CN117031228A - Triode reliability analysis method based on FEDformer model - Google Patents
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Abstract
The invention relates to a triode reliability analysis method based on an FEDformer model, belonging to the technical field of microelectronics; collecting the base width, aging temperature and working current of the triode in a normal working state; calculating a change delta beta of the current gain; the method comprises the steps of selecting the change delta beta of base width, aging temperature and current gain as characteristic data; processing abnormal values; performing noise reduction treatment; performing characteristic scaling treatment; performing set division; establishing an FEDformer model; obtaining a high-precision FEDformer model; obtaining optimal parameters of a high-precision FEDformer model; judging whether the establishment of the high-precision FEDformer model is completed; taking the base width and the aging temperature which are acquired subsequently as the input of a high-precision FEDformer model, and judging the reliability of the triode according to the change delta beta of the current gain subsequently; the FEDformer model reduces the NRMSE by 12.6 percent as a whole, improves the modeling performance by more than 20 percent, and has better modeling performance and high reliability modeling precision.
Description
Technical Field
The invention belongs to the technical field of microelectronics, and relates to a triode reliability analysis method based on an FEDformer model.
Background
Bipolar junction transistors (triodes) are an important semiconductor device that plays a critical role in electronic device and circuit design. It is widely used in amplification and switching circuits, including wireless communications, power management, audio amplifiers, and the like. The triode was invented by william schokril, john bardine, and walt brayton in 1947. It is the first transistor, marking a major breakthrough in semiconductor technology, and also inducing rapid development of the electronic industry. However, with the continuous development of technology, the production technology of the triode is gradually increasing in complexity. This results in the need to control the individual production links more precisely during production to ensure the reliability of the transistor.
In practical applications, the transistor may be affected by various factors, such as temperature, voltage, current, etc., which may cause degradation or even failure of the transistor. Therefore, modeling and predicting the reliability of the triode is extremely important, and the traditional reliability modeling method generally depends on physical and empirical models, and needs to perform deep analysis on the physical characteristics and the working environment of the triode, which not only increases the complexity of modeling, but also greatly increases the calculation cost, and may cause a large amount of prediction errors of the models in some cases due to the continuous change of the production technology of the triode. Therefore, it is particularly necessary to develop and develop a more accurate and efficient triode stability modeling method.
Disclosure of Invention
The invention solves the technical problems that: the triode reliability analysis method based on the FEDformer model is provided, the NRMSE of the FEDformer model is reduced by 12.6% as a whole, the improvement can exceed 20%, the modeling performance is better, and meanwhile, the reliability modeling precision is high.
The solution of the invention is as follows:
a triode reliability analysis method based on an FEDformer model comprises the following steps:
collecting the base width, aging temperature and working current of a triode in a normal working state; acquiring current before aging and current after aging of the triode by an aging experiment method; the current before aging is subjected to difference with the working current to obtain current gain before aging; the aged current and the working current are subjected to difference to obtain aged current gain; the current gain after aging is differenced with the current gain before aging to obtain the change delta beta of the current gain;
step two, selecting the base width and the aging temperature as input characteristic data; selecting the change delta beta of the current gain as output characteristic data; the change delta beta of the current gain is used for judging the reliability of the triode;
step three, carrying out abnormal value processing on all the characteristic data;
step four, noise reduction treatment is carried out on the characteristic data;
fifthly, performing feature scaling treatment on the feature data;
step six, carrying out set division on the characteristic data, wherein the set division comprises a training set, a verification set and a test set;
step seven, establishing an FEDformer model;
substituting the training set in the step six into the FEDformer model in the step seven to train so as to obtain a high-precision FEDformer model;
step nine, substituting the verification set in the step six into the high-precision FEDformer model in the step eight to obtain the optimal parameters of the high-precision FEDformer model;
step ten, obtaining normalized root mean square error and normalized deviation of the high-precision FEDformer model; taking the normalized root mean square error and the normalized deviation as prediction accuracy evaluation indexes of the high-accuracy FEDformer model; when the normalized root mean square error and the normalized deviation meet the preset requirements, judging that the establishment of the high-precision FEDformer model is completed, and entering a step eleventh; otherwise, returning to the first step, and reestablishing a high-precision FEDformer model;
step eleven, substituting the base width and aging temperature which are acquired subsequently into a high-precision FEDformer model to serve as the input of the high-precision FEDformer model, and outputting the change delta beta of the current gain of the high-precision FEDformer model; and judging the reliability of the triode according to the change delta beta of the current gain.
