CN111177970B - Multi-stage semiconductor process virtual metering method based on Gaussian process and convolutional neural network - Google Patents

Multi-stage semiconductor process virtual metering method based on Gaussian process and convolutional neural network Download PDF

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CN111177970B
CN111177970B CN201911260377.XA CN201911260377A CN111177970B CN 111177970 B CN111177970 B CN 111177970B CN 201911260377 A CN201911260377 A CN 201911260377A CN 111177970 B CN111177970 B CN 111177970B
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谢磊
吴小菲
陈启明
苏宏业
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Zhejiang University ZJU
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Abstract

The invention discloses a multi-stage semiconductor process virtual metering method based on a Gaussian process and a convolutional neural network, which comprises the following steps of: (1) collecting output signals of a process variable sensor related to a variable to be detected in a control process to be detected; (2) preprocessing the acquired signal data of the process variable to remove abnormal values; (3) rearranging the preprocessed data and reserving stage information of the data; (4) extracting features of all data and establishing a regression model; (5) saving the weight of the current parameter, calculating the final maximum posterior value, if the weight does not meet the stop condition, updating the parameter and repeating the step (4) until the stop condition is reached; (6) and storing parameter values of each layer, recalculating the new predicted points and obtaining the probability distribution of the geometric quality. By utilizing the method and the device, a higher-precision virtual measurement result can be obtained, the uncertainty of a prediction result is calculated, and a numerical basis is provided for further improving a model.

Description

Multi-stage semiconductor process virtual metering method based on Gaussian process and convolutional neural network
Technical Field
The invention relates to the field of data mining in industrial systems, in particular to a multi-stage semiconductor process probability type virtual metering method based on a Gaussian process and a convolutional neural network.
Background
Semiconductor manufacturing involves many stages. For example, in the production of electronic chips, wire saws first cut a silicon ingot into sections, then perform several flat stages including cleaning, polishing and grinding, and then transfer the processed wafers into front end and back end processes that form the final chips. Due to the high throughput nature of the semiconductor manufacturing industry and the high cost of measuring wafers, one cannot measure the quality variables of all production wafers at each stage. Due to the limitations of physical measurements, wafer-to-wafer modeling is increasingly used to predict the quality of the final product so that tools and equipment can be adjusted in time to reduce process variation. However, due to the complexity of the physical phenomena involved, it is difficult to account for the nanoscale deviations of these dimensions according to some basic mathematical models. Therefore, the data-driven virtual metrology technology is widely applied in the semiconductor industry to obtain terabyte-level manufacturing data with intrinsic value information from semiconductor devices, electronic boards and systems, and further establish models.
In the field of semiconductor manufacturing, researchers have conducted relevant studies on virtual metrology, such as local weighted partial least squares, support vector machines, k-NN regression, and the like. However, for wafer fabrication, there are typically several different process tools corresponding to different production stages, thereby generating large-scale data sets for analysis. Conventional machine learning methods are not easily applied with a certain number of inputs, requiring appropriate pre-processing. In the past, typical methods of reducing trace data to 4 summary statistics (including minimum, maximum, mean, and standard deviation) have been widely used in semiconductor processing. However, this method may cause a certain amount of information to be lost, and the predictive capability of the model may be affected. Because the raw data contains more information, it is particularly important for virtual metrology research how to process the raw data to obtain sufficient statistical information and ensure that no information is lost.
On the other hand, past methods only yield scalar predictions of the results, which means that the model cannot reflect the confidence of the predicted values. Theoretically, the higher the uncertainty, the less reliable the predicted value at that time. This clearly shows that data points near this point need to be added to improve the accuracy of the model. Thus, the accuracy of the predicted values should also be emphasized in the virtual metrology research.
Based on the background, a method for extracting multi-stage process characteristics through collected original sample data and simultaneously obtaining output uncertainty to show the reliability of prediction is found, virtual metering variable distribution is obtained, the method has very important use value for accurately obtaining the required quality variable value, and the method is also beneficial to evaluating the overall control performance of industrial engineering.
Disclosure of Invention
The invention provides a multi-stage semiconductor process virtual metering method based on a Gaussian process and a convolutional neural network, which can be suitable for a multi-stage industrial control loop process.
