초록 ▼

A method of building a set of experimental prediction model that requires fewer experimental frequency, shorter prediction time and higher prediction accuracy by using the advantages of combining the experimental data of Taguchi method and neural network learning is disclosed. The error between the

A method of building a set of experimental prediction model that requires fewer experimental frequency, shorter prediction time and higher prediction accuracy by using the advantages of combining the experimental data of Taguchi method and neural network learning is disclosed. The error between the experimentally measured result of photolithography and the simulated result of the theoretical model of near field photolithography is set as an objective function of an inverse method for back calculating fiber probe aperture size, which is adopted in the following Taguchi experiment. The analytical result of Taguchi neural network model of the present invention proves that the Taguchi neural network model can provide more accurate prediction result than the conventional Taguchi network model, and at the same time, improve the demerit of requiring massive training examples of the conventional neural network.

대표청구항 ▼

What is claimed is: 1. A prediction method of near field photolithography line fabrication by using the combination of Taguchi method and neural network, comprising: a first step of combining a theoretical model and the experiment of a near field photolithography line fabrication, using a non-destr

What is claimed is: 1. A prediction method of near field photolithography line fabrication by using the combination of Taguchi method and neural network, comprising: a first step of combining a theoretical model and the experiment of a near field photolithography line fabrication, using a non-destruction method to back calculate the fiber probe aperture size, setting the error between an experimentally measured result and a simulated result of the theoretical model of near field photolithography as an objective function, and using the objective function, an optimizing search and a reasonable convergence rule to back calculate a fiber probe aperture size that matches the experimental and theoretical model; a second step of using an orthogonal array of the Taguchi method to perform a near field photolithography line fabrication experiment, using a L9 orthogonal array to perform the near field photolithography line fabrication experiment so as to reduce experimental frequency; a third step of performing a data analysis of the Taguchi method, and producing a response table, a response chart and an analysis of variance (ANOVA) table; a fourth step of using the experimental data of the orthogonal array as training examples of a first stage network (ANN) to build a preliminary network, which also serves as a reference for improving the result of a second stage network and a third stage network; a fifth step of performing a second stage fine training of the network using light factors of Taguchi analysis as the training examples for the expansion of the second stage network and performing the second stage fine training, and increasing the frequency of the training examples of the experimental data to emphasize the importance of the information of the experimental data over the light factor data; a sixth step of determining third stage critical experimental training examples to be added according to the ‘important factors’, ‘uncertain factors’ and ‘preferred combination of factors according to ANN inferred Taguchi parameters’; and a seventh step of completing the third stage high prediction accuracy neural network to build a set of experimental prediction model that requires fewer experimental frequency, shorter prediction time and higher prediction accuracy. 2. The prediction model according to claim 1, wherein, in the step of performing a data analysis of the Taguchi method, producing the response table and the response chart comprises: step one: calculating a standard deviation s; and step two: calculating a signal-to-noise (S/N) ratio. 3. The prediction method according to claim 1, wherein, in the step of performing a data analysis of the Taguchi method, performing an analysis of variance (ANOVA) comprises: step one: calculating a total sum of squares of the S/N ratios; step two: calculating sum of squares due to the total mean of the S/N ratios; step three: calculating sum of squares of the variation from the mean of the S/N ratios; step four: calculating sum of squares of each control factor (SSFactor) using the level of the mean S/N ratio of each factor and the mean S/N ratio of all experimental groups, when factor A has three levels A1, A2 and A34, then the sum of squares of the A factor is: SSA=nA1·( S/NA1− S/N)2+nA2·( S/NA2− S/N)2+nA3·( S/NA3− S/N)2 wherein, nA1 is the number of experiments with the A factor being A1 in the orthogonal array experiment, and S/NA1 is the mean S/N ratio of these experiments; step five: determining the percentage contribution of each factor Pfactor according to SSFactor and SSTotal: PFactor=(SSFactor/SSTotal)×100% step six: calculating the degrees of freedom of each control factor, the degrees of freedom of each factor is equal to its levels minus 1; the total number of degrees of freedom is equal to the total number of measured values minus 1, the degree of freedom error is the total degrees of freedom minus the sum of the degree of freedom of each factor: DOFTotal=nexp−1 step seven: calculating the mean of sum of squares of the factors with the formula: MS = sum ⁢ ⁢ of ⁢ ⁢ squares ⁢ ⁢ of ⁢ ⁢ factors degree ⁢ ⁢ of ⁢ ⁢ freedom ⁢ ⁢ of ⁢ ⁢ factors step eight: calculating the error mean square of the experimental error factors with the formula: S e 2 = sum ⁢ ⁢ of ⁢ ⁢ square ⁢ ⁢ of ⁢ ⁢ errors degree ⁢ ⁢ of ⁢ ⁢ freedom ⁢ ⁢ of ⁢ ⁢ error ⁢ ⁢ factors step nine: calculating the importance of each control factor by quantizing the variance ratio F-ratio, the formula of the F-ratio is:   F = ⁢ MS S e 2 = ⁢ mean ⁢ ⁢ of ⁢ ⁢ sum ⁢ ⁢ ⁢ of ⁢ ⁢ squares ⁢ ⁢ of ⁢ ⁢ control ⁢ ⁢ ⁢ factors error ⁢ ⁢ mean ⁢ ⁢ square ⁢ ⁢ of ⁢ ⁢ error ⁢ ⁢ factors the F value is used to estimate the effect of each factor relative to the ‘importance’ of the experimental error because the larger the value of F, the lower the correlation between the two is, factors are used in a subsequent S/R ratio prediction only when their ‘importance’ reaches a definite level and these factors are called ‘important factors’, conversely, the effects of other factors are regarded as ‘infrequent effects’ caused by experimental errors and are called ‘light factors’. 