Patent Publication Number: US-2023153574-A1

Title: Deep auto-encoder for equipment health monitoring and fault detection in semiconductor and display process equipment tools

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is continuation of U.S. patent application Ser. No. 16/545,908, filed Aug. 20, 2019, which claims priority and claims benefit of U.S. Provisional Patent Application Ser. No. 62/730,477, filed Sep. 12, 2018, applications are hereby incorporated by reference herein. 
    
    
     BACKGROUND 
     Field 
     Implementations described herein generally relate to analyzing time-series traces to detect anomalies in sensors employed in one or more semiconductor processing chambers. 
     Description of the Related Art 
     Manufacturing silicon substrates involves a series of different processing operations that may be performed in a single processing system or “tool” which includes a plurality of processing chambers. During processing, each chamber in which a procedure is carried out may include a plurality of sensors, with each sensor configured to monitor a predefined metric relating to substrate processing. 
     Further, these multiple silicon substrate processing operations occur over an interval of time. A process may include a transition from a first operation to a second operation. Time-series data is data collected over the interval of time, including the transition (e.g., the time-series transition) called time-series traces. Equipment Health Monitoring (EHM) and Fault Detection (FD) techniques for semiconductor/display manufacturing equipment are needed for smoothly running device fabrication facilities. Efforts-to-date for EHM and FD are focused largely on classical machine learning efforts using time-series traces of sensors, which require significant feature engineering by domain experts. These techniques also suffer from overfitting, higher false positive rates and not automated in several cases. Traditional machine learning methods using feature engineering to produce models of time-series traces are also restricted to certain tool types or recipe types. Accordingly whenever a recipe or chamber changes, one needs to rebuild the model which is very time consuming. 
     Statistical methods cannot detect short-time signal perturbations in data received from sensors over time. Statistical methods also provide false positives (e.g., that an entire signal does not match a target signal because a minimal portion of the signal is outside of a guard band) and do not allow for adjustment of the sensitivity of outlier detection. 
     Therefore, there is a continual need for an improved method of detecting outliers/anomalies in sensor data retrieved during semiconductor processing. 
     SUMMARY 
     A method for detecting anomalies in time-series traces received from sensors of manufacturing tools is disclosed. In one implementation, a server feeds a set of training time-series traces to a neural network configured to derive a model of the training time-series traces that minimizes reconstruction error of the training time-series traces. The server extracts a set of input time-series traces from one or more sensors associated with one or more manufacturing tools configured to produce a silicon substrate. The server feeds the set of input time-series traces to the trained neural network to produce a set of output time series traces reconstructed based on the model. The server calculates a mean square error between a first input time series trace of the set of input time series traces and a corresponding first output time series trace of the set of output time-series traces. The server declares the sensor corresponding to the first input time-series trace as having an anomaly when the mean square error exceeds a pre-determined value. 
     In another implementation, a computer system is provided, which comprises a memory and a processor configured to perform a method for detecting anomalies in time-series traces received from sensors of manufacturing tools, the method includes feeding a set of training time-series traces to a neural network configured to derive a model of the training time-series traces that minimizes reconstruction error of the training time-series traces. The method further includes extracting a set of input time-series traces from one or more sensors associated with one or more manufacturing tools configured to produce a silicon substrate. The method further includes feeding the set of input time-series traces to the trained neural network to produce a set of output time series traces reconstructed based on the model. The method further includes calculating a mean square error between a first input time series trace of the set of input time series traces and a corresponding first output time series trace of the set of output time-series traces. The method further includes declaring the sensor corresponding to the first input time-series trace as having an anomaly when the mean square error exceeds a pre-determined value. 
     In yet another implementation, a non-transitory computer-readable medium is provided, which comprises instructions to perform a method for detecting anomalies in time-series traces received from sensors of manufacturing tools. In one embodiment, the method includes feeding a set of training time-series traces to a neural network configured to derive a model of the training time-series traces that minimizes reconstruction error of the training time-series traces. The method further includes extracting a set of input time-series traces from one or more sensors associated with one or more manufacturing tools configured to produce a silicon substrate. The method further includes feeding the set of input time-series traces to the trained neural network to produce a set of output time series traces reconstructed based on the model. The method further includes calculating a mean square error between a first input time series trace of the set of input time series traces and a corresponding first output time series trace of the set of output time-series traces. The method further includes declaring the sensor corresponding to the first input time-series trace as having an anomaly when the mean square error exceeds a pre-determined value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above-recited features of the present disclosure can be understood in detail, a more particular description of the implementations, briefly summarized above, may be had by reference to implementations, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical implementations of this disclosure and are therefore not to be considered limiting of its scope, for the disclosure may admit to other equally effective implementations. 
         FIG.  1    schematically illustrates a plurality of manufacturing tools for substrate processing, in accordance with one embodiment of the present disclosure. 
         FIG.  2    depicts a network environment in which embodiments of the present disclosure may be implemented. 
         FIG.  3    illustrates a deep auto-encoder to be employed in embodiments of the present disclosure. 
         FIG.  4    shows the architecture of the deep auto-encoder in a modular fashion. 
         FIG.  5    illustrates components of an anomaly analysis engine according to embodiments of the present disclosure. 
         FIG.  6    illustrates one embodiment of a method for detecting anomalies in time-series data received from a plurality of sensors of the manufacturing tools. 
         FIG.  7    depicts an example computer system with which embodiments of the present disclosure may be implemented. 
