanism of the traditional Autoregressive Moving Average (ARIMA) model has certain limitations in the current scenario. The reason is that in the standard ARIMA model, the moving average term (MA term) is used to correct the current prediction result using historical prediction residuals. However, this process assumes that all residuals can be regarded as random errors and participate in the feedback update in a uniform way.

[0004] In the current scenario, due to the long-term accelerated stress on the device (such as high-temperature carrier injection, electromigration accumulation, oxide layer degradation, etc.), the device exhibits obvious staged degradation characteristics. As a result, the performance parameters gradually transition from slow changes to accelerated changes over time, leading to different evolution patterns in the time series at different degradation stages. In this case, the prediction residuals no longer only reflect random disturbances but also introduce structural components related to the device degradation process. This causes the residual sequence to exhibit a continuous directional accumulation characteristic in the time dimension. However, the MA term still treats this type of residual as an error correction signal in the prediction update without distinguishing the statistical structural characteristics of the residuals. This may result in an inappropriate reverse correction effect on the actual accelerated degradation trend during the model update process, leading to trend response lag and prediction bias in the accelerated degradation stage. Summary of the Invention

[0005] To address the aforementioned technical problems, the present invention aims to provide a method for predicting trends in integrated circuit aging test data. The specific technical solution adopted is as follows: One embodiment of the present invention provides a method for predicting trends in integrated circuit aging test data, the method comprising: Collect various performance parameters of integrated circuits during aging tests, and take any one of the performance parameters as the target performance parameter; combine the target performance parameters at each time point into a target performance parameter sequence. The time period from a given moment to the current moment is taken as the local time period of that moment; the degree of random disturbance of the residual at that moment is obtained by integrating the cumulative residual distribution function and the standard normal distribution function of the target performance parameters within the local time period of a moment. The degree of continuous unidirectional drift of the residual at a given moment is obtained by observing the continuous changes in the residuals of the target performance parameters at each moment within a local time period. The degree of random disturbance of the residuals at that moment and the degree of continuous unidirectional drift of the residuals are fused to obtain the residual feedback weight value at that moment. The residual feedback weight values ​​at each moment and the target performance parameter sequence are combined with the ARIMA model to predict the target performance parameters at the current moment.

[0006] Preferably, the calculation model for the degree of residual random disturbance is as follows: , in, This indicates the degree of random perturbation in the residual at time t; and These are the maximum and minimum residual values ​​of the target performance parameters within a local time interval at time t, respectively. Represents the residual at time n. The residual cumulative distribution function represents the target performance parameters within a local time interval at time t; represents the standard normal distribution function; Norm represents the normalization operation.

[0007] Preferably, the degree of continuous unidirectional drift of the residual at a given moment is obtained based on the continuous change of the residual of the target performance parameter at each moment within a local time period, including: The process involves obtaining the difference between the residuals of the target performance parameters at any given time interval within a local time period. This difference is used as the residual change between any two adjacent time intervals. The residual changes between any two adjacent time intervals are then arranged into a residual change sequence according to time sequence. Each pair of adjacent residual changes in the residual change sequence is multiplied to obtain the product corresponding to each pair of adjacent residual changes. An indicator function is constructed, and this function is used to map the product corresponding to each pair of adjacent residual changes to obtain the mapped value. These mapped values ​​are then arranged into a mapped value sequence according to time sequence. Finally, the sum of the mapped values ​​corresponding to each pair of adjacent residual changes is multiplied by the sum of the products of each pair of adjacent mapped values ​​in the mapped value sequence, and normalized to obtain the degree of continuous unidirectional drift of the residual at that time interval.

[0008] Preferably, the indicator function is as follows: , in, It is an exponential function, where x represents the independent variable.

[0009] Preferably, the residual feedback weight value at that moment is obtained by fusing the degree of random disturbance of the residual at that moment and the degree of continuous unidirectional drift of the residual, including: The residual feedback weight value at a given moment is obtained by calculating the difference between the first preset value and the degree of continuous unidirectional drift of the residual at a certain moment, and the average value of the degree of random disturbance of the residual at that moment.

[0010] Preferably, the target performance parameters at the current time are predicted by combining the residual feedback weights at each time step with the target performance parameter sequence using an ARIMA model, including: Each residual term in the MA term of the ARIMA model is weighted and assigned a weight as the residual feedback weight value. Then, the target performance parameter sequence is combined to predict the target performance parameter at the current time step.