A multi-stage semiconductor process virtual metering method based on a Gaussian process and a convolutional neural network comprises the following steps:
(1) collecting output signals of a process variable sensor related to a variable to be detected in a control process to be detected;
(2) preprocessing the acquired signal data of the process variable to remove abnormal values;
(3) rearranging the preprocessed data and reserving stage information of the data;
(4) inputting each variable into a convolution filter, extracting local features in the correlation among the variables along the one-dimensional processing time direction layer by layer, and transmitting the feature output of each layer through an activation function; collecting all single features of all stages of the last layer of feature extraction, outputting the single features to a Gaussian process layer, and finally establishing a regression model;
(5) saving the parameter weight of the current model, calculating the final maximum posterior value, if the final maximum posterior value does not meet the stop condition, updating the parameter weight and repeating the step (4) until the stop condition is reached;
(6) and storing parameter values of each layer, recalculating the new predicted points and obtaining the probability distribution of the geometric quality.
The invention can improve the detection accuracy and reliability of virtual measurement, can provide data support for new test points, and has important practical value in the aspect of improving economic benefit.
The method directly and simultaneously extracts high-dimensional original data characteristics in the multi-stage industrial control loop, then adopts a probability model for modeling, outputs the obtained distribution, and reserves parameters of each layer, thereby predicting a new measuring point. And continuously updating the model according to the output credibility of the model, thereby enhancing the prediction accuracy of the model.
In the step (2), the specific process of the pretreatment is called as: and detecting a non-numerical value or a value which is greatly different from the distribution of the process variable in the process variable, and filling by adopting the variable mean value or zero value.
In the step (3), data are separated according to different stages so as to keep stage information of the data; the semiconductor data contains variable data collected by the sensors in time series dimensions at each stage, and the data is arranged into a single channel for each variable.
The specific process of the step (4) is as follows:
(4-1) order
Figure BDA0002311446600000031
s＝1，2，…，S，
Figure BDA0002311446600000032
L1, 2, …, L being the L-th layer, s-th stage wherein
Figure BDA0002311446600000033
One channel input (shared S phase, shared l th phase
Figure BDA0002311446600000034
One channel input),
Figure BDA0002311446600000035
and
Figure BDA0002311446600000036
the ith layer kernel and bias of the s stage, the ith layer output characteristic diagram of the s stage
Figure BDA0002311446600000037
Represented as the convolution process:
Figure BDA0002311446600000038
(4-2) calculating the characteristic diagram output after the activation function is calculated point by using the following formula:
Figure BDA0002311446600000039
wherein q is as defined above
Figure BDA00023114466000000310
F (-) is a sigmoid function, thus will
Figure BDA00023114466000000311
Conversion to the same size
Figure BDA00023114466000000312
(4-3) connecting all the characteristics after the operation of the multilayer convolution and activation function as the input of the last Gaussian process layer
Figure BDA0002311446600000041
Establishing joint probability distribution and obtaining output distribution, wherein the maximum posterior expression of the model is as follows:
Figure BDA0002311446600000042
wherein θ ═ a1,...,ad,v0) For the hyper-parameters in the gaussian process layer, for all data D (X, y),
Figure BDA0002311446600000043
inputting a matrix for the model (N is the total number of observations, and D is the corresponding dimension of each measurement sample input); y is formed by RN×1Outputting vectors for the corresponding models, and setting each value y in ynIndependently and equally distributed.
The final model loss function, i.e. the log of the maximum a posteriori mentioned above, is thus established:
Figure BDA0002311446600000044
wherein, KLTo input the data covariance matrix, the following covariance formula is calculated:
Figure BDA0002311446600000045
(4-4), training the update parameters according to a gradient descent method:
Figure BDA0002311446600000046
Figure BDA0002311446600000047
Figure BDA0002311446600000048
where α represents a fixed learning rate and α > 0, a parameter gradient
Figure BDA0002311446600000049
And
Figure BDA00023114466000000410
the following formula is used to obtain the following formula,
Figure BDA0002311446600000051
Figure BDA0002311446600000052
Figure BDA0002311446600000053
wherein
Figure BDA0002311446600000054
It is meant that in the convolution,
Figure BDA0002311446600000055
neutralization of
Figure BDA0002311446600000056
Parts multiplied by element correspondence
The iterative part of the middle is represented as:
Figure BDA0002311446600000057
Figure BDA0002311446600000058
Figure BDA0002311446600000059
wherein, the symbol
Figure BDA00023114466000000510
Referring to element-by-element one-to-one operations, rot180 is a function of the rotation of the matrix by 180 degrees in matlab.