     
    
    
     To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements and features of one implementation may be beneficially incorporated in other implementations without further recitation. 
     DETAILED DESCRIPTION 
     The following disclosure describes method for detecting anomalies in time-series data received from a plurality of sensors of the manufacturing tools. Certain details are set forth in the following description and in  FIGS.  1 - 7    to provide a thorough understanding of various implementations of the disclosure. Other details describing well-known structures and systems often associated with plasma etching are not set forth in the following disclosure to avoid unnecessarily obscuring the description of the various implementations. 
     Many of the details, dimensions, components, and other features shown in the Figures are merely illustrative of particular implementations. Accordingly, other implementations can have other details, components, dimensions, angles and features without departing from the spirit or scope of the present disclosure. In addition, further implementations of the disclosure can be practiced without several of the details described below. 
     As processes (e.g., manufacturing processes) include shorter operation times, smaller parts, tighter tolerances, and so forth, transitions (e.g., how to get from operation A to operation B in a manufacturing process) become more critical. Problems may occur if a process overshoots or undershoots a transition (e.g., transition from I0 degrees to 20 degrees too fast, transition from 10 degrees to 20 degrees too slow, etc.). Repeatable performance includes consistent transitions. Conventional monitoring methods (e.g., SPC, EHM, FDC) are not capable of monitoring transient time-series and cannot detect short-time signal perturbations in data received from sensors over time (referred to herein as time-series traces). These short anomalies can cause defects (e.g., on-substrate defects) or reduce yield. 
     Time-series anomaly analysis provides the ability to monitor time-series anomalies in process sensor time-series traces. Time-series anomaly analysis may detect rare, strange, and/or unexpected sequences (e.g., shape, magnitude, position, etc. of a curve of the time-series data (value plotted against sample)) that are undetectable via conventional methods. In one embodiment, the monitoring of anomalies in time-series data is performed by a deep auto-encoder type neural network that derives a model of training time-series traces that minimizes reconstruction error of the training time-series traces. A set of input time-series traces from one or more sensors associated with one or more manufacturing tools configured to produce a silicon substrate is fed to the trained neural network to produce a set of output time series traces reconstructed based on the model. A mean square error difference between each of the one or more output time-series traces and corresponding one or more input time-series traces is calculated and one or more sensors corresponding to the one or more input time-series traces is declared as having an anomaly when the corresponding mean square error difference exceeds a pre-determined value. In one example, the pre-determined value may be set to the mean plus three sigma of the training reconstruction mean squared error as the cutoff. 
     In semiconductor processing, multi-layered features are fabricated on semiconductor substrates using specific processing recipes having many processing operations. A cluster tool, which integrates a number of process chambers to perform a process sequence without removing substrates from a processing environment (e.g., a controlled environment) is generally used in processing semiconductor substrates. A process sequence is generally defined as the sequence of device fabrication operations, or process recipe operations, completed in one or more processing chambers in a cluster tool. A process sequence may generally contain various substrate electronic device fabrication processing operations. 
     In semiconductor fabrication, each operation must be performed with a sufficient level of precision so that the resulting device functions correctly. Certain defects which occur during the lithography, etching, deposition, or planarization operations may require significant corrective actions in order to rework the substrate. For example, if a substantial misalignment occurs during lithography, in certain cases the substrate must be stripped and lithography must be redone in order to correct the defect. Correcting these defects may result in substantial increases in time and cost. Various parameters of the substrates (e.g., thickness, optical reflective index, absorption index, strength, critical dimension variation across the substrate, and the like) may need to be within acceptable process windows in order for the completed substrate to be of sufficient quality for use. Problems with one or more parameters and the sensors that measure these parameters may require corrective action to be taken with respect to either an individual substrate or aspects of the manufacturing process. Checking all of these parameters for every substrate after the manufacturing process is complete is inefficient and costly. Sometimes, a representative sample of substrates is checked using metrology tools which measure various parameters of the substrates. Because only a representative sample is checked, however, this method of determining the quality of large numbers of substrates can be inaccurate. Therefore, there is a need for a more systematic and efficient way to determine the quality of a large number of manufactured substrates. 
     Embodiments of the present disclosure involve monitoring and analysis of process anomalies in time-series data from a plurality of sensors located in a plurality of manufacturing tools of semi-conductor processing equipment. In one implementation, a server extracts a plurality of time-series traces from a plurality of sensors associated with one or more manufacturing tools configured to produce a silicon substrate. The server employs a deep auto-encoder type neural network that is trained to derive a model of input training time-series traces that minimizes reconstruction error of the input training time-series traces. The server feeds the set of input time-series traces to the trained neural network to produce a set of output time series traces reconstructed based on the model. The server calculates a mean square error between a first input time series trace of the set of input time series traces and a corresponding first output time series trace of the set of output time-series traces. The server declares the sensor corresponding to the first input time-series trace as having an anomaly when the mean square error exceeds a pre-determined value. In one example, the pre-determined value may be set to the mean plus three sigma of the training reconstruction mean squared error as the cutoff. The server may instruct a manufacturing system to take corrective action to remove a source of the anomaly. 
     Embodiments of the present disclosure may allow for efficient and accurate predictions about substrate quality and yield. Furthermore, embodiments may allow for effective determinations to be made regarding improvements with respect to such processes as thin film deposition, etching, and implant processes in order to achieve predictable process windows and optimal thin film properties. 
