CN109543239B - LTCC shrinkage pre-judging method based on neural network technology - Google Patents

LTCC shrinkage pre-judging method based on neural network technology Download PDF

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CN109543239B
CN109543239B CN201811270751.XA CN201811270751A CN109543239B CN 109543239 B CN109543239 B CN 109543239B CN 201811270751 A CN201811270751 A CN 201811270751A CN 109543239 B CN109543239 B CN 109543239B
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杨士成
姜威
徐美娟
石伟
张婷
白浩
闫淑霞
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Xian Institute of Space Radio Technology
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Abstract

The invention relates to a LTCC shrinkage pre-judging method based on neural network technology, which comprises the steps of determining each influence factor of shrinkage through an orthogonal test; taking each influence factor as a structural parameter, and establishing an influence factor list for each layer of LTCC; setting a neural network, and training the neural network according to historical data of a production line to obtain a shrinkage rate prediction model; and predicting the shrinkage of the LTCC product by using a shrinkage prediction model. Aiming at the problem that the shrinkage rate of different LTCC products cannot be accurately known before production, the invention confirms the factors influencing the shrinkage rate from the design and process of the LTCC products, establishes a mathematical model between the influencing factors and the shrinkage rate by using a neural network technology, and realizes the accurate prediction of the shrinkage rate of the LTCC products.

Description

LTCC shrinkage pre-judging method based on neural network technology
Technical Field
The invention relates to an LTCC shrinkage pre-judging method based on a neural network technology, and belongs to the technical field of low-temperature co-fired ceramics.
Background
Microwave circuit components based on low temperature co-fired ceramic technology (LTCC), such as LTCC filters and power modules, have been successfully applied to the same-type satellite products in China, and since LTCC can realize three-dimensional design of microwave circuits, the LTCC is considered as one of key technologies for miniaturizing microwave circuits and further realizing satellite miniaturization.
The LTCC conventional process is shown in fig. 1, wherein step 9 is referred to as "low temperature cofiring" or simply "cofiring", in which the LTCC green ceramic shrinks to achieve a soft to hard transition of the ceramic, thereby forming a dense and hard multilayer ceramic circuit, the extent of shrinkage of the green ceramic being indicated by the "shrinkage factor". Therefore, the size of the process circuit pattern in the working procedures 1-8 needs to be amplified according to the shrinkage rate, so that the final product can be ensured to shrink to the required real size in the cofiring link.
However, the shrinkage of LTCC is affected by many factors, and raw material suppliers typically only give a fixed reference shrinkage value, so it is now common practice in the industry both at home and abroad: the process staff refers to the technical documents of the raw material suppliers, then the circuit diagram of the designer is amplified according to experience to a proper proportion, then the process is carried out, and finally the raw porcelain is shrunk to the size desired by the designer in the co-firing process. However, for some complex products, it is sometimes necessary to first produce a version of the product, measure shrinkage, correct magnification, and then re-produce the product. Because the LTCC product for the satellite uses gold as a raw material, the secondary plate throwing can cause waste of time and resources, and is unfavorable for controlling the cost and the progress.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides an LTCC shrinkage pre-judging method based on a neural network technology, which can accurately pre-judge the shrinkage of each LTCC product before production, thereby improving the yield and the circuit performance and shortening the processing period.
The invention aims at realizing the following technical scheme:
the LTCC shrinkage pre-judging method based on the neural network technology comprises the following steps:
(1) Determining each influencing factor of the shrinkage through an orthogonal test;
(2) Taking each influence factor as a structural parameter, and establishing an influence factor list for each layer of LTCC;
(3) Setting a neural network, and training the neural network according to historical data of a production line to obtain a shrinkage rate prediction model;
(4) And predicting the shrinkage of the LTCC product by using a shrinkage prediction model.
Preferably, the shrinkage prediction model is obtained as follows:
3.1, constructing a three-layer artificial neural network, and dividing the three-layer artificial neural network into three parts: the first layer is input neuron for receiving each influencing factor of shrinkage, the second layer is hidden neuron for processing nonlinear relation of input and output, and the third layer is output neuron for outputting LTCC shrinkage;
3.2, utilizing the historical data of the production line to adjust the weight value in the neural network, so that the output of the model is consistent with the historical shrinkage rate data;
3.3, verifying the accuracy of the shrinkage rate of the neural network model by using unused production line history data; and when the error between the output of the model and the historical shrinkage data meets the requirement, completing modeling, otherwise, returning to 3.1, and adjusting the number of the hidden neurons.
