Supervisor Control Design for Safe Coordination of Multicluster and Multiproduct Wafer Manufacturing Processes

In semiconductor manufacturing, a process module (PM) failure in cluster tools (CTs) happens from time to time. To effectively operate a CT, such a failure should be handled in a proper and timely manner. This issue becomes much more complicated because wafer residency time constraints (WRTCs) must be met to ensure the quality for some wafer fabrication processes. With such constraints, if a tool is operated under a periodic schedule and a PM fails, it is desired that the tool can still operate under a periodic schedule if it is possible. Nevertheless, the periodic schedule after a PM failure must be different from that before its failure since in this case the tool is degraded. Thus, there must be a transient process between them. It is a great challenge to operate a tool such that it can go through such a transient process with WRTCs being always satisfied. This paper aims to solve this problem by proposing PM failure response policies which can successfully transfer a CT to the feasible schedule after failure from the one before a failure. Then, efficient algorithms are developed to improve these response policies. The proposed policies are composed of simple control laws such that they can be realized in real time and online. Illustrative examples are presented to show their applications.

In semiconductor manufacturing, wafer residency time constraints make the scheduling problem of cluster tools complicated. A process module (PM) in cluster tools is prone to failure. It is crucial to deal with any such failure in a proper and timely manner. If there are feasible periodic schedules in operating a cluster tool before and after a PM failure, it is desired to make it operate continuously when such a failure occurs. However, due to wafer residency time constraints, it is highly challenging to control a tool such that it can be correctly transferred from a feasible schedule before failure to another after it. To solve this problem, a Petri net model is developed to describe the dynamic behavior of a single-arm cluster tool and failure response policies are proposed. The proposed policies are formulated via simple control laws for their easy implementation. Examples are given to show them.

We examine cyclic scheduling of single-armed and dual-armed cluster tools that concurrently process two wafer types by sharing a process module (PM). Because a PM is shared by two different wafers, the backward and swap sequences, which are prevalently used for single-armed and dual-armed tools without such complexity, respectively, are not effective. We therefore propose new sequences, called alternating backward and alternating swap sequences, for steady cycles of single-armed and dual-armed tools, respectively. We then develop optimality conditions for which the proposed sequences achieve the minimum cycle times in a fundamental cycle, and show that the optimality conditions hold for most practical cases. We also develop a condition for which a shared PM becomes the bottleneck and hence the PM sharing increases the cycle time. For general cycles, we propose heuristic scheduling methods that combine both the alternating backward (or swap) sequence and the conventional backward (or swap) sequence. Finally, we experimentally verify the efficiency and effectiveness of the proposed algorithm for dual-armed cluster tools.

For wafer fabrication, a process module (PM) in cluster tools is prone to failure. It is crucial to deal with such failure in a proper and timely manner. With residency time constraints, if there are feasible periodic schedules in operating a cluster tool before and after a PM failure, it is desired to make it operate continuously when such a failure occurs. A Petri net model is developed to describe the dynamic behavior of a single-arm cluster tool and failure response policies are proposed to deal with a failure. The proposed policies are formulated via simple control laws for their real-time and on-line implementation. An example is presented to show their application.

The next generation sub-micron devices requires control of wafer environment and the interfaces between film layers. A wafer must not be exposed to atmosphere between some processing steps. To meet these requirements, multiple processing integrated system or "Cluster" tool for IC fabrication has been a major tooling development in the last few years. This leads to the concept of open architecture system and the development of interface standards. This also creates new demands on the system control and user interfaces. An open architecture integrated system must operate in a seamless fashion with real-time control and communication among the process modules and the wafer transport platform. Furthermore, it must present the user with a single interface mechanism with all the flexibility and functions required from the process modules as well as the wafer transport platform. The user interface will need to be configurable to die unique requirements of each process modules. In essence, the user should have all the flexibility in selecting their process module of choice without any penalty in performance. This paper describes the control and communication architecture and methods used in an open architecture cluster host platform. The architecture provides the basis of an environment that is easily adaptable to the various requirements in this type of tool. Functions such as flexible wafer routing, process recipe selection and editing, interface with multiple modules are shown. Other useful functions such as data logging, system performance record and "intelligent process parameter control" are also described. Finally, the authors will discuss developments directions that will provide complete and quick integration between the process modules and cluster host platform while still retaining the unique identity of each supplier in the future.