       FIG.  1    schematically illustrates one or more manufacturing tools  101  for substrate processing, in accordance with one embodiment of the present disclosure. It is contemplated that the method described herein may be practiced in other tools configured to perform a process sequence. For example, the manufacturing tools  101  embodied in  FIG.  1    is the ENDURA® cluster tool commercially available from Applied Materials, Inc. in Santa Clara, Calif. 
     The manufacturing tools  101  include a vacuum-tight set of manufacturing tools  101  and a factory interface  102 . The manufacturing tools  101  comprise a plurality of processing chambers  110 ,  108 ,  114 ,  112 ,  118 ,  116 . The factory interface  102  is coupled to transfer chamber  104  by the load lock chamber  120 . 
     In one embodiment, the factory interface  202  comprises at least one docking station, at least one substrate transfer end effector  138 , and at least one substrate aligner  140 . The docking station is configured to accept one or more front opening unified pods  128  (FOUP). Two FOUPs  128 A,  128 B are shown in the embodiment of  FIG.  1   . The substrate transfer end effector  138  is configured to transfer the substrate from the factory interface  102  to the load lock chamber  120 . 
     The load lock chamber  120  has a first port coupled to the factory interface  102  and a second port coupled to a first transfer chamber  104 . The load lock chamber  120  is coupled to a pressure control system which pumps down and vents the chamber  120  as needed to facilitate passing the substrate between the vacuum environment of the transfer chamber  104  and the substantially ambient (e.g., atmospheric) environment of the factory interface  102 . 
     The first transfer chamber  104  and the second transfer chamber  103  respectively have a first end effector  107  and a second end effector  105  disposed therein. Two substrate transfer platforms  106 A,  106 B are disposed in the transfer chamber  104  to facilitate transfer of the substrate between end effectors  105 ,  107 . The platforms  106 A,  106 B can either be open to the transfer chambers  103 ,  104  or be selectively isolated (i.e., sealed) from the transfer chambers  103 ,  104  to allow different operational pressures to be maintained in each of the transfer chambers  103 ,  104 . 
     The end effector  107  disposed in the first transfer chamber  104  is capable of transferring substrates between the load lock chamber  120 , the processing chambers  116 ,  118 , and the substrate transfer platforms  106 A,  106 B. The end effector  105  disposed in the second transfer chamber  103  is capable of transferring substrates between the substrate transfer platforms  106 A,  106 B and the processing chambers  112 ,  114 ,  110 ,  108 . 
     Embodiments of the present disclosure involve gathering and analyzing data from sensors associated with various processes of substrates during the manufacturing process from various manufacturing tools  101  in order to detect and possibly eliminate anomalies. In some embodiments, the manufacturing tools are associated with a manufacturing execution system (MES). The data may include, for example, time-series traces of various sensors. The data may be aggregated and analyzed at a central location, such as a server, and used to detect anomalies/anomalies in real-time. For example, the server may employ a deep auto-encoder type neural network that is trained to derive a model of input training time-series traces that minimizes reconstruction error of the input training time-series traces. The server may feed the set of input time-series traces to the trained neural network to produce a set of output time series traces reconstructed based on the model. The server may calculate a mean square error between a first input time series trace of the set of input time series traces and a corresponding first output time series trace of the set of output time-series traces. The server may declare the sensor corresponding to the first input time-series trace as having an anomaly when the mean square error exceeds a pre-determined value. The server may instruct a manufacturing system (MES) to take corrective action to remove a source of the anomaly. 
     The anomaly and trace information may be provided from the server to the MES that can be analyzed by engineers and so that corrective action may be taken as needed regarding problems which are identified as a result of detected anomalies. The server may also determine appropriate corrective action to be taken based on analysis of the data (e.g., based on identifying correlations between time-series traces of sensors and metrology data taken from other sensors that measure parameters of a substrate), and provide instructions to perform corrective action. In some embodiments, the MES may automatically take corrective action (e.g., recalibrating or adjusting a parameter of a lithography tool, redoing a portion of the manufacturing process for a substrate, or other suitable computing device) based on the predictive information. In certain embodiments, if the predictive information identifies a problem with one or more parameters of a substrate, the problem may be verified by analyzing the substrate (e.g., using metrology tools). If the problem is confirmed by analyzing the substrate, corrective action may then be taken (e.g., manually or automatically by the MES). 
       FIG.  2    depicts a network environment  200  in which embodiments of the present disclosure may be implemented. As shown, network environment  200  includes a server  220  which is connected via network  210  to another server  230  which is connected to one or more manufacturing tools  101 . Network  210  may, for example, comprise the Internet. In another embodiment, manufacturing tools  101  manufacturing tools  101  is also connected directly to server  220 . 
     Server  220  may comprise a computing device such as a rack server, desktop or laptop computer, mobile phone, tablet, or other suitable computing device. As shown, server  220  comprises an anomaly analysis engine  222 , which may perform operations described herein related to making determinations and predictions regarding identifying and correcting anomalies. The anomaly analysis engine  222  identifies data sources  206 A-N (e.g., sensors) that define a system and/or that are used to monitor a system, such as the collection of manufacturing tools  101  corresponding to manufacturing tools  101 . The manufacturing tools  101  may be semiconductor processing equipment, such as one or more of a chamber for an etch reactor, a deposition chamber, and so on, corresponding to the platform  101  comprises the plurality of processing chambers  110 ,  108 ,  114 ,  112 ,  118 ,  116 , of  FIG.  1   . 