Preferably, each influencing factor of shrinkage includes: metal paste coverage, resistive paste coverage, pore density, and cavity density are commonly used.
Preferably, the common paste and resistor paste coverage includes paste CN30-080 coverage, paste CN30-025 coverage, paste CN36-020 coverage, paste DL10-088 coverage and paste FX87-101B coverage.
Preferably, the orthogonal test comprises matching different slurries with corresponding screens, and setting different coverage rates; printing a resistor on the white ceramic chip in a screen printing mode; different punching densities are realized on the white ceramic chip, and the bushing plate is used for filling holes; different sizes of cavities are realized on the white porcelain piece; and performing orthogonal tests to obtain shrinkage values and historical data of the production line.
Preferably, for a Ferro material, the procedure for the orthogonal test is as follows:
1.1, preparing 24 white porcelain tiles of 8 inches, corresponding to one bushing plate of a punching diagram, printing one silk screen L of a large-area diagram, printing one silk screen M of a medium-area diagram, and printing one silk screen S of a small-area diagram;
1.2 taking 3 Bai Ci sheets for punching, and filling holes by using slurry CN30-078 and a bushing plate to obtain a group 1;
3 sheets of Bai Ci sheets were taken and used as set 2 using screen L printing paste CN 30-080;
3 sheets of Bai Ci sheets were taken and screen L printing paste CN30-025 was used as group 3;
3 sheets of Bai Ci sheets were taken and screen M printing paste CN36-020 was used as set 4;
3 sheets of Bai Ci sheets were taken and screen S printing paste DL10-088 was used as set 5;
3 sheets of Bai Ci sheets were taken and screen S printing paste FX87-101B was used as set 6;
1.3, dividing each of the 24 white porcelain tiles into four blocks;
1.4, respectively stacking 12 1/4 blocks divided into groups 1-6;
1.5 taking 3 Bai Ci pieces and 12 1/4 pieces divided into pieces to be stacked together to be used as a group 7;
1.6, taking 3 Bai Ci pieces, dividing into 12 pieces of 1/4 pieces, stacking together, and processing through cavities by laser to obtain a group 8;
1.7 dividing each block in groups 1-8 into four;
1.8 measurement of the product sizes of groups 1-8, firing one product per group, and measuring shrinkage.
Preferably, the input signal of the shrinkage prediction model is a variable affecting the shrinkage, denoted as i= [ I ] 1 ,I 2 ,I 3 ,……I 147 ] T The input signals of the neural network model are output data, namely X-direction shrinkage and Y-direction shrinkage, and are marked as O= [ X, Y] T The method comprises the steps of carrying out a first treatment on the surface of the The nonlinear formulas of input and output are:
Figure SMS_1
Figure SMS_2
where p represents the number of hidden layer neurons,
Figure SMS_3
representing the weight parameter between the mth input neuron and the ith hidden neuron,/and (ii)>
Figure SMS_4
Is in the meaning of 1 st output neural networkA weight parameter with the ith neuron in the hidden layer,
Figure SMS_5
is a weight parameter between the 2 nd output neural network and the i th neuron in the hidden layer,/o>
Figure SMS_6
And->
Figure SMS_7
The bias weight values of the 1 st output neuron and the 2 nd output neuron are respectively expressed, and the sigmoid function formula is sigma (gamma) =1/(1+e) )。
Meanwhile, the LTCC shrinkage pre-judging method based on the neural network technology comprises the following steps:
(1) Determining the influence of the coverage rate of common metal slurry, the coverage rate of resistance slurry, the density of holes and the density of cavities required by production on the shrinkage rate through orthogonal experiments;
(2) Respectively establishing a shrinkage prediction model according to the slurry coverage rate, the resistance coverage rate, the hole density and the cavity density of each layer;
(3) And predicting the shrinkage of the LTCC product by using a shrinkage prediction model of each layer.
Preferably, the common metal pastes and resistor pastes required for production include pastes CN30-080, CN30-025, CN36-020 and DL10-088.