In the step (5), the stop condition is as follows: the maximum a posteriori increase is within a certain range or reaches a set maximum number of cycles.
In the step (6), for the new predicted point, the probability distribution of the geometric mass is represented by a mean value and a variance, and a specific formula of the mean value and the variance is represented as follows:
Figure BDA00023114466000000511
Figure BDA00023114466000000512
Figure BDA00023114466000000513
for the input value of the new predicted point in the L-th layer gaussian process,
Figure BDA00023114466000000514
the autocovariance value of the new predicted point characteristic (input of the L-th layer Gaussian process) is obtained, and K is a covariance matrix of the source data characteristic (input of the L-th layer Gaussian process);
Figure BDA00023114466000000515
i.e. the covariance matrix between the new prediction point and the source data feature (input of the L-th layer gaussian process); mean value μ*Sum variance
Figure BDA0002311446600000061
The output of the gaussian process layer in the regression model for the new predicted point.
Compared with the prior art, the invention has the following beneficial effects:
1. the method of the invention processes multi-stage high-dimensional input simultaneously, can well extract the characteristics between different variables and between different stages, and particularly can well express the characteristics between wafers in different stages.
2. In the invention, the distribution of the estimated observation values can be obtained due to the inherent characteristics of the Gaussian process. In conjunction with the generated features, the uncertainty of the output can be used to represent the reliability of the prediction.
3. In the invention, the deep architecture generates high-efficiency and low-dimensional characteristics, and can reduce the calculation load in the Gaussian process.
4. In the invention, the parameters can be effectively and automatically adjusted by a gradient method based on the maximum posterior.
5. The invention completely adopts a data driving type method, does not need prior knowledge of the process and does not need to design a filter in advance.
Drawings
FIG. 1 is a flow chart of a multi-stage semiconductor process virtual metrology method based on Gaussian process and convolutional neural network of the present invention;
FIG. 2 is a schematic structural diagram of a regression model in an embodiment of the present invention;
FIG. 3 is a diagram illustrating the actual values of process test data and model outputs according to an embodiment of the present invention.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples, which are intended to facilitate the understanding of the invention without limiting it in any way.
In the following, taking the estimation of the deposition process result of a certain factory in China as an example, the height value of the wafer passing through the multi-stage chemical process is virtually measured.
In the manufacturing process, the chemical vapor deposition process is similar to the process of applying a solid thin film coating on a surface that is often used in the semiconductor industry. This process is complex because it involves many chemical reactions, and the reactors in a multiple reactor system are independently controlled to deposit films in the process chamber under a variety of conditions. The chemical vapor deposition apparatus is equipped with a considerable number of sensors. Through virtual metrology development, the quality of the wafer will be predicted from historical process and production equipment data without the need for expensive quality measurements.
As shown in fig. 1, a multi-stage semiconductor process virtual metrology method based on a gaussian process and a convolutional neural network comprises the following steps:
step 1, collecting output signals of a process variable sensor related to a variable to be detected in a control process to be detected.
And 2, performing certain data preprocessing to remove abnormal values.
And detecting a non-numerical value or a value which is greatly different from the distribution of the input variable in the input variable, and filling by adopting a mean value or a zero value.
And 3, rearranging the data and keeping the stage information of the data.
The data is separated according to different stages to retain stage information of the data, and the semiconductor data contains sensor variable data in time series dimension at each stage, and the data are arranged into a single channel of each variable.
As shown in FIG. 2, at each stage(s), each wafer of produced dies is broken into
Figure BDA0002311446600000071
A variable, also called
Figure BDA0002311446600000072
A channel, each channel having TsAn input composed of time-series points
Figure BDA0002311446600000073
And 4, extracting features of all data and establishing a regression model.
Inputting each channel into a convolution filter, extracting local features in the correlation among variables along the one-dimensional processing time direction layer by layer, and transmitting the feature output of each layer through an activation function; and collecting all single features of all stages of the last layer of feature extraction, outputting the single features to a Gaussian process layer, and finally establishing a regression relation and obtaining the probability distribution of the geometric quality.