     For example, anomaly analysis engine  222  may analyze time-series sensor information received from MES  232  or directly from the manufacturing tools  101  in order to detect, analyze, and verify anomalies. 
     For example, the anomaly analysis engine  222  may analyze process and substrate sensor information received from MES  232  or directly from sensors applied within the manufacturing tools  101  in order to detect anomalies, corrective actions to eliminate future anomalies in the same sensors, and process improvements. In some embodiments, the server  220  is separate from the manufacturing tools  101 . In other embodiments, the server may be part of the manufacturing tools  101  or may be an off-line server. 
     For example the anomaly analysis engine  222  may receive time-series sensor traces from MES  232  representing temperature, gas flow, or RF power current, etc. collected from a plurality of sensors associated with one or more manufacturing tools configured to produce a silicon substrate. The anomaly analysis engine  222  may employ a deep auto-encoder type neural network that is trained to derive a model of input training time-series traces that minimizes reconstruction error of the input training time-series traces. The anomaly analysis engine  222  may feed the set of input time-series traces to the trained neural network to produce a set of output time series traces reconstructed based on the model. The anomaly analysis engine  222  may calculate a mean square error between a first input time series trace of the set of input time series traces and a corresponding first output time series trace of the set of output time-series traces. The anomaly analysis engine  222  may declare the sensor corresponding to the first input time-series trace as having an anomaly when the mean square error exceeds a pre-determined value. In one example, the pre-determined value may be set to the mean plus three sigma of the training reconstruction mean squared error as the cutoff. The anomaly analysis engine  222  may instruct a manufacturing system (MES) to take corrective action to remove a source of the anomaly. 
     The anomaly analysis engine  222  may provide predictive information to MES  232  about future anomalies in the sensor data. In some embodiments, the anomaly analysis engine  222  may also determine corrective action to be taken with respect to processes or individual substrates based on the data. For example, the anomaly analysis engine  222  may identify a correlation between a measured anomaly associated with a temperature sensor correlated with a certain substrate parameter problem and a tool parameter, and determine that the tool parameter should be adjusted by a certain amount. Furthermore, the anomaly analysis engine  222  may determine actions to be performed on a substrate to bring one or more predicted parameters into an acceptable range (e.g., correcting overlay marks, stripping and recoating the substrate, and the like). 
     Predictive information regarding substrate quality with respect to parameters may permit personnel or MES  232  to improve the manufacturing process (e.g., lithography, etching, deposition, and planarization may be improved to achieve predictable properties). 
     Server  230  may comprise a computing device such as a rack server, desktop or laptop computer, mobile phone, tablet, or other suitable computing device. As shown, server  220  comprises an MES  232 , which may perform operations described herein related to managing the manufacturing of silicon substrates. For example, MES  232  may coordinate processes performed by the manufacturing tools  101 , and may collect data from these tools (e.g., tool parameters, thickness, optical reflective index, absorption index, strength, overlay and alignment data, critical dimension variation across the substrate, and the like) and time traces from sensors used by the manufacturing tools  101 . In some embodiments, the data may be time-series traces which represent the behavior of sensors over time as manufacturing processes are performed. MES  232  may provide this information to the anomaly analysis engine  222  (e.g., over network  210 ), which may analyze the information and provide verification of the detection of anomalies. In some embodiments, the anomaly analysis engine  222  may provide instructions to MES  232  regarding corrective action to take with respect to an individual defect, the manufacturing tools  101 , or other aspects of the manufacturing process. In certain embodiments, MES  232  automatically takes corrective action, such as by instructing individual sensors of individual chambers within the manufacturing tools  101  to perform certain tasks (e.g., instructing a lithography tool to strip and recoat a substrate in order to correct an alignment defect or instructing a deposition tool to alter one or more parameters). 
     The manufacturing tools  101  may comprise one or more tools which perform processes related to manufacturing silicon substrates. For example, the manufacturing tools  101  may include lithography tools, etching tools, deposition tools, and planarization tools. The manufacturing tools  101  may communicate with MES  232  in order to receive instructions and provide data from sensors within a particular tool (e.g., time-series data representing the values output by one or more sensors associate with of parameters of substrates captured by sensors over time during manufacturing). 
     Embodiments of the present disclosure employ an artificial neural network architecture known as a deep auto-encoder. Artificial neural networks are machine learning models inspired by the operating principles of the neural network of the human brain and have been widely applied to problems of classification and function approximation. Deep learning is part of a broader family of machine learning methods based on learning data representations, as opposed to task-specific algorithms. Deep learning is a class of machine learning algorithms that use a cascade of multiple layers of nonlinear processing units for feature extraction and transformation of input data. Each successive layer of the multiple layers uses the output from the previous layer as input. The multiple layers are then trained to learn a representation (encoding) of a set of input data, typically for the purpose of dimensionality reduction in an unsupervised (e.g., pattern analysis) manner. 
     A deep auto-encoder is a type of deep learning feed-forward neural network with one or more layers of hidden nodes, of which there are usually fewer nodes in successive layers than the input nodes in the encoding half and the decoding half usually has a structure that is mirror symmetric to the encoding half. The structure of the deep auto-encoder aids the embedded the neural network to learn the best representation of the input data corresponding to a set of training data derived from non-anomalous input sensor traces and to reconstruct the input data as output data corresponding to the input sensor traces. In one embodiment, the deep auto-encoder is trained with non-anomalous sensor trace runs to learn a minimum set of features necessary to reproduce the input sensor traces at an output of the deep auto-encoder minimizing reconstruction error. More specifically, the learning is the process of determining the connection weights between the layers such that performance is maximized when solving a learning problem. The representation is the normal signature of each of the sensor traces. Accordingly, the auto-encoder generates an output that is identical to the input. 