Preferably, the orthogonal test comprises matching different slurries with corresponding screens, and setting different coverage rates; printing a resistor on the white ceramic chip in a screen printing mode; different punching densities are realized on the white ceramic chip, and the bushing plate is used for filling holes; different sizes of cavities are realized on the white porcelain piece; and carrying out orthogonal tests to obtain the shrinkage values respectively, and obtaining data of the influence of each slurry coverage rate, resistance coverage rate, hole density and cavity density on the shrinkage.
Compared with the prior art, the invention has the following advantages:
(1) Aiming at the problem that the shrinkage rate of different LTCC products cannot be accurately known before production, the invention confirms the factors influencing the shrinkage rate from the design and process of the LTCC products, establishes a mathematical model between the influencing factors and the shrinkage rate by using a neural network technology, and realizes the accurate prediction of the shrinkage rate of the LTCC products.
(2) According to the invention, the neural network is trained by using historical data, so that a mature neural network model is obtained, the shrinkage rate is rapidly and accurately predicted, and the shrinkage rate is prevented from being out of control.
(3) The invention ensures the success rate of one-time production for small-batch products and products of an all-gold system.
Drawings
FIG. 1 is a schematic diagram of a conventional process flow of LTCC of the present invention;
FIG. 2 is a graph showing the effect of different factors on shrinkage in the X direction;
FIG. 3 is a diagram showing statistical examples of Ferro-based product data;
FIG. 4 is a schematic diagram of a neural network verification experiment training process;
FIG. 5 is a schematic diagram of the accuracy of the neural network verification experiment training results;
fig. 6 is a structural diagram of a neural network model.
Detailed Description
The idea of the invention is as follows: 1. confirming factors affecting shrinkage; 2. and establishing a mathematical model corresponding relation between the influence factors and the shrinkage according to data generated by the production line history. The invention will take Ferro material in LTCC material system as an example, and specific implementation way will be described.
1. Factors affecting shrinkage are identified, typically including slurry material, pore density, cavity density.
As shown in figure 1, the operations related to the green porcelain are all located before the 9 th step of low-temperature co-firing, and the operations comprise green porcelain falling, green porcelain punching, through hole filling, conductor printing, secondary cavity opening, green porcelain stacking, green porcelain pressing and green porcelain cutting. The process parameters of these operations are set, the main differences being the type of slurry used, the open cell and the density of the perforations for each product. Therefore, first a single experiment of these factors was performed, and only the slurries commonly used in the production line were considered in the present invention, in view of the numerous slurries used in the Ferro system. In order to be close to the practical application, three different silk screens are used in a single experiment, and squares of 10mm by 10mm, 5mm by 5mm and 1mm by 1mm are respectively distributed on the upper sides of the silk screens and are respectively named as L, M, S type silk screens.
Different silk screens are matched with different sizing agents, resistors are matched with the silk screens to be printed on the white porcelain piece, different punching densities are realized on the white porcelain piece, and a bushing is used for filling gaps; different sizes of cavities are realized on the white ceramic chip, orthogonal tests are respectively carried out, and shrinkage values are respectively obtained.
The specific items to be examined are shown in Table 1.
TABLE 1
Figure SMS_8
Figure SMS_9
Since the LTCC is also co-fired after being cut in the actual production process, and the situation of full-page co-firing is rarely adopted, the experiment adopts full-page printing, the method is divided into four and then laminated, and the specific flow of the orthogonal experiment is as follows:
TABLE 2
Figure SMS_10
After cofiring, the invention performs statistics on single test results, as shown in table 3:
TABLE 3 Table 3
Figure SMS_11
Taking X direction as an example, the data of single test of different projects are counted, and a histogram is listed
(FIG. 2) to illustrate the effect of different items on shrinkage.
The shrinkage nominal value given by the Ferro manufacturer is: 84%, the data obtained by the experiment on the white ceramic chip is 84.68%, which basically accords with the nominal value, namely the shrinkage reference line of the white ceramic chip shown by the dotted line in fig. 2, and it can be seen that the slurry CN30-080, the slurry CN36-020 and the resistor FX87-101B of the 'Qiangqian' are the biggest from the reference line and are all prevented from shrinking, and the experience is the same as the experience of the production line in the use process, so that the slurry CN30-080, the slurry CN36-020 and the resistor cannot be used in a large area, and the slurry is easy to warp. Meanwhile, for the 'Gentle pie' slurry CN30-025 and CN30-078, the slurry is basically fused with white flakes. Solder mask DL10-088 has substantially no effect on the tile, while the cavity is the only factor contributing to tile shrinkage.
