Mixed product run-to-run process control – An ANOVA model with ARIMA disturbance 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:The 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 . The tool disturbances are represented by a constant plus an IMA(1, 1) process:
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)
- et al.
Stability and performance analysis of mixed product run-to-run control
Journal of Process Control
(2006) - et al.
Run-to-run control and state estimation in high-mix semiconductor manufacturing
Annual Reviews in Control
(2007) - et al.
Run-to-run process control: literature review and extensions
Journal of Quality Technology
(1997) Run-to-Run Control in Semiconductor Manufacturing
(2001)Statistical Process Adjustment for Quality Control
(2002)
Cited by (33)
An Application of the Seasonal Fractional ARIMA Model to the Semiconductor Manufacturing
2017, IFAC-PapersOnLineIdentification of Wiener Models in the Presence of ARIMA Process Noise
2016, IFAC-PapersOnLineGeneration and verification of optimal dispatching policies for multi-product multi-tool semiconductor manufacturing processes
2013, Computers and Chemical EngineeringDeterministic and stochastic model based run-to-run control for batch processes with measurement delays of uncertain duration
2012, Journal of Process ControlA G&P EWMA algorithm for high-mix semiconductor manufacturing processes
2011, Journal of Process ControlCitation 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.