In the above method for analyzing reliability of a triode based on an FEDformer model, in the first step, during an aging experiment, the environment is set to be a high temperature environment, and the temperature is not higher than the highest bearing temperature of the triode.
In the third step, the z-score method is adopted to process abnormal values of the characteristic data; the processing of outliers includes processing missing values and deleting duplicate values in the data.
In the above triode reliability analysis method based on the FEDformer model, in the fourth step, a high-pass filter is adopted to perform noise reduction treatment on the characteristic data; during noise reduction processing, the sampling rate is set to 1000Hz; the cut-off frequency is set to 50Hz; the order is set to 4.
In the above triode reliability analysis method based on the FEDformer model, in the fifth step, the feature data is subjected to feature scaling treatment by adopting a maximum absolute value scaling method; scaling the data to the range of [ -1,1] and retaining the sign information.
In the above triode reliability analysis method based on the FEDformer model, in the sixth step, 60% of the characteristic data is used as a training set, 20% of the characteristic data is used as a verification set, and 20% of the characteristic data is used as a test set.
In the above method for analyzing the reliability of a triode based on a FEDformer model, in the seventh step, the method for establishing the FEDformer model is as follows:
using an encoder-decoder architecture; the input length of the model is 6, and the output length is 3; taking 2 as a hidden state of the sequence; the input of the encoder is a 6×3 matrix; the decoder accepts 12 inputs; the encoder and decoder are of a multi-layer structure.
In the above method for analyzing triode reliability based on FEDformer model, in the step eight, when the FEDformer model is trained:
the loss function is set to MSE loss; an optimizer trained using Adam as a model; the learning rate is 10 -4 The method comprises the steps of carrying out a first treatment on the surface of the Each iteration is reduced to one tenth, setting the number of iterations to 5.
In the above triode reliability analysis method based on the FEDformer model, in the step nine, the optimal parameters include a learning rate, an iteration reduction amount and an iteration number; by substituting the verification set, a learning rate of 10 is obtained -4 Each iteration is reduced to one tenth and the number of iterations is 5.
In the above method for analyzing the reliability of a triode based on an FEDformer model, in the step ten, the test set in the step six is substituted into the high-precision FEDformer model after the optimal parameters are determined in the step nine, so as to obtain the normalized root mean square error and normalized deviation of the high-precision FEDformer model.
Compared with the prior art, the invention has the beneficial effects that:
(1) The invention provides a more flexible and concise way for capturing the dependence on different time scales, and realizes the highest triode reliability prediction precision with the least time and memory consumption in the multi-step prediction task of data processing, thereby improving the calculation efficiency and precision of the model;
(2) According to the invention, the preprocessing of the characteristic data is realized by adopting a z-score method to process abnormal values of the characteristic data, adopting a high-pass filter to perform noise reduction processing on the characteristic data and performing characteristic scaling processing on the characteristic data, so that the early-stage characteristic data processing work of high-precision FEDformer model establishment is completed;
(3) Substituting the training set into the FEDformer model for training to obtain a high-precision FEDformer model; substituting the verification set into the high-precision FEDformer model in the step eight to obtain the optimal parameters of the high-precision FEDformer model; substituting the test set into the high-precision FEDformer model after the optimal parameters are determined, obtaining normalized root mean square error and normalized deviation of the high-precision FEDformer model, verifying whether the high-precision FEDformer model is accurate or not, and making accurate matt for the reliability judgment of the follow-up triode.
Drawings
Fig. 1 is a flow chart of triode reliability analysis based on an FEDformer model according to the present invention.
Detailed Description
The invention is further illustrated below with reference to examples.
The invention provides a triode reliability analysis method based on an FEDformer model, which provides a modeling mode by utilizing machine learning, not only considers the complexity of structural parameters of a triode during modeling, but also accurately predicts the reliability of the triode, and by constructing the model, the problem can be conveniently found and solved in time during the production and use processes, and the high quality and reliability of the triode are ensured.