Accordingly, the present invention combes and confirms the main factors affecting shrinkage: slurry CN30-080 coverage, slurry CN30-025 coverage, slurry CN36-020 coverage, solder resist slurry (DL 10-088) coverage, resistance slurry coverage, hole density and cavity density, and the total number of the slurry is 7. Based on this, each LTCC product has its own process parameter attributes.
2. And establishing a mathematical model between the influencing factors and the shrinkage, and training the neural network according to the historical data of the production line.
In recent years, neural network technology is one of the hot spots of research at home and abroad. The neural network has the advantages of self-learning function, associative storage function and high-speed searching for an optimal solution, and is widely applied to aspects of image recognition and processing, semiconductor device modeling, future prediction and the like. In view of its excellent data processing capability and modeling flexibility, the present invention uses neural network techniques to build a mathematical model between influencing factors and shrinkage.
Because LTCC is a multi-layer structure, each layer of circuit is relatively independent, the processes undergone by each layer of raw ceramic chip are basically printing metal paste, solder resist, resistance, punching, cavity opening and the like, and each layer is possible to be a surface layer due to the cavity opening, the invention is provided with the same input data format for each layer: slurry CN30-080 coverage, slurry CN30-025 coverage, slurry CN36-020 coverage, solder resist slurry coverage, resistance slurry coverage, hole density and cavity density, and the total of 7 variables.
In order to facilitate the statistics of process personnel, the conventional LTCC products are provided with 21 layers, the upper limit of the data quantity is assumed to be 21 layers, namely the total input data number of the data model is 21×7=147 data, the products with the layers less than 21 layers are correspondingly complemented with 0 in the blank layer, and the output data are 2 data in total. The input data statistics are shown in figure 3.
The input signal of the neural network model is a variable affecting the shrinkage, and is denoted as i= [ I ] 1 ,I 2 ,I 3 ,······I 147 ] T The input signals of the neural network model are output data, namely X-direction shrinkage and Y-direction shrinkage, and are marked as O= [ X, Y] T .
The structure of the neural network model is shown in fig. 6, and the nonlinear formulas of input and output are:
Figure SMS_12
Figure SMS_13
where p represents the number of hidden layer neurons.
Figure SMS_14
Representing the weight parameter between the mth input neuron and the ith hidden neuron,/and (ii)>
Figure SMS_15
Is a weight parameter between the 1 st output neural network and the i-th neuron in the hidden layer.
Figure SMS_16
Is a weight parameter between the 2 nd output neural network and the i-th neuron in the hidden layer. />
Figure SMS_17
And->
Figure SMS_18
The bias weight values of the 1 st output neuron and the 2 nd output neuron are respectively represented. sigmoid function formula is sigma (gamma) =1/(1+e) )。
In fig. 3, each of the behaviors is a product (corresponding to a process number), each product has 21 layers, and each layer contains data as follows: CN30-080 coverage, CN30-025 coverage, CN36-020 coverage, solder resist coverage, resistance coverage, hole density and cavity density. After this data structure is determined, the present invention builds a neural network model. The neural network model is written by Java, has good compatibility with each platform, and is secondarily packaged into a Matlab program for facilitating the use of the craftsman, so that the craftsman can conveniently modify parameters in the Matlab program.
The procedure is very compact and contains a total of 3 main files:
Figure SMS_19
data: training data and test data for use with the neural network are included.
Figure SMS_20
Main function: the neural network parameters may be set, including data structures, neuron numbers, training data amounts, test data amounts, and the like.
Figure SMS_21
Track file: for running neural network training and testing programs.
By learning the line history data, the neural network can be used to predict LTCC shrinkage of newly manufactured products, and the invention uses the process number L17036 product to test the neural network model. The actual measured shrinkage of the L17036 product was 84.08% and 84.13%. The data of L17036 was used as test data, never appeared during the training process, nor was it entered into the training sample library in any form to ensure the correctness of the verification.
First, a neural network is set:
Figure SMS_22
input data column number i=147;
Figure SMS_23
the number of output data o=3;
Figure SMS_24
implicit neuron number h=15;
Figure SMS_25
training set number t=31;
Figure SMS_26
the number of test data e=1;
Figure SMS_27
training;
both training data and test data (L17036) are placed in the data file for a total of 32 rows of data, with the first 31 rows of training data and the last row being test data L17036, i.e. t=31 and e=1 inside is set.