       FIG.  3    illustrates a deep auto-encoder  300  to be employed in embodiments of the present disclosure. The input data  302  to the deep auto-encoder  300  comprises time slices of the sensor traces derived from a matrix representation of a plurality of time-series traces of a plurality of sensors associated with the manufacturing tools  101 . The deep auto-encoder  300  may comprise an input layer  304 , one or more hidden layers  306 , a central bottleneck layer  308 , an output layer  310 , and a full set of connections  312  between the layers. The structure of the hidden layers  306  is symmetric with respect to the bottleneck layer  308 , which has the smallest number of nodes. The bottleneck layer  308  is employed to help the neural network  300  find the minimal representation of the input data  302  reconstructed to the output data  314  by extracting a limited number of features that represent the input data  302 . A designer only needs to define the number of layers in the deep auto-encoder  300 , and how many nodes there are to be in each of the layers. The deep auto-encoder  300  is trained with example traces having no anomalies and is configured to produce output data  314  that is a reconstruction of the plurality of traces corresponding to the input data  302 , wherein the output data  314  has minimized reconstruction error (e.g., the mean squared error, or MSE) relative to the input traces. The reconstruction error is minimized for a minimum set of the global and time invariant features learns by the deep-auto encoder  300  during training necessary to reproduce the input sensor traces. 
     Minimizing reconstruction error forces the deep auto-encoder  300  to engage in dimensionality reduction, for example, by learning how to identify the global and time invariant features of the input data  302  corresponding to the input traces. The deep auto-encoder  300  learns to compress data from the input layer  304  into a short code, and then un-compress that code into something that closely matches the original input data  302 . 
     The deep auto-encoder  300  is trained before use on real data. The training algorithm for a deep auto-encoder can be summarized as follows: For each input x, do a feed-forward pass to compute activations at all hidden layers, then at the output layer to obtain an output x′; measure the deviation of x′ from the input x that minimizes reconstruction error, e.g. mean squared error); and back propagate the error through the net and perform weight updates. Accordingly, the hidden nodes of the hidden layers  306  are trained to reconstruct the input x at the output x′ by minimizing reconstruction error. As a result, the hidden nodes learn the global and time invariant features of the input traces necessary to reproduce the input traces. Minimizing the reconstruction error (e.g., the mean squared error, or MSE) yields a deep auto-encoder  300  that outputs the corresponding sensor signals. 
       FIG.  4    shows the architecture  400  of the deep auto-encoder  300  in a modular fashion. The multiple sensor time-series traces needed to train the deep auto-encoder  300  or to test actual trace runs are preprocessed by the anomaly analysis engine  222  before being fed into the deep auto-encoder  300  contained within the anomaly analysis engine  222 . Preprocessing includes normalizing each of the time-series traces to the range of [0,1] (min-max normalization, (x−min)/(max−min)). In deployment of the method, the min max value came from the training runs only. Preprocessing further includes extracting a plurality of rolling time windows  404  (sub-matrices) of each of the input time series traces at a plurality of timestamps from a matrix  402  comprising value/timestamp pairs of the input time-series traces from all of the sensors for all timestamps and feeding the plurality of rolling time windows  404  of value/timestamp data V ij  as input data to the deep auto-encoder  300 . 
     The matrix  402  has one dimension corresponding to trace point values V ij  of sensor S 1  to S m  from timestamp t 0  to t e  of run/substrate R 1  to timestamp t m  to t m+e  of run/substrate R m  as one dimension and sensors S 1  to S n  as a second dimension. An input vector/sub-matrix containing a rolling time window  404  of the input data  302  from all of the sensors S i  to S n  at a plurality of instances of time t s  to t s+w  is extracted from the matrix  402 . 
     From the plurality of rolling time windows  404 , a row of values V li -V (l+w)1  to V ln -V (l+w)n  is fed by the anomaly analysis engine  222  into the deep auto-encoder  300 . The minimal global and time invariant features set of the input trace data  302  is learned by the deep auto-encoder  300  by back-propagation and stochastic gradient descent based on the training (no fault) data. The nodes of the deep auto-encoder  304 ,  306 ,  308  encode the rolling window data  404 , compress the rolling window data  404 , and decode/decompress the rolling window data at nodes  308 - 312  to produce an output row of reconstructed input traces values as output trace values  408  for each time stamp (O li -O (l+w)1  to O ln -O (l+w)n) . While testing, the whole chain of the nodes  406  in the layers  304 - 310  is operated in a feed-forward fashion in real-time and provides the RMS reconstruction error for a time window. The output data is an output vector  408  of data O li -O (l+w)1  to O ln -O (l+w)n  corresponding to the signatures of the input traces from all of the sensors. 
     In one embodiment, the deep auto-encoder  300  is trained with the normal runs using an optimizer. One such optimizer is an adaptive moment estimation (Adam) optimizer. An Adam optimizer is algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The average reconstruction error (e.g., mean square error) of the time window over all sensors denotes how far the time window is from the nominal condition and is used as an anomaly indicator. 