[0011] The embodiments of this invention have at least the following beneficial effects: This application collects various performance parameters of integrated circuits during aging tests, and takes any one of the performance parameters as the target performance parameter, then obtains the target performance parameter sequence; next, it integrates the residual cumulative distribution function and the standard normal distribution function of the target performance parameter within a local time period to obtain the degree of residual random perturbation at that time; then, it obtains the degree of unidirectional continuous drift of the residual at that time based on the continuous change of the residual of the target performance parameter at each time within a local time period; furthermore, it fuses the two to obtain the residual feedback weight value at each time; finally... By combining the residual feedback weights at each time step with the target performance parameter sequence, the ARIMA model is used to predict the target performance parameters at the current time step. During the process of device degradation acceleration or phase change, it can avoid using the persistent deviations caused by the actual degradation evolution as random errors for feedback cancellation, thereby reducing the phenomenon of "reverse correction" of the actual degradation trend. The residual feedback weights enable the model to more stably track the actual performance evolution trajectory of the device at different aging stages, improve the trend identification ability of degradation inflection points, acceleration stages and critical life stages, thereby improving the smoothness and robustness of the overall trend prediction. Attached Figure Description

[0012] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 A flowchart illustrating a method for predicting trends in integrated circuit aging test data, provided in an embodiment of the present invention. Detailed Implementation

[0014] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a trend prediction method for integrated circuit aging test data proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0015] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0016] The following description, in conjunction with the accompanying drawings, details a specific scheme for a trend prediction method for integrated circuit aging test data provided by the present invention.

[0017] In this embodiment, the main application scenario of the present invention is as follows: This application analyzes various performance parameters of the aging test of the integrated circuit, constructs a residual feedback weight model based on the characteristics of these performance parameter data, and adaptively adjusts the intensity of the feedback correction of different residuals in the moving average term, thereby better predicting various performance parameters.

[0018] Please see Figure 1 The diagram illustrates a method flowchart for trend prediction of integrated circuit aging test data provided by an embodiment of the present invention. The method includes the following steps: Step S1: Collect various performance parameters of the integrated circuit during aging test, and take any one of the performance parameters as the target performance parameter; assemble the target performance parameters at each time point into a target performance parameter sequence.

[0019] First, integrated circuits need to undergo aging tests, which involves continuously operating the target integrated circuit (target device) under preset accelerated stress conditions and periodically collecting various key performance parameters of the integrated circuit according to a preset sampling period. In this application, the sampling frequency is set to once per second as a reference sampling frequency. The accelerated stress conditions include, but are not limited to, high-temperature operating conditions, bias stress conditions, and cyclic load conditions; the various key performance parameters include, but are not limited to, threshold voltage, leakage current, propagation delay, operating frequency, power consumption parameters, and noise margin—test indicators that reflect the device's degradation state.

[0020] Furthermore, for ease of explanation, we will use any one of the collected performance parameters as the target performance parameter for analysis. The analysis method for other types of performance parameters is the same.

[0021] Furthermore, for the target performance parameters, the extreme outliers at each time step need to be identified using the 3σ principle, corrected using neighborhood mean replacement, and then subjected to moving average filtering on the corrected time series. Finally, the target performance parameters at each time step are combined into a target performance parameter sequence. , Let be the target performance parameters at time n. Model and predict each performance parameter separately.

[0022] Step S2: Take the time period from a time point before the current time point to the current time point as the local time period of the current time point; obtain the degree of residual random disturbance at the current time point by integrating the residual cumulative distribution function and the standard normal distribution function of the target performance parameters within the local time period of the current time point.

[0023] During long-term accelerated aging testing of integrated circuits, the devices gradually develop structural trend shifts related to the evolution of their degradation state under continuous stress. This causes the predicted residuals to no longer reflect only random disturbance errors, but also incorporate structural components related to the device degradation process. In this case, the moving average term (MA term) in the traditional ARIMA model still defaults to treating all historical residuals as random errors for feedback correction. This can easily lead to the model using the actual trend deviations formed by the continuous evolution of device degradation as random errors to offset them, thus affecting the model's ability to respond to changes in device degradation trends.

