Using radial basis function networks and hyper-cubes for excursion classification in semi-conductor processing equipment

#The present disclosure relates to artificial neural networks, and, more particularly, to radial basis function networks for analyzing a system.

#Artificial neural networks may be used to analyze operation in a system based on known values of the system. For example, a user may be interested in analyzing sensor data, such as sensor data from semi-conductor processing equipment. A Radial Basis Function (RBF) network is an artificial neural network that uses radial basis functions as activation functions. In a typical RBF network, an RBF node or neuron is responsible for determining the activation value of the node, where each node has multiple inputs and one output. RBF networks typically can only differentiate between normal and abnormal values. Errors in RBF network analysis tend to be false negatives, and erroneous results tend to increase with increasing numbers of dimensions (e.g., numbers of sensors).

#The present disclosure is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings.

#FIG. 1 illustrates one embodiment of a network architecture.

#FIG. 2 illustrates one embodiment of a method for RBF network and hyper-cube analysis.

#Embodiments of the present invention are directed to a method and system for RBF network and hyper-cube analysis of data. For example, data samples may be sensor data from semi-conductor processing equipment. In one embodiment, the method and system can detect whether samples indicate “normal” versus “abnormal” operation in a sub-system, classify samples indicating “abnormal” behavior if the abnormal excursion can be labeled, and diagnose and correct the “abnormal” behavior if information on the root cause and solution are available. Embodiments of the present invention are extensible in that additionally identified excursions may be added to the system.

#An RBF function can be defined as any function that satisfies the following equation: Ø(x)=Ø(∥x∥)  Equation 1 An RBF network is a collection of RBF functions located in n-dimensional space. In one RBF network shown in FIG. 4, there are two layers, including an input layer 401 and an RBF layer 403. This network has 3 inputs and 4 RBF nodes. Here, each node is located in n-dimensional space, where the number of inputs defines n (e.g., n=3 in FIG. 4). Each node can be defined using an n-element vector, and the input to each node may also be an n-element vector. The network shown in FIG. 4 is capable of distinguishing 5 unique excursions or classes. Each node represents a unique excursion or class. Unknown samples can belong to either nodes 1 through 4 or no node.

#For example, an input sample may be a standardized value where the sample is expressed as a sigma difference between a known reference set, a specified number of runs in a process, or all runs from a specified number of days, which should provide greater than 90% accuracy.