     In other embodiments, other network structure hyperparameters may be employed based on: the number of layers, how many nodes are in each layer, the rolling window size, the activation function of the neural network, etc. 
     Once the minimal feature set is learned, an actual set of runs of time-series traces is fed to the deep-auto-encoder  300  which then produces output data  314  corresponding to minimum reconstruction error version of the input data  302  using the same rolling window technique and deep-auto-encoder  300  compression/decompression technique. The anomaly analysis engine  222  then calculates a mean squared error between the output data  408  (O li -O (l+w)1  to O ln -O (l+w)n ) representing the reconstructed input data corresponding to the input time-series traces and the input data  302  (V li -V (l+w)1  to V ln -V (l+w)n ) corresponding to the original time-series traces for each of the sensors of the plurality of sensors for the plurality of manufacturing tools  101 . If any one reconstructed output time-series trace has a calculated mean square error that is larger than a predetermined threshold, then the corresponding input run/time-series trace is declared to be abnormal, and an anomaly for that time-series trace is detected. 
     The individual mean square error timestamp values MSE ij  ( 410 ) contribute to the overall mean square error calculation. Suppose the input time series data is v 1 , v 2 , . . . , v t , then after the data is fit in the trained neural network model, the reconstructed output has the same dimension time series o 1 , o 2 , . . . , o t . The square reconstructed error 
     
       
         
           
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     is then calculated. Each timestamp has a squared error value. A mean of the squared error within the window is taken as the anomaly score. 
     The mean of the squared error for each timestamp per run (or per step) can then be aggregated. If this mean squared error per run (or per step) is above certain threshold, then the run (or step) is declared to be an anomaly in a given sensor. 
       FIG.  5    illustrates components of anomaly analysis engine  222  according to embodiments of the present disclosure. As shown, the anomaly analysis engine  222  includes a data acquisition module  510 , which may acquire data from MES  232  (e.g., over network  210 ). In alternative embodiments, data acquisition module  510  acquires time-series trace data directly from sensors within the manufacturing tools  101 . The anomaly analysis engine  222  further includes a data pre-processing module  520 , which may preprocess the time-series traces, time slices the traces, and feeds the time slices to the deep auto-encoder  300  according to the method described in  FIG.  4   . The anomaly analysis engine  222  further includes an anomaly verification module  530 , which employs the deep auto-encoder  300  to determine whether there are any anomalies in the input time-series traces based on whether a mean square error between an output reconstructed time-series trace and a corresponding input time-series trace exceed a predetermined threshold and is thus an time-series trace containing an anomaly. The anomaly analysis engine  222  further includes a transmission module  540 , which may transmit data such as sensor information and corrective instructions to MES  232  (e.g., over network  210 ) or to other destinations. 
       FIG.  6    illustrates one embodiment of a method  600  for detecting anomalies in time-series data received from one or more sensors of the manufacturing tools  101 . Method  600  can be performed by processing logic that can comprise hardware (e.g., circuitry, dedicated logic, programmable logic, microcode, etc.), software (e.g., instructions run on a processing device), or a combination thereof. In one embodiment, method  600  is performed by the anomaly analysis engine  222  of  FIG.  2   . 
     At block  605 , the anomaly analysis engine  222  feeds a set of training time-series traces to a neural network configured to derive a model of the training time-series traces that minimizes reconstruction error of the training time-series traces. At block  610 , the anomaly analysis engine  222  extracts one or more input time-series traces from one or more sensors associated with one or more manufacturing tools  101  configured to produce a silicon substrate. Each of the input time-series traces are min-max normalized. Preprocessing further includes extracting an input time slice of each of the input time series traces at a moment in time from a matrix comprising time slices of the input time-series traces from all of the sensors for all moments in time of and feeding the time slice as input data to the deep auto-encoder  300 . The anomaly analysis engine  222  further extracts an input vector from the matrix comprising a time slice of the input time-series traces from all of the sensors and feeds the time slice as input data to the neural network. 
     At block  615 , the anomaly analysis engine  222  feeds the one or more input time-series traces to the trained neural network  300  to produce a set of output time series traces reconstructed based on the model. The neural network  300  is a deep learning, feed-forward, fully connected neural network. The neural network minimizes reconstruction error of the input time-series traces. Minimizing reconstruction error minimizes mean square error. 
     Nodes of the neural network  300  are organized into a plurality of layers. The plurality of layers comprises an input layer, an output layer, a central bottleneck layer, and one or more hidden layers disposed between the input layer and the output layer. The one or more hidden layers are trained to minimize reconstruction error. Nodes of the one or more hidden layers are trained to learn the global and time invariant features of the input time-series traces necessary to reconstruct the input time-series traces as the output time-series traces. 
     The neural network  300  is trained with normal time-series traces using an hyperparameter optimizer. 
     At block  620 , the anomaly analysis engine  322  calculates a mean square error between each of the one or more output time-series traces and corresponding one or more input time-series traces. At block  625 , the anomaly analysis engine  322  declares one or more sensors corresponding to the one or more input time-series traces as having an anomaly when the corresponding mean square error exceeds a pre-determined value. In one example, the pre-determined value may be set to the mean plus three sigma of the training reconstruction mean squared error as the cutoff. 
     At block  630 , the anomaly analysis engine  322  instructs a manufacturing system to take corrective action to remove a cause of the declared anomaly. 