[0024] Therefore, it is necessary to construct a residual feedback weight model to adaptively adjust the strength of different residuals participating in the feedback correction of the moving average term. When the residuals contain strong structural trend components and do not meet the statistical assumptions of the moving average term regarding "random error feedback", the strength of the corresponding residuals participating in the feedback correction of the moving average term is reduced, thereby weakening the inappropriate correction effect of structural trend bias on the prediction results.

[0025] Because the degradation process of integrated circuit devices has phased and non-uniform evolution characteristics, the model prediction residuals in some states no longer only reflect random disturbances, but also contain structural components related to the changes in the device degradation state. Theoretically, random disturbance residuals usually have an approximately symmetrical random distribution, and their cumulative distribution is close to the standard normal distribution. Therefore, by analyzing the deviation of the cumulative distribution of residuals from the standard normal distribution in a local time period, the degree of deviation of the current residuals from the random disturbance characteristics can be determined, which serves as the first factor for the residual feedback weight.

[0026] Therefore, the time period from a given moment up to that moment is taken as the local time period of that moment. Preferably, since the device degradation process usually maintains a relatively continuous evolution state within a short time range, it is necessary to ensure that the local residual samples have basic statistical stability, and it is also necessary to avoid the averaging of structural features when crossing different degradation stages. In this application, the reference value of the preset time length is 20 seconds, that is, 20 seconds including that moment. Implementers can make different settings according to the actual situation.

[0027] The degree of random disturbance of the residuals at a given moment is obtained by integrating the cumulative residual distribution function and the standard normal distribution function of the target performance parameters within a local time period.

[0028] The specific calculation model for the degree of random disturbance in the residuals is as follows: , in, When analyzing the target performance parameters, the degree of random perturbation of the residual at time t represents the degree of random perturbation of the residual in the local time period at time t. Norm represents the normalization operation, which restricts the target output result to [0,1]. The larger the final output result, the closer the current residual distribution characteristics are to the standard normal distribution. The current predicted residual mainly comes from random perturbation factors. The residual contains less structural degradation components, indicating that the current model has a higher degree of characterization of the device degradation trend. Its statistical characteristics are more in line with the error feedback assumption of the MA term, and it has higher reference value for future prediction correction. and The maximum and minimum residual values ​​of the target performance parameters within a local time interval at time t are respectively used as the upper and lower limits of integration. Let n represent the residual at time n; Let be the absolute integral difference between the cumulative residual distribution function and the standard normal distribution function of the target performance parameters within a local time interval at time t. This allows us to obtain the degree of random disturbance in the residuals at each time step.

[0029] Step S3: Based on the continuous change of the residuals of the target performance parameters at each time point within a local time period, obtain the degree of continuous unidirectional drift of the residuals at that time point; fuse the degree of random disturbance of the residuals at that time point with the degree of continuous unidirectional drift of the residuals to obtain the residual feedback weight value at that time point; use the residual feedback weight values ​​at each time point and the target performance parameter sequence in combination with the ARIMA model to predict the target performance parameters at the current time point.

[0030] During long-term accelerated aging tests of integrated circuits, degradation mechanisms such as hot carrier effects, electromigration accumulation, bias temperature instability, and oxide trap growth exhibit continuous accumulation characteristics, causing the actual degradation trajectory of device performance parameters to typically manifest as a continuous, phased evolution process over time. When the degradation trend learned by the model cannot keep up with the changes in the current degradation state, the predicted results will continuously deviate in the same direction from the actual test data at multiple consecutive sampling times, resulting in a concentrated and continuous unidirectional drift phenomenon in the residual sequence within a local time range.

[0031] Therefore, based on the above idea, the degree of continuous unidirectional drift of the residual at a given moment is obtained by observing the continuous changes in the residual of the target performance parameter at each moment within a local time period.

[0032] Specifically, the difference between the residuals of the target performance parameters at any given time interval is obtained as the residual change between any two adjacent time intervals. These residual changes are then arranged in a time sequence to form a residual change sequence. The residual changes between any two adjacent time intervals are multiplied to obtain the product corresponding to each pair of adjacent residual changes. An indicator function is constructed, and this function is used to map the product corresponding to each pair of adjacent residual changes to obtain the mapped value. These mapped values ​​are then arranged in a time sequence to form a mapped value sequence. Finally, the sum of the mapped values ​​corresponding to each pair of adjacent residual changes is multiplied by the sum of the products of each pair of adjacent mapped values ​​in the mapped value sequence, and normalized to obtain the degree of continuous unidirectional drift of the residual at that time.

