Polycrystalline silicon resistivity detection method based on principal component analysis and neural network model

Abstract

The invention relates to a polycrystalline silicon resistivity detection method based on principal component analysis and a neural network model, which comprises the following steps: acquiring daily total analysis detection data of tower bottoms of a heavy component removal tower in a historical rectification section and resistivity data of discharged finished products of a reduction furnace, removing most samples, replacing undetected data with 1 / 2 of detection limit, and calculating the resistivity of the finished products of the heavy component removal tower; obtaining a data set Xi and finished product resistivity data Y; carrying out standardization processing and principal component analysis on the data set Xi to obtain a principal component function and a data set Fi; acquiring a data set F'i and finished product resistivity data Y 'according to the data set Fi and the finished product resistivity data Y, establishing a corresponding relation between the finished product resistivity data Y' and the data set F'i, and constructing an ANN neural network model to obtain a model NET; and carrying out standardization processing on daily total analysis detection data of the tower bottoms of the heavy component removal tower in the new rectification section, substituting the data into the principal component function to obtain a data set Fnew, outputting the data set Fnew to the model NET to obtain the resistivity rho'of furnace polycrystalline silicon, and correcting to obtain the furnace discharge resistivity rho on the current day. The problems of hysteresis and the like in the prior art are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of polysilicon, and in particular relates to a polysilicon resistivity detection method based on principal component analysis and a neural network model. Background Art

[0002] At present, the production process of electronic-grade polysilicon is mainly based on the modified Siemens method, and its main process is: silicon powder reacts with hydrogen chloride and hydrogen in a cold hydrogenation synthesis furnace to produce a mixture of chlorosilanes such as trichlorosilane (TCS) and silicon tetrachloride, and recovers chlorosilanes from the tail gas of the reduction process to form a material cycle. Impurities such as B and P enter the distillation system together with silicon powder and material cycles. The high-purity trichlorosilane obtained in the distillation section is reduced by hydrogen on the surface of the high-temperature silicon core and gradually deposited into silicon rods to obtain polysilicon products.

[0003] Due to the batch fluctuations in the content of B, P and metal impurities in the cold hydrogenation raw silicon powder, the dynamic characteristics of the production process make it impossible to maintain a stable quality of high-purity TCS in the distillation section, and whether the hydrogen in the tail gas recovery section contains PH3 will directly affect the quality of the finished polysilicon. Because the finished polysilicon needs to go through a vapor deposition process of about 100 hours, the physical and chemical indicators are difficult to measure online, so the prediction of the resistivity of the finished product is extremely important.

[0004] At present, in production, the impurity content in the high-purity TCS buffer tank entering the reduction furnace is usually tested on a daily basis. Combined with the resistivity data of the finished product after the furnace is shut down, the impurity removal level of the distillation and tail gas is manually judged, and the distillation operation is adjusted. However, the existing technology has the following problems: (1) The use of this strategy in production has obvious lag, and the quality of the finished product that has been discharged from the furnace is a fact, and there is no possibility of making up for it. (2) The key indicator monitoring point detection of the distillation section in production is based on experience combined with the resistivity of the finished product to judge the operating level of the distillation. This method is heavily dependent on the experience of the operator. Because the resistivity of the finished product is not linearly related to many impurity detection items, the manual judgment results are also prone to errors, resulting in frequent quality accidents. Therefore, there is an urgent need for a polysilicon resistivity detection method that can be dynamically monitored, does not rely on manual judgment, and can achieve standardization.

[0005] In view of this, the present invention proposes a polysilicon resistivity detection method based on principal component analysis and a neural network model, which is not dependent on the operator's experience and can realize a standardized polysilicon finished product resistivity prediction method. Summary of the invention

[0006] The purpose of the present invention is to provide a polysilicon resistivity detection method based on principal component analysis and a neural network model. The detection method provides an effective polysilicon finished product resistivity prediction method based on the characteristics of the polysilicon production process and the current situation that the finished product resistance cannot be detected, thereby solving the problems of hysteresis and poor accuracy in the prior art.