The triode reliability analysis method based on the FEDformer model specifically comprises the following steps as shown in fig. 1:
collecting the base width, aging temperature and working current of a triode in a normal working state; acquiring current before aging and current after aging of the triode by an aging experiment method; in the ageing experiment, the environment is set to be a high-temperature environment, and the temperature is not higher than the highest bearing temperature of the triode. The current before aging is subjected to difference with the working current to obtain current gain before aging; the aged current and the working current are subjected to difference to obtain aged current gain; and (3) performing difference between the current gain after aging and the current gain before aging to obtain the change delta beta of the current gain.
Step two, selecting the base width and the aging temperature as input characteristic data; selecting the change delta beta of the current gain as output characteristic data; the change in current gain Δβ is used to evaluate the reliability of the transistor.
And thirdly, carrying out abnormal value processing on all the characteristic data.
The invention adopts a z-score method to process abnormal values of the characteristic data; the processing of outliers includes processing missing values and deleting duplicate values in the data.
And step four, noise reduction processing is carried out on the characteristic data.
The invention adopts a high-pass filter to carry out noise reduction treatment on the characteristic data; during noise reduction processing, the sampling rate is set to 1000Hz; the cut-off frequency is set to 50Hz; the order is set to 4.
And fifthly, performing feature scaling processing on the feature data.
The invention adopts a maximum absolute value scaling method to perform characteristic scaling treatment on the characteristic data; scaling the data to the range of [ -1,1] and retaining the sign information.
And step six, carrying out set division on the characteristic data, wherein the set division comprises a training set, a verification set and a test set. Wherein, 60% of the characteristic data is used as a training set, 20% of the characteristic data is used as a verification set, and 20% of the characteristic data is used as a test set.
And step seven, establishing an FEDformer model.
The method for establishing the FEDformer model comprises the following steps:
using an encoder-decoder architecture; the input length of the model is 6, and the output length is 3; taking 2 as a hidden state of the sequence; the input of the encoder is a 6×3 matrix; the decoder accepts 12 inputs; the encoder and decoder are of a multi-layer structure.
And step eight, substituting the training set in the step six into the FEDformer model in the step seven to train so as to obtain the high-precision FEDformer model. When training the FEDformer model, the loss function is set as MSE loss; an optimizer trained using Adam as a model; the learning rate is 10 -4 The method comprises the steps of carrying out a first treatment on the surface of the Each iteration is reduced to one tenth, setting the number of iterations to 5.
And step nine, substituting the verification set in the step six into the high-precision FEDformer model in the step eight to obtain the optimal parameters of the high-precision FEDformer model.
The optimal parameters selected by the invention comprise learning rate, iteration reduction amount and iteration times; by substituting the verification set, a learning rate of 10 is obtained -4 Each iteration is reduced to one tenth and the number of iterations is 5.
Step ten, substituting the test set in the step six into the high-precision FEDformer model after the optimal parameters are determined in the step nine, and obtaining normalized root mean square error and normalized deviation of the high-precision FEDformer model; taking the normalized root mean square error and the normalized deviation as prediction accuracy evaluation indexes of the high-accuracy FEDformer model; when the normalized root mean square error and the normalized deviation meet the preset requirements, judging that the establishment of the high-precision FEDformer model is completed, and entering a step eleventh; otherwise, returning to the first step, and reestablishing the high-precision FEDformer model.
Step eleven, substituting the base width and aging temperature which are acquired subsequently into a high-precision FEDformer model to serve as the input of the high-precision FEDformer model, and outputting the change delta beta of the current gain of the high-precision FEDformer model; and judging the reliability of the triode according to the change delta beta of the current gain.
Examples
Step one, acquiring data. And simulating the BJT equipment by utilizing Silvaco TCAD software to obtain relevant model data, and constructing various BJT devices by utilizing an ATLAS tool aiming at the base width and the aging temperature. The initial current gain is obtained by TCAD simulation before the device ages. Setting an aging environment as a high temperature condition, ensuring that the aging environment is not higher than the highest junction temperature of the equipment, and selecting high temperature pressure values of 370K, 400K and 420K respectively. And simulating the BJT device by using TCAD simulation again to obtain the final current gain, and calculating the change (delta beta) of the current gain.
And step two, selecting input and output characteristics. The feature base width of the structure, which has a significant impact on device performance and is affected by the temperature of the aging environment, is selected as an input feature. The change in current gain (Δβ) is a core parameter reflecting the reliability of the device, and therefore, it is decided to characterize the reliability level of the BJT device with the change in current gain (Δβ) as an output characteristic.