By extrapolating technological trends, one can expect future fabs to consist largely of highly reliable cluster tools. Such trends raise the issues of how cluster tools should be configured (i.e., how modules should be grouped together), and the impact of configuration on optimal lot size. This paper generates equation-based models to compare the throughput and cycle time of different systems that perform the same sequence of process steps, with the same total number of modules grouped in different ways into multiple cluster tools. The two extremes of the spectrum of possible cluster tool configurations are considered: the serial configuration, in which a wafer visits each module in the cluster tool, and the parallel configuration, in which all of the modules in the cluster tool are identical. The models predict the following for typical cluster tool parameters and process times. When all process step times are identical, systems of serial-configured tools can achieve the same throughputs with lower cycle times, as their parallel-configured counterparts. However, if process times in the sequence significantly differ from one another, then systems of parallel-configured tools may achieve lower cycle times than their serial-configured counterparts at high throughputs. Finally, the serial configuration significantly reduces the lot size required to achieve total throughput capacity.

In a cluster tool where process modules have residency constraints, an optimal schedule may need to buffer the partially processed wafers. In previous approaches, one of the active resources (i.e. the transport module) was used as a temporary buffer. In this approach we try to use a resource that is usually available in cluster tools and is only used for tool maintenance reasons. This passive module that we refer to as buffer module, can hold the partially processed wafers, and free the transport module (TM). Our experiment shows that in 57% of the cases, because the TM can perform other actions while the wafer is buffered in the buffer module, a schedule with better throughput was found.

Modeling and implementing a real-time scheduler for dual-armed cluster tools

Cyclic scheduling and operation of a residency time- constrained single-arm cluster tool with failure-prone process modules are highly challenging. In some cases, when a fail- ure occurs, there still exists a feasible cyclic schedule for the performance-degraded tool. In other cases, such a schedule no longer exists. For the latter, it is highly desired to respond to a process module failure properly such that the tool can continue working and the wafers in the tool can be completed in a feasi- ble way. This work is the first one to study this important issue. The idea is to apply Petri nets to describe the dynamic behav- ior of a single-arm cluster tool. With the developed Petri net model, this paper formulates failure response policies to control the cluster tool such that it can keep working without violat- ing any residency time constraint. The failure response policies are implemented via efficient real-time control laws. Illustrative examples are presented to show their usage. Index Terms—Wafer fabrication, Cluster tools, Petri net, Scheduling, Failure response.

A single-wafer cluster tool refers to a group of single-wafer process modules organized around a group of wafer transporters to perform a series of process steps on a wafer. To achieve high throughput, redundant modules and transporters are added to the cluster tool. The networking of the many redundant modules and transporters brings about complex wafer flow which requires complex coordination of wafer processing and transporting. Invariably, occur in transporting the wafer. If the occur at a gating module, the throughput slows down. If they occur in critical process modules, the on-wafer results are adversely affected. Furthermore, the process results will not be consistent because the wafers are not processed in similar flow paths. This paper presents a method for reducing the wafer flow complexity. By introducing planned delays to the process times of noncritical process modules, it is shown that (a) zero transport can be assured in gating modules and critical process modules; (b) periodicity can be introduced into the wafer flow. The consequence of (a) is an improvement in quality and throughput. The consequence of (b) is a drastic reduction in the number of possible wafer flow paths, thus ensuring consistent process results. A real life example of queueing to reduce the complexity in a photoresist processing system is presented to illustrate the concept and methodology.

We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We introduce compressibility measures as a useful tool to classify the intersection problem for certain classes of finite semigroups into circuit complexity classes and Turing machine complexity classes. Using this framework, we obtain a new and simple proof that for groups and commutative semigroups, the problem is contained in \(\mathsf {NP}\). We uncover certain structural and non-structural properties determining the complexity of the intersection problem for varieties of semigroups containing only trivial submonoids. More specifically, we prove \(\mathsf {NP}\)-hardness for classes of semigroups having a property called unbounded order and for the class of all nilpotent semigroups of bounded order. On the contrary, we show that bounded order and commutativity imply containment in the circuit complexity class \(\mathsf {qAC}^k\) (for some \(k \in \mathbb {N}\)) and decidability in quasi-polynomial time. We also establish connections to the monoid variant of the problem.

The intersection problem for finite semigroups asks, given a set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. In previous work, it was shown that is problem is [Formula: see text]-complete. We introduce compressibility measures as a useful tool to classify the complexity of the intersection problem for certain classes of finite semigroups. Using this framework, we obtain a new and simple proof that for groups and for commutative semigroups, the problem (as well as the variant where the languages are represented by finite automata) is contained in [Formula: see text]. We uncover certain structural and non-structural properties determining the complexity of the intersection problem for varieties of semigroups containing only trivial submonoids. More specifically, we prove [Formula: see text]-hardness for classes of semigroups having a property called unbounded order and for the class of all nilpotent semigroups of bounded order. On the contrary, we show that bounded order and commutativity imply decidability in poly-logarithmic time on alternating random-access Turing machines with a single alternation. We also establish connections to the monoid variant of the problem.