       FIG.  7    illustrates an example computing system  700  used to detect and analyze anomalies, according to some embodiments of the present disclosure. In certain embodiments, computer system  700  is representative of the server  120 . Aspects of computer system  700  may also be representative of other devices used to perform techniques described herein (e.g., server  130 ). For example, computing system  700  may be a personal computer, industrial processor, personal digital assistant, mobile phone, mobile device or any other device suitable for practicing one or more embodiments of the present invention. 
     The system  700  includes a central processing unit (CPU)  702  and a system memory  704  communicating via a bus path that may include a memory bridge  705 . CPU  702  includes one or more processing cores, and, in operation, CPU  702  is the master processor of the system  700 , controlling and coordinating operations of other system components. System memory  704  stores a software application  706 , and data, for use by CPU  702 . CPU  702  runs software applications and optionally an operating system. 
     Illustratively, the system memory  704  includes the anomaly analysis engine  780 , which may correspond to the anomaly analysis engine  222 , which performs operations related to detecting sensor anomalies, according to techniques described herein. For example, the anomaly analysis engine  780  may be equivalent to the anomaly analysis engine  222  in  FIG.  2   , and may employ a deep auto-encoder type neural network  300  that reconstructs one or more input time-series traces as corresponding one or more output time-series traces based on a model which minimizes reconstruction error of training time-series traces, and, based on that set, detects and verifies sensor anomalies and other aspects of the manufacturing process. 
     Memory bridge  705 , which may be, e.g., a Northbridge chip, is connected via a bus or other communication path (e.g., a HyperTransport link) to an I/O (input/output) bridge  707 . I/O bridge  707 , which may be, e.g., a Southbridge chip, receives user input from one or more user input devices  708  (e.g., keyboard, mouse, joystick, digitizer tablets, touch pads, touch screens, still or video cameras, motion sensors, and/or microphones) and forwards the input to CPU  702  via memory bridge  705 . 
     A display processor  712  is coupled to the memory bridge  785  via a bus or other communication path (e.g., a PCI Express, Accelerated Graphics Port, or HyperTransport link); in one embodiment display processor  712  is a graphics subsystem that includes at least one graphics processing unit (GPU) and graphics memory. Graphics memory includes a display memory (e.g., a frame buffer) used for storing pixel data for each pixel of an output image. Graphics memory can be integrated in the same device as the GPU, connected as a separate device with the GPU, and/or implemented within system memory  704 . 
     Display processor  712  periodically delivers pixels of the dashboard to a display device  710  (e.g., a screen or conventional CRT, plasma, OLED, SED or LCD based monitor or television). Additionally, display processor  712  may output pixels to film recorders adapted to reproduce computer generated images on photographic film. Display processor  712  can provide display device  710  with an analog or digital signal. 
     Persistent storage  720  is also connected to I/O bridge  707  and may be configured to store content and applications and data, such as a database library  715 , for use by CPU  702  and display processor  712 . Persistent storage  720  provides non-volatile storage for applications and data and may include fixed or removable hard disk drives, flash memory devices, and CD-ROM, DVD-ROM, Blu-ray, HD-DVD, or other magnetic, optical, or solid state storage devices. 
     Illustratively, persistent storage  720  includes manufacturing data  790 , which may comprise information acquired by the anomaly analysis engine  222 . Manufacturing data  790  may, for example, comprise information received from MES  232 , collected by the manufacturing tools  101 , related to various sensors taking measurements from substrates and tools over time during the manufacturing processes. 
     A switch  716  provides connections between the I/O bridge  707  and other components such as a network adapter  718  and various add-in cards  720  and  7721 . Network adapter  718  allows the system  700  to communicate with other systems via an electronic communications network, and may include wired or wireless communication over local area networks  740  and wide area networks such as the Internet. 
     Other components (not shown), including USB or other port connections, film recording devices, or other suitable computing device, may also be connected to I/O bridge  707 . For example, process equipment  770  may operate from instructions and/or data provided by CPU  702 , system memory  704 , or persistent storage  720 . Communication paths interconnecting the various components in  FIG.  7    may be implemented using any suitable protocols, such as PCI (Peripheral Component Interconnect), PCI Express (PCI-E), AGP (Accelerated Graphics Port), HyperTransport, or any other bus or point-to-point communication protocol(s), and connections between different devices may use different protocols, as is known in the art. 
     The process equipment  770  may be one or more semiconductor chambers such as a plasma enhanced chemical vapor deposition (PECVD) or other plasma processing tool, such as the processing tools contained in the manufacturing tools  101 . For example, process equipment  270  may be an etch chamber, a chemical vapor deposition chamber, a physical vapor deposition chamber, an implant chamber, a plasma treatment chamber, or other plasma processing chamber, either alone or in combination with one or more other chambers. 
     In one embodiment, display processor  712  incorporates circuitry optimized for performing mathematical operations, including, for example, math co-processor, and may additionally constitute a graphics processing unit (GPU). In another embodiment, display processor  712  incorporates circuitry optimized for general purpose processing. In yet another embodiment, display processor  712  may be integrated with one or more other system elements, such as the memory bridge  705 , CPU  702 , and I/O bridge  707  to form a system on chip (SoC). In still further embodiments, display processor  712  is omitted and software executed by CPU  702  performs the functions of display processor  712 . 