And thirdly, preprocessing data. Firstly, cleaning data, processing missing values in the data, deleting repeated values, and completing processing of abnormal values of the data by adopting a z-score method, wherein the formula is as follows:
where Z is the Z-score value, x is the value of a data point, u is the average value of the data set, and σ is the standard deviation of the data set.
The high-pass filter is adopted to reduce the noise of the whole data, the sampling rate is 1000Hz, the cut-off frequency is 50Hz, the order is 4, and the transfer function formula is as follows:
where H(s) is the transfer function of the filter, s is the complex variable, ω c Is the cut-off frequency and n is the order of the filter.
For feature scaling, the data features are scaled to the range of [ -1,1] using a maximum absolute value scaling (Max Absolute Scaling) method, and the sign information of the features is preserved, as follows:
where x is the original data feature and max abs is the maximum absolute value of the feature.
For data partitioning, 60% training sets, 20% validation sets and 20% test sets are partitioned.
And fourthly, establishing an FEDformer model through Python, wherein the Python version is more than 3.8, and the PyTorch library version is 1.9.0. Using the encoder-decoder architecture, the input length of the model is taken as 6 and the output length as 3. The hidden state of the sequence is taken to be 2. The input to the encoder is a 6 x 3 matrix and the decoder accepts 12 inputs. The encoder adopts a multi-layer structure, expressed as:where l ε {1, …, N } represents the output of the layer I encoder, and +.>Is an embedded history sequence, and the specific form is as follows:
wherein the method comprises the steps ofRespectively representing the i-th separated seasonal components of the layer. For the frequency enhancement module (FEB), there are two different versions (fourier frequency enhanced attention and wavelet frequency enhanced attention), implemented by Discrete Fourier Transform (DFT) and Discrete Wavelet Transform (DWT) mechanisms, respectively, that can be seamlessly replaced with the self-attention module.
The decoder also adopts a multi-layer structure:where l ε {1, …, M } represents the first output decoder layer, and is specifically:
wherein the method comprises the steps ofRespectively representing the season and trend components after the i-th layer separates the blocks. />i.e {1,2,3} represents the i-th extraction trend +.>Is a projector of (a). Similar to the frequency enhancement module, the frequency enhancement attention module (FEA) has two different versions (fourier frequency enhancement attention and wavelet frequency enhancement attention), the attention design is implemented by Discrete Fourier Transform (DFT) and Discrete Wavelet Transform (DWT) projections, respectively, instead of the cross attention module.
The model was designed for Mixture Of Experts Decomposition block (MOEDecomp), which contains a set of averaging filters of different sizes for extracting a number of trend components from the input signal, and a set of data-dependent weights for grouping these trend components into the final trend, given by:
X trend =Softmax(L(x))*(F(x)),
where F (x) is a set of average pool filters and Softmax (L (x)) is the weight to mix these extraction trends.
The final output is the sum of the two refined decomposition componentsWherein->Is to change the depth of seasonsSex component->Projected to the target dimension.
And fifthly, training an FEDformer model. The loss function was set to MSE loss, the learning rate was 10-4 using Adam as the model trained optimizer, each iteration was reduced to one tenth, and the number of iterations was set to 5.
And step six, model evaluation and testing. Substituting the model into a training set to test unknown data, and adopting Normalized Root Mean Square Error (NRMSE) and Normalized Deviation (ND) as evaluation indexes for measuring the model prediction effect, wherein a normalized root mean square error formula is as follows:
the normalized deviation formula is:
wherein x is j,t As a result of the fact that the value,for the predicted value, N is the total number of samples in the data set, and T is the length of the data sequence.
Substituting the base width and aging temperature which are acquired subsequently into a high-precision FEDformer model to be used as the input of the high-precision FEDformer model, and outputting the change delta beta of the current gain by the high-precision FEDformer model; and judging the reliability of the triode according to the change delta beta of the current gain.
The triode reliability analysis method based on the FEDformer model provided by the invention provides a modeling mode by utilizing machine learning, not only can consider the structural parameter complexity of the triode during modeling, but also can accurately predict the reliability of the triode, and by constructing the model, the problem can be conveniently found and solved in time during the production and use processes, and the high quality and reliability of the triode are ensured.