Running the program, the neural network reaches the accuracy requirement after 10 iterations, the training and the prejudgment of the neural network are completed, and the training accuracy reaches 10 -6 As shown in fig. 4 and 5:
for the test data, the estimated shrinkage rates are 84.102% and 84.1822%, and the output result and the actual measurement result are compared:
X Y
neural network prejudgment 84.1020 84.1822
Actual measured value 84.08 84.13
Error of 0.022% 0.1522%
It can be seen that the neural network has given very good pre-judgment in the X and Y directions, is better than the error level of +/-2%, meets the set requirements, and realizes the function of accurately estimating the shrinkage rate of each product. And the shrinkage rate of the newly-produced LTCC product is estimated by using a neural network, and the estimated efficiency and the estimated accuracy are satisfactory.
In another embodiment, a polynomial fitting mode may be used to obtain a mathematical model between the influencing factors and the shrinkage, and the shrinkage is estimated mathematically.
The invention fundamentally turns the situation that the shrinkage ratio pre-judging result is out of control by process staff, so that each product has relative accurate LTCC shrinkage ratio data, and the quality of the LTCC product is improved substantially.
The foregoing is merely illustrative of the best embodiments of the present invention, and the present invention is not limited thereto, but any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be construed as falling within the scope of the present invention.
What is not described in detail in the present specification belongs to the known technology of those skilled in the art.

Claims (9)

1. The LTCC shrinkage pre-judging method based on the neural network technology is characterized by comprising the following steps of:
(1) Determining each influencing factor of the shrinkage through an orthogonal test;
(2) Taking each influence factor as a structural parameter, and establishing an influence factor list for each layer of LTCC;
(3) Setting a neural network, and training the neural network according to historical data of a production line to obtain a shrinkage rate prediction model; the method for obtaining the shrinkage prediction model comprises the following steps:
3.1, constructing a three-layer artificial neural network, and dividing the three-layer artificial neural network into three parts: the first layer is input neuron for receiving each influencing factor of shrinkage, the second layer is hidden neuron for processing nonlinear relation of input and output, and the third layer is output neuron for outputting LTCC shrinkage;
3.2, utilizing the historical data of the production line to adjust the weight value in the neural network, so that the output of the model is consistent with the historical shrinkage rate data;
3.3, verifying the accuracy of the shrinkage rate of the neural network model by using unused production line history data; when the error between the output of the model and the historical shrinkage rate data meets the requirement, completing modeling, otherwise returning to 3.1, and adjusting the number of the hidden neurons;
(4) And predicting the shrinkage of the LTCC product by using a shrinkage prediction model.
2. The LTCC shrinkage prediction method based on neural network technology as claimed in claim 1, wherein each influencing factor of shrinkage comprises: metal paste coverage, resistive paste coverage, pore density, and cavity density are commonly used.
3. The LTCC shrinkage prediction method based on neural network technology according to claim 2, wherein the common slurry and the resistive slurry coverage include slurry CN30-080 coverage, slurry CN30-025 coverage, slurry CN36-020 coverage, slurry DL10-088 coverage, and slurry FX87-101B coverage.
4. The neural network technology-based LTCC shrinkage prediction method of claim 1, wherein the orthogonal test comprises setting different coverage rates for different slurries with corresponding screens; printing a resistor on the white ceramic chip in a screen printing mode; different punching densities are realized on the white ceramic chip, and the bushing plate is used for filling holes; different sizes of cavities are realized on the white porcelain piece; and performing orthogonal tests to obtain shrinkage values and historical data of the production line.
