Kuo-Hao Chang

Stochastic Nelder–Mead simplex method – A new globally convergent direct search method for simulation optimization

Nelder–Mead simplex method (NM), originally developed in deterministic optimization, is an efficient direct search method that optimizes the response function merely by comparing function values. While successful in deterministic settings, the application of NM to simulation optimization suffers from two problems: (1) It lacks an effective sample size scheme for controlling noise; consequently the algorithm can be misled to the wrong direction because of noise, and (2) it is a heuristic algorithm; the quality of estimated optimal solution cannot be quantified. We propose a new variant, called Stochastic Nelder–Mead simplex method (SNM), that employs an effective sample size scheme and a specially-designed global and local search framework to address these two problems. Without the use of gradient information, SNM can handle problems where the response functions are nonsmooth or gradient does not exist. This is complementary to the existing gradient-based approaches. We prove that SNM can converge to the true global optima with probability one. An extensive numerical study also shows that the performance SNM is promising and is worthy of further investigation.

Stochastic Trust-Region Response-Surface Method STRONG---A New Response-Surface Framework for Simulation Optimization

Response surface methodology RSM is a widely used method for simulation optimization. Its strategy is to explore small subregions of the decision space in succession instead of attempting to explore the entire decision space in a single attempt. This method is especially suitable for complex stochastic systems where little knowledge is available. Although RSM is popular in practice, its current applications in simulation optimization treat simulation experiments the same as real experiments. However, the unique properties of simulation experiments make traditional RSM inappropriate in two important aspects: 1 It is not automated; human involvement is required at each step of the search process; 2 RSM is a heuristic procedure without convergence guarantee; the quality of the final solution cannot be quantified. We propose the stochastic trust-region response-surface method STRONG for simulation optimization in attempts to solve these problems. STRONG combines RSM with the classic trust-region method developed for deterministic optimization to eliminate the need for human intervention and to achieve the desired convergence properties. The numerical study shows that STRONG can outperform the existing methodologies, especially for problems that have grossly noisy response surfaces, and its computational advantage becomes more obvious when the dimension of the problem increases.

MODELING OVERLAY ERRORS AND SAMPLING STRATEGIES TO IMPROVE YIELD

ABSTRACT Overlay is one of the key designed rules for producing VLSI devices. In order to have a better resolution and alignment accuracy in lithography process, it is important to model the overlay errors and then to compensate them into tolerances. This study aimed to develop a new model that bridges the gap between the existing theoretical models and the data obtained in real settings and to discuss the overlay sampling strategies with empirical data in a wafer fab. In addition, we used simulation to examine the relations between the various factors and the caused overlay errors. This paper concluded with discussions on further research.

Overall Wafer Effectiveness (OWE): A novel industry standard for semiconductor ecosystem as a whole

As semiconductor industry reached nanotechnology generation and consumer electronics era, the competition is no longer among individual semiconductor companies. Indeed, the collaborations among horizontally specialized value providers are critical for the success of the companies as well as the whole ecosystem. This paper aims to propose a novel index, i.e., Overall Wafer Effectiveness (OWE), to measure wafer productivity and drive various improvement directions for semiconductor ecosystem as a whole. Furthermore, the proposed OWE can be easily extended to incorporate additional attributes such as mask-field-utilization, throughput, and yield for effective management. We conducted a number of case studies in real settings. The results have shown that OWE can be employed as a semiconductor industry standard to drive collaborative efforts among IC designers, equipment vendors, and manufacturers in the ecosystem to enhance total wafer effectiveness. This paper concludes with discussions on value propositions of proposed OWE indices and future research directions.

Optimal vehicle allocation for an Automated Materials Handling System using simulation optimisation

The Automated Materials Handling System (AMHS) in the semiconductor industry plays a vital role in reducing wafer cycle times and enhancing fabrication facility (fab) productivity. Due to the complexity of the manufacturing process and the stochasticity introduced by the inherent variability of processing times, the vehicle allocation for the AMHS is a challenging task, especially in 300 mm wafer fabs where the AMHS comprises both the interbay and intrabay systems to perform the timely deliveries. This paper studied the vehicle allocation problem in a typical 300 mm wafer fab. We formulated it as a simulation optimisation problem and proposed a conceptual framework to handle the problem. A discrete event simulation model was developed to characterise the AMHS, and the technique of simulation optimisation was applied to obtain the optimal vehicle allocation for both the interbay and intrabay systems. To demonstrate the feasibility and advantages of the simulation optimisation approach, a photobay example was used to compare the solution derived from the analytical model and simulation optimisation model. Finally, an empirical problem based on real data was conducted to show the viability of the proposed framework in practice.