[0033] The specific calculation model for the degree of continuous drift of residuals in one direction is as follows: , in, denoted as the degree of continuous unidirectional drift of the residual at time t, representing the continuous unidirectional drift of the sequence of residuals at each time step in the local time period at time t; tanh() represents the hyperbolic tangent function, which restricts the target output result to [0,1], ensuring that the larger the final output result, the stronger the current residual sequence exhibits unidirectional drift characteristics, and the more concentrated and continuous the drift is, the more this means that the current performance degradation process of the device no longer maintains the stable evolution characteristics under the original degradation stage, but under long-term accelerated stress conditions, as degradation effects such as hot carrier injection, electromigration accumulation, bias temperature instability, and oxide layer trap growth accumulate, it enters the accelerated degradation stage. The more obvious the structural degradation components contained in the current residual, the more inappropriate the reverse correction effect will be if such residuals continue to participate in the MA term feedback correction in the traditional way. This is the i-th product among the products of every two adjacent residual changes in the residual change sequence corresponding to the local time interval at that moment, where m represents the number of products. The formula for calculating the residual change is: , and Let be the residuals at time t+1 and time t, respectively. The residual change at these two adjacent moments. For indicator functions, Let x represent the independent variable, which is the product of two adjacent changes in residuals. When the product of these two adjacent changes in residuals is greater than or equal to 0, it indicates that the trend of residual change has not changed between adjacent time points. =1; The output is used to reflect the degree of unidirectional drift of the residuals at each time point within the local time period, that is, to measure the degree to which the residuals shift in the same direction. The larger the cumulative sum, the more unidirectional changes there are in the residuals of adjacent time points within the local time period, indicating that the unidirectionality of the residual changes at each time point within the local time period is stronger. and Let J and J represent the (j+1)th and jth mapped values ​​in the mapped value sequence, respectively. These are the mapped values ​​corresponding to the product of the changes in each pair of adjacent residuals after the exponential function mapping, representing the trend of residual changes between two adjacent time points; J represents the number of mapped values ​​in the mapped value sequence. The output is used to reflect the continuity of the unidirectional drift of the residuals at each time point within the local time period. If the trend of the residuals at two adjacent time points appears to be continuous, =1, otherwise The value is 0, therefore, through each of the mapping value sequences... After performing adjacent multiplication, the product results are accumulated. The larger the accumulated sum, the stronger the continuity of this adjacent unidirectional change behavior in the time dimension. right and When performing multiplication, the overall result will be suppressed when either feature is low, thus avoiding misjudgment as trend drift due to local directional bias or short-term continuous changes. Only when both features are large will the product result increase significantly, indicating that the current residual sequence is simultaneously enhanced in both directional consistency and temporal continuity, thereby reflecting its obvious unidirectional continuous drift characteristics.

[0034] Therefore, the unidirectional continuous drift characteristics at each time step can be obtained. Further, the difference between the first preset value and the degree of unidirectional continuous drift of the residual at a given time step, along with the average value of the degree of random disturbance of the residual at that time step, are used to obtain the residual feedback weight value at that time step. The specific calculation model is as follows: , in, This represents the residual feedback weight value at time t. A smaller value indicates a greater degree of random disturbance and continuous unidirectional drift in the residual sequence within the local time period. This suggests that the current prediction bias is no longer primarily due to random noise, but more likely stems from a systematic trend shift caused by the continuous evolution of device degradation. The residual contains a strong structural trend component, indicating that this part of the residual no longer satisfies the statistical assumption of the moving average term regarding "random error feedback." Therefore, it is necessary to reduce the intensity of this part of the residual participating in the MA term feedback correction to weaken the excessive correction effect of the structural trend residual on the prediction results. Let be the degree of random perturbation of the residual at time t, and 1 be the first preset value. The degree of continuous unidirectional drift of the residual at time t.

[0035] Finally, the target performance parameters at the current time are predicted by combining the residual feedback weights at each time step with the target performance parameter sequence using the ARIMA model.