[0007] In order to achieve the above purpose, the technical solution adopted is:

[0008] A polysilicon resistivity detection method based on principal component analysis and neural network model comprises the following steps:

[0009] S10: Obtain the historical daily full analysis test data of the bottom liquid of the deweighting tower in the distillation section and the resistivity data of the finished product discharged from the reduction furnace;

[0010] S20: After removing the majority of samples from the daily full analysis test data of the bottom liquid of the deweighting tower in the distillation section and the resistivity data of the finished product, a full analysis test data set and resistivity data of the finished product Y are obtained;

[0011] S30: The full analysis detection data set is replaced with 1 / 2 of the detection limit of the analytical instrument to obtain the data set X i ;

[0012] S40: for the data set X i After standardization, principal component analysis is performed to obtain the principal components and their corresponding eigenvalues, load coefficients, contribution rates, principal component functions, and the reduced-dimensional data set F i ;

[0013] S50: According to the data set F i , get the data set F' of the average value of the same furnace i Then, according to the finished product resistivity data Y, obtain the finished product resistivity data Y' of the last day of the same furnace, and establish the finished product resistivity data Y' and the data set F' i The corresponding relationship;

[0014] S60: Build ANN neural network model and set data set F' i is the input layer, Y' is the output layer, and the model NET is obtained;

[0015] S70: Collect the daily full analysis test data of the bottom liquid of the new distillation section de-weighting tower, standardize it, and substitute it into the principal component function to obtain the real-time data set F new ;

[0016] S80: The real-time data set F new Input into the model NET to obtain the resistivity ρ' of furnace polysilicon;

[0017] S90: After the out-of-furnace resistivity ρ' is corrected, the out-of-furnace resistivity ρ on the same day is obtained.

[0018] Furthermore, in the step S10, the bottom liquid of the deweighting tower in the distillation section is fully analyzed and tested every day, including the impurity content of Ti, Ni, Cr, Zn, Mn, Cu, Ca, As, Al, Fe, P, and B.

[0019] Furthermore, in the step S20, under-sampling is adopted to randomly remove the majority class samples;

[0020] In step S40, the formula for standardization is as follows:

[0021] Standardized dataset In the formula, i=80, k=12.

[0022] Furthermore, in the step S20, samples are taken from 0 to 8000 at intervals of 1000 Ω·cm, with 10 samples in each interval.

[0023] Furthermore, in step S40, according to the principle that the eigenvalue is greater than 1, the principal component is extracted to obtain the principal component function and the reduced-dimensional data set F i ;

[0024] The principal component eigenvector Φ is the corresponding load coefficient divided by the square root of the eigenvalue. The principal component eigenvector Φ is multiplied by the standardized data set to obtain the reduced-dimensional data set F. i .

[0025] Furthermore, in step S40, the main components are selected in descending order of contribution rate, and the cumulative contribution rate is not less than 0.9.

[0026] Furthermore, in step S50, the data of the current day and the data of the previous three days, a total of four days, are averaged. Where, 4≤i≤n;

[0027] In step S60, the ANN neural network model includes: an input layer, a training set, a test set, a hidden layer and an output layer.

[0028] Furthermore, the step S60 also includes training the model with training set data and testing the model with test set data until the training and testing results are good, thereby obtaining the model NET.

[0029] Furthermore, the training set data accounts for 60-70% of the total data, and the training method is the Levenberg-Marguardt method;

[0030] When the correlation coefficients of the training set, test set, and validation set are all greater than 0.9, the training and testing results are good, and the model training is completed.

[0031] Furthermore, in the step S90, the formula of the corrected resistivity ρ of the day is: ρ=θρ'+100;

[0032] Wherein, θ is the correction term. When PH3 is detected in hydrogen, θ=0, otherwise θ=1.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. The present invention provides a polysilicon resistivity detection method based on principal component analysis and neural network model, which can predict the resistivity of finished products according to the detection data of the bottom liquid of the deweighting tower in the distillation section, thereby avoiding the delay caused by detecting the resistivity of finished products after the silicon rods are out of the furnace.

[0035] 2. The present invention provides a polysilicon resistivity detection method based on principal component analysis and neural network model, which can timely correct distillation parameters and tail gas parameters by predicting the resistivity of finished products, thereby improving the purity of high-purity trichlorosilane entering the reduction furnace and reducing the defective rate.