Design of a sampling strategy for measuring and compensating for overlay errors in semiconductor manufacturing

To enhance the resolution and alignment accuracy in semiconductor manufacturing, it is important to measure overlay errors and control them into the tolerances by removing assignable causes. A number of related studies have been done to examine the factors causing the overlay errors, to propose mathematical models and to develop overlay error control methods. However, the involved sampling strategies received little attention. This study aimed to propose specific designs of sampling patterns effectively to measure and compensate for overlay errors within the limited number of samples in practice. To verify the validity of the proposed approach, the sampling strategies were compared using empirical data from a wafer fabrication facility. The proposed sampling patterns had a higher goodness of fit for the overlay model and lower residuals after compensation. This paper concludes with our findings and discussions on further research.

Stochastic trust region gradient-free method (strong): a new response-surface-based algorithm in simulation optimization

Response Surface Methodology (RSM) is a metamodel- based optimization method. Its strategy is to explore small subregions of the parameter space in succession instead of attempting to explore the entire parameter space directly. This method has been widely used in simulation optimization. However, RSM has two significant shortcomings: Firstly, it is not automated. Human involvements are usually required in the search process. Secondly, RSM is heuristic without convergence guarantee. This paper proposes Stochastic Trust Region Gradient-Free Method (STRONG) for simulation optimization with continuous decision variables to solve these two problems. STRONG combines the traditional RSM framework with the trust region method for deterministic optimization to achieve convergence property and eliminate the requirement of human involvement. Combined with appropriate experimental designs and specifically efficient screening experiments, STRONG has the potential of solving high-dimensional problems efficiently.

An empirical study of design-of-experiment data mining for yield-loss diagnosis for semiconductor manufacturing

To maintain competitive advantages, semiconductor industry has strived for continuous technology migrations and quick response to yield excursion. As wafer fabrication has been increasingly complicated in nano technologies, many factors including recipe, process, tool, and chamber with the multicollinearity affect the yield that are hard to detect and interpret. Although design of experiment (DOE) is a cost effective approach to consider multiple factors simultaneously, it is difficult to follow the design to conduct experiments in real settings. Alternatively, data mining has been widely applied to extract potential useful patterns for manufacturing intelligence. However, because hundreds of factors must be considered simultaneously to accurately characterize the yield performance of newly released technology and tools for diagnosis, data mining requires tremendous time for analysis and often generates too many patterns that are hard to be interpreted by domain experts. To address the needs in real settings, this study aims to develop a retrospective DOE data mining that matches potential designs with a huge amount of data automatically collected in semiconductor manufacturing to enable effective and meaningful knowledge extraction from the data. DOE can detect high-order interactions and show how interconnected factors respond to a wide range of values. To validate the proposed approach, an empirical study was conducted in a semiconductor manufacturing company in Taiwan and the results demonstrated its practical viability.

Efficient development of cycle time response surfaces using progressive simulation metamodeling

In semiconductor manufacturing, hot lots are to provide marketing and engineering with extra flexibility regarding delivery lead times, and in turn enhance its competitive advantages against other companies. On the other hand, hot lots are among major sources of disruption of the smoothness of the manufacturing flow. They can lead to a significant increase of cycle time of normal lots, and in turn result in delayed delivery times and serious service deteriorations. Due to the complex nature of semiconductor manufacturing, evaluating the impact of hot lots on the cycle time of normal lots presents major challenges. In this paper, we propose a methodology, called progressive simulation metamodelling (PSM), that allows for an efficient development of the response surface between the cycle time of normal lots and the percentage of hot lots in semiconductor manufacturing. The response surface generated by the proposed PSM is like an easy-to-use analytical model, but with the fidelity of simulation that takes into account all important manufacturing details. The specially-designed mechanisms, including identifying the critical region and sequentially adding design points in the critical region, further grants PSM computational advantages compared to the traditional response surface method. An empirical study conducted in collaboration with a semiconductor company validates the viability of PSM in real settings.

Vehicle fleet sizing for automated material handling systems to minimize cost subject to time constraints

Vehicle fleet sizing for an Automated Material Handling System (AMHS) is an important but challenging problem due to the complexity of AMHS design and uncertainty involved in the production process; e.g., random processing time. For a complex manufacturing system such as semiconductor manufacturing, the problem is even more complex. This article studies the vehicle fleet sizing problem in semiconductor manufacturing and proposes a formulation and solution method, called Simulation Sequential Metamodeling (SSM), to facilitate the determination of the optimal vehicle fleet size that minimizes the vehicle cost while satisfying time constraints. The proposed approach is to sequentially construct a series of metamodels, solve the approximate problem, and evaluate the quality of the resulting solution. Once the resulting solution is satisfactory, the algorithm is terminated. Compared with the existing metamodeling approaches that employ a large number of observations for one time, the sequential nature of SSM allows it to achieve much better computational efficiency. Furthermore, a newly developed estimation method enables SSM to quantify the quality of the resulting solution. Extensive numerical experiments show that SSM outperforms the existing methods and the computational advantage of SSM is increasing with the problem size and the level of the variance of response variables. An empirical study based on real data is conducted to validate the viability of SSM in practical settings.