The whole model feature extraction and modeling steps are as follows:
(4-1) order
Figure BDA0002311446600000081
s＝1,2,…,S,
Figure BDA0002311446600000082
For the l-th layer, one of the channels is input in the s-th stage,
Figure BDA0002311446600000083
and
Figure BDA0002311446600000084
the core and the bias of the first layer output characteristic diagram
Figure BDA0002311446600000085
Can be expressed as the following convolution procedure:
Figure BDA0002311446600000086
(4-2) calculating the characteristic diagram output after the activation function is calculated point by using the following formula:
Figure BDA0002311446600000087
wherein q is as defined above
Figure BDA0002311446600000088
Of each element, thereby to be
Figure BDA0002311446600000089
Conversion to the same size
Figure BDA00023114466000000810
(4-3) connecting all the characteristics after the operation of the multilayer convolution and activation function as the input of the last Gaussian process layer
Figure BDA00023114466000000811
Establishing joint probability distribution and obtaining output distribution, wherein the maximum posterior expression of the model is as follows:
Figure BDA00023114466000000812
wherein θ ═ a1,...,ad,v0) Is the hyperparameter (parameter in covariance matrix) in the Gaussian process layer, D (X, y),
Figure BDA00023114466000000813
is the model input.
Thereby establishing a final model loss function:
Figure BDA00023114466000000814
wherein, KLTo input the data covariance matrix, the following covariance formula is calculated:
Figure BDA00023114466000000815
(4-4), training the update parameters according to a gradient descent method:
Figure BDA0002311446600000091
Figure BDA0002311446600000092
Figure BDA0002311446600000093
wherein the parameter gradient can be obtained by the following formula,
Figure BDA0002311446600000094
Figure BDA0002311446600000095
Figure BDA0002311446600000096
the iterative part of the middle can be expressed as:
Figure BDA0002311446600000097
Figure BDA0002311446600000098
Figure BDA0002311446600000099
feature extraction is according to the prior art "LeCun Y, Bottou L, Bengio Y, & Haffner P.gradient-based learning application to document retrieval. proceedings of the IEEE 1998; 86: 2278-.
The gaussian regression model is based on the prior art "Rasmussen ce. gaussian processes in machine learning. advanced selection on machine learning. spring; 2004, p.63-71.
Step 5, saving the current weight, calculating the final maximum posterior value, if the stopping condition is not met, updating the weight and repeating the step 4 until the stopping condition is reached;
the stop condition means that the maximum posterior increase is within a certain range or reaches a set maximum number of cycles.
And 6, storing the parameter values of each layer, and recalculating the new predicted points. The corresponding mean value of the predicted values obtained from the joint probability distribution and the method are expressed as:
Figure BDA0002311446600000101
Figure BDA0002311446600000102
wherein the content of the first and second substances,
Figure BDA0002311446600000103
mean value μ*Sum variance
Figure BDA0002311446600000104
The output of the gaussian process layer in the regression model for the new predicted point.
In this embodiment, the result is shown in fig. 3, and the proposed method performs well, extracts features in high-dimensional data, matches a predicted value with actual data, and can show uncertainty of the result.
By utilizing the method, the uncertainty of the prediction result can be calculated on the basis of carrying out multi-stage original data virtual measurement, and a numerical basis is provided for further improving the model.
The embodiments described above are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only specific embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the present invention.