[0036] 3. The present invention provides a polysilicon resistivity detection method based on principal component analysis and neural network model, which is not dependent on the operator's experience and can achieve standardized resistivity prediction of polysilicon finished products. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flow chart of the present invention;

[0038] Figure 2 This is a graph of the experimental results. DETAILED DESCRIPTION

[0039] In order to further explain the polysilicon resistivity detection method based on principal component analysis and neural network model of the present invention and achieve the expected purpose of the invention, the following is a detailed description of the specific implementation method, structure, characteristics and efficacy of the polysilicon resistivity detection method based on principal component analysis and neural network model proposed by the present invention in combination with the preferred embodiment. In the following description, different "one embodiment" or "embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0040] The following will further introduce in detail a polysilicon resistivity detection method based on principal component analysis and neural network model of the present invention in conjunction with specific embodiments:

[0041] There is no method for predicting the resistivity of finished polysilicon products in the prior art. There is a method in the prior art that combines principal component analysis with a neural network model to predict the quality of other chemical products or process products. Principal component analysis is a dimensionality reduction method that extracts the main components from many influencing factors, while the neural network model is a nonlinear regression model based on big data with good convergence and small evaluation error. Based on this, the present invention uses principal component analysis and neural network models for polysilicon resistivity detection. However, the reason why the existing principal component analysis combined with neural network model technology has not been applied in the polysilicon industry is related to the characteristics of the polysilicon industry. When the applicant used it for polysilicon resistivity detection, he found the following problems:

[0042] (1) The high-purity TCS sampled from the reduction furnace has a low metal impurity content, close to or below the detection limit, resulting in inaccurate analysis results and the model training failing to converge.

[0043] (2) In most cases of historical data, the resistivity of polysilicon is at a high value, there are few low-resistivity samples, and the data is uneven. The principal component analysis algorithm is sensitive to the distribution of data. If the data is uneven, it will affect the effect of the algorithm.

[0044] (3) The metal impurity content in high-purity TCS can be regarded as a changing continuous variable, while the PH3 in the tail gas recovery hydrogen is only marked as detected or not detected and can be regarded as a discrete variable. However, the principal component analysis method cannot reduce the dimension of continuous variables and discrete variables at the same time.

[0045] The applicant conducted further research and proposed a polysilicon resistivity detection method based on principal component analysis and neural network model as described in the present invention. The technical solution of the present invention is:

[0046] A polysilicon resistivity detection method based on principal component analysis and neural network model comprises the following steps:

[0047] S10: Obtain the historical daily full analysis test data of the bottom liquid of the deweighting tower in the distillation section and the resistivity data of the finished product discharged from the reduction furnace;

[0048] S20: After removing the majority of samples from the daily full analysis test data of the bottom liquid of the deweighting tower in the distillation section and the resistivity data of the finished product, a full analysis test data set and resistivity data of the finished product Y are obtained;

[0049] S30: The full analysis detection data set is replaced with 1 / 2 of the detection limit of the analytical instrument to obtain the data set X i ;

[0050] S40: for the data set X i After standardization, principal component analysis is performed to obtain the principal components and their corresponding eigenvalues, load coefficients, contribution rates, principal component functions, and the reduced-dimensional data set Fi ;

[0051] S50: According to the data set F i , get the data set F' of the average value of the same furnace i Then, according to the finished product resistivity data Y, obtain the finished product resistivity data Y' of the last day of the same furnace, and establish the finished product resistivity data Y' and the data set F' i The corresponding relationship;

[0052] S60: Build ANN neural network model and set data set F' i is the input layer, Y' is the output layer, and the model NET is obtained;

[0053] S70: Collect the daily full analysis test data of the bottom liquid of the new distillation section de-weighting tower, standardize it, and substitute it into the principal component function to obtain the real-time data set F new ;

[0054] S80: The real-time data set F new Input into the model NET to obtain the resistivity ρ of furnace polysilicon ’ ;

[0055] S90: After the out-of-furnace resistivity ρ' is corrected, the out-of-furnace resistivity ρ on the same day is obtained.

[0056] In the above technical solution, the improvements are as follows:

[0057] (1) Since the impurity content of the sample introduced into the reduction furnace is low, the process from the reduction furnace to the deweighting tower in the distillation section is stable. Therefore, the present invention moves the sampling point forward to the bottom liquid of the deweighting tower in the distillation section to obtain effective impurity content data.