An algebra $\left \langle {\mathcal {L},f,g} \right \rangle$ of languages over a finite alphabet $\Sigma = \{ {a_1}, \ldots ,{a_n}\}$ is defined with operations $f({L_1}, \ldots ,{L_n}) = {a_1}{L_1} \cup \cdots \cup {a_n}{L_n} \cup \{ \lambda \}$ and $g({L_1}, \ldots ,{L_n}) = {a_1}{L_1} \cup \cdots \cup {a_n}{L_n}$ and its first order theory is shown to be model complete. A characterization of the regular languages as unique solutions of sets of equations in $\left \langle {\mathcal {L},f,g} \right \rangle$ is given and it is shown that the subalgebra $\left \langle {\mathcal {R},f,g} \right \rangle$ where $\mathcal {R}$ is the set of regular languages is a prime model for the theory of $\left \langle {\mathcal {L},f,g} \right \rangle$. We show also that the theory of $\left \langle {\mathcal {L},f,g} \right \rangle$ is decidable.

Over the course of this program, Applied Materials, Inc., with generous support from the United States Department of Energy, developed a world-class three chamber III-Nitride epi cluster tool for low-cost, high volume GaN growth for the solid state lighting industry. One of the major achievements of the program was to design, build, and demonstrate the world’s largest wafer capacity HVPE chamber suitable for repeatable high volume III-Nitride template and device manufacturing. Applied Materials’ experience in developing deposition chambers for the silicon chip industry over many decades resulted in many orders of magnitude reductions in the price of transistors. That experience and understanding was used in developing this GaN epi deposition tool. The multi-chamber approach, which continues to be unique in the ability of the each chamber to deposit a section of the full device structure, unlike other cluster tools, allows for extreme flexibility in the manufacturing process. This robust architecture is suitable for not just the LED industry, but GaN power devices as well, both horizontal and vertical designs. The new HVPE technology developed allows GaN to be grown at a rate unheard of with MOCVD, up to 20x the typical MOCVD rates of 3{micro}m per hour, with bulk crystal quality better than the highest-quality commercial GaN films grown by MOCVD at a much cheaper overall cost. This is a unique development as the HVPE process has been known for decades, but never successfully commercially developed for high volume manufacturing. This research shows the potential of the first commercial-grade HVPE chamber, an elusive goal for III-V researchers and those wanting to capitalize on the promise of HVPE. Additionally, in the course of this program, Applied Materials built two MOCVD chambers, in addition to the HVPE chamber, and a robot that moves wafers between them. The MOCVD chambers demonstrated industry-leading wavelength yield for GaN based LED wafers and industry-leading uptime enabled in part by a novel in-situ cleaning process developed in this program.

Ukrainian health and medical tourism needs a change in strategic planning approaches due, firstly, to the outdated post-Soviet organization of mass rehabilitation and sanatorium-resort treatment, and, secondly, in connection with the expected changes in the structure of consumers and their advantages, both as a result of the full-scale invasion of the russian federation. The subject of the study is the clustering processes in the field of health and medical tourism of Ukraine. The purpose of the study is to substantiate the methodical approach to the clustering of health and medical tourism based on spatial modeling of the relevant resource and material base. The task of the research: substantiating the main directions of health and medical tourism development; generalization of statistical data on the resource and material base based on the method of cartographic visualization; development of proposals for the activation of cluster processes based on statistical groupings of regions. The following methods were used: abstract (theoretical generalizations, formulation of conclusions), systematic approach, method of structural generalization, statistical grouping, graphic method. The following results were obtained: on the basis of statistical analysis, it was proposed to divide the regions of Ukraine into the following groups: the first - seaside regions, specialization – family and children's recreational and health tourism; the second – Volyn and Carpathian region, specialization - sanatorium-resort and rehabilitation vacation with an emphasis on inbound tourism; the third – capital and central-eastern regions, specialization – medical tourism; the fourth – regions without a pronounced potential for health and medical tourism, in total make up 46.47% of the area. The stages for the clustering policy implementation of health and medical tourism in Ukraine have been developed. Conclusions: to improve the management of health and medical tourism, a clustering tool is proposed. The regions of Ukraine are divided into four groups according to the level of resource and material base development, each of which has a clear specialization and target tourist groups, as well as the direction of strategic development. This improves the strategic promotion of domestic health and medical tourist destinations at the inbound and outbound directions.