Claims (4)

1. A multi-stage semiconductor process virtual metering method based on a Gaussian process and a convolutional neural network is characterized by comprising the following steps:
(1) collecting output signals of a process variable sensor related to a variable to be detected in a control process to be detected;
(2) preprocessing the acquired signal data of the process variable to remove abnormal values;
(3) rearranging the preprocessed data and reserving stage information of the data;
(4) inputting each variable into a convolution filter, extracting local features in the correlation among the variables along the one-dimensional processing time direction layer by layer, and transmitting the feature output of each layer through an activation function; collecting all single features of all stages of the last layer of feature extraction, outputting the single features to a Gaussian process layer, and finally establishing a regression model; the specific process is as follows:
(4-1) order
Figure FDA0003170575020000011
Indicates a common S stage, the l th stage of the S stage has a common Vs l-1The input of each channel is provided with a channel,
Figure FDA0003170575020000012
and
Figure FDA0003170575020000013
the ith layer kernel and bias of the s stage, the ith layer output characteristic diagram of the s stage
Figure FDA0003170575020000014
Represented as the convolution process:
Figure FDA0003170575020000015
(4-2) calculating the characteristic diagram output after the activation function is calculated point by using the following formula:
Figure FDA0003170575020000016
wherein q is as defined above
Figure FDA0003170575020000017
F (-) is a sigmoid function, thus will
Figure FDA0003170575020000018
Conversion to the same size
Figure FDA0003170575020000019
(4-3) connecting all the characteristics after the operation of the multilayer convolution and activation function as the input of the last Gaussian process layer
Figure FDA00031705750200000110
Establishing joint probability distribution and obtaining output distribution, wherein the maximum posterior expression of the model is as follows:
Figure FDA0003170575020000021
wherein θ ═ a1,...,ad,v0) For the hyper-parameters in the gaussian process layer, for all data D (X, y),
Figure FDA0003170575020000022
inputting a matrix for the model, wherein N is the total number of observations, and D is the corresponding dimension of each input measurement sample; y is formed by RN×1Outputting vectors for the corresponding models, and setting each value y in ynIndependently and equally distributed;
the final model loss function, i.e. the log of the maximum a posteriori mentioned above, is thus established:
Figure FDA0003170575020000023
wherein, KLTo input the data covariance matrix, the following covariance formula is calculated:
Figure FDA0003170575020000024
(4-4), training the update parameters according to a gradient descent method:
Figure FDA0003170575020000025
Figure FDA0003170575020000026
Figure FDA0003170575020000027
where α represents a fixed learning rate and α > 0, a parameter gradient
Figure FDA0003170575020000028
And
Figure FDA0003170575020000029
the following formula is used to obtain the following formula,
Figure FDA00031705750200000210
Figure FDA00031705750200000211
Figure FDA0003170575020000031
wherein the content of the first and second substances,
Figure FDA0003170575020000032
it is meant that in the convolution,
Figure FDA0003170575020000033
neutralization of
Figure FDA0003170575020000034
A portion multiplied by element correspondence;
the iterative part of the middle is represented as:
Figure FDA0003170575020000035
Figure FDA0003170575020000036
Figure FDA0003170575020000037
wherein, the symbol
Figure FDA0003170575020000038
Indicating a one-to-one operation by element, rot180 is a function of rotating the matrix 180 degrees in matlab;
(5) saving the parameter weight of the current model, calculating the final maximum posterior value, if the final maximum posterior value does not meet the stop condition, updating the parameter weight and repeating the step (4) until the stop condition is reached; the stop conditions are as follows: the maximum posterior increment is within a certain range or reaches a set maximum cycle number;
(6) and storing parameter values of each layer, recalculating the new predicted points and obtaining the probability distribution of the geometric quality.
2. The multi-stage semiconductor process virtual metrology method based on gaussian process and convolutional neural network as claimed in claim 1, characterized in that in step (2), the specific process of the preprocessing is called as: and detecting a non-numerical value or a value which is greatly different from the distribution of the process variable in the process variable, and filling by adopting the variable mean value or zero value.
3. The multi-stage semiconductor process virtual metrology method based on gaussian processes and convolutional neural networks as claimed in claim 1, characterized in that in step (3), the semiconductor data contains variable data collected by sensors in time series dimensions at each stage, and these data are arranged into a single channel for each variable.
4. The multi-stage semiconductor process virtual metrology method based on gaussian process and convolutional neural network as claimed in claim 1, characterized in that in step (6), for the new predicted point, according to the joint probability distribution, the probability distribution of the geometric quality of the measurement sample is obtained, i.e. the corresponding mean and variance are obtained, and the specific formula is represented as:
Figure FDA0003170575020000041
Figure FDA0003170575020000042
wherein the content of the first and second substances,
Figure FDA0003170575020000043
for the input value of the new predicted point in the L-th layer gaussian process,
Figure FDA0003170575020000044
the feature auto-covariance value of the new predicted point is obtained;
Figure FDA0003170575020000045
a covariance matrix between the new predicted point and the source data feature; k is the covariance matrix of the source data characteristics, mean mu and variance
Figure FDA0003170575020000046
The output of the gaussian process layer in the regression model for the new predicted point.
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