[0058] (2) The present invention moves the sampling point forward to the bottom liquid of the de-weighting tower in the distillation section. Although most of the valid data can be obtained, there are still data close to or below the detection limit. The present invention replaces the "undetected" data with 1 / 2 of the detection limit of the analytical instrument, avoiding the influence of invalid data on the analysis results.

[0059] (3) The present invention achieves sample balance by randomly removing some majority class samples according to the resistivity gradient of the finished product through under-sampling.

[0060] Preferably, in step S10, the bottom liquid of the deweighting tower in the distillation section is fully analyzed and tested every day, including the impurity contents of Ti, Ni, Cr, Zn, Mn, Cu, Ca, As, Al, Fe, P, B, etc.

[0061] Preferably, in step S20, under-sampling is adopted to randomly remove majority class samples;

[0062] In step S40, the formula for standardization is as follows:

[0063] Standardized dataset In the formula, i=80, k=12.

[0064] Further preferably, in the step S20, samples are taken from 0 to 8000 at intervals of 1000 Ω·cm, with 10 samples in each interval.

[0065] Preferably, in step S40, according to the principle of eigenvalue>1, the principal component is extracted to obtain the principal component function and the reduced-dimensional data set F i ;

[0066] The principal component eigenvector Φ is the corresponding load coefficient divided by the square root of the eigenvalue. The principal component eigenvector Φ is multiplied by the standardized data set to obtain the reduced-dimensional data set F. i .

[0067] Further preferably, in step S40, the main components are selected in descending order of contribution rate, and the cumulative contribution rate is not less than 0.9.

[0068] Preferably, in step S50, the data of the current day and the data of the previous three days, a total of four days, are averaged. Where, 4≤i≤n;

[0069] In step S60, the ANN neural network model includes: an input layer, a training set, a test set, a hidden layer and an output layer.

[0070] Preferably, the step S60 further includes training the model with training set data and testing the model with test set data until the training and testing results are good, thereby obtaining the model NET.

[0071] Further preferably, the training set data accounts for 60-70% of the total data, and the training method is the Levenberg-Marguardt method;

[0072] When the correlation coefficients of the training set, test set, and validation set are all greater than 0.9, the training and testing results are good, and the model training is completed.

[0073] Preferably, in the step S90, the formula of the corrected resistivity ρ of the day is: ρ=θρ'+100;

[0074] Wherein, θ is the correction term. When PH3 is detected in hydrogen, θ=0, otherwise θ=1.

[0075] In the above technical solution, PH3 detection in hydrogen is used as correction. When PH3 is detected in hydrogen, the polysilicon product in this reduction furnace can be directly judged as unqualified. Therefore, the present invention can achieve the effect of accurately judging the quality of polysilicon by using PH3 detection in hydrogen as correction.

[0076] Example 1.

[0077] Combination Figure 1 , the specific steps are as follows:

[0078] S1: Obtain the daily full analysis results of the deweighting tower bottom liquid in the distillation section of the polysilicon production process and the historical data of the finished products discharged from the reduction furnace. Specific:

[0079] Through the LIMS system interface, the detection data of the bottom liquid of the deweighting tower in the distillation section in the past three years were obtained, including the contents of 12 impurities such as Ti, Ni, Cr, Zn, Mn, Cu, Ca, As, Al, Fe, P, and B, which were recorded as X. n =[X n (1),X n (2(,…X n (m)]; where n is the batch and m represents the impurity element.

[0080] Collect the finished product resistivity data of the reduction furnace of the corresponding production line in the past three years.

[0081] S2: The daily full analysis results of the deweighting tower bottom liquid in the distillation section of the polysilicon production process and the historical data of the finished products from the reduction furnace are taken through under-sampling. According to the resistivity gradient of the finished products, some majority samples are randomly removed to achieve sample balance.

[0082] Samples are taken from 0 to 8000 at intervals of 1000 Ω·cm, with 10 samples in each interval, recorded as X n '; The corresponding finished product resistivity data of the reduction furnace of the production line is Y = [Y(1), Y(2), ...Y(k)].

[0083] S3: Replace data set X with 1 / 2 of the detection limit of the analytical instrument n 'The "undetected" data in the dataset X i , X i =[X i (1),X i (2),…X i (k)], i=80, k=12.