5. The LTCC shrinkage prediction method based on neural network technology according to claim 1, wherein for the Ferro material, the orthogonal test steps are as follows:
1.1, preparing 24 white porcelain tiles of 8 inches, corresponding to one bushing plate of a punching diagram, printing one silk screen L of a large-area diagram, printing one silk screen M of a medium-area diagram, and printing one silk screen S of a small-area diagram;
1.2 taking 3 Bai Ci sheets for punching, and filling holes by using slurry CN30-078 and a bushing plate to obtain a group 1;
3 sheets of Bai Ci sheets were taken and used as set 2 using screen L printing paste CN 30-080;
3 sheets of Bai Ci sheets were taken and screen L printing paste CN30-025 was used as group 3;
3 sheets of Bai Ci sheets were taken and screen M printing paste CN36-020 was used as set 4;
3 sheets of Bai Ci sheets were taken and screen S printing paste DL10-088 was used as set 5;
3 sheets of Bai Ci sheets were taken and screen S printing paste FX87-101B was used as set 6;
1.3, dividing each of the 24 white porcelain tiles into four blocks;
1.4, respectively stacking 12 1/4 blocks divided into groups 1-6;
1.5 taking 3 Bai Ci pieces and 12 1/4 pieces divided into pieces to be stacked together to be used as a group 7;
1.6, taking 3 Bai Ci pieces, dividing into 12 pieces of 1/4 pieces, stacking together, and processing through cavities by laser to obtain a group 8;
1.7 dividing each block in groups 1-8 into four;
1.8 measurement of the product sizes of groups 1-8, firing one product per group, and measuring shrinkage.
6. The LTCC shrinkage pre-determination method based on neural network technology as claimed in claim 1, wherein the input signal of the shrinkage prediction model is a variable affecting the shrinkage, denoted as i= [ I ] 1 ,I 2 ,I 3 ,·····I 147 ] T The input signals of the neural network model are output data, namely X-direction shrinkage and Y-direction shrinkage, and are marked as O= [ X, Y] T The method comprises the steps of carrying out a first treatment on the surface of the The nonlinear formulas of input and output are:
Figure FDA0004045684800000031
Figure FDA0004045684800000032
where p represents the number of hidden layer neurons,
Figure FDA0004045684800000033
representing the weight parameter between the mth input neuron and the ith hidden neuron,/and (ii)>
Figure FDA0004045684800000034
Is a weight parameter between the 1 st output neural network and the i-th neuron in the hidden layer,/i>
Figure FDA0004045684800000035
Is a weight parameter between the 2 nd output neural network and the i th neuron in the hidden layer,/o>
Figure FDA0004045684800000036
And->
Figure FDA0004045684800000037
The bias weight values of the 1 st output neuron and the 2 nd output neuron are respectively expressed, and the sigmoid function formula is sigma (gamma) =1/(1+e) )。
7. The LTCC shrinkage pre-judging method based on the neural network technology is characterized by comprising the following steps of:
(1) Determining the influence of the coverage rate of common metal slurry, the coverage rate of resistance slurry, the density of holes and the density of cavities required by production on the shrinkage rate through orthogonal experiments;
(2) Respectively establishing a shrinkage prediction model according to the slurry coverage rate, the resistance coverage rate, the hole density and the cavity density of each layer; the shrinkage rate prediction model is established as follows:
2.1, constructing a three-layer artificial neural network, and dividing the three-layer artificial neural network into three parts: the first layer is input neuron for receiving each influencing factor of shrinkage, the second layer is hidden neuron for processing nonlinear relation of input and output, and the third layer is output neuron for outputting LTCC shrinkage;
2.2, utilizing the historical data of the production line to adjust the weight value in the neural network, so that the output of the model is consistent with the historical shrinkage rate data;
2.3, verifying the accuracy of the shrinkage rate of the neural network model by using unused production line history data; when the error between the output of the model and the historical shrinkage rate data meets the requirement, completing modeling, otherwise returning to 2.1, and adjusting the number of the hidden neurons;
(3) And predicting the shrinkage of the LTCC product by using a shrinkage prediction model of each layer.
8. The LTCC shrinkage prediction method based on neural network technology according to claim 7, wherein the production of the required common metal paste and resistance paste comprises paste CN30-080, paste CN30-025, paste CN36-020 and paste DL10-088.
9. The neural network technology-based LTCC shrinkage prediction method of claim 7, wherein the orthogonal test comprises setting different coverage rates for different slurries with corresponding screens; printing a resistor on the white ceramic chip in a screen printing mode; different punching densities are realized on the white ceramic chip, and the bushing plate is used for filling holes; different sizes of cavities are realized on the white porcelain piece; and carrying out orthogonal tests to obtain the shrinkage values respectively, and obtaining data of the influence of each slurry coverage rate, resistance coverage rate, hole density and cavity density on the shrinkage.
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