     Pixel data can be provided to display processor  712  directly from CPU  702 . In some embodiments, instructions and/or data representing an anomaly verification analysis is provided to set of server computers, each similar to the system  700 , via network adapter  718  or system disk  714 . The servers may perform operations on subsets of the data using the provided instructions for analysis. The results from these operations may be stored on computer-readable media in a digital format and optionally returned to the system  700  for further analysis or display. Similarly, data may be output to other systems for display, stored in a database library  715  on the system disk  714 , or stored on computer-readable media in a digital format. 
     Alternatively, CPU  702  provides display processor  712  with data and/or instructions defining the desired output images, from which display processor  712  generates the pixel data of one or more output images, including characterizing and/or adjusting the offset between stereo image pairs. The data and/or instructions defining the desired output images can be stored in system memory  804  or graphics memory within display processor  712 . CPU  702  and/or display processor  712  can employ any mathematical, function or technique known in the art to create one or more results from the provided data and instructions, including running models and comparing data from sensors to track the service life of chamber components. 
     It will be appreciated that the system shown herein is illustrative and that variations and modifications are possible. The connection topology, including the number and arrangement of bridges, may be modified as desired. For instance, in some embodiments, system memory  704  is connected to CPU  702  directly rather than through a bridge, and other devices communicate with system memory  704  via memory bridge  705  and CPU  702 . In other alternative topologies display processor  712  is connected to I/O bridge  807  or directly to CPU  702 , rather than to memory bridge  705 . In still other embodiments, I/O bridge  707  and memory bridge  705  might be integrated into a single chip. The particular components shown herein are optional; for instance, any number of add-in cards or peripheral devices might be supported. In some embodiments, the process equipment  770  may be connected directly to the I/O bridge  707 . In some embodiments, the switch  816  is eliminated, and the network adapter  718  and the add-in cards  720 ,  721  connect directly to the I/O bridge  707 . 
     Various embodiments of the invention may be implemented as a program product for use with a computer system. The software routines of the program product define functions of the embodiments (including the methods described herein) and can be contained on a variety of computer-readable storage media. Illustrative computer-readable storage media include, but are not limited to: (i) non-writable storage media (e.g., read-only memory devices within a computer such as CD-ROM disks readable by a CD-ROM drive, flash memory, ROM chips or any type of solid-state non-volatile semiconductor memory) on which information is permanently stored; and (ii) writable storage media (e.g., floppy disks within a diskette drive or hard-disk drive or any type of solid-state random-access semiconductor memory) on which alterable information is stored. 
     Any combination of one or more computer readable medium(s) may be utilized for storing a program product which, when executed, is configured to perform method for determining the service life of a chamber components. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as JAVA™, SMALLTALK™, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). 
     The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operations to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     Embodiments of the invention may be provided to end users through a cloud computing infrastructure. Cloud computing refers to the provision of scalable computing resources as a service over a network. More formally, cloud computing may be defined as a computing capability that provides an abstraction between the computing resource and its underlying technical architecture (e.g., servers, storage, networks), enabling convenient, on-demand network access to a shared pool of configurable computing resources that can be rapidly provisioned and released with minimal management effort or service provider interaction. Thus, cloud computing allows a user to access virtual computing resources (e.g., storage, data, applications, and even complete virtualized computing systems) in “the cloud,” without regard for the underlying physical systems (or locations of those systems) used to provide the computing resources. 
     Advantageously, the techniques presented herein allow for real-time anomaly detection, off-line problem diagnosis, and chamber matching. With respect to real-time anomaly detection, embodiments train a model beforehand, and-real time detects whether there is a large deviation from a good trace and whether to make a correction accordingly. With respect to off-line problem diagnosis, when certain problem happens during a marathon of runs, embodiments use good runs to train a model and check the difference of a bad run compared to the good run. This determines the top contributor sensors of the difference to help diagnose what is the real problem in either hardware or the process itself (e.g., a flow valve, power strike delayed, etc.). With respect to chamber matching, embodiments permit training the model with multiple runs from one/multiple good chambers, and checking differences in output traces from a good chamber but coming from a bad chamber. As stated above, the autoencoder will ignore the baseline difference between good chambers, and focus on finding the more important differences (e.g., pattern, process, etc.). This is more efficient than conventional methods for chamber matching that run the same/similar recipe. 
     The techniques allow for intelligent predictions of substrate quality based on manufacturing data, and allow for efficient decisions to be made regarding corrective actions to be taken with respect to individual substrates and other aspects of the manufacturing process. Use of embodiments of the present disclosure may reduce costs, improve efficiency, and allow for better strategic planning with respect to the manufacturing process. 
     As will be appreciated by one of ordinary skill in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. 
     In the preceding, reference is made to embodiments presented in this disclosure. However, the scope of the present disclosure is not limited to specific described embodiments. Instead, any combination of the following features and elements, whether related to different embodiments or not, is contemplated to implement and practice contemplated embodiments. Furthermore, although embodiments disclosed herein may achieve advantages over other possible solutions or over the prior art, whether or not a particular advantage is achieved by a given embodiment is not limiting of the scope of the present disclosure. Thus, the following aspects, features, embodiments and advantages are merely illustrative and are not considered elements or limitations of the appended claims except where explicitly recited in a claim(s). Likewise, reference to “the invention” shall not be construed as a generalization of any inventive subject matter disclosed herein and shall not be considered to be an element or limitation of the appended claims except where explicitly recited in a claim(s). 
     While the foregoing is directed to embodiments of the present disclosure, other and further embodiments of the disclosure may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.