[0084] S4: For dataset X i Standardize and use the following formula to get the standardized data set X' i .

[0085]

[0086] S5: The standardized data set X' obtained based on S40 i , perform principal component analysis to obtain the principal components and their corresponding eigenvalues, contribution rates, principal component functions, and the reduced-dimensional data set F i Specifically: The principal component analysis method is used to comprehensively evaluate the above samples and 12 test items, and the standardized data set X' i Perform principal component analysis to obtain the principal components and their corresponding eigenvalues, load coefficients, contribution rates, and cumulative contribution rates. Extract the principal components based on the principle that the eigenvalue is greater than 1; and the principal components are selected in descending order of contribution rate, with a cumulative contribution rate of no less than 0.9.

[0087] The principal component eigenvector Φ is equal to the corresponding load coefficient divided by the square root of the eigenvalue, that is

[0088] Dataset F i Establishment: The obtained eigenvector Φ is combined with the standardized variable X' i Multiply them together to get the reduced dimension dataset F i =ΦX' i .

[0089] S6: Since the reduction furnace vapor deposition time is about 4 days, based on the data set F i , find the average value of the data set F' for 4 consecutive days i That is, according to the data set F i , get the data set F' of the average value of the same furnace i Then, the finished resistor data set Y' for the day and the average data set F' for the previous 4 days are established. i Specific:

[0090] Average the data of the current day and the data of the previous three days, a total of four days. Where 4≤i≤n, we get a new data set F' i . Delete the first three days of data in the finished product resistivity data set Y to obtain data sets Y' and F' i The number of data in the data set Y' is the same as that in the data set Y', so the finished resistor data set Y' and data set F' are established for that day. i The corresponding relationship.

[0091] S7: Based on the finished resistor data set Y' and data set F' i The corresponding relationship between F' and ANN neural network model is constructed, including input layer, training set, test set, hidden layer and output layer. i is the input layer, and Y' is the output layer. Specifically:

[0092] Build an ANN neural network model and set F' i is the input layer, Y' is the output layer, the number of hidden layers is set to 10, the number of training sets is 50, the number of test sets and validation sets is 15 each, the loss function of the model is set to root mean square error, and the training method is Levenberg-Marguardt.

[0093] S8: Train the model with training data and test the model with test data. If the training and test results are good, save the model NET; otherwise, retrain and test until the results are good.

[0094] Taking the correlation coefficient>0.9 as the model training result standard, the finished product resistivity prediction model NET based on principal component analysis and ANN neural network was obtained.

[0095] S9: Collect the daily full analysis results of the bottom liquid of the new de-weighting tower in the distillation section and standardize them. For the newly collected samples in the process, they need to be standardized, that is, the content of each component is divided by the mean value when modeling.

[0096] S10: Substitute the standardized new data obtained in S9 into the principal component function expression generated in step S5 (data set F i =ΦX' i ), get the real-time data set, and get the prediction input layer F new .

[0097] S11: Input layer F new The data was imported into the NET model to obtain the resistivity ρ' of the polysilicon produced on that day.

[0098] S12: Define the correction term θ. If PH3 is detected in hydrogen during the day, θ=0, otherwise θ=1.

[0099] S13: The corrected resistivity of the product out of the furnace on the same day is ρ=θρ'+100.

[0100] The resistivity of the product in the reduction furnace of a production line in Daquan, Inner Mongolia was predicted using the method of Example 1 for a period of 98 days. The predicted value was compared with the actual value, and the results were as follows: Figure 2 shown.

[0101] Figure 2 A comparison between the model training prediction value and the actual value of the method is given. It can be seen that the method of the present invention has a good effect on the prediction of the resistivity of the finished product and can better reflect the change trend of the resistivity of the finished product.

[0102] Example 2.

[0103] The steps of Example 2 are the same as those of Example 1, except that S11: after obtaining the resistivity ρ' of the polysilicon discharged on the day, the resistivity data prediction value of the day and the resistivity data predicted for the previous three days are averaged to obtain the average resistivity data of the silicon rods stopped on the day. Corrected resistivity of the same day

[0104] By obtaining resistivity data from the same furnace for four days, the quality of polysilicon finished products can be better monitored.