4. The prediction method according to claim 1, wherein the step of building a preliminary network comprises: step one: scheduling a network structure by using a back-propagation neural network as a system network, the back-propagation neural network has a three-layer structure: an input layer, a hidden layer and an output layer, wherein the neural element of a single-layer hidden layer is: n H = n WG n I + n O wherein, nH is the number of neural elements in the hidden layer, nI is the number of neural elements in the input layer, nO is the number of neural elements in the output layer, nWG is the number of neural keys; and the number of neural elements of a network having multiple hidden layers is: n H = - ( n O + n H ) + ( n O + n H ) 2 + 4 ⁢ ( r - 1 ) × n WG 2 ⁢ ( r - 1 ) wherein, r is the number of hidden layers; step two: building input modules and output modules of network training examples, after performing a normalization procedure on each combination of the control factors in the Taguchi orthogonal array experiment, the control factors are converted into an input module of training examples of the neural network, after performing a normalization procedure on the S/N ratios of the orthogonal array experiment, the S/N ratios are converted into an output module of training examples of the network, and in the aforementioned L9 orthogonal array, the input module of network training examples comprises probe aperture, exposure energy/μm and developing time, and the output module comprises the S/N ratios of the orthogonal array; step three: normalizing the input module and the output module, the formula is: D nor = D min + V orig - V min V max - V min ⁢ ( D max - D min ) wherein, Dnor is the value after the normalization of the input module and the output module, Vorig is the original value before the normalization of the input module and the output module, Vmin is the smallest value before the normalization of the input module and the output module, Vmax is the largest value before the normalization of the input module and the output module, Dmin is the smallest value after the normalization of the input module and the output module, and Dmax is the largest value after the normalization of the input module and the output module; step four: performing a network training, according to the difference between the expected output value of the network and the actual output value of the network training examples, adjusting the weight between the neural element of the output layer and the neural element of an adjacent layer, and performing this kind of adjustment layer by layer until all the related weights are renewed; and step five: predicting the output module of the network, after performing a network training, inputting the module parameters to be predicted, which comprises the probe aperture, the exposure energy/μm and the developing time, to obtain the normalized values of the predicted S/N ratios, and performing an inverse normalization procedure on the normalized values of the predicted S/N ratios to obtain the true values of the S/N ratios using the formula below: V pre = V min + ( V nor - D min ) · ( V max - V min ) D max - D min wherein, Vpre is the true value of the predicted S/N ratio, and Vnor is the normalized value of the predicted S/N ratio. 5. The prediction method according to claim 1, wherein the step of performing a second stage fine training of the network comprises: step one: performing a second stage fine training of the network using light factor expansion examples, scheduling the training examples for the fine training of the second stage network based on the assumption of ignoring the effects of the ‘light factors’, and using the addition model of the Taguchi method on the parameter combination of already executed experiment to calculate the S/N ratios of ‘light factors’ whose level combinations have not yet been executed, assuming (A B C1) is the already experimented parameter combination and (A B C2) is the parameter combination of the light factors that have not been executed, the S/N ratio is calculated using the following addition module: S/N(A B C2)=S/N(A B C1)+C2−C1 wherein, C1 and C2 are the S/N ratios after performing the Taguchi experimental analysis; step two: increasing the frequency of the training example of the experimental data to emphasize the importance of the information of the experimental data over the light factors. 6. The prediction method according to claim 1, wherein the step of back adding critical experimental training examples comprises: step one: identifying the ‘important factors’ and the ‘light factors’ according to the result of the ANOVA, calculating variance ratios and percentages of the degree of contribution (P %) of each factor, and if the F value is greater than a set confidence level of a variance ratio, then the factor is regarded as ‘an important factor’, otherwise, it is regarded as a ‘light factor’; step two: using the Taguchi addition model to calculate the predicted S/N value of factor combination, predicting the S/N ratios of other not yet executed experimented factor combination according to the S/N ratio data of the orthogonal array experiment and using the linear addition module; step three: scheduling the second stage expansion training examples according to the ‘light factors’, and according to the assumption of ignoring the effects of ‘light factors’, scheduling the second stage network expansion training examples step four: performing the second stage network training, converting the network training examples obtained in the third step to normalized input module of network training and executing the second stage network training; step five: determining the ‘uncertain factor combination’ to test the consistent prediction of network inference and Taguchi addition model, all the Taguchi factor combinations are input to the second stage network to perform an all factor test, if the difference between the predicted value of network inference and the predicted value of Taguchi addition model is greater than the experimental error range, the presence of controversy is implied and these groups of factors are judged to be ‘uncertain factor combinations’. 7. The prediction method according to claim 1, wherein a half height line width of the near field photolithography line fabrication larger than 100 nm or smaller than or equal to 100 nm is within the range of application.