Detlef Pabst

An Effective Problem Decomposition Method for Scheduling of Diffusion Processes Based on Mixed Integer Linear Programming

Diffusion processes in semiconductor fabrication facilities (Fabs) usually refer to the series of processes from wafer cleaning processes to furnace processes. Most furnace tools are batch tools with large batch sizes and have relatively long process times when compared to the other processes. Strict time window constraints link cleaning processes with furnace processes for quality control. Those operational requirements for diffusion processes make their scheduling very difficult. This paper proposes an advanced scheduling approach based on a rolling horizon scheduling concept. Due to the combinatorial nature of the scheduling problem, the complexity of the problem increases exponentially when the number of jobs and tools increase. However, the computation time allowed for the scheduler is limited in practice, because the variability in most fabs requires schedulers to update the schedule in short intervals. We suggest an MILP (Mixed Integer Linear Programming) model for diffusion processes and propose an effective decomposition method to deal with this complexity problem. The decomposition method repeats multiple scheduling iterations as it gradually extends the number of runs on tools enabling the scheduler to generate near-optimal schedules in limited time intervals. The scheduler could make large improvements on KPIs such as queue time violation rates, batch sizes, throughput, etc. The software architecture of the scheduler implementation is also addressed in this paper.

Compensating for the Initialization and Sampling of EWMA Run-to-Run Controlled Processes

The exponentially weighted moving average (EWMA) filter is commonly used for state estimation of run-to-run controllers in semiconductor manufacturing. It is widely known that, when at steady state, the EWMA filter provides the minimum mean square error (MSE) forecast for an integrated moving average (IMA) process. The forecast, however, is optimal if and only if every output of the IMA process is measured. If an EWMA controller is implemented utilizing sampled process data, then it is necessary to retune the controller to maintain optimal performance. Furthermore, in practice, the complex interacting selection criteria of advanced sampling applications often cause measurement frequency to be highly irregular. In this paper, a sampling compensation algorithm (SCA) is derived based on the minimum-norm IMA (MNIMA) forecast. The algorithm provides the minimum mean-square-error (MMSE) forecast of an IMA process for irregularly sampled processes and is robust to initialization.

An effective problem decomposition method for scheduling of diffusion processes based on mixed integer linear programming

Diffusion processes in semiconductor fabrication facilities (Fabs) refer to the series of processes from wafer cleaning processes to furnace processes. Most furnace tools are batch tools, with large batch sizes, and have relatively long process times, when compared to the other processes. Strict time window constraints link cleaning processes with furnace processes for quality control. Those operational requirements for diffusion processes make their scheduling very difficult. This paper proposes an advanced scheduling approach based on a rolling horizon scheduling concept. Due to the combinatorial nature of the scheduling problem, the complexity of the problem increases exponentially, when the number of jobs and tools increase. However, the computation time allowed for the scheduler is limited in practice, because the variability in most Fabs requires schedulers to update the schedule in short intervals. We suggest an mixed integer linear programming model for diffusion processes, and propose an effective decomposition method to deal with this complexity problem. The decomposition method repeats multiple scheduling iterations, as it gradually extends the number of runs on tools, enabling the scheduler to generate near-optimal schedules in limited time intervals. The scheduler could make large improvements on key performance indicators, such as time window violation rates, batch sizes, throughput, etc. The software architecture of the scheduler implementation is also addressed in this paper.

Methodology to evaluate the impact of amhs design characteristics on operational fab performance

Todays 300mm semiconductor facilities rely almost completely on Automated Material Handling Systems (AMHS) to transport wafers to equipment and storage areas in the wafer fabrication plant (fab). As the cost of equipment increases and the process technology becomes more and more sensitive to delivery times between steps, AMHS performance has become increasingly important to overall factory performance. Current AMHS design methods focus primarily on optimizing the balance between AMHS cost and AMHS performance. Understanding the influence of AMHS performance on fab operations has become an area of focus during the design process. This paper proposes a methodology to correlate AMHS performance measurements with simulated fab performance measures using a linked AMHS-fab model. This methodology facilitates model setup, scenario modification, model linkage, and calculations of performance impact. A sample evaluation study demonstrates the validation and analysis process, and derives conclusions applicable during the AMHS design process.

An optimization model for qualification management in wafer fabs

The individual tools of a tool group need to be qualified to run lots of certain families in wafer fabs. A qualification time window is associated with each family and each tool. This window lasts typically from a couple of days to few weeks. The time window can be re-initialized with separate qualification effort on a need by basis and can be extended by on-time processing of qualifying families. In this paper, we propose a mixed integer programming formulation for this problem assuming a given demand for a planning horizon of several periods. The objective function takes into account qualification costs, backlog costs, and inventory holding costs among others. Results of computational experiments based on randomly generated problem instances are presented that demonstrate that a tradeoff between production objectives and qualification costs can be reached by an appropriate configuration of the model.

Using fractal dimensions as performance indicators for manufacturing systems

Chaos theory has been a young research field with successful applications to a variety of areas. Even though former publications have assessed the question if production systems behave chaotic, little work has been published on real life production systems, especially about semiconductor manufacturing. This paper applies the concept of fractal dimensions to assess the performance of production toolsets and demonstrates fractal dimension as an alternative for graphical analysis of performance indicators. Two examples illustrate the variety of applications and the capability of fractal dimensions to compare different zoom levels and to be tolerant against patterns in the data.