[0105] The above is only a preferred embodiment of the embodiment of the present invention, and does not impose any form of limitation on the embodiment of the present invention. Any simple modification, equivalent changes and modifications made to the above embodiment based on the technical essence of the embodiment of the present invention are still within the scope of the technical solution of the embodiment of the present invention.

Claims

1. A polysilicon resistivity detection method based on principal component analysis and neural network model, characterized in that: The following steps are involved: S10: Obtain the historical daily full analysis test data of the bottom liquid of the deweighting tower in the distillation section and the resistivity data of the finished product discharged from the reduction furnace; S20: After removing the majority of samples from the daily full analysis test data of the bottom liquid of the deweighting tower in the distillation section and the resistivity data of the finished product, a full analysis test data set and resistivity data of the finished product Y are obtained; S30: The full analysis detection data set is replaced with 1 / 2 of the detection limit of the analytical instrument to obtain the data set X i ; S40: for the data set X i After standardization, principal component analysis is performed to obtain the principal components and their corresponding eigenvalues, load coefficients, contribution rates, principal component functions, and the reduced-dimensional data set F i ; S50: According to the data set F i , get the data set F' of the average value of the same furnace i Then, according to the finished product resistivity data Y, obtain the finished product resistivity data Y' of the last day of the same furnace, and establish the finished product resistivity data Y' and the data set F' i The corresponding relationship; S60: Build ANN neural network model and set data set F' i is the input layer, Y' is the output layer, and the model NET is obtained; S70: Collect the daily full analysis test data of the bottom liquid of the new distillation section de-weighting tower, standardize it, and substitute it into the principal component function to obtain the real-time data set F new ; S80: The real-time data set F new Input into the model NET to obtain the resistivity ρ' of furnace polysilicon; S90: After the out-of-furnace resistivity ρ' is corrected, the out-of-furnace resistivity ρ on the same day is obtained.

2. The polysilicon resistivity detection method according to claim 1, characterized in that: In the step S10, the bottom liquid of the deweighting tower in the distillation section is fully analyzed and tested every day, including the impurity content of Ti, Ni, Cr, Zn, Mn, Cu, Ca, As, Al, Fe, P, and B.

3. The polysilicon resistivity detection method according to claim 1, characterized in that: In the step S20, under-sampling is adopted to randomly remove majority class samples; In step S40, the formula for standardization is as follows: Standardized dataset In the formula, i=80, k=12.

4. The polysilicon resistivity detection method according to claim 3, characterized in that: In the step S20, samples are taken from 0 to 8000 at intervals of 1000 Ω·cm, with 10 samples in each interval.

5. The polysilicon resistivity detection method according to claim 1, characterized in that: In step S40, according to the principle of eigenvalue>1, the principal component is extracted to obtain the principal component function and the reduced-dimensional data set F i ; The principal component eigenvector Φ is the corresponding load coefficient divided by the square root of the eigenvalue. The principal component eigenvector Φ is multiplied by the standardized data set to obtain the reduced-dimensional data set F. i .

6. The polysilicon resistivity detection method according to claim 5, characterized in that: In the step S40, the main components are selected in descending order of contribution rate, and the cumulative contribution rate is not less than 0.

9.

7. The polysilicon resistivity detection method according to claim 1, characterized in that: In step S50, the data of the current day and the data of the previous three days, a total of four days, are averaged. Where, 4≤i≤n; In step S60, the ANN neural network model includes: an input layer, a training set, a test set, a hidden layer and an output layer.

8. The polysilicon resistivity detection method according to claim 1, characterized in that: The step S60 also includes training the model with the training set data and testing the model with the test set data until the training and testing results are good, thereby obtaining the model NET.

9. The polysilicon resistivity detection method according to claim 8, characterized in that: The training set data accounts for 60-70% of the total data, and the training method is the Levenberg-Marguardt method; When the correlation coefficients of the training set, test set, and validation set are all greater than 0.9, the training and testing results are good, and the model training is completed.

10. The polysilicon resistivity detection method according to claim 1, characterized in that: In the step S90, the formula for the corrected resistivity ρ of the furnace output on the same day is: ρ=θρ'+100; wherein θ is a correction term, and if PH3 is detected in hydrogen, θ=0, otherwise θ=1.

Images