Mixed product run-to-run process control – An ANOVA model with ARIMA disturbance approach

https://doi.org/10.1016/j.jprocont.2008.09.002Get rights and content

Abstract

A novel run-to-run control algorithm based on a dynamic analysis of variance (ANOVA) approach is proposed to deal with run-to-run (RtR) control of a high mixed operation, i.e., many different products are manufactured in many different tools. The conditions of different tools and products are identified based on the ANOVA analysis of the system output. A dynamic term in the form of an autoregressive integrated moving average (ARIMA) disturbance model is included in the process model to characterize the run-to-run disturbances such as drift, shift and/or some other unknown disturbances of different tools. It is shown from the study below that controller performance can be improved by introduction of the dynamic term, especially for products which are produced only occasionally. This makes it highly suitable for mixed product control system. An industrial example is also included to demonstrate superiority of this approach.

Introduction

Run-to-run (RtR) control has been identified as a key enabling technology of maintaining quality in semiconductor manufacturing. Active researches in this area have been summarized by many authors in books and review articles [1], [2], [3]. Most RtR control algorithms are based on the assumption that there is only a single product fabricated in the manufacturing line. However, an actual semiconductor manufacturing facility is an assembly line consisting of a sequence of operations performed by parallel machines that manufacture products of many different grades. The most common practice is to classify the situation of a specific tool used and a specific product manufactured as a “thread”, and creates a RtR controller for each thread. Typically there will be thousands of threads for each operation. Several papers [4], [5], [6] have discussed the possibility of cross utilization of information of different threads to isolate changes of condition of tool and products. Zheng et al. [7] considered the stability of a single tool with different products. They demonstrated that exponentially weighted moving average (EWMA) control of the tool disturbance may not be stable if the effect of the tool is not stationary and the error of process gain estimates of different products are different.

Pasadyn and Edgar [5] noted that the absolute value of the product and tool disturbances cannot be estimated independently even if they are constant because each run must consist of a specific product manufactured on a specific tool. They proposed to use of monitoring wafers to condition of the tool. Firth et al. [6] proposed a method assuming that the tool noise and product noise are stationary. The resulting tool and product estimates may be biased, i.e. changes in condition of one tool may lead to changes in estimates of disturbance estimates of other tools and products. However, the estimates of different threads remained unbiased. Thus the model can be used for control but not fault detection and diagnosis. Bode et al. [8] recognized that specific regression techniques must be used to obtain unbiased estimates of tool and product states.

Analysis of variance (ANOVA) is a standard statistical tool in the area of linear modeling of multi-factor systems [9]. In [10], we have proposed a state estimation method of a mixed run plant based on analysis of variance. However, the method also assumed that the states of the tools are unchanged and a recursive Karman filter estimator is used. In this work, we shall relinquish the assumption that the condition of tool is unchanged and demonstrate that improved controller performance and diagnosis of tool conditions can be obtained.

Section snippets

Plant

Fig. 1 shows the schematic plots of a “mixed run” manufacturing system. A number of products are manufactured on a number of tools. In each run, most operation variables follow a basic recipe for each product. After each run, an output y related to the quality of the product is measured. In run-to-run control, certain manipulated variable in the recipe will be adjusted based on measurement of output variables y of previous runs. Consider a simplified multi-tool and multi-product production

IMA(1, 1) disturbance

To demonstrate the ability of the dynamic ANOVA control, a simulation example consisting of two tools and three products was used:y(k1)=x(k1)+c1T(k1)+cj(k1)P+ν1(k1)k1=1K1,j(ki)=1,2,3y(k2)=x(k2)+c2T(k2)+cj(k2)P+ν2(k2)k2=1K2,j(k2)=1,2,3The metrology noise is normally distributed with zero mean and variance of 0.01, i.e. νi(ki)  N(0, 0.12). The product disturbances are constant with [c1P,c2P,c3P]=[6,10,17]. The tool disturbances are represented by a constant plus an IMA(1, 1) process:c1T(k1)=5+η1(k1

Industrial example

In this section, wafer etching production data is used to test the effectiveness of the proposed algorithm. The collected wafer etching production data was originally under the control of s-ANOVA method. For such a process, it is known that aging effects such as the depletion of the etch solution or the degradation of the thermocouples in high temperature furnaces can induce trend or ramp disturbances. We use an IMA(1, 1) process, the dynamic term, to characterize the disturbance. 2 tools, 6

Conclusions

It is very important in RtR control of a mixed run plant to correctly identify the changes in condition of tool as well as the difference in behavior between tools and products. In this work, a novel mixed product run-to-run controller is proposed. The method of ANOVA is used to estimate the difference in behavior between tools and products and a dynamic term is included in the process model to characterize the run-to-run disturbance such as drift, shift and/or some other unknown disturbances.

References (11)

There are more references available in the full text version of this article.

Cited by (33)

  • A G&P EWMA algorithm for high-mix semiconductor manufacturing processes

    2011, Journal of Process Control
    Citation Excerpt :

    Two examples based on reversed engineering from industrial data are used to demonstrate the successful application of the G&P-EWMA in the semiconductor manufacturing process. The method of reversed engineered simulation was described by Ma et al. [16]. In the first example, a photolithography process, there are five products produced on one tool.

View all citing articles on Scopus
View full text