Although the present invention has been described in terms of the preferred embodiments, it is not intended to be limited to the embodiments, and any person skilled in the art can make any possible variations and modifications to the technical solution of the present invention by using the methods and technical matters disclosed above without departing from the spirit and scope of the present invention, so any simple modifications, equivalent variations and modifications to the embodiments described above according to the technical matters of the present invention are within the scope of the technical matters of the present invention.
Claims (10)
1. A triode reliability analysis method based on an FEDformer model is characterized in that: comprising the following steps:
collecting the base width, aging temperature and working current of a triode in a normal working state; acquiring current before aging and current after aging of the triode by an aging experiment method; the current before aging is subjected to difference with the working current to obtain current gain before aging; the aged current and the working current are subjected to difference to obtain aged current gain; the current gain after aging is differenced with the current gain before aging to obtain the change delta beta of the current gain;
step two, selecting the base width and the aging temperature as input characteristic data; selecting the change delta beta of the current gain as output characteristic data; the change delta beta of the current gain is used for judging the reliability of the triode;
step three, carrying out abnormal value processing on all the characteristic data;
step four, noise reduction treatment is carried out on the characteristic data;
fifthly, performing feature scaling treatment on the feature data;
step six, carrying out set division on the characteristic data, wherein the set division comprises a training set, a verification set and a test set;
step seven, establishing an FEDformer model;
substituting the training set in the step six into the FEDformer model in the step seven to train so as to obtain a high-precision FEDformer model;
step nine, substituting the verification set in the step six into the high-precision FEDformer model in the step eight to obtain the optimal parameters of the high-precision FEDformer model;
step ten, obtaining normalized root mean square error and normalized deviation of the high-precision FEDformer model; taking the normalized root mean square error and the normalized deviation as prediction accuracy evaluation indexes of the high-accuracy FEDformer model; when the normalized root mean square error and the normalized deviation meet the preset requirements, judging that the establishment of the high-precision FEDformer model is completed, and entering a step eleventh; otherwise, returning to the first step, and reestablishing a high-precision FEDformer model;
step eleven, substituting the base width and aging temperature which are acquired subsequently into a high-precision FEDformer model to serve as the input of the high-precision FEDformer model, and outputting the change delta beta of the current gain of the high-precision FEDformer model; and judging the reliability of the triode according to the change delta beta of the current gain.
2. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the first step, during the aging test, the environment is set to be a high-temperature environment, and the temperature is not higher than the highest bearing temperature of the triode.
3. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the third step, the z-score method is adopted to process abnormal values of the characteristic data; the processing of outliers includes processing missing values and deleting duplicate values in the data.
4. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the fourth step, a high-pass filter is adopted to perform noise reduction treatment on the characteristic data; during noise reduction processing, the sampling rate is set to 1000Hz; the cut-off frequency is set to 50Hz; the order is set to 4.
5. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the fifth step, the characteristic data is subjected to characteristic scaling treatment by adopting a maximum absolute value scaling method; scaling the data to the range of [ -1,1] and retaining the sign information.
6. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the sixth step, 60% of the feature data is used as a training set, 20% of the feature data is used as a verification set, and 20% of the feature data is used as a test set.
7. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the seventh step, the method for establishing the FEDformer model comprises the following steps:
using an encoder-decoder architecture; the input length of the model is 6, and the output length is 3; taking 2 as a hidden state of the sequence; the input of the encoder is a 6×3 matrix; the decoder accepts 12 inputs; the encoder and decoder are of a multi-layer structure.
8. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the eighth step, when training the FEDformer model:
the loss function is set to MSE loss; an optimizer trained using Adam as a model; the learning rate is 10 -4 The method comprises the steps of carrying out a first treatment on the surface of the Each iteration is reduced to one tenth, setting the number of iterations to 5.
9. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the step nine, the optimal parameters comprise a learning rate, iteration reduction and iteration times; by substituting the verification set, a learning rate of 10 is obtained -4 Each iteration is reduced to one tenth and the number of iterations is 5.
10. The triode reliability analysis method based on the FEDformer model as claimed in claim 1, wherein the method comprises the following steps: in the tenth step, the test set in the sixth step is substituted into the high-precision FEDformer model after the optimal parameters are determined in the ninth step, and the normalized root mean square error and normalized deviation of the high-precision FEDformer model are obtained.
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