[0036] Specifically, a weight is added to each residual term in the MA term of the ARIMA model. The added weight is the residual feedback weight value. Then, the target performance parameter sequence is combined to predict the target performance parameter at the current time.

[0037] The ARIMA model after adding weights is as follows: , in, This represents the model output (target performance parameters at the current moment). For the MA term of the model, Then represents the residual feedback weight value; c represents the constant term. Represents the parameters of the autoregressive term. This represents the parameters of the moving average (MA) term. p and q are the order of the model. This represents the residual term. Here, corresponding residual feedback weights are added to the residuals of each term in the MA term of the existing ARIMA model to complete the prediction. Similarly, the same method can be used to predict other types of performance parameters.

[0038] Through the above operations, the output of the residual weight feedback model is used to reduce the excessive correction effect of structural trend residuals on the prediction results. The final output of ARIMA is used as the predicted value of performance parameters, providing a data foundation and decision-making basis for device reliability analysis and life assessment.

[0039] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, the above description focuses on specific embodiments of this specification. Additionally, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0040] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0041] 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 principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting trends in integrated circuit aging test data, characterized in that, The method includes: Collect various performance parameters of integrated circuits during aging tests, and take any one of the performance parameters as the target performance parameter; combine the target performance parameters at each time point into a target performance parameter sequence. The time period from a given moment to the current moment is taken as the local time period of that moment; the degree of random disturbance of the residual at that moment is obtained by integrating the cumulative residual distribution function and the standard normal distribution function of the target performance parameters within the local time period of a moment. The degree of continuous unidirectional drift of the residual at a given moment is obtained by continuously changing the residual of the target performance parameter at each moment within a local time period. The degree of random disturbance of the residual at that moment and the degree of continuous unidirectional drift of the residual are fused to obtain the residual feedback weight value at that moment. The residual feedback weight value at each moment and the target performance parameter sequence are combined with the ARIMA model to predict the target performance parameter at the current moment. The specific calculation model for the degree of residual random perturbation is as follows: ， in, This indicates the degree of random perturbation in the residual at time t; and These are the maximum and minimum residual values ​​of the target performance parameters within a local time interval at time t, respectively. Represents the residual at time n. The residual cumulative distribution function represents the target performance parameters within a local time interval at time t; Norm represents the standard normal distribution function; Norm represents the normalization operation. The method of obtaining the degree of continuous unidirectional drift of the residual at a given moment based on the continuous change of the residual of the target performance parameter at each moment within a local time period includes: obtaining the difference between the residual of the target performance parameter at each of the two adjacent moments within a local time period as the residual change amount at each of the two adjacent moments; forming a residual change amount sequence by arranging the residual change amounts at each of the two adjacent moments in a time sequence; multiplying each of the residual change amounts at each of the two adjacent moments in the residual change amount sequence to obtain the product corresponding to each of the two adjacent residual change amounts; constructing an indicator function and using the indicator function to map the product corresponding to each of the two adjacent residual change amounts to obtain the mapping value corresponding to each of the two adjacent residual change amounts; forming a mapping value sequence by arranging the mapping values ​​corresponding to each of the two adjacent residual change amounts in a time sequence; and calculating the product of the sum of the mapping values ​​corresponding to each of the two adjacent residual change amounts and the sum of the products of each of the two adjacent mapping values ​​in the mapping value sequence, and normalizing it to obtain the degree of continuous unidirectional drift of the residual at that moment. The step of fusing the residual random perturbation degree and the residual unidirectional continuous drift degree at a given moment to obtain the residual feedback weight value at that moment includes: calculating the difference between a first preset value and the residual unidirectional continuous drift degree at a given moment, and the average value of the residual random perturbation degree at that moment to obtain the residual feedback weight value at that moment; the step of using the residual feedback weight values ​​at each moment and the target performance parameter sequence to combine with the ARIMA model to predict the target performance parameter at the current moment includes: adding weights to each residual term in the MA term of the ARIMA model, the added weights being the residual feedback weight values, and then combining with the target performance parameter sequence to predict the target performance parameter at the current moment.

2. The method for trend prediction of integrated circuit aging test data according to claim 1, characterized in that, The indicator function is specifically: ， in, It is an exponential function, where x represents the independent variable.

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