Matthew A. Purdy

Recursive least squares estimation for run-to-run control with metrology delay and its application to STI etch process

Run-to-run (RtR) control technology has received tremendous interest in semiconductor manufacturing. Exponentially weighted moving average (EWMA), double-EWMA, and internal model control (IMC) filters are recognized methods for online RtR estimation. In this paper, we consider recursive least squares (RLS) as an alternative for online estimation and RtR control. The relationship between EWMA-type and RLS-type estimates is analyzed and verified with simulations. Because measurement delay is almost inevitable in semiconductor manufacturing, we discuss and compare the performance of EWMA, RtR-IMC, and RLS controllers in handling measurement delay and measurement noise for processes with a deterministic drift. An ad hoc solution is proposed to handle measurement delay for processes with time-varying drifts. The results are illustrated through several simulations and a shallow trench isolation (STI) etch process as an industrial example.

An MILP Approach to Wafer Sampling and Selection

This paper introduces a novel algorithm for selecting the optimal wafers for measurement given a set of selection rules. The algorithm is based on assigning a penalty to each of the sampling rules and then using a mixed-integer linear program to pick the wafers which minimize the sum of the penalties. By waiting until the metrology step to determine the best wafers to measure, a real-time decision can be made based on which wafers have previously been measured, the tools and chambers on which wafers were processed, and other user-specified selection criteria. The penalties can also be increased after a rule violation to ensure that each of the selection rules are satisfied at a finite frequency.

Dynamic, weight-based sampling algorithm

In this paper, a novel sampling algorithm that allows for multiple, independent rules to be efficiently merged into a single sampling decision will be presented. A brief discussion of past sampling technologies that motivated the development of the new system will also be included. Finally, the ability of the application to deal with various factory dynamics will be discussed.

Method for efficiently managing metrology queues

A method of efficiently managing metrology WIP queues which ensures quality metrology data collection is presented in this paper. The principle behind the system is to identify and measure lots that provide the most recent information while allowing older lots to be removed from the queue. The factory system for making sampling decisions and how it interacts with the metrology queue management application is discussed. Examples of the logic flow for determining which lots can be removed from a metrology queue is used for demonstration purposes. Finally, a discussion on how the system has changed the way different factory departments define metrology sampling rules is discussed

Scatterometry for shallow trench isolation (STI) process metrology

Scatterometry is a non-destructive optical metrology based on the analysis of light scattered form a periodic sample. In this research angular scatterometry measurements were performed on three wafers processed using shallow trench isolation (STI) technology. The periodic features that were measured on these wafers were composite etched gratings comprised of SiN on oxide on Si. The wafers were processed at three different etch times in order to generate different etch depths (shallow, nominal and deep). It was at this point in the process that the scatterometry measurements were performed. The scatterometry model was comprised of four parameters: Si thickness, SiN thickness, linewidth and sidewall angle. For comparison purposes measurements were also performed using a critical dimension scanning electron microscope (CD-SEM), a cross-section SEM and an atomic force microscope (AFM). The results show good agreement between the scatterometry measurements and the other technologies.

Recursive least squares estimation and its application to shallow trench isolation

In recent years, run-to-run (R2R) control technology has received tremendous interest in semiconductor manufacturing. One class of widely used run-to-run controllers is based on the exponentially weighted moving average (EWMA) statistics to estimate process deviations. Using an EWMA filter to smooth the control action on a linear process has been shown to provide good results in a number of applications. However, for a process with severe drifts, the EWMA controller is insufficient even when large weights are used. This problem becomes more severe when there is measurement delay, which is almost inevitable in semiconductor industry. In order to control drifting processes, a predictor-corrector controller (PCC) and a double EWMA controller have been developed. Chen and Guo (2001) show that both PCC and double-EWMA controller are in effect Integral-double-Integral (I-II) controllers, which are able to control drifting processes. However, since offset is often within the noise of the process, the second integrator can actually cause jittering. Besides, tuning the second filter is not as intuitive as a single EWMA filter. In this work, we look at an alternative way Recursive Least Squares (RLS), to estimate and control the drifting process. EWMA and double-EWMA are shown to be the least squares estimate for locally constant mean model and locally constant linear trend model. Then the recursive least squares with exponential factor is applied to shallow trench isolation etch process to predict the future etch rate. The etch process, which is a critical process in the flash memory manufacturing, is known to suffer from significant etch rate drift due to chamber seasoning. In order to handle the metrology delay, we propose a new time update scheme. RLS with the new time update method gives very good result. The estimate error variance is smaller than that from EWMA, and mean square error decrease more than 10% compared to that from EWMA.

Cost and revenue impact of advanced process control (APC) with an emphasis on run-to-run control (R2R)

This paper takes published improvements in fabricator metrics that result from Advanced Process Control,and, applying an International SEMATECH cost model to the results, quantifies the expected economic impact. By converting the improvements in factory metrics to dollars, they can be compared. The benefits are given by equipment type, and by factory benefit mechanism. The majority of these calculations are based on Run-to-Run control.